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            source: "// Numbas version: finer_feedback_settings\n{\"name\": \"MGTT170 2025/26\", \"metadata\": {\"description\": \"\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"duration\": 0, \"percentPass\": 0, \"showQuestionGroupNames\": false, \"shuffleQuestionGroups\": false, \"showstudentname\": true, \"question_groups\": [{\"name\": \"Group\", \"pickingStrategy\": \"all-ordered\", \"pickQuestions\": 1, \"questionNames\": [\"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"], \"variable_overrides\": [[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], []], \"questions\": [{\"name\": \"AC16 Rearrange Formulae\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Ben McGovern\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4872/\"}, {\"name\": \"Luigi Pivano\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/18182/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eRearrange a specific formula. No randomisation.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eRearrange the following equation, to make $y$ the subject:\u003c/p\u003e\\n\u003cp\u003e\\\\[{cy -b = 3x}\\\\]\u0026nbsp;\u003c/p\u003e\", \"advice\": \"\u003cp\u003eIn order to rearrange the equation so that it is in terms of $y$, we must first add $b$ to both sides, and then divide both sides of the equation by $c$:\u003c/p\u003e\\n\u003cp\u003e\\\\begin{split} cy-b\u0026nbsp; \u0026amp;= 3x \\\\\\\\ cy \u0026amp;= 3x + b \\\\\\\\ y \u0026amp;=\\\\frac{3x+b}{c} \\\\end{split}\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Rearranging\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e$y=$ [[0]]\u003c/p\u003e\", \"gaps\": [{\"type\": \"jme\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"answer\": \"(3x+b)/c\", \"showPreview\": true, \"checkingType\": \"absdiff\", \"checkingAccuracy\": 0.001, \"failureRate\": 1, \"vsetRangePoints\": 5, \"vsetRange\": [0, 1], \"checkVariableNames\": false, \"singleLetterVariables\": false, \"allowUnknownFunctions\": true, \"implicitFunctionComposition\": false, \"caseSensitive\": false, \"valuegenerators\": [{\"name\": \"b\", \"value\": \"\"}, {\"name\": \"c\", \"value\": \"\"}, {\"name\": \"x\", \"value\": \"\"}]}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"AC19 Cancelling algebraic fractions\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Luke Park\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/826/\"}, {\"name\": \"Anna Strzelecka\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/2945/\"}, {\"name\": \"heike hoffmann\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/2960/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eA question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eSimplify the following algebraic expression.\u003cem\u003e\u003c/em\u003e\u003c/p\u003e\", \"advice\": \"\u003cp\u003e\\\\[\\\\frac{{\\\\simplify{(n^2+({e1}+{e2})n+{e1}{e2})}}}{{\\\\simplify{(n^2+({e1}+{e3})n+{e1}{e3})}}}\\\\]\u003c/p\u003e\\n\u003cp\u003eIn this question there is a quadratic expression which needs to be factorised into the products of binomials in both the numerator and denominator.\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\frac{({\\\\simplify{n+{e1}}})({\\\\simplify{n+{e2}}})}{({\\\\simplify{n+{e1}}})({\\\\simplify{n+{e3}}})}\\\\]\u003c/p\u003e\\n\u003cp\u003eThe repeated binomials in the numerator and denominator cancel, leaving:\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\frac{({\\\\simplify{n+{e2}}})}{({\\\\simplify{n+{e3}}})}\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#AlgFrac\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"e2\": {\"name\": \"e2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-5..5 except 0)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"e1\": {\"name\": \"e1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-5..5 except 0)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"e3\": {\"name\": \"e3\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-5..5 except 0 except e2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"e1\", \"e2\", \"e3\"], \"variable_groups\": [], \"functions\": {\"\": {\"parameters\": [], \"type\": \"number\", \"language\": \"jme\", \"definition\": \"\"}}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"jme\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e\\\\[\\\\frac{\\\\simplify{(n^2+({e1}+{e2})n+{e1}{e2})}}{\\\\simplify{(n^2+({e1}+{e3})n+{e1}{e3})}}\\\\]\u003c/p\u003e\", \"answer\": \"(n+{e2})/(n+{e3})\", \"showPreview\": true, \"checkingType\": \"absdiff\", \"checkingAccuracy\": 0.001, \"failureRate\": 1, \"vsetRangePoints\": 5, \"vsetRange\": [0, 1], \"checkVariableNames\": false, \"singleLetterVariables\": false, \"allowUnknownFunctions\": true, \"implicitFunctionComposition\": false, \"caseSensitive\": false, \"notallowed\": {\"strings\": [\"^2\", \"^\"], \"showStrings\": false, \"partialCredit\": 0, \"message\": \"\"}, \"valuegenerators\": [{\"name\": \"n\", \"value\": \"\"}]}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"AF01 Sigma Notation\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eBasic calculation from a sum given in Sigma notation.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eCalculate:\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\displaystyle{\\\\Sigma_{n=1}^3} \\\\var{b}n.\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"advice\": \"\u003cp\u003eThe sigma notation $\\\\displaystyle\u003cspan class=\\\"enlighter-k0\\\"\u003e\\\\sum_\u003c/span\u003e\u003cspan class=\\\"enlighter-g1\\\"\u003e{\u003c/span\u003e\u003cspan class=\\\"enlighter-text\\\"\u003en=\u003c/span\u003e\u003cspan class=\\\"enlighter-n1\\\"\u003e1\u003c/span\u003e\u003cspan class=\\\"enlighter-g1\\\"\u003e}\u003c/span\u003e\u003cspan class=\\\"enlighter-text\\\"\u003e^\u003c/span\u003e\u003cspan class=\\\"enlighter-g1\\\"\u003e{\u003c/span\u003e\u003cspan class=\\\"enlighter-k0\\\"\u003e3\u003c/span\u003e\u003cspan class=\\\"enlighter-g1\\\"\u003e}\\\\var{b}n$ is asking us to find the \u003c/span\u003esum of the first three terms of the sequence $\\\\var{b}n$\u003cspan class=\\\"enlighter-g1\\\"\u003e.\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\begin{split}\\\\Sigma_{n=1}^3 \\\\var{b}n \u0026amp;\\\\, = (\\\\var{b}\\\\times 1) + (\\\\var{b}\\\\times 2) + (\\\\var{b}\\\\times 3) \\\\\\\\ \u0026amp;\\\\, = \\\\var{b1} + \\\\var{b2} + \\\\var{b3} \\\\\\\\ \u0026amp;\\\\, = \\\\var{sum}.\\\\end{split}\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Sigma\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find resources to help you revise sigma notation.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"b\": {\"name\": \"b\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2 .. 9#1)\", \"description\": \"\", \"templateType\": \"randrange\", \"can_override\": false}, \"b1\": {\"name\": \"b1\", \"group\": \"Ungrouped variables\", \"definition\": \"b*1\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"b2\": {\"name\": \"b2\", \"group\": \"Ungrouped variables\", \"definition\": \"b*2\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"b3\": {\"name\": \"b3\", \"group\": \"Ungrouped variables\", \"definition\": \"b*3\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"sum\": {\"name\": \"sum\", \"group\": \"Ungrouped variables\", \"definition\": \"b1+b2+b3\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"b\", \"b1\", \"b2\", \"b3\", \"sum\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"jme\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"answer\": \"{sum}\", \"showPreview\": true, \"checkingType\": \"absdiff\", \"checkingAccuracy\": 0.001, \"failureRate\": 1, \"vsetRangePoints\": 5, \"vsetRange\": [0, 1], \"checkVariableNames\": false, \"singleLetterVariables\": false, \"allowUnknownFunctions\": true, \"implicitFunctionComposition\": false, \"caseSensitive\": false, \"valuegenerators\": []}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"AF02 Straight Line Graphs\", \"extensions\": [\"geogebra\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eCalculating gradient and finding intercept from a geogebra graph.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003e{app}\u003cbr/\u003eFind the gradient of the line.\u003cbr/\u003e\u003cbr/\u003e\u003cbr/\u003e\u003c/p\u003e\", \"advice\": \"\u003cp\u003eFirstly draw a right angled \u0027step\u0027 from left to right. This triangle can be anywhere, but it is more helpful for it to have corners on the vertices (whole number points) of the graph and it is easier to calculate with postive numbers.\u003c/p\u003e\\n\u003cp\u003e{app_advice}\u003c/p\u003e\\n\u003cp\u003eBefore we start to calculate, notice that the line is {uod}, so the gradient will be {pon} and the line is {sos}, so the absolute value of the number will be {mol}.\u003cbr/\u003e\u003cbr/\u003eNow find the coordinates of the places your triangle meets the line\u003c/p\u003e\\n\u003cp\u003e$(x_1,y_1)=(\\\\var{ax},\\\\var{ay})$ and $(x_2,y_2)=(\\\\var{bx},\\\\var{by})$\u003c/p\u003e\\n\u003cp\u003eWe need to compare the \u0027rise on the y-axis\u0027 to the \u0027run across the x-axis\u0027, we can say that:\u003c/p\u003e\\n\u003cp\u003e$\\\\text{gradient} = \\\\frac{\\\\text{rise}}{\\\\text{run}}$\u003c/p\u003e\\n\u003cp\u003eThis is equivalent to using the formula:\u003cbr/\u003e\u003cbr/\u003e$\u0026nbsp; m = \\\\frac{y_2 - y_1}{x_2 - x_1} $\u003c/p\u003e\\n\u003cp\u003eand substitute the coordinates of the vertices of the triangle:\u003cbr/\u003e\u003cbr/\u003e$\\\\begin{split} \u0026amp;\\\\, m = \\\\frac{\\\\var{by} - \\\\var{ay}}{\\\\var{bx} - \\\\var{ax}} \\\\\\\\ \u0026nbsp;\u003cbr/\u003e\u0026amp;\\\\, = \\\\frac{\\\\var{by-ay}}{\\\\var{bx-ax}} \\\\\\\\\u0026nbsp;\u003cbr/\u003e\u0026amp;\\\\, \u0026nbsp;= \\\\var[fractionNumbers]{m} \\\\\\\\\u003cbr/\u003e\\\\end{split} $\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Lines\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find resources to help you revise straight line graphs and how to find the gradient of them.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"app\": {\"name\": \"app\", \"group\": \"Ungrouped variables\", \"definition\": \"geogebra_applet(\\n  800,500,\\n  [\\n    A: [\\n      definition: p1,\\n      label_visible: false,\\n      visible: false\\n    ],\\n    B: [\\n      definition: p2,\\n      label_visible: false,\\n      visible: false      \\n    ],\\n    line: [\\n      definition: \\\"Line(A,B)\\\",\\n      label_visible: false\\n    ]\\n  ]\\n)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"m\": {\"name\": \"m\", \"group\": \"Ungrouped variables\", \"definition\": \"(ay-by)/(ax-bx)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"c\": {\"name\": \"c\", \"group\": \"Ungrouped variables\", \"definition\": \"ay-m*ax\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"P1\": {\"name\": \"P1\", \"group\": \"Ungrouped variables\", \"definition\": \"vector(ax, ay)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"P2\": {\"name\": \"P2\", \"group\": \"Ungrouped variables\", \"definition\": \"vector(bx,by)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"uod\": {\"name\": \"uod\", \"group\": \"Ungrouped variables\", \"definition\": \"if(m=0,\u0027horizontal\u0027,if(m=abs(m),\u0027going up\u0027,\u0027going down\u0027))\", \"description\": \"\u003cp\u003eif(m=abs(m),\u0027positive\u0027,\u0027negative\u0027)\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"ax\": {\"name\": \"ax\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0,1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"ay\": {\"name\": \"ay\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0,1,2,3)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"bx\": {\"name\": \"bx\", \"group\": \"Ungrouped variables\", \"definition\": \"random(ax+1..3) \\n\", \"description\": \"\", \"templateType\": \"anything\", 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label_visible: false,\\n      visible: true\\n    ]\\n  ]\\n)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"p3\": {\"name\": \"p3\", \"group\": \"Ungrouped variables\", \"definition\": \"vector(bx,ay)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"pon\": {\"name\": \"pon\", \"group\": \"Ungrouped variables\", \"definition\": \"if(m=0,\u0027zero\u0027,if(m=abs(m),\u0027a positive number\u0027,\u0027a negative number\u0027))\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"sos\": {\"name\": \"sos\", \"group\": \"Ungrouped variables\", \"definition\": \"if(m=0,\u0027horizontal\u0027,if(abs(m)\u003c1,\u0027shallow\u0027,\u0027steep\u0027))\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"mol\": {\"name\": \"mol\", \"group\": \"Ungrouped variables\", \"definition\": \"if(m=0,\u0027zero\u0027,if(abs(m)\u003c1,\u0027less than 1\u0027,\u0027greater than or equal to 1\u0027))\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"m\u003c\u003e1\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"app\", \"m\", \"c\", \"P1\", \"P2\", \"uod\", \"ax\", \"ay\", \"bx\", \"by\", \"app_advice\", \"p3\", \"pon\", \"sos\", \"mol\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"jme\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"alternatives\": [{\"type\": \"jme\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"alternativeFeedbackMessage\": \"\u003cp\u003eIt looks like you have incorrectly rounded this answer. \u0026nbsp;You might want to look at some resources on rounded decimals. \u0026nbsp;You can also leave your answer in fraction form as \u003cbr/\u003e$\\\\var[fractionNumbers]{m}$\u003c/p\u003e\", \"useAlternativeFeedback\": false, \"answer\": \"{m}\", \"showPreview\": true, \"checkingType\": \"absdiff\", \"checkingAccuracy\": \"0.1\", \"failureRate\": 1, \"vsetRangePoints\": 5, \"vsetRange\": [0, 1], \"checkVariableNames\": false, \"singleLetterVariables\": false, \"allowUnknownFunctions\": true, \"implicitFunctionComposition\": false, \"caseSensitive\": false, \"valuegenerators\": []}], \"answer\": \"{m}\", \"showPreview\": true, \"checkingType\": \"dp\", \"checkingAccuracy\": \"1\", \"failureRate\": 1, \"vsetRangePoints\": 5, \"vsetRange\": [0, 1], \"checkVariableNames\": false, \"singleLetterVariables\": false, \"allowUnknownFunctions\": true, \"implicitFunctionComposition\": false, \"caseSensitive\": false, \"valuegenerators\": []}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"AS01 Solve linear equations\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Ben Brawn\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/605/\"}, {\"name\": \"heike hoffmann\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/2960/\"}, {\"name\": \"sean hunte\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3167/\"}, {\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Ben McGovern\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4872/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eSolve linear equations with unkowns on both sides. Including brackets and fractions.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\", \"advice\": \"\u003cp\u003eGiven $\\\\simplify{{m}w-{n} = {p}w+{q}}$, we can get all the $w$\u0027s on the left hand side and all the numbers on the right hand side, and then divide both sides by the coefficient of $w$ to get $w$ by itself.\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003ctable style=\\\"height: 342px;\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e\u0026nbsp;\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e$\\\\simplify{{m}w+{n}}$\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e$=$\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e$\\\\simplify{{p}w+{q}}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e\u0026nbsp;\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 36px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 36px; width: 218.312px;\\\"\u003e$\\\\simplify[!cancelTerms,unitFactor]{{m}w-{n}-{p}w}$\u003c/td\u003e\\n\u003ctd style=\\\"height: 36px; width: 29.2656px;\\\"\u003e$=$\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 36px; width: 283.422px;\\\"\u003e$\\\\simplify[!cancelTerms,unitFactor]{{p}w+{q}-{p}w}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e\u0026nbsp;\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e$\\\\simplify{{m-p}w-{n}}$\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e$=$\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e$\\\\var{q}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e\u0026nbsp;\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 36px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 36px; width: 218.312px;\\\"\u003e$\\\\var{m-p}w-\\\\var{n}+\\\\var{n}$\u003c/td\u003e\\n\u003ctd style=\\\"height: 36px; width: 29.2656px;\\\"\u003e$=$\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 36px; width: 283.422px;\\\"\u003e$\\\\var{q}+\\\\var{n}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e\u0026nbsp;\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e$\\\\var{m-p}w$\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e$=$\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e$\\\\var{q+n}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e\u0026nbsp;\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 36px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 36px; width: 218.312px;\\\"\u003e$\\\\displaystyle{\\\\frac{\\\\var{m-p}w}{\\\\var{m-p}}}$\u003c/td\u003e\\n\u003ctd style=\\\"height: 36px; width: 29.2656px;\\\"\u003e$=$\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 36px; width: 283.422px;\\\"\u003e$\\\\displaystyle{\\\\frac{\\\\var{q+n}}{\\\\var{m-p}}}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 18px; width: 218.312px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 29.2656px;\\\"\u003e\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 18px; width: 283.422px;\\\"\u003e\u0026nbsp;\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 36px;\\\"\u003e\\n\u003ctd style=\\\"text-align: right; height: 36px; width: 218.312px;\\\"\u003e$w$\u003c/td\u003e\\n\u003ctd style=\\\"height: 36px; width: 29.2656px;\\\"\u003e$=$\u003c/td\u003e\\n\u003ctd style=\\\"text-align: left; height: 36px; width: 283.422px;\\\"\u003e$\\\\displaystyle{\\\\simplify{{q+n}/{m-p}}} = \\\\var{precround(ansA,1)} \\\\text{ to 1 dp}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Equations\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003e\u003cbr/\u003eUse this link to find resources to help you revise how to solve linear equations\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"p\": {\"name\": \"p\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..3)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"m\": {\"name\": \"m\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..12)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"q\": {\"name\": \"q\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..12)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"n\": {\"name\": \"n\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..12)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"l\": {\"name\": \"l\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..12)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"ansA\": {\"name\": \"ansA\", \"group\": \"Ungrouped variables\", \"definition\": \"(q+n)/(m-p)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": \"100\"}, \"ungrouped_variables\": [\"l\", \"m\", \"n\", \"p\", \"q\", \"ansA\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eSolve\u0026nbsp; $\\\\simplify{({m}w-{n}) = {p}w+{q}}$\u003c/p\u003e\\n\u003cp\u003e$w=$\u0026nbsp;[[0]]\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"ansA\", \"maxValue\": \"ansA\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"precisionType\": \"dp\", \"precision\": \"1\", \"precisionPartialCredit\": \"100\", \"precisionMessage\": \"You have not given your answer to the correct precision.\", \"strictPrecision\": true, \"showPrecisionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"AS03 Simultaneous Equations (2 linear)\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Ben McGovern\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4872/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}], \"tags\": [\"Category: Simultaneous equations\"], \"metadata\": {\"description\": \"\u003cp\u003eSolving a pair of linear simultaneous equations, giving answers as integers or fractions.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eSolve the simultaneous equations for x and y, giving your answers as integers or fractions, but not decimals.\u003c/p\u003e\\n\u003cp\u003e\\\\[ \\\\begin{split}\u0026nbsp;\\\\simplify[!noLeadingminus,unitFactor]{{a}x+{b}y} \u0026amp;\\\\,=\\\\var{c} \\\\\\\\ \\\\simplify[!noLeadingminus,unitFactor]{{a1}x +{b1}y}\u0026nbsp; \u0026amp;\\\\,=\\\\var{c1} \\\\end{split}\\\\]\u003c/p\u003e\", \"advice\": \"\u003cp\u003e\\\\[\\\\begin{split}\\\\simplify[!noLeadingminus,unitFactor]{{a}x+{b}y} \u0026amp;\\\\,=\\\\var{c} \\\\qquad\\\\qquad\u0026amp;(1)\\\\\\\\ \\\\simplify[!noLeadingminus,unitFactor]{{a1}x +{b1}y}\u0026nbsp; \u0026amp;\\\\,=\\\\var{c1} \\\\qquad\\\\qquad\u0026amp;(2)\\\\end{split}\\\\]\u003c/p\u003e\\n\u003cp\u003e{advice1}\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Rearranging\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Sim\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"a\": {\"name\": \"a\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-2..8 except [0,1])\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"b\": {\"name\": \"b\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-8..8 except [0,1,a])\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a1\": {\"name\": \"a1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-5..8 except [0,1])\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"b1\": {\"name\": \"b1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..10 except [round(a1*b/a),b,0,1])\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"c\": {\"name\": \"c\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-6..6 except 0)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"c1\": {\"name\": \"c1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-7..7 except 0)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"aorsb\": {\"name\": \"aorsb\", \"group\": \"Ungrouped variables\", \"definition\": \"if(b*abs(b1)=b1*abs(b),\u0027subtract\u0027,\u0027add\u0027)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"torfb\": {\"name\": \"torfb\", \"group\": \"Ungrouped variables\", \"definition\": \"if(b*abs(b1)=b1*abs(b),\u0027from\u0027,\u0027to\u0027)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"sgn\": {\"name\": \"sgn\", \"group\": \"Ungrouped variables\", \"definition\": \"if(b*abs(b1)=b1*abs(b),-1,1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"xn\": {\"name\": \"xn\", \"group\": \"Ungrouped variables\", \"definition\": \"c*abs(b1)+sgn*c1*abs(b)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"xd\": {\"name\": \"xd\", \"group\": \"Ungrouped variables\", \"definition\": \"a*abs(b1)+sgn*a1*abs(b)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"xsimp\": {\"name\": \"xsimp\", \"group\": \"Ungrouped variables\", \"definition\": \"xn/xd\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"samex\": {\"name\": \"samex\", \"group\": \"Ungrouped variables\", \"definition\": \"\\\"\u003cp\u003eFor these equations, it is easiest to get a solution for $y$ first, due to the $x$-terms having {eqoroppa} coefficients.\u003c/p\u003e\\\\n\u003cp\u003eIf we {aorsa} equation (2) {torfa} equation (1) this eliminates the $x$-terms leaving us with one equation in terms of $y$:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[!collectNumbers, !noLeadingminus]{({b}+{sgna*(b1)})y} \u0026amp;\\\\\\\\,=\u0026nbsp;\\\\\\\\simplify[!collectNumbers, !noLeadingminus]{{c}+{sgna*(c1)}}\\\\\\\\\\\\\\\\ \\\\\\\\simplify{{b+sgna*(b1)}y} \u0026amp;\\\\\\\\,= \\\\\\\\simplify{{c+sgna*(c1)}} \\\\\\\\\\\\\\\\ y \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, fractionNumbers]{{c+sgna*(c1)}/{b+sgna*(b1)}} \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003e\u003c/p\u003e\\\\n\u003cp\u003eTo obtain a solution for $x$ we can substitute this $y$-value into either of our initial equations. Using equation (1), we obtain\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\var{a}x + \\\\\\\\var{b} \\\\\\\\times \\\\\\\\simplify[all, fractionNumbers]{{c+sgna*(c1)}/{b+sgna*(b1)}} \u0026amp;\\\\\\\\,= \\\\\\\\var{c} \\\\\\\\\\\\\\\\ \\\\\\\\var{a}x \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, !collectNumbers, !noLeadingminus]{{c} - {c*b+b*sgna*(c1)}/{b+sgna*(b1)}} \\\\\\\\\\\\\\\\ x \u0026amp;\\\\\\\\,= \\\\\\\\simplify[fractionNumbers]{{(c*abs(b1)+sgn*c1*abs(b))/(a*abs(b1)+sgn*a1*abs(b))}}. \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\"\", \"description\": \"\", \"templateType\": \"long string\", \"can_override\": false}, \"eqoroppb\": {\"name\": \"eqoroppb\", \"group\": \"Ungrouped variables\", \"definition\": \"if(abs(b)*b1=abs(b1)*b,\u0027equal\u0027,\u0027equal and opposite\u0027)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"eqoroppa\": {\"name\": \"eqoroppa\", \"group\": \"Ungrouped variables\", \"definition\": \"if(abs(a)*a1=abs(a1)*a,\u0027equal\u0027,\u0027equal and opposite\u0027)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"samey\": {\"name\": \"samey\", \"group\": \"Ungrouped variables\", \"definition\": \"\\\"\u003cp\u003eFor these equations, it is easiest to get a solution for $x$ first, due to the $y$-terms having {eqoroppb} coefficients.\u003c/p\u003e\\\\n\u003cp\u003eIf we {aorsb} equation (2) {torfb} equation (1) this eliminates the $y$-terms, leaving us with one equation in terms of $x$:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[!collectNumbers, !noLeadingminus]{({a}+{sgn*(a1)})x} \u0026amp;\\\\\\\\,=\u0026nbsp;\\\\\\\\simplify[!collectNumbers, !noLeadingminus]{{c}+{sgn*(c1)}}\\\\\\\\\\\\\\\\ \\\\\\\\simplify{{a+sgn*(a1)}x} \u0026amp;\\\\\\\\,= \\\\\\\\simplify{{c+sgn*(c1)}} \\\\\\\\\\\\\\\\ x \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, fractionNumbers]{{c+sgn*(c1)}/{a+sgn*(a1)}} \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003e\u003c/p\u003e\\\\n\u003cp\u003eTo obtain a solution for $y$ we can substitute this $x$-value into either of our initial equations. Using equation (1), we obtain\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\var{a} \\\\\\\\times\\\\\\\\simplify[fractionNumbers]{{c+sgn*(c1)}/{a+sgn*(a1)}} + \\\\\\\\var{b}y \u0026amp;\\\\\\\\,= \\\\\\\\var{c} \\\\\\\\\\\\\\\\ \\\\\\\\var{b}y \u0026amp;\\\\\\\\,= \\\\\\\\simplify[!collectNumbers, !noLeadingminus]{{c} - {c*a+a*sgn*(c1)}/{a+sgn*(a1)}} \\\\\\\\\\\\\\\\ y \u0026amp;\\\\\\\\,= \\\\\\\\simplify[fractionNumbers]{{(c-a*xsimp)/b}}. \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\"\", \"description\": \"\", \"templateType\": \"long string\", \"can_override\": false}, \"lcmb\": {\"name\": \"lcmb\", \"group\": \"Ungrouped variables\", \"definition\": \"\\\"\u003cp\u003eTo get a solution for $x$, if we multiply equation (2) by $\\\\\\\\simplify{{abs(b/b1)}}$ we will have two equations with {eqoroppb} $y$-coefficients:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split}\u0026nbsp;\\\\\\\\simplify[!noLeadingminus,unitFactor]{{a}x+{b}y} \u0026amp;\\\\\\\\,=\\\\\\\\var{c} \\\\\\\\qquad\\\\\\\\qquad\u0026amp;(3)\\\\\\\\\\\\\\\\ \\\\\\\\simplify[!noLeadingminus,unitFactor]{{a1*abs(b/b1)}x +{b1*abs(b/b1)}y}\u0026nbsp; \u0026amp;\\\\\\\\,=\\\\\\\\var{c1*abs(b/b1)} \\\\\\\\qquad\\\\\\\\qquad\u0026amp;(4)\\\\\\\\end{split}\\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003eIf we {aorsb} equation (4) {torfb} equation (3) this eliminates the $y$-terms, leaving us with one equation in terms of $x$:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[!collectNumbers, !noLeadingminus]{({a}+{sgn*(a1*abs(b/b1))})x} \u0026amp;\\\\\\\\,=\u0026nbsp;\\\\\\\\simplify[all, !collectNumbers, !noLeadingminus]{{c}+{sgn*(c1*abs(b/b1))}}\\\\\\\\\\\\\\\\ \\\\\\\\simplify{{a+sgn*(a1*abs(b/b1))}x} \u0026amp;\\\\\\\\,= \\\\\\\\simplify{{c+sgn*(c1*abs(b/b1))}} \\\\\\\\\\\\\\\\ x \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all,fractionNumbers]{{c+sgn*(c1*abs(b/b1))}/{a+sgn*(a1*abs(b/b1))}}. \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003e\u003c/p\u003e\\\\n\u003cp\u003eTo obtain a solution for $y$ we can substitute this $x$-value into either of our initial equations. Using equation (1), we obtain\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\var{a}\\\\\\\\times\\\\\\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{({c+sgn*c1*abs(b/b1)}/{(a)+sgn*a1*abs(b/b1)}) + {b}y} \u0026amp;\\\\\\\\,= \\\\\\\\var{c} \\\\\\\\\\\\\\\\ \\\\\\\\simplify{{b}y} \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, !noLeadingminus, fractionNumbers]{{c} -({(a*c)+a*sgn*c1*abs(b/b1)}/{(a)+sgn*a1*abs(b/b1)})} \\\\\\\\\\\\\\\\ \\\\\\\\simplify{{b}y} \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, !noLeadingminus, fractionNumbers]{{c -(a*c+a*sgn*c1*abs(b/b1))/(a+sgn*a1*abs(b/b1))}} \\\\\\\\\\\\\\\\ y \u0026amp;\\\\\\\\,=\\\\\\\\simplify[fractionNumbers]{{(c-a*xsimp)/b}}. \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\"\", \"description\": \"\", \"templateType\": \"long string\", \"can_override\": false}, \"lcmb1\": {\"name\": \"lcmb1\", \"group\": \"Ungrouped variables\", \"definition\": \"\\\"\u003cp\u003eTo get a solution for $x$, if we multiply equation (1) by $\\\\\\\\simplify{{abs(b1/b)}}$ we will have two equations with {eqoroppb} $y$-coefficients:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[!noLeadingminus,unitFactor]{{a*abs(b1/b)}x +{b*abs(b1/b)}y}\u0026nbsp; \u0026amp;\\\\\\\\,=\\\\\\\\var{c*abs(b1/b)} \\\\\\\\qquad\\\\\\\\qquad\u0026amp;(3) \\\\\\\\\\\\\\\\\\\\\\\\simplify[!noLeadingminus,unitFactor]{{a1}x+{b1}y} \u0026amp;\\\\\\\\,=\\\\\\\\var{c1} \\\\\\\\qquad\\\\\\\\qquad\u0026amp;(4)\\\\\\\\\\\\\\\\ \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003eIf we {aorsb} equation (4) {torfb} equation (3) this eliminates the $y$-terms, leaving us with one equation in terms of $x$:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[!collectNumbers, !noLeadingminus]{({(a*abs(b1/b))}+{sgn*a1})x} \u0026amp;\\\\\\\\,=\u0026nbsp;\\\\\\\\simplify[!collectNumbers, !noLeadingminus]{{(c*abs(b1/b))}+{sgn*c1}}\\\\\\\\\\\\\\\\ \\\\\\\\simplify{{(a*abs(b1/b))+sgn*a1}x} \u0026amp;\\\\\\\\,= \\\\\\\\simplify{{(c*abs(b1/b))+sgn*c1}} \\\\\\\\\\\\\\\\ x \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, fractionNumbers]{{(c*abs(b1/b))+sgn*c1}/{(a*abs(b1/b))+sgn*a1}}. \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003e\u003c/p\u003e\\\\n\u003cp\u003eTo obtain a solution for $y$ we can substitute this $x$-value into either of our initial equations. Using equation (1), we obtain\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\var{a}\\\\\\\\times\\\\\\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{({(c*abs(b1/b))+sgn*c1}/{(a*abs(b1/b))+sgn*a1}) + {b}y} \u0026amp;\\\\\\\\,= \\\\\\\\var{c} \\\\\\\\\\\\\\\\ \\\\\\\\simplify{{b}y} \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, !noLeadingminus, fractionNumbers]{{c} -({(a*c*abs(b1/b))+a*sgn*c1}/{(a*abs(b1/b))+sgn*a1})} \\\\\\\\\\\\\\\\ \\\\\\\\simplify{{b}y} \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, !noLeadingminus, fractionNumbers]{{c -(a*c*abs(b1/b)+a*sgn*c1)/(a*abs(b1/b)+sgn*a1)}} \\\\\\\\\\\\\\\\ y \u0026amp;\\\\\\\\,=\\\\\\\\simplify[fractionNumbers]{{(c-a*xsimp)/b}}. \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\"\", \"description\": \"\", \"templateType\": \"long string\", \"can_override\": false}, \"full\": {\"name\": \"full\", \"group\": \"Ungrouped variables\", \"definition\": \"\\\"\u003cp\u003eTo get a solution for $x$, if we multiply equation (1) by $\\\\\\\\var{abs(b1)}$ and equation (2) by $\\\\\\\\var{abs(b)}$, we will have two equations with {eqoroppb} $y$-coefficients:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split}\u0026nbsp;\\\\\\\\simplify[!noLeadingminus,unitFactor]{{a*abs(b1)}x+{b*abs(b1)}y} \u0026amp;\\\\\\\\,=\\\\\\\\var{c*abs(b1)} \\\\\\\\qquad\\\\\\\\qquad\u0026amp;(3)\\\\\\\\\\\\\\\\\\\\\\\\simplify[!noLeadingminus,unitFactor]{{a1*abs(b)}x +{b1*abs(b)}y}\u0026nbsp; \u0026amp;\\\\\\\\,=\\\\\\\\var{c1*abs(b)} \\\\\\\\qquad\\\\\\\\qquad\u0026amp;(4) \\\\\\\\end{split}\\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003eNow, {aorsb} equation (4) {torfb} equation (3) to eliminate the $y$ terms:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} (\\\\\\\\simplify[!collectNumbers]{{a*abs(b1)} +{sgn*a1*abs(b)}}) x \u0026amp;\\\\\\\\,= \\\\\\\\simplify[!collectNumbers]{{c*abs(b1)}+{sgn*c1*abs(b)}}\u0026nbsp;\\\\\\\\\\\\\\\\\u0026nbsp;\u0026nbsp;\\\\\\\\simplify{{a*abs(b1)+sgn*a1*abs(b)}} x \u0026amp;\\\\\\\\,= \\\\\\\\simplify{{c*abs(b1)+sgn*c1*abs(b)}} .\\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003eSo the solution for $x$ is \\\\\\\\[ x=\\\\\\\\simplify{{c*abs(b1)+sgn*c1*abs(b)}/{a*abs(b1)+sgn*a1*abs(b)}}.\\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003eTo obtain a solution for $y$ we can substitute this value of $x$ into either of our initial equations. Using equation (1), we obtain\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[noLeadingminus,fractionNumbers,unitFactor]{{a}\u0026nbsp; {xsimp} + {b}y} \u0026amp;\\\\\\\\,=\\\\\\\\var{c} \\\\\\\\\\\\\\\\ \\\\\\\\var{b}y \u0026amp;\\\\\\\\,= \\\\\\\\simplify[!collectNumbers,fractionNumbers]{{c}-{a*xsimp}} \\\\\\\\\\\\\\\\\\\\\\\\var{b}y \u0026amp;\\\\\\\\,= \\\\\\\\simplify[fractionNumbers]{{c-a*xsimp}} \\\\\\\\\\\\\\\\y \u0026amp;\\\\\\\\,= \\\\\\\\simplify[fractionNumbers]{{(c-a*xsimp)/b}} \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\"\", \"description\": \"\", \"templateType\": \"long string\", \"can_override\": false}, \"aorsa\": {\"name\": \"aorsa\", \"group\": \"Ungrouped variables\", \"definition\": \"if(a*abs(a1)=abs(a)*a1,\u0027subtract\u0027,\u0027add\u0027)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"torfa\": {\"name\": \"torfa\", \"group\": \"Ungrouped variables\", \"definition\": \"if(a*abs(a1)=abs(a)*a1,\u0027from\u0027,\u0027to\u0027)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"sgna\": {\"name\": \"sgna\", \"group\": \"Ungrouped variables\", \"definition\": \"if(a*abs(a1)=abs(a)*a1,-1,1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"lcma\": {\"name\": \"lcma\", \"group\": \"Ungrouped variables\", \"definition\": \"\\\"\u003cp\u003eTo get a solution for $y$, if we multiply equation (2) by $\\\\\\\\simplify{{abs(a/a1)}}$ we will have two equations with {eqoroppa} $x$-coefficients:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split}\u0026nbsp;\\\\\\\\simplify[!noLeadingminus,unitFactor]{{a}x+{b}y} \u0026amp;\\\\\\\\,=\\\\\\\\var{c} \\\\\\\\qquad\\\\\\\\qquad\u0026amp;(3)\\\\\\\\\\\\\\\\ \\\\\\\\simplify[!noLeadingminus,unitFactor]{{a1*abs(a/a1)}x +{b1*abs(a/a1)}y}\u0026nbsp; \u0026amp;\\\\\\\\,=\\\\\\\\var{c1*abs(a/a1)} \\\\\\\\qquad\\\\\\\\qquad\u0026amp;(4)\\\\\\\\end{split}\\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003eIf we {aorsa} equation (4) {torfa} equation (3) this eliminates the $x$-terms, leaving us with one equation in terms of $y$:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[!collectNumbers, !noLeadingminus]{({b}+{sgna*(b1*abs(a/a1))})y} \u0026amp;\\\\\\\\,=\u0026nbsp;\\\\\\\\simplify[all, !collectNumbers, !noLeadingminus]{{c}+{sgna*(c1*abs(a/a1))}}\\\\\\\\\\\\\\\\ \\\\\\\\simplify{{b+sgna*(b1*abs(a/a1))}y} \u0026amp;\\\\\\\\,= \\\\\\\\simplify{{c+sgna*(c1*abs(a/a1))}} \\\\\\\\\\\\\\\\ y \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all,fractionNumbers]{{c+sgna*(c1*abs(a/a1))}/{b+sgna*(b1*abs(a/a1))}}. \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003e\u003c/p\u003e\\\\n\u003cp\u003eTo obtain a solution for $x$ we can substitute this $y$-value into either of our initial equations. Using equation (1), we obtain\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{{a}x + {b}}\\\\\\\\times \\\\\\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{({c+sgna*c1*abs(a/a1)}/{(b)+sgna*b1*abs(a/a1)})} \u0026amp;\\\\\\\\,= \\\\\\\\var{c} \\\\\\\\\\\\\\\\ \\\\\\\\simplify{{a}x} \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, !noLeadingminus, fractionNumbers]{{c} -({(b*c)+b*sgna*c1*abs(a/a1)}/{(b)+sgna*b1*abs(a/a1)})} \\\\\\\\\\\\\\\\ \\\\\\\\simplify{{a}x} \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, !noLeadingminus, fractionNumbers]{{c -(b*c+b*sgna*c1*abs(a/a1))/(b+sgna*b1*abs(a/a1))}} \\\\\\\\\\\\\\\\ x \u0026amp;\\\\\\\\,=\\\\\\\\simplify[fractionNumbers]{{(c*abs(b1)+sgn*c1*abs(b))/(a*abs(b1)+sgn*a1*abs(b))}}. \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\"\", \"description\": \"\", \"templateType\": \"long string\", \"can_override\": false}, \"lcma1\": {\"name\": \"lcma1\", \"group\": \"Ungrouped variables\", \"definition\": \"\\\"\u003cp\u003eTo get a solution for $y$, if we multiply equation (1) by $\\\\\\\\simplify{{abs(a1/a)}}$ we will have two equations with {eqoroppa} $x$-coefficients:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[!noLeadingminus,unitFactor]{{a*abs(a1/a)}x +{b*abs(a1/a)}y}\u0026nbsp; \u0026amp;\\\\\\\\,=\\\\\\\\var{c*abs(a1/a)} \\\\\\\\qquad\\\\\\\\qquad\u0026amp;(3) \\\\\\\\\\\\\\\\\\\\\\\\simplify[!noLeadingminus,unitFactor]{{a1}x+{b1}y} \u0026amp;\\\\\\\\,=\\\\\\\\var{c1} \\\\\\\\qquad\\\\\\\\qquad\u0026amp;(4) \\\\\\\\end{split}\\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003eIf we {aorsa} equation (4) {torfa} equation (3) this eliminates the $x$-terms, leaving us with one equation in terms of $y$:\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[!collectNumbers, !noLeadingminus]{({(b*abs(a1/a))}+{sgna*b1})y} \u0026amp;\\\\\\\\,=\u0026nbsp;\\\\\\\\simplify[!collectNumbers, !noLeadingminus]{{(c*abs(a1/a))}+{sgna*c1}}\\\\\\\\\\\\\\\\ \\\\\\\\simplify{{(b*abs(a1/a))+sgna*b1}y} \u0026amp;\\\\\\\\,= \\\\\\\\simplify{{(c*abs(a1/a))+sgna*c1}} \\\\\\\\\\\\\\\\ y \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, fractionNumbers]{{(c*abs(a1/a))+sgna*c1}/{(b*abs(a1/a))+sgna*b1}}. \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\\n\u003cp\u003e\u003c/p\u003e\\\\n\u003cp\u003eTo obtain a solution for $x$ we can substitute this $y$-value into either of our initial equations. Using equation (1), we obtain\u003c/p\u003e\\\\n\u003cp\u003e\\\\\\\\[ \\\\\\\\begin{split} \\\\\\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{{a}x + {b}}\\\\\\\\times \\\\\\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{({c*abs(a1/a)+sgna*c1}/{(b*abs(a1/a))+sgna*b1})} \u0026amp;\\\\\\\\,= \\\\\\\\var{c} \\\\\\\\\\\\\\\\ \\\\\\\\simplify{{a}x} \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, !noLeadingminus, fractionNumbers]{{c} -({(b*c*abs(a1/a))+b*sgna*c1}/{(b*abs(a1/a))+sgna*b1})} \\\\\\\\\\\\\\\\ \\\\\\\\simplify{{a}x} \u0026amp;\\\\\\\\,= \\\\\\\\simplify[all, !noLeadingminus, fractionNumbers]{{c -(b*c*abs(a1/a)+b*sgna*c1)/(b*abs(a1/a)+sgna*b1)}} \\\\\\\\\\\\\\\\ x \u0026amp;\\\\\\\\,=\\\\\\\\simplify[fractionNumbers]{{(c*abs(b1)+sgn*c1*abs(b))/(a*abs(b1)+sgn*a1*abs(b))}}. \\\\\\\\end{split} \\\\\\\\]\u003c/p\u003e\\\"\", \"description\": \"\", \"templateType\": \"long string\", \"can_override\": false}, \"advice1\": {\"name\": \"advice1\", \"group\": \"Ungrouped variables\", \"definition\": \"if(abs(b)=abs(b1), {samey},if(abs(a)=abs(a1),{samex},if(lcm(abs(b),abs(b1))=abs(b),{lcmb},if(lcm(abs(b),abs(b1))=abs(b1),{lcmb1},if(lcm(abs(a),abs(a1))=abs(a),{lcma},if(lcm(abs(a),abs(a1))=abs(a1),{lcma1},{full}))))))\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"abs(b-b1)\u003e1 and\\nabs(a-a1)\u003e1 and\\ngcd(a,c)=1 and\\ngcd(a1,c1)=1\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"a\", \"b\", \"a1\", \"b1\", \"c\", \"c1\", \"aorsa\", \"torfa\", \"aorsb\", \"torfb\", \"sgna\", \"sgn\", \"xn\", \"xd\", \"xsimp\", \"eqoroppa\", \"eqoroppb\", \"advice1\", \"samey\", \"samex\", \"lcmb\", \"lcmb1\", \"lcma\", \"lcma1\", \"full\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e$x=$ [[0]]\u003c/p\u003e\\n\u003cp\u003e$y=$ [[1]]\u003c/p\u003e\", \"gaps\": [{\"type\": \"jme\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"answer\": \"{(c*abs(b1)+sgn*c1*abs(b))/(a*abs(b1)+sgn*a1*abs(b))}\", \"answerSimplification\": \"fractionNumbers\", \"showPreview\": true, \"checkingType\": \"absdiff\", \"checkingAccuracy\": 0.001, \"failureRate\": 1, \"vsetRangePoints\": 5, \"vsetRange\": [0, 1], \"checkVariableNames\": false, \"singleLetterVariables\": false, \"allowUnknownFunctions\": true, \"implicitFunctionComposition\": false, \"caseSensitive\": false, \"valuegenerators\": []}, {\"type\": \"jme\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"answer\": \"{(c-a*xsimp)/b}\", \"answerSimplification\": \"fractionNumbers\", \"showPreview\": true, \"checkingType\": \"absdiff\", \"checkingAccuracy\": 0.001, \"failureRate\": 1, \"vsetRangePoints\": 5, \"vsetRange\": [0, 1], \"checkVariableNames\": false, \"singleLetterVariables\": false, \"allowUnknownFunctions\": true, \"implicitFunctionComposition\": false, \"caseSensitive\": false, \"valuegenerators\": []}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA04 Inequalities (understanding notation)\", \"extensions\": [\"chemistry\", \"geogebra\", \"jsxgraph\", \"codewords\", \"permutations\", \"polynomials\", \"quantities\", \"random_person\", \"stats\", \"visjs\"], \"custom_part_types\": [{\"source\": {\"pk\": 28, \"author\": {\"name\": \"Marie Nicholson\", \"pk\": 1799}, \"edit_page\": \"/part_type/28/edit\"}, \"name\": \"True/False\", \"short_name\": \"true-false\", \"description\": \"\u003cp\u003eThe answer is either \u0027True\u0027 or \u0027False\u0027\u003c/p\u003e\", \"help_url\": \"\", \"input_widget\": \"radios\", \"input_options\": {\"correctAnswer\": \"if(eval(settings[\\\"correct_answer_expr\\\"]), 0, 1)\", \"hint\": {\"static\": true, \"value\": \"\"}, \"choices\": {\"static\": true, \"value\": [\"True\", \"False\"]}}, \"can_be_gap\": true, \"can_be_step\": true, \"marking_script\": \"mark:\\nif(studentanswer=correct_answer,\\n  correct(),\\n  incorrect()\\n)\\n\\ninterpreted_answer:\\nstudentAnswer=0\\n\\ncorrect_answer:\\nif(eval(settings[\\\"correct_answer_expr\\\"]),0,1)\", \"marking_notes\": [{\"name\": \"mark\", \"description\": \"This is the main marking note. It should award credit and provide feedback based on the student\u0027s answer.\", \"definition\": \"if(studentanswer=correct_answer,\\n  correct(),\\n  incorrect()\\n)\"}, {\"name\": \"interpreted_answer\", \"description\": \"A value representing the student\u0027s answer to this part.\", \"definition\": \"studentAnswer=0\"}, {\"name\": \"correct_answer\", \"description\": \"\", \"definition\": \"if(eval(settings[\\\"correct_answer_expr\\\"]),0,1)\"}], \"settings\": [{\"name\": \"correct_answer_expr\", \"label\": \"Is the answer \\\"True\\\"\", \"help_url\": \"\", \"hint\": \"\", \"input_type\": \"mathematical_expression\", \"default_value\": \"true\", \"subvars\": false}], \"public_availability\": \"always\", \"published\": true, \"extensions\": []}], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Don Shearman\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/680/\"}, {\"name\": \"Merryn Horrocks\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4052/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eIdentify the truth value of an inequality (T/F) between two numbers\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\", \"advice\": \"\u003cp\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eThe symbol is a comparitor that $\u0026lt;$ says that the object to its left is less than the object to its right. Similarly, $\u0026gt;$ says the object to its left is greater than the object to its right.\u003c/span\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003e\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eIn each case the sentence can be read in two ways e.g. $a\u0026lt;b$ can be read as \\\"$a$ is less than $b$\\\" OR \\\"$b$ is greater than $a$\\\".\u003c/span\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003e\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eThe symbol $\\\\leq$ just changes the sentence to include \\\"...or equal to...\\\". This can be of particular relevance when dealing with integers (whole numbers) e.g. $x \\\\geq 4$ and $x$ is a whole number means that $x$ could be $4, 5, 6,$ or $7$ and so on. Whereas, $x\u0026gt;4$ and $x$ is a whole number means that $x$ could be $5,6,$... etc. Notably in the second case $x$ cannot be $4$.\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003e\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Inequalities\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"a\": {\"name\": \"a\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..15)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"operations\": {\"name\": \"operations\", \"group\": \"Ungrouped variables\", \"definition\": \"[latex(\\\"\\\\\\\\gt\\\"),latex(\\\"\\\\\\\\ge\\\")]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"values\": {\"name\": \"values\", \"group\": \"Ungrouped variables\", \"definition\": \"[a,-random(1..15),random(1..15),random(1..15)]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"disp_values\": {\"name\": \"disp_values\", \"group\": \"Ungrouped variables\", \"definition\": \"shuffle(values)[0..2]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"disp_op\": {\"name\": \"disp_op\", \"group\": \"Ungrouped variables\", \"definition\": \"operations[random(0,1)]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a2\": {\"name\": \"a2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..15)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"operations2\": {\"name\": \"operations2\", \"group\": \"Ungrouped variables\", \"definition\": \"[latex(\\\"\\\\\\\\lt\\\"),latex(\\\"\\\\\\\\le\\\")]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"values2\": {\"name\": \"values2\", \"group\": \"Ungrouped variables\", \"definition\": \"[a2,-random(1..15),random(1..15),random(1..15)]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"disp_values2\": {\"name\": \"disp_values2\", \"group\": \"Ungrouped variables\", \"definition\": \"shuffle(values2)[0..2]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"disp_op2\": {\"name\": \"disp_op2\", \"group\": \"Ungrouped variables\", \"definition\": \"operations2[random(0,1)]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"a\", \"operations\", \"values\", \"disp_values\", \"disp_op\", \"a2\", \"operations2\", \"values2\", \"disp_values2\", \"disp_op2\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"true-false\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eIs the following statement true or false?\u003c/p\u003e\\n\u003cp\u003e\\\\(\\\\var{disp_values[0]}\\\\var{disp_op}\\\\var{disp_values[1]}\\\\)\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"alternatives\": [{\"type\": \"true-false\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"alternativeFeedbackMessage\": \"\", \"useAlternativeFeedback\": false, \"settings\": {\"correct_answer_expr\": \"eval(expression(disp_values[0]+if(disp_op=\\\"\\\\\\\\gt\\\",\\\"\u003e\\\",\\\"\u003e=\\\")+disp_values[1]))\"}}], \"settings\": {\"correct_answer_expr\": \"eval(expression(disp_values[0]+if(disp_op=\\\"\\\\\\\\gt\\\",\\\"\u003e\\\",\\\"\u003e=\\\")+disp_values[1]))\"}}, {\"type\": \"true-false\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eIs the following statement true or false?\u003c/p\u003e\\n\u003cp\u003e\\\\(\\\\var{disp_values2[0]}\\\\var{disp_op2}\\\\var{disp_values2[1]}\\\\)\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"settings\": {\"correct_answer_expr\": \"eval(expression(disp_values2[0]+if(disp_op2=\\\"\\\\\\\\lt\\\",\\\"\u003c\\\",\\\"\u003c=\\\")+disp_values2[1]))\"}}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA05 Number sequences - find a missing number\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Marie Nicholson\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1799/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eNumber sequences - find a missing number\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eFind the missing number from the following sequence\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\var{a}, \\\\var{a+d}, \\\\var{a+2*d}, \\\\var{a+3d}, ?, \\\\var{a+5d}, \\\\var{a+6d}, \\\\var{a+7d}, \\\\ldots\\\\]\u003c/p\u003e\", \"advice\": \"\u003cp\u003eIn this sequence it is important to spot that the terms are changing by the same amount each time ($\\\\var{d}$ in this case). This type of sequence is called an \u003cstrong\u003eArithmetic Sequence\u003c/strong\u003e.\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Sequences\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"n\": {\"name\": \"n\", \"group\": \"Ungrouped variables\", \"definition\": \"random(30..40)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a\": {\"name\": \"a\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-20..30)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"d\": {\"name\": \"d\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-9..9)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"a\", \"d\", \"n\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e[[0]]\u003c/p\u003e\", \"gaps\": [{\"type\": \"jme\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"answer\": \"{a+4d}\", \"showPreview\": true, \"checkingType\": \"absdiff\", \"checkingAccuracy\": 0.001, \"failureRate\": 1, \"vsetRangePoints\": 5, \"vsetRange\": [0, 1], \"checkVariableNames\": false, \"singleLetterVariables\": false, \"allowUnknownFunctions\": true, \"implicitFunctionComposition\": false, \"caseSensitive\": false, \"valuegenerators\": []}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA09 BIDMAS without a division\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Newcastle University Mathematics and Statistics\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/697/\"}, {\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Ben McGovern\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4872/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eQuestions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eEvaluate the following expression:\u003c/p\u003e\", \"advice\": \"\u003cp\u003eBIDMAS stands for:\u003c/p\u003e\\n\u003cp\u003eBrackets\u003c/p\u003e\\n\u003cp\u003eIndices\u003c/p\u003e\\n\u003cp\u003eDivision\u003c/p\u003e\\n\u003cp\u003eMultiplication\u003c/p\u003e\\n\u003cp\u003eAddition\u003c/p\u003e\\n\u003cp\u003eSubtraction\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003eAnd is a way for us to remember guidance about the order in which calculations are carried out to ensure that everyone doing teh same sum gets the same answer. In this case the first thing that is in the question is Multiplication.\u003c/p\u003e\\n\u003cp\u003eFirst work through the expression from left to right, evaluating any multiplication as you come to them. You should be left with an expression involving only pluses and minuses. Evaluate this expression, again working from left to right. Thus:\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\var{a}-\\\\var{b} \\\\times \\\\var{c}\\\\]\u003c/p\u003e\\n\u003cp\u003e\\\\[=\\\\var{a}-\\\\var{b*c}\\\\]\u003c/p\u003e\\n\u003cp\u003e\\\\[=\\\\var{a-b*c}\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"c\": {\"name\": \"c\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..8 except [a,b])\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a\": {\"name\": \"a\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..9)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"b\": {\"name\": \"b\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..11 except a)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"a\", \"c\", \"b\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eCalculate\u003c/p\u003e\\n\u003cp\u003e$\\\\var{a}-\\\\var{b} \\\\times\\\\var{c}$\u003c/p\u003e\", \"minValue\": \"{a-b*c}\", \"maxValue\": \"{a-b*c}\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA10 BIDMAS with a division\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Newcastle University Mathematics and Statistics\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/697/\"}, {\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Ben McGovern\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4872/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eQuestions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eEvaluate the following expression:\u003c/p\u003e\", \"advice\": \"\u003cp\u003eBIDMAS stands for:\u003c/p\u003e\\n\u003cp\u003eBrackets\u003c/p\u003e\\n\u003cp\u003eIndices\u003c/p\u003e\\n\u003cp\u003eDivision\u003c/p\u003e\\n\u003cp\u003eMultiplication\u003c/p\u003e\\n\u003cp\u003eAddition\u003c/p\u003e\\n\u003cp\u003eSubtraction\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003eAnd is a way for us to remember guidance about the order in which calculations are carried out to ensure that everyone doing teh same sum gets the same answer. In this case the first thing that is in the question is Division.\u003c/p\u003e\\n\u003cp\u003eFirst work through the expression from left to right, evaluating any division as you come to it. You should be left with an expression involving only pluses and minuses. Evaluate this expression, again working from left to right. Thus:\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\var{h}-\\\\var{a2*b2} \\\\div \\\\var{b2}\\\\]\u003c/p\u003e\\n\u003cp\u003e\\\\[=\\\\var{h}-\\\\var{a2}\\\\]\u003c/p\u003e\\n\u003cp\u003e\\\\[=\\\\var{h-a2}\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"b2\": {\"name\": \"b2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..9 except a2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"h\": {\"name\": \"h\", \"group\": \"Ungrouped variables\", \"definition\": \"random(7..15)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a2\": {\"name\": \"a2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..9)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"h\", \"a2\", \"b2\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e$\\\\var{h}-\\\\var{a2*b2} \\\\div \\\\var{b2}$\u003c/p\u003e\", \"minValue\": \"{h-a2}\", \"maxValue\": \"{h-a2}\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA11 BIDMAS with a division 2\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eApplying the order of operators.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eTo calculate the following expression you press a sequence of buttons on your calculator.\u003c/p\u003e\\n\u003cp\u003e\\\\begin{align}\\\\frac{\\\\var{num}}{\\\\var{a}\\\\times\\\\var{b}}\\\\end{align}\u003c/p\u003e\\n\u003cp\u003eWhich of the following would give the WRONG answer?\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"advice\": \"\u003cp\u003eBIDMAS stands for:\u003c/p\u003e\\n\u003cp\u003eBrackets\u003c/p\u003e\\n\u003cp\u003eIndices\u003c/p\u003e\\n\u003cp\u003eDivision\u003c/p\u003e\\n\u003cp\u003eMultiplication\u003c/p\u003e\\n\u003cp\u003eAddition\u003c/p\u003e\\n\u003cp\u003eSubtraction\u003c/p\u003e\\n\u003cp\u003eThis is the standardized order of operations that we carry out and is part of how the calculator is designed to work. The most effective way to use most modern calculators is to use either the fraction button (on scientific calculators) or as is hinted at in this question, use brackets.\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"a\": {\"name\": \"a\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2 .. 20#1)\", \"description\": \"\", \"templateType\": \"randrange\", \"can_override\": false}, \"b\": {\"name\": \"b\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2 .. 20#1)\", \"description\": \"\", \"templateType\": \"randrange\", \"can_override\": false}, \"num\": {\"name\": \"num\", \"group\": \"Ungrouped variables\", \"definition\": \"a*b*3\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"a\u003c\u003eb\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"a\", \"b\", \"num\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"1_n_2\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minMarks\": 0, \"maxMarks\": 0, \"shuffleChoices\": true, \"displayType\": \"radiogroup\", \"displayColumns\": 0, \"showCellAnswerState\": true, \"choices\": [\"$\\\\var{num}\\\\div (\\\\var{a}\\\\times\\\\var{b})$\", \"$\\\\var{num} \\\\div \\\\var{a} \\\\times \\\\var{b}$\", \"$\\\\var{num} \\\\div \\\\var{a} \\\\div \\\\var{b}$\"], \"matrix\": [0, \"1\", 0], \"distractors\": [\"\", \"\", \"\"]}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA12 Negatives (add/subtract) 1\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eCalculations with negative numbers.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eCalculate $\\\\var{x}+(\\\\var{y})$.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eWhen you add a negative number that is the same as subtracting the number so\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\var{x}+(\\\\var{y})=\\\\var{x}-\\\\var{-y}=\\\\var{x+y}.\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"x\": {\"name\": \"x\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..50)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"y\": {\"name\": \"y\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-50..-1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"x\", \"y\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"{x}+{y}\", \"maxValue\": \"{x}+{y}\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA13 Negatives (add/subtract) 2\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eCalculations with negative numbers.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eCalculate $\\\\var{x}-(\\\\var{y})$.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eWhen you subtract a negative number that is the same as adding the number so\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\var{x}-(\\\\var{y})=\\\\var{x}+\\\\var{-y}=\\\\var{x-y}\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"x\": {\"name\": \"x\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..50)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"y\": {\"name\": \"y\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-50..-1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"x\", \"y\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"{x}-{y}\", \"maxValue\": \"{x}-{y}\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA14 Multiplying Negatives 1\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eCalculations with negative numbers.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eCalculate $\\\\var{x}\\\\times(\\\\var{y})$.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eWhen you multiply by a negative number that is the same as doing the multiplication as if the numbers were positive and then making the result negative. This means we have\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\var{x}\\\\times(\\\\var{y})=-(\\\\var{x}\\\\times\\\\var{-y})=\\\\var{x*y}.\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"x\": {\"name\": \"x\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..10)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"y\": {\"name\": \"y\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-10..-1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"x\", \"y\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"{x*y}\", \"maxValue\": \"{x*y}\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA15 Multiplying Negatives 2\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eCalculations with negative numbers.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eCalculate $(\\\\var{x})\\\\times(\\\\var{y})$.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eMultiplying two negative numbers gives a positive so we just calculate the multiplication as if both numbers were positive. This means we have\u003c/p\u003e\\n\u003cp\u003e\\\\[(\\\\var{x})\\\\times(\\\\var{y})=\\\\var{-x}\\\\times\\\\var{-y}=\\\\var{x*y}.\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"x\": {\"name\": \"x\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-10..-1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"y\": {\"name\": \"y\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-10..-1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"x\", \"y\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"{x*y}\", \"maxValue\": \"{x*y}\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA16 Dividing Negatives\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eCalculations with negative numbers.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eCalculate $(\\\\var{x})\\\\div(\\\\var{y})$.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eWhen we divide two numbers the rule is,\u003c/p\u003e\\n\u003cul\u003e\\n\u003cli\u003eplus $\\\\div$ plus = plus\u003c/li\u003e\\n\u003cli\u003eminus $\\\\div$ plus = minus\u003c/li\u003e\\n\u003cli\u003eplus $\\\\div$ minus = minus\u003c/li\u003e\\n\u003cli\u003eminus $\\\\div$ minus = plus\u003c/li\u003e\\n\u003c/ul\u003e\\n\u003cp\u003eIn this calculation we have\u003c/p\u003e\\n\u003cp\u003e\\\\[(\\\\var{x})\\\\div(\\\\var{y})=\\\\var{x/y}.\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"x\": {\"name\": \"x\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-10..10)*y\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"y\": {\"name\": \"y\", \"group\": \"Ungrouped variables\", \"definition\": \"random(-10..10 except 0)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"x\", \"y\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"{x/y}\", \"maxValue\": \"{x/y}\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NA17 Worded proportion\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eProportional calculation in context.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eIf {n1} adult cinema tickets cost \u0026pound;{n1price}, how much would it cost for {n2} adults to buy tickets to the cinema?\u003c/p\u003e\", \"advice\": \"\u003cp\u003eIf {n1} tickets cost \u0026pound;{n1price} then we can calculate that one ticket costs\u003c/p\u003e\\n\u003cp\u003e\\\\[\u0026pound;\\\\var{n1price}\\\\div\\\\var{n1}=\u0026pound;\\\\var{price}.\\\\]\u003c/p\u003e\\n\u003cp\u003eThis means that {n2} tickets cost $\\\\var{n2}\\\\times\u0026pound;\\\\var{price}=\u0026pound;\\\\var{n2price}$\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Ratio\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"n1\": {\"name\": \"n1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..9)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"price\": {\"name\": \"price\", \"group\": \"Ungrouped variables\", \"definition\": \"precround(random(2..9 # 0.01),2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"n2\": {\"name\": \"n2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..9 except n1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"n1price\": {\"name\": \"n1price\", \"group\": \"Ungrouped variables\", \"definition\": \"precround(n1*price,2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"n2price\": {\"name\": \"n2price\", \"group\": \"Ungrouped variables\", \"definition\": \"precround(n2*price,2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"n1\", \"price\", \"n2\", \"n1price\", \"n2price\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e\u0026pound;[[0]]\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"n2*price\", \"maxValue\": \"n2*price\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"precisionType\": \"dp\", \"precision\": \"2\", \"precisionPartialCredit\": 0, \"precisionMessage\": \"You have not given your answer to the correct precision.\", \"strictPrecision\": true, \"showPrecisionHint\": false, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF01  Rounding DP\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Stanislav Duris\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1590/\"}, {\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Oliver Spenceley\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23557/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eRound\u0026nbsp;numbers to\u0026nbsp;a given number of\u0026nbsp;decimal places.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eWe can approximate numbers by rounding.\u003c/p\u003e\\n\u003cp\u003eRound $\\\\var{c1}$ to\u0026nbsp;a given number of\u0026nbsp;decimal places.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eThe\u0026nbsp;first\u0026nbsp;thing to do\u0026nbsp;when we are rounding numbers is to identify the last digit we are keeping.\u003c/p\u003e\\n\u003cp\u003eWhen you\u0027re asked to \u003cstrong\u003eround\u003c/strong\u003e your answer to a number of decimal places, you need to decide whether to keep the last\u0026nbsp;digit the same (rounding down) or increase it by 1 (rounding up). If the following digit is less than 5 we round down and we round up\u0026nbsp;when the next digit is 5 or more.\u003c/p\u003e\\n\u003cp\u003eTo write it down in steps:\u003c/p\u003e\\n\u003col\u003e\\n\u003col\u003e\\n\u003col\u003e\\n\u003col\u003e\\n\u003cli style=\\\"text-align: left;\\\"\u003eIdentify the last digit we need to keep.\u003c/li\u003e\\n\u003cli style=\\\"text-align: left;\\\"\u003eLook at the following digit.\u003c/li\u003e\\n\u003cli style=\\\"text-align: left;\\\"\u003eIf it\u0027s 5 or more, increase the previous digit by one.\u003c/li\u003e\\n\u003cli class=\\\"c-list__ordered-item\\\" style=\\\"text-align: left;\\\"\u003eIf it\u0027s 4 or less, keep the previous digit the same.\u003c/li\u003e\\n\u003cli class=\\\"c-list__ordered-item\\\" style=\\\"text-align: left;\\\"\u003eFill any spaces to the right of the digit with zeros if needed.\u003c/li\u003e\\n\u003c/ol\u003e\\n\u003c/ol\u003e\\n\u003c/ol\u003e\\n\u003c/ol\u003e\\n\u003cp class=\\\"c-list__ordered-item\\\"\u003eIt is important to keep in mind that if the digit we are increasing is 9, it becomes zero and we increase the previous digit instead. If this digit is 9 as well, we\u0026nbsp;move along\u0026nbsp;to the left side until we find a digit less than 9.\u003c/p\u003e\\n\u003chr/\u003e\\n\u003cp class=\\\"c-list__ordered-item\\\"\u003eTo round a number to a given number $n$ of decimal places, we look at the\u0026nbsp;$n$th\u0026nbsp;digit after the decimal point.\u003c/p\u003e\\n\u003cp style=\\\"padding-left: 30px;\\\"\u003eWe have $\\\\var{c1}$.\u003c/p\u003e\\n\u003cp class=\\\"k-type-body-article\\\"\u003e\u003cem\u003ei)\u003c/em\u003e\u003c/p\u003e\\n\u003cp class=\\\"k-type-body-article\\\" style=\\\"padding-left: 30px;\\\"\u003eWe look at the first digit after the decimal point. This is $\\\\var{cdig[4]}$ and the following digit is $\\\\var{cdig[3]}$ so we round \u003cspan data-jme-visible=\\\"cdig[3] \u0026gt; 4\\\"\u003eup\u003c/span\u003e\u003cspan data-jme-visible=\\\"cdig[3] \u0026lt; 5\\\"\u003edown\u003c/span\u003e to get $\\\\var{precround(c1, 1)}$.\u003c/p\u003e\\n\u003cp class=\\\"k-type-body-article\\\"\u003e\u003cem\u003eii)\u003c/em\u003e\u003c/p\u003e\\n\u003cp class=\\\"k-type-body-article\\\" style=\\\"padding-left: 30px;\\\"\u003eThe second digit after the decimal point is $\\\\var{cdig[3]}$. It is followed by $\\\\var{cdig[2]}$ so we round \u003cspan data-jme-visible=\\\"cdig[2] \u0026gt; 4\\\"\u003eup\u003c/span\u003e\u003cspan data-jme-visible=\\\"cdig[2] \u0026lt; 5\\\"\u003edown\u003c/span\u003e to get $\\\\var{precround(c1, 2)}$.\u003c/p\u003e\\n\u003cp class=\\\"k-type-body-article\\\"\u003e\u003cem\u003eiii)\u003c/em\u003e\u003c/p\u003e\\n\u003cp style=\\\"padding-left: 30px;\\\"\u003e\u003cspan data-jme-visible=\\\"dp = 3\\\"\u003eThe 3rd decimal place is $\\\\var{cdig[2]}$, followed by $\\\\var{cdig[1]}$. We get $\\\\var{precround(c1, 3)}$.\u0026nbsp;\u003c/span\u003e\u003cspan data-jme-visible=\\\"dp = 4\\\"\u003eThe 4th decimal place is $\\\\var{cdig[1]}$, followed by $\\\\var{cdig[0]}$.\u0026nbsp;We get $\\\\var{precround(c1, 4)}$.\u003c/span\u003e\u003c/p\u003e\\n\u003cp style=\\\"padding-left: 30px;\\\"\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic\u003c/a\u003e\u003c/p\u003e\\n\u003cp style=\\\"padding-left: 30px;\\\"\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"c1\": {\"name\": \"c1\", \"group\": \"Ungrouped variables\", \"definition\": \"n_from_digits(cdig)*10^(-5) + random(1..5)\", \"description\": \"\u003cp\u003eRandom number with 5 decimal places.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"cdig\": {\"name\": \"cdig\", \"group\": \"Ungrouped variables\", \"definition\": \"repeat(random(1..9), 5)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"dp\": {\"name\": \"dp\", \"group\": \"Ungrouped variables\", \"definition\": \"random(3..4)\", \"description\": \"\u003cp\u003eNumber of decimal places to round.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": \"100\"}, \"ungrouped_variables\": [\"dp\", \"cdig\", \"c1\"], \"variable_groups\": [], \"functions\": {\"n_from_digits\": {\"parameters\": [[\"digits\", \"list\"]], \"type\": \"number\", \"language\": \"jme\", \"definition\": \"if(\\n  len(digits)=0,\\n    0,\\n    digits[0]+10*n_from_digits(digits[1..len(digits)])\\n)\"}}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp style=\\\"padding-left: 60px;\\\"\u003e\u003cem\u003ei)\u003c/em\u003e\u0026nbsp;\u0026nbsp; $\\\\var{c1}$ rounded\u0026nbsp;to 1 decimal place is:\u0026nbsp; [[0]]\u003c/p\u003e\\n\u003cp style=\\\"padding-left: 60px;\\\"\u003e\u003cem\u003eii)\u003c/em\u003e\u0026nbsp;\u0026nbsp; $\\\\var{c1}$ rounded\u0026nbsp;to 2 decimal places is:\u0026nbsp; [[1]]\u003c/p\u003e\\n\u003cp style=\\\"padding-left: 60px;\\\"\u003e\u003cem\u003eiii)\u003c/em\u003e\u0026nbsp;\u0026nbsp; $\\\\var{c1}$ rounded\u0026nbsp;to {dp} decimal places is:\u0026nbsp; [[2]]\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"precround(c1, 1)\", \"maxValue\": \"precround(c1, 1)\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"precround(c1, 2)\", \"maxValue\": \"precround(c1, 2)\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"precround(c1, dp)\", \"maxValue\": \"precround(c1, dp)\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF06 Percentage increase\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eCalculate the percentage increase (as a percentage) given a number and the size of the increase.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eWhat is the percentage increase in a class of {total} if {additional} more are added to it?\u003c/p\u003e\\n\u003cp\u003eGive your answer to 2 decimal places.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eTo calculate a percentage increase you need to find how much the increase is as a percentage of the original number. In this question the increase is {additional} and the original number is {total} so the percentage is\u003c/p\u003e\\n\u003cp\u003e\\\\[ \\\\frac{\\\\var{additional}}{\\\\var{total}}\\\\times100\\\\%=\\\\var{dpformat(additional/total,4)}\\\\times 100\\\\%=\\\\var{dpformat(percentage,2)}\\\\%\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"total\": {\"name\": \"total\", \"group\": \"Ungrouped variables\", \"definition\": \"random(15..60)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"additional\": {\"name\": \"additional\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..10)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"percentage\": {\"name\": \"percentage\", \"group\": \"Ungrouped variables\", \"definition\": \"additional/total*100\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"total\", \"additional\", \"percentage\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e[[0]]%\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"percentage\", \"maxValue\": \"percentage\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"precisionType\": \"dp\", \"precision\": \"2\", \"precisionPartialCredit\": 0, \"precisionMessage\": \"You have not given your answer to the correct precision.\", \"strictPrecision\": false, \"showPrecisionHint\": false, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF07 Percentage change (decrease then increase)\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eCompound percentage change.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eThe value of a car is initially {StartingPrice}. If the value decreases by {dec}%, and then increases by {inc}%, what is the final value?\u003c/p\u003e\\n\u003cp\u003eGive your answer correct to two decimal places.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eThere is a {dec}% decrease in price. This means that price after the decrease will be {100-dec}% of the old price.\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\frac{\\\\var{100-dec}}{100} \\\\times \\\\var{StartingPrice} = \\\\var{(100-dec)/100*StartingPrice}\\\\]\u003c/p\u003e\\n\u003cp\u003eThen there is a {inc}% increase in price. This means the final price will be {100+inc}% of the price after the decrease.\u003c/p\u003e\\n\u003cp\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003e\\\\[\\\\frac{\\\\var{100+inc}}{100} \\\\times \\\\var{(100-dec)/100*StartingPrice} = \u0026pound;\\\\var{dpformat((100+inc)/100*(100-dec)/100*StartingPrice,2)}\\\\]\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"dec\": {\"name\": \"dec\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..50)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"inc\": {\"name\": \"inc\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..50)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"FinalPrice\": {\"name\": \"FinalPrice\", \"group\": \"Ungrouped variables\", \"definition\": \"StartingPrice*(1-dec/100)*(1+inc/100)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"StartingPrice\": {\"name\": \"StartingPrice\", \"group\": \"Ungrouped variables\", \"definition\": \"random(600..8000 # 10)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"dec\", \"inc\", \"FinalPrice\", \"StartingPrice\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u0026pound;[[0]]\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"FinalPrice\", \"maxValue\": \"FinalPrice\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"precisionType\": \"dp\", \"precision\": \"2\", \"precisionPartialCredit\": 0, \"precisionMessage\": \"You have not given your answer to the correct precision.\", \"strictPrecision\": false, \"showPrecisionHint\": false, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF08 Reverse percentages\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Stanislav Duris\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1590/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [\"decrease\", \"percentages\", \"taxonomy\"], \"metadata\": {\"description\": \"\u003cp\u003eFind the original price before a discount by dividing the new price by the percentage discount.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003e{name1} and {name2} are friends. {name1} noticed {name2}\u0027s new {item} when he came over to visit her house. He immediately knew he wanted to buy the same model. When he got home, he bought the {item} online for \u0026pound;{newprice}.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eWe need to find the original price paid by {name2}. This value represents 100%.\u003c/p\u003e\\n\u003cp\u003eBy the time {name1} bought the {item}, the price had decreased by {percentage}%.\u003c/p\u003e\\n\u003cp\u003e{name1} therefore paid {100-percentage}% of the price {name2} paid.\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003eWe use the unitary method to find the original price. We know the price paid by {name1}.\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\var{100-percentage}\\\\text{%} = \\\\var{newprice} \\\\text{.}\\\\]\u003c/p\u003e\\n\u003cp\u003eDivide both sides\u0026nbsp;by {100-percentage} to get\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\begin{align} 1\\\\text{%} \u0026amp;= \\\\var{newprice} \\\\div \\\\var{100-percentage} \\\\\\\\\u0026amp;= \\\\var{newprice/(100-percentage)} \\\\text{.} \\\\end{align}\\\\]\u003c/p\u003e\\n\u003cp\u003eMultiply\u0026nbsp;both sides\u0026nbsp;by\u0026nbsp;100 to get\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\begin{align} 100\\\\text{%} \u0026amp;= \\\\var{newprice/(100-percentage)} \\\\times\u0026nbsp;100 \\\\\\\\\u0026amp;= \\\\var{newprice/(100-percentage)*100} \\\\\\\\\u0026amp;= \\\\var{oldprice}\\\\text{.} \\\\end{align}\\\\]\u003c/p\u003e\\n\u003cp\u003eThis is the original price paid by {name2} before the {percentage}% decrease.\u003c/p\u003e\\n\u003cp\u003eWe can check our answer with a different method.\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\begin{align} \\\\var{100-percentage}\\\\text{% of } \\\\var{oldprice} \u0026amp;= \\\\var{(100-percentage)/100} \\\\times \\\\var{oldprice}\u0026nbsp;\\\\\\\\\u0026amp;= \u0026nbsp;\\\\var{(100-percentage)/100*oldprice} \\\\\\\\\u0026amp;= \\\\var{precround((100-percentage)/100*oldprice, 2)}\u0026nbsp;\u0026nbsp;\\\\text{.} \\\\end{align}\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"newprice\": {\"name\": \"newprice\", \"group\": \"Ungrouped variables\", \"definition\": \"precround(oldprice*(100-percentage)/100,2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"name2\": {\"name\": \"name2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(\\\"Kaden\\\",\\\"Ola\\\",\\\"Pat\\\",\\\"Skylar\\\",\\\"Wren\\\",\\\"Zendaya\\\")\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"name1\": {\"name\": \"name1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(\\\"Adair\\\",\\\"Aya\\\",\\\"Bergen\\\",\\\"Dua\\\",\\\"Fadhili\\\",\\\"Harper\\\")\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"oldprice\": {\"name\": \"oldprice\", \"group\": \"Ungrouped variables\", \"definition\": \"switch(\\n  item = \\\"TV\\\", random(179.99..1199.99 #10), \\n  item = \\\"laptop\\\", random(209.99..799.99 #10),\\n  item = \\\"smartphone\\\", random(109.99..799.99 #10),\\n  item = \\\"PC\\\", random(209.99..969.99 #10),\\n  item = \\\"gaming console\\\", random(89.99..349.99 #10),\\n  399.99)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"percentage\": {\"name\": \"percentage\", \"group\": \"Ungrouped variables\", \"definition\": \"random(5..30)\", \"description\": \"\u003cp\u003eDiscount percentage.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"item\": {\"name\": \"item\", \"group\": \"Ungrouped variables\", \"definition\": \"random(\\\"TV\\\", \\\"laptop\\\", \\\"smartphone\\\", \\\"PC\\\", \\\"gaming console\\\")\", \"description\": \"\u003cp\u003eThe bought item.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"precround(precround(oldprice*(100-percentage)/100,2)*100/(100-percentage),2) = oldprice\", \"maxRuns\": \"1000\"}, \"ungrouped_variables\": [\"item\", \"name1\", \"percentage\", \"name2\", \"oldprice\", \"newprice\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eWhen {name1} told {name2} how much he had paid for the {item}, {name2} said the price had decreased by {percentage}% since she bought it.\u003c/p\u003e\\n\u003cp\u003eHow much did\u0026nbsp;{name2} pay for the {item}?\u003c/p\u003e\\n\u003cp\u003e\u0026pound;\u0026nbsp; [[0]]\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": \"1\", \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"oldprice\", \"maxValue\": \"oldprice\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"precisionType\": \"dp\", \"precision\": \"2\", \"precisionPartialCredit\": 0, \"precisionMessage\": \"You have not given your answer to the correct precision.\", \"strictPrecision\": false, \"showPrecisionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF09 Percentage of amount 1\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eFind a percentage of an amount.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eWhat is {x}% of {y}?\u003c/p\u003e\", \"advice\": \"\u003cp\u003eTaking {x}% of {y} is calculated by multiplying,\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\frac{\\\\var{x}}{100}\\\\times\\\\var{y}.\\\\]\u003c/p\u003e\\n\u003cp\u003eFor this question we can calculate this by noticing that 10% of {y} is {y*0.1} and then since $\\\\var{x}\\\\%=\\\\var{x/10}\\\\times10\\\\%$ we can calculate {x}% of {y} as,\u003cbr/\u003e\\\\[\\\\var{x/10}\\\\times10\\\\%\\\\times \\\\var{y}=\\\\var{x/10}\\\\times\\\\var{y*0.1}=\\\\var{x/100*y}.\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"x\": {\"name\": \"x\", \"group\": \"Ungrouped variables\", \"definition\": \"random(10..90 #10)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"y\": {\"name\": \"y\", \"group\": \"Ungrouped variables\", \"definition\": \"random(10.. 100 # 10)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"x\", \"y\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"y*(x/100)\", \"maxValue\": \"y*(x/100)\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF10 Percentage of amount 2\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Ben McGovern\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4872/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eCalculate one number as percentage of another.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\", \"advice\": \"\u003cp\u003eTo find the percentage of a number we can use the formula:\u003c/p\u003e\\n\u003cp\u003e\\\\[ \\\\text{New value } = \\\\text{Original value } \\\\times \\\\text{Percentage in decimal form} \\\\]\u003c/p\u003e\\n\u003cp\u003eFirstly, to convert a percentage into decimal form we need to divide by $100$:\u003c/p\u003e\\n\u003cp\u003e\\\\[ \\\\var{p} \\\\% =\u0026nbsp; \\\\var{p/100} \\\\]\u003c/p\u003e\\n\u003cp\u003eTherefore,\u003c/p\u003e\\n\u003cp\u003e\\\\[ \\\\begin{split} \\\\var{p} \\\\% \\\\,\\\\text{ of } \\\\var{og} \u0026amp;\\\\,= \\\\var{og} \\\\times \\\\var{p/100} \\\\\\\\ \u0026amp;\\\\,= \\\\var{ans} \\\\end{split} \\\\]\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find resources to help you revise how to work out percentages.\u003c/a\u003e\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"p\": {\"name\": \"p\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..99)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"og\": {\"name\": \"og\", \"group\": \"Ungrouped variables\", \"definition\": \"random(101..999)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"ans\": {\"name\": \"ans\", \"group\": \"Ungrouped variables\", \"definition\": \"og*p*0.01\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"p\", \"og\", \"ans\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eFind {p}% of {og}\u003c/p\u003e\", \"minValue\": \"ans\", \"maxValue\": \"ans\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF11 One number as a percentage of another\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Don Shearman\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/680/\"}, {\"name\": \"Adelle Colbourn\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/2083/\"}, {\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Ben McGovern\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4872/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eGiven the number of international students enrolled on a course of $n$ students, calculate the percentage of \u0027home\u0027 students.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cdiv id=\\\"MathJax_Message\\\" style=\\\"display: none;\\\"\u003e\u003c/div\u003e\\n\u003cdiv id=\\\"MathJax_Message\\\" style=\\\"display: none;\\\"\u003e\u003c/div\u003e\\n\u003cdiv id=\\\"MathJax_Message\\\" style=\\\"display: none;\\\"\u003e\u003c/div\u003e\\n\u003cdiv id=\\\"MathJax_Message\\\" style=\\\"display: none;\\\"\u003e\u003c/div\u003e\\n\u003cp\u003e{num_students}\u0026nbsp;of the\u0026nbsp;{class_size} students enrolled on a course are international students. \u0026nbsp;What percentage are \u0027home\u0027 students?\u003c/p\u003e\", \"advice\": \"\u003cp\u003eFirst work out the number of students who are not international. In this case it is\u0026nbsp;{class_size} - {num_students} = {class_size-num_students} students.\u003c/p\u003e\\n\u003cp\u003eThen\u0026nbsp;write this as a fraction out of {class_size}.\u0026nbsp; \u0026nbsp;$ \\\\frac{\\\\var{class_size-num_students}} {\\\\var{class_size}} $\u003c/p\u003e\\n\u003cp\u003eThen convert this to a percentage. You\u0026nbsp;should put this fraction into your calculator and then multiply by 100:\u003c/p\u003e\\n\u003cp\u003e\u0026nbsp;$ \\\\frac{\\\\var{class_size-num_students}} {\\\\var{class_size}} \\\\times\u0026nbsp;100\u0026nbsp;= \\\\var{(class_size-num_students)/class_size*100}\\\\%$\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find resources to help you revise how to calculate percentages.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"num_students\": {\"name\": \"num_students\", \"group\": \"Ungrouped variables\", \"definition\": \"per*class_size/100\\n\", \"description\": \"\u003cp\u003eThe number of students in the class who do speak a language other than English.\u0026nbsp;\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"class_size\": {\"name\": \"class_size\", \"group\": \"Ungrouped variables\", \"definition\": \"random(80..300)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"per\": {\"name\": \"per\", \"group\": \"Ungrouped variables\", \"definition\": \"random(5..90 except 50)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"num_students = precround(num_students,0) AND (num_students\u003c\u003eclass_size/2 AND class_size\u003c\u003e100)\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"num_students\", \"class_size\", \"per\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"1_n_2\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cdiv id=\\\"MathJax_Message\\\" style=\\\"display: none;\\\"\u003e\u003c/div\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"minMarks\": 0, \"maxMarks\": 0, \"shuffleChoices\": true, \"displayType\": \"radiogroup\", \"displayColumns\": 0, \"showCellAnswerState\": true, \"choices\": [\"$\\\\var{class_size-num_students}\\\\%$\", \"$\\\\var{num_students*100/class_size}\\\\%$\", \"$\\\\var{num_students}\\\\%$\", \"$\\\\var{(class_size-num_students)/class_size*100}\\\\%$\"], \"matrix\": [0, 0, 0, \"1\"], \"distractors\": [\"Have you converted this to a percentage? Click on Reveal Answer and scroll down for Advice regarding this question.\", \"How many students do NOT speak a language other than English at home? Click on Reveal Answer and scroll down for Advice regarding this question.\", \"How many students do NOT speak a language other than English at home? Then convert this to a percentage. Click on Reveal Answer and scroll down for Advice regarding this question.\", \"Well done!\"]}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF12 Simplify (cancel down) Fractions\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Simon Thomas\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3148/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"Calculating the LCM and HCF of numbers by using prime factorisation.\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eExpress the fraction below in its simplest form:\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\frac{\\\\var{x}}{\\\\var{y}}\\\\]\u003c/p\u003e\", \"advice\": \"\u003cp\u003eTo simplify a fraction we need to divide both numbers by their common factors.\u003c/p\u003e\\n\u003cp\u003eWe can write $\\\\var{x}$ and $\\\\var{y}$ as a product of prime factors as follows:\u003c/p\u003e\\n\u003cp\u003e$\\\\var{x}=\\\\var{show_factors(x)}$\u003c/p\u003e\\n\u003cp\u003e$\\\\var{y}=\\\\var{show_factors(y)}$.\u003c/p\u003e\\n\u003cp\u003eSo to fully simplify the fraction we need to divide both $\\\\var{x}$ and $\\\\var{y}$ by\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\var{show_factors(hcf_xy)}.\\\\]\u003c/p\u003e\\n\u003cp\u003eThis gives us the fraction\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\frac{\\\\var{x/hcf_xy}}{\\\\var{y/hcf_xy}}\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"x_powers\": {\"name\": \"x_powers\", \"group\": \"Ungrouped variables\", \"definition\": \"[random(1..3),random(0..3),random(0,1)]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"y_powers\": {\"name\": \"y_powers\", \"group\": \"Ungrouped variables\", \"definition\": \"[random(1..3),random(0..3),random(0,1)]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"x\": {\"name\": \"x\", \"group\": \"Ungrouped variables\", \"definition\": \"2^x_powers[0]*3^x_powers[1]*5^x_powers[2]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"y\": {\"name\": \"y\", \"group\": \"Ungrouped variables\", \"definition\": \"2^y_powers[0]*3^y_powers[1]*5^y_powers[2]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"hcf_xy\": {\"name\": \"hcf_xy\", \"group\": \"Ungrouped variables\", \"definition\": \"2^min(x_powers[0],y_powers[0])*3^min(x_powers[1],y_powers[1])*5^min(x_powers[2],y_powers[2])\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"lcm_xy\": {\"name\": \"lcm_xy\", \"group\": \"Ungrouped variables\", \"definition\": \"2^max(x_powers[0],y_powers[0])*3^max(x_powers[1],y_powers[1])*5^max(x_powers[2],y_powers[2])\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"primes\": {\"name\": \"primes\", \"group\": \"Ungrouped variables\", \"definition\": \"[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": \"500\"}, \"ungrouped_variables\": [\"x_powers\", \"y_powers\", \"x\", \"y\", \"hcf_xy\", \"lcm_xy\", \"primes\"], \"variable_groups\": [], \"functions\": {\"show_factors\": {\"parameters\": [[\"n\", \"number\"]], \"type\": \"string\", \"language\": \"jme\", \"definition\": \"latex(  // mark the output as a string of raw LaTeX\\n  join(\\n    map(\\n      if(a=1,p,p+\u0027^{\u0027+a+\u0027}\u0027), // when the exponent is 1, return p, otherwise return p^{exponent}\\n      [p,a],\\n      filter(x[1]\u003e0,x,zip(primes,factorise(n)))  // for all the primes p which are factors of n, return p and its exponent\\n    ),\\n    \u0027 \\\\\\\\times \u0027 // join all the prime powers up with \\\\times symbols\\n  )\\n)\"}}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"{x/y}\", \"maxValue\": \"{x/y}\", \"correctAnswerFraction\": true, \"allowFractions\": true, \"mustBeReduced\": true, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": false, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF13 Converting mixed numbers to top heavy\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Lauren Richards\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1589/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}], \"tags\": [\"converting improper fractions to mixed numbers\", \"converting mixed numbers to improper fractions\", \"equivalent fractions\", \"improper fractions\", \"mixed numbers\"], \"metadata\": {\"description\": \"\u003cp\u003eThis question tests the student\u0027s ability to identify equivalent fractions\u0026nbsp;through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number.\u0026nbsp;\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\", \"advice\": \"\u003cp\u003eA \u003cem\u003emixed number\u003c/em\u003e is a number consisting of an integer and a proper fraction, i.e. a number in the form $\u0026nbsp;a \\\\displaystyle \\\\frac{b}{c}$ where $a$ is an integer and $\\\\displaystyle\\\\frac{b}{c}$ is a proper fraction: $b$ is smaller than $c$.\u003c/p\u003e\\n\u003cp\u003eAn \u003cem\u003eimproper fraction\u003c/em\u003e is a fraction where the numerator is larger than the denominator, i.e. a number of the form $\\\\displaystyle\\\\frac{d}{e}$ where\u0026nbsp;the numerator, $d$, is greater than the denominator, $e$.\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003eTo convert a mixed number into an improper fraction, multiply the integer part of the mixed number, $a$, by the denominator, $c$.\u003c/p\u003e\\n\u003cp\u003eThe numerator of the improper fraction will be equal to this\u0026nbsp;added to what was already on the numerator of the proper fraction.\u003c/p\u003e\\n\u003cp\u003eThe denominator of the proper fraction will stay the same when it converts to an improper fraction to give a final answer of\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e$\\\\displaystyle\\\\frac{({a}\\\\times{c})+b}{c}$.\u003c/p\u003e\\n\u003cp\u003e\\\\[\u003cbr/\u003e{\\\\var{f}\\\\frac{\\\\var{g_coprime}}{\\\\var{h_coprime}}} = \\\\frac{({\\\\var{f}}\\\\times{\\\\var{h_coprime}})+{\\\\var{g_coprime}}}{{\\\\var{h_coprime}}}=\\\\simplify{{num}/{h_coprime}}\\\\text{.}\u003cbr/\u003e\\\\]\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Fractions\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"g\": {\"name\": \"g\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..h except h)\", \"description\": \"\u003cp\u003eRandom number between 1 and 15\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"g_coprime\": {\"name\": \"g_coprime\", \"group\": \"Ungrouped variables\", \"definition\": \"g/gcd_gh\", \"description\": \"\u003cp\u003ePART C\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"gcd_gh\": {\"name\": \"gcd_gh\", \"group\": \"Ungrouped variables\", \"definition\": \"gcd(g,h)\", \"description\": \"\u003cp\u003ePART C\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"num\": {\"name\": \"num\", \"group\": \"Ungrouped variables\", \"definition\": \"((h_coprime*f)+g_coprime)\", \"description\": \"\u003cp\u003enumerator for the improper fraction c(i)\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"h\": {\"name\": \"h\", \"group\": \"Ungrouped variables\", \"definition\": \"random(10 .. 24#1)\", \"description\": \"\u003cp\u003eRandom number between 1 and 24\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"h_coprime\": {\"name\": \"h_coprime\", \"group\": \"Ungrouped variables\", \"definition\": \"h/gcd_gh\", \"description\": \"\u003cp\u003ePART C\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"gcdb\": {\"name\": \"gcdb\", \"group\": \"Ungrouped variables\", \"definition\": \"gcd({num},{h_coprime})\", \"description\": \"\u003cp\u003egcd of num and h\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"f\": {\"name\": \"f\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2 .. 5#1)\", \"description\": \"\u003cp\u003eRandom number between 1 and 5\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"f\", \"g\", \"h\", \"gcd_gh\", \"g_coprime\", \"h_coprime\", \"num\", \"gcdb\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"fraction {\\n  display: inline-block;\\n  vertical-align: middle;\\n}\\nfraction \u003e numerator, fraction \u003e denominator {\\n  float: left;\\n  width: 100%;\\n  text-align: center;\\n  line-height: 2.5em;\\n}\\nfraction \u003e numerator {\\n  border-bottom: 1px solid;\\n  padding-bottom: 5px;\\n}\\nfraction \u003e denominator {\\n  padding-top: 5px;\\n}\\nfraction input {\\n    line-height: 1em;\\n}\\n\\nfraction .part {\\n    margin: 0;\\n}\\n\\n.table-responsive, .fractiontable {\\n  display:inline-block;\\n}\\n.fractiontable {\\n  padding: 0; \\n  border: 0;\\n}\\n\\n.fractiontable  .tddenom \\n{\\n text-align: center;\\n}\\n\\n.fractiontable .tdnum \\n{\\n  border-bottom: 1px solid black; \\n  text-align: center;\\n}\\n\\n\\n.fractiontable tr {\\n    height: 3em;\\n}\\n\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eWrite the mixed number as an improper fraction and reduce it down to its simplest form.\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003e$\\\\displaystyle{\\\\var{f}\\\\frac{\\\\var{g_coprime}}{\\\\var{h_coprime}}} =$\u0026nbsp;\u003cfraction\u003e \u003cnumerator\u003e[[0]]\u003c/numerator\u003e \u003cdenominator\u003e[[1]]\u003c/denominator\u003e \u003c/fraction\u003e.\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"num/gcdb\", \"maxValue\": \"num/gcdb\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"h_coprime/gcdb\", \"maxValue\": \"h_coprime/gcdb\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF14 Add Fractions\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Lauren Richards\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1589/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Oliver Spenceley\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23557/\"}], \"tags\": [\"adding and subtracting fractions\", \"adding fractions\", \"converting between decimals and fractions\", \"converting integers to fractions\", \"Fractions\", \"fractions\", \"integers\", \"manipulation of fractions\", \"subtracting fractions\", \"taxonomy\"], \"metadata\": {\"description\": \"\u003cp\u003eManipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer\u0026nbsp;and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.\u0026nbsp;\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eEvaluate the following addition, giving the fraction in its simplest form.\u003c/p\u003e\", \"advice\": \"\u003cp\u003e$\\\\displaystyle\\\\frac{\\\\var{a_coprime}}{\\\\var{b_coprime}}+\\\\frac{\\\\var{c_coprime}}{\\\\var{d_coprime}}$\u003c/p\u003e\\n\u003cp\u003eTo add or subtract fractions, we need to have a common denominator on both fractions.\u003c/p\u003e\\n\u003cp\u003eTo get a common denominator, we need to find the lowest common multiple of the two denominators.\u003c/p\u003e\\n\u003cp\u003eThe lowest common multiple of $\\\\var{b_coprime}$ and $\\\\var{d_coprime}$ is $\\\\var{lcm}.$\u003c/p\u003e\\n\u003cp\u003eThis will be the new denominator, and we need to multiply each fraction individually to ensure we get this denominator.\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003eFor\u0026nbsp;$\\\\displaystyle\\\\frac{\\\\var{a_coprime}}{\\\\var{b_coprime}}$, we need to multiply the fraction by $\\\\displaystyle\\\\frac{\\\\var{lcm_b}}{\\\\var{lcm_b}}$ to give $\\\\displaystyle\\\\frac{\\\\var{alcm_b}}{\\\\var{lcm}}.$\u003c/p\u003e\\n\u003cp\u003eFor\u0026nbsp;$\\\\displaystyle\\\\frac{\\\\var{c_coprime}}{\\\\var{d_coprime}}$, we need to multiply the fraction by\u0026nbsp;$\\\\displaystyle\\\\frac{\\\\var{lcm_d}}{\\\\var{lcm_d}}$ to give $\\\\displaystyle\\\\frac{\\\\var{clcm_d}}{\\\\var{lcm}}.$\u003c/p\u003e\\n\u003cp\u003eNow that we have each fraction in terms of a common denominator, we can now add the fractions together.\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003e$\\\\displaystyle\\\\frac{\\\\var{alcm_b}}{\\\\var{lcm}}+\\\\frac{\\\\var{clcm_d}}{\\\\var{lcm}}=\\\\frac{(\\\\var{alcm_b}+\\\\var{clcm_d})}{\\\\var{lcm}}=\\\\frac{\\\\var{alcmclcm}}{\\\\var{lcm}}.$\u003c/p\u003e\\n\u003cp\u003eFrom this, we can try to simplify the result down by finding the greatest common divisor of the numerator and denominator and dividing the whole fraction by this amount.\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003eThe greatest common divisor of $\\\\var{alcmclcm}$ and $\\\\var{lcm}$ is $\\\\var{gcd}.$\u003c/p\u003e\\n\u003cp\u003e\u003cspan data-jme-visible=\\\"gcd \u0026gt; 1\\\"\u003eSimplifying using this value gives a final answer of $\\\\displaystyle\\\\frac{\\\\var{num}}{\\\\var{denom}}.$\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003e\u003cspan data-jme-visible=\\\"gcd = 1\\\"\u003eTherefore, the expression cannot be simplified further, and $\\\\displaystyle\\\\frac{\\\\var{num}}{\\\\var{denom}}$ is the final answer.\u003c/span\u003e\u003c/p\u003e\\n\u003cp style=\\\"text-align: left;\\\"\u003e\u003c/p\u003e\\n\u003cp style=\\\"text-align: left;\\\"\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eFind out more about this topic using our resource\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"d_coprime\": {\"name\": \"d_coprime\", \"group\": \"Part a\", \"definition\": \"d/gcd_cd\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"denom\": {\"name\": \"denom\", \"group\": \"Part a\", \"definition\": \"lcm/gcd\", \"description\": \"\u003cp\u003ePART A answer for the denominator of part a\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"a\": {\"name\": \"a\", \"group\": \"Part a\", \"definition\": \"random(1..5)\", \"description\": \"\u003cp\u003ePART A variable a - random number between 1 and 5.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"d\": {\"name\": \"d\", \"group\": \"Part a\", \"definition\": \"random(5..15)\", \"description\": \"\u003cp\u003ePART A variable d - random number between 5 and 15.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"c_coprimeb_coprime\": {\"name\": \"c_coprimeb_coprime\", \"group\": \"Part a\", \"definition\": \"c_coprime*b_coprime\", \"description\": \"\u003cp\u003ePART A variable c times variable b\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"gcd_ab\": {\"name\": \"gcd_ab\", \"group\": \"Part a\", \"definition\": \"gcd(a,b)\", \"description\": \"\u003cp\u003ePART A simplification of fractions in the question.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lcm_b\": {\"name\": \"lcm_b\", \"group\": \"Part a\", \"definition\": \"lcm/b_coprime\", \"description\": \"\u003cp\u003ePART A lcm of b and d, divided by b\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"num\": {\"name\": \"num\", \"group\": \"Part a\", \"definition\": \"alcmclcm/gcd\", \"description\": \"\u003cp\u003ePART A answer for the numerator input\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"b\": {\"name\": \"b\", \"group\": \"Part a\", \"definition\": \"random(5..10 except d)\", \"description\": \"\u003cp\u003ePART A variable b - random number between 5 and 10 and not the same value as d.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"a_coprimed_coprime\": {\"name\": \"a_coprimed_coprime\", \"group\": \"Part a\", \"definition\": \"a_coprime*d_coprime\", \"description\": \"\u003cp\u003ePART A variable a times variable d\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lcm_d\": {\"name\": \"lcm_d\", \"group\": \"Part a\", \"definition\": \"lcm/d_coprime\", \"description\": \"\u003cp\u003ePART A lcm of b and d, divided by d\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"c\": {\"name\": \"c\", \"group\": \"Part a\", \"definition\": \"random(1..5)\", \"description\": \"\u003cp\u003ePART A variable c - random number between 1 and 5.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"clcm_d\": {\"name\": \"clcm_d\", \"group\": \"Part a\", \"definition\": \"c_coprime*lcm_d\", \"description\": \"\u003cp\u003ePART A variable c times the lcm of b and d, divided by d\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"gcd\": {\"name\": \"gcd\", \"group\": \"Part a\", \"definition\": \"gcd(alcmclcm,lcm)\", \"description\": \"\u003cp\u003ePART A greatest common divisor of the variables alcmclcm and lcm\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"alcm_b\": {\"name\": \"alcm_b\", \"group\": \"Part a\", \"definition\": \"a_coprime*lcm_b\", \"description\": \"\u003cp\u003ePART A variable a times the lcm of b and d, divided by b\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"a_coprime\": {\"name\": \"a_coprime\", \"group\": \"Part a\", \"definition\": \"a/gcd_ab\", \"description\": \"\u003cp\u003ePART A\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"b_coprime\": {\"name\": \"b_coprime\", \"group\": \"Part a\", \"definition\": \"b/gcd_ab\", \"description\": \"\u003cp\u003ePART A\u0026nbsp;\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"gcd_cd\": {\"name\": \"gcd_cd\", \"group\": \"Part a\", \"definition\": \"gcd(c,d)\", \"description\": \"\u003cp\u003ePART A\u0026nbsp;\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lcm\": {\"name\": \"lcm\", \"group\": \"Part a\", \"definition\": \"lcm(b_coprime,d_coprime)\", \"description\": \"\u003cp\u003ePART A lowest common multiple of variable b_coprime and variable d_coprime.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"alcmclcm\": {\"name\": \"alcmclcm\", \"group\": \"Part a\", \"definition\": \"alcm_b+clcm_d\", \"description\": \"\u003cp\u003ePART A\u0026nbsp;\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"c_coprime\": {\"name\": \"c_coprime\", \"group\": \"Part a\", \"definition\": \"c/gcd_cd\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [], \"variable_groups\": [{\"name\": \"Part a\", \"variables\": [\"a\", \"a_coprime\", \"b\", \"b_coprime\", \"gcd_ab\", \"c\", \"c_coprime\", \"d\", \"d_coprime\", \"gcd_cd\", \"lcm\", \"a_coprimed_coprime\", \"c_coprimeb_coprime\", \"lcm_b\", \"lcm_d\", \"alcm_b\", \"clcm_d\", \"alcmclcm\", \"gcd\", \"num\", \"denom\"]}], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"fraction {\\n  display: inline-block;\\n  vertical-align: middle;\\n}\\nfraction \u003e numerator, fraction \u003e denominator {\\n  float: left;\\n  width: 100%;\\n  text-align: center;\\n  line-height: 2.5em;\\n}\\nfraction \u003e numerator {\\n  border-bottom: 1px solid;\\n  padding-bottom: 5px;\\n}\\nfraction \u003e denominator {\\n  padding-top: 5px;\\n}\\nfraction input {\\n    line-height: 1em;\\n}\\n\\nfraction .part {\\n    margin: 0;\\n}\\n\\n.table-responsive, .fractiontable {\\n  display:inline-block;\\n}\\n.fractiontable {\\n  padding: 0; \\n  border: 0;\\n}\\n\\n.fractiontable  .tddenom \\n{\\n text-align: center;\\n}\\n\\n.fractiontable .tdnum \\n{\\n  border-bottom: 1px solid black; \\n  text-align: center;\\n}\\n\\n\\n.fractiontable tr {\\n    height: 3em;\\n}\\n\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], 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null, \"minValue\": \"num\", \"maxValue\": \"num\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"denom\", \"maxValue\": \"denom\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF15 Subtract fractions\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Lauren Richards\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1589/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}], \"tags\": [\"adding and subtracting fractions\", \"adding fractions\", \"converting between decimals and fractions\", \"converting integers to fractions\", \"Fractions\", \"fractions\", \"integers\", \"manipulation of fractions\", \"subtracting fractions\", \"taxonomy\"], \"metadata\": {\"description\": \"\u003cp\u003eManipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer\u0026nbsp;and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.\u0026nbsp;\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eEvaluate the following additions and subtractions, giving each fraction in its simplest form. Write the numerator (the top number) as negative if the fraction is negative.\u003c/p\u003e\", \"advice\": \"\u003cp\u003e$\\\\displaystyle\\\\frac{\\\\var{f_coprime}}{\\\\var{g_coprime}}-\\\\frac{\\\\var{h_coprime}}{\\\\var{j_coprime}}+2.$\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003eThe two fractions can be individually multiplied to achieve a common denominator of the lowest common multiple, $\\\\var{lcm2}.$\u003c/p\u003e\\n\u003cp\u003e$\\\\displaystyle\\\\frac{\\\\var{f_coprime}}{\\\\var{g_coprime}}$ becomes $\\\\displaystyle\\\\frac{\\\\var{flcm2_g}}{\\\\var{lcm2}}$ and $\\\\displaystyle\\\\frac{\\\\var{h_coprime}}{\\\\var{j_coprime}}$ becomes\u0026nbsp;$\\\\displaystyle\\\\frac{\\\\var{hlcm2_j}}{\\\\var{lcm2}}.$\u003c/p\u003e\\n\u003cp\u003eWe can now subtract the second fraction from the first.\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e$\\\\displaystyle\\\\frac{\\\\var{flcm2_g}}{\\\\var{lcm2}}-\\\\frac{\\\\var{hlcm2_j}}{\\\\var{lcm2}}=\\\\frac{\\\\var{flcmhlcm}}{\\\\var{lcm2}}.$\u003c/p\u003e\\n\u003cp style=\\\"text-align: left;\\\"\u003e\u003c/p\u003e\\n\u003cp style=\\\"text-align: left;\\\"\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eFind out more about this topic using our resource.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"hlcm2_j\": {\"name\": \"hlcm2_j\", \"group\": \"Part b\", \"definition\": \"h_coprime*lcm2_j\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lcm2\": {\"name\": \"lcm2\", \"group\": \"Part b\", \"definition\": \"lcm(g_coprime,j_coprime)\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"gcd_fg\": {\"name\": \"gcd_fg\", \"group\": \"Part b\", \"definition\": \"gcd(f,g)\", \"description\": \"\u003cp\u003ePART B gcd of first fraction num and denom\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"j\": {\"name\": \"j\", \"group\": \"Part b\", \"definition\": \"random(2..10 except h)\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"h\": {\"name\": \"h\", \"group\": \"Part b\", \"definition\": \"random(1..10)\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"f\": {\"name\": \"f\", \"group\": \"Part b\", \"definition\": \"random(1..10)\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"h_coprime\": {\"name\": \"h_coprime\", \"group\": \"Part b\", \"definition\": \"h/gcd_hj\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lcm2_j\": {\"name\": \"lcm2_j\", \"group\": \"Part b\", \"definition\": \"lcm2/j_coprime\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"j_coprime\": {\"name\": \"j_coprime\", \"group\": \"Part b\", \"definition\": \"j/gcd_hj\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"flcmhlcm\": {\"name\": \"flcmhlcm\", \"group\": \"Part b\", \"definition\": \"flcm2_g-hlcm2_j\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"g_coprime\": {\"name\": \"g_coprime\", \"group\": \"Part b\", \"definition\": \"g/gcd_fg\", \"description\": \"\u003cp\u003ePART B g_coprime\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"gcd_hj\": {\"name\": \"gcd_hj\", \"group\": \"Part b\", \"definition\": \"gcd(h,j)\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"g\": {\"name\": \"g\", \"group\": \"Part b\", \"definition\": \"random(2..10 except f except j)\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"flcm2_g\": {\"name\": \"flcm2_g\", \"group\": \"Part b\", \"definition\": \"f_coprime*lcm2_g\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lcm2_g\": {\"name\": \"lcm2_g\", \"group\": \"Part b\", \"definition\": \"lcm2/g_coprime\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"f_coprime\": {\"name\": \"f_coprime\", \"group\": \"Part b\", \"definition\": \"f/gcd_fg\", \"description\": \"\u003cp\u003ePART B\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [], \"variable_groups\": [{\"name\": \"Part b\", \"variables\": [\"f\", \"f_coprime\", \"g\", \"g_coprime\", \"gcd_fg\", \"h\", \"h_coprime\", \"j\", \"j_coprime\", \"gcd_hj\", \"lcm2\", \"lcm2_g\", \"flcm2_g\", \"lcm2_j\", \"hlcm2_j\", \"flcmhlcm\"]}], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"fraction {\\n  display: inline-block;\\n  vertical-align: middle;\\n}\\nfraction \u003e numerator, fraction \u003e denominator {\\n  float: left;\\n  width: 100%;\\n  text-align: center;\\n  line-height: 2.5em;\\n}\\nfraction \u003e numerator {\\n  border-bottom: 1px solid;\\n  padding-bottom: 5px;\\n}\\nfraction \u003e denominator {\\n  padding-top: 5px;\\n}\\nfraction input {\\n    line-height: 1em;\\n}\\n\\nfraction .part {\\n    margin: 0;\\n}\\n\\n.table-responsive, .fractiontable {\\n  display:inline-block;\\n}\\n.fractiontable {\\n  padding: 0; \\n  border: 0;\\n}\\n\\n.fractiontable  .tddenom \\n{\\n text-align: center;\\n}\\n\\n.fractiontable .tdnum \\n{\\n  border-bottom: 1px solid black; \\n  text-align: center;\\n}\\n\\n\\n.fractiontable tr {\\n    height: 3em;\\n}\\n\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e$\\\\displaystyle\\\\frac{\\\\var{f_coprime}}{\\\\var{g_coprime}}-\\\\frac{\\\\var{h_coprime}}{\\\\var{j_coprime}}=$\u0026nbsp;\u003cfraction\u003e \u003cnumerator\u003e[[0]]\u003c/numerator\u003e \u003cdenominator\u003e[[1]]\u003c/denominator\u003e \u003c/fraction\u003e\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": \"2\", \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"flcmhlcm\", \"maxValue\": \"flcmhlcm\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"lcm2\", \"maxValue\": \"lcm2\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF16 Multiply Fractions\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Lauren Richards\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1589/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Oliver Spenceley\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23557/\"}], \"tags\": [\"improper fractions\", \"mixed numbers\", \"multiplication of fractions\", \"multiplying fractions\", \"squared fraction\", \"taxonomy\"], \"metadata\": {\"description\": \"\u003cp\u003eSeveral problems involving the multiplication of fractions, with increasingly difficult examples, including\u0026nbsp;a mixed fraction and a squared fraction. The final part is a word problem.\u0026nbsp;\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eEvaluate the following multiplication, giving the answer in its simplest form.\u003c/p\u003e\", \"advice\": \"\u003ch4\u003e\u003c/h4\u003e\\n\u003cp\u003eTo multiply $\\\\displaystyle\\\\frac{\\\\var{a_coprime}}{\\\\var{c_coprime}}\\\\times\\\\frac{\\\\var{b_coprime}}{\\\\var{d_coprime}}$, address the numerators and denominators separately.\u003c/p\u003e\\n\u003cp\u003eMultiply the numerators across both fractions.\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e$\\\\var{a_coprime}\\\\times\\\\var{b_coprime}=\\\\var{ab}$,\u003c/p\u003e\\n\u003cp\u003eand then multiply the denominators across both fractions.\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e$\\\\var{c_coprime}\\\\times\\\\var{d_coprime}=\\\\var{cd}$.\u003c/p\u003e\\n\u003cp\u003eThe values of the multiplied numerators and denominators will be the numerator and denominator of the new fraction: $\\\\displaystyle\\\\frac{\\\\var{ab}}{\\\\var{cd}}$.\u003c/p\u003e\\n\u003cp\u003eThis answer may need simplifying down, and to do this, find the greatest common divisor in both the numerator and denominator and divide by this number.\u003c/p\u003e\\n\u003cp\u003eThe greatest common divisor of $\\\\var{ab}$ and $\\\\var{cd}$ is $\\\\var{gcd}$.\u003c/p\u003e\\n\u003cp\u003eBy using $\\\\var{gcd}$ to cancel down the fraction, the final answer is $\\\\displaystyle\\\\simplify{{ab}/{cd}}$.\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\\n\u003ch4\u003e\u003c/h4\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"k\": {\"name\": \"k\", \"group\": \"Part b\", \"definition\": \"random(1..7 except j)\", \"description\": \"\u003cp\u003eRandom number between 1 and 20\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"bb\": {\"name\": \"bb\", \"group\": \"Part d\", \"definition\": \"28*aa\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"cc\": {\"name\": \"cc\", \"group\": \"Part d\", \"definition\": \"bb/7\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"g\": {\"name\": \"g\", \"group\": \"Part b\", \"definition\": \"random(1 .. 7#1)\", \"description\": \"\u003cp\u003eRandom number between 1 and 20.\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"cd\": {\"name\": \"cd\", \"group\": \"Part a\", \"definition\": \"c_coprime*d_coprime\", \"description\": \"\u003cp\u003eVariable c times variable d.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"a\": {\"name\": \"a\", \"group\": \"Part a\", \"definition\": \"random(2..12 except c)\", \"description\": \"\u003cp\u003eRandom number from 1 to 12.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"d\": {\"name\": \"d\", \"group\": \"Part a\", \"definition\": \"random(2 .. 12#1)\", \"description\": \"\u003cp\u003eRandom number from 1 to 12.\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"l\": {\"name\": \"l\", \"group\": \"Part c\", \"definition\": \"random(1..12)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"numif\": {\"name\": \"numif\", \"group\": \"Part b\", \"definition\": \"(f*h_coprime)+g_coprime\", \"description\": \"\u003cp\u003eNumerator of the improper fraction converted from a mixed number.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"gcd_gh\": {\"name\": \"gcd_gh\", \"group\": \"Part b\", \"definition\": \"gcd(g,h)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"fh\": {\"name\": \"fh\", \"group\": \"Part b\", \"definition\": \"f*h_coprime\", \"description\": \"\u003cp\u003eVariable f times variable h\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"g_coprime\": {\"name\": \"g_coprime\", \"group\": \"Part b\", \"definition\": \"g/gcd_gh\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"j_coprime\": {\"name\": \"j_coprime\", \"group\": \"Part b\", \"definition\": \"j/gcd_kj\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"gcd_kj\": {\"name\": \"gcd_kj\", \"group\": \"Part b\", \"definition\": \"gcd(k,j)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"f\": {\"name\": \"f\", \"group\": \"Part b\", \"definition\": \"random(1 .. 4#1)\", \"description\": \"\u003cp\u003eRandom number between 1 and 4 - integer part of the mixed number.\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"c_coprime\": {\"name\": \"c_coprime\", \"group\": \"Part a\", \"definition\": \"c/gcd_ac\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"gcd\": {\"name\": \"gcd\", \"group\": \"Part a\", \"definition\": \"gcd(ab,cd)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"b\": {\"name\": \"b\", \"group\": \"Part a\", \"definition\": \"random(2 .. 12#1)\", \"description\": \"\u003cp\u003eRandom number from 1 to 12.\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"d_coprime\": {\"name\": \"d_coprime\", \"group\": \"Part a\", \"definition\": \"d/gcd_bd\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"ddcc\": {\"name\": \"ddcc\", \"group\": \"Part d\", \"definition\": \"dd*cc\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"gcdb\": {\"name\": \"gcdb\", \"group\": \"Part b\", \"definition\": \"gcd(num,denom)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"gcd_ac\": {\"name\": \"gcd_ac\", \"group\": \"Part a\", \"definition\": \"gcd(a,c)\", \"description\": \"\u003cp\u003ePART A\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"denom\": {\"name\": \"denom\", \"group\": \"Part b\", \"definition\": \"j_coprime*(h_coprime/gcda)\", \"description\": \"\u003cp\u003eDenominator of new fraction.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"l_coprime\": {\"name\": \"l_coprime\", \"group\": \"Part c\", \"definition\": \"l/gcd_lm\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"m\": {\"name\": \"m\", \"group\": \"Part c\", \"definition\": \"random(1..12 except l)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a_coprime\": {\"name\": \"a_coprime\", \"group\": \"Part a\", \"definition\": \"a/gcd_ac\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"h\": {\"name\": \"h\", \"group\": \"Part b\", \"definition\": \"random(7 .. 10#1)\", \"description\": \"\u003cp\u003eRandom number between 1 and 20.\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"num\": {\"name\": \"num\", \"group\": \"Part b\", \"definition\": \"k_coprime*{numif/gcda}\", \"description\": \"\u003cp\u003eNumerator of gap 0\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"m_coprime\": {\"name\": \"m_coprime\", \"group\": \"Part c\", \"definition\": \"m/gcd_lm\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"aa\": {\"name\": \"aa\", \"group\": \"Part d\", \"definition\": \"random(1..6)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"gcda\": {\"name\": \"gcda\", \"group\": \"Part b\", \"definition\": \"gcd({numif},{h_coprime})\", \"description\": \"\u003cp\u003egcd of the numerator of the improper fraction\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"h_coprime\": {\"name\": \"h_coprime\", \"group\": \"Part b\", \"definition\": \"h/gcd_gh\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"ee\": {\"name\": \"ee\", \"group\": \"Part d\", \"definition\": \"ddcc/4\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"c\": {\"name\": \"c\", \"group\": \"Part a\", \"definition\": \"random(3,5,7,11)\", \"description\": \"\u003cp\u003eRandom number from 1 to 12.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"b_coprime\": {\"name\": \"b_coprime\", \"group\": \"Part a\", \"definition\": \"b/gcd_bd\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"l_coprime2\": {\"name\": 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denominator {\\n  padding-top: 5px;\\n}\\nfraction input {\\n    line-height: 1em;\\n}\\n\\nfraction .part {\\n    margin: 0;\\n}\\n\\n.table-responsive, .fractiontable {\\n  display:inline-block;\\n}\\n.fractiontable {\\n  padding: 0; \\n  border: 0;\\n}\\n\\n.fractiontable  .tddenom \\n{\\n text-align: center;\\n}\\n\\n.fractiontable .tdnum \\n{\\n  border-bottom: 1px solid black; \\n  text-align: center;\\n}\\n\\n\\n.fractiontable tr {\\n    height: 3em;\\n}\\n\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": 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\"penaltyVisibility\": \"always\"}, {\"name\": \"NF17 Divide Fractions\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Lauren Richards\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1589/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Oliver Spenceley\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23557/\"}], \"tags\": [\"dividing fractions\", \"division of fractions\", \"Fractions\", \"fractions\", \"mixed numbers\", \"taxonomy\"], \"metadata\": {\"description\": \"\u003cp\u003eSeveral problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions.\u0026nbsp;\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eEvaluate the following sums\u0026nbsp;involving division of fractions. Simplify your answers where possible.\u0026nbsp;\u003c/p\u003e\", \"advice\": \"\u003cp\u003eWhen faced with dividing fractions, it much easier to switch one of the fractions around and multiply them together instead of divide them.\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\\\\[ \\\\left( \\\\frac{\\\\var{f_coprime}}{\\\\var{g_coprime}}\\\\div\\\\frac{\\\\var{h_coprime}}{\\\\var{j_coprime}} \\\\right) \\\\equiv \\\\left( \\\\frac{\\\\var{f_coprime}}{\\\\var{g_coprime}}\\\\times\\\\frac{\\\\var{j_coprime}}{\\\\var{h_coprime}} \\\\right) = \\\\frac{\\\\var{fj}}{\\\\var{gh}} \\\\]\u003c/p\u003e\\n\u003cp\u003eThen, simplify by finding the highest common divisor in the numerator and denominator which in this case is $\\\\var{gcd1}$.\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003eThis gives a final answer of $\\\\displaystyle\\\\simplify{{fj}/{gh}}$.\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"f4h4\": {\"name\": \"f4h4\", \"group\": \"Ungrouped variables\", \"definition\": \"f4*h4_coprime\", \"description\": \"\u003cp\u003evariable f4 times h4.\u003c/p\u003e\\n\u003cp\u003eUsed in part c)\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"g4_coprime\": {\"name\": \"g4_coprime\", \"group\": \"Ungrouped variables\", \"definition\": \"g4/gcd(g4,h4)\", \"description\": \"\u003cp\u003ePART C\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"h4\": {\"name\": \"h4\", \"group\": \"Ungrouped variables\", \"definition\": \"random(5..8 except g4)\", \"description\": \"\u003cp\u003eRandom number but not the same number as variable g4.\u003c/p\u003e\\n\u003cp\u003eUsed in part c.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"h3_coprime\": {\"name\": \"h3_coprime\", \"group\": \"Ungrouped variables\", \"definition\": \"h3/gcd(g3,h3)\", \"description\": \"\u003cp\u003ePART C\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"f_coprime\": {\"name\": \"f_coprime\", \"group\": \"part a\", \"definition\": \"f/gcd(f,g)\", \"description\": \"\u003cp\u003ePART A\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"g_coprime\": {\"name\": \"g_coprime\", \"group\": \"part a\", \"definition\": \"g/gcd(f,g)\", \"description\": \"\u003cp\u003ePART A\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"j1_coprime\": {\"name\": \"j1_coprime\", \"group\": \"Ungrouped variables\", \"definition\": 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\\n  border: 0;\\n}\\n\\n.fractiontable  .tddenom \\n{\\n text-align: center;\\n}\\n\\n.fractiontable .tdnum \\n{\\n  border-bottom: 1px solid black; \\n  text-align: center;\\n}\\n\\n\\n.fractiontable tr {\\n    height: 3em;\\n}\\n\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e$\\\\displaystyle\\\\frac{\\\\var{f_coprime}}{\\\\var{g_coprime}}\\\\div\\\\frac{\\\\var{h_coprime}}{\\\\var{j_coprime}}=$\u0026nbsp;\u003cfraction\u003e \u003cnumerator\u003e[[0]]\u003c/numerator\u003e \u003cdenominator\u003e[[1]]\u003c/denominator\u003e \u003c/fraction\u003e\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"fj/gcd1\", \"maxValue\": \"fj/gcd1\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"gh/gcd1\", \"maxValue\": \"gh/gcd1\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF19 Ordering fractions\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003ePut fractions in size order.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eWhich of these two fractions is the largest?\u003c/p\u003e\", \"advice\": \"\u003cp\u003eTo find which is bigger of $\\\\frac{\\\\var{top1}}{\\\\var{bot1}}$ and $\\\\frac{\\\\var{top2}}{\\\\var{bot2}}$ we need them to have the same denominator. A way to do this is to multiply the top and bottom of $\\\\frac{\\\\var{top1}}{\\\\var{bot1}}$ by $\\\\var{bot2}$ and multiply the top and bottom of $\\\\frac{\\\\var{top2}}{\\\\var{bot2}}$ by {bot1}. This doesn\u0027t change the the value of the fractions as this is just like multiplying by one.\u003c/p\u003e\\n\u003cp\u003e\\\\[\\\\frac{\\\\var{top1}}{\\\\var{bot1}}=\\\\frac{\\\\var{top1*bot2}}{\\\\var{bot1*bot2}},\\\\quad \\\\frac{\\\\var{top2}}{\\\\var{bot2}}=\\\\frac{\\\\var{top2*bot1}}{\\\\var{bot1*bot2}}\\\\]\u003c/p\u003e\\n\u003cp\u003eNow we can easily see which is bigger by comparing the numerator.\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Fractions\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"top1\": {\"name\": \"top1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..(bot1-1))\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"top2\": {\"name\": \"top2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..(bot2-1))\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"bot1\": {\"name\": \"bot1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..10)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"bot2\": {\"name\": \"bot2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..10 except bot1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"frac1\": {\"name\": \"frac1\", \"group\": \"Ungrouped variables\", \"definition\": \"top1/bot1\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"frac2\": {\"name\": \"frac2\", \"group\": \"Ungrouped variables\", \"definition\": \"top2/bot2\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"Is1Bigger\": {\"name\": \"Is1Bigger\", \"group\": \"Ungrouped variables\", \"definition\": \"award(1,frac1\u003efrac2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"Is2Bigger\": {\"name\": \"Is2Bigger\", \"group\": \"Ungrouped variables\", \"definition\": \"award(1,frac2\u003efrac1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"Question\": {\"name\": \"Question\", \"group\": \"Ungrouped variables\", \"definition\": \"[string(top1)+\\\"/\\\"+string(bot1),string(top2)+\\\"/\\\"+string(bot2)]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"abs(frac1-frac2)\u003e0\", \"maxRuns\": \"250\"}, \"ungrouped_variables\": [\"top1\", \"top2\", \"bot1\", \"bot2\", \"frac1\", \"frac2\", \"Is1Bigger\", \"Is2Bigger\", \"Question\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"1_n_2\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minMarks\": 0, \"maxMarks\": 0, \"shuffleChoices\": true, \"displayType\": \"radiogroup\", \"displayColumns\": 0, \"showCellAnswerState\": true, \"choices\": \"Question\", \"matrix\": \"[Is1Bigger,Is2Bigger]\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NF22 FDP convert 3 - Fraction into decimal\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Andrew Neate\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21832/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eConvert a fraction into a decimal.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eWrite $\\\\frac{\\\\var{x}}{\\\\var{y}}$ as a decimal. Round your answer to 3 decimal places.\u003c/p\u003e\", \"advice\": \"\u003cp\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003e\u003c/span\u003eYou can calculate the decimals by hand using long division of $\\\\var{x}.000$ divided by $\\\\var{y}$.\u003cspan style=\\\"font-weight: 400;\\\"\u003e\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003eIn some cases you may be able to simplify the fraction to something that you know the decimal for.\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Fractions\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"x\": {\"name\": \"x\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1..(y-1))\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"y\": {\"name\": \"y\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2..10)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"x\", \"y\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"x/y\", \"maxValue\": \"x/y\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"precisionType\": \"dp\", \"precision\": \"3\", \"precisionPartialCredit\": 0, \"precisionMessage\": \"You have not given your answer to the correct precision.\", \"strictPrecision\": false, \"showPrecisionHint\": false, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"NU01 Convert Currency\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eExchange rates.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eOn a particular day, 1 Pound Sterling (\u0026pound;) is equivalent to {exchanget} United States Dollars (\\\\$). If you have \\\\$ {amount}, what does this equate to in Pound Sterling?\u0026nbsp;\u003c/p\u003e\", \"advice\": \"\u003cp\u003eTo convert Dollars (\\\\$) into Pounds (\u0026pound;) you will need to caculate:\u003c/p\u003e\\n\u003cp\u003e\\\\begin{align}\u003cbr/\u003e\\\\frac{\\\\var{amount}}{\\\\var{exchange}} \u0026amp;= \\\\var{answer}\\\\\\\\\u003cbr/\u003e\u0026amp;= \\\\var{answert},\u003cbr/\u003e\\\\end{align}\u003c/p\u003e\\n\u003cp\u003eensuring to round off to the nearest penny.\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic\u003c/span\u003e\u003c/a\u003e.\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"exchange\": {\"name\": \"exchange\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0.9 .. 1.2#0.01)\", \"description\": \"\u003cp\u003ePound to dollar exchange rate.\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"amount\": {\"name\": \"amount\", \"group\": \"Ungrouped variables\", \"definition\": \"random(100 .. 1000#5)\", \"description\": \"\u003cp\u003eAmount of dollars.\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"answer\": {\"name\": \"answer\", \"group\": \"Ungrouped variables\", \"definition\": \"amount/exchange\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"answert\": {\"name\": \"answert\", \"group\": \"Ungrouped variables\", \"definition\": \"currency(answer,\\\"\\u00a3\\\",\\\"p\\\")\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"exchanget\": {\"name\": \"exchanget\", \"group\": \"Ungrouped variables\", \"definition\": \"dpformat(exchange,2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"exchange\", \"amount\", \"answer\", \"answert\", \"exchanget\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e[[0]]\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"answer\", \"maxValue\": \"answer\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"answert\", \"precisionType\": \"dp\", \"precision\": \"2\", \"precisionPartialCredit\": 0, \"precisionMessage\": \"You have not given your answer to the correct precision.\", \"strictPrecision\": true, \"showPrecisionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SD02 Interpret Pie Charts\", \"extensions\": [\"geogebra\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}, {\"name\": \"Michael Pan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23528/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eThis question is about correctly interpreting pie charts.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003e{geogebra_applet{\\\"https://www.geogebra.org/calculator/pmvumdrv\\\",[C: C,M: M]}}\u003c/p\u003e\\n\u003cp\u003eThe Pie Chart above shows the responses to a question asked by someone trying to plan a social event for their workplace. It shows answers given to the question \\\"Where would you like to go for a staff social?\\\" with the options \\\"Meal\\\", \\\"Cinema\\\" and \\\"Games Cafe\\\".\u003c/p\u003e\", \"advice\": \"\u003cp\u003eA Pie chart of this type can only be used to make statements about the\u0026nbsp;\u003cstrong\u003eproportions\u0026nbsp;\u003c/strong\u003eof data in each category and does not provide information about the actual frequencies.\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\\\"\u003eFor more information on Pie Charts follow this link.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"C\": {\"name\": \"C\", \"group\": \"Ungrouped variables\", \"definition\": \"random(60 .. 70#5)\", \"description\": \"\", \"templateType\": \"randrange\", \"can_override\": false}, \"M\": {\"name\": \"M\", \"group\": \"Ungrouped variables\", \"definition\": \"random(5 .. 25#5)\", \"description\": \"\", \"templateType\": \"randrange\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"C\u003c\u003eM\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"C\", \"M\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"m_n_x\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eFrom the following comments which can you say are definitely true, definitely false and which do you not have enough information to know?\u003c/p\u003e\", \"minMarks\": 0, \"maxMarks\": 0, \"minAnswers\": 0, \"maxAnswers\": 0, \"shuffleChoices\": true, \"shuffleAnswers\": true, \"displayType\": \"radiogroup\", \"warningType\": \"none\", \"showCellAnswerState\": true, \"markingMethod\": \"sum ticked cells\", \"choices\": [\"50 people responded that they would like to go to the cinema.\", \"About one third of people said they wanted to go for a meal.\", \"Over half the people responding said they wanted to go to the Games Cafe.\"], \"matrix\": [[0, 0, \"1\"], [0, \"1\", 0], [\"1\", 0, 0]], \"layout\": {\"type\": \"all\", \"expression\": \"\"}, \"answers\": [\"Definitely true.\", \"Definitely false.\", \"Not enough information to know.\"]}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SD03 Interpret Bar Chart\", \"extensions\": [\"jsxgraph\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Gareth Woods\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/978/\"}, {\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eReading a value from a simple bar chart.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\", \"advice\": \"\u003cp\u003eThe bar heights give the values of the spend.\u003cbr/\u003e\u003cbr/\u003eEach company has two bars, the left one for last year (in red) and the\u0026nbsp;right one for this year (in purple).\u003cbr/\u003eIsolate last years spend by looking at the\u0026nbsp;the bars on the right side, and choose the tallest bar, corresponding to the highest value.\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {\"std\": [\"all\", \"fractionNumbers\"]}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"answervector\": {\"name\": \"answervector\", \"group\": \"Ungrouped variables\", \"definition\": \"vector((yo5-yo0)/yo0*100, (yo6-yo1)/yo1*100,(yo7-yo2)/yo2*100,(yo8-yo3)/yo3*100, (yo9-yo4)/yo4*100)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"cc\": {\"name\": \"cc\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0.7..1.3#0.01 except 1 except aa except bb)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"aa\": {\"name\": \"aa\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0.7..1.3#0.01 except 1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"year\": {\"name\": \"year\", \"group\": \"Ungrouped variables\", \"definition\": \"yearvector[ii]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yn\": {\"name\": \"yn\", \"group\": \"Ungrouped variables\", \"definition\": \"map(vsc*y+vsh,y,yo)\", \"description\": \"\u003cp\u003enew y values after the transformation\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"eee\": {\"name\": \"eee\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1.1..1.3#0.01 except a except b except c except d)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo\": {\"name\": \"yo\", \"group\": \"Ungrouped variables\", \"definition\": \"repeat(random(-5..5),5)\", \"description\": \"\u003cp\u003ethe (random) original y values which relate to the x values\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"d\": {\"name\": \"d\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1.1..1.3#0.01 except a except b except c)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo9\": {\"name\": \"yo9\", \"group\": \"Ungrouped variables\", \"definition\": \"random(41..70#1 except yo5 except yo6 except yo7 except yo8)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"vsh\": {\"name\": \"vsh\", \"group\": \"Ungrouped variables\", \"definition\": \"if(selector=\u0027vsh\u0027,random(-3..3#0.5 except 0),0)\\n\", \"description\": \"\u003cp\u003evertical shift\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"vsc\": {\"name\": \"vsc\", \"group\": \"Ungrouped variables\", \"definition\": \"if(selector=\u0027vsc\u0027,random(-2,-1,-0.5,0.5,2),1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"c\": {\"name\": \"c\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1.1..1.3#0.01 except a except b)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"bb\": {\"name\": \"bb\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0.7..1.3#0.01 except 1 except aa)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"answer\": {\"name\": \"answer\", \"group\": \"Ungrouped variables\", \"definition\": \"max([yo1,yo0,yo2,yo3,yo4])\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"students\": {\"name\": \"students\", \"group\": \"Ungrouped variables\", \"definition\": \"random(120..320#1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a\": {\"name\": \"a\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1.1..1.3#0.01)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo2\": {\"name\": \"yo2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(20..40#1 except yo1 except yo0)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo5\": {\"name\": \"yo5\", \"group\": \"Ungrouped variables\", \"definition\": \"random(41..70#1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo8\": {\"name\": \"yo8\", \"group\": \"Ungrouped variables\", \"definition\": \"random(41..70#1 except yo5 except yo6 except yo7)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo1\": {\"name\": \"yo1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(20..40#1 except yo0)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo7\": {\"name\": \"yo7\", \"group\": \"Ungrouped variables\", \"definition\": \"random(41..70#1 except yo5 except yo6)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"maxx\": {\"name\": \"maxx\", \"group\": \"Ungrouped variables\", \"definition\": \"max(map(abs(a),a,xn)+5)+1\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yearvector\": {\"name\": \"yearvector\", \"group\": \"Ungrouped variables\", \"definition\": \"vector(2007,2008,2009,2010,2011,2012,2013)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"ii\": {\"name\": \"ii\", \"group\": \"Ungrouped variables\", \"definition\": \"random(3..6#1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo3\": {\"name\": \"yo3\", \"group\": \"Ungrouped variables\", \"definition\": \"random(20..40#1 except yo1 except yo0 except yo2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"selector\": {\"name\": \"selector\", \"group\": \"Ungrouped variables\", \"definition\": \"\u0027vsc\u0027\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"fakeanswer1\": {\"name\": \"fakeanswer1\", \"group\": \"Ungrouped variables\", \"definition\": \"random([yo1,yo0,yo2,yo3,yo4] except answer)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"hsh\": {\"name\": \"hsh\", \"group\": \"Ungrouped variables\", \"definition\": \"if(selector=\u0027hsh\u0027,random(-3..3 except 0),0)\", \"description\": \"\u003cp\u003ehorizontal shift\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"fakeanswer4\": {\"name\": \"fakeanswer4\", \"group\": \"Ungrouped variables\", \"definition\": \"random([yo9,yo7,yo8] except fakeanswer3)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"dd\": {\"name\": \"dd\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0.7..1.3#0.01 except 1 except aa except bb except cc)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"percent\": {\"name\": \"percent\", \"group\": \"Ungrouped variables\", \"definition\": \"random(5..15#0.1 except 5 except 6 except 7 except 8 except 9 except 10 except 11 except 12 except 13 except 14 except 15)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo0\": {\"name\": \"yo0\", \"group\": \"Ungrouped variables\", \"definition\": \"random(20..40#1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"xn\": {\"name\": \"xn\", \"group\": \"Ungrouped variables\", \"definition\": \"map((x-hsh)/hsc,x,xo)\", \"description\": \"\u003cp\u003enew transformed x values\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"b\": {\"name\": \"b\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1.1..1.3#0.01 except a)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"xo\": {\"name\": \"xo\", \"group\": \"Ungrouped variables\", \"definition\": \"list(-2..2)\", \"description\": \"\u003cp\u003eoriginal x values\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"yo4\": {\"name\": \"yo4\", \"group\": \"Ungrouped variables\", \"definition\": \"random(20..40#1 except yo1 except yo0 except yo2 except yo3)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"fakeanswer2\": {\"name\": \"fakeanswer2\", \"group\": \"Ungrouped variables\", \"definition\": \"random([yo1,yo0,yo2,yo3,yo4] except answer except fakeanswer1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"f\": {\"name\": \"f\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1.1..1.3#0.01 except a except b except c except d except e)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo51\": {\"name\": \"yo51\", \"group\": \"Ungrouped variables\", \"definition\": \"eee*yo5\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"fakeanswer3\": {\"name\": \"fakeanswer3\", \"group\": \"Ungrouped variables\", \"definition\": \"random([yo6,yo7,yo8])\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"increase\": {\"name\": \"increase\", \"group\": \"Ungrouped variables\", \"definition\": \"random(10..40#5)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo6\": {\"name\": \"yo6\", \"group\": \"Ungrouped variables\", \"definition\": \"random(41..70#1 except yo5)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"hsc\": {\"name\": \"hsc\", \"group\": \"Ungrouped variables\", \"definition\": \"if(selector=\u0027hsc\u0027,random(-2,-1,-0.5,0.5,2),1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo41\": {\"name\": \"yo41\", \"group\": \"Ungrouped variables\", \"definition\": \"d*yo4\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"selector\", \"vsh\", \"hsh\", \"vsc\", \"hsc\", \"yo\", \"yn\", \"xo\", \"xn\", \"yo0\", \"yo1\", \"yo2\", \"yo3\", \"yo4\", \"maxx\", \"yo6\", \"yo7\", \"yo8\", \"yo9\", \"yo41\", \"yo5\", \"yo51\", \"a\", \"b\", \"c\", \"d\", \"eee\", \"f\", \"answer\", \"fakeanswer1\", \"fakeanswer2\", \"fakeanswer3\", \"fakeanswer4\", \"aa\", \"bb\", \"cc\", \"dd\", \"percent\", \"students\", \"yearvector\", \"ii\", \"year\", \"answervector\", \"increase\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"function dragpoint_board() {\\n  var scope = question.scope;\\n\\n  JXG.Options.text.display = \u0027internal\u0027;\\n  \\n  var yo0 = scope.variables.yo0.value;\\n  var yo1 = scope.variables.yo1.value;\\n  var yo2 = scope.variables.yo2.value;\\n  var yo3 = scope.variables.yo3.value;\\n  var yo4 = scope.variables.yo4.value;\\n  var yo5 = scope.variables.yo5.value;\\n  var yo6 = scope.variables.yo6.value;\\n  var yo7 = scope.variables.yo7.value; \\n  var yo8 = scope.variables.yo8.value;\\n  var yo9 = scope.variables.yo9.value; \\n  \\n  var div = Numbas.extensions.jsxgraph.makeBoard(\u0027550px\u0027,\u0027550px\u0027,{boundingBox:[-0.8,82,16,-8], axis:false, grid:true});\\n \\n  question.display.html.querySelector(\u0027#dragpoint\u0027).append(div);\\n  \\n  var board = div.board;\\n  \\n// board.suspendUpdate();           \\n\\n  \\n var dataArr = [yo0,yo5,0,yo1,yo6,0,yo2,yo7,0,yo3,yo8,0,yo4,yo9]; \\n  \\n var xaxis = board.create(\u0027axis\u0027, [[0, 0], [12, 0]], {withLabel: true, name: \\\"Bank\\\", label: {offset: [250,-30]}});\\n  \\n  xaxis.removeAllTicks();  \\n   \\n  board.create(\u0027axis\u0027, [[0, 0], [0, 10]], {hideTicks:true, withLabel: false, name: \\\"\\\", label: {offset: [-110,300]}});\\n  \\n  var pop0 = board.create(\u0027point\u0027, [1.5,0],{name:\u0027Morgan\u0027,fixed:true,size:0,color:\u0027black\u0027,face:\u0027diamond\u0027, label:{offset:[-20,-8]}});\\n  var pop1 = board.create(\u0027point\u0027,[4.5,0],{name:\u0027Strome\u0027,fixed:true,size:0,color:\u0027black\u0027,face:\u0027diamond\u0027, label:{offset:[-20,-8]}});\\n  var pop2 = board.create(\u0027point\u0027,[7.5,0],{name:\u0027Bentley\u0027,fixed:true,size:0,color:\u0027black\u0027, face:\u0027diamond\u0027, label:{offset:[-15,-8]}});\\n  var pop3 = board.create(\u0027point\u0027,[10.5,0],{name:\u0027Sand\u0027,fixed:true,size:0,color:\u0027black\u0027, face:\u0027diamond\u0027, label:{offset:[-15,-8]}});\\n  var pop4 = board.create(\u0027point\u0027,[13.5,0],{name:\u0027Karchen\u0027,fixed:true,size:0,color:\u0027black\u0027, face:\u0027diamond\u0027, label:{offset:[-15,-8]}});\\n  var leg1 = board.create(\u0027point\u0027,[12,75],{name:\u0027last year\u0027,fixed:true,size:6,color:\u0027#DA2228\u0027, face:\u0027square\u0027, label:{offset:[9,0]}});\\n  var leg2 = board.create(\u0027point\u0027,[12,72],{name:\u0027this year\u0027,fixed:true,size:6,color:\u0027#6F1B75\u0027, face:\u0027square\u0027, label:{offset:[9,0]}});\\n  \\n  \\n//  var chart = board.createElement(\u0027chart\u0027, dataArr, \\n  //                              {chartStyle:\u0027bar\u0027, fillOpacity:1, width:1,\\n    //     colorArray:[\u0027#8E1B77\u0027,\u0027#8E1B77\u0027,\u0027Red\u0027,\u0027Red\u0027,\u0027blue\u0027,\u0027red\u0027,\u0027blue\u0027,\u0027red\u0027,\u0027red\u0027,\u0027blue\u0027, \u0027red\u0027,\u0027blue\u0027,\u0027red\u0027,\u0027red\u0027], shadow:false});\\n \\n//var chart = board.createElement(\u0027chart\u0027, dataArr, \\n  //                              {chartStyle:\u0027bar\u0027, width:1,fillOpacity:1, fillColor:\u0027red\u0027, shadow:false});  \\n  \\n  \\n    var a = board.create(\u0027chart\u0027, [[1,2,3],[yo0,yo5,0]], {chartStyle:\u0027bar\u0027,colors:[\u0027#DA2228\u0027,\u0027#6F1B75\u0027,\u0027#6F1B75\u0027],width:1,fillOpacity:1});\\n    var b = board.create(\u0027chart\u0027, [[4,5,6],[yo1,yo6,0]], {chartStyle:\u0027bar\u0027,width:1,colors:[\u0027#DA2228\u0027,\u0027#6F1B75\u0027,\u0027#6F1B75\u0027],fillOpacity:1});\\n    var c = board.create(\u0027chart\u0027, [[7,8,9],[yo2,yo7,0]], {chartStyle:\u0027bar\u0027,width:1,colors:[\u0027#DA2228\u0027,\u0027#6F1B75\u0027,\u0027#6F1B75\u0027],fillOpacity:1});\\n    var d = board.create(\u0027chart\u0027, [[10,11,12],[yo3,yo8,0]], {chartStyle:\u0027bar\u0027,width:1,colors:[\u0027#DA2228\u0027,\u0027#6F1B75\u0027,\u0027#6F1B75\u0027],fillOpacity:1});\\n    var e = board.create(\u0027chart\u0027, [[13,14],[yo4,yo9]], {chartStyle:\u0027bar\u0027,width:1,colors:[\u0027#DA2228\u0027,\u0027#6F1B75\u0027],fillOpacity:1});\\n  \\n    board.unsuspendUpdate();\\n  \\n  var txt1 = board.create(\u0027text\u0027,[-0.3,30, \u0027Investment \\u00a3(m)\u0027], {fontColor:\u0027black\u0027, fontSize:14, rotate:90});\\n  \\n // var txt = board.create(\u0027text\u0027,[0.5,75, \u0027Investment (m)\u0027], {fontSize:14, rotate:90});\\n  \\n // var txt1 = board.create(\u0027text\u0027,[8,76, \u0027red bars represent 2010\u0027], {fontColor:\u0027red\u0027, fontSize:14, rotate:90});\\n  \\n // var txt2 = board.create(\u0027text\u0027,[8,73, \u0027blue bars represents 2011\u0027], {fontSize:14, rotate:90});\\n\\n // var myColors = new Array(\u0027red\u0027, \u0027blue\u0027, \u0027white\u0027,\u0027red\u0027, \u0027blue\u0027, \u0027white\u0027,\u0027red\u0027, \u0027blue\u0027, \u0027white\u0027,\u0027red\u0027, \u0027blue\u0027, \u0027white\u0027,\u0027red\u0027, \u0027blue\u0027);\\n  \\n  \\n  \\n  //board.unsuspendUpdate();\\n\\n    // Rotate text around the lower left corner (-2,-1) by 30 degrees.\\n   // var tRot = board.create(\u0027transform\u0027, [90.0*Math.PI/180.0, -1,40], {type:\u0027rotate\u0027}); \\n  //  tRot.bindTo(txt);\\n  //  board.update();\\n\\n  \\n//var chart2 = board.createElement(\u0027chart\u0027, dataArr, {chartStyle:\u0027line,point\u0027});\\n//chart2[0].setProperty(\u0027strokeColor:black\u0027,\u0027strokeWidth:2\u0027,\u0027shadow:true\u0027);\\n//for(var i=0; i\u003c11;i++) {\\n //   chart2[1][i].setProperty({strokeColor:\u0027black\u0027,fillColor:\u0027white\u0027,face:\u0027[]\u0027, size:4, strokeWidth:2});\\n//}\\n//board.unsuspendUpdate();  \\n                       \\n  //board.unsuspendUpdate();\\n\\n}\\n\\nquestion.signals.on(\u0027HTMLAttached\u0027,function() {\\n  dragpoint_board();\\n});\", \"css\": \"table#values th {\\n  background: none;\\n  text-align: center;\\n}\"}, \"parts\": [{\"type\": \"1_n_2\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cdiv id=\\\"dragpoint\\\"\u003e\u003cstrong\u003eBanking Sector: IT Infrastructure Spending\u003c/strong\u003e\u003c/div\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003cem\u003e\u003c/em\u003e\u003c/p\u003e\\n\u003cp\u003eWhat was the maximum spend by a single company last year?\u003c/p\u003e\", \"minMarks\": 0, \"maxMarks\": 0, \"shuffleChoices\": true, \"displayType\": \"radiogroup\", \"displayColumns\": 0, \"showBlankOption\": true, \"showCellAnswerState\": true, \"choices\": [\"\u003cp\u003e\u0026pound;{answer} m\u003c/p\u003e\", \"\u003cp\u003e\u0026pound;{fakeanswer1} m \u0026nbsp; \u0026nbsp;\u003c/p\u003e\", \"\u003cp\u003e\u0026pound;{fakeanswer2} m \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/p\u003e\", \"\u003cp\u003e\u0026pound;{fakeanswer3} m \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/p\u003e\", \"\u003cp\u003e\u0026pound;{fakeanswer4} m \u0026nbsp;\u0026nbsp;\u003c/p\u003e\"], \"matrix\": [\"1\", 0, 0, 0, 0], \"distractors\": [\"\", \"\", \"\", \"\", \"\"]}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SD04 Interpret a Box Plot\", \"extensions\": [\"geogebra\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Michael Pan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23528/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eInterpreting the elements of a box plot\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eThe diagram below shows a box plot of some data.\u003c/p\u003e\\n\u003cp\u003e{geogebra_applet{\\\"https://www.geogebra.org/m/aj2hcbhg\\\",[lv: lv,lq: lq,m: m,uq: uq,hv: hv]}}\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"advice\": \"\u003cp\u003e\u003cspan style=\\\"font-family: arial, helvetica, sans-serif;\\\"\u003eA boxplot (also known as a box-and-whisker diagram or plot) is a convenient way of graphically depicting groups of numerical data through their five-number summaries: the smallest observation (sample minimum), lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation (sample maximum). A boxplot may also indicate which observations, if any, might be considered outliers.\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\\\"\u003e\u003cspan style=\\\"font-family: arial, helvetica, sans-serif;\\\"\u003eFor more information on box plots follow this link.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"lv\": {\"name\": \"lv\", \"group\": \"Ungrouped variables\", \"definition\": \"random(2 .. 6#1)\", \"description\": \"\", \"templateType\": \"randrange\", \"can_override\": false}, \"lq\": {\"name\": \"lq\", \"group\": \"Ungrouped variables\", \"definition\": \"random(7 .. 10#1)\", \"description\": \"\", \"templateType\": \"randrange\", \"can_override\": false}, \"m\": {\"name\": \"m\", \"group\": \"Ungrouped variables\", \"definition\": \"random(11 .. 14#1)\", \"description\": \"\", \"templateType\": \"randrange\", \"can_override\": false}, \"uq\": {\"name\": \"uq\", \"group\": \"Ungrouped variables\", \"definition\": \"random(15 .. 22#1)\", \"description\": \"\", \"templateType\": \"randrange\", \"can_override\": false}, \"hv\": {\"name\": \"hv\", \"group\": \"Ungrouped variables\", \"definition\": \"random(23 .. 30#1)\", \"description\": \"\", \"templateType\": \"randrange\", \"can_override\": false}, \"IQR\": {\"name\": \"IQR\", \"group\": \"Ungrouped variables\", \"definition\": \"uq-lq\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"range\": {\"name\": \"range\", \"group\": \"Ungrouped variables\", \"definition\": \"hv-lv\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"lv\", \"lq\", \"m\", \"uq\", \"hv\", \"IQR\", \"range\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"m_n_x\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eWhich of these statements are true and which are false?\u003c/p\u003e\", \"minMarks\": 0, \"maxMarks\": 0, \"minAnswers\": 0, \"maxAnswers\": 0, \"shuffleChoices\": true, \"shuffleAnswers\": false, \"displayType\": \"radiogroup\", \"warningType\": \"none\", \"showCellAnswerState\": true, \"markingMethod\": \"sum ticked cells\", \"choices\": [\"The range of the data is $\\\\var{range}$.\", \"The Interquarttile range of the data is larger than the range of the data.\", \"You can calculate the mean of the data from this Box plot.\", \"\u003cp\u003eThe median of the data is $\\\\var{m}$.\u003c/p\u003e\", \"The mode of the data is $\\\\var{lv-3}$.\"], \"matrix\": [[\"1\", 0], [0, \"1\"], [0, \"1\"], [\"1\", 0], [0, \"1\"]], \"layout\": {\"type\": \"all\", \"expression\": \"\"}, \"answers\": [\"True.\", \"False.\"]}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SD06 Reading a Histogram\", \"extensions\": [\"jsxgraph\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Gareth Woods\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/978/\"}, {\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eReading a value from a histogram.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eThe histogram shows information about distances run on a Sunday by some randomly asked people in a park.\u0026nbsp;\u003c/p\u003e\\n\u003cdiv id=\\\"dragpoint\\\"\u003e\u003c/div\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"advice\": \"\u003cp\u003e\u003cstrong\u003ea)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo calculate the frequencies using the following formula:\u003c/p\u003e\\n\u003cp style=\\\"padding-left: 40px;\\\"\u003efrequency = class width $\\\\times$ frequency density\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003eHence our table becomes:\u003c/p\u003e\\n\u003ctable style=\\\"width: 439px; height: 106px;\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 148.969px; height: 18px;\\\"\u003e\u003cstrong\u003eDistance, $km$\u003c/strong\u003e\u003c/td\u003e\\n\u003ctd style=\\\"width: 257.031px; height: 18px;\\\"\u003e\u003cstrong\u003eFrequency\u0026nbsp;\u003c/strong\u003e\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 22px;\\\"\u003e\\n\u003ctd style=\\\"width: 148.969px; height: 22px;\\\"\u003e$0 \u0026lt; t \\\\leq 10$\u003c/td\u003e\\n\u003ctd style=\\\"width: 257.031px; height: 22px;\\\"\u003e$10 \\\\times \\\\var{yo0} = \\\\var{freq0}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 22px;\\\"\u003e\\n\u003ctd style=\\\"width: 148.969px; height: 22px;\\\"\u003e$10 \u0026lt; t \\\\leq 15$\u003c/td\u003e\\n\u003ctd style=\\\"width: 257.031px; height: 22px;\\\"\u003e$5 \\\\times \\\\var{yo1} = \\\\var{freq1}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 22px;\\\"\u003e\\n\u003ctd style=\\\"width: 148.969px; height: 22px;\\\"\u003e$15 \u0026lt; t \\\\leq 20$\u003c/td\u003e\\n\u003ctd style=\\\"width: 257.031px; height: 22px;\\\"\u003e$5 \\\\times \\\\var{yo2} = \\\\var{freq2}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 22px;\\\"\u003e\\n\u003ctd style=\\\"width: 148.969px; height: 22px;\\\"\u003e$20 \u0026lt; t \\\\leq 30$\u003c/td\u003e\\n\u003ctd style=\\\"width: 257.031px; height: 22px;\\\"\u003e$10 \\\\times \\\\var{yo3} = \\\\var{freq3}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\\n\u003cp\u003eHence, to find the total number of people that ran that day:\u003c/p\u003e\\n\u003cp\u003e$\\\\var{freq0} + \\\\var{freq1} + \\\\var{freq2} + \\\\var{freq3} = \\\\var{total}.$\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003eb)\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eThe frequency of runners that ran less than $10km$ is found by calculating the frequency from the first bar on the histogram:\u003c/p\u003e\\n\u003cp\u003eclass width $\\\\times$ frequency density $= 10 \\\\times \\\\var{yo0} = \\\\var{freq0}$.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ec)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eThe frequency of runners that ran between $15km$ and $20km$ is found by calculating the frequency from the third bar on the histogram:\u003c/p\u003e\\n\u003cp\u003eclass width $\\\\times$ frequency density $= 5 \\\\times \\\\var{yo2} = \\\\var{freq2}$.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ed)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo estimate how many runners ran more than $25km$ we need again need to use the frequency = class width \\\\times frequency density formula.\u003c/p\u003e\\n\u003cp\u003eHere the class width is $5$ because we are looking for the frequency of runners that ran between $25km$ and $30km$ from the college.\u003c/p\u003e\\n\u003cp\u003eFrequency $= 5 \\\\times \\\\var{yo3} = \\\\var{5*yo3}.$\u003c/p\u003e\\n\u003cp\u003eIf this number is a decimal we round up to get $\\\\var{m25}$.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ee)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eAs in part \u003cstrong\u003ed)\u003c/strong\u003e,to estimate how many runners ran less than $7km$ we use the frequency = class width \\\\times frequency density formula.\u003c/p\u003e\\n\u003cp\u003eHere the class width is $7$ because we are looking for the frequency of runners that ran between 0 and 7 km.\u003c/p\u003e\\n\u003cp\u003eFrequency $= 7 \\\\times \\\\var{yo0} = \\\\var{7*yo0}.$\u003c/p\u003e\\n\u003cp\u003eIf this number is a decimal we round up to get $\\\\var{l7}$.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ef)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo estimate how many runners ran between $5km$ and $12.5km$ we use a method similar to that in part \u003cstrong\u003ed)\u003c/strong\u003e and \u003cstrong\u003ee)\u003c/strong\u003e but, this time, we need to use information from both the first and second bar on the histogram.\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003eLet\u0027s first calculate how many runners ran between $5km$ and $10km$:\u003c/p\u003e\\n\u003cp\u003efrequency $=$ class width $\\\\times$ frequency density $= 5 \\\\times \\\\var{yo0} = \\\\var{5*yo0}$.\u003c/p\u003e\\n\u003cp\u003eNow we need to calculate how many runners ran between $10km$ and $12.5km$:\u003c/p\u003e\\n\u003cp\u003efrequency $=$ class width $\\\\times$ frequency density $= 2.5 \\\\times \\\\var{yo1} = \\\\var{2.5*yo1}$.\u003c/p\u003e\\n\u003cp\u003ePutting this together the number of runners that ran between $5km$ and $12.5km$ is $\\\\var{5*yo0} + \\\\var{2.5*yo1} = \\\\var{5*yo0 + 2.5*yo1}.$\u003c/p\u003e\\n\u003cp\u003eIf this number is a decimal we round up to get $\\\\var{ef}.$\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003eg)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eThe number of runners that ran between $10km$ and $14km$ is $4 \\\\times \\\\var{yo1} = \\\\var{4*yo1}.$\u003cbr/\u003e\u003cbr/\u003eIf this number is a decimal we round up to get $\\\\var{eh}.$\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ei)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eThe number of runners that ran further than $18km$ is:\u003c/p\u003e\\n\u003cp\u003e$2 \\\\times \\\\var{yo2} + 10 \\\\times \\\\var{yo3} = \\\\var{2*yo2} + \\\\var{freq3} = \\\\var{2*yo2+freq3}.$\u003cbr/\u003e\u003cbr/\u003eIf this number is a decimal we round up to get $\\\\var{ej}.$\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003eDid you get a decimal \u003c/strong\u003e\u003cstrong\u003eanswer? \u003c/strong\u003eWere you surprised to see a whole number answer when you got a decimal on one of the estimate questions? Look at the context of the question, you cannot have $0.5$ of a student so we round our answers up to the next whole number!\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {\"std\": [\"all\", \"fractionNumbers\"]}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"yo2\": {\"name\": \"yo2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1 .. 39#1)\", \"description\": \"\u003cp\u003eFrequency Density\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"yo1\": {\"name\": \"yo1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1 .. 39#1)\", \"description\": \"\u003cp\u003eFrequency Density\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"yo3\": {\"name\": \"yo3\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1 .. 39#1)\", \"description\": \"\u003cp\u003eFrequency Density\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"selector\": {\"name\": \"selector\", \"group\": \"Ungrouped variables\", \"definition\": \"\u0027vsc\u0027\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"yo0\": {\"name\": \"yo0\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1 .. 39#1)\", \"description\": \"\u003cp\u003eFrequency Density\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"total\": {\"name\": \"total\", \"group\": \"Ungrouped variables\", \"definition\": \"freq0+freq1+freq2+freq3\", \"description\": \"\u003cp\u003eSum of frequencies\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"freq0\": {\"name\": \"freq0\", \"group\": \"Ungrouped variables\", \"definition\": \"10*yo0\", \"description\": \"\u003cp\u003eFrequency\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"freq1\": {\"name\": \"freq1\", \"group\": \"Ungrouped variables\", \"definition\": \"yo1*5\", \"description\": \"\u003cp\u003eFrequency\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"freq2\": {\"name\": \"freq2\", \"group\": \"Ungrouped variables\", \"definition\": \"5*yo2\", \"description\": \"\u003cp\u003eFrequency\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"freq3\": {\"name\": \"freq3\", \"group\": \"Ungrouped variables\", \"definition\": \"10*yo3\", \"description\": \"\u003cp\u003eFrequency\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"m25\": {\"name\": \"m25\", \"group\": \"Ungrouped variables\", \"definition\": \"round(5*yo3)\", \"description\": \"\u003cp\u003eHow many people ran more than 25km\u0026nbsp;\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"l7\": {\"name\": \"l7\", \"group\": \"Ungrouped variables\", \"definition\": \"round(7*yo0)\", \"description\": \"\u003cp\u003eHow many runners ran less than 7km\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"Ef\": {\"name\": \"Ef\", \"group\": \"Ungrouped variables\", \"definition\": \"round(5*yo0 + 2.5*yo1)\", \"description\": \"\u003cp\u003eNumber of people running between 5 \u0026amp; 12.5 km\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"eh\": {\"name\": \"eh\", \"group\": \"Ungrouped variables\", \"definition\": \"round(4*yo1)\", \"description\": \"\u003cp\u003eNumber of runners running between 10 \u0026amp; 14km\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"ej\": {\"name\": \"ej\", \"group\": \"Ungrouped variables\", \"definition\": \"round(2*yo2 + freq3)\", \"description\": \"\u003cp\u003eNumber of runners running more than 18km\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"selector\", \"yo0\", \"yo1\", \"yo2\", \"yo3\", \"total\", \"freq0\", \"freq1\", \"freq2\", \"freq3\", \"m25\", \"l7\", \"Ef\", \"eh\", \"ej\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"function dragpoint_board() {\\n  var scope = question.scope;\\n\\n  JXG.Options.text.display = \u0027internal\u0027;\\n  \\n  var yo0 = scope.variables.yo0.value;\\n  var yo1 = scope.variables.yo1.value;\\n  var yo2 = scope.variables.yo2.value;\\n  var yo3 = scope.variables.yo3.value;\\n  \\n  var div = Numbas.extensions.jsxgraph.makeBoard(\u0027550px\u0027,\u0027550px\u0027,{boundingBox:[-5,42,35,-5], axis:false, grid:true});\\n \\n  question.display.html.querySelector(\u0027#dragpoint\u0027).append(div);\\n  \\n  var board = div.board;\\n  \\nboard.suspendUpdate();           \\n\\n var dataArr = [yo0,0,yo1,0,yo2,0,yo3]; \\n  \\n var xaxis = board.create(\u0027axis\u0027, [[0, 0], [12, 0]], {withLabel: true, name: \\\"Distance, km\\\", label: {offset: [250,-30]}});\\n   \\n var yaxis = board.create(\u0027axis\u0027, [[0, 0], [0, 10]], {hideTicks:true, withLabel: true, name: \\\"Frequency Density\\\", label: {rotation: 90, offset: [-60,300]}});\\n// var yaxis = board.create(\u0027axis\u0027, [[0, 0], [0, 10]], {hideTicks:true, withLabel: false, name: \\\"Frequency Density\\\", label: {rotation: 90, offset: [-60,300]}});\\n//var Rot board.create(\u0027transform\u0027,[Math.PI/2,0,5],{type:\u0027rotate\u0027});\\n//  var ylabel = board.create(\u0027text\u0027, [0,5,\\\"Frequency Density\\\"], {label: {rotation: 90}});\\n//  Rot.bindTo(ylabel);\\n// board.update();\\n\\n  \\n   var a = board.create(\u0027chart\u0027, [[5,10],[yo0,0]], {chartStyle:\u0027bar\u0027,colors:[\u0027#76ba1e\u0027],width:10,fillOpacity:0.4});\\n   var b = board.create(\u0027chart\u0027, [[12.5,15],[yo1,0]], {chartStyle:\u0027bar\u0027,width:5,colors:[\u0027#89CFF0\u0027],fillOpacity:0.4});\\n   var c = board.create(\u0027chart\u0027, [[17.5,20],[yo2,0]], {chartStyle:\u0027bar\u0027,width:5,colors:[\u0027#76ba1e\u0027],fillOpacity:0.4});\\n   var d = board.create(\u0027chart\u0027, [[25,30],[yo3,0]], {chartStyle:\u0027bar\u0027,width:10,colors:[\u0027#89CFF0\u0027],fillOpacity:0.4});\\n  \\n}\\n\\nquestion.signals.on(\u0027HTMLAttached\u0027,function() {\\n  dragpoint_board();\\n});\", \"css\": \"table#values th {\\n  background: none;\\n  text-align: center;\\n}\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"a)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eHow many people were asked about the distance they ran that day?\u003c/p\u003e\", \"minValue\": \"total\", \"maxValue\": \"total\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"b)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eHow many runners ran less than 10 km that day?\u003c/p\u003e\", \"minValue\": \"freq0\", \"maxValue\": \"freq0\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"c)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eHow many people ran between 10 and 15 km that day?\u003c/p\u003e\", \"minValue\": \"freq1\", \"maxValue\": \"freq1\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"d)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eEstimate how many runners ran more than 25 km that day?\u003c/p\u003e\", \"minValue\": \"m25\", \"maxValue\": \"m25\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"e)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eEstimate how many runners ran less than 7 km that day?\u003c/p\u003e\", \"minValue\": \"l7\", \"maxValue\": \"l7\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"f)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eEstimate how many people ran between 5 km and 12.5 km.\u003c/p\u003e\", \"minValue\": \"Ef\", \"maxValue\": \"Ef\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SD07 Interpreting Line Graphs\", \"extensions\": [\"geogebra\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eFrancesca recorded the number of customers in a supermarket every two hours.\u003c/p\u003e\\n\u003cp\u003eShe began at 9 am and finished at 7 pm.\u003c/p\u003e\\n\u003cp\u003eThe line graph below shows her results.\u003c/p\u003e\\n\u003cp\u003e{geogebra_applet{\\\"https://www.geogebra.org/classic/s4w7nmga\\\",[y1:y1,y3:y3,y4:y4,y6:y6]}}\u003c/p\u003e\", \"advice\": \"\u003cp\u003e\u003cstrong\u003ea)\u003c/strong\u003e You want to find the point on the graph with the greatest frequency. You can see that this is at 1pm when there were $\\\\var{y3}$ cars in the car park.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003eb)\u003c/strong\u003e We find 11am on the $x$-axis and look vertically upwards until we find the point. From here we go horiztonally across to the $y$-axis to read the frequency. We can see that at 11am there were $\\\\var{y2}$ cars in the car park.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ec)\u003c/strong\u003e We want to find $\\\\var{number}$ on the $y$-axis and then look horiztonally across until we find the point. From here we move down to the $x$-axis to see at which time there were $\\\\var{number}$ cars in the car park. We can see this occured at $\\\\var{answerc}\\\\var{time}$.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ed)\u003c/strong\u003e We must find 6pm on the $x$-axis. This isn\u0027t marked on like the other times but we know it sits half way between 5pm and 7pm. From here we look vertically upwards until we meet the red line on our graph. Notice we don\u0027t have a point for this time, hence why this is an estimate. From here we move hortizontally across to the $y$-axis to find the frequency. At 6pm we estimate that there were $\\\\var{y56}$ cars in the car park.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ee)\u003c/strong\u003e We must find the frequency of cars at 1pm and at 3pm using the same steps as in part\u0026nbsp;\u003cstrong\u003eb\u003c/strong\u003e. At 3pm there were $\\\\var{y4}$ cars in the car park and we subtract this from $\\\\var{y3}$ which is the number of cars in the car park at 1pm. Hence, $\\\\var{y3}-\\\\var{y4}=\\\\var{y3-y4}$.\u003c/p\u003e\\n\u003cform autocomplete=\\\"off\\\"\u003e\\n\u003cdiv class=\\\"adviceContainer\\\" data-bind=\\\"visible: hasAdvice() \u0026amp;\u0026amp; adviceDisplayed()\\\" localise-data-jme-context-description=\\\"question.advice\\\"\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\\n\u003c/div\u003e\\n\u003c/form\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"y6\": {\"name\": \"y6\", \"group\": \"Ungrouped variables\", \"definition\": \"random(10 .. 40#10)\", \"description\": \"\u003cp\u003eNumber of customers in supermarket at 7pm.\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"y5\": {\"name\": \"y5\", \"group\": \"Ungrouped variables\", \"definition\": \"y6+20\", \"description\": \"\u003cp\u003eNumber of customers in supermarket at 5pm.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"y3\": {\"name\": \"y3\", \"group\": \"Ungrouped variables\", \"definition\": \"random(82 .. 100#1)\", \"description\": \"\u003cp\u003eNumber of customers in supermarket at 1pm.\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"y4\": {\"name\": \"y4\", \"group\": \"Ungrouped variables\", \"definition\": \"random(50 .. 75#1)\", \"description\": \"\u003cp\u003eNumber of customers in supermarket at 3pm.\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"y2\": {\"name\": \"y2\", \"group\": \"Ungrouped variables\", \"definition\": \"y1+10\", \"description\": \"\u003cp\u003eNumber of customers in supermarket at 11am.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"y1\": {\"name\": \"y1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(10 .. 20#5)\", \"description\": \"\u003cp\u003eNumber of customers in supermarket at 9am\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"y56\": {\"name\": \"y56\", \"group\": \"Ungrouped variables\", \"definition\": \"(y5+y6)/2\", \"description\": \"\u003cp\u003eNumber of customers in supermarket at 6pm.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"number\": {\"name\": \"number\", \"group\": \"Ungrouped variables\", \"definition\": \"random(y1,y3,y4,y5,y6)\", \"description\": \"\u003cp\u003eRandomly select which number of customers user needs to identify associated time for.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"answerc\": {\"name\": \"answerc\", \"group\": \"Ungrouped variables\", \"definition\": \"if(number=y1,9,if(number=y3,1,if(number=y4,3,if(number=y5,5,if(number=y6,7,0)))))\", \"description\": \"\u003cp\u003eAssociated time to randomly selected frequency variable (number)\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"time\": {\"name\": \"time\", \"group\": \"Ungrouped variables\", \"definition\": \"if(answerc=9, \u0027am\u0027, if(answerc=11,\u0027am\u0027,if(answerc=1,\u0027pm\u0027,if(answerc=3,\u0027pm\u0027,if(answerc=5,\u0027pm\u0027,if(answerc=7,\u0027pm\u0027,0))))))\", \"description\": \"\u003cp\u003eFor printing am or pm depending on time selelected - to appear in advice only\u0026nbsp;\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"y6\", \"y5\", \"y3\", \"y4\", \"y2\", \"y1\", \"y56\", \"number\", \"answerc\", \"time\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"1_n_2\", \"useCustomName\": true, \"customName\": \"a)\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eWhen were the most customers in the supermarker?\u003c/p\u003e\", \"minMarks\": 0, \"maxMarks\": 0, \"shuffleChoices\": false, \"displayType\": \"radiogroup\", \"displayColumns\": 0, \"showCellAnswerState\": true, \"choices\": [\"9 am\", \"11 am\", \"1 pm\", \"3 pm\", \"5 pm\", \"7 pm\"], \"matrix\": [0, 0, \"1\", 0, 0, 0], \"distractors\": [\"\", \"\", \"\", \"\", \"\", \"\"]}, {\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"b)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eHow many customers were in the supermarket at 11 am?\u003c/p\u003e\", \"minValue\": \"y2\", \"maxValue\": \"y2\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"c)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eAt what time were there {number} customers in the supermarket?\u003c/p\u003e\\n\u003cp\u003e\u003cem\u003eIf your answer was 12pm you would just write 12 in the box.\u003c/em\u003e\u003c/p\u003e\", \"minValue\": \"answerc\", \"maxValue\": \"answerc\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"d)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eEstimate the number of customers in the supermarket at 6pm.\u003c/p\u003e\", \"minValue\": \"y56\", \"maxValue\": \"y56\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"e)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eHow many less customers were there in the supermarket at 3pm than 1pm?\u003c/p\u003e\", \"minValue\": \"y3-y4\", \"maxValue\": \"y3-y4\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SE01 Types of data\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Stanislav Duris\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1590/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Michael Pan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23528/\"}], \"tags\": [\"continuous data\", \"discrete data\", \"taxonomy\"], \"metadata\": {\"description\": \"\u003cp\u003eDecide whether each of the described sets of data is drawn from a discrete or continuous distribution.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eDecide whether the following data sets are discrete or continuous.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eData can either be \u003cstrong\u003ediscrete\u003c/strong\u003e or \u003cstrong\u003econtinuous\u003c/strong\u003e.\u003c/p\u003e\\n\u003cul\u003e\\n\u003cli\u003e\u003cstrong\u003eDiscrete data\u003c/strong\u003e consists of integers, units of measurement cannot be split. Only certain values have a meaning.\u003c/li\u003e\\n\u003cli\u003e\u003cstrong\u003eContinuous data\u003c/strong\u003e can be shown on a number line, all points on this line have a meaning. In between two measurements there\u0027s always a valid \\\"middle\\\" measurement. So for example, between 156.3cm and 156.4cm there\u0027s 156.35cm.\u003c/li\u003e\\n\u003c/ul\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003ch4\u003ea)\u003c/h4\u003e\\n\u003cp\u003e\u003cspan data-jme-visible=\\\"ranc = 0\\\"\u003eHeight is a continuous variable. For example, 180.3cm\u0026nbsp;and 180.4cm have a valid midpoint 180.35cm.\u003c/span\u003e\u003cspan data-jme-visible=\\\"ranc = 1\\\"\u003eWeight is a continuous variable. For example, 54.5kg and 54.6kg have a valid midpoint 54.55kg.\u003c/span\u003e\u003cspan data-jme-visible=\\\"ranc = 2\\\"\u003eTime is a continuous variable. For example, 54.2s\u0026nbsp;and 54.3s have a valid midpoint 54.25s.\u003c/span\u003e\u003cspan data-jme-visible=\\\"ranc = 3\\\"\u003eTemperature is a continuous variable,\u0026nbsp;it can take any\u0026nbsp;value between\u0026nbsp;-273.15\u0026deg;C (absolute zero)\u0026nbsp;and positive infinity. For example, 25\u0026deg;C and 26\u0026deg;C\u0026nbsp;have a valid\u0026nbsp;midpoint 25.5\u0026deg;C.\u003c/span\u003e\u0026nbsp;Hence, this data is \u003cstrong\u003econtinuous\u003c/strong\u003e.\u003c/p\u003e\\n\u003ch4\u003eb)\u003c/h4\u003e\\n\u003cp\u003e\u003cspan data-jme-visible=\\\"rand = 0\\\"\u003eThe number of Stage 1 students will always be an integer. You cannot split one student into two, for example value 19.5 students does not make sense. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand = 1\\\"\u003eThe result of rolling 3 dice can take values of integers from 3 up to 18.\u0026nbsp;For example, values 3 and 4 do not have any valid middle measurement. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand = 2\\\"\u003eShoe sizes are a\u003cstrong\u003e discrete\u003c/strong\u003e set of data. For example, sizes 39 and 40 mean something while the middle value 39.5 does not.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand = 3\\\"\u003eThe number of chocolate bars sold on Monday will always be an integer. There is no middle measurement between 1 and 2 bars\u0026nbsp;sold. You cannot buy a\u0026nbsp;half of a bar. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand = 4\\\"\u003eThe number of movies downloaded will always be an integer. You can either download a movie successfully or unsuccessfuly, so this is a\u003cstrong\u003e discrete\u003c/strong\u003e set of data. It is impossible to split 0 and 1 movies downloaded into 0.5. \u003c/span\u003e\u003cspan data-jme-visible=\\\"rand = 5\\\"\u003eThe number of cinema tickets sold will always be a whole number. There is no middle measurement between 1 and 2 tickets sold. You simply cannot buy half of a ticket. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003c/p\u003e\\n\u003ch4\u003ec)\u003c/h4\u003e\\n\u003cp\u003e\u003cspan data-jme-visible=\\\"rand2 = 0\\\"\u003eThe number of Stage 1 students will always be an integer. You cannot split one student into two, for example value 19.5 students does not make sense. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand2 = 1\\\"\u003eThe result of rolling 3 dice can take values of integers from 3 up to 18.\u0026nbsp;For example, values 3 and 4 do not have any valid middle measurement. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand2 = 2\\\"\u003eShoe sizes are a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data. For example, sizes 39 and 40 mean something while the middle value 39.5 does not..\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand2 = 3\\\"\u003eThe number of chocolate bars sold on Monday will always be an integer. There is no middle measurement between 1 and 2 bars sold. You cannot buy a half of a bar. Therefore, this is a\u003cstrong\u003e discrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand2 = 4\\\"\u003eThe number of movies downloaded will always be an integer. You can either download a movie successfully or unsuccessfuly, so this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data. It is impossible to split 0 and 1 movies\u0026nbsp;downloaded into 0.5.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand2 = 5\\\"\u003eThe number of cinema tickets sold will always be a whole number. There is no middle measurement between 1 and 2 tickets sold. You simply cannot buy half of a ticket. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003c/p\u003e\\n\u003ch4\u003ed)\u003c/h4\u003e\\n\u003cp\u003e\u003cspan data-jme-visible=\\\"ranc2 = 0\\\"\u003eHeight is a continuous variable. For example, 180.3cm and 180.4cm have a valid midpoint 180.35cm.\u003c/span\u003e\u003cspan data-jme-visible=\\\"ranc2 = 1\\\"\u003eWeight is a continuous variable. For example, 54.5kg and 54.6kg have a valid midpoint 54.55kg.\u003c/span\u003e\u003cspan data-jme-visible=\\\"ranc2 = 2\\\"\u003eTime is a continuous variable. For example, 54.2s and 54.3s have a valid midpoint 54.25s.\u003c/span\u003e\u003cspan data-jme-visible=\\\"ranc2 = 3\\\"\u003eTemperature is a continuous variable,\u0026nbsp;it can take any\u0026nbsp;value between\u0026nbsp;-273.15\u0026deg;C (absolute zero)\u0026nbsp;and positive infinity. For example, 25\u0026deg;C and 26\u0026deg;C have a valid midpoint 25.5\u0026deg;C.\u003c/span\u003e\u0026nbsp;Hence, this data is \u003cstrong\u003econtinuous\u003c/strong\u003e.\u003c/p\u003e\\n\u003ch4\u003ee)\u003c/h4\u003e\\n\u003cp\u003eWhen we round continuous variables to the nearest integer,\u0026nbsp;this data\u0026nbsp;becomes discrete, as there are no valid middle measurements between the integers. Therefore, \u003cspan data-jme-visible=\\\"rant = 0\\\"\u003ethe weight of a dog to the nearest kg\u003c/span\u003e\u003cspan data-jme-visible=\\\"rant = 1\\\"\u003ethe height of Olympic medalists to the nearest cm\u003c/span\u003e\u003cspan data-jme-visible=\\\"rant = 2\\\"\u003ethe time taken to run 10km to the nearest min\u003c/span\u003e is \u003cstrong\u003ediscrete\u003c/strong\u003e and not continuous.\u003c/p\u003e\\n\u003ch4\u003ef)\u003c/h4\u003e\\n\u003cp\u003e\u003cspan data-jme-visible=\\\"rand3 = 0\\\"\u003eThe number of Stage 1 students will always be an integer. You cannot split one student into two, for example value 19.5 students does not make sense. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand3 = 1\\\"\u003eThe result of rolling 3 dice can take values of integers from 3 up to 18.\u0026nbsp;For example, values 3 and 4 do not have any valid middle measurement. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand3 = 2\\\"\u003eShoe sizes are a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data. For example, sizes 39 and 40 mean something while the middle value 39.5 does not.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand3 = 3\\\"\u003eThe number of chocolate bars sold on Monday will always be an integer. There is no middle measurement between 1 and 2 bars sold. You cannot buy half of a bar of chocolate. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand3 = 4\\\"\u003eThe number of movies downloaded will always be an integer. You can either download a movie successfully or unsuccessfuly, so this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data. It is impossible to split 0 and 1 movies downloaded into 0.5.\u003c/span\u003e\u003cspan data-jme-visible=\\\"rand3 = 5\\\"\u003eThe number of cinema tickets sold will always be a whole number. There is no middle measurement between 1 and 2 tickets sold. You simply cannot buy half of a ticket. Therefore, this is a \u003cstrong\u003ediscrete\u003c/strong\u003e set of data.\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#types-of-data\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic\u003c/a\u003e\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"rand3\": {\"name\": \"rand3\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0..5 except rand except rand2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"cont\": {\"name\": \"cont\", \"group\": \"Ungrouped variables\", \"definition\": \"[\\\"The height of Newcastle University students.\\\", \\\"The weight of Olympic medalists.\\\", \\\"The time taken to brush teeth.\\\", \\\"The maximum daily temperature.\\\"]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"disc\": {\"name\": \"disc\", \"group\": \"Ungrouped variables\", \"definition\": \"[\\\"The number of Stage 1 students.\\\", \\\"The result of rolling 3 dice.\\\", \\\"Shoe sizes.\\\", \\\"The number of chocolate bars sold on Monday.\\\", \\\"The number of movies downloaded.\\\", \\\"The number of cinema tickets sold.\\\"]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"trick\": {\"name\": \"trick\", \"group\": \"Ungrouped variables\", \"definition\": \"[\\\"The weight of a dog to the nearest kg.\\\", \\\"The height of Olympic medalists to the nearest cm.\\\", \\\"The time taken to run 10km to the nearest min.\\\"]\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"ranc2\": {\"name\": \"ranc2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0..3 except ranc)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"rant\": {\"name\": \"rant\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0..2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"rand\": {\"name\": \"rand\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0..5)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"rand2\": {\"name\": \"rand2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0..5 except rand)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"ranc\": {\"name\": \"ranc\", \"group\": \"Ungrouped variables\", \"definition\": \"random(0..3)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"disc\", \"cont\", \"trick\", \"ranc\", \"rant\", \"ranc2\", \"rand2\", \"rand3\", \"rand\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"1_n_2\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e{cont[ranc]}\u003c/p\u003e\", \"minMarks\": 0, \"maxMarks\": 0, \"shuffleChoices\": false, \"displayType\": \"radiogroup\", \"displayColumns\": 0, \"showCellAnswerState\": true, \"choices\": [\"\u003cp\u003eDiscrete\u003c/p\u003e\", \"\u003cp\u003eContinuous\u003c/p\u003e\"], \"matrix\": [0, \"1\"], \"distractors\": [\"\", \"\"]}, {\"type\": \"1_n_2\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, 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\"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e{disc[rand2]}\u003c/p\u003e\", \"minMarks\": 0, \"maxMarks\": 0, \"shuffleChoices\": false, \"displayType\": \"radiogroup\", \"displayColumns\": 0, \"showCellAnswerState\": true, \"choices\": [\"\u003cp\u003eDiscrete\u003c/p\u003e\", \"\u003cp\u003eContinuous\u003c/p\u003e\"], \"matrix\": [\"1\", 0], \"distractors\": [\"\", \"\"]}, {\"type\": \"1_n_2\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e{cont[ranc2]}\u003c/p\u003e\", \"minMarks\": 0, \"maxMarks\": 0, \"shuffleChoices\": false, \"displayType\": \"radiogroup\", \"displayColumns\": 0, \"showCellAnswerState\": true, \"choices\": [\"\u003cp\u003eDiscrete\u003c/p\u003e\", \"\u003cp\u003eContinuous\u003c/p\u003e\"], \"matrix\": [0, \"1\"], \"distractors\": [\"\", \"\"]}, {\"type\": \"1_n_2\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003e{trick[rant]}\u003c/p\u003e\", \"minMarks\": 0, \"maxMarks\": 0, \"shuffleChoices\": false, \"displayType\": \"radiogroup\", \"displayColumns\": 0, \"showCellAnswerState\": true, 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\"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SM01 Calculate Range\", \"extensions\": [\"stats\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Chris Graham\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/369/\"}, {\"name\": \"Stanislav Duris\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1590/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Michael Pan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23528/\"}], \"tags\": [\"mean\", \"measures of average and spread\", \"median\", \"mode\", \"range\", \"taxonomy\"], \"metadata\": {\"description\": \"\u003cp\u003eThis question provides a list of data to the student. They are asked to find the \\\"range\\\".\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eA random sample of 20 residents from Newcastle were asked about the number of times they\u0026nbsp;went\u0026nbsp;to see a play at\u0026nbsp;the\u0026nbsp;theatre\u0026nbsp;last year.\u003c/p\u003e\\n\u003cp\u003eHere is the list of their answers:\u003c/p\u003e\\n\u003ctable border=\\\"1\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr\u003e\\n\u003ctd\u003e$\\\\var{a[0]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[1]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[2]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[3]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[4]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[5]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[6]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[7]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[8]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[9]}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd\u003e$\\\\var{a[10]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[11]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[12]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[13]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[14]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[15]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[16]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[17]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[18]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[19]}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003c/p\u003e\", \"advice\": \"\u003cp\u003eRange is the difference between the highest and the lowest value in the data.\u003c/p\u003e\\n\u003cp\u003eTo find this, we subtract the lowest value from the highest value:\u003c/p\u003e\\n\u003cp\u003e\\\\[ \\\\var{max(a)} - \\\\var{min(a)} = \\\\var{range} \\\\text{.}\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#measures-of-spread\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"a2\": {\"name\": \"a2\", \"group\": \"Ungrouped variables\", \"definition\": \"repeat(random(1..9), 20)\", \"description\": \"\u003cp\u003eOption\u0026nbsp;2 for the list. Only used if there is only one mode and option 1 was not used.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"modea1\": {\"name\": \"modea1\", \"group\": \"Ungrouped variables\", \"definition\": \"mode(a1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a1\": {\"name\": \"a1\", \"group\": \"Ungrouped variables\", \"definition\": \"repeat(random(1..9), 20)\", \"description\": \"\u003cp\u003eOption 1 for the list. Only used if there is only one mode.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"a_s\": {\"name\": \"a_s\", \"group\": \"final list\", \"definition\": \"sort(a)\", \"description\": \"\u003cp\u003eSorted list.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"modea2\": {\"name\": \"modea2\", \"group\": \"Ungrouped variables\", \"definition\": \"mode(a2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a3\": {\"name\": \"a3\", \"group\": \"Ungrouped variables\", \"definition\": \"shuffle([ random(0..1),\\n  2, \\n  random(4..6),\\n  random(0..3 except 2), \\n  random(0..3 except 2),\\n  random(4..6),\\n  2,\\n  2,\\n  random(4..6),\\n  random(7..8),\\n  random(0..3 except 2 except 1), \\n  random(4..6),\\n  2,\\n  random(1..3 except 2), \\n  random(7..8),\\n  2,\\n  random(7..8),\\n  random(4..6), \\n  random(0..3 except 2), \\n  2\\n])\", \"description\": \"\u003cp\u003eOption 3 for the list. Ensures there is only one mode (2) while still randomising the data.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"modetimes\": {\"name\": \"modetimes\", \"group\": \"final list\", \"definition\": \"map(\\nlen(filter(x=j,x,a)),\\nj, 0..8)\", \"description\": \"\u003cp\u003eThe vector of\u0026nbsp;number of times of each value in the data.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"range\": {\"name\": \"range\", \"group\": \"final list\", \"definition\": \"max(a) - min(a)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a\": {\"name\": \"a\", \"group\": \"final list\", \"definition\": \"if(len(modea1) = 1, a1, if(len(modea2) = 1, a2, a3))\", \"description\": \"\u003cp\u003eThe final list.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"modea1\", \"modea2\", \"a1\", \"a2\", \"a3\"], \"variable_groups\": [{\"name\": \"final list\", \"variables\": [\"a\", \"a_s\", \"range\", \"modetimes\"]}], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eFind the range.\u003c/p\u003e\", \"minValue\": \"range\", \"maxValue\": \"range\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SM02 Calculate Mean from a list\", \"extensions\": [\"stats\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Upuli Wickramaarachchi\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23527/\"}, {\"name\": \"Michael Pan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23528/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eCalculating the Mean from a basic list of integers.\u003c/p\u003e\", \"licence\": \"None specified\"}, \"statement\": \"\u003cp\u003eCalculate the Mean from a list\u003c/p\u003e\", \"advice\": \"\u003cp\u003eThe MEAN is the sum, divided by the number of values summed i.e.\u003cbr/\u003e\u003cbr/\u003e$\\\\frac{\\\\var{list[0]} +\u0026nbsp;\\\\var{list[1]} +\u0026nbsp;\\\\var{list[2]} +\u0026nbsp;\\\\var{list[3]} +\u0026nbsp;\\\\var{list[4]}}{5}$\u003c/p\u003e\\n\u003cp\u003euse your calculator to find\u003c/p\u003e\\n\u003cp\u003emean = $\\\\var{mean}$.\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"list\": {\"name\": \"list\", \"group\": \"Ungrouped variables\", \"definition\": \"repeat(random(0..20), 5)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"mean\": {\"name\": \"mean\", \"group\": \"Ungrouped variables\", \"definition\": \"mean(list)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"median\": {\"name\": \"median\", \"group\": \"Ungrouped variables\", \"definition\": \"median(list)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"order\": {\"name\": \"order\", \"group\": \"Ungrouped variables\", \"definition\": \"sort(list)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"list\", \"mean\", \"median\", \"order\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"gapfill\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eGiven a list of numbers:\u003cbr/\u003e\u003cbr/\u003e{list}\u003cbr/\u003e\u003cbr/\u003eCalculate the mean: \u0026nbsp;\u0026nbsp;[[0]]\u003c/p\u003e\", \"gaps\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minValue\": \"mean\", \"maxValue\": \"mean\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"sortAnswers\": false}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SM03 Calculate Mode From a list\", \"extensions\": [\"stats\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Chris Graham\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/369/\"}, {\"name\": \"Stanislav Duris\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1590/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Michael Pan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23528/\"}], \"tags\": [\"mean\", \"measures of average and spread\", \"median\", \"mode\", \"range\", \"taxonomy\"], \"metadata\": {\"description\": \"\u003cp\u003eThis question provides a list of data to the student. They are asked to find the \\\"mode\\\".\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eA random sample of 20 residents from Newcastle were asked about the number of times they\u0026nbsp;went\u0026nbsp;to see a play at\u0026nbsp;the\u0026nbsp;theatre\u0026nbsp;last year.\u003c/p\u003e\\n\u003cp\u003eHere is the list of their answers:\u003c/p\u003e\\n\u003ctable border=\\\"1\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr\u003e\\n\u003ctd\u003e$\\\\var{a[0]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[1]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[2]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[3]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[4]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[5]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[6]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[7]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[8]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[9]}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd\u003e$\\\\var{a[10]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[11]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[12]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[13]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[14]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[15]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[16]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[17]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[18]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[19]}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003c/p\u003e\", \"advice\": \"\u003cp\u003eThe mode is the value that occurs the most often in the data.\u003c/p\u003e\\n\u003cp\u003eTo find a mode, we can look at our sorted list:\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e$\\\\var{a_s[0]}, \\\\var{a_s[1]}, \\\\var{a_s[2]}, \\\\var{a_s[3]}, \\\\var{a_s[4]}, \\\\var{a_s[5]}, \\\\var{a_s[6]}, \\\\var{a_s[7]}, \\\\var{a_s[8]}, \\\\var{a_s[9]}, \\\\var{a_s[10]}, \\\\var{a_s[11]}, \\\\var{a_s[12]}, \\\\var{a_s[13]}, \\\\var{a_s[14]}, \\\\var{a_s[15]}, \\\\var{a_s[16]}, \\\\var{a_s[17]}, \\\\var{a_s[18]}, \\\\var{a_s[19]}$.\u003c/p\u003e\\n\u003cp\u003eWe\u0026nbsp;notice that $\\\\var{mode1}$ occurs the most ($\\\\var{modetimes[mode1]}$ times) so $\\\\var{mode1}$ is the mode.\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"a2\": {\"name\": \"a2\", \"group\": \"Ungrouped variables\", \"definition\": \"repeat(random(0..8), 20)\", \"description\": \"\u003cp\u003eOption\u0026nbsp;2 for the list. Only used if there is only one mode and option 1 was not used.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"modea1\": {\"name\": \"modea1\", \"group\": \"Ungrouped variables\", \"definition\": \"mode(a1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a1\": {\"name\": \"a1\", \"group\": \"Ungrouped variables\", \"definition\": \"repeat(random(0..8), 20)\", \"description\": \"\u003cp\u003eOption 1 for the list. Only used if there is only one mode.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"a_s\": {\"name\": \"a_s\", \"group\": \"final list\", \"definition\": \"sort(a)\", \"description\": \"\u003cp\u003eSorted list.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"modea2\": {\"name\": \"modea2\", \"group\": \"Ungrouped variables\", \"definition\": \"mode(a2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a3\": {\"name\": \"a3\", \"group\": \"Ungrouped variables\", \"definition\": \"shuffle([ random(0..1),\\n  2, \\n  random(4..6),\\n  random(0..3 except 2), \\n  random(0..3 except 2),\\n  random(4..6),\\n  2,\\n  2,\\n  random(4..6),\\n  random(7..8),\\n  random(0..3 except 2 except 1), \\n  random(4..6),\\n  2,\\n  random(1..3 except 2), \\n  random(7..8),\\n  2,\\n  random(7..8),\\n  random(4..6), \\n  random(0..3 except 2), \\n  2\\n])\", \"description\": \"\u003cp\u003eOption 3 for the list. Ensures there is only one mode (2) while still randomising the data.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"modetimes\": {\"name\": \"modetimes\", \"group\": \"final list\", \"definition\": \"map(\\nlen(filter(x=j,x,a)),\\nj, 0..8)\", \"description\": \"\u003cp\u003eThe vector of\u0026nbsp;number of times of each value in the data.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"mode1\": {\"name\": \"mode1\", \"group\": \"final list\", \"definition\": \"mode[0]\", \"description\": \"\u003cp\u003eMode as a value.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"mode\": {\"name\": \"mode\", \"group\": \"final list\", \"definition\": \"mode(a)\", \"description\": \"\u003cp\u003eMode as a vector.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"a\": {\"name\": \"a\", \"group\": \"final list\", \"definition\": \"if(len(modea1) = 1, a1, if(len(modea2) = 1, a2, a3))\", \"description\": \"\u003cp\u003eThe final list.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"modea1\", \"modea2\", \"a1\", \"a2\", \"a3\"], \"variable_groups\": [{\"name\": \"final list\", \"variables\": [\"a\", \"a_s\", \"mode\", \"mode1\", \"modetimes\"]}], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eFind the mode.\u003c/p\u003e\", \"minValue\": \"mode1\", \"maxValue\": \"mode1\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SM04 Calculate Median from a list\", \"extensions\": [\"stats\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Chris Graham\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/369/\"}, {\"name\": \"Stanislav Duris\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1590/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Upuli Wickramaarachchi\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23527/\"}, {\"name\": \"Michael Pan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23528/\"}], \"tags\": [\"mean\", \"measures of average and spread\", \"median\", \"mode\", \"range\", \"taxonomy\"], \"metadata\": {\"description\": \"\u003cp\u003eThis question provides a list of data to the student. They are asked to find the \\\"median\\\".\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eA random sample of 20 residents from Newcastle were asked about the number of times they\u0026nbsp;went\u0026nbsp;to see a play at\u0026nbsp;the\u0026nbsp;theatre\u0026nbsp;last year.\u003c/p\u003e\\n\u003cp\u003eHere is the list of their answers:\u003c/p\u003e\\n\u003ctable border=\\\"1\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr\u003e\\n\u003ctd\u003e$\\\\var{a[0]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[1]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[2]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[3]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[4]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[5]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[6]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[7]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[8]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[9]}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd\u003e$\\\\var{a[10]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[11]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[12]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[13]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[14]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[15]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[16]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[17]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[18]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[19]}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003c/p\u003e\", \"advice\": \"\u003cp\u003eThe median is\u0026nbsp;the middle value. We need to sort the list in order:\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\\\\[ \\\\var{a_s[0]}, \\\\quad \\\\var{a_s[1]}, \\\\quad\u0026nbsp;\\\\var{a_s[2]}, \\\\quad \\\\var{a_s[3]}, \\\\quad \\\\var{a_s[4]}, \\\\quad \\\\var{a_s[5]}, \\\\quad \\\\var{a_s[6]}, \\\\quad \\\\var{a_s[7]}, \\\\quad \\\\var{a_s[8]}, \\\\quad \\\\var{a_s[9]}, \\\\quad \\\\var{a_s[10]}, \\\\quad \\\\var{a_s[11]}, \\\\quad\u0026nbsp;\\\\var{a_s[12]}, \\\\quad \\\\var{a_s[13]}, \\\\quad \\\\var{a_s[14]}, \\\\quad \\\\var{a_s[15]}, \\\\quad \\\\var{a_s[16]}, \\\\quad \\\\var{a_s[17]}, \\\\quad \\\\var{a_s[18]}, \\\\quad \\\\var{a_s[19]} \\\\]\u003c/p\u003e\\n\u003cp\u003eThere is an even number of responses, so there are\u0026nbsp;two numbers in the middle (10\u003csup\u003eth\u003c/sup\u003e and 11\u003csup\u003eth\u003c/sup\u003e place). To\u0026nbsp;find the median, we need to\u0026nbsp;find the mean of these two numbers $\\\\var{a_s[9]}$ and $\\\\var{a_s[10]}$:\u003c/p\u003e\\n\u003cp\u003e\\\\begin{align} \u003cbr/\u003e\\\\frac{\\\\var{a_s[9]} + \\\\var{a_s[10]}}{2} \u0026amp;= \u0026nbsp;\\\\frac{\\\\var{a_s[9] + a_s[10]}}{2} \\\\\\\\\u003cbr/\u003e\u0026amp;= \\\\var{median} \\\\text{.}\u0026nbsp;\u003cbr/\u003e\\\\end{align}\u003c/p\u003e\\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003e\u003cspan style=\\\"font-weight: 400;\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/span\u003e\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"a2\": {\"name\": \"a2\", \"group\": \"Ungrouped variables\", \"definition\": \"repeat(random(0..8), 20)\", \"description\": \"\u003cp\u003eOption\u0026nbsp;2 for the list. Only used if there is only one mode and option 1 was not used.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"modea1\": {\"name\": \"modea1\", \"group\": \"Ungrouped variables\", \"definition\": \"mode(a1)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"median\": {\"name\": \"median\", \"group\": \"final list\", \"definition\": \"median(a)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a1\": {\"name\": \"a1\", \"group\": \"Ungrouped variables\", \"definition\": \"repeat(random(0..8), 20)\", \"description\": \"\u003cp\u003eOption 1 for the list. Only used if there is only one mode.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"a_s\": {\"name\": \"a_s\", \"group\": \"final list\", \"definition\": \"sort(a)\", \"description\": \"\u003cp\u003eSorted list.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"modea2\": {\"name\": \"modea2\", \"group\": \"Ungrouped variables\", \"definition\": \"mode(a2)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"a3\": {\"name\": \"a3\", \"group\": \"Ungrouped variables\", \"definition\": \"shuffle([ random(0..1),\\n  2, \\n  random(4..6),\\n  random(0..3 except 2), \\n  random(0..3 except 2),\\n  random(4..6),\\n  2,\\n  2,\\n  random(4..6),\\n  random(7..8),\\n  random(0..3 except 2 except 1), \\n  random(4..6),\\n  2,\\n  random(1..3 except 2), \\n  random(7..8),\\n  2,\\n  random(7..8),\\n  random(4..6), \\n  random(0..3 except 2), \\n  2\\n])\", \"description\": \"\u003cp\u003eOption 3 for the list. Ensures there is only one mode (2) while still randomising the data.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"mean\": {\"name\": \"mean\", \"group\": \"final list\", \"definition\": \"mean(a)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"modetimes\": {\"name\": \"modetimes\", \"group\": \"final list\", \"definition\": \"map(\\nlen(filter(x=j,x,a)),\\nj, 0..8)\", \"description\": \"\u003cp\u003eThe vector of\u0026nbsp;number of times of each value in the data.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"range\": {\"name\": \"range\", \"group\": \"final list\", \"definition\": \"max(a) - min(a)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"mode1\": {\"name\": \"mode1\", \"group\": \"final list\", \"definition\": \"mode[0]\", \"description\": \"\u003cp\u003eMode as a value.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"mode\": {\"name\": \"mode\", \"group\": \"final list\", \"definition\": \"mode(a)\", \"description\": \"\u003cp\u003eMode as a vector.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"a\": {\"name\": \"a\", \"group\": \"final list\", \"definition\": \"if(len(modea1) = 1, a1, if(len(modea2) = 1, a2, a3))\", \"description\": \"\u003cp\u003eThe final list.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"modea1\", \"modea2\", \"a1\", \"a2\", \"a3\"], \"variable_groups\": [{\"name\": \"final list\", \"variables\": [\"a\", \"a_s\", \"mean\", \"median\", \"mode\", \"mode1\", \"range\", \"modetimes\"]}], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eFind the median.\u003c/p\u003e\", \"minValue\": \"median\", \"maxValue\": \"median\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SM05 Calculate the mean (Frequency table) - With a calculator\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/496/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Marta Emmett\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/11961/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eUsing a calculator, work out the mean for each of these frequency tables, give your answers to \u003cstrong\u003etwo decimal places\u003c/strong\u003e.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eTo calculate the mean shoe size we need to add a third column to our table where we multiply the grade by the number (frequency) of students who are that shoe size.\u003c/p\u003e\\n\u003ctable style=\\\"margin-right: auto; height: 126px; width: 391px;\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"height: 18px; width: 48.2031px; text-align: center;\\\"\u003e\u003cb\u003eShoe Size\u003c/b\u003e\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 82.0625px; text-align: center;\\\"\u003e\u003cstrong\u003eFrequency\u003c/strong\u003e\u003c/td\u003e\\n\u003ctd style=\\\"width: 211.734px; text-align: center;\\\"\u003e\u003cstrong\u003eShoe Size * Frequency\u003c/strong\u003e\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"text-align: center;\\\"\u003e\\n\u003ctd style=\\\"height: 18px; width: 48.2031px; text-align: center;\\\"\u003e3\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 82.0625px; text-align: center;\\\"\u003e{p1}\u003c/td\u003e\\n\u003ctd style=\\\"width: 211.734px; text-align: center;\\\"\u003e3 * {p1} = {3*p1}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"text-align: center;\\\"\u003e\\n\u003ctd style=\\\"height: 18px; width: 48.2031px; text-align: center;\\\"\u003e4\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 82.0625px; text-align: center;\\\"\u003e{p2}\u003c/td\u003e\\n\u003ctd style=\\\"width: 211.734px; text-align: center;\\\"\u003e4 * {p2} = {4*p2}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"text-align: center;\\\"\u003e\\n\u003ctd style=\\\"height: 18px; width: 48.2031px; text-align: center;\\\"\u003e5\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 82.0625px; text-align: center;\\\"\u003e{p3}\u003c/td\u003e\\n\u003ctd style=\\\"width: 211.734px; text-align: center;\\\"\u003e5 * {p3} = {5*p3}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 48.2031px; text-align: center; height: 18px;\\\"\u003e6\u003c/td\u003e\\n\u003ctd style=\\\"width: 82.0625px; text-align: center; height: 18px;\\\"\u003e{p4}\u003c/td\u003e\\n\u003ctd style=\\\"width: 211.734px; text-align: center;\\\"\u003e6 * {p4} = {6*p4}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 48.2031px; text-align: center; height: 18px;\\\"\u003e7\u003c/td\u003e\\n\u003ctd style=\\\"width: 82.0625px; text-align: center; height: 18px;\\\"\u003e{p5}\u003c/td\u003e\\n\u003ctd style=\\\"width: 211.734px; text-align: center;\\\"\u003e7 * {p5} = {7*p5}\u0026nbsp;\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"text-align: center;\\\"\u003e\\n\u003ctd style=\\\"height: 18px; width: 48.2031px; text-align: center;\\\"\u003e8\u003c/td\u003e\\n\u003ctd style=\\\"height: 18px; width: 82.0625px; text-align: center;\\\"\u003e{p6}\u003c/td\u003e\\n\u003ctd style=\\\"width: 211.734px; text-align: center;\\\"\u003e8 * {p6} = {8*p6}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\\n\u003cp\u003eNow we find the total sum of that third column:\u003c/p\u003e\\n\u003cp\u003e$\\\\var{3*p1} + \\\\var{4*p2} + \\\\var{5*p3} + \\\\var{6*p4} + \\\\var{7*p5} + \\\\var{8*p6} = \\\\var{3*p1 + 4*p2 + 5*p3 + 6*p4 + 7*p5 + 8*p6}.$\u003c/p\u003e\\n\u003cp\u003eTo find the mean shoe size we must divide this total by the total number of students:\u003c/p\u003e\\n\u003cp\u003e$\\\\frac{\\\\var{3*p1 + 4*p2 + 5*p3 + 6*p4 + 7*p5 + 8*p6}}{\\\\var{p1}+\\\\var{p2}+\\\\var{p3}+\\\\var{p4}+\\\\var{p5}+\\\\var{p6}} = \\\\frac{\\\\var{3*p1 + 4*p2 + 5*p3 + 6*p4 + 7*p5 + 8*p6}}{\\\\var{sum1}} = \\\\var{mean1a}.$\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003eThe question asks us for our answer to two decimal places so the last thing we need to do is round. Hence, the mean is $\\\\var{mean1}$.\u003c/p\u003e\\n\u003cp\u003eYou can use this same method to answer the other parts of this question!\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"mean1a\": {\"name\": \"mean1a\", \"group\": \"Part a\", \"definition\": \"((3*p1)+(4*p2)+(5*p3)+(6*p4)+(7*p5)+(8*p6))/sum1\", \"description\": \"\u003cp\u003eThe mean - part a\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"p1\": {\"name\": \"p1\", \"group\": \"Part a\", \"definition\": \"random(0 .. 50#1)\", \"description\": \"\u003cp\u003eFrequency 1 - part a\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"p2\": {\"name\": \"p2\", \"group\": \"Part a\", \"definition\": \"random(0 .. 50#1)\", \"description\": \"\u003cp\u003eFrequency 2 - part a\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"p3\": {\"name\": \"p3\", \"group\": \"Part a\", \"definition\": \"random(0 .. 50#1)\", \"description\": \"\u003cp\u003eFrequency 3 - part a\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"p4\": {\"name\": \"p4\", \"group\": \"Part a\", \"definition\": \"random(0 .. 50#1)\", \"description\": \"\u003cp\u003eFrequency 4 - part a\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"p5\": {\"name\": \"p5\", \"group\": \"Part a\", \"definition\": \"random(0 .. 50#1)\", \"description\": \"\u003cp\u003eFrequency 5 - part a\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"p6\": {\"name\": \"p6\", \"group\": \"Part a\", \"definition\": \"random(0 .. 50#1)\", \"description\": \"\u003cp\u003eFrequency 6 - part a\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"mean1\": {\"name\": \"mean1\", \"group\": \"Part a\", \"definition\": \"precround(mean1a,2)\", \"description\": \"\u003cp\u003eMean rounded to two decimal places - part a\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"sum1\": {\"name\": \"sum1\", \"group\": \"Part a\", \"definition\": \"p1+p2+p3+p4+p5+p6\", \"description\": \"\u003cp\u003eSum of frequencies - part a\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"sum2\": {\"name\": \"sum2\", \"group\": \"Part b\", \"definition\": \"p1b+p2b+p3b+p4b\", \"description\": \"\u003cp\u003eSum of frequencies - part b\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"p1b\": {\"name\": \"p1b\", \"group\": \"Part b\", \"definition\": \"random(1 .. 100#1)\", \"description\": \"\u003cp\u003eFrequency 1 - part 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{\"description\": \"\u003cp\u003eThis question asks the student to choose the appropriate measure of average and spread for a data with outliers.\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eWhich of the following measures would you choose if you were dealing with data which includes outliers? Select one measure of average and one measure of spread.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eThe median is a more appropriate measure of average when your data contains outliers because outliers do not affect the median.\u003c/p\u003e\\n\u003cp\u003eThe interquartile range is the best measure of variability for skewed distributions or data sets with outliers. Because it\u0026rsquo;s based on values that come from the middle half of the distribution, it\u0026rsquo;s unlikely to be influenced by outliers.\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"m_n_2\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minMarks\": 0, \"maxMarks\": 0, \"shuffleChoices\": true, \"displayType\": \"checkbox\", \"displayColumns\": 0, \"minAnswers\": 0, \"maxAnswers\": 0, \"warningType\": \"none\", \"showCellAnswerState\": true, \"markingMethod\": \"sum ticked cells\", \"choices\": [\"Mean\", \"Median\", \"Standard deviation\", \"P-value\", \"Range\", \"Inter-quartile range\"], \"matrix\": [0, \"1\", 0, 0, 0, \"1\"], \"distractors\": [\"\", \"\", \"\", \"\", \"\", \"\"]}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SM07 Identify measures of spread/location\", \"extensions\": [\"jsxgraph\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Gareth Woods\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/978/\"}, {\"name\": \"Ruth Hand\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/3228/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Michael Pan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23528/\"}], \"tags\": [], \"metadata\": {\"description\": \"\u003cp\u003eIdentifying measures of spread or location (average)\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eMatch each of the following with what they measure.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eThe mean is a measure of location or central tendancy. It is calcuated by summing all of the data values and dividing by the number of values.\u003c/p\u003e\\n\u003cp\u003eThe median is a measure of location or central tendancy. It is the middle value of an ordered data set.\u003c/p\u003e\\n\u003cp\u003eThe inter-quartile range is a measure of spread. The interquartile range is the difference between upper and lower quartiles.The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order. The inter-quartile range therefore gives us an idea of the middle 50% of the ordered data set.\u003c/p\u003e\\n\u003cp\u003eThe standard deviation is a measure of spread. It measures the dispersion of a data set relative to its mean.\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003eThe variance is a measure spread because it is the square of the standard deviation.\u003c/p\u003e\\n\u003cp\u003eA p-value the probability that a particular statistical measure, such as the mean or standard deviation, of an assumed probability distribution will be greater than or equal to (or less than or equal to in some instances) observed results. A p-value is used to determine statistical significance, not measures of spread or location.\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {\"std\": [\"all\", \"fractionNumbers\"]}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"function dragpoint_board() {\\n  var scope = question.scope;\\n\\n  JXG.Options.text.display = \u0027internal\u0027;\\n  \\n  var yo0 = scope.variables.yo0.value;\\n  var yo1 = scope.variables.yo1.value;\\n  var yo2 = scope.variables.yo2.value;\\n  var yo3 = scope.variables.yo3.value;\\n  var yo4 = scope.variables.yo4.value;\\n  var yo5 = scope.variables.yo5.value;\\n  var yo6 = scope.variables.yo6.value;\\n  var yo7 = scope.variables.yo7.value; \\n  var yo8 = scope.variables.yo8.value;\\n  var yo9 = scope.variables.yo9.value; \\n  \\n  var div = Numbas.extensions.jsxgraph.makeBoard(\u0027550px\u0027,\u0027550px\u0027,{boundingBox:[-0.8,82,16,-8], axis:false, grid:true});\\n \\n  $(question.display.html).find(\u0027#dragpoint\u0027).append(div);\\n  \\n  var board = div.board;\\n  \\nboard.suspendUpdate();           \\n\\n  \\n var dataArr = [yo0,yo5,0,yo1,yo6,0,yo2,yo7,0,yo3,yo8,0,yo4,yo9]; \\n  \\n var xaxis = board.create(\u0027axis\u0027, [[0, 0], [12, 0]], {withLabel: true, name: \\\"Bank\\\", label: {offset: [250,-30]}});\\n  \\n  xaxis.removeAllTicks();  \\n   \\n  board.create(\u0027axis\u0027, [[0, 0], [0, 10]], {hideTicks:true, withLabel: false, name: \\\"\\\", label: {offset: [-110,300]}});\\n  \\n  var pop0 = board.create(\u0027point\u0027, [1.5,0],{name:\u0027Morgan\u0027,fixed:true,size:0,color:\u0027black\u0027,face:\u0027diamond\u0027, label:{offset:[-20,-8]}});\\n  var pop1 = board.create(\u0027point\u0027,[4.5,0],{name:\u0027Strome\u0027,fixed:true,size:0,color:\u0027black\u0027,face:\u0027diamond\u0027, label:{offset:[-20,-8]}});\\n  var pop2 = board.create(\u0027point\u0027,[7.5,0],{name:\u0027Bentley\u0027,fixed:true,size:0,color:\u0027black\u0027, face:\u0027diamond\u0027, label:{offset:[-15,-8]}});\\n  var pop3 = board.create(\u0027point\u0027,[10.5,0],{name:\u0027Sand\u0027,fixed:true,size:0,color:\u0027black\u0027, face:\u0027diamond\u0027, label:{offset:[-15,-8]}});\\n  var pop4 = board.create(\u0027point\u0027,[13.5,0],{name:\u0027Karchen\u0027,fixed:true,size:0,color:\u0027black\u0027, face:\u0027diamond\u0027, label:{offset:[-15,-8]}});\\n\\n  var leg1 = board.create(\u0027point\u0027,[12,75],{name:\u0027last year\u0027,fixed:true,size:6,color:\u0027#DA2228\u0027, face:\u0027square\u0027, label:{offset:[9,0]}});\\n  var leg2 = board.create(\u0027point\u0027,[12,72],{name:\u0027this year\u0027,fixed:true,size:6,color:\u0027#6F1B75\u0027, face:\u0027square\u0027, label:{offset:[9,0]}});\\n  \\n  \\n//  var chart = board.createElement(\u0027chart\u0027, dataArr, \\n  //                              {chartStyle:\u0027bar\u0027, fillOpacity:1, width:1,\\n    //     colorArray:[\u0027#8E1B77\u0027,\u0027#8E1B77\u0027,\u0027Red\u0027,\u0027Red\u0027,\u0027blue\u0027,\u0027red\u0027,\u0027blue\u0027,\u0027red\u0027,\u0027red\u0027,\u0027blue\u0027, \u0027red\u0027,\u0027blue\u0027,\u0027red\u0027,\u0027red\u0027], shadow:false});\\n \\n//var chart = board.createElement(\u0027chart\u0027, dataArr, \\n  //                              {chartStyle:\u0027bar\u0027, width:1,fillOpacity:1, fillColor:\u0027red\u0027, shadow:false});  \\n  \\n  \\n    var a = board.create(\u0027chart\u0027, [[1,2,3],[yo0,yo5,0]], {chartStyle:\u0027bar\u0027,colors:[\u0027#DA2228\u0027,\u0027#6F1B75\u0027,\u0027#6F1B75\u0027],width:1,fillOpacity:1});\\n    var b = board.create(\u0027chart\u0027, [[4,5,6],[yo1,yo6,0]], {chartStyle:\u0027bar\u0027,width:1,colors:[\u0027#DA2228\u0027,\u0027#6F1B75\u0027,\u0027#6F1B75\u0027],fillOpacity:1});\\n    var c = board.create(\u0027chart\u0027, [[7,8,9],[yo2,yo7,0]], {chartStyle:\u0027bar\u0027,width:1,colors:[\u0027#DA2228\u0027,\u0027#6F1B75\u0027,\u0027#6F1B75\u0027],fillOpacity:1});\\n    var d = board.create(\u0027chart\u0027, [[10,11,12],[yo3,yo8,0]], {chartStyle:\u0027bar\u0027,width:1,colors:[\u0027#DA2228\u0027,\u0027#6F1B75\u0027,\u0027#6F1B75\u0027],fillOpacity:1});\\n    var e = board.create(\u0027chart\u0027, [[13,14],[yo4,yo9]], {chartStyle:\u0027bar\u0027,width:1,colors:[\u0027#DA2228\u0027,\u0027#6F1B75\u0027],fillOpacity:1});\\n  \\n    board.unsuspendUpdate();\\n  \\n  var txt1 = board.create(\u0027text\u0027,[-0.3,30, \u0027Investment \\u00a3(m)\u0027], {fontColor:\u0027black\u0027, fontSize:14, rotate:90});\\n  \\n // var txt = board.create(\u0027text\u0027,[0.5,75, \u0027Investment (m)\u0027], {fontSize:14, rotate:90});\\n  \\n // var txt1 = board.create(\u0027text\u0027,[8,76, \u0027red bars represent 2010\u0027], {fontColor:\u0027red\u0027, fontSize:14, rotate:90});\\n  \\n // var txt2 = board.create(\u0027text\u0027,[8,73, \u0027blue bars represents 2011\u0027], {fontSize:14, rotate:90});\\n\\n // var myColors = new Array(\u0027red\u0027, \u0027blue\u0027, \u0027white\u0027,\u0027red\u0027, \u0027blue\u0027, \u0027white\u0027,\u0027red\u0027, \u0027blue\u0027, \u0027white\u0027,\u0027red\u0027, \u0027blue\u0027, \u0027white\u0027,\u0027red\u0027, \u0027blue\u0027);\\n  \\n  \\n  \\n  //board.unsuspendUpdate();\\n\\n    // Rotate text around the lower left corner (-2,-1) by 30 degrees.\\n   // var tRot = board.create(\u0027transform\u0027, [90.0*Math.PI/180.0, -1,40], {type:\u0027rotate\u0027}); \\n  //  tRot.bindTo(txt);\\n  //  board.update();\\n\\n  \\n//var chart2 = board.createElement(\u0027chart\u0027, dataArr, {chartStyle:\u0027line,point\u0027});\\n//chart2[0].setProperty(\u0027strokeColor:black\u0027,\u0027strokeWidth:2\u0027,\u0027shadow:true\u0027);\\n//for(var i=0; i\u003c11;i++) {\\n //   chart2[1][i].setProperty({strokeColor:\u0027black\u0027,fillColor:\u0027white\u0027,face:\u0027[]\u0027, size:4, strokeWidth:2});\\n//}\\n//board.unsuspendUpdate();  \\n                       \\n  //board.unsuspendUpdate();\\n\\n}\\n\\nquestion.signals.on(\u0027HTMLAttached\u0027,function() {\\n  dragpoint_board();\\n});\", \"css\": \"table#values th {\\n  background: none;\\n  text-align: center;\\n}\"}, \"parts\": [{\"type\": \"m_n_x\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 0, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"minMarks\": 0, \"maxMarks\": 0, \"minAnswers\": 0, \"maxAnswers\": 0, \"shuffleChoices\": true, \"shuffleAnswers\": true, \"displayType\": \"radiogroup\", \"warningType\": \"none\", \"showCellAnswerState\": true, \"markingMethod\": \"sum ticked cells\", \"choices\": [\"Variance\", \"Mean\", \"Median\", \"Inter-quartile range\", \"P-value\", \"Standard deviation\"], \"matrix\": [[\"1\", 0, 0], [0, \"1\", 0], [0, \"1\", 0], [\"1\", 0, 0], [0, 0, \"1\"], [\"1\", 0, 0]], \"layout\": {\"type\": \"all\", \"expression\": \"\"}, \"answers\": [\"Measure of Spread\", \"Measure of location (average)\", \"Neither measure of location nor measure of spread\"]}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SM08 Calculate Range (Decimal)\", \"extensions\": [\"stats\"], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Christian Lawson-Perfect\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/7/\"}, {\"name\": \"Chris Graham\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/369/\"}, {\"name\": \"Stanislav Duris\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/1590/\"}, {\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Lauren Desoysa\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21504/\"}, {\"name\": \"Will Morgan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/21933/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}, {\"name\": \"Michael Pan\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23528/\"}], \"tags\": [\"mean\", \"measures of average and spread\", \"median\", \"mode\", \"range\", \"taxonomy\"], \"metadata\": {\"description\": \"\u003cp\u003eThis question provides a list of data to the student. They are asked to find the \\\"range\\\".\u003c/p\u003e\", \"licence\": \"Creative Commons Attribution 4.0 International\"}, \"statement\": \"\u003cp\u003eHere is a list of 20 random numbers:\u003c/p\u003e\\n\u003ctable border=\\\"1\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr\u003e\\n\u003ctd\u003e$\\\\var{a[0]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[1]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[2]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[3]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[4]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[5]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[6]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[7]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[8]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[9]}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd\u003e$\\\\var{a[10]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[11]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[12]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[13]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[14]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[15]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[16]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[17]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[18]}$\u003c/td\u003e\\n\u003ctd\u003e$\\\\var{a[19]}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003c/p\u003e\", \"advice\": \"\u003cp\u003eRange is the difference between the highest and the lowest value in the data.\u003c/p\u003e\\n\u003cp\u003eTo find this, we subtract the lowest value from the highest value:\u003c/p\u003e\\n\u003cp\u003e\\\\[ \\\\var{max(a)} - \\\\var{min(a)} = \\\\var{range} \\\\text{.}\\\\]\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#measures-of-spread\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"a\": {\"name\": \"a\", \"group\": \"Ungrouped variables\", \"definition\": \"repeat(random(z), 20)\", \"description\": \"\u003cp\u003eOption 1 for the list. Only used if there is only one mode.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"a_s\": {\"name\": \"a_s\", \"group\": \"final list\", \"definition\": \"sort(a)\", \"description\": \"\u003cp\u003eSorted list.\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"range\": {\"name\": \"range\", \"group\": \"final list\", \"definition\": \"max(a) - min(a)\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"z\": {\"name\": \"z\", \"group\": \"Ungrouped variables\", \"definition\": \"0.7 .. 9.7#0.1\", \"description\": \"\", \"templateType\": \"range\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"a\", \"z\"], \"variable_groups\": [{\"name\": \"final list\", \"variables\": [\"a_s\", \"range\"]}], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": false, \"customName\": \"\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eFind the range.\u003c/p\u003e\", \"minValue\": \"range\", \"maxValue\": \"range\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SM09 Range and Interquartile Range\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eHere are the ages of 7 people:\u003c/p\u003e\\n\u003cp\u003e{a1}, {a2}, {a3}, {a4}, {a5}, {a6}, {a7}.\u003c/p\u003e\", \"advice\": \"\u003cp\u003eFirst we should order our list of ages from smallest to largest:\u003c/p\u003e\\n\u003cp\u003e$\\\\var{list[0]}, \\\\var{list[1]}, \\\\var{list[2]}, \\\\var{list[3]}, \\\\var{list[4]}, \\\\var{list[5]}, \\\\var{list[6]}$.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ea)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo find the range of ages we must subtract the smallest age from the largest age,\u003c/p\u003e\\n\u003cp\u003e$\\\\var{max(list)} - \\\\var{min(list)} = \\\\var{range}$.\u003c/p\u003e\\n\u003cp\u003eHence, the range is $\\\\var{range}$.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003eb)\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo calculate the interquartile range we subtract the lower quartile from the upper quartile.\u003c/p\u003e\\n\u003cp\u003e\u003cspan style=\\\"text-decoration: underline;\\\"\u003eTo calculate the lower quartile:\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003eSince we have an odd number of ages we had one to the total and divide by 4,\u003c/p\u003e\\n\u003cp\u003e$\\\\frac{7+1}{4} = \\\\frac{8}{4} = 2.$\u003c/p\u003e\\n\u003cp\u003eSo we are looking for the $2^{nd}$ value in our list which is $\\\\var{lq}$.\u003c/p\u003e\\n\u003cp\u003eHence the lower quartile is $\\\\var{lq}$.\u003c/p\u003e\\n\u003cp\u003e\u003cspan style=\\\"text-decoration: underline;\\\"\u003eTo find the upper quartile:\u003c/span\u003e\u003c/p\u003e\\n\u003cp\u003eWe still add one to the number of ages because this number is odd and then we find $75$% of it,\u003c/p\u003e\\n\u003cp\u003e$\\\\frac{3\\\\times(7+1)}{4} = \\\\frac{3\\\\times8}{4} = \\\\frac{24}{4} = 6.$\u003c/p\u003e\\n\u003cp\u003eSo we are looking for the $6^{th}$ value in our list which is $\\\\var{uq}$.\u003c/p\u003e\\n\u003cp\u003eHence the lower quartile is $\\\\var{uq}$.\u003c/p\u003e\\n\u003cp\u003eNow we can calculate the interquartile range by subtracting the lower quartile from the upper quartile,\u003c/p\u003e\\n\u003cp\u003e$\\\\var{uq}-\\\\var{lq} = \\\\var{iqr}.$\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"a1\": {\"name\": \"a1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(16 .. 60#1)\", \"description\": \"\u003cp\u003eAge 1\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"a2\": {\"name\": \"a2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(16 .. 60#1)\", \"description\": \"\u003cp\u003eAge 2\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"a3\": {\"name\": \"a3\", \"group\": \"Ungrouped variables\", \"definition\": \"random(16 .. 60#1)\", \"description\": \"\u003cp\u003eAge 3\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"a4\": {\"name\": \"a4\", \"group\": \"Ungrouped variables\", \"definition\": \"random(16 .. 60#1)\", \"description\": \"\u003cp\u003eAge 4\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"a5\": {\"name\": \"a5\", \"group\": \"Ungrouped variables\", \"definition\": \"random(16 .. 60#1)\", \"description\": \"\u003cp\u003eAge 5\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"a6\": {\"name\": \"a6\", \"group\": \"Ungrouped variables\", \"definition\": \"random(16 .. 60#1)\", \"description\": \"\u003cp\u003eAge 6\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"a7\": {\"name\": \"a7\", \"group\": \"Ungrouped variables\", \"definition\": \"random(16 .. 60#1)\", \"description\": \"\u003cp\u003eAge 7\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"list\": {\"name\": \"list\", \"group\": \"Ungrouped variables\", \"definition\": \"sort([a1,a2,a3,a4,a5,a6,a7])\", \"description\": \"\u003cp\u003eAges in ascending order\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"range\": {\"name\": \"range\", \"group\": \"Ungrouped variables\", \"definition\": \"max(list)-min(list)\", \"description\": \"\u003cp\u003eRange\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lq\": {\"name\": \"lq\", \"group\": \"Ungrouped variables\", \"definition\": \"list[((8/4)-1)]\", \"description\": \"\u003cp\u003eLower quartile\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"uq\": {\"name\": \"uq\", \"group\": \"Ungrouped variables\", \"definition\": \"list[(((3*8)/4)-1)]\", \"description\": \"\u003cp\u003eUpper quartile\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"iqr\": {\"name\": \"iqr\", \"group\": \"Ungrouped variables\", \"definition\": \"uq-lq\", \"description\": \"\u003cp\u003eInterquartile range\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"a1\", \"a2\", \"a3\", \"a4\", \"a5\", \"a6\", \"a7\", \"list\", \"range\", \"lq\", \"uq\", \"iqr\"], \"variable_groups\": [{\"name\": \"Unnamed group\", \"variables\": []}], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"a)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eWork out the range of ages.\u003c/p\u003e\", \"minValue\": \"range\", \"maxValue\": \"range\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"b)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eWork out the interquartile range of the ages.\u003c/p\u003e\", \"minValue\": \"iqr\", \"maxValue\": \"iqr\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SM10 Estimated Mean\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eTina needs to take a train to work.\u003c/p\u003e\\n\u003cp\u003eThe table below shows information about how long the train is delayed for on each day.\u003c/p\u003e\\n\u003cp\u003eThe policy of the train company is that if your train is delayed for longer than 30 minutes, you will recieve a 50% discount on your train ticket.\u003c/p\u003e\\n\u003ctable width=\\\"294\\\" height=\\\"161\\\" style=\\\"height: 108px;\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e\u003cstrong\u003eDelay Time\u003c/strong\u003e\u003c/td\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e\u003cstrong\u003eFrequency\u0026nbsp;\u003c/strong\u003e\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e0 \u0026lt; t $\\\\leq$ 10\u003c/td\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e{f1}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e10 \u0026lt; t $\\\\leq$ 20\u003c/td\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e{f2}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e20 \u0026lt; t $\\\\leq$ 30\u003c/td\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e{f3}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e30 \u0026lt; t $\\\\leq$ 40\u003c/td\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e{f4}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e40 \u0026lt; t $\\\\leq$ 50\u003c/td\u003e\\n\u003ctd style=\\\"width: 130.5px; height: 18px;\\\"\u003e{f5}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\", \"advice\": \"\u003cp\u003e\u003cstrong\u003ea)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo find the estimated mean we must work out the midpoint of the delay time intervals and multiply this by the frequency to create the $fx$ column on the table.\u003c/p\u003e\\n\u003ctable width=\\\"294\\\" height=\\\"361\\\" style=\\\"width: 747px;\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 154.688px;\\\"\u003e\u003cstrong\u003eDelay Time\u003c/strong\u003e\u003c/td\u003e\\n\u003ctd style=\\\"width: 167px;\\\"\u003e\u003cstrong\u003eFrequency\u0026nbsp;\u003c/strong\u003e\u003c/td\u003e\\n\u003ctd style=\\\"width: 119.891px;\\\"\u003e\u003cstrong\u003eMidpoint\u003c/strong\u003e\u003c/td\u003e\\n\u003ctd style=\\\"width: 240.422px;\\\"\u003e\u003cstrong\u003eFrequency $\\\\times$ Midpoint, $fx$\u003c/strong\u003e\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 154.688px;\\\"\u003e0 \u0026lt; t $\\\\leq$ 10\u003c/td\u003e\\n\u003ctd style=\\\"width: 167px;\\\"\u003e{f1}\u003c/td\u003e\\n\u003ctd style=\\\"width: 119.891px;\\\"\u003e5\u003c/td\u003e\\n\u003ctd style=\\\"width: 240.422px;\\\"\u003e= 5$\\\\times\\\\var{f1} = \\\\var{f1m}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 154.688px;\\\"\u003e10 \u0026lt; t $\\\\leq$ 20\u003c/td\u003e\\n\u003ctd style=\\\"width: 167px;\\\"\u003e{f2}\u003c/td\u003e\\n\u003ctd style=\\\"width: 119.891px;\\\"\u003e15\u003c/td\u003e\\n\u003ctd style=\\\"width: 240.422px;\\\"\u003e= 15$\\\\times\\\\var{f2} = \\\\var{f2m}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 154.688px;\\\"\u003e20 \u0026lt; t $\\\\leq$ 30\u003c/td\u003e\\n\u003ctd style=\\\"width: 167px;\\\"\u003e{f3}\u003c/td\u003e\\n\u003ctd style=\\\"width: 119.891px;\\\"\u003e25\u003c/td\u003e\\n\u003ctd style=\\\"width: 240.422px;\\\"\u003e= 25$\\\\times\\\\var{f3} = \\\\var{f3m}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 154.688px;\\\"\u003e30 \u0026lt; t $\\\\leq$ 40\u003c/td\u003e\\n\u003ctd style=\\\"width: 167px;\\\"\u003e{f4}\u003c/td\u003e\\n\u003ctd style=\\\"width: 119.891px;\\\"\u003e35\u003c/td\u003e\\n\u003ctd style=\\\"width: 240.422px;\\\"\u003e= 35$\\\\times\\\\var{f4} = \\\\var{f4m}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 154.688px;\\\"\u003e40 \u0026lt; t $\\\\leq$ 50\u003c/td\u003e\\n\u003ctd style=\\\"width: 167px;\\\"\u003e{f5}\u003c/td\u003e\\n\u003ctd style=\\\"width: 119.891px;\\\"\u003e45\u003c/td\u003e\\n\u003ctd style=\\\"width: 240.422px;\\\"\u003e= 45$\\\\times\\\\var{f5} = \\\\var{f5m}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\\n\u003cp\u003eNow to find the mean we calculate the sum of the $fx$ column and divide it by the sum of the frequencies:\u003c/p\u003e\\n\u003cp\u003eEstimated Mean = $\\\\frac{\\\\var{f1m}+\\\\var{f2m}+\\\\var{f3m}+\\\\var{f4m}+\\\\var{f5m}}{5+15+25+35+45} = \\\\frac{\\\\var{freqmid}}{\\\\var{sum}} = \\\\var{meana}.$\u003c/p\u003e\\n\u003cp\u003eHence the estimated mean delay time is $\\\\var{mean}$ to two decimal places.\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003eb)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo work out what percentage of delays that were over 30 minutes we first need to calculate the number of days where the train was delayed for over 30 minutes.\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003eThe number of delays that over 30 minutes is $\\\\var{f4}+\\\\var{f5} = \\\\var{f4+f5}$.\u003c/p\u003e\\n\u003cp\u003eWe divide this by the total number of deliveries to find the fraction of delays that were over 30 minutes and then multiply this number by 100 to find the percentage:\u003c/p\u003e\\n\u003cp\u003e$\\\\frac{\\\\var{f4+f5}}{\\\\var{f1}+\\\\var{f2}+\\\\var{f3}+\\\\var{f4}+\\\\var{f5}} \\\\times 100\\\\% = \\\\frac{\\\\var{f4+f5}}{\\\\var{sum}} \\\\times 100\\\\% = \\\\var{percentagea} \\\\times 100\\\\%$.\u003c/p\u003e\\n\u003cp\u003eHence, the percentage of delays that were over 30 minutes is $\\\\var{percentage}\\\\%$ to two decimal places.\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ec)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eThe percentage of delays that take over 40 minutes is:\u003c/p\u003e\\n\u003cp\u003e$\\\\frac{\\\\var{f5}}{\\\\var{f1}+\\\\var{f2}+\\\\var{f3}+\\\\var{f4}+\\\\var{f5}} \\\\times 100\\\\% = \\\\frac{\\\\var{f5}}{\\\\var{sum}} \\\\times 100\\\\% = \\\\var{percent40} \\\\times 100\\\\%$, to one decimal place.\u003c/p\u003e\\n\u003cp\u003eSo, only $\\\\var{percent40}\\\\%$ of the time, delays were longer than 40 minutes so the manager would probably wanto the policy changed to 40 minutes.\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"f1\": {\"name\": \"f1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1 .. 20#1)\", \"description\": \"\u003cp\u003eFrequency 1\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"f2\": {\"name\": \"f2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1 .. 20#1)\", \"description\": \"\u003cp\u003eFrequency 2\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"f3\": {\"name\": \"f3\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1 .. 20#1)\", \"description\": \"\u003cp\u003eFrequency 3\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"f4\": {\"name\": \"f4\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1 .. 20#1)\", \"description\": \"\u003cp\u003eFrequency 4\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"f5\": {\"name\": \"f5\", \"group\": \"Ungrouped variables\", \"definition\": \"random(1 .. 5#1)\", \"description\": \"\u003cp\u003eFrequency 5\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"meana\": {\"name\": \"meana\", \"group\": \"Ungrouped variables\", \"definition\": \"freqmid/sum\", \"description\": \"\u003cp\u003eMean\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"sum\": {\"name\": \"sum\", \"group\": \"Ungrouped variables\", \"definition\": \"f1+f2+f3+f4+f5\", \"description\": \"\u003cp\u003eSum of frequencies\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"f1m\": {\"name\": \"f1m\", \"group\": \"Ungrouped variables\", \"definition\": \"5*f1\", \"description\": \"\u003cp\u003eFrequency * midpoint 1\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"f2m\": {\"name\": \"f2m\", \"group\": \"Ungrouped variables\", \"definition\": \"15*f2\", \"description\": \"\u003cp\u003eFrequency * midpoint 2\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"f3m\": {\"name\": \"f3m\", \"group\": \"Ungrouped variables\", \"definition\": \"25*f3\", \"description\": \"\u003cp\u003eFrequency * midpoint 3\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"f4m\": {\"name\": \"f4m\", \"group\": \"Ungrouped variables\", \"definition\": \"35*f4\", \"description\": \"\u003cp\u003eFrequency * midpoint 4\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"f5m\": {\"name\": \"f5m\", \"group\": \"Ungrouped variables\", \"definition\": \"45*f5\", \"description\": \"\u003cp\u003eFrequency * midpoint 5\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"freqmid\": {\"name\": \"freqmid\", \"group\": \"Ungrouped variables\", \"definition\": \"f1m+f2m+f3m+f4m+f5m\", \"description\": \"\u003cp\u003eSum of Frequency * midpoint\u0026nbsp;\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"mean\": {\"name\": \"mean\", \"group\": \"Ungrouped variables\", \"definition\": \"precround(meana,2)\", \"description\": \"\u003cp\u003eMean rounded to two decimal places\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"f30\": {\"name\": \"f30\", \"group\": \"Ungrouped variables\", \"definition\": \"f4+f5\", \"description\": \"\u003cp\u003eSum of 4th \u0026amp; 5th frequencies\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"percentagea\": {\"name\": \"percentagea\", \"group\": \"Ungrouped variables\", \"definition\": \"(f30/sum)*100\", \"description\": \"\u003cp\u003ePercentage over 30 mins\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"percentage\": {\"name\": \"percentage\", \"group\": \"Ungrouped variables\", \"definition\": \"precround(percentagea,1)\", \"description\": \"\u003cp\u003ePercentage rounded to one decimal place\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"percent40\": {\"name\": \"percent40\", \"group\": \"Ungrouped variables\", \"definition\": \"precround(((f5/sum)*100),1)\", \"description\": \"\u003cp\u003ePercentage over 40 mins\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}}, \"variablesTest\": {\"condition\": \"\", \"maxRuns\": 100}, \"ungrouped_variables\": [\"f1\", \"f2\", \"f3\", \"f4\", \"f5\", \"meana\", \"sum\", \"f1m\", \"f2m\", \"f3m\", \"f4m\", \"f5m\", \"freqmid\", \"mean\", \"f30\", \"percentagea\", \"percentage\", \"percent40\"], \"variable_groups\": [], \"functions\": {}, \"preamble\": {\"js\": \"\", \"css\": \"\"}, \"parts\": [{\"type\": \"numberentry\", \"useCustomName\": true, \"customName\": \"a)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": 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Give your answer to one decimal place.\u003c/p\u003e\", \"minValue\": \"percentage\", \"maxValue\": \"percentage\", \"correctAnswerFraction\": false, \"allowFractions\": false, \"mustBeReduced\": false, \"mustBeReducedPC\": 0, \"displayAnswer\": \"\", \"showFractionHint\": true, \"notationStyles\": [\"plain\", \"en\", \"si-en\"], \"correctAnswerStyle\": \"plain\"}, {\"type\": \"jme\", \"useCustomName\": true, \"customName\": \"c)\", \"marks\": 1, \"scripts\": {}, \"customMarkingAlgorithm\": \"\", \"extendBaseMarkingAlgorithm\": true, \"unitTests\": [], \"showCorrectAnswer\": true, \"showFeedbackIcon\": true, \"variableReplacements\": [], \"variableReplacementStrategy\": \"originalfirst\", \"nextParts\": [], \"suggestGoingBack\": false, \"adaptiveMarkingPenalty\": 0, \"exploreObjective\": null, \"prompt\": \"\u003cp\u003eThe train company propose that they should only offer the 50% discount if the train is delayed for over 40 minutes.\u003c/p\u003e\\n\u003cp\u003eIf you were the manager of the train company would you agree? Type yes or no into the box and think about the reasons for your answer.\u003c/p\u003e\", \"answer\": \"yes\", \"showPreview\": true, \"checkingType\": \"absdiff\", \"checkingAccuracy\": 0.001, \"failureRate\": 1, \"vsetRangePoints\": 5, \"vsetRange\": [0, 1], \"checkVariableNames\": false, \"singleLetterVariables\": false, \"allowUnknownFunctions\": true, \"implicitFunctionComposition\": false, \"caseSensitive\": false, \"valuegenerators\": [{\"name\": \"yes\", \"value\": \"\"}]}], \"partsMode\": \"all\", \"maxMarks\": 0, \"objectives\": [], \"penalties\": [], \"objectiveVisibility\": \"always\", \"penaltyVisibility\": \"always\"}, {\"name\": \"SM11 Linear Interpolation\", \"extensions\": [], \"custom_part_types\": [], \"resources\": [], \"navigation\": {\"allowregen\": true, \"showfrontpage\": false, \"preventleave\": false, \"typeendtoleave\": false}, \"contributors\": [{\"name\": \"Mash Sheffield\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/4679/\"}, {\"name\": \"Megan Oliver\", \"profile_url\": \"https://numbas.mathcentre.ac.uk/accounts/profile/23526/\"}], \"tags\": [], \"metadata\": {\"description\": \"\", \"licence\": \"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International\"}, \"statement\": \"\u003cp\u003eThis frequence table stores data about the lengths of some plants:\u003c/p\u003e\\n\u003ctable style=\\\"width: 285px;\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 163.625px; text-align: left;\\\"\u003e\u003cstrong\u003eLength ($x$ cm)\u003c/strong\u003e\u003c/td\u003e\\n\u003ctd style=\\\"width: 88.375px; text-align: left;\\\"\u003e\u003cstrong\u003eFrequency\u003c/strong\u003e\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 163.625px; text-align: left;\\\"\u003e10 \u0026lt; $x$ $\\\\leq$ 20\u003c/td\u003e\\n\u003ctd style=\\\"width: 88.375px; text-align: left;\\\"\u003e{f1}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 163.625px; text-align: left;\\\"\u003e20 \u0026lt; $x$ $\\\\leq$ 30\u003c/td\u003e\\n\u003ctd style=\\\"width: 88.375px; text-align: left;\\\"\u003e{f2}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 163.625px; text-align: left;\\\"\u003e30 \u0026lt; $x$ $\\\\leq$ 40\u003c/td\u003e\\n\u003ctd style=\\\"width: 88.375px; text-align: left;\\\"\u003e{f3}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr\u003e\\n\u003ctd style=\\\"width: 163.625px; text-align: left;\\\"\u003e40 \u0026lt; $x$ $\\\\leq$ 50\u003c/td\u003e\\n\u003ctd style=\\\"width: 88.375px; text-align: left;\\\"\u003e{f4}\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\", \"advice\": \"\u003cp\u003e\u003cstrong\u003ea)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo find the median we must find the middle value. To do this we sum the frequencies and divide the result by 2:\u003c/p\u003e\\n\u003cp\u003e$\\\\frac{\\\\var{f1}+\\\\var{f2}+\\\\var{f3}+\\\\var{f4}}{2} = \\\\frac{\\\\var{total}}{2} = \\\\var{middle1}$.\u003c/p\u003e\\n\u003cp\u003eHence we must find value number $\\\\var{middle1}$, we can do this by totalling the cumulative frequency in the table below.\u003c/p\u003e\\n\u003ctable style=\\\"height: 235px;\\\" width=\\\"966\\\"\u003e\\n\u003ctbody\u003e\\n\u003ctr style=\\\"height: 46px;\\\"\u003e\\n\u003ctd style=\\\"width: 176.25px; height: 14px; text-align: left;\\\"\u003e\\n\u003cp\u003e\u003cstrong\u003eLength $x$ cm\u003c/strong\u003e\u003c/p\u003e\\n\u003c/td\u003e\\n\u003ctd style=\\\"width: 165.375px; height: 14px; text-align: left;\\\"\u003e\u003cstrong\u003eFrequency\u003c/strong\u003e\u003c/td\u003e\\n\u003ctd style=\\\"width: 575.375px; height: 14px; text-align: left;\\\"\u003e\u003cstrong\u003eCumulative Frequency\u003c/strong\u003e\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 176.25px; text-align: left; height: 18px;\\\"\u003e\u003cstrong\u003e1.\u003c/strong\u003e 10 \u0026lt; $x$ $\\\\leq$ 20\u003c/td\u003e\\n\u003ctd style=\\\"width: 165.375px; height: 18px; text-align: left;\\\"\u003e{f1}\u003c/td\u003e\\n\u003ctd style=\\\"width: 575.375px; height: 18px; text-align: left;\\\"\u003e$\\\\var{f1}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 176.25px; text-align: left; height: 18px;\\\"\u003e\u003cstrong\u003e2.\u003c/strong\u003e 20 \u0026lt; $x$ $\\\\leq$ 30\u003c/td\u003e\\n\u003ctd style=\\\"width: 165.375px; height: 18px; text-align: left;\\\"\u003e{f2}\u003c/td\u003e\\n\u003ctd style=\\\"width: 575.375px; height: 18px; text-align: left;\\\"\u003e$\\\\var{f1}+\\\\var{f2}=\\\\var{cf2}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 18px;\\\"\u003e\\n\u003ctd style=\\\"width: 176.25px; text-align: left; height: 18px;\\\"\u003e\u003cstrong\u003e3.\u003c/strong\u003e 30 \u0026lt; $x$ $\\\\leq$ 40\u0026nbsp;\u003c/td\u003e\\n\u003ctd style=\\\"width: 165.375px; height: 18px; text-align: left;\\\"\u003e{f3}\u003c/td\u003e\\n\u003ctd style=\\\"width: 575.375px; height: 18px; text-align: left;\\\"\u003e$\\\\var{f1}+\\\\var{f2} +\\\\var{f3} =\\\\var{cf3}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003ctr style=\\\"height: 10px;\\\"\u003e\\n\u003ctd style=\\\"width: 176.25px; text-align: left; height: 10px;\\\"\u003e\u003cstrong\u003e4.\u003c/strong\u003e 40 \u0026lt; $x$ $\\\\leq$ 50\u003c/td\u003e\\n\u003ctd style=\\\"width: 165.375px; height: 10px; text-align: left;\\\"\u003e{f4}\u003c/td\u003e\\n\u003ctd style=\\\"width: 575.375px; height: 10px; text-align: left;\\\"\u003e$\\\\var{f1}+\\\\var{f2} +\\\\var{f3} + \\\\var{f4} =\\\\var{total}$\u003c/td\u003e\\n\u003c/tr\u003e\\n\u003c/tbody\u003e\\n\u003c/table\u003e\\n\u003cp\u003eYou can see value number $\\\\var{middle1}$ lies in interval number $\\\\var{interval1}$ hence this is the median class interval for the time taken.\u003c/p\u003e\\n\u003cp\u003eWe can estimate the median by using interpolation:\u003c/p\u003e\\n\u003cp\u003e$$\u003cbr/\u003e\\\\text{Estimate of median} = \\\\text{class start value} + \\\\frac{\\\\text{position in class}}{\\\\text{frequency in class}}\\\\times \\\\text{class width}\u003cbr/\u003e$$\u003c/p\u003e\\n\u003cp\u003eIn this case this is $\\\\var{lower1}+\\\\frac{\\\\var{middle1}-\\\\var{cf11}}{\\\\var{fint1}}\\\\times 10 =\\\\var{lower1}+\\\\var{interpolation1}=\\\\var{median1}.$\u003c/p\u003e\\n\u003cp\u003e(Note: that sometimes it is convenient to use $(\\\\var{total} + 1)/2 = \\\\var{middle2}$ as the way to work out the median position. The distinction does not really matter as this is an estimated value and often the decision is made based on which is the most convenient to calculate). This question has been written so that both answers will be marked correctly.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003eb)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo calculate the $i^{th}$ quartile ($Q_i$) we must use the following formula:\u003c/p\u003e\\n\u003cp\u003e$Q_i = l + \\\\frac{\\\\frac{iN}{4}-F}{f}\\\\times h,$\u003c/p\u003e\\n\u003cp\u003ewhere:\u003c/p\u003e\\n\u003cp\u003e$l$ = lower limit of the interval in which $Q_i$ lies;\u003c/p\u003e\\n\u003cp\u003e$N$ = Total number of observations;\u003c/p\u003e\\n\u003cp\u003e$F$ = Cumulative frequency of class previous to the $i^{th}$ quartile class;\u003cbr/\u003e\u003cbr/\u003e$f$ = Frequency of $i^{th}$ quartile class.\u003c/p\u003e\\n\u003cp\u003eSince we want to calculate the lower quartile, $i=1$.\u003c/p\u003e\\n\u003cp\u003eIf we calculate $\\\\frac{iN}{4} = \\\\frac{\\\\var{total}}{4} = \\\\var{quarter}$, we can see in the table from part \u003cstrong\u003ea)\u003c/strong\u003e that the lower quartile will be in interval number $\\\\var{intervallq}$. This means that $F = \\\\var{fprev}$ and $f = \\\\var{frequency}$.\u003c/p\u003e\\n\u003cp\u003eHence,\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003e$Q_1 = \\\\var{lowerlq} + \\\\frac{\\\\var{quarter} - \\\\var{Fprev}}{\\\\var{frequency}} \\\\times 10 = \\\\var{lowerlq} + \\\\frac{\\\\var{quarter-Fprev}}{\\\\var{frequency}} \\\\times 10 = \\\\var{lowerlq} + \\\\var{((quarter-Fprev)/frequency)*10} = \\\\var{lq}.$\u0026nbsp;\u003cbr/\u003e\u003cbr/\u003eSo, The lower quartile is $\\\\var{lqround}$ to two decimal places.\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ec)\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo calculate the upper quartile we use the same formula as in part \u003cstrong\u003eb) \u003c/strong\u003ebut this time $i=3$. So, $\\\\frac{iN}{4} = \\\\frac{\\\\var{3*total}}{4} = \\\\var{3*quarter}$, we can see in the table from part \u003cstrong\u003ea)\u003c/strong\u003e that the lower quartile will be in interval number $\\\\var{intervaluq}$. This means that $F = \\\\var{ufprev}$ and $f = \\\\var{ufrequency}$.\u003c/p\u003e\\n\u003cp\u003eHence,\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003e$Q_3 = \\\\var{upperlq} + \\\\frac{\\\\var{3*quarter} - \\\\var{uFprev}}{\\\\var{ufrequency}} \\\\times 10 = \\\\var{upperlq} + \\\\frac{\\\\var{3*quarter-uFprev}}{\\\\var{ufrequency}} \\\\times 10 = \\\\var{upperlq} + \\\\var{((3*quarter-uFprev)/ufrequency)*10} = \\\\var{uq}.$\u0026nbsp;\u003cbr/\u003e\u003cbr/\u003eSo, The lower quartile is $\\\\var{uqround}$ to two decimal places.\u003c/p\u003e\\n\u003cp\u003e\u003cstrong\u003ed)\u003c/strong\u003e\u003c/p\u003e\\n\u003cp\u003eTo calculate the interquartile range we subtract the lower quartile from the upper quartile.\u003c/p\u003e\\n\u003cp\u003eHence,\u0026nbsp;\u003c/p\u003e\\n\u003cp\u003e$IQR = Q_3 - Q_1 = \\\\var{uq}-\\\\var{lq}=\\\\var{iqr}$.\u003c/p\u003e\\n\u003cp\u003eSo the interquartile range rounded to two decimal places is $\\\\var{iqrround}$.\u003c/p\u003e\\n\u003cp\u003e\u003c/p\u003e\\n\u003cp style=\\\"text-align: center;\\\"\u003e\u003ca href=\\\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\\\" target=\\\"_blank\\\" rel=\\\"noopener\\\"\u003eUse this link to find some resources which will help you revise this topic.\u003c/a\u003e\u003c/p\u003e\", \"rulesets\": {}, \"builtin_constants\": {\"e\": true, \"pi,\\u03c0\": true, \"i\": true, \"j\": false}, \"constants\": [], \"variables\": {\"f1\": {\"name\": \"f1\", \"group\": \"Ungrouped variables\", \"definition\": \"random(4 .. 24#4)\", \"description\": \"\u003cp\u003eFrequency 1\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"f2\": {\"name\": \"f2\", \"group\": \"Ungrouped variables\", \"definition\": \"random(4 .. 24#4)\", \"description\": \"\u003cp\u003eFrequency 2\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"f3\": {\"name\": \"f3\", \"group\": \"Ungrouped variables\", \"definition\": \"random(4 .. 24#4)\", \"description\": \"\u003cp\u003eFrequency 3\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"f4\": {\"name\": \"f4\", \"group\": \"Ungrouped variables\", \"definition\": \"random(4 .. 24#4)\", \"description\": \"\u003cp\u003eFrequency 4\u003c/p\u003e\", \"templateType\": \"randrange\", \"can_override\": false}, \"median1\": {\"name\": \"median1\", \"group\": \"Part a\", \"definition\": \"lower1 + interpolation1\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"total\": {\"name\": \"total\", \"group\": \"Ungrouped variables\", \"definition\": \"f1+f2+f3+f4\", \"description\": \"\u003cp\u003eSum of frequencies\u0026nbsp;\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"middle1\": {\"name\": \"middle1\", \"group\": \"Part a\", \"definition\": \"total/2\", \"description\": \"\u003cp\u003eMiddle Value\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": true}, \"cf2\": {\"name\": \"cf2\", \"group\": \"Ungrouped variables\", \"definition\": \"f1+f2\", \"description\": \"\u003cp\u003eCumulative Frequency - first and second frequencies\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"cf3\": {\"name\": \"cf3\", \"group\": \"Ungrouped variables\", \"definition\": \"f1+f2+f3\", \"description\": \"\u003cp\u003eCumulative freqeuncy - sum of first, second, third frequencies\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lower1\": {\"name\": \"lower1\", \"group\": \"Part a\", \"definition\": \"if(interval1=1,10,if(interval1=2,20,if(interval1=3,30,if(interval1=4,40,0))))\", \"description\": \"\u003cp\u003eLower bound of interval which median sits\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"interval1\": {\"name\": \"interval1\", \"group\": \"Part a\", \"definition\": \"if(middle1\u003cf1,1,if(middle1\u003ccf2,2,if(middle1\u003ccf3,3,if(middle1\u003c=total,4,0))))\", \"description\": \"\u003cp\u003eInterval which median sits in\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lq\": {\"name\": \"lq\", \"group\": \"Part b\", \"definition\": \"rational(lowerlq + ((quarter - Fprev)/frequency) * 10)\", \"description\": \"\u003cp\u003eFormula to find lower quartile\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"intervallq\": {\"name\": \"intervallq\", \"group\": \"Part b\", \"definition\": \"if(quarter\u003c=f1,1,if(quarter\u003c=cf2,2,if(quarter\u003c=cf3,3,if(quarter\u003c=total,4,0))))\", \"description\": \"\u003cp\u003eInterval which lower quartile sits in\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"quarter\": {\"name\": \"quarter\", \"group\": \"Part b\", \"definition\": \"total/4\", \"description\": \"\u003cp\u003eQuarter value\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"fprev\": {\"name\": \"fprev\", \"group\": \"Part b\", \"definition\": \"if(intervallq=1,0,if(intervallq=2,f1,if(intervallq=3,cf2,if(intervallq=4,cf3,0))))\", \"description\": \"\u003cp\u003eCumulative frequency of class previous to one which lower quartile sits in\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"frequency\": {\"name\": \"frequency\", \"group\": \"Part b\", \"definition\": \"if(intervallq=1,f1,if(intervallq=2,f2,if(intervallq=3,f3,if(intervallq=4,f4,0))))\", \"description\": \"\u003cp\u003eFrequency of class which lower quartile sits in\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lqround\": {\"name\": \"lqround\", \"group\": \"Part b\", \"definition\": \"precround(lq,2)\", \"description\": \"\u003cp\u003eLower quartile rounded to 2 decimal places\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"uqround\": {\"name\": \"uqround\", \"group\": \"Part c\", \"definition\": \"precround(uq,2)\", \"description\": \"\u003cp\u003eUpper quartile rounded to 2 decimal places\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"uq\": {\"name\": \"uq\", \"group\": \"Part c\", \"definition\": \"rational(upperlq + (((total*0.75) - UFprev)/Ufrequency) * 10)\", \"description\": \"\u003cp\u003eUpper quartile\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"ufprev\": {\"name\": \"ufprev\", \"group\": \"Part c\", \"definition\": \"if(intervaluq=1,0,if(intervaluq=2,f1,if(intervaluq=3,cf2,if(intervaluq=4,cf3,0))))\", \"description\": \"\u003cp\u003ecumulative frequency of class previous to the one which the upper quartile sits in\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"ufrequency\": {\"name\": \"ufrequency\", \"group\": \"Part c\", \"definition\": \"if(intervaluq=1,f1,if(intervaluq=2,f2,if(intervaluq=3,f3,if(intervaluq=4,f4,0))))\", \"description\": \"\u003cp\u003eFrequency of class upper quartile sits in\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"intervaluq\": {\"name\": \"intervaluq\", \"group\": \"Part c\", \"definition\": \"if(3*quarter\u003c=f1,1,if(3*quarter\u003c=cf2,2,if(3*quarter\u003c=cf3,3,if(3*quarter\u003c=total,4,0))))\", \"description\": \"\u003cp\u003eclass which upper quartile sits in\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"iqr\": {\"name\": \"iqr\", \"group\": \"Part d\", \"definition\": \"rational(uq-lq)\", \"description\": \"\u003cp\u003eInterquartile range\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"lowerlq\": {\"name\": \"lowerlq\", \"group\": \"Part b\", \"definition\": \"if(intervallq=1,10,if(intervallq=2,20,if(intervallq=3,30,if(intervallq=4,40,0))))\", \"description\": \"\u003cp\u003ewidth of class which lower quartile sits in\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"upperlq\": {\"name\": \"upperlq\", \"group\": \"Part c\", \"definition\": \"if(intervaluq=1,10,if(intervaluq=2,20,if(intervaluq=3,30,if(intervaluq=4,40,0))))\", \"description\": \"\u003cp\u003ewidth of class upper quartile sits in\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"iqrround\": {\"name\": \"iqrround\", \"group\": \"Part d\", \"definition\": \"precround(iqr,2)\", \"description\": \"\u003cp\u003eRound interquartle range to two decimal places\u003c/p\u003e\", \"templateType\": \"anything\", \"can_override\": false}, \"interpolation1\": {\"name\": \"interpolation1\", \"group\": \"Part a\", \"definition\": \"if(middle1\u003cf1,((middle1-0)/f1)*10,if(middle1\u003ccf2,((middle1-f1)/f2)*10,if(middle1\u003ccf3,((middle1-cf2)/f3)*10,if(middle1\u003c=total,((middle1-cf3)/f4)*10,0))))\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"median2\": {\"name\": \"median2\", \"group\": \"Part a\", \"definition\": \"lower2 + interpolation2\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"middle2\": {\"name\": \"middle2\", \"group\": \"Part a\", \"definition\": \"(total+1)/2\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"interval2\": {\"name\": \"interval2\", \"group\": \"Part a\", \"definition\": \"if(middle2\u003cf1,1,if(middle2\u003ccf2,2,if(middle2\u003ccf3,3,if(middle2\u003c=total,4,0))))\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"lower2\": {\"name\": \"lower2\", \"group\": \"Part a\", \"definition\": \"if(interval2=1,10,if(interval2=2,20,if(interval2=3,30,if(interval2=4,40,0))))\", \"description\": \"\", \"templateType\": \"anything\", \"can_override\": false}, \"interpolation2\": {\"name\": \"interpolation2\", \"group\": \"Part a\", \"definition\": 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</dialog>
<dialog class="modal" id="confirm-end-exam-modal" aria-labelledby="confirm-end-exam-modal-title" aria-describedby="confirm-end-exam-modal-body" data-bind="modal: {submit: $root.modal.ok, cancel: $root.modal.cancel}">
    <form method="dialog">
        <header>
            <h4 id="confirm-end-exam-modal-title" data-localise="modal.confirm"></h4>
        </header>
        <div class="modal-body" id="confirm-end-exam-modal-body" data-bind="with: $root.exam">
            <p id="confirm-end-exam-modal-message"></p>
            <form class="form-inline" data-bind="submit: $root.modal.ok">
                <label for="confirm-end-text-input" id="confirm-end-exam-modal-input-message"></label>
                <input autofocus id="confirm-end-text-input" type="text" data-bind="textInput: confirmEndHandler.value, autosize: confirmEndHandler.value">
                <span class="password-feedback feedback-icon" data-bind="css: confirmEndHandler.feedback().iconClass, attr: {title: confirmEndHandler.feedback().title}"></span>
            </form>
        </div>
        <footer>
            <button value="cancel" class="cancel btn" data-localise="modal.cancel"></button>
            <button value="ok" class="ok btn primary" data-bind="disable: !confirmEndHandler.valid(), css: confirmEndHandler.feedback().buttonClass" data-localise="modal.end exam button"></button>
        </footer>
    </form>
</dialog>
<dialog class="modal force-default-style" id="style-modal" aria-labelledby="style-modal-title" aria-describedby="style-modal-explanation" data-bind="with: $root.style_customiser, modal: {submit: $root.saveStyle}">
    <form method="dialog">
        <header>
            <h4 id="style-modal-title" data-localise="control.style options"></h4>
        </header>

        
        <p class="help-block" id="style-modal-explanation" data-localise="modal.style.explanation"></p>

        <p class="help-block warning" data-bind="visible: forced_colors" data-localise="modal.forced colours warning"></p>

        
        <section class="style-controls">
            <fieldset>
                <label for="main-font-picker" data-localise="modal.style.main font"></label>
                <select id="main-font-picker" data-bind="value: staged_style['--main-font'], options: font_options, optionsText: 'label', optionsValue: 'name'">
                </select>
            </fieldset>
            <fieldset>
                <label for="text-size-picker" data-localise="modal.style.text size"></label>
                <input id="text-size-picker" type="number" step="0.1" min="0.5" max="4" data-bind="value: staged_style['--text-size']">
                <output id="text-size-preview" class="big" data-localise="modal.style.text preview"></output>
            </fieldset>
            <fieldset>
                <label for="font-weight-picker" data-localise="modal.style.font weight"></label>
                <input id="font-weight-picker" type="range" step="100" min="200" max="800" data-bind="value: staged_style['--font-weight'], valueUpdate: 'input'">
                <output id="font-weight-preview" data-bind="text: staged_style['--font-weight']"></output>
            </fieldset>
            <fieldset>
                <label for="spacing-picker" data-localise="modal.style.spacing"></label>
                <input id="spacing-picker" type="range" step="0.1" min="0.1" max="3" data-bind="value: staged_style['--spacing-scale'], valueUpdate: 'input'">
                <output id="spacing-preview" data-bind="percentage: parseFloat(staged_style['--spacing-scale']())"></output>
            </fieldset>
            <fieldset>
                <label for="color-scheme-picker" data-localise="modal.style.colour scheme"></label>
                <select id="color-scheme-picker" data-bind="value: color_scheme">
                    <option value="automatic" data-localise="modal.style.automatic colour scheme"></option>
                    <option value="light" data-localise="modal.style.light colour scheme"></option>
                    <option value="dark" data-localise="modal.style.dark colour scheme"></option>
                    <option value="custom" data-localise="modal.style.custom colour scheme"></option>
                </select>
            </fieldset>
            <fieldset>
                <label for="invert-images" data-localise="modal.style.invert images in dark mode"></label>
                <input id="invert-images" type="checkbox" data-bind="checked: invert_images">
            </fieldset>
        </section>

        <section class="style-controls" data-bind="visible: using_custom_color_scheme">
            <fieldset>
                <label for="background-colour-picker" data-localise="modal.style.background colour"></label>
                <input id="background-colour-picker" type="color" data-bind="value: style['--custom-background-color']">
            </fieldset>
            <fieldset>
                <label for="text-colour-picker" data-localise="modal.style.text colour"></label>
                <input id="text-colour-picker" type="color" data-bind="value: style['--custom-text-color']">
            </fieldset>
            <fieldset>
                <label for="main-colour-picker" data-localise="modal.style.main colour"></label>
                <input id="main-colour-picker" type="color" data-bind="value: style['--custom-main-color']">
            </fieldset>
            <fieldset>
                <label for="primary-colour-picker" data-localise="modal.style.primary colour"></label>
                <input id="primary-colour-picker" type="color" data-bind="value: style['--custom-primary-color']">
            </fieldset>
            <fieldset>
                <label for="link-colour-picker" data-localise="modal.style.link colour"></label>
                <input id="link-colour-picker" type="color" data-bind="value: style['--custom-link-color']">
            </fieldset>
            <fieldset>
                <label for="success-colour-picker" data-localise="modal.style.success colour"></label>
                <input id="success-colour-picker" type="color" data-bind="value: style['--custom-success-color']">
            </fieldset>
            <fieldset>
                <label for="info-colour-picker" data-localise="modal.style.info colour"></label>
                <input id="info-colour-picker" type="color" data-bind="value: style['--custom-info-color']">
            </fieldset>
            <fieldset>
                <label for="warning-colour-picker" data-localise="modal.style.warning colour"></label>
                <input id="warning-colour-picker" type="color" data-bind="value: style['--custom-warning-color']">
            </fieldset>
            <fieldset>
                <label for="danger-colour-picker" data-localise="modal.style.danger colour"></label>
                <input id="danger-colour-picker" type="color" data-bind="value: style['--custom-danger-color']">
            </fieldset>
            <fieldset>
                <label for="muted-colour-picker" data-localise="modal.style.muted colour"></label>
                <input id="muted-colour-picker" type="color" data-bind="value: style['--custom-muted-color']">
            </fieldset>
            <fieldset>
                <label for="highlight-colour-picker" data-localise="modal.style.highlight colour"></label>
                <input id="highlight-colour-picker" type="color" data-bind="value: style['--custom-highlight-color']">
            </fieldset>
        </section>

        

        

        
        <hr/>
        <p class="help-block"><a href="https://docs.numbas.org.uk/en/latest/accessibility/exam.html" target="_blank" data-localise="accessibility statement"></a></p>
        

        <footer>
            <button type="button" class="btn danger sm" data-localise="modal.style.reset to defaults" data-bind="click: reset"></button>
            <button class="cancel btn" value="cancel" autofocus data-localise="modal.cancel"></button>
            <button value="ok" class="ok btn primary" data-localise="modal.ok"></button>
        </footer>
    </form>
</dialog>
<dialog class="modal" id="next-actions-modal" aria-labelledby="next-actions-modal-title">
    <form method="dialog" data-bind="with: diagnostic_next_actions">
        <header>
            <h4 id="next-actions-modal-title" data-localise="diagnostic.make a choice"></h4>
        </header>
        <div data-bind="latex: feedback"></div>

        <menu data-bind="foreach: actions" class="list-unstyled actions">
            <li>
                <button type="button" data-bind="click: go"><span data-bind="latex: label"></span></button>
            </li>
        </menu>
    </form>
</dialog>

<dialog id="lightbox"></dialog>
        <div id="everything">
            <a class="sr-only" id="skip-link" data-bind="attr: {href: infoPage() ? '#infoDisplay' : '#questionContainer'}" data-localise="page.skip to content"></a>
            <!-- ko if: exam.settings.navigateMode=='sequence' -->
    <!-- side menu, slides out on narrow screens -->
<nav id="sideNav">

    <header>
        <img class="logo center-block" src="resources/numbas-logo.svg" alt="Numbas"/>

        <h1 class="exam-name" data-bind="text: exam.settings.name, typeset: exam.settings.name"></h1>

        <button type="button" class="navbar-toggle btn" aria-controls="navMenu">
            <svg viewBox="0 0 9 9">
    <title data-localise="control.toggle navigation menu"></title>
    <line x1="1" y1="1" x2="8" y2="8" stroke="currentColor"/>
    <line x1="1" y1="8" x2="8" y2="1" stroke="currentColor"/>
</svg>
        </button>
    </header>

    <!-- ko if: numQuestions() > 1 -->
    <label class="sr-only" for="exam-progress" data-localise="exam.progress"></label>
    <progress id="exam-progress" data-bind="attr: {max: numQuestions(), value: questionsAttempted(), title: questionsAttemptedDisplay}, text: questionsAttemptedDisplay"></progress>
    <!-- /ko -->

    <menu id="questionList" class="nav navmenu-nav" role="tablist" aria-orientation="vertical" data-bind="tablist: true">
        <li class="introduction" data-bind="visible: exam.hasIntro, css: {active: $root.exam().infoPage()=='introduction'}">
            <a href="#" role="tab" data-bind="click: () => showInfoPage('introduction'), attr: {'aria-current': $root.exam().infoPage()=='introduction' ? 'step' : false, tabindex: $root.exam().infoPage()=='introduction' ? 0 : -1, 'data-name': R('control.show introduction')}" data-localise="control.show introduction"></a>
       </li>
        <!-- ko foreach: question_groups -->
            <!-- ko if: $root.exam().showQuestionGroupNames -->
            <li class="question-group-header" data-bind="visible: show_name">
                <h2 data-bind="text: name, typeset: name"></h2>
                <span class="score" data-bind="html: feedback.message"></span>
            </li>
            <!-- /ko -->
            <!-- ko foreach: questions -->
            <li class="questionSelector" data-bind="visible: visible, css: {active: $root.exam().currentQuestion()==$data}">
                <a href="#" role="tab" data-bind="click: Numbas.controls.makeQuestionJumper(question.number, question.exam), attr: {'aria-current': isCurrentQuestion() ? 'step' : false, tabindex: isCurrentQuestion() ? 0 : -1, 'data-number': question.number+1, 'data-name': displayName}">
                    <div class="question-info">
                        <span class="feedback-icon" data-bind="css: scoreFeedback.iconClass, attr: scoreFeedback.iconAttr" aria-hidden="true"></span>
                        <span class="name" data-bind="text: displayName"></span>
                        <span class="sr-only" data-bind="text: scoreFeedback.iconAttr().title"></span>
                        <span class="score" data-bind="html: scoreFeedback.message"></span>
                    </div>
                    <div class="messages">
                        <div class="answered-state" data-bind="">
                            <span data-bind="text: scoreFeedback.answeredString"></span>
                        </div>
                        <div data-bind="visible: isDirty" class="dirty-message">
                            <span class="warning-icon icon-exclamation-sign"></span>
                            <span data-localise="question.selector.unsubmitted changes"></span>
                        </div>
                    </div>
                </a>
            </li>
            <!-- /ko -->
        <!-- /ko -->
        <!-- total exam score display -->
        <li class="examScore" data-bind="visible: showActualMark">
            <span data-localise="control.total"></span> 
            <span id="examScore" data-bind="html: examScoreDisplay"></span>
        </li>
    </menu>

    <div class="stopWatch" data-bind="visible: showTime">
    <span class="" data-localise="timing.time remaining"></span>
    <time class="time" data-bind="duration: timeRemaining"></time>
</div>

    <menu class="nav navmenu-nav menuButtons">
        <li><button class="btn center-block thin-button display-options force-original-color" type="button" data-bind="click: $root.showStyleModal" data-localise="control.style options"></button></li>
        <li data-bind="visible: allowPause && mode()=='normal'"><button class="btn center-block thin-button" id="pauseBtn" data-localise="control.pause" data-bind="click: pause"></button></li>
        <li data-bind="visible: mode()=='normal'"><button class="btn danger center-block" id="endBtn" data-localise="control.end exam" data-bind="click: endExam"></button></li>
        <li data-bind="visible: mode()=='review'"><button class="btn center-block" data-localise="control.back to results" data-bind="click: () => showInfoPage('result')"></button></li>
    </menu>

</nav>

<!-- top menu shown on narrow screens -->
<nav id="topNav" class="navbar">
    <!-- ko if: numQuestions() > 1 -->
    <div class="prev"><button type="button" class="btn" data-bind="click: reverse, attr: {disabled: !canReverse()}"><span class="sr-only" data-localise="control.previous"></span>&larr;</button></div>
    <div class="next"><button type="button" class="btn" data-bind="click: advance, attr: {disabled: !canAdvance()}"><span class="sr-only" data-localise="control.next"></span>&rarr;</span></button></div>
    <!-- /ko -->
    <div class="end"><button class="btn danger" data-localise="control.end exam" data-bind="click: endExam, visible: mode()=='normal' && !canAdvance()"></button></div>
    <div class="titleBits" data-bind="with: currentQuestion">
        <span class="review-header" data-bind="visible: $root.exam().mode()=='review'" data-localise="exam.review header"></span>
        <span id="questionNameDisplay" data-bind="text: displayName"></span>
    </div>

    <div class="stopWatch" data-bind="visible: showTime">
    <span class="" data-localise="timing.time remaining"></span>
    <time class="time" data-bind="duration: timeRemaining"></time>
</div>

    <button type="button" class="navbar-toggle btn" aria-controls="navMenu">
        <svg viewBox="0 0 9 9">
    <title data-localise="control.toggle navigation menu"></title>
    <rect x="0" y="0" width="9" height="1" fill="currentColor"/>
    <rect x="0" y="4" width="9" height="1" fill="currentColor"/>
    <rect x="0" y="8" width="9" height="1" fill="currentColor"/>
</svg>
    </button>
</nav>
<!-- /ko -->

<!-- ko if: exam.settings.navigateMode=='menu' -->
    <nav id="topNav" class="navbar">
    <button type="button" class="btn primary" data-bind="visible: mode()=='normal', click: showMenu">&larr; <span data-localise="control.back to menu"></span></button>
    <button type="button" class="btn primary" data-bind="visible: mode()=='review', click: () => showInfoPage('result')">&larr; <span data-localise="control.back to results"></span></button>
    <div class="titleBits" data-bind="with: currentQuestion">
        <span class="review-header" data-bind="visible: $root.exam().mode()=='review'" data-localise="exam.review header"></span>
        <span id="questionNameDisplay" data-bind="latex: displayName"></span>
    </div>
    <button class="btn thin-button display-options force-original-color" type="button" data-bind="click: $root.showStyleModal" data-localise="control.style options"></button>
</nav>
<!-- /ko -->

<!-- ko if: exam.settings.navigateMode=='diagnostic' -->
    <!-- side menu, slides out on narrow screens -->
<nav id="sideNav">

    <header>
        <div class="navmenu-brand">
            <img class="logo center-block" src="resources/numbas-logo.svg" alt="Numbas"/>
        </div>
        <h1 class="exam-name navmenu-brand" data-bind="text: exam.settings.name, typeset: exam.settings.name"></h1>
        <button type="button" class="navbar-toggle btn" aria-controls="navMenu">
            <svg viewBox="0 0 9 9">
    <title data-localise="control.toggle navigation menu"></title>
    <line x1="1" y1="1" x2="8" y2="8" stroke="currentColor"/>
    <line x1="1" y1="8" x2="8" y2="1" stroke="currentColor"/>
</svg>
        </button>
    </header>

    <dl id="learning-objective-list" class="nav navemnu-nav">
        <!-- ko foreach: diagnostic_progress -->
        <dt class="name" data-bind="latex: name"></dt>
        <dd data-bind="text: Math.floor(100*progress)+'%'"></dd>
        <!-- /ko -->
    </dl>


    <div class="stopWatch" data-bind="visible: showTime">
    <span class="" data-localise="timing.time remaining"></span>
    <time class="time" data-bind="duration: timeRemaining"></time>
</div>

    <menu class="nav navmenu-nav menuButtons">
        <li><button class="btn center-block thin-button display-options force-original-color" type="button" data-bind="click: $root.showStyleModal" data-localise="control.style options"></button></li>
        <li data-bind="visible: allowPause && mode()=='normal'"><button class="btn center-block thin-button" id="pauseBtn" data-localise="control.pause" data-bind="click: pause"></button></li>
        <li data-bind="visible: mode()=='normal'"><button class="btn danger center-block" id="endBtn" data-localise="control.end exam" data-bind="click: endExam"></button></li>
        <li data-bind="visible: mode()=='review'"><button class="btn center-block" data-localise="control.back to results" data-bind="click: () => showInfoPage('result')"></button></li>
    </menu>

</nav>

<!-- top menu shown on narrow screens -->
<nav id="topNav" class="navbar">
    <div class="nav">
        <div class="titleBits" data-bind="with: currentQuestion">
            <span class="review-header" data-bind="visible: $root.exam().mode()=='review'" data-localise="exam.review header"></span>
            <span id="questionNameDisplay" data-bind="text: displayName"></span>
        </div>

        <div class="stopWatch" data-bind="visible: showTime">
    <span class="" data-localise="timing.time remaining"></span>
    <time class="time" data-bind="duration: timeRemaining"></time>
</div>
    </div>

    <button type="button" class="navbar-toggle btn" aria-controls="navMenu">
        <svg viewBox="0 0 9 9">
    <title data-localise="control.toggle navigation menu"></title>
    <rect x="0" y="0" width="9" height="1" fill="currentColor"/>
    <rect x="0" y="4" width="9" height="1" fill="currentColor"/>
    <rect x="0" y="8" width="9" height="1" fill="currentColor"/>
</svg>
    </button>
</nav>
<!-- /ko -->

            <!-- main content area - info pages or questions go in here -->
            <main class="mainDisplay" role="main" data-bind="attr: {'aria-labelledby': main_labelledby}">
                <div id="infoDisplay" class="main-content" data-bind="visible: infoPage">
    <div id="frontpage" data-bind="visible: infoPage()=='frontpage', if: infoPage()=='frontpage'">
        <h1 class="break-words" id="infopage-frontpage-header" data-bind="html: exam.settings.name"></h1>
<table class="summary">
    <tbody>
    <!-- ko if: exam.settings.navigateMode != 'diagnostic' -->
    <tr>
        <th data-localise="exam.number of questions"></th>
        <td class="rtd" data-bind="html: numAssessedQuestions"></td>
    </tr>
    <tr data-bind="visible: exam.settings.showTotalMark">
        <th data-localise="exam.marks available"></th>
        <td class="rtd" data-bind="niceNumber: marks"></td>
    </tr>
    <!-- /ko -->
    <tr data-bind="visible: exam.settings.percentPass>0">
        <th data-localise="exam.pass percentage"></th>
        <td class="rtd" data-bind="text: percentPass"></td>
    </tr>
    <tr data-bind="visible: duration()>0">
        <th data-localise="exam.time allowed"></th>
        <td class="rtd"><time data-bind="duration: duration"></time></td>
    </tr>
    <tr data-bind="visible: exam.settings.showStudentName && exam.student_name && !needsStudentName">
        <th data-localise="exam.student name"></th>
        <td><span data-bind="text: exam.student_name"></span><span data-bind="visible: exam.student_id"> (<span data-bind="text: exam.student_id"></span>)</span></td>
    </tr>
    </tbody>
</table>

<div id="intro" data-bind="visible: exam.hasIntro, latex: exam.introMessage" localise-data-jme-context-description="exam.introduction"></div>

<div class="alert danger" data-bind="visible: showAttemptDownloadSecurityWarning">
    <p data-localise="exam.attempt download security warning"></p>
</div>
<div id="standalone-warning" class="alert info" data-bind="visible: !Numbas.storage.lmsConnected && !allowAttemptDownload" data-localise="frontpage.scorm.lms not connected"></div>

<form data-bind="submit: beginExam" class="info-buttons">
    <button class="btn display-options force-original-color" type="button" data-bind="click: $root.showStyleModal" data-localise="control.style options"></button>
    <div class="student-name" data-bind="visible: needsStudentName">
        <label for="begin-exam-student-name" data-localise="exam.enter your name"></label>
        <input id="begin-exam-student-name" name="begin-exam-student-name" type="text" data-bind="textInput: student_name, autosize: student_name"/>
    </div>
    <div class="password" data-bind="visible: needsPassword">
        <label for="begin-exam-password" data-localise="exam.enter password"></label>
        <input id="begin-exam-password" autocomplete="off" name="begin-exam-password" type="text" data-bind="textInput: passwordHandler.value, autosize: passwordHandler.value, css: {'has-errors': passwordHandler.value().length && !passwordHandler.valid(), 'success': passwordHandler.valid()}"/>
        <span class="password-feedback feedback-icon" data-bind="css: passwordHandler.feedback().iconClass, attr: {title: passwordHandler.feedback().title}"></span>
    </div>
    <button class="btn" id="startBtn" type="submit" data-bind="disable: !canBegin(), css: passwordHandler.feedback().buttonClass" data-localise="frontpage.start"></button>
</form>
    </div>
    <div id="menu" data-bind="visible: infoPage()=='menu', if: infoPage()=='menu'">
        <h1 id="infopage-menu-header" class="break-words" data-bind="html: exam.settings.name"></h1>

<div class="intro" class="alert" data-bind="visible: exam.hasIntro, latex: exam.introMessage" localise-data-jme-context-description="exam.introduction"></div>

<nav id="question-chooser">
    <table class="table questionSelector">
        <colgroup>
            <col class="question">
            <col class="score">
            <col class="icon">
        </colgroup>
        <tbody>
        <!-- ko foreach: question_groups -->
            <!-- ko if: $parent.showQuestionGroupNames -->
            <tr>
                <th data-bind="visible: $parent.question_groups.length>1">
                    <span data-bind="latex: name"></span>
                </th>
                <th class="messages">
                    <span class="score" data-bind="html: feedback.plainMessage"></span>
                </th>
                <th class="icon">
                    <span class="feedback-icon" data-bind="css: feedback.iconClass, attr: feedback.iconAttr" aria-hidden="true"></span>
                </th>
            </tr>
            <!-- /ko -->
            <!-- ko foreach: questions -->
            <tr class="" role="button" data-bind="click: Numbas.controls.makeQuestionJumper(question.number, question.exam), attr: {'aria-labelledby': question.path+'-menu-name'}">
                <td class="info">
                    <button class="btn link" type="button" class="name" data-bind="latex: displayName, attr: {id: question.path+'-menu-name'}"></button>
                </td>
                <td class="messages">
                    <span class="sr-only" data-bind="text: scoreFeedback.iconAttr().title"></span>
                    <span class="score" data-bind="html: scoreFeedback.plainMessage"></span>
                    <div class="answered-state" data-bind="">
                        <span data-bind="text: scoreFeedback.attemptedString"></span>
                    </div>
                    <div data-bind="visible: isDirty" class="dirty-message">
                        <span class="warning-icon icon-exclamation-sign"></span>
                        <span data-localise="question.selector.unsubmitted changes"></span>
                    </div>
                </td>
                <td class="icon">
                    <span class="feedback-icon" data-bind="css: scoreFeedback.iconClass, attr: scoreFeedback.iconAttr" aria-hidden="true"></span>
                </td>
            </tr>
            <!-- /ko -->
        <!-- /ko -->
        </tbody>
    </table>
</nav>

<menu class="nav navmenu-nav menuButtons">
    <li><button class="btn thin-button" type="button" data-bind="click: $root.showStyleModal" data-localise="control.style options"></button></li>
    <li><button class="btn danger thin-button" id="endBtn" data-localise="control.end exam" data-bind="click: endExam"></button></li>
</menu>
    </div>
    <div id="introduction" data-bind="visible: infoPage()=='introduction', if: infoPage()=='introduction'">
        <h1 id="infopage-introduction-header" data-localise="exam.introduction"></h1>
<div data-bind="latex: exam.introMessage" localise-data-jme-context-description="exam.introduction"></div>
    </div>
    <div id="suspend" data-bind="visible: infoPage()=='paused' || infoPage()=='resumed', if: infoPage()=='paused' || infoPage()=='resumed'">
        <h1 id="infopage-suspend-header">
    <span data-bind="visible: infoPage()=='paused'" data-localise="suspend.paused header" ></span>
    <span data-bind="visible: infoPage()=='resumed'" data-localise="suspend.resumed header" ></span>
</h1>
<p data-localise="suspend.exam suspended"></p>
<p data-localise="suspend.you can resume"></p>
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            <numbas-exam storage="scorm">
                <script type="application/numbas-exam">// Numbas version: finer_feedback_settings
{"name": "MGTT170 2025/26", "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], []], "questions": [{"name": "AC16 Rearrange Formulae", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Luigi Pivano", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18182/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Rearrange a specific formula. No randomisation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Rearrange the following equation, to make $y$ the subject:</p>\n<p>\\[{cy -b = 3x}\\]&nbsp;</p>", "advice": "<p>In order to rearrange the equation so that it is in terms of $y$, we must first add $b$ to both sides, and then divide both sides of the equation by $c$:</p>\n<p>\\begin{split} cy-b&nbsp; &amp;= 3x \\\\ cy &amp;= 3x + b \\\\ y &amp;=\\frac{3x+b}{c} \\end{split}</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Rearranging\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$y=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "(3x+b)/c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "b", "value": ""}, {"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "AC19 Cancelling algebraic fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Luke Park", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/826/"}, {"name": "Anna Strzelecka", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2945/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "<p>A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Simplify the following algebraic expression.<em></em></p>", "advice": "<p>\\[\\frac{{\\simplify{(n^2+({e1}+{e2})n+{e1}{e2})}}}{{\\simplify{(n^2+({e1}+{e3})n+{e1}{e3})}}}\\]</p>\n<p>In this question there is a quadratic expression which needs to be factorised into the products of binomials in both the numerator and denominator.</p>\n<p>\\[\\frac{({\\simplify{n+{e1}}})({\\simplify{n+{e2}}})}{({\\simplify{n+{e1}}})({\\simplify{n+{e3}}})}\\]</p>\n<p>The repeated binomials in the numerator and denominator cancel, leaving:</p>\n<p>\\[\\frac{({\\simplify{n+{e2}}})}{({\\simplify{n+{e3}}})}\\]</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#AlgFrac\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"e2": {"name": "e2", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "e1": {"name": "e1", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "e3": {"name": "e3", "group": "Ungrouped variables", "definition": "random(-5..5 except 0 except e2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["e1", "e2", "e3"], "variable_groups": [], "functions": {"": {"parameters": [], "type": "number", "language": "jme", "definition": ""}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\[\\frac{\\simplify{(n^2+({e1}+{e2})n+{e1}{e2})}}{\\simplify{(n^2+({e1}+{e3})n+{e1}{e3})}}\\]</p>", "answer": "(n+{e2})/(n+{e3})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": ["^2", "^"], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": [{"name": "n", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "AF01 Sigma Notation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "<p>Basic calculation from a sum given in Sigma notation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate:</p>\n<p>\\[\\displaystyle{\\Sigma_{n=1}^3} \\var{b}n.\\]</p>\n<p></p>", "advice": "<p>The sigma notation $\\displaystyle<span class=\"enlighter-k0\">\\sum_</span><span class=\"enlighter-g1\">{</span><span class=\"enlighter-text\">n=</span><span class=\"enlighter-n1\">1</span><span class=\"enlighter-g1\">}</span><span class=\"enlighter-text\">^</span><span class=\"enlighter-g1\">{</span><span class=\"enlighter-k0\">3</span><span class=\"enlighter-g1\">}\\var{b}n$ is asking us to find the </span>sum of the first three terms of the sequence $\\var{b}n$<span class=\"enlighter-g1\">.&nbsp;</span></p>\n<p>\\[\\begin{split}\\Sigma_{n=1}^3 \\var{b}n &amp;\\, = (\\var{b}\\times 1) + (\\var{b}\\times 2) + (\\var{b}\\times 3) \\\\ &amp;\\, = \\var{b1} + \\var{b2} + \\var{b3} \\\\ &amp;\\, = \\var{sum}.\\end{split}\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Sigma\" target=\"_blank\" rel=\"noopener\">Use this link to find resources to help you revise sigma notation.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2 .. 9#1)", "description": "", "templateType": "randrange", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "b*1", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "b*2", "description": "", "templateType": "anything", "can_override": false}, "b3": {"name": "b3", "group": "Ungrouped variables", "definition": "b*3", "description": "", "templateType": "anything", "can_override": false}, "sum": {"name": "sum", "group": "Ungrouped variables", "definition": "b1+b2+b3", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["b", "b1", "b2", "b3", "sum"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sum}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "AF02 Straight Line Graphs", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "<p>Calculating gradient and finding intercept from a geogebra graph.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>{app}<br/>Find the gradient of the line.<br/><br/><br/></p>", "advice": "<p>Firstly draw a right angled 'step' from left to right. This triangle can be anywhere, but it is more helpful for it to have corners on the vertices (whole number points) of the graph and it is easier to calculate with postive numbers.</p>\n<p>{app_advice}</p>\n<p>Before we start to calculate, notice that the line is {uod}, so the gradient will be {pon} and the line is {sos}, so the absolute value of the number will be {mol}.<br/><br/>Now find the coordinates of the places your triangle meets the line</p>\n<p>$(x_1,y_1)=(\\var{ax},\\var{ay})$ and $(x_2,y_2)=(\\var{bx},\\var{by})$</p>\n<p>We need to compare the 'rise on the y-axis' to the 'run across the x-axis', we can say that:</p>\n<p>$\\text{gradient} = \\frac{\\text{rise}}{\\text{run}}$</p>\n<p>This is equivalent to using the formula:<br/><br/>$&nbsp; m = \\frac{y_2 - y_1}{x_2 - x_1} $</p>\n<p>and substitute the coordinates of the vertices of the triangle:<br/><br/>$\\begin{split} &amp;\\, m = \\frac{\\var{by} - \\var{ay}}{\\var{bx} - \\var{ax}} \\\\ &nbsp;<br/>&amp;\\, = \\frac{\\var{by-ay}}{\\var{bx-ax}} \\\\&nbsp;<br/>&amp;\\, &nbsp;= \\var[fractionNumbers]{m} \\\\<br/>\\end{split} $</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Lines\" target=\"_blank\" rel=\"noopener\">Use this link to find resources to help you revise straight line graphs and how to find the gradient of them.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"app": {"name": "app", "group": "Ungrouped variables", "definition": "geogebra_applet(\n  800,500,\n  [\n    A: [\n      definition: p1,\n      label_visible: false,\n      visible: false\n    ],\n    B: [\n      definition: p2,\n      label_visible: false,\n      visible: false      \n    ],\n    line: [\n      definition: \"Line(A,B)\",\n      label_visible: false\n    ]\n  ]\n)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "(ay-by)/(ax-bx)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "ay-m*ax", "description": "", "templateType": "anything", "can_override": false}, "P1": {"name": "P1", "group": "Ungrouped variables", "definition": "vector(ax, ay)", "description": "", "templateType": "anything", "can_override": false}, "P2": {"name": "P2", "group": "Ungrouped variables", "definition": "vector(bx,by)", "description": "", "templateType": "anything", "can_override": false}, "uod": {"name": "uod", "group": "Ungrouped variables", "definition": "if(m=0,'horizontal',if(m=abs(m),'going up','going down'))", "description": "<p>if(m=abs(m),'positive','negative')</p>", "templateType": "anything", "can_override": false}, "ax": {"name": "ax", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "ay": {"name": "ay", "group": "Ungrouped variables", "definition": "random(0,1,2,3)", "description": "", "templateType": "anything", "can_override": false}, "bx": {"name": "bx", "group": "Ungrouped variables", "definition": "random(ax+1..3) \n", "description": "", "templateType": "anything", "can_override": false}, "by": {"name": "by", "group": "Ungrouped variables", "definition": "random(0..4 except ay)\n", "description": "", "templateType": "anything", "can_override": false}, "app_advice": {"name": "app_advice", "group": "Ungrouped variables", "definition": "geogebra_applet(\n  800,500,\n  [\n    A: [\n      definition: p1,\n      label_visible: false,\n      visible: true\n    ],\n    B: [\n      definition: p2,\n      label_visible: false,\n      visible: true      \n    ],\n    \n    C: [\n      definition: p3,\n      label_visible: false,\n      visible: false      \n    ],\n    \n    line1: [\n      definition: \"Line(A,B)\",\n      label_visible: false,\n      visible: true\n    ],\n    \n    line2: [\n      definition: \"Segment(A,C)\",\n      label_visible: false,\n      visible: true\n    ],\n    \n   \n    \n    line3: [\n      definition: \"Segment(C,B)\",\n      label_visible: false,\n      visible: true\n    ]\n  ]\n)", "description": "", "templateType": "anything", "can_override": false}, "p3": {"name": "p3", "group": "Ungrouped variables", "definition": "vector(bx,ay)", "description": "", "templateType": "anything", "can_override": false}, "pon": {"name": "pon", "group": "Ungrouped variables", "definition": "if(m=0,'zero',if(m=abs(m),'a positive number','a negative number'))", "description": "", "templateType": "anything", "can_override": false}, "sos": {"name": "sos", "group": "Ungrouped variables", "definition": "if(m=0,'horizontal',if(abs(m)<1,'shallow','steep'))", "description": "", "templateType": "anything", "can_override": false}, "mol": {"name": "mol", "group": "Ungrouped variables", "definition": "if(m=0,'zero',if(abs(m)<1,'less than 1','greater than or equal to 1'))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "m<>1", "maxRuns": 100}, "ungrouped_variables": ["app", "m", "c", "P1", "P2", "uod", "ax", "ay", "bx", "by", "app_advice", "p3", "pon", "sos", "mol"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "<p>It looks like you have incorrectly rounded this answer. &nbsp;You might want to look at some resources on rounded decimals. &nbsp;You can also leave your answer in fraction form as <br/>$\\var[fractionNumbers]{m}$</p>", "useAlternativeFeedback": false, "answer": "{m}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.1", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "answer": "{m}", "showPreview": true, "checkingType": "dp", "checkingAccuracy": "1", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "AS01 Solve linear equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}, {"name": "sean hunte", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3167/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "<p>Solve linear equations with unkowns on both sides. Including brackets and fractions.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>Given $\\simplify{{m}w-{n} = {p}w+{q}}$, we can get all the $w$'s on the left hand side and all the numbers on the right hand side, and then divide both sides by the coefficient of $w$ to get $w$ by itself.</p>\n<p></p>\n<table style=\"height: 342px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\">&nbsp;</td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\">$\\simplify{{m}w+{n}}$</td>\n<td style=\"height: 18px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">$\\simplify{{p}w+{q}}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\">&nbsp;</td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 218.312px;\">$\\simplify[!cancelTerms,unitFactor]{{m}w-{n}-{p}w}$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\simplify[!cancelTerms,unitFactor]{{p}w+{q}-{p}w}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\">$\\simplify{{m-p}w-{n}}$</td>\n<td style=\"height: 18px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">$\\var{q}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 218.312px;\">$\\var{m-p}w-\\var{n}+\\var{n}$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\var{q}+\\var{n}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\">$\\var{m-p}w$</td>\n<td style=\"height: 18px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">$\\var{q+n}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 218.312px;\">$\\displaystyle{\\frac{\\var{m-p}w}{\\var{m-p}}}$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\displaystyle{\\frac{\\var{q+n}}{\\var{m-p}}}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 218.312px;\">$w$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\displaystyle{\\simplify{{q+n}/{m-p}}} = \\var{precround(ansA,1)} \\text{ to 1 dp}$</td>\n</tr>\n</tbody>\n</table>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Equations\" target=\"_blank\" rel=\"noopener\"><br/>Use this link to find resources to help you revise how to solve linear equations</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"p": {"name": "p", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "ansA": {"name": "ansA", "group": "Ungrouped variables", "definition": "(q+n)/(m-p)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["l", "m", "n", "p", "q", "ansA"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve&nbsp; $\\simplify{({m}w-{n}) = {p}w+{q}}$</p>\n<p>$w=$&nbsp;[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ansA", "maxValue": "ansA", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "100", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "AS03 Simultaneous Equations (2 linear)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": ["Category: Simultaneous equations"], "metadata": {"description": "<p>Solving a pair of linear simultaneous equations, giving answers as integers or fractions.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Solve the simultaneous equations for x and y, giving your answers as integers or fractions, but not decimals.</p>\n<p>\\[ \\begin{split}&nbsp;\\simplify[!noLeadingminus,unitFactor]{{a}x+{b}y} &amp;\\,=\\var{c} \\\\ \\simplify[!noLeadingminus,unitFactor]{{a1}x +{b1}y}&nbsp; &amp;\\,=\\var{c1} \\end{split}\\]</p>", "advice": "<p>\\[\\begin{split}\\simplify[!noLeadingminus,unitFactor]{{a}x+{b}y} &amp;\\,=\\var{c} \\qquad\\qquad&amp;(1)\\\\ \\simplify[!noLeadingminus,unitFactor]{{a1}x +{b1}y}&nbsp; &amp;\\,=\\var{c1} \\qquad\\qquad&amp;(2)\\end{split}\\]</p>\n<p>{advice1}</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Rearranging\"><span style=\"font-weight: 400;\"><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Sim\">Use this link to find some resources which will help you revise this topic.</a></span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-2..8 except [0,1])", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-8..8 except [0,1,a])", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(-5..8 except [0,1])", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(2..10 except [round(a1*b/a),b,0,1])", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-6..6 except 0)", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "random(-7..7 except 0)", "description": "", "templateType": "anything", "can_override": false}, "aorsb": {"name": "aorsb", "group": "Ungrouped variables", "definition": "if(b*abs(b1)=b1*abs(b),'subtract','add')", "description": "", "templateType": "anything", "can_override": false}, "torfb": {"name": "torfb", "group": "Ungrouped variables", "definition": "if(b*abs(b1)=b1*abs(b),'from','to')", "description": "", "templateType": "anything", "can_override": false}, "sgn": {"name": "sgn", "group": "Ungrouped variables", "definition": "if(b*abs(b1)=b1*abs(b),-1,1)", "description": "", "templateType": "anything", "can_override": false}, "xn": {"name": "xn", "group": "Ungrouped variables", "definition": "c*abs(b1)+sgn*c1*abs(b)", "description": "", "templateType": "anything", "can_override": false}, "xd": {"name": "xd", "group": "Ungrouped variables", "definition": "a*abs(b1)+sgn*a1*abs(b)", "description": "", "templateType": "anything", "can_override": false}, "xsimp": {"name": "xsimp", "group": "Ungrouped variables", "definition": "xn/xd", "description": "", "templateType": "anything", "can_override": false}, "samex": {"name": "samex", "group": "Ungrouped variables", "definition": "\"<p>For these equations, it is easiest to get a solution for $y$ first, due to the $x$-terms having {eqoroppa} coefficients.</p>\\n<p>If we {aorsa} equation (2) {torfa} equation (1) this eliminates the $x$-terms leaving us with one equation in terms of $y$:</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[!collectNumbers, !noLeadingminus]{({b}+{sgna*(b1)})y} &amp;\\\\,=&nbsp;\\\\simplify[!collectNumbers, !noLeadingminus]{{c}+{sgna*(c1)}}\\\\\\\\ \\\\simplify{{b+sgna*(b1)}y} &amp;\\\\,= \\\\simplify{{c+sgna*(c1)}} \\\\\\\\ y &amp;\\\\,= \\\\simplify[all, fractionNumbers]{{c+sgna*(c1)}/{b+sgna*(b1)}} \\\\end{split} \\\\]</p>\\n<p></p>\\n<p>To obtain a solution for $x$ we can substitute this $y$-value into either of our initial equations. Using equation (1), we obtain</p>\\n<p>\\\\[ \\\\begin{split} \\\\var{a}x + \\\\var{b} \\\\times \\\\simplify[all, fractionNumbers]{{c+sgna*(c1)}/{b+sgna*(b1)}} &amp;\\\\,= \\\\var{c} \\\\\\\\ \\\\var{a}x &amp;\\\\,= \\\\simplify[all, !collectNumbers, !noLeadingminus]{{c} - {c*b+b*sgna*(c1)}/{b+sgna*(b1)}} \\\\\\\\ x &amp;\\\\,= \\\\simplify[fractionNumbers]{{(c*abs(b1)+sgn*c1*abs(b))/(a*abs(b1)+sgn*a1*abs(b))}}. \\\\end{split} \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "eqoroppb": {"name": "eqoroppb", "group": "Ungrouped variables", "definition": "if(abs(b)*b1=abs(b1)*b,'equal','equal and opposite')", "description": "", "templateType": "anything", "can_override": false}, "eqoroppa": {"name": "eqoroppa", "group": "Ungrouped variables", "definition": "if(abs(a)*a1=abs(a1)*a,'equal','equal and opposite')", "description": "", "templateType": "anything", "can_override": false}, "samey": {"name": "samey", "group": "Ungrouped variables", "definition": "\"<p>For these equations, it is easiest to get a solution for $x$ first, due to the $y$-terms having {eqoroppb} coefficients.</p>\\n<p>If we {aorsb} equation (2) {torfb} equation (1) this eliminates the $y$-terms, leaving us with one equation in terms of $x$:</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[!collectNumbers, !noLeadingminus]{({a}+{sgn*(a1)})x} &amp;\\\\,=&nbsp;\\\\simplify[!collectNumbers, !noLeadingminus]{{c}+{sgn*(c1)}}\\\\\\\\ \\\\simplify{{a+sgn*(a1)}x} &amp;\\\\,= \\\\simplify{{c+sgn*(c1)}} \\\\\\\\ x &amp;\\\\,= \\\\simplify[all, fractionNumbers]{{c+sgn*(c1)}/{a+sgn*(a1)}} \\\\end{split} \\\\]</p>\\n<p></p>\\n<p>To obtain a solution for $y$ we can substitute this $x$-value into either of our initial equations. Using equation (1), we obtain</p>\\n<p>\\\\[ \\\\begin{split} \\\\var{a} \\\\times\\\\simplify[fractionNumbers]{{c+sgn*(c1)}/{a+sgn*(a1)}} + \\\\var{b}y &amp;\\\\,= \\\\var{c} \\\\\\\\ \\\\var{b}y &amp;\\\\,= \\\\simplify[!collectNumbers, !noLeadingminus]{{c} - {c*a+a*sgn*(c1)}/{a+sgn*(a1)}} \\\\\\\\ y &amp;\\\\,= \\\\simplify[fractionNumbers]{{(c-a*xsimp)/b}}. \\\\end{split} \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "lcmb": {"name": "lcmb", "group": "Ungrouped variables", "definition": "\"<p>To get a solution for $x$, if we multiply equation (2) by $\\\\simplify{{abs(b/b1)}}$ we will have two equations with {eqoroppb} $y$-coefficients:</p>\\n<p>\\\\[ \\\\begin{split}&nbsp;\\\\simplify[!noLeadingminus,unitFactor]{{a}x+{b}y} &amp;\\\\,=\\\\var{c} \\\\qquad\\\\qquad&amp;(3)\\\\\\\\ \\\\simplify[!noLeadingminus,unitFactor]{{a1*abs(b/b1)}x +{b1*abs(b/b1)}y}&nbsp; &amp;\\\\,=\\\\var{c1*abs(b/b1)} \\\\qquad\\\\qquad&amp;(4)\\\\end{split}\\\\]</p>\\n<p>If we {aorsb} equation (4) {torfb} equation (3) this eliminates the $y$-terms, leaving us with one equation in terms of $x$:</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[!collectNumbers, !noLeadingminus]{({a}+{sgn*(a1*abs(b/b1))})x} &amp;\\\\,=&nbsp;\\\\simplify[all, !collectNumbers, !noLeadingminus]{{c}+{sgn*(c1*abs(b/b1))}}\\\\\\\\ \\\\simplify{{a+sgn*(a1*abs(b/b1))}x} &amp;\\\\,= \\\\simplify{{c+sgn*(c1*abs(b/b1))}} \\\\\\\\ x &amp;\\\\,= \\\\simplify[all,fractionNumbers]{{c+sgn*(c1*abs(b/b1))}/{a+sgn*(a1*abs(b/b1))}}. \\\\end{split} \\\\]</p>\\n<p></p>\\n<p>To obtain a solution for $y$ we can substitute this $x$-value into either of our initial equations. Using equation (1), we obtain</p>\\n<p>\\\\[ \\\\begin{split} \\\\var{a}\\\\times\\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{({c+sgn*c1*abs(b/b1)}/{(a)+sgn*a1*abs(b/b1)}) + {b}y} &amp;\\\\,= \\\\var{c} \\\\\\\\ \\\\simplify{{b}y} &amp;\\\\,= \\\\simplify[all, !noLeadingminus, fractionNumbers]{{c} -({(a*c)+a*sgn*c1*abs(b/b1)}/{(a)+sgn*a1*abs(b/b1)})} \\\\\\\\ \\\\simplify{{b}y} &amp;\\\\,= \\\\simplify[all, !noLeadingminus, fractionNumbers]{{c -(a*c+a*sgn*c1*abs(b/b1))/(a+sgn*a1*abs(b/b1))}} \\\\\\\\ y &amp;\\\\,=\\\\simplify[fractionNumbers]{{(c-a*xsimp)/b}}. \\\\end{split} \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "lcmb1": {"name": "lcmb1", "group": "Ungrouped variables", "definition": "\"<p>To get a solution for $x$, if we multiply equation (1) by $\\\\simplify{{abs(b1/b)}}$ we will have two equations with {eqoroppb} $y$-coefficients:</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[!noLeadingminus,unitFactor]{{a*abs(b1/b)}x +{b*abs(b1/b)}y}&nbsp; &amp;\\\\,=\\\\var{c*abs(b1/b)} \\\\qquad\\\\qquad&amp;(3) \\\\\\\\\\\\simplify[!noLeadingminus,unitFactor]{{a1}x+{b1}y} &amp;\\\\,=\\\\var{c1} \\\\qquad\\\\qquad&amp;(4)\\\\\\\\ \\\\end{split} \\\\]</p>\\n<p>If we {aorsb} equation (4) {torfb} equation (3) this eliminates the $y$-terms, leaving us with one equation in terms of $x$:</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[!collectNumbers, !noLeadingminus]{({(a*abs(b1/b))}+{sgn*a1})x} &amp;\\\\,=&nbsp;\\\\simplify[!collectNumbers, !noLeadingminus]{{(c*abs(b1/b))}+{sgn*c1}}\\\\\\\\ \\\\simplify{{(a*abs(b1/b))+sgn*a1}x} &amp;\\\\,= \\\\simplify{{(c*abs(b1/b))+sgn*c1}} \\\\\\\\ x &amp;\\\\,= \\\\simplify[all, fractionNumbers]{{(c*abs(b1/b))+sgn*c1}/{(a*abs(b1/b))+sgn*a1}}. \\\\end{split} \\\\]</p>\\n<p></p>\\n<p>To obtain a solution for $y$ we can substitute this $x$-value into either of our initial equations. Using equation (1), we obtain</p>\\n<p>\\\\[ \\\\begin{split} \\\\var{a}\\\\times\\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{({(c*abs(b1/b))+sgn*c1}/{(a*abs(b1/b))+sgn*a1}) + {b}y} &amp;\\\\,= \\\\var{c} \\\\\\\\ \\\\simplify{{b}y} &amp;\\\\,= \\\\simplify[all, !noLeadingminus, fractionNumbers]{{c} -({(a*c*abs(b1/b))+a*sgn*c1}/{(a*abs(b1/b))+sgn*a1})} \\\\\\\\ \\\\simplify{{b}y} &amp;\\\\,= \\\\simplify[all, !noLeadingminus, fractionNumbers]{{c -(a*c*abs(b1/b)+a*sgn*c1)/(a*abs(b1/b)+sgn*a1)}} \\\\\\\\ y &amp;\\\\,=\\\\simplify[fractionNumbers]{{(c-a*xsimp)/b}}. \\\\end{split} \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "full": {"name": "full", "group": "Ungrouped variables", "definition": "\"<p>To get a solution for $x$, if we multiply equation (1) by $\\\\var{abs(b1)}$ and equation (2) by $\\\\var{abs(b)}$, we will have two equations with {eqoroppb} $y$-coefficients:</p>\\n<p>\\\\[ \\\\begin{split}&nbsp;\\\\simplify[!noLeadingminus,unitFactor]{{a*abs(b1)}x+{b*abs(b1)}y} &amp;\\\\,=\\\\var{c*abs(b1)} \\\\qquad\\\\qquad&amp;(3)\\\\\\\\\\\\simplify[!noLeadingminus,unitFactor]{{a1*abs(b)}x +{b1*abs(b)}y}&nbsp; &amp;\\\\,=\\\\var{c1*abs(b)} \\\\qquad\\\\qquad&amp;(4) \\\\end{split}\\\\]</p>\\n<p>Now, {aorsb} equation (4) {torfb} equation (3) to eliminate the $y$ terms:</p>\\n<p>\\\\[ \\\\begin{split} (\\\\simplify[!collectNumbers]{{a*abs(b1)} +{sgn*a1*abs(b)}}) x &amp;\\\\,= \\\\simplify[!collectNumbers]{{c*abs(b1)}+{sgn*c1*abs(b)}}&nbsp;\\\\\\\\&nbsp;&nbsp;\\\\simplify{{a*abs(b1)+sgn*a1*abs(b)}} x &amp;\\\\,= \\\\simplify{{c*abs(b1)+sgn*c1*abs(b)}} .\\\\end{split} \\\\]</p>\\n<p>So the solution for $x$ is \\\\[ x=\\\\simplify{{c*abs(b1)+sgn*c1*abs(b)}/{a*abs(b1)+sgn*a1*abs(b)}}.\\\\]</p>\\n<p>To obtain a solution for $y$ we can substitute this value of $x$ into either of our initial equations. Using equation (1), we obtain</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[noLeadingminus,fractionNumbers,unitFactor]{{a}&nbsp; {xsimp} + {b}y} &amp;\\\\,=\\\\var{c} \\\\\\\\ \\\\var{b}y &amp;\\\\,= \\\\simplify[!collectNumbers,fractionNumbers]{{c}-{a*xsimp}} \\\\\\\\\\\\var{b}y &amp;\\\\,= \\\\simplify[fractionNumbers]{{c-a*xsimp}} \\\\\\\\y &amp;\\\\,= \\\\simplify[fractionNumbers]{{(c-a*xsimp)/b}} \\\\end{split} \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "aorsa": {"name": "aorsa", "group": "Ungrouped variables", "definition": "if(a*abs(a1)=abs(a)*a1,'subtract','add')", "description": "", "templateType": "anything", "can_override": false}, "torfa": {"name": "torfa", "group": "Ungrouped variables", "definition": "if(a*abs(a1)=abs(a)*a1,'from','to')", "description": "", "templateType": "anything", "can_override": false}, "sgna": {"name": "sgna", "group": "Ungrouped variables", "definition": "if(a*abs(a1)=abs(a)*a1,-1,1)", "description": "", "templateType": "anything", "can_override": false}, "lcma": {"name": "lcma", "group": "Ungrouped variables", "definition": "\"<p>To get a solution for $y$, if we multiply equation (2) by $\\\\simplify{{abs(a/a1)}}$ we will have two equations with {eqoroppa} $x$-coefficients:</p>\\n<p>\\\\[ \\\\begin{split}&nbsp;\\\\simplify[!noLeadingminus,unitFactor]{{a}x+{b}y} &amp;\\\\,=\\\\var{c} \\\\qquad\\\\qquad&amp;(3)\\\\\\\\ \\\\simplify[!noLeadingminus,unitFactor]{{a1*abs(a/a1)}x +{b1*abs(a/a1)}y}&nbsp; &amp;\\\\,=\\\\var{c1*abs(a/a1)} \\\\qquad\\\\qquad&amp;(4)\\\\end{split}\\\\]</p>\\n<p>If we {aorsa} equation (4) {torfa} equation (3) this eliminates the $x$-terms, leaving us with one equation in terms of $y$:</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[!collectNumbers, !noLeadingminus]{({b}+{sgna*(b1*abs(a/a1))})y} &amp;\\\\,=&nbsp;\\\\simplify[all, !collectNumbers, !noLeadingminus]{{c}+{sgna*(c1*abs(a/a1))}}\\\\\\\\ \\\\simplify{{b+sgna*(b1*abs(a/a1))}y} &amp;\\\\,= \\\\simplify{{c+sgna*(c1*abs(a/a1))}} \\\\\\\\ y &amp;\\\\,= \\\\simplify[all,fractionNumbers]{{c+sgna*(c1*abs(a/a1))}/{b+sgna*(b1*abs(a/a1))}}. \\\\end{split} \\\\]</p>\\n<p></p>\\n<p>To obtain a solution for $x$ we can substitute this $y$-value into either of our initial equations. Using equation (1), we obtain</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{{a}x + {b}}\\\\times \\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{({c+sgna*c1*abs(a/a1)}/{(b)+sgna*b1*abs(a/a1)})} &amp;\\\\,= \\\\var{c} \\\\\\\\ \\\\simplify{{a}x} &amp;\\\\,= \\\\simplify[all, !noLeadingminus, fractionNumbers]{{c} -({(b*c)+b*sgna*c1*abs(a/a1)}/{(b)+sgna*b1*abs(a/a1)})} \\\\\\\\ \\\\simplify{{a}x} &amp;\\\\,= \\\\simplify[all, !noLeadingminus, fractionNumbers]{{c -(b*c+b*sgna*c1*abs(a/a1))/(b+sgna*b1*abs(a/a1))}} \\\\\\\\ x &amp;\\\\,=\\\\simplify[fractionNumbers]{{(c*abs(b1)+sgn*c1*abs(b))/(a*abs(b1)+sgn*a1*abs(b))}}. \\\\end{split} \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "lcma1": {"name": "lcma1", "group": "Ungrouped variables", "definition": "\"<p>To get a solution for $y$, if we multiply equation (1) by $\\\\simplify{{abs(a1/a)}}$ we will have two equations with {eqoroppa} $x$-coefficients:</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[!noLeadingminus,unitFactor]{{a*abs(a1/a)}x +{b*abs(a1/a)}y}&nbsp; &amp;\\\\,=\\\\var{c*abs(a1/a)} \\\\qquad\\\\qquad&amp;(3) \\\\\\\\\\\\simplify[!noLeadingminus,unitFactor]{{a1}x+{b1}y} &amp;\\\\,=\\\\var{c1} \\\\qquad\\\\qquad&amp;(4) \\\\end{split}\\\\]</p>\\n<p>If we {aorsa} equation (4) {torfa} equation (3) this eliminates the $x$-terms, leaving us with one equation in terms of $y$:</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[!collectNumbers, !noLeadingminus]{({(b*abs(a1/a))}+{sgna*b1})y} &amp;\\\\,=&nbsp;\\\\simplify[!collectNumbers, !noLeadingminus]{{(c*abs(a1/a))}+{sgna*c1}}\\\\\\\\ \\\\simplify{{(b*abs(a1/a))+sgna*b1}y} &amp;\\\\,= \\\\simplify{{(c*abs(a1/a))+sgna*c1}} \\\\\\\\ y &amp;\\\\,= \\\\simplify[all, fractionNumbers]{{(c*abs(a1/a))+sgna*c1}/{(b*abs(a1/a))+sgna*b1}}. \\\\end{split} \\\\]</p>\\n<p></p>\\n<p>To obtain a solution for $x$ we can substitute this $y$-value into either of our initial equations. Using equation (1), we obtain</p>\\n<p>\\\\[ \\\\begin{split} \\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{{a}x + {b}}\\\\times \\\\simplify[all, !noLeadingminus, !expandBrackets, fractionNumbers]{({c*abs(a1/a)+sgna*c1}/{(b*abs(a1/a))+sgna*b1})} &amp;\\\\,= \\\\var{c} \\\\\\\\ \\\\simplify{{a}x} &amp;\\\\,= \\\\simplify[all, !noLeadingminus, fractionNumbers]{{c} -({(b*c*abs(a1/a))+b*sgna*c1}/{(b*abs(a1/a))+sgna*b1})} \\\\\\\\ \\\\simplify{{a}x} &amp;\\\\,= \\\\simplify[all, !noLeadingminus, fractionNumbers]{{c -(b*c*abs(a1/a)+b*sgna*c1)/(b*abs(a1/a)+sgna*b1)}} \\\\\\\\ x &amp;\\\\,=\\\\simplify[fractionNumbers]{{(c*abs(b1)+sgn*c1*abs(b))/(a*abs(b1)+sgn*a1*abs(b))}}. \\\\end{split} \\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "advice1": {"name": "advice1", "group": "Ungrouped variables", "definition": "if(abs(b)=abs(b1), {samey},if(abs(a)=abs(a1),{samex},if(lcm(abs(b),abs(b1))=abs(b),{lcmb},if(lcm(abs(b),abs(b1))=abs(b1),{lcmb1},if(lcm(abs(a),abs(a1))=abs(a),{lcma},if(lcm(abs(a),abs(a1))=abs(a1),{lcma1},{full}))))))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(b-b1)>1 and\nabs(a-a1)>1 and\ngcd(a,c)=1 and\ngcd(a1,c1)=1", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "a1", "b1", "c", "c1", "aorsa", "torfa", "aorsb", "torfb", "sgna", "sgn", "xn", "xd", "xsimp", "eqoroppa", "eqoroppb", "advice1", "samey", "samex", "lcmb", "lcmb1", "lcma", "lcma1", "full"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$x=$ [[0]]</p>\n<p>$y=$ [[1]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(c*abs(b1)+sgn*c1*abs(b))/(a*abs(b1)+sgn*a1*abs(b))}", "answerSimplification": "fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(c-a*xsimp)/b}", "answerSimplification": "fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA04 Inequalities (understanding notation)", "extensions": ["chemistry", "geogebra", "jsxgraph", "codewords", "permutations", "polynomials", "quantities", "random_person", "stats", "visjs"], "custom_part_types": [{"source": {"pk": 28, "author": {"name": "Marie Nicholson", "pk": 1799}, "edit_page": "/part_type/28/edit"}, "name": "True/False", "short_name": "true-false", "description": "<p>The answer is either 'True' or 'False'</p>", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["True", "False"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n  correct(),\n  incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=correct_answer,\n  correct(),\n  incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"True\"", "help_url": "", "hint": "", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Identify the truth value of an inequality (T/F) between two numbers</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p><span style=\"font-weight: 400;\">The symbol is a comparitor that $&lt;$ says that the object to its left is less than the object to its right. Similarly, $&gt;$ says the object to its left is greater than the object to its right.</span><span style=\"font-weight: 400;\"></span></p>\n<p><span style=\"font-weight: 400;\">In each case the sentence can be read in two ways e.g. $a&lt;b$ can be read as \"$a$ is less than $b$\" OR \"$b$ is greater than $a$\".</span><span style=\"font-weight: 400;\"></span></p>\n<p><span style=\"font-weight: 400;\">The symbol $\\leq$ just changes the sentence to include \"...or equal to...\". This can be of particular relevance when dealing with integers (whole numbers) e.g. $x \\geq 4$ and $x$ is a whole number means that $x$ could be $4, 5, 6,$ or $7$ and so on. Whereas, $x&gt;4$ and $x$ is a whole number means that $x$ could be $5,6,$... etc. Notably in the second case $x$ cannot be $4$.</span></p>\n<p><span style=\"font-weight: 400;\"></span></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Inequalities\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "can_override": false}, "operations": {"name": "operations", "group": "Ungrouped variables", "definition": "[latex(\"\\\\gt\"),latex(\"\\\\ge\")]", "description": "", "templateType": "anything", "can_override": false}, "values": {"name": "values", "group": "Ungrouped variables", "definition": "[a,-random(1..15),random(1..15),random(1..15)]", "description": "", "templateType": "anything", "can_override": false}, "disp_values": {"name": "disp_values", "group": "Ungrouped variables", "definition": "shuffle(values)[0..2]", "description": "", "templateType": "anything", "can_override": false}, "disp_op": {"name": "disp_op", "group": "Ungrouped variables", "definition": "operations[random(0,1)]", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "can_override": false}, "operations2": {"name": "operations2", "group": "Ungrouped variables", "definition": "[latex(\"\\\\lt\"),latex(\"\\\\le\")]", "description": "", "templateType": "anything", "can_override": false}, "values2": {"name": "values2", "group": "Ungrouped variables", "definition": "[a2,-random(1..15),random(1..15),random(1..15)]", "description": "", "templateType": "anything", "can_override": false}, "disp_values2": {"name": "disp_values2", "group": "Ungrouped variables", "definition": "shuffle(values2)[0..2]", "description": "", "templateType": "anything", "can_override": false}, "disp_op2": {"name": "disp_op2", "group": "Ungrouped variables", "definition": "operations2[random(0,1)]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "operations", "values", "disp_values", "disp_op", "a2", "operations2", "values2", "disp_values2", "disp_op2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "true-false", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Is the following statement true or false?</p>\n<p>\\(\\var{disp_values[0]}\\var{disp_op}\\var{disp_values[1]}\\)</p>\n<p></p>", "alternatives": [{"type": "true-false", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "settings": {"correct_answer_expr": "eval(expression(disp_values[0]+if(disp_op=\"\\\\gt\",\">\",\">=\")+disp_values[1]))"}}], "settings": {"correct_answer_expr": "eval(expression(disp_values[0]+if(disp_op=\"\\\\gt\",\">\",\">=\")+disp_values[1]))"}}, {"type": "true-false", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Is the following statement true or false?</p>\n<p>\\(\\var{disp_values2[0]}\\var{disp_op2}\\var{disp_values2[1]}\\)</p>\n<p></p>", "settings": {"correct_answer_expr": "eval(expression(disp_values2[0]+if(disp_op2=\"\\\\lt\",\"<\",\"<=\")+disp_values2[1]))"}}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA05 Number sequences - find a missing number", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Number sequences - find a missing number</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Find the missing number from the following sequence</p>\n<p>\\[\\var{a}, \\var{a+d}, \\var{a+2*d}, \\var{a+3d}, ?, \\var{a+5d}, \\var{a+6d}, \\var{a+7d}, \\ldots\\]</p>", "advice": "<p>In this sequence it is important to spot that the terms are changing by the same amount each time ($\\var{d}$ in this case). This type of sequence is called an <strong>Arithmetic Sequence</strong>.</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Sequences\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(30..40)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-20..30)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "d", "n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a+4d}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA09 BIDMAS without a division", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following expression:</p>", "advice": "<p>BIDMAS stands for:</p>\n<p>Brackets</p>\n<p>Indices</p>\n<p>Division</p>\n<p>Multiplication</p>\n<p>Addition</p>\n<p>Subtraction</p>\n<p></p>\n<p>And is a way for us to remember guidance about the order in which calculations are carried out to ensure that everyone doing teh same sum gets the same answer. In this case the first thing that is in the question is Multiplication.</p>\n<p>First work through the expression from left to right, evaluating any multiplication as you come to them. You should be left with an expression involving only pluses and minuses. Evaluate this expression, again working from left to right. Thus:</p>\n<p>\\[\\var{a}-\\var{b} \\times \\var{c}\\]</p>\n<p>\\[=\\var{a}-\\var{b*c}\\]</p>\n<p>\\[=\\var{a-b*c}\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2..8 except [a,b])", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..11 except a)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate</p>\n<p>$\\var{a}-\\var{b} \\times\\var{c}$</p>", "minValue": "{a-b*c}", "maxValue": "{a-b*c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA10 BIDMAS with a division", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following expression:</p>", "advice": "<p>BIDMAS stands for:</p>\n<p>Brackets</p>\n<p>Indices</p>\n<p>Division</p>\n<p>Multiplication</p>\n<p>Addition</p>\n<p>Subtraction</p>\n<p></p>\n<p>And is a way for us to remember guidance about the order in which calculations are carried out to ensure that everyone doing teh same sum gets the same answer. In this case the first thing that is in the question is Division.</p>\n<p>First work through the expression from left to right, evaluating any division as you come to it. You should be left with an expression involving only pluses and minuses. Evaluate this expression, again working from left to right. Thus:</p>\n<p></p>\n<p>\\[\\var{h}-\\var{a2*b2} \\div \\var{b2}\\]</p>\n<p>\\[=\\var{h}-\\var{a2}\\]</p>\n<p>\\[=\\var{h-a2}\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"b2": {"name": "b2", "group": "Ungrouped variables", "definition": "random(2..9 except a2)", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(7..15)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["h", "a2", "b2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\var{h}-\\var{a2*b2} \\div \\var{b2}$</p>", "minValue": "{h-a2}", "maxValue": "{h-a2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA11 BIDMAS with a division 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Applying the order of operators.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>To calculate the following expression you press a sequence of buttons on your calculator.</p>\n<p>\\begin{align}\\frac{\\var{num}}{\\var{a}\\times\\var{b}}\\end{align}</p>\n<p>Which of the following would give the WRONG answer?</p>\n<p></p>", "advice": "<p>BIDMAS stands for:</p>\n<p>Brackets</p>\n<p>Indices</p>\n<p>Division</p>\n<p>Multiplication</p>\n<p>Addition</p>\n<p>Subtraction</p>\n<p>This is the standardized order of operations that we carry out and is part of how the calculator is designed to work. The most effective way to use most modern calculators is to use either the fraction button (on scientific calculators) or as is hinted at in this question, use brackets.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}, "num": {"name": "num", "group": "Ungrouped variables", "definition": "a*b*3", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "a<>b", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "num"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\var{num}\\div (\\var{a}\\times\\var{b})$", "$\\var{num} \\div \\var{a} \\times \\var{b}$", "$\\var{num} \\div \\var{a} \\div \\var{b}$"], "matrix": [0, "1", 0], "distractors": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA12 Negatives (add/subtract) 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Calculations with negative numbers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate $\\var{x}+(\\var{y})$.</p>", "advice": "<p>When you add a negative number that is the same as subtracting the number so</p>\n<p>\\[\\var{x}+(\\var{y})=\\var{x}-\\var{-y}=\\var{x+y}.\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(1..50)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(-50..-1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x}+{y}", "maxValue": "{x}+{y}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA13 Negatives (add/subtract) 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Calculations with negative numbers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate $\\var{x}-(\\var{y})$.</p>", "advice": "<p>When you subtract a negative number that is the same as adding the number so</p>\n<p>\\[\\var{x}-(\\var{y})=\\var{x}+\\var{-y}=\\var{x-y}\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(1..50)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(-50..-1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x}-{y}", "maxValue": "{x}-{y}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA14 Multiplying Negatives 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Calculations with negative numbers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate $\\var{x}\\times(\\var{y})$.</p>", "advice": "<p>When you multiply by a negative number that is the same as doing the multiplication as if the numbers were positive and then making the result negative. This means we have</p>\n<p>\\[\\var{x}\\times(\\var{y})=-(\\var{x}\\times\\var{-y})=\\var{x*y}.\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x*y}", "maxValue": "{x*y}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA15 Multiplying Negatives 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Calculations with negative numbers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate $(\\var{x})\\times(\\var{y})$.</p>", "advice": "<p>Multiplying two negative numbers gives a positive so we just calculate the multiplication as if both numbers were positive. This means we have</p>\n<p>\\[(\\var{x})\\times(\\var{y})=\\var{-x}\\times\\var{-y}=\\var{x*y}.\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x*y}", "maxValue": "{x*y}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA16 Dividing Negatives", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Calculations with negative numbers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate $(\\var{x})\\div(\\var{y})$.</p>", "advice": "<p>When we divide two numbers the rule is,</p>\n<ul>\n<li>plus $\\div$ plus = plus</li>\n<li>minus $\\div$ plus = minus</li>\n<li>plus $\\div$ minus = minus</li>\n<li>minus $\\div$ minus = plus</li>\n</ul>\n<p>In this calculation we have</p>\n<p>\\[(\\var{x})\\div(\\var{y})=\\var{x/y}.\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Arithmetic\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(-10..10)*y", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x/y}", "maxValue": "{x/y}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA17 Worded proportion", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Proportional calculation in context.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>If {n1} adult cinema tickets cost &pound;{n1price}, how much would it cost for {n2} adults to buy tickets to the cinema?</p>", "advice": "<p>If {n1} tickets cost &pound;{n1price} then we can calculate that one ticket costs</p>\n<p>\\[&pound;\\var{n1price}\\div\\var{n1}=&pound;\\var{price}.\\]</p>\n<p>This means that {n2} tickets cost $\\var{n2}\\times&pound;\\var{price}=&pound;\\var{n2price}$</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Ratio\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"n1": {"name": "n1", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "price": {"name": "price", "group": "Ungrouped variables", "definition": "precround(random(2..9 # 0.01),2)", "description": "", "templateType": "anything", "can_override": false}, "n2": {"name": "n2", "group": "Ungrouped variables", "definition": "random(2..9 except n1)", "description": "", "templateType": "anything", "can_override": false}, "n1price": {"name": "n1price", "group": "Ungrouped variables", "definition": "precround(n1*price,2)", "description": "", "templateType": "anything", "can_override": false}, "n2price": {"name": "n2price", "group": "Ungrouped variables", "definition": "precround(n2*price,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n1", "price", "n2", "n1price", "n2price"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>&pound;[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "n2*price", "maxValue": "n2*price", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF01  Rounding DP", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Oliver Spenceley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23557/"}], "tags": [], "metadata": {"description": "<p>Round&nbsp;numbers to&nbsp;a given number of&nbsp;decimal places.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>We can approximate numbers by rounding.</p>\n<p>Round $\\var{c1}$ to&nbsp;a given number of&nbsp;decimal places.</p>", "advice": "<p>The&nbsp;first&nbsp;thing to do&nbsp;when we are rounding numbers is to identify the last digit we are keeping.</p>\n<p>When you're asked to <strong>round</strong> your answer to a number of decimal places, you need to decide whether to keep the last&nbsp;digit the same (rounding down) or increase it by 1 (rounding up). If the following digit is less than 5 we round down and we round up&nbsp;when the next digit is 5 or more.</p>\n<p>To write it down in steps:</p>\n<ol>\n<ol>\n<ol>\n<ol>\n<li style=\"text-align: left;\">Identify the last digit we need to keep.</li>\n<li style=\"text-align: left;\">Look at the following digit.</li>\n<li style=\"text-align: left;\">If it's 5 or more, increase the previous digit by one.</li>\n<li class=\"c-list__ordered-item\" style=\"text-align: left;\">If it's 4 or less, keep the previous digit the same.</li>\n<li class=\"c-list__ordered-item\" style=\"text-align: left;\">Fill any spaces to the right of the digit with zeros if needed.</li>\n</ol>\n</ol>\n</ol>\n</ol>\n<p class=\"c-list__ordered-item\">It is important to keep in mind that if the digit we are increasing is 9, it becomes zero and we increase the previous digit instead. If this digit is 9 as well, we&nbsp;move along&nbsp;to the left side until we find a digit less than 9.</p>\n<hr/>\n<p class=\"c-list__ordered-item\">To round a number to a given number $n$ of decimal places, we look at the&nbsp;$n$th&nbsp;digit after the decimal point.</p>\n<p style=\"padding-left: 30px;\">We have $\\var{c1}$.</p>\n<p class=\"k-type-body-article\"><em>i)</em></p>\n<p class=\"k-type-body-article\" style=\"padding-left: 30px;\">We look at the first digit after the decimal point. This is $\\var{cdig[4]}$ and the following digit is $\\var{cdig[3]}$ so we round <span data-jme-visible=\"cdig[3] &gt; 4\">up</span><span data-jme-visible=\"cdig[3] &lt; 5\">down</span> to get $\\var{precround(c1, 1)}$.</p>\n<p class=\"k-type-body-article\"><em>ii)</em></p>\n<p class=\"k-type-body-article\" style=\"padding-left: 30px;\">The second digit after the decimal point is $\\var{cdig[3]}$. It is followed by $\\var{cdig[2]}$ so we round <span data-jme-visible=\"cdig[2] &gt; 4\">up</span><span data-jme-visible=\"cdig[2] &lt; 5\">down</span> to get $\\var{precround(c1, 2)}$.</p>\n<p class=\"k-type-body-article\"><em>iii)</em></p>\n<p style=\"padding-left: 30px;\"><span data-jme-visible=\"dp = 3\">The 3rd decimal place is $\\var{cdig[2]}$, followed by $\\var{cdig[1]}$. We get $\\var{precround(c1, 3)}$.&nbsp;</span><span data-jme-visible=\"dp = 4\">The 4th decimal place is $\\var{cdig[1]}$, followed by $\\var{cdig[0]}$.&nbsp;We get $\\var{precround(c1, 4)}$.</span></p>\n<p style=\"padding-left: 30px;\"><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic</a></p>\n<p style=\"padding-left: 30px;\"></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"c1": {"name": "c1", "group": "Ungrouped variables", "definition": "n_from_digits(cdig)*10^(-5) + random(1..5)", "description": "<p>Random number with 5 decimal places.</p>", "templateType": "anything", "can_override": false}, "cdig": {"name": "cdig", "group": "Ungrouped variables", "definition": "repeat(random(1..9), 5)", "description": "", "templateType": "anything", "can_override": false}, "dp": {"name": "dp", "group": "Ungrouped variables", "definition": "random(3..4)", "description": "<p>Number of decimal places to round.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["dp", "cdig", "c1"], "variable_groups": [], "functions": {"n_from_digits": {"parameters": [["digits", "list"]], "type": "number", "language": "jme", "definition": "if(\n  len(digits)=0,\n    0,\n    digits[0]+10*n_from_digits(digits[1..len(digits)])\n)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"padding-left: 60px;\"><em>i)</em>&nbsp;&nbsp; $\\var{c1}$ rounded&nbsp;to 1 decimal place is:&nbsp; [[0]]</p>\n<p style=\"padding-left: 60px;\"><em>ii)</em>&nbsp;&nbsp; $\\var{c1}$ rounded&nbsp;to 2 decimal places is:&nbsp; [[1]]</p>\n<p style=\"padding-left: 60px;\"><em>iii)</em>&nbsp;&nbsp; $\\var{c1}$ rounded&nbsp;to {dp} decimal places is:&nbsp; [[2]]</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(c1, 1)", "maxValue": "precround(c1, 1)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(c1, 2)", "maxValue": "precround(c1, 2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(c1, dp)", "maxValue": "precround(c1, dp)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF06 Percentage increase", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Calculate the percentage increase (as a percentage) given a number and the size of the increase.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>What is the percentage increase in a class of {total} if {additional} more are added to it?</p>\n<p>Give your answer to 2 decimal places.</p>", "advice": "<p>To calculate a percentage increase you need to find how much the increase is as a percentage of the original number. In this question the increase is {additional} and the original number is {total} so the percentage is</p>\n<p>\\[ \\frac{\\var{additional}}{\\var{total}}\\times100\\%=\\var{dpformat(additional/total,4)}\\times 100\\%=\\var{dpformat(percentage,2)}\\%\\]</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"total": {"name": "total", "group": "Ungrouped variables", "definition": "random(15..60)", "description": "", "templateType": "anything", "can_override": false}, "additional": {"name": "additional", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "percentage": {"name": "percentage", "group": "Ungrouped variables", "definition": "additional/total*100", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["total", "additional", "percentage"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>[[0]]%</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "percentage", "maxValue": "percentage", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF07 Percentage change (decrease then increase)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Compound percentage change.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The value of a car is initially {StartingPrice}. If the value decreases by {dec}%, and then increases by {inc}%, what is the final value?</p>\n<p>Give your answer correct to two decimal places.</p>", "advice": "<p>There is a {dec}% decrease in price. This means that price after the decrease will be {100-dec}% of the old price.</p>\n<p>\\[\\frac{\\var{100-dec}}{100} \\times \\var{StartingPrice} = \\var{(100-dec)/100*StartingPrice}\\]</p>\n<p>Then there is a {inc}% increase in price. This means the final price will be {100+inc}% of the price after the decrease.</p>\n<p><span style=\"font-weight: 400;\">\\[\\frac{\\var{100+inc}}{100} \\times \\var{(100-dec)/100*StartingPrice} = &pound;\\var{dpformat((100+inc)/100*(100-dec)/100*StartingPrice,2)}\\]</span></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\" target=\"_blank\" rel=\"noopener\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"dec": {"name": "dec", "group": "Ungrouped variables", "definition": "random(1..50)", "description": "", "templateType": "anything", "can_override": false}, "inc": {"name": "inc", "group": "Ungrouped variables", "definition": "random(1..50)", "description": "", "templateType": "anything", "can_override": false}, "FinalPrice": {"name": "FinalPrice", "group": "Ungrouped variables", "definition": "StartingPrice*(1-dec/100)*(1+inc/100)", "description": "", "templateType": "anything", "can_override": false}, "StartingPrice": {"name": "StartingPrice", "group": "Ungrouped variables", "definition": "random(600..8000 # 10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["dec", "inc", "FinalPrice", "StartingPrice"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p></p>\n<p>&pound;[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "FinalPrice", "maxValue": "FinalPrice", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF08 Reverse percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": ["decrease", "percentages", "taxonomy"], "metadata": {"description": "<p>Find the original price before a discount by dividing the new price by the percentage discount.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{name1} and {name2} are friends. {name1} noticed {name2}'s new {item} when he came over to visit her house. He immediately knew he wanted to buy the same model. When he got home, he bought the {item} online for &pound;{newprice}.</p>", "advice": "<p>We need to find the original price paid by {name2}. This value represents 100%.</p>\n<p>By the time {name1} bought the {item}, the price had decreased by {percentage}%.</p>\n<p>{name1} therefore paid {100-percentage}% of the price {name2} paid.</p>\n<p></p>\n<p>We use the unitary method to find the original price. We know the price paid by {name1}.</p>\n<p>\\[\\var{100-percentage}\\text{%} = \\var{newprice} \\text{.}\\]</p>\n<p>Divide both sides&nbsp;by {100-percentage} to get</p>\n<p>\\[\\begin{align} 1\\text{%} &amp;= \\var{newprice} \\div \\var{100-percentage} \\\\&amp;= \\var{newprice/(100-percentage)} \\text{.} \\end{align}\\]</p>\n<p>Multiply&nbsp;both sides&nbsp;by&nbsp;100 to get</p>\n<p>\\[\\begin{align} 100\\text{%} &amp;= \\var{newprice/(100-percentage)} \\times&nbsp;100 \\\\&amp;= \\var{newprice/(100-percentage)*100} \\\\&amp;= \\var{oldprice}\\text{.} \\end{align}\\]</p>\n<p>This is the original price paid by {name2} before the {percentage}% decrease.</p>\n<p>We can check our answer with a different method.</p>\n<p>\\[\\begin{align} \\var{100-percentage}\\text{% of } \\var{oldprice} &amp;= \\var{(100-percentage)/100} \\times \\var{oldprice}&nbsp;\\\\&amp;= &nbsp;\\var{(100-percentage)/100*oldprice} \\\\&amp;= \\var{precround((100-percentage)/100*oldprice, 2)}&nbsp;&nbsp;\\text{.} \\end{align}\\]</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"newprice": {"name": "newprice", "group": "Ungrouped variables", "definition": "precround(oldprice*(100-percentage)/100,2)", "description": "", "templateType": "anything", "can_override": false}, "name2": {"name": "name2", "group": "Ungrouped variables", "definition": "random(\"Kaden\",\"Ola\",\"Pat\",\"Skylar\",\"Wren\",\"Zendaya\")", "description": "", "templateType": "anything", "can_override": false}, "name1": {"name": "name1", "group": "Ungrouped variables", "definition": "random(\"Adair\",\"Aya\",\"Bergen\",\"Dua\",\"Fadhili\",\"Harper\")", "description": "", "templateType": "anything", "can_override": false}, "oldprice": {"name": "oldprice", "group": "Ungrouped variables", "definition": "switch(\n  item = \"TV\", random(179.99..1199.99 #10), \n  item = \"laptop\", random(209.99..799.99 #10),\n  item = \"smartphone\", random(109.99..799.99 #10),\n  item = \"PC\", random(209.99..969.99 #10),\n  item = \"gaming console\", random(89.99..349.99 #10),\n  399.99)", "description": "", "templateType": "anything", "can_override": false}, "percentage": {"name": "percentage", "group": "Ungrouped variables", "definition": "random(5..30)", "description": "<p>Discount percentage.</p>", "templateType": "anything", "can_override": false}, "item": {"name": "item", "group": "Ungrouped variables", "definition": "random(\"TV\", \"laptop\", \"smartphone\", \"PC\", \"gaming console\")", "description": "<p>The bought item.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "precround(precround(oldprice*(100-percentage)/100,2)*100/(100-percentage),2) = oldprice", "maxRuns": "1000"}, "ungrouped_variables": ["item", "name1", "percentage", "name2", "oldprice", "newprice"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>When {name1} told {name2} how much he had paid for the {item}, {name2} said the price had decreased by {percentage}% since she bought it.</p>\n<p>How much did&nbsp;{name2} pay for the {item}?</p>\n<p>&pound;&nbsp; [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "oldprice", "maxValue": "oldprice", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF09 Percentage of amount 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Find a percentage of an amount.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>What is {x}% of {y}?</p>", "advice": "<p>Taking {x}% of {y} is calculated by multiplying,</p>\n<p>\\[\\frac{\\var{x}}{100}\\times\\var{y}.\\]</p>\n<p>For this question we can calculate this by noticing that 10% of {y} is {y*0.1} and then since $\\var{x}\\%=\\var{x/10}\\times10\\%$ we can calculate {x}% of {y} as,<br/>\\[\\var{x/10}\\times10\\%\\times \\var{y}=\\var{x/10}\\times\\var{y*0.1}=\\var{x/100*y}.\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\" target=\"_blank\" rel=\"noopener\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(10..90 #10)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(10.. 100 # 10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "y*(x/100)", "maxValue": "y*(x/100)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF10 Percentage of amount 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "<p>Calculate one number as percentage of another.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>To find the percentage of a number we can use the formula:</p>\n<p>\\[ \\text{New value } = \\text{Original value } \\times \\text{Percentage in decimal form} \\]</p>\n<p>Firstly, to convert a percentage into decimal form we need to divide by $100$:</p>\n<p>\\[ \\var{p} \\% =&nbsp; \\var{p/100} \\]</p>\n<p>Therefore,</p>\n<p>\\[ \\begin{split} \\var{p} \\% \\,\\text{ of } \\var{og} &amp;\\,= \\var{og} \\times \\var{p/100} \\\\ &amp;\\,= \\var{ans} \\end{split} \\]</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\" target=\"_blank\" rel=\"noopener\">Use this link to find resources to help you revise how to work out percentages.</a></p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"p": {"name": "p", "group": "Ungrouped variables", "definition": "random(1..99)", "description": "", "templateType": "anything", "can_override": false}, "og": {"name": "og", "group": "Ungrouped variables", "definition": "random(101..999)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "og*p*0.01", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["p", "og", "ans"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find {p}% of {og}</p>", "minValue": "ans", "maxValue": "ans", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF11 One number as a percentage of another", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "<p>Given the number of international students enrolled on a course of $n$ students, calculate the percentage of 'home' students.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>{num_students}&nbsp;of the&nbsp;{class_size} students enrolled on a course are international students. &nbsp;What percentage are 'home' students?</p>", "advice": "<p>First work out the number of students who are not international. In this case it is&nbsp;{class_size} - {num_students} = {class_size-num_students} students.</p>\n<p>Then&nbsp;write this as a fraction out of {class_size}.&nbsp; &nbsp;$ \\frac{\\var{class_size-num_students}} {\\var{class_size}} $</p>\n<p>Then convert this to a percentage. You&nbsp;should put this fraction into your calculator and then multiply by 100:</p>\n<p>&nbsp;$ \\frac{\\var{class_size-num_students}} {\\var{class_size}} \\times&nbsp;100&nbsp;= \\var{(class_size-num_students)/class_size*100}\\%$</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Percentages\" target=\"_blank\" rel=\"noopener\">Use this link to find resources to help you revise how to calculate percentages.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"num_students": {"name": "num_students", "group": "Ungrouped variables", "definition": "per*class_size/100\n", "description": "<p>The number of students in the class who do speak a language other than English.&nbsp;</p>", "templateType": "anything", "can_override": false}, "class_size": {"name": "class_size", "group": "Ungrouped variables", "definition": "random(80..300)", "description": "", "templateType": "anything", "can_override": false}, "per": {"name": "per", "group": "Ungrouped variables", "definition": "random(5..90 except 50)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "num_students = precround(num_students,0) AND (num_students<>class_size/2 AND class_size<>100)", "maxRuns": 100}, "ungrouped_variables": ["num_students", "class_size", "per"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p></p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\var{class_size-num_students}\\%$", "$\\var{num_students*100/class_size}\\%$", "$\\var{num_students}\\%$", "$\\var{(class_size-num_students)/class_size*100}\\%$"], "matrix": [0, 0, 0, "1"], "distractors": ["Have you converted this to a percentage? Click on Reveal Answer and scroll down for Advice regarding this question.", "How many students do NOT speak a language other than English at home? Click on Reveal Answer and scroll down for Advice regarding this question.", "How many students do NOT speak a language other than English at home? Then convert this to a percentage. Click on Reveal Answer and scroll down for Advice regarding this question.", "Well done!"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF12 Simplify (cancel down) Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "Calculating the LCM and HCF of numbers by using prime factorisation.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Express the fraction below in its simplest form:</p>\n<p>\\[\\frac{\\var{x}}{\\var{y}}\\]</p>", "advice": "<p>To simplify a fraction we need to divide both numbers by their common factors.</p>\n<p>We can write $\\var{x}$ and $\\var{y}$ as a product of prime factors as follows:</p>\n<p>$\\var{x}=\\var{show_factors(x)}$</p>\n<p>$\\var{y}=\\var{show_factors(y)}$.</p>\n<p>So to fully simplify the fraction we need to divide both $\\var{x}$ and $\\var{y}$ by</p>\n<p>\\[\\var{show_factors(hcf_xy)}.\\]</p>\n<p>This gives us the fraction</p>\n<p>\\[\\frac{\\var{x/hcf_xy}}{\\var{y/hcf_xy}}\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x_powers": {"name": "x_powers", "group": "Ungrouped variables", "definition": "[random(1..3),random(0..3),random(0,1)]", "description": "", "templateType": "anything", "can_override": false}, "y_powers": {"name": "y_powers", "group": "Ungrouped variables", "definition": "[random(1..3),random(0..3),random(0,1)]", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "2^x_powers[0]*3^x_powers[1]*5^x_powers[2]", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "2^y_powers[0]*3^y_powers[1]*5^y_powers[2]", "description": "", "templateType": "anything", "can_override": false}, "hcf_xy": {"name": "hcf_xy", "group": "Ungrouped variables", "definition": "2^min(x_powers[0],y_powers[0])*3^min(x_powers[1],y_powers[1])*5^min(x_powers[2],y_powers[2])", "description": "", "templateType": "anything", "can_override": false}, "lcm_xy": {"name": "lcm_xy", "group": "Ungrouped variables", "definition": "2^max(x_powers[0],y_powers[0])*3^max(x_powers[1],y_powers[1])*5^max(x_powers[2],y_powers[2])", "description": "", "templateType": "anything", "can_override": false}, "primes": {"name": "primes", "group": "Ungrouped variables", "definition": "[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "500"}, "ungrouped_variables": ["x_powers", "y_powers", "x", "y", "hcf_xy", "lcm_xy", "primes"], "variable_groups": [], "functions": {"show_factors": {"parameters": [["n", "number"]], "type": "string", "language": "jme", "definition": "latex(  // mark the output as a string of raw LaTeX\n  join(\n    map(\n      if(a=1,p,p+'^{'+a+'}'), // when the exponent is 1, return p, otherwise return p^{exponent}\n      [p,a],\n      filter(x[1]>0,x,zip(primes,factorise(n)))  // for all the primes p which are factors of n, return p and its exponent\n    ),\n    ' \\\\times ' // join all the prime powers up with \\times symbols\n  )\n)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x/y}", "maxValue": "{x/y}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF13 Converting mixed numbers to top heavy", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": ["converting improper fractions to mixed numbers", "converting mixed numbers to improper fractions", "equivalent fractions", "improper fractions", "mixed numbers"], "metadata": {"description": "<p>This question tests the student's ability to identify equivalent fractions&nbsp;through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>A <em>mixed number</em> is a number consisting of an integer and a proper fraction, i.e. a number in the form $&nbsp;a \\displaystyle \\frac{b}{c}$ where $a$ is an integer and $\\displaystyle\\frac{b}{c}$ is a proper fraction: $b$ is smaller than $c$.</p>\n<p>An <em>improper fraction</em> is a fraction where the numerator is larger than the denominator, i.e. a number of the form $\\displaystyle\\frac{d}{e}$ where&nbsp;the numerator, $d$, is greater than the denominator, $e$.&nbsp;</p>\n<p>To convert a mixed number into an improper fraction, multiply the integer part of the mixed number, $a$, by the denominator, $c$.</p>\n<p>The numerator of the improper fraction will be equal to this&nbsp;added to what was already on the numerator of the proper fraction.</p>\n<p>The denominator of the proper fraction will stay the same when it converts to an improper fraction to give a final answer of</p>\n<p style=\"text-align: center;\">$\\displaystyle\\frac{({a}\\times{c})+b}{c}$.</p>\n<p>\\[<br/>{\\var{f}\\frac{\\var{g_coprime}}{\\var{h_coprime}}} = \\frac{({\\var{f}}\\times{\\var{h_coprime}})+{\\var{g_coprime}}}{{\\var{h_coprime}}}=\\simplify{{num}/{h_coprime}}\\text{.}<br/>\\]&nbsp;</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Fractions\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"g": {"name": "g", "group": "Ungrouped variables", "definition": "random(1..h except h)", "description": "<p>Random number between 1 and 15</p>", "templateType": "anything", "can_override": false}, "g_coprime": {"name": "g_coprime", "group": "Ungrouped variables", "definition": "g/gcd_gh", "description": "<p>PART C</p>", "templateType": "anything", "can_override": false}, "gcd_gh": {"name": "gcd_gh", "group": "Ungrouped variables", "definition": "gcd(g,h)", "description": "<p>PART C</p>", "templateType": "anything", "can_override": false}, "num": {"name": "num", "group": "Ungrouped variables", "definition": "((h_coprime*f)+g_coprime)", "description": "<p>numerator for the improper fraction c(i)</p>", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(10 .. 24#1)", "description": "<p>Random number between 1 and 24</p>", "templateType": "randrange", "can_override": false}, "h_coprime": {"name": "h_coprime", "group": "Ungrouped variables", "definition": "h/gcd_gh", "description": "<p>PART C</p>", "templateType": "anything", "can_override": false}, "gcdb": {"name": "gcdb", "group": "Ungrouped variables", "definition": "gcd({num},{h_coprime})", "description": "<p>gcd of num and h</p>", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(2 .. 5#1)", "description": "<p>Random number between 1 and 5</p>", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["f", "g", "h", "gcd_gh", "g_coprime", "h_coprime", "num", "gcdb"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n"}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Write the mixed number as an improper fraction and reduce it down to its simplest form.&nbsp;</p>\n<p>$\\displaystyle{\\var{f}\\frac{\\var{g_coprime}}{\\var{h_coprime}}} =$&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction>.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "num/gcdb", "maxValue": "num/gcdb", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "h_coprime/gcdb", "maxValue": "h_coprime/gcdb", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF14 Add Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Oliver Spenceley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23557/"}], "tags": ["adding and subtracting fractions", "adding fractions", "converting between decimals and fractions", "converting integers to fractions", "Fractions", "fractions", "integers", "manipulation of fractions", "subtracting fractions", "taxonomy"], "metadata": {"description": "<p>Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer&nbsp;and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following addition, giving the fraction in its simplest form.</p>", "advice": "<p>$\\displaystyle\\frac{\\var{a_coprime}}{\\var{b_coprime}}+\\frac{\\var{c_coprime}}{\\var{d_coprime}}$</p>\n<p>To add or subtract fractions, we need to have a common denominator on both fractions.</p>\n<p>To get a common denominator, we need to find the lowest common multiple of the two denominators.</p>\n<p>The lowest common multiple of $\\var{b_coprime}$ and $\\var{d_coprime}$ is $\\var{lcm}.$</p>\n<p>This will be the new denominator, and we need to multiply each fraction individually to ensure we get this denominator.&nbsp;</p>\n<p>For&nbsp;$\\displaystyle\\frac{\\var{a_coprime}}{\\var{b_coprime}}$, we need to multiply the fraction by $\\displaystyle\\frac{\\var{lcm_b}}{\\var{lcm_b}}$ to give $\\displaystyle\\frac{\\var{alcm_b}}{\\var{lcm}}.$</p>\n<p>For&nbsp;$\\displaystyle\\frac{\\var{c_coprime}}{\\var{d_coprime}}$, we need to multiply the fraction by&nbsp;$\\displaystyle\\frac{\\var{lcm_d}}{\\var{lcm_d}}$ to give $\\displaystyle\\frac{\\var{clcm_d}}{\\var{lcm}}.$</p>\n<p>Now that we have each fraction in terms of a common denominator, we can now add the fractions together.&nbsp;</p>\n<p>$\\displaystyle\\frac{\\var{alcm_b}}{\\var{lcm}}+\\frac{\\var{clcm_d}}{\\var{lcm}}=\\frac{(\\var{alcm_b}+\\var{clcm_d})}{\\var{lcm}}=\\frac{\\var{alcmclcm}}{\\var{lcm}}.$</p>\n<p>From this, we can try to simplify the result down by finding the greatest common divisor of the numerator and denominator and dividing the whole fraction by this amount.&nbsp;</p>\n<p>The greatest common divisor of $\\var{alcmclcm}$ and $\\var{lcm}$ is $\\var{gcd}.$</p>\n<p><span data-jme-visible=\"gcd &gt; 1\">Simplifying using this value gives a final answer of $\\displaystyle\\frac{\\var{num}}{\\var{denom}}.$</span></p>\n<p><span data-jme-visible=\"gcd = 1\">Therefore, the expression cannot be simplified further, and $\\displaystyle\\frac{\\var{num}}{\\var{denom}}$ is the final answer.</span></p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\"><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\" target=\"_blank\" rel=\"noopener\">Find out more about this topic using our resource</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"d_coprime": {"name": "d_coprime", "group": "Part a", "definition": "d/gcd_cd", "description": "", "templateType": "anything", "can_override": false}, "denom": {"name": "denom", "group": "Part a", "definition": "lcm/gcd", "description": "<p>PART A answer for the denominator of part a</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Part a", "definition": "random(1..5)", "description": "<p>PART A variable a - random number between 1 and 5.</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Part a", "definition": "random(5..15)", "description": "<p>PART A variable d - random number between 5 and 15.</p>", "templateType": "anything", "can_override": false}, "c_coprimeb_coprime": {"name": "c_coprimeb_coprime", "group": "Part a", "definition": "c_coprime*b_coprime", "description": "<p>PART A variable c times variable b</p>", "templateType": "anything", "can_override": false}, "gcd_ab": {"name": "gcd_ab", "group": "Part a", "definition": "gcd(a,b)", "description": "<p>PART A simplification of fractions in the question.</p>", "templateType": "anything", "can_override": false}, "lcm_b": {"name": "lcm_b", "group": "Part a", "definition": "lcm/b_coprime", "description": "<p>PART A lcm of b and d, divided by b</p>", "templateType": "anything", "can_override": false}, "num": {"name": "num", "group": "Part a", "definition": "alcmclcm/gcd", "description": "<p>PART A answer for the numerator input</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Part a", "definition": "random(5..10 except d)", "description": "<p>PART A variable b - random number between 5 and 10 and not the same value as d.</p>", "templateType": "anything", "can_override": false}, "a_coprimed_coprime": {"name": "a_coprimed_coprime", "group": "Part a", "definition": "a_coprime*d_coprime", "description": "<p>PART A variable a times variable d</p>", "templateType": "anything", "can_override": false}, "lcm_d": {"name": "lcm_d", "group": "Part a", "definition": "lcm/d_coprime", "description": "<p>PART A lcm of b and d, divided by d</p>", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Part a", "definition": "random(1..5)", "description": "<p>PART A variable c - random number between 1 and 5.</p>", "templateType": "anything", "can_override": false}, "clcm_d": {"name": "clcm_d", "group": "Part a", "definition": "c_coprime*lcm_d", "description": "<p>PART A variable c times the lcm of b and d, divided by d</p>", "templateType": "anything", "can_override": false}, "gcd": {"name": "gcd", "group": "Part a", "definition": "gcd(alcmclcm,lcm)", "description": "<p>PART A greatest common divisor of the variables alcmclcm and lcm</p>", "templateType": "anything", "can_override": false}, "alcm_b": {"name": "alcm_b", "group": "Part a", "definition": "a_coprime*lcm_b", "description": "<p>PART A variable a times the lcm of b and d, divided by b</p>", "templateType": "anything", "can_override": false}, "a_coprime": {"name": "a_coprime", "group": "Part a", "definition": "a/gcd_ab", "description": "<p>PART A</p>", "templateType": "anything", "can_override": false}, "b_coprime": {"name": "b_coprime", "group": "Part a", "definition": "b/gcd_ab", "description": "<p>PART A&nbsp;</p>", "templateType": "anything", "can_override": false}, "gcd_cd": {"name": "gcd_cd", "group": "Part a", "definition": "gcd(c,d)", "description": "<p>PART A&nbsp;</p>", "templateType": "anything", "can_override": false}, "lcm": {"name": "lcm", "group": "Part a", "definition": "lcm(b_coprime,d_coprime)", "description": "<p>PART A lowest common multiple of variable b_coprime and variable d_coprime.</p>", "templateType": "anything", "can_override": false}, "alcmclcm": {"name": "alcmclcm", "group": "Part a", "definition": "alcm_b+clcm_d", "description": "<p>PART A&nbsp;</p>", "templateType": "anything", "can_override": false}, "c_coprime": {"name": "c_coprime", "group": "Part a", "definition": "c/gcd_cd", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Part a", "variables": ["a", "a_coprime", "b", "b_coprime", "gcd_ab", "c", "c_coprime", "d", "d_coprime", "gcd_cd", "lcm", "a_coprimed_coprime", "c_coprimeb_coprime", "lcm_b", "lcm_d", "alcm_b", "clcm_d", "alcmclcm", "gcd", "num", "denom"]}], "functions": {}, "preamble": {"js": "", "css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n"}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle\\frac{\\var{a_coprime}}{\\var{b_coprime}}+\\frac{\\var{c_coprime}}{\\var{d_coprime}}=$ <fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "num", "maxValue": "num", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "denom", "maxValue": "denom", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF15 Subtract fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": ["adding and subtracting fractions", "adding fractions", "converting between decimals and fractions", "converting integers to fractions", "Fractions", "fractions", "integers", "manipulation of fractions", "subtracting fractions", "taxonomy"], "metadata": {"description": "<p>Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer&nbsp;and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following additions and subtractions, giving each fraction in its simplest form. Write the numerator (the top number) as negative if the fraction is negative.</p>", "advice": "<p>$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}-\\frac{\\var{h_coprime}}{\\var{j_coprime}}+2.$</p>\n<p></p>\n<p>The two fractions can be individually multiplied to achieve a common denominator of the lowest common multiple, $\\var{lcm2}.$</p>\n<p>$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}$ becomes $\\displaystyle\\frac{\\var{flcm2_g}}{\\var{lcm2}}$ and $\\displaystyle\\frac{\\var{h_coprime}}{\\var{j_coprime}}$ becomes&nbsp;$\\displaystyle\\frac{\\var{hlcm2_j}}{\\var{lcm2}}.$</p>\n<p>We can now subtract the second fraction from the first.</p>\n<p style=\"text-align: center;\">$\\displaystyle\\frac{\\var{flcm2_g}}{\\var{lcm2}}-\\frac{\\var{hlcm2_j}}{\\var{lcm2}}=\\frac{\\var{flcmhlcm}}{\\var{lcm2}}.$</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\"><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\" target=\"_blank\" rel=\"noopener\">Find out more about this topic using our resource.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"hlcm2_j": {"name": "hlcm2_j", "group": "Part b", "definition": "h_coprime*lcm2_j", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "lcm2": {"name": "lcm2", "group": "Part b", "definition": "lcm(g_coprime,j_coprime)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "gcd_fg": {"name": "gcd_fg", "group": "Part b", "definition": "gcd(f,g)", "description": "<p>PART B gcd of first fraction num and denom</p>", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Part b", "definition": "random(2..10 except h)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Part b", "definition": "random(1..10)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Part b", "definition": "random(1..10)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "h_coprime": {"name": "h_coprime", "group": "Part b", "definition": "h/gcd_hj", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "lcm2_j": {"name": "lcm2_j", "group": "Part b", "definition": "lcm2/j_coprime", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "j_coprime": {"name": "j_coprime", "group": "Part b", "definition": "j/gcd_hj", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "flcmhlcm": {"name": "flcmhlcm", "group": "Part b", "definition": "flcm2_g-hlcm2_j", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "g_coprime": {"name": "g_coprime", "group": "Part b", "definition": "g/gcd_fg", "description": "<p>PART B g_coprime</p>", "templateType": "anything", "can_override": false}, "gcd_hj": {"name": "gcd_hj", "group": "Part b", "definition": "gcd(h,j)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Part b", "definition": "random(2..10 except f except j)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "flcm2_g": {"name": "flcm2_g", "group": "Part b", "definition": "f_coprime*lcm2_g", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "lcm2_g": {"name": "lcm2_g", "group": "Part b", "definition": "lcm2/g_coprime", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "f_coprime": {"name": "f_coprime", "group": "Part b", "definition": "f/gcd_fg", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Part b", "variables": ["f", "f_coprime", "g", "g_coprime", "gcd_fg", "h", "h_coprime", "j", "j_coprime", "gcd_hj", "lcm2", "lcm2_g", "flcm2_g", "lcm2_j", "hlcm2_j", "flcmhlcm"]}], "functions": {}, "preamble": {"js": "", "css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n"}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}-\\frac{\\var{h_coprime}}{\\var{j_coprime}}=$&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "flcmhlcm", "maxValue": "flcmhlcm", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "lcm2", "maxValue": "lcm2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF16 Multiply Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Oliver Spenceley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23557/"}], "tags": ["improper fractions", "mixed numbers", "multiplication of fractions", "multiplying fractions", "squared fraction", "taxonomy"], "metadata": {"description": "<p>Several problems involving the multiplication of fractions, with increasingly difficult examples, including&nbsp;a mixed fraction and a squared fraction. The final part is a word problem.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following multiplication, giving the answer in its simplest form.</p>", "advice": "<h4></h4>\n<p>To multiply $\\displaystyle\\frac{\\var{a_coprime}}{\\var{c_coprime}}\\times\\frac{\\var{b_coprime}}{\\var{d_coprime}}$, address the numerators and denominators separately.</p>\n<p>Multiply the numerators across both fractions.</p>\n<p style=\"text-align: center;\">$\\var{a_coprime}\\times\\var{b_coprime}=\\var{ab}$,</p>\n<p>and then multiply the denominators across both fractions.</p>\n<p style=\"text-align: center;\">$\\var{c_coprime}\\times\\var{d_coprime}=\\var{cd}$.</p>\n<p>The values of the multiplied numerators and denominators will be the numerator and denominator of the new fraction: $\\displaystyle\\frac{\\var{ab}}{\\var{cd}}$.</p>\n<p>This answer may need simplifying down, and to do this, find the greatest common divisor in both the numerator and denominator and divide by this number.</p>\n<p>The greatest common divisor of $\\var{ab}$ and $\\var{cd}$ is $\\var{gcd}$.</p>\n<p>By using $\\var{gcd}$ to cancel down the fraction, the final answer is $\\displaystyle\\simplify{{ab}/{cd}}$.</p>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: center;\"><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>\n<h4></h4>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"k": {"name": "k", "group": "Part b", "definition": "random(1..7 except j)", "description": "<p>Random number between 1 and 20</p>", "templateType": "anything", "can_override": false}, "bb": {"name": "bb", "group": "Part d", "definition": "28*aa", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "Part d", "definition": "bb/7", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Part b", "definition": "random(1 .. 7#1)", "description": "<p>Random number between 1 and 20.</p>", "templateType": "randrange", "can_override": false}, "cd": {"name": "cd", "group": "Part a", "definition": "c_coprime*d_coprime", "description": "<p>Variable c times variable d.</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Part a", "definition": "random(2..12 except c)", "description": "<p>Random number from 1 to 12.</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Part a", "definition": "random(2 .. 12#1)", "description": "<p>Random number from 1 to 12.</p>", "templateType": "randrange", "can_override": false}, "l": {"name": "l", "group": "Part c", "definition": "random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "numif": {"name": "numif", "group": "Part b", "definition": "(f*h_coprime)+g_coprime", "description": "<p>Numerator of the improper fraction converted from a mixed number.</p>", "templateType": "anything", "can_override": false}, "gcd_gh": {"name": "gcd_gh", "group": "Part b", "definition": "gcd(g,h)", "description": "", "templateType": "anything", "can_override": false}, "fh": {"name": "fh", "group": "Part b", "definition": "f*h_coprime", "description": "<p>Variable f times variable h</p>", "templateType": "anything", "can_override": false}, "g_coprime": {"name": "g_coprime", "group": "Part b", "definition": "g/gcd_gh", "description": "", "templateType": "anything", "can_override": false}, "j_coprime": {"name": "j_coprime", "group": "Part b", "definition": "j/gcd_kj", "description": "", "templateType": "anything", "can_override": false}, "gcd_kj": {"name": "gcd_kj", "group": "Part b", "definition": "gcd(k,j)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Part b", "definition": "random(1 .. 4#1)", "description": "<p>Random number between 1 and 4 - integer part of the mixed number.</p>", "templateType": "randrange", "can_override": false}, "c_coprime": {"name": "c_coprime", "group": "Part a", "definition": "c/gcd_ac", "description": "", "templateType": "anything", "can_override": false}, "gcd": {"name": "gcd", "group": "Part a", "definition": "gcd(ab,cd)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Part a", "definition": "random(2 .. 12#1)", "description": "<p>Random number from 1 to 12.</p>", "templateType": "randrange", "can_override": false}, "d_coprime": {"name": "d_coprime", "group": "Part a", "definition": "d/gcd_bd", "description": "", "templateType": "anything", "can_override": false}, "ddcc": {"name": "ddcc", "group": "Part d", "definition": "dd*cc", "description": "", "templateType": "anything", "can_override": false}, "gcdb": {"name": "gcdb", "group": "Part b", "definition": "gcd(num,denom)", "description": "", "templateType": "anything", "can_override": false}, "gcd_ac": {"name": "gcd_ac", "group": "Part a", "definition": "gcd(a,c)", "description": "<p>PART A</p>", "templateType": "anything", "can_override": false}, "denom": {"name": "denom", "group": "Part b", "definition": "j_coprime*(h_coprime/gcda)", "description": "<p>Denominator of new fraction.</p>", "templateType": "anything", "can_override": false}, "l_coprime": {"name": "l_coprime", "group": "Part c", "definition": "l/gcd_lm", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Part c", "definition": "random(1..12 except l)", "description": "", "templateType": "anything", "can_override": false}, "a_coprime": {"name": "a_coprime", "group": "Part a", "definition": "a/gcd_ac", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Part b", "definition": "random(7 .. 10#1)", "description": "<p>Random number between 1 and 20.</p>", "templateType": "randrange", "can_override": false}, "num": {"name": "num", "group": "Part b", "definition": "k_coprime*{numif/gcda}", "description": "<p>Numerator of gap 0</p>", "templateType": "anything", "can_override": false}, "m_coprime": {"name": "m_coprime", "group": "Part c", "definition": "m/gcd_lm", "description": "", "templateType": "anything", "can_override": false}, "aa": {"name": "aa", "group": "Part d", "definition": "random(1..6)", "description": "", "templateType": "anything", "can_override": false}, "gcda": {"name": "gcda", "group": "Part b", "definition": "gcd({numif},{h_coprime})", "description": "<p>gcd of the numerator of the improper fraction</p>", "templateType": "anything", "can_override": false}, "h_coprime": {"name": "h_coprime", "group": "Part b", "definition": "h/gcd_gh", "description": "", "templateType": "anything", "can_override": false}, "ee": {"name": "ee", "group": "Part d", "definition": "ddcc/4", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Part a", "definition": "random(3,5,7,11)", "description": "<p>Random number from 1 to 12.</p>", "templateType": "anything", "can_override": false}, "b_coprime": {"name": "b_coprime", "group": "Part a", "definition": "b/gcd_bd", "description": "", "templateType": "anything", "can_override": false}, "l_coprime2": {"name": "l_coprime2", "group": "Part c", "definition": "l_coprime^2/gcd_lcmc", "description": "", "templateType": "anything", "can_override": false}, "k_coprime": {"name": "k_coprime", "group": "Part b", "definition": "k/gcd_kj", "description": "", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Part b", "definition": "Random(3,5,7,11,13,17)", "description": "<p>Random number between 1 and 20</p>", "templateType": "anything", "can_override": false}, "dd": {"name": "dd", "group": "Part d", "definition": "random(1..3)", "description": "", "templateType": "anything", "can_override": false}, "gcd_lcmc": {"name": "gcd_lcmc", "group": "Part c", "definition": "gcd((l_coprime)^2,(m_coprime)^2)", "description": "", "templateType": "anything", "can_override": false}, "m_coprime2": {"name": "m_coprime2", "group": "Part c", "definition": "m_coprime^2/gcd_lcmc", "description": "", "templateType": "anything", "can_override": false}, "gcd_lm": {"name": "gcd_lm", "group": "Part c", "definition": "gcd(l,m)", "description": "", "templateType": "anything", "can_override": false}, "ab": {"name": "ab", "group": "Part a", "definition": "a_coprime*b_coprime", "description": "<p>Variable a times variable b</p>", "templateType": "anything", "can_override": false}, "gcd_bd": {"name": "gcd_bd", "group": "Part a", "definition": "gcd(b,d)", "description": "", "templateType": "anything", "can_override": false}, "gcd2": {"name": "gcd2", "group": "Part b", "definition": "gcd(num,denom)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Part a", "variables": ["a", "b", "c", "d", "a_coprime", "b_coprime", "c_coprime", "d_coprime", "gcd_ac", "gcd_bd", "ab", "cd", "gcd"]}, {"name": "Part b", "variables": ["f", "g", "g_coprime", "h", "h_coprime", "gcd_gh", "k", "k_coprime", "j", "j_coprime", "gcd_kj", "fh", "numif", "num", "denom", "gcda", "gcdb", "gcd2"]}, {"name": "Part d", "variables": ["aa", "bb", "cc", "dd", "ddcc", "ee"]}, {"name": "Part c", "variables": ["l", "m", "gcd_lm", "l_coprime", "m_coprime", "gcd_lcmc", "l_coprime2", "m_coprime2"]}], "functions": {}, "preamble": {"js": "", "css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n"}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle\\frac{\\var{a_coprime}}{\\var{c_coprime}}\\times\\frac{\\var{b_coprime}}{\\var{d_coprime}}$ =&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ab}/{gcd}", "maxValue": "{ab}/{gcd}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{cd}/{gcd}", "maxValue": "{cd}/{gcd}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF17 Divide Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Oliver Spenceley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23557/"}], "tags": ["dividing fractions", "division of fractions", "Fractions", "fractions", "mixed numbers", "taxonomy"], "metadata": {"description": "<p>Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following sums&nbsp;involving division of fractions. Simplify your answers where possible.&nbsp;</p>", "advice": "<p>When faced with dividing fractions, it much easier to switch one of the fractions around and multiply them together instead of divide them.</p>\n<p style=\"text-align: center;\">\\[ \\left( \\frac{\\var{f_coprime}}{\\var{g_coprime}}\\div\\frac{\\var{h_coprime}}{\\var{j_coprime}} \\right) \\equiv \\left( \\frac{\\var{f_coprime}}{\\var{g_coprime}}\\times\\frac{\\var{j_coprime}}{\\var{h_coprime}} \\right) = \\frac{\\var{fj}}{\\var{gh}} \\]</p>\n<p>Then, simplify by finding the highest common divisor in the numerator and denominator which in this case is $\\var{gcd1}$.&nbsp;</p>\n<p>This gives a final answer of $\\displaystyle\\simplify{{fj}/{gh}}$.</p>\n<p></p>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: center;\"><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"f4h4": {"name": "f4h4", "group": "Ungrouped variables", "definition": "f4*h4_coprime", "description": "<p>variable f4 times h4.</p>\n<p>Used in part c)</p>", "templateType": "anything", "can_override": false}, "g4_coprime": {"name": "g4_coprime", "group": "Ungrouped variables", "definition": "g4/gcd(g4,h4)", "description": "<p>PART C</p>", "templateType": "anything", "can_override": false}, "h4": {"name": "h4", "group": "Ungrouped variables", "definition": "random(5..8 except g4)", "description": "<p>Random number but not the same number as variable g4.</p>\n<p>Used in part c.</p>", "templateType": "anything", "can_override": false}, "h3_coprime": {"name": "h3_coprime", "group": "Ungrouped variables", "definition": "h3/gcd(g3,h3)", "description": "<p>PART C</p>", "templateType": "anything", "can_override": false}, "f_coprime": {"name": "f_coprime", "group": "part a", "definition": "f/gcd(f,g)", "description": "<p>PART A</p>", "templateType": "anything", "can_override": false}, "g_coprime": {"name": "g_coprime", "group": "part a", "definition": "g/gcd(f,g)", "description": "<p>PART A</p>", "templateType": "anything", "can_override": false}, "j1_coprime": {"name": "j1_coprime", "group": "Ungrouped variables", "definition": "j1/gcd(h1,j1)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "gcd2": {"name": "gcd2", "group": "Ungrouped variables", "definition": "gcd(f1j1,g1h1)", "description": "<p>greatest common divisor of variables f1j1 and g1h1.</p>\n<p>Used in part b).</p>", "templateType": "anything", "can_override": false}, "g1_coprime": {"name": "g1_coprime", "group": "Ungrouped variables", "definition": "g1/gcd(f1,g1)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "h1_coprime": {"name": "h1_coprime", "group": "Ungrouped variables", "definition": "h1/gcd(h1,j1)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "gcd3": {"name": "gcd3", "group": "Ungrouped variables", "definition": "gcd(num,denom)", "description": "<p>greatest common denominator for part c.&nbsp;</p>", "templateType": "anything", "can_override": false}, "j1": {"name": "j1", "group": "Ungrouped variables", "definition": "random(h1..11 except h1)", "description": "<p>Random number between 2 and 20 and not the same value as variable h1.</p>\n<p>Used in part b).</p>", "templateType": "anything", "can_override": false}, "g1h1": {"name": "g1h1", "group": "Ungrouped variables", "definition": "g1_coprime*h1_coprime", "description": "<p>variable g1 times h1.&nbsp;</p>\n<p>Used in part b).</p>", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "part a", "definition": "random(2..10)", "description": "<p>Random number between 2 and 10.</p>\n<p>Used in part a).</p>", "templateType": "anything", "can_override": false}, "f4": {"name": "f4", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "<p>Random number.</p>\n<p>Used in part c).</p>", "templateType": "anything", "can_override": false}, "f1": {"name": "f1", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "<p>Random number between 2 and 20.</p>\n<p>Used in part b)</p>", "templateType": "anything", "can_override": false}, "g3": {"name": "g3", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "<p>Random number.</p>\n<p>Used in part c).</p>", "templateType": "anything", "can_override": false}, "f3h3": {"name": "f3h3", "group": "Ungrouped variables", "definition": "f3*h3_coprime", "description": "<p>variable f3 times h3.</p>", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "part a", "definition": "random(2..10)", "description": "<p>Random number from 2 to 10.</p>\n<p>Used in part a).</p>", "templateType": "anything", "can_override": false}, "gh": {"name": "gh", "group": "part a", "definition": "g_coprime*h_coprime", "description": "<p>variable g times variable h.</p>\n<p>Used in part a).</p>", "templateType": "anything", "can_override": false}, "j_coprime": {"name": "j_coprime", "group": "part a", "definition": "j/gcd(h,j)", "description": "<p>PART A</p>", "templateType": "anything", "can_override": false}, "denom": {"name": "denom", "group": "Ungrouped variables", "definition": "h3_coprime*(f4h4+g4_coprime)", "description": "<p>Unsimplified denominator of part c.</p>", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "part a", "definition": "random(h..12 except h)", "description": "<p>Random number between 2 and 10 and not the same value as h.</p>\n<p>Used in part a).</p>", "templateType": "anything", "can_override": false}, "f1j1": {"name": "f1j1", "group": "Ungrouped variables", "definition": "f1_coprime*j1_coprime", "description": "<p>variable f1 times j1.</p>\n<p>Used in part b).</p>", "templateType": "anything", "can_override": false}, "h4_coprime": {"name": "h4_coprime", "group": "Ungrouped variables", "definition": "h4/gcd(g4,h4)", "description": "<p>PART C</p>", "templateType": "anything", "can_override": false}, "g1": {"name": "g1", "group": "Ungrouped variables", "definition": "random(f1..11 except f1) ", "description": "<p>Random number between 2 and 30 and not the same value as variable f1.</p>\n<p>Used in part b).</p>", "templateType": "anything", "can_override": false}, "fj": {"name": "fj", "group": "part a", "definition": "f_coprime*j_coprime", "description": "<p>variable f times variable j.</p>\n<p>Used in part a).</p>", "templateType": "anything", "can_override": false}, "f3": {"name": "f3", "group": "Ungrouped variables", "definition": "random(1 .. 3#1)", "description": "<p>Random number between 2 and 6.</p>\n<p>Used in part c).</p>", "templateType": "randrange", "can_override": false}, "f1_coprime": {"name": "f1_coprime", "group": "Ungrouped variables", "definition": "f1/gcd(f1,g1)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "h3": {"name": "h3", "group": "Ungrouped variables", "definition": "random(5..8)", "description": "<p>Random number and not the same value as variable g3.&nbsp;</p>\n<p>Used in part c).</p>", "templateType": "anything", "can_override": false}, "gcd1": {"name": "gcd1", "group": "part a", "definition": "gcd(fj,gh)", "description": "<p>greatest common divisor of variable fj and gh.</p>\n<p>Used in part a).</p>", "templateType": "anything", "can_override": false}, "g3_coprime": {"name": "g3_coprime", "group": "Ungrouped variables", "definition": "g3/gcd(g3,h3)", "description": "<p>PART C</p>", "templateType": "anything", "can_override": false}, "h_coprime": {"name": "h_coprime", "group": "part a", "definition": "h/gcd(h,j)", "description": "<p>PART A</p>", "templateType": "anything", "can_override": false}, "g4": {"name": "g4", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "<p>Random number.</p>\n<p>Used in part c).</p>", "templateType": "anything", "can_override": false}, "h1": {"name": "h1", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "<p>Random number between 2 and 20.&nbsp;</p>\n<p>Used in part b).</p>", "templateType": "anything", "can_override": false}, "num": {"name": "num", "group": "Ungrouped variables", "definition": "h4_coprime*(f3h3+g3_coprime)", "description": "<p>numerator of the improper fraction in part c. Unsimplified.&nbsp;</p>", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "part a", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["f1", "g1", "f1_coprime", "g1_coprime", "h1", "j1", "h1_coprime", "j1_coprime", "f1j1", "g1h1", "gcd2", "f3", "g3", "h3", "g3_coprime", "h3_coprime", "f4", "g4", "h4", "g4_coprime", "h4_coprime", "f3h3", "f4h4", "num", "denom", "gcd3"], "variable_groups": [{"name": "part a", "variables": ["g", "f", "f_coprime", "g_coprime", "h", "j", "h_coprime", "j_coprime", "fj", "gh", "gcd1"]}], "functions": {}, "preamble": {"js": "", "css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n"}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}\\div\\frac{\\var{h_coprime}}{\\var{j_coprime}}=$&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "fj/gcd1", "maxValue": "fj/gcd1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "gh/gcd1", "maxValue": "gh/gcd1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF19 Ordering fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Put fractions in size order.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Which of these two fractions is the largest?</p>", "advice": "<p>To find which is bigger of $\\frac{\\var{top1}}{\\var{bot1}}$ and $\\frac{\\var{top2}}{\\var{bot2}}$ we need them to have the same denominator. A way to do this is to multiply the top and bottom of $\\frac{\\var{top1}}{\\var{bot1}}$ by $\\var{bot2}$ and multiply the top and bottom of $\\frac{\\var{top2}}{\\var{bot2}}$ by {bot1}. This doesn't change the the value of the fractions as this is just like multiplying by one.</p>\n<p>\\[\\frac{\\var{top1}}{\\var{bot1}}=\\frac{\\var{top1*bot2}}{\\var{bot1*bot2}},\\quad \\frac{\\var{top2}}{\\var{bot2}}=\\frac{\\var{top2*bot1}}{\\var{bot1*bot2}}\\]</p>\n<p>Now we can easily see which is bigger by comparing the numerator.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Fractions\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"top1": {"name": "top1", "group": "Ungrouped variables", "definition": "random(1..(bot1-1))", "description": "", "templateType": "anything", "can_override": false}, "top2": {"name": "top2", "group": "Ungrouped variables", "definition": "random(1..(bot2-1))", "description": "", "templateType": "anything", "can_override": false}, "bot1": {"name": "bot1", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "bot2": {"name": "bot2", "group": "Ungrouped variables", "definition": "random(1..10 except bot1)", "description": "", "templateType": "anything", "can_override": false}, "frac1": {"name": "frac1", "group": "Ungrouped variables", "definition": "top1/bot1", "description": "", "templateType": "anything", "can_override": false}, "frac2": {"name": "frac2", "group": "Ungrouped variables", "definition": "top2/bot2", "description": "", "templateType": "anything", "can_override": false}, "Is1Bigger": {"name": "Is1Bigger", "group": "Ungrouped variables", "definition": "award(1,frac1>frac2)", "description": "", "templateType": "anything", "can_override": false}, "Is2Bigger": {"name": "Is2Bigger", "group": "Ungrouped variables", "definition": "award(1,frac2>frac1)", "description": "", "templateType": "anything", "can_override": false}, "Question": {"name": "Question", "group": "Ungrouped variables", "definition": "[string(top1)+\"/\"+string(bot1),string(top2)+\"/\"+string(bot2)]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(frac1-frac2)>0", "maxRuns": "250"}, "ungrouped_variables": ["top1", "top2", "bot1", "bot2", "frac1", "frac2", "Is1Bigger", "Is2Bigger", "Question"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": "Question", "matrix": "[Is1Bigger,Is2Bigger]"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF22 FDP convert 3 - Fraction into decimal", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Convert a fraction into a decimal.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write $\\frac{\\var{x}}{\\var{y}}$ as a decimal. Round your answer to 3 decimal places.</p>", "advice": "<p><span style=\"font-weight: 400;\"></span>You can calculate the decimals by hand using long division of $\\var{x}.000$ divided by $\\var{y}$.<span style=\"font-weight: 400;\"></span></p>\n<p>In some cases you may be able to simplify the fraction to something that you know the decimal for.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Fractions\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(1..(y-1))", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "x/y", "maxValue": "x/y", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NU01 Convert Currency", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "<p>Exchange rates.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>On a particular day, 1 Pound Sterling (&pound;) is equivalent to {exchanget} United States Dollars (\\$). If you have \\$ {amount}, what does this equate to in Pound Sterling?&nbsp;</p>", "advice": "<p>To convert Dollars (\\$) into Pounds (&pound;) you will need to caculate:</p>\n<p>\\begin{align}<br/>\\frac{\\var{amount}}{\\var{exchange}} &amp;= \\var{answer}\\\\<br/>&amp;= \\var{answert},<br/>\\end{align}</p>\n<p>ensuring to round off to the nearest penny.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all\" target=\"_blank\" rel=\"noopener\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic</span></a>.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"exchange": {"name": "exchange", "group": "Ungrouped variables", "definition": "random(0.9 .. 1.2#0.01)", "description": "<p>Pound to dollar exchange rate.</p>", "templateType": "randrange", "can_override": false}, "amount": {"name": "amount", "group": "Ungrouped variables", "definition": "random(100 .. 1000#5)", "description": "<p>Amount of dollars.</p>", "templateType": "randrange", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "amount/exchange", "description": "", "templateType": "anything", "can_override": false}, "answert": {"name": "answert", "group": "Ungrouped variables", "definition": "currency(answer,\"\u00a3\",\"p\")", "description": "", "templateType": "anything", "can_override": false}, "exchanget": {"name": "exchanget", "group": "Ungrouped variables", "definition": "dpformat(exchange,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["exchange", "amount", "answer", "answert", "exchanget"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "answer", "maxValue": "answer", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "answert", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SD02 Interpret Pie Charts", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": [], "metadata": {"description": "<p>This question is about correctly interpreting pie charts.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>{geogebra_applet{\"https://www.geogebra.org/calculator/pmvumdrv\",[C: C,M: M]}}</p>\n<p>The Pie Chart above shows the responses to a question asked by someone trying to plan a social event for their workplace. It shows answers given to the question \"Where would you like to go for a staff social?\" with the options \"Meal\", \"Cinema\" and \"Games Cafe\".</p>", "advice": "<p>A Pie chart of this type can only be used to make statements about the&nbsp;<strong>proportions&nbsp;</strong>of data in each category and does not provide information about the actual frequencies.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\">For more information on Pie Charts follow this link.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"C": {"name": "C", "group": "Ungrouped variables", "definition": "random(60 .. 70#5)", "description": "", "templateType": "randrange", "can_override": false}, "M": {"name": "M", "group": "Ungrouped variables", "definition": "random(5 .. 25#5)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "C<>M", "maxRuns": 100}, "ungrouped_variables": ["C", "M"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>From the following comments which can you say are definitely true, definitely false and which do you not have enough information to know?</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["50 people responded that they would like to go to the cinema.", "About one third of people said they wanted to go for a meal.", "Over half the people responding said they wanted to go to the Games Cafe."], "matrix": [[0, 0, "1"], [0, "1", 0], ["1", 0, 0]], "layout": {"type": "all", "expression": ""}, "answers": ["Definitely true.", "Definitely false.", "Not enough information to know."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SD03 Interpret Bar Chart", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}], "tags": [], "metadata": {"description": "<p>Reading a value from a simple bar chart.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>The bar heights give the values of the spend.<br/><br/>Each company has two bars, the left one for last year (in red) and the&nbsp;right one for this year (in purple).<br/>Isolate last years spend by looking at the&nbsp;the bars on the right side, and choose the tallest bar, corresponding to the highest value.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {"std": ["all", "fractionNumbers"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"answervector": {"name": "answervector", "group": "Ungrouped variables", "definition": "vector((yo5-yo0)/yo0*100, (yo6-yo1)/yo1*100,(yo7-yo2)/yo2*100,(yo8-yo3)/yo3*100, (yo9-yo4)/yo4*100)", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "Ungrouped variables", "definition": "random(0.7..1.3#0.01 except 1 except aa except bb)", "description": "", "templateType": "anything", "can_override": false}, "aa": {"name": "aa", "group": "Ungrouped variables", "definition": "random(0.7..1.3#0.01 except 1)", "description": "", "templateType": "anything", "can_override": false}, "year": {"name": "year", "group": "Ungrouped variables", "definition": "yearvector[ii]", "description": "", "templateType": "anything", "can_override": false}, "yn": {"name": "yn", "group": "Ungrouped variables", "definition": "map(vsc*y+vsh,y,yo)", "description": "<p>new y values after the transformation</p>", "templateType": "anything", "can_override": false}, "eee": {"name": "eee", "group": "Ungrouped variables", "definition": "random(1.1..1.3#0.01 except a except b except c except d)", "description": "", "templateType": "anything", "can_override": false}, "yo": {"name": "yo", "group": "Ungrouped variables", "definition": "repeat(random(-5..5),5)", "description": "<p>the (random) original y values which relate to the x values</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(1.1..1.3#0.01 except a except b except c)", "description": "", "templateType": "anything", "can_override": false}, "yo9": {"name": "yo9", "group": "Ungrouped variables", "definition": "random(41..70#1 except yo5 except yo6 except yo7 except yo8)", "description": "", "templateType": "anything", "can_override": false}, "vsh": {"name": "vsh", "group": "Ungrouped variables", "definition": "if(selector='vsh',random(-3..3#0.5 except 0),0)\n", "description": "<p>vertical shift</p>", "templateType": "anything", "can_override": false}, "vsc": {"name": "vsc", "group": "Ungrouped variables", "definition": "if(selector='vsc',random(-2,-1,-0.5,0.5,2),1)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1.1..1.3#0.01 except a except b)", "description": "", "templateType": "anything", "can_override": false}, "bb": {"name": "bb", "group": "Ungrouped variables", "definition": "random(0.7..1.3#0.01 except 1 except aa)", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "max([yo1,yo0,yo2,yo3,yo4])", "description": "", "templateType": "anything", "can_override": false}, "students": {"name": "students", "group": "Ungrouped variables", "definition": "random(120..320#1)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1.1..1.3#0.01)", "description": "", "templateType": "anything", "can_override": false}, "yo2": {"name": "yo2", "group": "Ungrouped variables", "definition": "random(20..40#1 except yo1 except yo0)", "description": "", "templateType": "anything", "can_override": false}, "yo5": {"name": "yo5", "group": "Ungrouped variables", "definition": "random(41..70#1)", "description": "", "templateType": "anything", "can_override": false}, "yo8": {"name": "yo8", "group": "Ungrouped variables", "definition": "random(41..70#1 except yo5 except yo6 except yo7)", "description": "", "templateType": "anything", "can_override": false}, "yo1": {"name": "yo1", "group": "Ungrouped variables", "definition": "random(20..40#1 except yo0)", "description": "", "templateType": "anything", "can_override": false}, "yo7": {"name": "yo7", "group": "Ungrouped variables", "definition": "random(41..70#1 except yo5 except yo6)", "description": "", "templateType": "anything", "can_override": false}, "maxx": {"name": "maxx", "group": "Ungrouped variables", "definition": "max(map(abs(a),a,xn)+5)+1", "description": "", "templateType": "anything", "can_override": false}, "yearvector": {"name": "yearvector", "group": "Ungrouped variables", "definition": "vector(2007,2008,2009,2010,2011,2012,2013)", "description": "", "templateType": "anything", "can_override": false}, "ii": {"name": "ii", "group": "Ungrouped variables", "definition": "random(3..6#1)", "description": "", "templateType": "anything", "can_override": false}, "yo3": {"name": "yo3", "group": "Ungrouped variables", "definition": "random(20..40#1 except yo1 except yo0 except yo2)", "description": "", "templateType": "anything", "can_override": false}, "selector": {"name": "selector", "group": "Ungrouped variables", "definition": "'vsc'", "description": "", "templateType": "anything", "can_override": false}, "fakeanswer1": {"name": "fakeanswer1", "group": "Ungrouped variables", "definition": "random([yo1,yo0,yo2,yo3,yo4] except answer)", "description": "", "templateType": "anything", "can_override": false}, "hsh": {"name": "hsh", "group": "Ungrouped variables", "definition": "if(selector='hsh',random(-3..3 except 0),0)", "description": "<p>horizontal shift</p>", "templateType": "anything", "can_override": false}, "fakeanswer4": {"name": "fakeanswer4", "group": "Ungrouped variables", "definition": "random([yo9,yo7,yo8] except fakeanswer3)", "description": "", "templateType": "anything", "can_override": false}, "dd": {"name": "dd", "group": "Ungrouped variables", "definition": "random(0.7..1.3#0.01 except 1 except aa except bb except cc)", "description": "", "templateType": "anything", "can_override": false}, "percent": {"name": "percent", "group": "Ungrouped variables", "definition": "random(5..15#0.1 except 5 except 6 except 7 except 8 except 9 except 10 except 11 except 12 except 13 except 14 except 15)", "description": "", "templateType": "anything", "can_override": false}, "yo0": {"name": "yo0", "group": "Ungrouped variables", "definition": "random(20..40#1)", "description": "", "templateType": "anything", "can_override": false}, "xn": {"name": "xn", "group": "Ungrouped variables", "definition": "map((x-hsh)/hsc,x,xo)", "description": "<p>new transformed x values</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1.1..1.3#0.01 except a)", "description": "", "templateType": "anything", "can_override": false}, "xo": {"name": "xo", "group": "Ungrouped variables", "definition": "list(-2..2)", "description": "<p>original x values</p>", "templateType": "anything", "can_override": false}, "yo4": {"name": "yo4", "group": "Ungrouped variables", "definition": "random(20..40#1 except yo1 except yo0 except yo2 except yo3)", "description": "", "templateType": "anything", "can_override": false}, "fakeanswer2": {"name": "fakeanswer2", "group": "Ungrouped variables", "definition": "random([yo1,yo0,yo2,yo3,yo4] except answer except fakeanswer1)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(1.1..1.3#0.01 except a except b except c except d except e)", "description": "", "templateType": "anything", "can_override": false}, "yo51": {"name": "yo51", "group": "Ungrouped variables", "definition": "eee*yo5", "description": "", "templateType": "anything", "can_override": false}, "fakeanswer3": {"name": "fakeanswer3", "group": "Ungrouped variables", "definition": "random([yo6,yo7,yo8])", "description": "", "templateType": "anything", "can_override": false}, "increase": {"name": "increase", "group": "Ungrouped variables", "definition": "random(10..40#5)", "description": "", "templateType": "anything", "can_override": false}, "yo6": {"name": "yo6", "group": "Ungrouped variables", "definition": "random(41..70#1 except yo5)", "description": "", "templateType": "anything", "can_override": false}, "hsc": {"name": "hsc", "group": "Ungrouped variables", "definition": "if(selector='hsc',random(-2,-1,-0.5,0.5,2),1)", "description": "", "templateType": "anything", "can_override": false}, "yo41": {"name": "yo41", "group": "Ungrouped variables", "definition": "d*yo4", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["selector", "vsh", "hsh", "vsc", "hsc", "yo", "yn", "xo", "xn", "yo0", "yo1", "yo2", "yo3", "yo4", "maxx", "yo6", "yo7", "yo8", "yo9", "yo41", "yo5", "yo51", "a", "b", "c", "d", "eee", "f", "answer", "fakeanswer1", "fakeanswer2", "fakeanswer3", "fakeanswer4", "aa", "bb", "cc", "dd", "percent", "students", "yearvector", "ii", "year", "answervector", "increase"], "variable_groups": [], "functions": {}, "preamble": {"js": "function dragpoint_board() {\n  var scope = question.scope;\n\n  JXG.Options.text.display = 'internal';\n  \n  var yo0 = scope.variables.yo0.value;\n  var yo1 = scope.variables.yo1.value;\n  var yo2 = scope.variables.yo2.value;\n  var yo3 = scope.variables.yo3.value;\n  var yo4 = scope.variables.yo4.value;\n  var yo5 = scope.variables.yo5.value;\n  var yo6 = scope.variables.yo6.value;\n  var yo7 = scope.variables.yo7.value; \n  var yo8 = scope.variables.yo8.value;\n  var yo9 = scope.variables.yo9.value; \n  \n  var div = Numbas.extensions.jsxgraph.makeBoard('550px','550px',{boundingBox:[-0.8,82,16,-8], axis:false, grid:true});\n \n  question.display.html.querySelector('#dragpoint').append(div);\n  \n  var board = div.board;\n  \n// board.suspendUpdate();           \n\n  \n var dataArr = [yo0,yo5,0,yo1,yo6,0,yo2,yo7,0,yo3,yo8,0,yo4,yo9]; \n  \n var xaxis = board.create('axis', [[0, 0], [12, 0]], {withLabel: true, name: \"Bank\", label: {offset: [250,-30]}});\n  \n  xaxis.removeAllTicks();  \n   \n  board.create('axis', [[0, 0], [0, 10]], {hideTicks:true, withLabel: false, name: \"\", label: {offset: [-110,300]}});\n  \n  var pop0 = board.create('point', [1.5,0],{name:'Morgan',fixed:true,size:0,color:'black',face:'diamond', label:{offset:[-20,-8]}});\n  var pop1 = board.create('point',[4.5,0],{name:'Strome',fixed:true,size:0,color:'black',face:'diamond', label:{offset:[-20,-8]}});\n  var pop2 = board.create('point',[7.5,0],{name:'Bentley',fixed:true,size:0,color:'black', face:'diamond', label:{offset:[-15,-8]}});\n  var pop3 = board.create('point',[10.5,0],{name:'Sand',fixed:true,size:0,color:'black', face:'diamond', label:{offset:[-15,-8]}});\n  var pop4 = board.create('point',[13.5,0],{name:'Karchen',fixed:true,size:0,color:'black', face:'diamond', label:{offset:[-15,-8]}});\n  var leg1 = board.create('point',[12,75],{name:'last year',fixed:true,size:6,color:'#DA2228', face:'square', label:{offset:[9,0]}});\n  var leg2 = board.create('point',[12,72],{name:'this year',fixed:true,size:6,color:'#6F1B75', face:'square', label:{offset:[9,0]}});\n  \n  \n//  var chart = board.createElement('chart', dataArr, \n  //                              {chartStyle:'bar', fillOpacity:1, width:1,\n    //     colorArray:['#8E1B77','#8E1B77','Red','Red','blue','red','blue','red','red','blue', 'red','blue','red','red'], shadow:false});\n \n//var chart = board.createElement('chart', dataArr, \n  //                              {chartStyle:'bar', width:1,fillOpacity:1, fillColor:'red', shadow:false});  \n  \n  \n    var a = board.create('chart', [[1,2,3],[yo0,yo5,0]], {chartStyle:'bar',colors:['#DA2228','#6F1B75','#6F1B75'],width:1,fillOpacity:1});\n    var b = board.create('chart', [[4,5,6],[yo1,yo6,0]], {chartStyle:'bar',width:1,colors:['#DA2228','#6F1B75','#6F1B75'],fillOpacity:1});\n    var c = board.create('chart', [[7,8,9],[yo2,yo7,0]], {chartStyle:'bar',width:1,colors:['#DA2228','#6F1B75','#6F1B75'],fillOpacity:1});\n    var d = board.create('chart', [[10,11,12],[yo3,yo8,0]], {chartStyle:'bar',width:1,colors:['#DA2228','#6F1B75','#6F1B75'],fillOpacity:1});\n    var e = board.create('chart', [[13,14],[yo4,yo9]], {chartStyle:'bar',width:1,colors:['#DA2228','#6F1B75'],fillOpacity:1});\n  \n    board.unsuspendUpdate();\n  \n  var txt1 = board.create('text',[-0.3,30, 'Investment \u00a3(m)'], {fontColor:'black', fontSize:14, rotate:90});\n  \n // var txt = board.create('text',[0.5,75, 'Investment (m)'], {fontSize:14, rotate:90});\n  \n // var txt1 = board.create('text',[8,76, 'red bars represent 2010'], {fontColor:'red', fontSize:14, rotate:90});\n  \n // var txt2 = board.create('text',[8,73, 'blue bars represents 2011'], {fontSize:14, rotate:90});\n\n // var myColors = new Array('red', 'blue', 'white','red', 'blue', 'white','red', 'blue', 'white','red', 'blue', 'white','red', 'blue');\n  \n  \n  \n  //board.unsuspendUpdate();\n\n    // Rotate text around the lower left corner (-2,-1) by 30 degrees.\n   // var tRot = board.create('transform', [90.0*Math.PI/180.0, -1,40], {type:'rotate'}); \n  //  tRot.bindTo(txt);\n  //  board.update();\n\n  \n//var chart2 = board.createElement('chart', dataArr, {chartStyle:'line,point'});\n//chart2[0].setProperty('strokeColor:black','strokeWidth:2','shadow:true');\n//for(var i=0; i<11;i++) {\n //   chart2[1][i].setProperty({strokeColor:'black',fillColor:'white',face:'[]', size:4, strokeWidth:2});\n//}\n//board.unsuspendUpdate();  \n                       \n  //board.unsuspendUpdate();\n\n}\n\nquestion.signals.on('HTMLAttached',function() {\n  dragpoint_board();\n});", "css": "table#values th {\n  background: none;\n  text-align: center;\n}"}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<div id=\"dragpoint\"><strong>Banking Sector: IT Infrastructure Spending</strong></div>\n<p style=\"text-align: center;\"><em></em></p>\n<p>What was the maximum spend by a single company last year?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showBlankOption": true, "showCellAnswerState": true, "choices": ["<p>&pound;{answer} m</p>", "<p>&pound;{fakeanswer1} m &nbsp; &nbsp;</p>", "<p>&pound;{fakeanswer2} m &nbsp; &nbsp; &nbsp;&nbsp;</p>", "<p>&pound;{fakeanswer3} m &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p>", "<p>&pound;{fakeanswer4} m &nbsp;&nbsp;</p>"], "matrix": ["1", 0, 0, 0, 0], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SD04 Interpret a Box Plot", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": [], "metadata": {"description": "<p>Interpreting the elements of a box plot</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The diagram below shows a box plot of some data.</p>\n<p>{geogebra_applet{\"https://www.geogebra.org/m/aj2hcbhg\",[lv: lv,lq: lq,m: m,uq: uq,hv: hv]}}</p>\n<p></p>", "advice": "<p><span style=\"font-family: arial, helvetica, sans-serif;\">A boxplot (also known as a box-and-whisker diagram or plot) is a convenient way of graphically depicting groups of numerical data through their five-number summaries: the smallest observation (sample minimum), lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation (sample maximum). A boxplot may also indicate which observations, if any, might be considered outliers.</span></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\"><span style=\"font-family: arial, helvetica, sans-serif;\">For more information on box plots follow this link.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"lv": {"name": "lv", "group": "Ungrouped variables", "definition": "random(2 .. 6#1)", "description": "", "templateType": "randrange", "can_override": false}, "lq": {"name": "lq", "group": "Ungrouped variables", "definition": "random(7 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(11 .. 14#1)", "description": "", "templateType": "randrange", "can_override": false}, "uq": {"name": "uq", "group": "Ungrouped variables", "definition": "random(15 .. 22#1)", "description": "", "templateType": "randrange", "can_override": false}, "hv": {"name": "hv", "group": "Ungrouped variables", "definition": "random(23 .. 30#1)", "description": "", "templateType": "randrange", "can_override": false}, "IQR": {"name": "IQR", "group": "Ungrouped variables", "definition": "uq-lq", "description": "", "templateType": "anything", "can_override": false}, "range": {"name": "range", "group": "Ungrouped variables", "definition": "hv-lv", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["lv", "lq", "m", "uq", "hv", "IQR", "range"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of these statements are true and which are false?</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["The range of the data is $\\var{range}$.", "The Interquarttile range of the data is larger than the range of the data.", "You can calculate the mean of the data from this Box plot.", "<p>The median of the data is $\\var{m}$.</p>", "The mode of the data is $\\var{lv-3}$."], "matrix": [["1", 0], [0, "1"], [0, "1"], ["1", 0], [0, "1"]], "layout": {"type": "all", "expression": ""}, "answers": ["True.", "False."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SD06 Reading a Histogram", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "<p>Reading a value from a histogram.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The histogram shows information about distances run on a Sunday by some randomly asked people in a park.&nbsp;</p>\n<div id=\"dragpoint\"></div>\n<p></p>", "advice": "<p><strong>a)</strong></p>\n<p>To calculate the frequencies using the following formula:</p>\n<p style=\"padding-left: 40px;\">frequency = class width $\\times$ frequency density&nbsp;</p>\n<p>Hence our table becomes:</p>\n<table style=\"width: 439px; height: 106px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 148.969px; height: 18px;\"><strong>Distance, $km$</strong></td>\n<td style=\"width: 257.031px; height: 18px;\"><strong>Frequency&nbsp;</strong></td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"width: 148.969px; height: 22px;\">$0 &lt; t \\leq 10$</td>\n<td style=\"width: 257.031px; height: 22px;\">$10 \\times \\var{yo0} = \\var{freq0}$</td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"width: 148.969px; height: 22px;\">$10 &lt; t \\leq 15$</td>\n<td style=\"width: 257.031px; height: 22px;\">$5 \\times \\var{yo1} = \\var{freq1}$</td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"width: 148.969px; height: 22px;\">$15 &lt; t \\leq 20$</td>\n<td style=\"width: 257.031px; height: 22px;\">$5 \\times \\var{yo2} = \\var{freq2}$</td>\n</tr>\n<tr style=\"height: 22px;\">\n<td style=\"width: 148.969px; height: 22px;\">$20 &lt; t \\leq 30$</td>\n<td style=\"width: 257.031px; height: 22px;\">$10 \\times \\var{yo3} = \\var{freq3}$</td>\n</tr>\n</tbody>\n</table>\n<p>Hence, to find the total number of people that ran that day:</p>\n<p>$\\var{freq0} + \\var{freq1} + \\var{freq2} + \\var{freq3} = \\var{total}.$</p>\n<p><strong>b)&nbsp;</strong></p>\n<p>The frequency of runners that ran less than $10km$ is found by calculating the frequency from the first bar on the histogram:</p>\n<p>class width $\\times$ frequency density $= 10 \\times \\var{yo0} = \\var{freq0}$.</p>\n<p><strong>c)</strong></p>\n<p>The frequency of runners that ran between $15km$ and $20km$ is found by calculating the frequency from the third bar on the histogram:</p>\n<p>class width $\\times$ frequency density $= 5 \\times \\var{yo2} = \\var{freq2}$.</p>\n<p><strong>d)</strong></p>\n<p>To estimate how many runners ran more than $25km$ we need again need to use the frequency = class width \\times frequency density formula.</p>\n<p>Here the class width is $5$ because we are looking for the frequency of runners that ran between $25km$ and $30km$ from the college.</p>\n<p>Frequency $= 5 \\times \\var{yo3} = \\var{5*yo3}.$</p>\n<p>If this number is a decimal we round up to get $\\var{m25}$.</p>\n<p><strong>e)</strong></p>\n<p>As in part <strong>d)</strong>,to estimate how many runners ran less than $7km$ we use the frequency = class width \\times frequency density formula.</p>\n<p>Here the class width is $7$ because we are looking for the frequency of runners that ran between 0 and 7 km.</p>\n<p>Frequency $= 7 \\times \\var{yo0} = \\var{7*yo0}.$</p>\n<p>If this number is a decimal we round up to get $\\var{l7}$.</p>\n<p><strong>f)</strong></p>\n<p>To estimate how many runners ran between $5km$ and $12.5km$ we use a method similar to that in part <strong>d)</strong> and <strong>e)</strong> but, this time, we need to use information from both the first and second bar on the histogram.&nbsp;</p>\n<p>Let's first calculate how many runners ran between $5km$ and $10km$:</p>\n<p>frequency $=$ class width $\\times$ frequency density $= 5 \\times \\var{yo0} = \\var{5*yo0}$.</p>\n<p>Now we need to calculate how many runners ran between $10km$ and $12.5km$:</p>\n<p>frequency $=$ class width $\\times$ frequency density $= 2.5 \\times \\var{yo1} = \\var{2.5*yo1}$.</p>\n<p>Putting this together the number of runners that ran between $5km$ and $12.5km$ is $\\var{5*yo0} + \\var{2.5*yo1} = \\var{5*yo0 + 2.5*yo1}.$</p>\n<p>If this number is a decimal we round up to get $\\var{ef}.$</p>\n<p><strong>g)</strong></p>\n<p>The number of runners that ran between $10km$ and $14km$ is $4 \\times \\var{yo1} = \\var{4*yo1}.$<br/><br/>If this number is a decimal we round up to get $\\var{eh}.$</p>\n<p><strong>i)</strong></p>\n<p>The number of runners that ran further than $18km$ is:</p>\n<p>$2 \\times \\var{yo2} + 10 \\times \\var{yo3} = \\var{2*yo2} + \\var{freq3} = \\var{2*yo2+freq3}.$<br/><br/>If this number is a decimal we round up to get $\\var{ej}.$</p>\n<p><strong>Did you get a decimal </strong><strong>answer? </strong>Were you surprised to see a whole number answer when you got a decimal on one of the estimate questions? Look at the context of the question, you cannot have $0.5$ of a student so we round our answers up to the next whole number!</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {"std": ["all", "fractionNumbers"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"yo2": {"name": "yo2", "group": "Ungrouped variables", "definition": "random(1 .. 39#1)", "description": "<p>Frequency Density</p>", "templateType": "randrange", "can_override": false}, "yo1": {"name": "yo1", "group": "Ungrouped variables", "definition": "random(1 .. 39#1)", "description": "<p>Frequency Density</p>", "templateType": "randrange", "can_override": false}, "yo3": {"name": "yo3", "group": "Ungrouped variables", "definition": "random(1 .. 39#1)", "description": "<p>Frequency Density</p>", "templateType": "randrange", "can_override": false}, "selector": {"name": "selector", "group": "Ungrouped variables", "definition": "'vsc'", "description": "", "templateType": "anything", "can_override": false}, "yo0": {"name": "yo0", "group": "Ungrouped variables", "definition": "random(1 .. 39#1)", "description": "<p>Frequency Density</p>", "templateType": "randrange", "can_override": false}, "total": {"name": "total", "group": "Ungrouped variables", "definition": "freq0+freq1+freq2+freq3", "description": "<p>Sum of frequencies</p>", "templateType": "anything", "can_override": false}, "freq0": {"name": "freq0", "group": "Ungrouped variables", "definition": "10*yo0", "description": "<p>Frequency</p>", "templateType": "anything", "can_override": false}, "freq1": {"name": "freq1", "group": "Ungrouped variables", "definition": "yo1*5", "description": "<p>Frequency</p>", "templateType": "anything", "can_override": false}, "freq2": {"name": "freq2", "group": "Ungrouped variables", "definition": "5*yo2", "description": "<p>Frequency</p>", "templateType": "anything", "can_override": false}, "freq3": {"name": "freq3", "group": "Ungrouped variables", "definition": "10*yo3", "description": "<p>Frequency</p>", "templateType": "anything", "can_override": false}, "m25": {"name": "m25", "group": "Ungrouped variables", "definition": "round(5*yo3)", "description": "<p>How many people ran more than 25km&nbsp;</p>", "templateType": "anything", "can_override": false}, "l7": {"name": "l7", "group": "Ungrouped variables", "definition": "round(7*yo0)", "description": "<p>How many runners ran less than 7km</p>", "templateType": "anything", "can_override": false}, "Ef": {"name": "Ef", "group": "Ungrouped variables", "definition": "round(5*yo0 + 2.5*yo1)", "description": "<p>Number of people running between 5 &amp; 12.5 km</p>", "templateType": "anything", "can_override": false}, "eh": {"name": "eh", "group": "Ungrouped variables", "definition": "round(4*yo1)", "description": "<p>Number of runners running between 10 &amp; 14km</p>", "templateType": "anything", "can_override": false}, "ej": {"name": "ej", "group": "Ungrouped variables", "definition": "round(2*yo2 + freq3)", "description": "<p>Number of runners running more than 18km</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["selector", "yo0", "yo1", "yo2", "yo3", "total", "freq0", "freq1", "freq2", "freq3", "m25", "l7", "Ef", "eh", "ej"], "variable_groups": [], "functions": {}, "preamble": {"js": "function dragpoint_board() {\n  var scope = question.scope;\n\n  JXG.Options.text.display = 'internal';\n  \n  var yo0 = scope.variables.yo0.value;\n  var yo1 = scope.variables.yo1.value;\n  var yo2 = scope.variables.yo2.value;\n  var yo3 = scope.variables.yo3.value;\n  \n  var div = Numbas.extensions.jsxgraph.makeBoard('550px','550px',{boundingBox:[-5,42,35,-5], axis:false, grid:true});\n \n  question.display.html.querySelector('#dragpoint').append(div);\n  \n  var board = div.board;\n  \nboard.suspendUpdate();           \n\n var dataArr = [yo0,0,yo1,0,yo2,0,yo3]; \n  \n var xaxis = board.create('axis', [[0, 0], [12, 0]], {withLabel: true, name: \"Distance, km\", label: {offset: [250,-30]}});\n   \n var yaxis = board.create('axis', [[0, 0], [0, 10]], {hideTicks:true, withLabel: true, name: \"Frequency Density\", label: {rotation: 90, offset: [-60,300]}});\n// var yaxis = board.create('axis', [[0, 0], [0, 10]], {hideTicks:true, withLabel: false, name: \"Frequency Density\", label: {rotation: 90, offset: [-60,300]}});\n//var Rot board.create('transform',[Math.PI/2,0,5],{type:'rotate'});\n//  var ylabel = board.create('text', [0,5,\"Frequency Density\"], {label: {rotation: 90}});\n//  Rot.bindTo(ylabel);\n// board.update();\n\n  \n   var a = board.create('chart', [[5,10],[yo0,0]], {chartStyle:'bar',colors:['#76ba1e'],width:10,fillOpacity:0.4});\n   var b = board.create('chart', [[12.5,15],[yo1,0]], {chartStyle:'bar',width:5,colors:['#89CFF0'],fillOpacity:0.4});\n   var c = board.create('chart', [[17.5,20],[yo2,0]], {chartStyle:'bar',width:5,colors:['#76ba1e'],fillOpacity:0.4});\n   var d = board.create('chart', [[25,30],[yo3,0]], {chartStyle:'bar',width:10,colors:['#89CFF0'],fillOpacity:0.4});\n  \n}\n\nquestion.signals.on('HTMLAttached',function() {\n  dragpoint_board();\n});", "css": "table#values th {\n  background: none;\n  text-align: center;\n}"}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "a)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How many people were asked about the distance they ran that day?</p>", "minValue": "total", "maxValue": "total", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "b)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How many runners ran less than 10 km that day?</p>", "minValue": "freq0", "maxValue": "freq0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "c)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How many people ran between 10 and 15 km that day?</p>", "minValue": "freq1", "maxValue": "freq1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "d)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Estimate how many runners ran more than 25 km that day?</p>", "minValue": "m25", "maxValue": "m25", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "e)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Estimate how many runners ran less than 7 km that day?</p>", "minValue": "l7", "maxValue": "l7", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "f)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Estimate how many people ran between 5 km and 12.5 km.</p>", "minValue": "Ef", "maxValue": "Ef", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SD07 Interpreting Line Graphs", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Francesca recorded the number of customers in a supermarket every two hours.</p>\n<p>She began at 9 am and finished at 7 pm.</p>\n<p>The line graph below shows her results.</p>\n<p>{geogebra_applet{\"https://www.geogebra.org/classic/s4w7nmga\",[y1:y1,y3:y3,y4:y4,y6:y6]}}</p>", "advice": "<p><strong>a)</strong> You want to find the point on the graph with the greatest frequency. You can see that this is at 1pm when there were $\\var{y3}$ cars in the car park.</p>\n<p><strong>b)</strong> We find 11am on the $x$-axis and look vertically upwards until we find the point. From here we go horiztonally across to the $y$-axis to read the frequency. We can see that at 11am there were $\\var{y2}$ cars in the car park.</p>\n<p><strong>c)</strong> We want to find $\\var{number}$ on the $y$-axis and then look horiztonally across until we find the point. From here we move down to the $x$-axis to see at which time there were $\\var{number}$ cars in the car park. We can see this occured at $\\var{answerc}\\var{time}$.</p>\n<p><strong>d)</strong> We must find 6pm on the $x$-axis. This isn't marked on like the other times but we know it sits half way between 5pm and 7pm. From here we look vertically upwards until we meet the red line on our graph. Notice we don't have a point for this time, hence why this is an estimate. From here we move hortizontally across to the $y$-axis to find the frequency. At 6pm we estimate that there were $\\var{y56}$ cars in the car park.</p>\n<p><strong>e)</strong> We must find the frequency of cars at 1pm and at 3pm using the same steps as in part&nbsp;<strong>b</strong>. At 3pm there were $\\var{y4}$ cars in the car park and we subtract this from $\\var{y3}$ which is the number of cars in the car park at 1pm. Hence, $\\var{y3}-\\var{y4}=\\var{y3-y4}$.</p>\n<form autocomplete=\"off\">\n<div class=\"adviceContainer\" data-bind=\"visible: hasAdvice() &amp;&amp; adviceDisplayed()\" localise-data-jme-context-description=\"question.advice\">\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#data-display\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>\n</div>\n</form>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"y6": {"name": "y6", "group": "Ungrouped variables", "definition": "random(10 .. 40#10)", "description": "<p>Number of customers in supermarket at 7pm.</p>", "templateType": "randrange", "can_override": false}, "y5": {"name": "y5", "group": "Ungrouped variables", "definition": "y6+20", "description": "<p>Number of customers in supermarket at 5pm.</p>", "templateType": "anything", "can_override": false}, "y3": {"name": "y3", "group": "Ungrouped variables", "definition": "random(82 .. 100#1)", "description": "<p>Number of customers in supermarket at 1pm.</p>", "templateType": "randrange", "can_override": false}, "y4": {"name": "y4", "group": "Ungrouped variables", "definition": "random(50 .. 75#1)", "description": "<p>Number of customers in supermarket at 3pm.</p>", "templateType": "randrange", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "y1+10", "description": "<p>Number of customers in supermarket at 11am.</p>", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "random(10 .. 20#5)", "description": "<p>Number of customers in supermarket at 9am</p>", "templateType": "randrange", "can_override": false}, "y56": {"name": "y56", "group": "Ungrouped variables", "definition": "(y5+y6)/2", "description": "<p>Number of customers in supermarket at 6pm.</p>", "templateType": "anything", "can_override": false}, "number": {"name": "number", "group": "Ungrouped variables", "definition": "random(y1,y3,y4,y5,y6)", "description": "<p>Randomly select which number of customers user needs to identify associated time for.</p>", "templateType": "anything", "can_override": false}, "answerc": {"name": "answerc", "group": "Ungrouped variables", "definition": "if(number=y1,9,if(number=y3,1,if(number=y4,3,if(number=y5,5,if(number=y6,7,0)))))", "description": "<p>Associated time to randomly selected frequency variable (number)</p>", "templateType": "anything", "can_override": false}, "time": {"name": "time", "group": "Ungrouped variables", "definition": "if(answerc=9, 'am', if(answerc=11,'am',if(answerc=1,'pm',if(answerc=3,'pm',if(answerc=5,'pm',if(answerc=7,'pm',0))))))", "description": "<p>For printing am or pm depending on time selelected - to appear in advice only&nbsp;</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["y6", "y5", "y3", "y4", "y2", "y1", "y56", "number", "answerc", "time"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": true, "customName": "a)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>When were the most customers in the supermarker?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["9 am", "11 am", "1 pm", "3 pm", "5 pm", "7 pm"], "matrix": [0, 0, "1", 0, 0, 0], "distractors": ["", "", "", "", "", ""]}, {"type": "numberentry", "useCustomName": true, "customName": "b)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How many customers were in the supermarket at 11 am?</p>", "minValue": "y2", "maxValue": "y2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "c)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>At what time were there {number} customers in the supermarket?</p>\n<p><em>If your answer was 12pm you would just write 12 in the box.</em></p>", "minValue": "answerc", "maxValue": "answerc", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "d)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Estimate the number of customers in the supermarket at 6pm.</p>", "minValue": "y56", "maxValue": "y56", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "e)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How many less customers were there in the supermarket at 3pm than 1pm?</p>", "minValue": "y3-y4", "maxValue": "y3-y4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SE01 Types of data", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": ["continuous data", "discrete data", "taxonomy"], "metadata": {"description": "<p>Decide whether each of the described sets of data is drawn from a discrete or continuous distribution.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Decide whether the following data sets are discrete or continuous.</p>", "advice": "<p>Data can either be <strong>discrete</strong> or <strong>continuous</strong>.</p>\n<ul>\n<li><strong>Discrete data</strong> consists of integers, units of measurement cannot be split. Only certain values have a meaning.</li>\n<li><strong>Continuous data</strong> can be shown on a number line, all points on this line have a meaning. In between two measurements there's always a valid \"middle\" measurement. So for example, between 156.3cm and 156.4cm there's 156.35cm.</li>\n</ul>\n<p></p>\n<h4>a)</h4>\n<p><span data-jme-visible=\"ranc = 0\">Height is a continuous variable. For example, 180.3cm&nbsp;and 180.4cm have a valid midpoint 180.35cm.</span><span data-jme-visible=\"ranc = 1\">Weight is a continuous variable. For example, 54.5kg and 54.6kg have a valid midpoint 54.55kg.</span><span data-jme-visible=\"ranc = 2\">Time is a continuous variable. For example, 54.2s&nbsp;and 54.3s have a valid midpoint 54.25s.</span><span data-jme-visible=\"ranc = 3\">Temperature is a continuous variable,&nbsp;it can take any&nbsp;value between&nbsp;-273.15&deg;C (absolute zero)&nbsp;and positive infinity. For example, 25&deg;C and 26&deg;C&nbsp;have a valid&nbsp;midpoint 25.5&deg;C.</span>&nbsp;Hence, this data is <strong>continuous</strong>.</p>\n<h4>b)</h4>\n<p><span data-jme-visible=\"rand = 0\">The number of Stage 1 students will always be an integer. You cannot split one student into two, for example value 19.5 students does not make sense. Therefore, this is a <strong>discrete</strong> set of data.</span><span data-jme-visible=\"rand = 1\">The result of rolling 3 dice can take values of integers from 3 up to 18.&nbsp;For example, values 3 and 4 do not have any valid middle measurement. Therefore, this is a <strong>discrete</strong> set of data.</span><span data-jme-visible=\"rand = 2\">Shoe sizes are a<strong> discrete</strong> set of data. For example, sizes 39 and 40 mean something while the middle value 39.5 does not.</span><span data-jme-visible=\"rand = 3\">The number of chocolate bars sold on Monday will always be an integer. There is no middle measurement between 1 and 2 bars&nbsp;sold. You cannot buy a&nbsp;half of a bar. Therefore, this is a <strong>discrete</strong> set of data.</span><span data-jme-visible=\"rand = 4\">The number of movies downloaded will always be an integer. You can either download a movie successfully or unsuccessfuly, so this is a<strong> discrete</strong> set of data. It is impossible to split 0 and 1 movies downloaded into 0.5. </span><span data-jme-visible=\"rand = 5\">The number of cinema tickets sold will always be a whole number. There is no middle measurement between 1 and 2 tickets sold. You simply cannot buy half of a ticket. Therefore, this is a <strong>discrete</strong> set of data.</span></p>\n<h4>c)</h4>\n<p><span data-jme-visible=\"rand2 = 0\">The number of Stage 1 students will always be an integer. You cannot split one student into two, for example value 19.5 students does not make sense. Therefore, this is a <strong>discrete</strong> set of data.</span><span data-jme-visible=\"rand2 = 1\">The result of rolling 3 dice can take values of integers from 3 up to 18.&nbsp;For example, values 3 and 4 do not have any valid middle measurement. Therefore, this is a <strong>discrete</strong> set of data.</span><span data-jme-visible=\"rand2 = 2\">Shoe sizes are a <strong>discrete</strong> set of data. For example, sizes 39 and 40 mean something while the middle value 39.5 does not..</span><span data-jme-visible=\"rand2 = 3\">The number of chocolate bars sold on Monday will always be an integer. There is no middle measurement between 1 and 2 bars sold. You cannot buy a half of a bar. Therefore, this is a<strong> discrete</strong> set of data.</span><span data-jme-visible=\"rand2 = 4\">The number of movies downloaded will always be an integer. You can either download a movie successfully or unsuccessfuly, so this is a <strong>discrete</strong> set of data. It is impossible to split 0 and 1 movies&nbsp;downloaded into 0.5.</span><span data-jme-visible=\"rand2 = 5\">The number of cinema tickets sold will always be a whole number. There is no middle measurement between 1 and 2 tickets sold. You simply cannot buy half of a ticket. Therefore, this is a <strong>discrete</strong> set of data.</span></p>\n<h4>d)</h4>\n<p><span data-jme-visible=\"ranc2 = 0\">Height is a continuous variable. For example, 180.3cm and 180.4cm have a valid midpoint 180.35cm.</span><span data-jme-visible=\"ranc2 = 1\">Weight is a continuous variable. For example, 54.5kg and 54.6kg have a valid midpoint 54.55kg.</span><span data-jme-visible=\"ranc2 = 2\">Time is a continuous variable. For example, 54.2s and 54.3s have a valid midpoint 54.25s.</span><span data-jme-visible=\"ranc2 = 3\">Temperature is a continuous variable,&nbsp;it can take any&nbsp;value between&nbsp;-273.15&deg;C (absolute zero)&nbsp;and positive infinity. For example, 25&deg;C and 26&deg;C have a valid midpoint 25.5&deg;C.</span>&nbsp;Hence, this data is <strong>continuous</strong>.</p>\n<h4>e)</h4>\n<p>When we round continuous variables to the nearest integer,&nbsp;this data&nbsp;becomes discrete, as there are no valid middle measurements between the integers. Therefore, <span data-jme-visible=\"rant = 0\">the weight of a dog to the nearest kg</span><span data-jme-visible=\"rant = 1\">the height of Olympic medalists to the nearest cm</span><span data-jme-visible=\"rant = 2\">the time taken to run 10km to the nearest min</span> is <strong>discrete</strong> and not continuous.</p>\n<h4>f)</h4>\n<p><span data-jme-visible=\"rand3 = 0\">The number of Stage 1 students will always be an integer. You cannot split one student into two, for example value 19.5 students does not make sense. Therefore, this is a <strong>discrete</strong> set of data.</span><span data-jme-visible=\"rand3 = 1\">The result of rolling 3 dice can take values of integers from 3 up to 18.&nbsp;For example, values 3 and 4 do not have any valid middle measurement. Therefore, this is a <strong>discrete</strong> set of data.</span><span data-jme-visible=\"rand3 = 2\">Shoe sizes are a <strong>discrete</strong> set of data. For example, sizes 39 and 40 mean something while the middle value 39.5 does not.</span><span data-jme-visible=\"rand3 = 3\">The number of chocolate bars sold on Monday will always be an integer. There is no middle measurement between 1 and 2 bars sold. You cannot buy half of a bar of chocolate. Therefore, this is a <strong>discrete</strong> set of data.</span><span data-jme-visible=\"rand3 = 4\">The number of movies downloaded will always be an integer. You can either download a movie successfully or unsuccessfuly, so this is a <strong>discrete</strong> set of data. It is impossible to split 0 and 1 movies downloaded into 0.5.</span><span data-jme-visible=\"rand3 = 5\">The number of cinema tickets sold will always be a whole number. There is no middle measurement between 1 and 2 tickets sold. You simply cannot buy half of a ticket. Therefore, this is a <strong>discrete</strong> set of data.</span></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#types-of-data\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic</a></p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"rand3": {"name": "rand3", "group": "Ungrouped variables", "definition": "random(0..5 except rand except rand2)", "description": "", "templateType": "anything", "can_override": false}, "cont": {"name": "cont", "group": "Ungrouped variables", "definition": "[\"The height of Newcastle University students.\", \"The weight of Olympic medalists.\", \"The time taken to brush teeth.\", \"The maximum daily temperature.\"]", "description": "", "templateType": "anything", "can_override": false}, "disc": {"name": "disc", "group": "Ungrouped variables", "definition": "[\"The number of Stage 1 students.\", \"The result of rolling 3 dice.\", \"Shoe sizes.\", \"The number of chocolate bars sold on Monday.\", \"The number of movies downloaded.\", \"The number of cinema tickets sold.\"]", "description": "", "templateType": "anything", "can_override": false}, "trick": {"name": "trick", "group": "Ungrouped variables", "definition": "[\"The weight of a dog to the nearest kg.\", \"The height of Olympic medalists to the nearest cm.\", \"The time taken to run 10km to the nearest min.\"]", "description": "", "templateType": "anything", "can_override": false}, "ranc2": {"name": "ranc2", "group": "Ungrouped variables", "definition": "random(0..3 except ranc)", "description": "", "templateType": "anything", "can_override": false}, "rant": {"name": "rant", "group": "Ungrouped variables", "definition": "random(0..2)", "description": "", "templateType": "anything", "can_override": false}, "rand": {"name": "rand", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "rand2": {"name": "rand2", "group": "Ungrouped variables", "definition": "random(0..5 except rand)", "description": "", "templateType": "anything", "can_override": false}, "ranc": {"name": "ranc", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["disc", "cont", "trick", "ranc", "rant", "ranc2", "rand2", "rand3", "rand"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{cont[ranc]}</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>Discrete</p>", "<p>Continuous</p>"], "matrix": [0, "1"], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{disc[rand]}</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>Discrete</p>", "<p>Continuous</p>"], "matrix": ["1", 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{disc[rand2]}</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>Discrete</p>", "<p>Continuous</p>"], "matrix": ["1", 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{cont[ranc2]}</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>Discrete</p>", "<p>Continuous</p>"], "matrix": [0, "1"], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{trick[rant]}</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>Discrete</p>", "<p>Continuous</p>"], "matrix": ["1", 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{disc[rand3]}</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>Discrete</p>", "<p>Continuous</p>"], "matrix": ["1", 0], "distractors": ["", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM01 Calculate Range", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": ["mean", "measures of average and spread", "median", "mode", "range", "taxonomy"], "metadata": {"description": "<p>This question provides a list of data to the student. They are asked to find the \"range\".</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>A random sample of 20 residents from Newcastle were asked about the number of times they&nbsp;went&nbsp;to see a play at&nbsp;the&nbsp;theatre&nbsp;last year.</p>\n<p>Here is the list of their answers:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>$\\var{a[0]}$</td>\n<td>$\\var{a[1]}$</td>\n<td>$\\var{a[2]}$</td>\n<td>$\\var{a[3]}$</td>\n<td>$\\var{a[4]}$</td>\n<td>$\\var{a[5]}$</td>\n<td>$\\var{a[6]}$</td>\n<td>$\\var{a[7]}$</td>\n<td>$\\var{a[8]}$</td>\n<td>$\\var{a[9]}$</td>\n</tr>\n<tr>\n<td>$\\var{a[10]}$</td>\n<td>$\\var{a[11]}$</td>\n<td>$\\var{a[12]}$</td>\n<td>$\\var{a[13]}$</td>\n<td>$\\var{a[14]}$</td>\n<td>$\\var{a[15]}$</td>\n<td>$\\var{a[16]}$</td>\n<td>$\\var{a[17]}$</td>\n<td>$\\var{a[18]}$</td>\n<td>$\\var{a[19]}$</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"></p>", "advice": "<p>Range is the difference between the highest and the lowest value in the data.</p>\n<p>To find this, we subtract the lowest value from the highest value:</p>\n<p>\\[ \\var{max(a)} - \\var{min(a)} = \\var{range} \\text{.}\\]</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#measures-of-spread\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a2": {"name": "a2", "group": "Ungrouped variables", "definition": "repeat(random(1..9), 20)", "description": "<p>Option&nbsp;2 for the list. Only used if there is only one mode and option 1 was not used.</p>", "templateType": "anything", "can_override": false}, "modea1": {"name": "modea1", "group": "Ungrouped variables", "definition": "mode(a1)", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "repeat(random(1..9), 20)", "description": "<p>Option 1 for the list. Only used if there is only one mode.</p>", "templateType": "anything", "can_override": false}, "a_s": {"name": "a_s", "group": "final list", "definition": "sort(a)", "description": "<p>Sorted list.</p>", "templateType": "anything", "can_override": false}, "modea2": {"name": "modea2", "group": "Ungrouped variables", "definition": "mode(a2)", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "shuffle([ random(0..1),\n  2, \n  random(4..6),\n  random(0..3 except 2), \n  random(0..3 except 2),\n  random(4..6),\n  2,\n  2,\n  random(4..6),\n  random(7..8),\n  random(0..3 except 2 except 1), \n  random(4..6),\n  2,\n  random(1..3 except 2), \n  random(7..8),\n  2,\n  random(7..8),\n  random(4..6), \n  random(0..3 except 2), \n  2\n])", "description": "<p>Option 3 for the list. Ensures there is only one mode (2) while still randomising the data.</p>", "templateType": "anything", "can_override": false}, "modetimes": {"name": "modetimes", "group": "final list", "definition": "map(\nlen(filter(x=j,x,a)),\nj, 0..8)", "description": "<p>The vector of&nbsp;number of times of each value in the data.</p>", "templateType": "anything", "can_override": false}, "range": {"name": "range", "group": "final list", "definition": "max(a) - min(a)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "final list", "definition": "if(len(modea1) = 1, a1, if(len(modea2) = 1, a2, a3))", "description": "<p>The final list.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["modea1", "modea2", "a1", "a2", "a3"], "variable_groups": [{"name": "final list", "variables": ["a", "a_s", "range", "modetimes"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the range.</p>", "minValue": "range", "maxValue": "range", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM02 Calculate Mean from a list", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Upuli Wickramaarachchi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23527/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": [], "metadata": {"description": "<p>Calculating the Mean from a basic list of integers.</p>", "licence": "None specified"}, "statement": "<p>Calculate the Mean from a list</p>", "advice": "<p>The MEAN is the sum, divided by the number of values summed i.e.<br/><br/>$\\frac{\\var{list[0]} +&nbsp;\\var{list[1]} +&nbsp;\\var{list[2]} +&nbsp;\\var{list[3]} +&nbsp;\\var{list[4]}}{5}$</p>\n<p>use your calculator to find</p>\n<p>mean = $\\var{mean}$.</p>\n<p></p>\n<p style=\"text-align: center;\"><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"list": {"name": "list", "group": "Ungrouped variables", "definition": "repeat(random(0..20), 5)", "description": "", "templateType": "anything", "can_override": false}, "mean": {"name": "mean", "group": "Ungrouped variables", "definition": "mean(list)", "description": "", "templateType": "anything", "can_override": false}, "median": {"name": "median", "group": "Ungrouped variables", "definition": "median(list)", "description": "", "templateType": "anything", "can_override": false}, "order": {"name": "order", "group": "Ungrouped variables", "definition": "sort(list)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["list", "mean", "median", "order"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given a list of numbers:<br/><br/>{list}<br/><br/>Calculate the mean: &nbsp;&nbsp;[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "mean", "maxValue": "mean", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM03 Calculate Mode From a list", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": ["mean", "measures of average and spread", "median", "mode", "range", "taxonomy"], "metadata": {"description": "<p>This question provides a list of data to the student. They are asked to find the \"mode\".</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>A random sample of 20 residents from Newcastle were asked about the number of times they&nbsp;went&nbsp;to see a play at&nbsp;the&nbsp;theatre&nbsp;last year.</p>\n<p>Here is the list of their answers:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>$\\var{a[0]}$</td>\n<td>$\\var{a[1]}$</td>\n<td>$\\var{a[2]}$</td>\n<td>$\\var{a[3]}$</td>\n<td>$\\var{a[4]}$</td>\n<td>$\\var{a[5]}$</td>\n<td>$\\var{a[6]}$</td>\n<td>$\\var{a[7]}$</td>\n<td>$\\var{a[8]}$</td>\n<td>$\\var{a[9]}$</td>\n</tr>\n<tr>\n<td>$\\var{a[10]}$</td>\n<td>$\\var{a[11]}$</td>\n<td>$\\var{a[12]}$</td>\n<td>$\\var{a[13]}$</td>\n<td>$\\var{a[14]}$</td>\n<td>$\\var{a[15]}$</td>\n<td>$\\var{a[16]}$</td>\n<td>$\\var{a[17]}$</td>\n<td>$\\var{a[18]}$</td>\n<td>$\\var{a[19]}$</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"></p>", "advice": "<p>The mode is the value that occurs the most often in the data.</p>\n<p>To find a mode, we can look at our sorted list:</p>\n<p style=\"text-align: center;\">$\\var{a_s[0]}, \\var{a_s[1]}, \\var{a_s[2]}, \\var{a_s[3]}, \\var{a_s[4]}, \\var{a_s[5]}, \\var{a_s[6]}, \\var{a_s[7]}, \\var{a_s[8]}, \\var{a_s[9]}, \\var{a_s[10]}, \\var{a_s[11]}, \\var{a_s[12]}, \\var{a_s[13]}, \\var{a_s[14]}, \\var{a_s[15]}, \\var{a_s[16]}, \\var{a_s[17]}, \\var{a_s[18]}, \\var{a_s[19]}$.</p>\n<p>We&nbsp;notice that $\\var{mode1}$ occurs the most ($\\var{modetimes[mode1]}$ times) so $\\var{mode1}$ is the mode.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a2": {"name": "a2", "group": "Ungrouped variables", "definition": "repeat(random(0..8), 20)", "description": "<p>Option&nbsp;2 for the list. Only used if there is only one mode and option 1 was not used.</p>", "templateType": "anything", "can_override": false}, "modea1": {"name": "modea1", "group": "Ungrouped variables", "definition": "mode(a1)", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "repeat(random(0..8), 20)", "description": "<p>Option 1 for the list. Only used if there is only one mode.</p>", "templateType": "anything", "can_override": false}, "a_s": {"name": "a_s", "group": "final list", "definition": "sort(a)", "description": "<p>Sorted list.</p>", "templateType": "anything", "can_override": false}, "modea2": {"name": "modea2", "group": "Ungrouped variables", "definition": "mode(a2)", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "shuffle([ random(0..1),\n  2, \n  random(4..6),\n  random(0..3 except 2), \n  random(0..3 except 2),\n  random(4..6),\n  2,\n  2,\n  random(4..6),\n  random(7..8),\n  random(0..3 except 2 except 1), \n  random(4..6),\n  2,\n  random(1..3 except 2), \n  random(7..8),\n  2,\n  random(7..8),\n  random(4..6), \n  random(0..3 except 2), \n  2\n])", "description": "<p>Option 3 for the list. Ensures there is only one mode (2) while still randomising the data.</p>", "templateType": "anything", "can_override": false}, "modetimes": {"name": "modetimes", "group": "final list", "definition": "map(\nlen(filter(x=j,x,a)),\nj, 0..8)", "description": "<p>The vector of&nbsp;number of times of each value in the data.</p>", "templateType": "anything", "can_override": false}, "mode1": {"name": "mode1", "group": "final list", "definition": "mode[0]", "description": "<p>Mode as a value.</p>", "templateType": "anything", "can_override": false}, "mode": {"name": "mode", "group": "final list", "definition": "mode(a)", "description": "<p>Mode as a vector.</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "final list", "definition": "if(len(modea1) = 1, a1, if(len(modea2) = 1, a2, a3))", "description": "<p>The final list.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["modea1", "modea2", "a1", "a2", "a3"], "variable_groups": [{"name": "final list", "variables": ["a", "a_s", "mode", "mode1", "modetimes"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the mode.</p>", "minValue": "mode1", "maxValue": "mode1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM04 Calculate Median from a list", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Upuli Wickramaarachchi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23527/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": ["mean", "measures of average and spread", "median", "mode", "range", "taxonomy"], "metadata": {"description": "<p>This question provides a list of data to the student. They are asked to find the \"median\".</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>A random sample of 20 residents from Newcastle were asked about the number of times they&nbsp;went&nbsp;to see a play at&nbsp;the&nbsp;theatre&nbsp;last year.</p>\n<p>Here is the list of their answers:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>$\\var{a[0]}$</td>\n<td>$\\var{a[1]}$</td>\n<td>$\\var{a[2]}$</td>\n<td>$\\var{a[3]}$</td>\n<td>$\\var{a[4]}$</td>\n<td>$\\var{a[5]}$</td>\n<td>$\\var{a[6]}$</td>\n<td>$\\var{a[7]}$</td>\n<td>$\\var{a[8]}$</td>\n<td>$\\var{a[9]}$</td>\n</tr>\n<tr>\n<td>$\\var{a[10]}$</td>\n<td>$\\var{a[11]}$</td>\n<td>$\\var{a[12]}$</td>\n<td>$\\var{a[13]}$</td>\n<td>$\\var{a[14]}$</td>\n<td>$\\var{a[15]}$</td>\n<td>$\\var{a[16]}$</td>\n<td>$\\var{a[17]}$</td>\n<td>$\\var{a[18]}$</td>\n<td>$\\var{a[19]}$</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"></p>", "advice": "<p>The median is&nbsp;the middle value. We need to sort the list in order:</p>\n<p style=\"text-align: center;\">\\[ \\var{a_s[0]}, \\quad \\var{a_s[1]}, \\quad&nbsp;\\var{a_s[2]}, \\quad \\var{a_s[3]}, \\quad \\var{a_s[4]}, \\quad \\var{a_s[5]}, \\quad \\var{a_s[6]}, \\quad \\var{a_s[7]}, \\quad \\var{a_s[8]}, \\quad \\var{a_s[9]}, \\quad \\var{a_s[10]}, \\quad \\var{a_s[11]}, \\quad&nbsp;\\var{a_s[12]}, \\quad \\var{a_s[13]}, \\quad \\var{a_s[14]}, \\quad \\var{a_s[15]}, \\quad \\var{a_s[16]}, \\quad \\var{a_s[17]}, \\quad \\var{a_s[18]}, \\quad \\var{a_s[19]} \\]</p>\n<p>There is an even number of responses, so there are&nbsp;two numbers in the middle (10<sup>th</sup> and 11<sup>th</sup> place). To&nbsp;find the median, we need to&nbsp;find the mean of these two numbers $\\var{a_s[9]}$ and $\\var{a_s[10]}$:</p>\n<p>\\begin{align} <br/>\\frac{\\var{a_s[9]} + \\var{a_s[10]}}{2} &amp;= &nbsp;\\frac{\\var{a_s[9] + a_s[10]}}{2} \\\\<br/>&amp;= \\var{median} \\text{.}&nbsp;<br/>\\end{align}</p>\n<p>&nbsp;</p>\n<p style=\"text-align: center;\"><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\" target=\"_blank\" rel=\"noopener\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a2": {"name": "a2", "group": "Ungrouped variables", "definition": "repeat(random(0..8), 20)", "description": "<p>Option&nbsp;2 for the list. Only used if there is only one mode and option 1 was not used.</p>", "templateType": "anything", "can_override": false}, "modea1": {"name": "modea1", "group": "Ungrouped variables", "definition": "mode(a1)", "description": "", "templateType": "anything", "can_override": false}, "median": {"name": "median", "group": "final list", "definition": "median(a)", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "repeat(random(0..8), 20)", "description": "<p>Option 1 for the list. Only used if there is only one mode.</p>", "templateType": "anything", "can_override": false}, "a_s": {"name": "a_s", "group": "final list", "definition": "sort(a)", "description": "<p>Sorted list.</p>", "templateType": "anything", "can_override": false}, "modea2": {"name": "modea2", "group": "Ungrouped variables", "definition": "mode(a2)", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "shuffle([ random(0..1),\n  2, \n  random(4..6),\n  random(0..3 except 2), \n  random(0..3 except 2),\n  random(4..6),\n  2,\n  2,\n  random(4..6),\n  random(7..8),\n  random(0..3 except 2 except 1), \n  random(4..6),\n  2,\n  random(1..3 except 2), \n  random(7..8),\n  2,\n  random(7..8),\n  random(4..6), \n  random(0..3 except 2), \n  2\n])", "description": "<p>Option 3 for the list. Ensures there is only one mode (2) while still randomising the data.</p>", "templateType": "anything", "can_override": false}, "mean": {"name": "mean", "group": "final list", "definition": "mean(a)", "description": "", "templateType": "anything", "can_override": false}, "modetimes": {"name": "modetimes", "group": "final list", "definition": "map(\nlen(filter(x=j,x,a)),\nj, 0..8)", "description": "<p>The vector of&nbsp;number of times of each value in the data.</p>", "templateType": "anything", "can_override": false}, "range": {"name": "range", "group": "final list", "definition": "max(a) - min(a)", "description": "", "templateType": "anything", "can_override": false}, "mode1": {"name": "mode1", "group": "final list", "definition": "mode[0]", "description": "<p>Mode as a value.</p>", "templateType": "anything", "can_override": false}, "mode": {"name": "mode", "group": "final list", "definition": "mode(a)", "description": "<p>Mode as a vector.</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "final list", "definition": "if(len(modea1) = 1, a1, if(len(modea2) = 1, a2, a3))", "description": "<p>The final list.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["modea1", "modea2", "a1", "a2", "a3"], "variable_groups": [{"name": "final list", "variables": ["a", "a_s", "mean", "median", "mode", "mode1", "range", "modetimes"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the median.</p>", "minValue": "median", "maxValue": "median", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM05 Calculate the mean (Frequency table) - With a calculator", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/496/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Marta Emmett", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11961/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Using a calculator, work out the mean for each of these frequency tables, give your answers to <strong>two decimal places</strong>.</p>", "advice": "<p>To calculate the mean shoe size we need to add a third column to our table where we multiply the grade by the number (frequency) of students who are that shoe size.</p>\n<table style=\"margin-right: auto; height: 126px; width: 391px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 48.2031px; text-align: center;\"><b>Shoe Size</b></td>\n<td style=\"height: 18px; width: 82.0625px; text-align: center;\"><strong>Frequency</strong></td>\n<td style=\"width: 211.734px; text-align: center;\"><strong>Shoe Size * Frequency</strong></td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 48.2031px; text-align: center;\">3</td>\n<td style=\"height: 18px; width: 82.0625px; text-align: center;\">{p1}</td>\n<td style=\"width: 211.734px; text-align: center;\">3 * {p1} = {3*p1}</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 48.2031px; text-align: center;\">4</td>\n<td style=\"height: 18px; width: 82.0625px; text-align: center;\">{p2}</td>\n<td style=\"width: 211.734px; text-align: center;\">4 * {p2} = {4*p2}</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 48.2031px; text-align: center;\">5</td>\n<td style=\"height: 18px; width: 82.0625px; text-align: center;\">{p3}</td>\n<td style=\"width: 211.734px; text-align: center;\">5 * {p3} = {5*p3}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 48.2031px; text-align: center; height: 18px;\">6</td>\n<td style=\"width: 82.0625px; text-align: center; height: 18px;\">{p4}</td>\n<td style=\"width: 211.734px; text-align: center;\">6 * {p4} = {6*p4}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 48.2031px; text-align: center; height: 18px;\">7</td>\n<td style=\"width: 82.0625px; text-align: center; height: 18px;\">{p5}</td>\n<td style=\"width: 211.734px; text-align: center;\">7 * {p5} = {7*p5}&nbsp;</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 48.2031px; text-align: center;\">8</td>\n<td style=\"height: 18px; width: 82.0625px; text-align: center;\">{p6}</td>\n<td style=\"width: 211.734px; text-align: center;\">8 * {p6} = {8*p6}</td>\n</tr>\n</tbody>\n</table>\n<p>Now we find the total sum of that third column:</p>\n<p>$\\var{3*p1} + \\var{4*p2} + \\var{5*p3} + \\var{6*p4} + \\var{7*p5} + \\var{8*p6} = \\var{3*p1 + 4*p2 + 5*p3 + 6*p4 + 7*p5 + 8*p6}.$</p>\n<p>To find the mean shoe size we must divide this total by the total number of students:</p>\n<p>$\\frac{\\var{3*p1 + 4*p2 + 5*p3 + 6*p4 + 7*p5 + 8*p6}}{\\var{p1}+\\var{p2}+\\var{p3}+\\var{p4}+\\var{p5}+\\var{p6}} = \\frac{\\var{3*p1 + 4*p2 + 5*p3 + 6*p4 + 7*p5 + 8*p6}}{\\var{sum1}} = \\var{mean1a}.$&nbsp;</p>\n<p>The question asks us for our answer to two decimal places so the last thing we need to do is round. Hence, the mean is $\\var{mean1}$.</p>\n<p>You can use this same method to answer the other parts of this question!</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"mean1a": {"name": "mean1a", "group": "Part a", "definition": "((3*p1)+(4*p2)+(5*p3)+(6*p4)+(7*p5)+(8*p6))/sum1", "description": "<p>The mean - part a</p>", "templateType": "anything", "can_override": false}, "p1": {"name": "p1", "group": "Part a", "definition": "random(0 .. 50#1)", "description": "<p>Frequency 1 - part a</p>", "templateType": "randrange", "can_override": false}, "p2": {"name": "p2", "group": "Part a", "definition": "random(0 .. 50#1)", "description": "<p>Frequency 2 - part a</p>", "templateType": "randrange", "can_override": false}, "p3": {"name": "p3", "group": "Part a", "definition": "random(0 .. 50#1)", "description": "<p>Frequency 3 - part a</p>", "templateType": "randrange", "can_override": false}, "p4": {"name": "p4", "group": "Part a", "definition": "random(0 .. 50#1)", "description": "<p>Frequency 4 - part a</p>", "templateType": "randrange", "can_override": false}, "p5": {"name": "p5", "group": "Part a", "definition": "random(0 .. 50#1)", "description": "<p>Frequency 5 - part a</p>", "templateType": "randrange", "can_override": false}, "p6": {"name": "p6", "group": "Part a", "definition": "random(0 .. 50#1)", "description": "<p>Frequency 6 - part a</p>", "templateType": "randrange", "can_override": false}, "mean1": {"name": "mean1", "group": "Part a", "definition": "precround(mean1a,2)", "description": "<p>Mean rounded to two decimal places - part a</p>", "templateType": "anything", "can_override": false}, "sum1": {"name": "sum1", "group": "Part a", "definition": "p1+p2+p3+p4+p5+p6", "description": "<p>Sum of frequencies - part a</p>", "templateType": "anything", "can_override": false}, "sum2": {"name": "sum2", "group": "Part b", "definition": "p1b+p2b+p3b+p4b", "description": "<p>Sum of frequencies - part b</p>", "templateType": "anything", "can_override": false}, "p1b": {"name": "p1b", "group": "Part b", "definition": "random(1 .. 100#1)", "description": "<p>Frequency 1 - part b</p>", "templateType": "randrange", "can_override": false}, "p2b": {"name": "p2b", "group": "Part b", "definition": "random(1 .. 100#1)", "description": "<p>Frequency 2 - part b</p>", "templateType": "randrange", "can_override": false}, "p3b": {"name": "p3b", "group": "Part b", "definition": "random(1 .. 100#1)", "description": "<p>Frequency 3 - part b</p>", "templateType": "randrange", "can_override": false}, "p4b": {"name": "p4b", "group": "Part b", "definition": "random(1 .. 100#1)", "description": "<p>Frequency 4 - part b</p>", "templateType": "randrange", "can_override": false}, "mean2a": {"name": "mean2a", "group": "Part b", "definition": "((0*p1b)+(1*p2b)+(2*p3b)+(3*p4b))/sum2", "description": "<p>The mean - part b</p>", "templateType": "anything", "can_override": false}, "mean2": {"name": "mean2", "group": "Part b", "definition": "precround(mean2a,2)", "description": "<p>Mean rounded to two decimal places - part b</p>", "templateType": "anything", "can_override": false}, "p1c": {"name": "p1c", "group": "Part c", "definition": "random(1 .. 70#1)", "description": "<p>Frequency 1 - part c</p>", "templateType": "randrange", "can_override": false}, "p2c": {"name": "p2c", "group": "Part c", "definition": "random(1 .. 70#1)", "description": "<p>Frequency 2 - part c</p>", "templateType": "randrange", "can_override": false}, "p3c": {"name": "p3c", "group": "Part c", "definition": "random(1 .. 70#1)", "description": "<p>Frequency 3 - part c</p>", "templateType": "randrange", "can_override": false}, "p4c": {"name": "p4c", "group": "Part c", "definition": "random(1 .. 70#1)", "description": "<p>Frequency 4 - part c</p>", "templateType": "randrange", "can_override": false}, "p5c": {"name": "p5c", "group": "Part c", "definition": "random(1 .. 70#1)", "description": "<p>Frequency 5 - part c</p>", "templateType": "randrange", "can_override": false}, "p6c": {"name": "p6c", "group": "Part c", "definition": "random(1 .. 70#1)", "description": "<p>Frequency 6 - part c</p>", "templateType": "randrange", "can_override": false}, "mean3": {"name": "mean3", "group": "Part c", "definition": "precround(mean3a,2)", "description": "<p>Mean rounded to two decimal places - part c</p>", "templateType": "anything", "can_override": false}, "sum3": {"name": "sum3", "group": "Part c", "definition": "p1c+p2c+p3c+p4c+p5c+p6c", "description": "<p>Sum of frequencies - part c</p>", "templateType": "anything", "can_override": false}, "mean3a": {"name": "mean3a", "group": "Part c", "definition": "((0*p1c)+(1*p2c)+(2*p3c)+(3*p4c)+(4*p5c)+(5*p6c))/sum3", "description": "<p>The mean - part c</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Part a", "variables": ["mean1", "mean1a", "p1", "p2", "p3", "p4", "p5", "p6", "sum1"]}, {"name": "Part b", "variables": ["mean2", "mean2a", "p1b", "p2b", "p3b", "p4b", "sum2"]}, {"name": "Part c", "variables": ["mean3a", "mean3", "p1c", "p2c", "p3c", "p4c", "p5c", "p6c", "sum3"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "a)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The table below shows the distribution of shoe sizes amongst {sum1} students at a school in Sheffield.&nbsp;</p>\n<table style=\"margin-right: auto; height: 126px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\"><b>Shoe size</b></td>\n<td style=\"height: 18px; width: 95px; text-align: center;\"><strong>Frequency</strong></td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">3</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p1}</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">4</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p2}</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">5</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p3}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 87px; text-align: center; height: 18px;\">6</td>\n<td style=\"width: 95px; text-align: center; height: 18px;\">{p4}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 87px; text-align: center; height: 18px;\">7</td>\n<td style=\"width: 95px; text-align: center; height: 18px;\">{p5}</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">8</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p6}</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "minValue": "mean1", "maxValue": "mean1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "b)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The table below shows the distribution of number of pets that {sum2} randomly asked people have.</p>\n<table style=\"margin-right: auto; height: 123px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\"><b>Number of Pets</b></td>\n<td style=\"height: 18px; width: 95px; text-align: center;\"><strong>Frequency</strong></td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">0</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p1b}</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">1</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p2b}</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">2</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p3b}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 87px; text-align: center; height: 15px;\">3</td>\n<td style=\"width: 95px; text-align: center; height: 15px;\">{p4b}</td>\n</tr>\n</tbody>\n</table>", "minValue": "mean2", "maxValue": "mean2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "c)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The table below shows the distribution of the number of drinks per order at a coffee shop in Manchester.&nbsp;</p>\n<table style=\"margin-right: auto; height: 126px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\"><b>Number of Drinks</b></td>\n<td style=\"height: 18px; width: 95px; text-align: center;\"><strong>Frequency</strong></td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">0</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p1c}</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">1</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p2c}</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">2</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p3c}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 87px; text-align: center; height: 18px;\">3</td>\n<td style=\"width: 95px; text-align: center; height: 18px;\">{p4c}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 87px; text-align: center; height: 18px;\">4</td>\n<td style=\"width: 95px; text-align: center; height: 18px;\">{p5c}</td>\n</tr>\n<tr style=\"text-align: center;\">\n<td style=\"height: 18px; width: 87px; text-align: center;\">5</td>\n<td style=\"height: 18px; width: 95px; text-align: center;\">{p6c}</td>\n</tr>\n</tbody>\n</table>", "minValue": "mean3", "maxValue": "mean3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM06 Choosing the appropriate average", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": [], "metadata": {"description": "<p>This question asks the student to choose the appropriate measure of average and spread for a data with outliers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Which of the following measures would you choose if you were dealing with data which includes outliers? Select one measure of average and one measure of spread.</p>", "advice": "<p>The median is a more appropriate measure of average when your data contains outliers because outliers do not affect the median.</p>\n<p>The interquartile range is the best measure of variability for skewed distributions or data sets with outliers. Because it&rsquo;s based on values that come from the middle half of the distribution, it&rsquo;s unlikely to be influenced by outliers.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["Mean", "Median", "Standard deviation", "P-value", "Range", "Inter-quartile range"], "matrix": [0, "1", 0, 0, 0, "1"], "distractors": ["", "", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM07 Identify measures of spread/location", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": [], "metadata": {"description": "<p>Identifying measures of spread or location (average)</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Match each of the following with what they measure.</p>", "advice": "<p>The mean is a measure of location or central tendancy. It is calcuated by summing all of the data values and dividing by the number of values.</p>\n<p>The median is a measure of location or central tendancy. It is the middle value of an ordered data set.</p>\n<p>The inter-quartile range is a measure of spread. The interquartile range is the difference between upper and lower quartiles.The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order. The inter-quartile range therefore gives us an idea of the middle 50% of the ordered data set.</p>\n<p>The standard deviation is a measure of spread. It measures the dispersion of a data set relative to its mean.&nbsp;</p>\n<p>The variance is a measure spread because it is the square of the standard deviation.</p>\n<p>A p-value the probability that a particular statistical measure, such as the mean or standard deviation, of an assumed probability distribution will be greater than or equal to (or less than or equal to in some instances) observed results. A p-value is used to determine statistical significance, not measures of spread or location.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {"std": ["all", "fractionNumbers"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "function dragpoint_board() {\n  var scope = question.scope;\n\n  JXG.Options.text.display = 'internal';\n  \n  var yo0 = scope.variables.yo0.value;\n  var yo1 = scope.variables.yo1.value;\n  var yo2 = scope.variables.yo2.value;\n  var yo3 = scope.variables.yo3.value;\n  var yo4 = scope.variables.yo4.value;\n  var yo5 = scope.variables.yo5.value;\n  var yo6 = scope.variables.yo6.value;\n  var yo7 = scope.variables.yo7.value; \n  var yo8 = scope.variables.yo8.value;\n  var yo9 = scope.variables.yo9.value; \n  \n  var div = Numbas.extensions.jsxgraph.makeBoard('550px','550px',{boundingBox:[-0.8,82,16,-8], axis:false, grid:true});\n \n  $(question.display.html).find('#dragpoint').append(div);\n  \n  var board = div.board;\n  \nboard.suspendUpdate();           \n\n  \n var dataArr = [yo0,yo5,0,yo1,yo6,0,yo2,yo7,0,yo3,yo8,0,yo4,yo9]; \n  \n var xaxis = board.create('axis', [[0, 0], [12, 0]], {withLabel: true, name: \"Bank\", label: {offset: [250,-30]}});\n  \n  xaxis.removeAllTicks();  \n   \n  board.create('axis', [[0, 0], [0, 10]], {hideTicks:true, withLabel: false, name: \"\", label: {offset: [-110,300]}});\n  \n  var pop0 = board.create('point', [1.5,0],{name:'Morgan',fixed:true,size:0,color:'black',face:'diamond', label:{offset:[-20,-8]}});\n  var pop1 = board.create('point',[4.5,0],{name:'Strome',fixed:true,size:0,color:'black',face:'diamond', label:{offset:[-20,-8]}});\n  var pop2 = board.create('point',[7.5,0],{name:'Bentley',fixed:true,size:0,color:'black', face:'diamond', label:{offset:[-15,-8]}});\n  var pop3 = board.create('point',[10.5,0],{name:'Sand',fixed:true,size:0,color:'black', face:'diamond', label:{offset:[-15,-8]}});\n  var pop4 = board.create('point',[13.5,0],{name:'Karchen',fixed:true,size:0,color:'black', face:'diamond', label:{offset:[-15,-8]}});\n\n  var leg1 = board.create('point',[12,75],{name:'last year',fixed:true,size:6,color:'#DA2228', face:'square', label:{offset:[9,0]}});\n  var leg2 = board.create('point',[12,72],{name:'this year',fixed:true,size:6,color:'#6F1B75', face:'square', label:{offset:[9,0]}});\n  \n  \n//  var chart = board.createElement('chart', dataArr, \n  //                              {chartStyle:'bar', fillOpacity:1, width:1,\n    //     colorArray:['#8E1B77','#8E1B77','Red','Red','blue','red','blue','red','red','blue', 'red','blue','red','red'], shadow:false});\n \n//var chart = board.createElement('chart', dataArr, \n  //                              {chartStyle:'bar', width:1,fillOpacity:1, fillColor:'red', shadow:false});  \n  \n  \n    var a = board.create('chart', [[1,2,3],[yo0,yo5,0]], {chartStyle:'bar',colors:['#DA2228','#6F1B75','#6F1B75'],width:1,fillOpacity:1});\n    var b = board.create('chart', [[4,5,6],[yo1,yo6,0]], {chartStyle:'bar',width:1,colors:['#DA2228','#6F1B75','#6F1B75'],fillOpacity:1});\n    var c = board.create('chart', [[7,8,9],[yo2,yo7,0]], {chartStyle:'bar',width:1,colors:['#DA2228','#6F1B75','#6F1B75'],fillOpacity:1});\n    var d = board.create('chart', [[10,11,12],[yo3,yo8,0]], {chartStyle:'bar',width:1,colors:['#DA2228','#6F1B75','#6F1B75'],fillOpacity:1});\n    var e = board.create('chart', [[13,14],[yo4,yo9]], {chartStyle:'bar',width:1,colors:['#DA2228','#6F1B75'],fillOpacity:1});\n  \n    board.unsuspendUpdate();\n  \n  var txt1 = board.create('text',[-0.3,30, 'Investment \u00a3(m)'], {fontColor:'black', fontSize:14, rotate:90});\n  \n // var txt = board.create('text',[0.5,75, 'Investment (m)'], {fontSize:14, rotate:90});\n  \n // var txt1 = board.create('text',[8,76, 'red bars represent 2010'], {fontColor:'red', fontSize:14, rotate:90});\n  \n // var txt2 = board.create('text',[8,73, 'blue bars represents 2011'], {fontSize:14, rotate:90});\n\n // var myColors = new Array('red', 'blue', 'white','red', 'blue', 'white','red', 'blue', 'white','red', 'blue', 'white','red', 'blue');\n  \n  \n  \n  //board.unsuspendUpdate();\n\n    // Rotate text around the lower left corner (-2,-1) by 30 degrees.\n   // var tRot = board.create('transform', [90.0*Math.PI/180.0, -1,40], {type:'rotate'}); \n  //  tRot.bindTo(txt);\n  //  board.update();\n\n  \n//var chart2 = board.createElement('chart', dataArr, {chartStyle:'line,point'});\n//chart2[0].setProperty('strokeColor:black','strokeWidth:2','shadow:true');\n//for(var i=0; i<11;i++) {\n //   chart2[1][i].setProperty({strokeColor:'black',fillColor:'white',face:'[]', size:4, strokeWidth:2});\n//}\n//board.unsuspendUpdate();  \n                       \n  //board.unsuspendUpdate();\n\n}\n\nquestion.signals.on('HTMLAttached',function() {\n  dragpoint_board();\n});", "css": "table#values th {\n  background: none;\n  text-align: center;\n}"}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["Variance", "Mean", "Median", "Inter-quartile range", "P-value", "Standard deviation"], "matrix": [["1", 0, 0], [0, "1", 0], [0, "1", 0], ["1", 0, 0], [0, 0, "1"], ["1", 0, 0]], "layout": {"type": "all", "expression": ""}, "answers": ["Measure of Spread", "Measure of location (average)", "Neither measure of location nor measure of spread"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM08 Calculate Range (Decimal)", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": ["mean", "measures of average and spread", "median", "mode", "range", "taxonomy"], "metadata": {"description": "<p>This question provides a list of data to the student. They are asked to find the \"range\".</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Here is a list of 20 random numbers:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>$\\var{a[0]}$</td>\n<td>$\\var{a[1]}$</td>\n<td>$\\var{a[2]}$</td>\n<td>$\\var{a[3]}$</td>\n<td>$\\var{a[4]}$</td>\n<td>$\\var{a[5]}$</td>\n<td>$\\var{a[6]}$</td>\n<td>$\\var{a[7]}$</td>\n<td>$\\var{a[8]}$</td>\n<td>$\\var{a[9]}$</td>\n</tr>\n<tr>\n<td>$\\var{a[10]}$</td>\n<td>$\\var{a[11]}$</td>\n<td>$\\var{a[12]}$</td>\n<td>$\\var{a[13]}$</td>\n<td>$\\var{a[14]}$</td>\n<td>$\\var{a[15]}$</td>\n<td>$\\var{a[16]}$</td>\n<td>$\\var{a[17]}$</td>\n<td>$\\var{a[18]}$</td>\n<td>$\\var{a[19]}$</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"></p>", "advice": "<p>Range is the difference between the highest and the lowest value in the data.</p>\n<p>To find this, we subtract the lowest value from the highest value:</p>\n<p>\\[ \\var{max(a)} - \\var{min(a)} = \\var{range} \\text{.}\\]</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#measures-of-spread\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "repeat(random(z), 20)", "description": "<p>Option 1 for the list. Only used if there is only one mode.</p>", "templateType": "anything", "can_override": false}, "a_s": {"name": "a_s", "group": "final list", "definition": "sort(a)", "description": "<p>Sorted list.</p>", "templateType": "anything", "can_override": false}, "range": {"name": "range", "group": "final list", "definition": "max(a) - min(a)", "description": "", "templateType": "anything", "can_override": false}, "z": {"name": "z", "group": "Ungrouped variables", "definition": "0.7 .. 9.7#0.1", "description": "", "templateType": "range", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "z"], "variable_groups": [{"name": "final list", "variables": ["a_s", "range"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the range.</p>", "minValue": "range", "maxValue": "range", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM09 Range and Interquartile Range", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Here are the ages of 7 people:</p>\n<p>{a1}, {a2}, {a3}, {a4}, {a5}, {a6}, {a7}.</p>", "advice": "<p>First we should order our list of ages from smallest to largest:</p>\n<p>$\\var{list[0]}, \\var{list[1]}, \\var{list[2]}, \\var{list[3]}, \\var{list[4]}, \\var{list[5]}, \\var{list[6]}$.</p>\n<p><strong>a)</strong></p>\n<p>To find the range of ages we must subtract the smallest age from the largest age,</p>\n<p>$\\var{max(list)} - \\var{min(list)} = \\var{range}$.</p>\n<p>Hence, the range is $\\var{range}$.</p>\n<p><strong>b)&nbsp;</strong></p>\n<p>To calculate the interquartile range we subtract the lower quartile from the upper quartile.</p>\n<p><span style=\"text-decoration: underline;\">To calculate the lower quartile:</span></p>\n<p>Since we have an odd number of ages we had one to the total and divide by 4,</p>\n<p>$\\frac{7+1}{4} = \\frac{8}{4} = 2.$</p>\n<p>So we are looking for the $2^{nd}$ value in our list which is $\\var{lq}$.</p>\n<p>Hence the lower quartile is $\\var{lq}$.</p>\n<p><span style=\"text-decoration: underline;\">To find the upper quartile:</span></p>\n<p>We still add one to the number of ages because this number is odd and then we find $75$% of it,</p>\n<p>$\\frac{3\\times(7+1)}{4} = \\frac{3\\times8}{4} = \\frac{24}{4} = 6.$</p>\n<p>So we are looking for the $6^{th}$ value in our list which is $\\var{uq}$.</p>\n<p>Hence the lower quartile is $\\var{uq}$.</p>\n<p>Now we can calculate the interquartile range by subtracting the lower quartile from the upper quartile,</p>\n<p>$\\var{uq}-\\var{lq} = \\var{iqr}.$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 1</p>", "templateType": "randrange", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 2</p>", "templateType": "randrange", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 3</p>", "templateType": "randrange", "can_override": false}, "a4": {"name": "a4", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 4</p>", "templateType": "randrange", "can_override": false}, "a5": {"name": "a5", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 5</p>", "templateType": "randrange", "can_override": false}, "a6": {"name": "a6", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 6</p>", "templateType": "randrange", "can_override": false}, "a7": {"name": "a7", "group": "Ungrouped variables", "definition": "random(16 .. 60#1)", "description": "<p>Age 7</p>", "templateType": "randrange", "can_override": false}, "list": {"name": "list", "group": "Ungrouped variables", "definition": "sort([a1,a2,a3,a4,a5,a6,a7])", "description": "<p>Ages in ascending order</p>", "templateType": "anything", "can_override": false}, "range": {"name": "range", "group": "Ungrouped variables", "definition": "max(list)-min(list)", "description": "<p>Range</p>", "templateType": "anything", "can_override": false}, "lq": {"name": "lq", "group": "Ungrouped variables", "definition": "list[((8/4)-1)]", "description": "<p>Lower quartile</p>", "templateType": "anything", "can_override": false}, "uq": {"name": "uq", "group": "Ungrouped variables", "definition": "list[(((3*8)/4)-1)]", "description": "<p>Upper quartile</p>", "templateType": "anything", "can_override": false}, "iqr": {"name": "iqr", "group": "Ungrouped variables", "definition": "uq-lq", "description": "<p>Interquartile range</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "a5", "a6", "a7", "list", "range", "lq", "uq", "iqr"], "variable_groups": [{"name": "Unnamed group", "variables": []}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "a)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Work out the range of ages.</p>", "minValue": "range", "maxValue": "range", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "b)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Work out the interquartile range of the ages.</p>", "minValue": "iqr", "maxValue": "iqr", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM10 Estimated Mean", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Tina needs to take a train to work.</p>\n<p>The table below shows information about how long the train is delayed for on each day.</p>\n<p>The policy of the train company is that if your train is delayed for longer than 30 minutes, you will recieve a 50% discount on your train ticket.</p>\n<table width=\"294\" height=\"161\" style=\"height: 108px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 130.5px; height: 18px;\"><strong>Delay Time</strong></td>\n<td style=\"width: 130.5px; height: 18px;\"><strong>Frequency&nbsp;</strong></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 130.5px; height: 18px;\">0 &lt; t $\\leq$ 10</td>\n<td style=\"width: 130.5px; height: 18px;\">{f1}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 130.5px; height: 18px;\">10 &lt; t $\\leq$ 20</td>\n<td style=\"width: 130.5px; height: 18px;\">{f2}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 130.5px; height: 18px;\">20 &lt; t $\\leq$ 30</td>\n<td style=\"width: 130.5px; height: 18px;\">{f3}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 130.5px; height: 18px;\">30 &lt; t $\\leq$ 40</td>\n<td style=\"width: 130.5px; height: 18px;\">{f4}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 130.5px; height: 18px;\">40 &lt; t $\\leq$ 50</td>\n<td style=\"width: 130.5px; height: 18px;\">{f5}</td>\n</tr>\n</tbody>\n</table>", "advice": "<p><strong>a)</strong></p>\n<p>To find the estimated mean we must work out the midpoint of the delay time intervals and multiply this by the frequency to create the $fx$ column on the table.</p>\n<table width=\"294\" height=\"361\" style=\"width: 747px;\">\n<tbody>\n<tr>\n<td style=\"width: 154.688px;\"><strong>Delay Time</strong></td>\n<td style=\"width: 167px;\"><strong>Frequency&nbsp;</strong></td>\n<td style=\"width: 119.891px;\"><strong>Midpoint</strong></td>\n<td style=\"width: 240.422px;\"><strong>Frequency $\\times$ Midpoint, $fx$</strong></td>\n</tr>\n<tr>\n<td style=\"width: 154.688px;\">0 &lt; t $\\leq$ 10</td>\n<td style=\"width: 167px;\">{f1}</td>\n<td style=\"width: 119.891px;\">5</td>\n<td style=\"width: 240.422px;\">= 5$\\times\\var{f1} = \\var{f1m}$</td>\n</tr>\n<tr>\n<td style=\"width: 154.688px;\">10 &lt; t $\\leq$ 20</td>\n<td style=\"width: 167px;\">{f2}</td>\n<td style=\"width: 119.891px;\">15</td>\n<td style=\"width: 240.422px;\">= 15$\\times\\var{f2} = \\var{f2m}$</td>\n</tr>\n<tr>\n<td style=\"width: 154.688px;\">20 &lt; t $\\leq$ 30</td>\n<td style=\"width: 167px;\">{f3}</td>\n<td style=\"width: 119.891px;\">25</td>\n<td style=\"width: 240.422px;\">= 25$\\times\\var{f3} = \\var{f3m}$</td>\n</tr>\n<tr>\n<td style=\"width: 154.688px;\">30 &lt; t $\\leq$ 40</td>\n<td style=\"width: 167px;\">{f4}</td>\n<td style=\"width: 119.891px;\">35</td>\n<td style=\"width: 240.422px;\">= 35$\\times\\var{f4} = \\var{f4m}$</td>\n</tr>\n<tr>\n<td style=\"width: 154.688px;\">40 &lt; t $\\leq$ 50</td>\n<td style=\"width: 167px;\">{f5}</td>\n<td style=\"width: 119.891px;\">45</td>\n<td style=\"width: 240.422px;\">= 45$\\times\\var{f5} = \\var{f5m}$</td>\n</tr>\n</tbody>\n</table>\n<p>Now to find the mean we calculate the sum of the $fx$ column and divide it by the sum of the frequencies:</p>\n<p>Estimated Mean = $\\frac{\\var{f1m}+\\var{f2m}+\\var{f3m}+\\var{f4m}+\\var{f5m}}{5+15+25+35+45} = \\frac{\\var{freqmid}}{\\var{sum}} = \\var{meana}.$</p>\n<p>Hence the estimated mean delay time is $\\var{mean}$ to two decimal places.</p>\n<p></p>\n<p><strong>b)</strong></p>\n<p>To work out what percentage of delays that were over 30 minutes we first need to calculate the number of days where the train was delayed for over 30 minutes.&nbsp;</p>\n<p>The number of delays that over 30 minutes is $\\var{f4}+\\var{f5} = \\var{f4+f5}$.</p>\n<p>We divide this by the total number of deliveries to find the fraction of delays that were over 30 minutes and then multiply this number by 100 to find the percentage:</p>\n<p>$\\frac{\\var{f4+f5}}{\\var{f1}+\\var{f2}+\\var{f3}+\\var{f4}+\\var{f5}} \\times 100\\% = \\frac{\\var{f4+f5}}{\\var{sum}} \\times 100\\% = \\var{percentagea} \\times 100\\%$.</p>\n<p>Hence, the percentage of delays that were over 30 minutes is $\\var{percentage}\\%$ to two decimal places.</p>\n<p></p>\n<p><strong>c)</strong></p>\n<p>The percentage of delays that take over 40 minutes is:</p>\n<p>$\\frac{\\var{f5}}{\\var{f1}+\\var{f2}+\\var{f3}+\\var{f4}+\\var{f5}} \\times 100\\% = \\frac{\\var{f5}}{\\var{sum}} \\times 100\\% = \\var{percent40} \\times 100\\%$, to one decimal place.</p>\n<p>So, only $\\var{percent40}\\%$ of the time, delays were longer than 40 minutes so the manager would probably wanto the policy changed to 40 minutes.</p>\n<p></p>\n<p style=\"text-align: center;\"><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"f1": {"name": "f1", "group": "Ungrouped variables", "definition": "random(1 .. 20#1)", "description": "<p>Frequency 1</p>", "templateType": "randrange", "can_override": false}, "f2": {"name": "f2", "group": "Ungrouped variables", "definition": "random(1 .. 20#1)", "description": "<p>Frequency 2</p>", "templateType": "randrange", "can_override": false}, "f3": {"name": "f3", "group": "Ungrouped variables", "definition": "random(1 .. 20#1)", "description": "<p>Frequency 3</p>", "templateType": "randrange", "can_override": false}, "f4": {"name": "f4", "group": "Ungrouped variables", "definition": "random(1 .. 20#1)", "description": "<p>Frequency 4</p>", "templateType": "randrange", "can_override": false}, "f5": {"name": "f5", "group": "Ungrouped variables", "definition": "random(1 .. 5#1)", "description": "<p>Frequency 5</p>", "templateType": "randrange", "can_override": false}, "meana": {"name": "meana", "group": "Ungrouped variables", "definition": "freqmid/sum", "description": "<p>Mean</p>", "templateType": "anything", "can_override": false}, "sum": {"name": "sum", "group": "Ungrouped variables", "definition": "f1+f2+f3+f4+f5", "description": "<p>Sum of frequencies</p>", "templateType": "anything", "can_override": false}, "f1m": {"name": "f1m", "group": "Ungrouped variables", "definition": "5*f1", "description": "<p>Frequency * midpoint 1</p>", "templateType": "anything", "can_override": false}, "f2m": {"name": "f2m", "group": "Ungrouped variables", "definition": "15*f2", "description": "<p>Frequency * midpoint 2</p>", "templateType": "anything", "can_override": false}, "f3m": {"name": "f3m", "group": "Ungrouped variables", "definition": "25*f3", "description": "<p>Frequency * midpoint 3</p>", "templateType": "anything", "can_override": false}, "f4m": {"name": "f4m", "group": "Ungrouped variables", "definition": "35*f4", "description": "<p>Frequency * midpoint 4</p>", "templateType": "anything", "can_override": false}, "f5m": {"name": "f5m", "group": "Ungrouped variables", "definition": "45*f5", "description": "<p>Frequency * midpoint 5</p>", "templateType": "anything", "can_override": false}, "freqmid": {"name": "freqmid", "group": "Ungrouped variables", "definition": "f1m+f2m+f3m+f4m+f5m", "description": "<p>Sum of Frequency * midpoint&nbsp;</p>", "templateType": "anything", "can_override": false}, "mean": {"name": "mean", "group": "Ungrouped variables", "definition": "precround(meana,2)", "description": "<p>Mean rounded to two decimal places</p>", "templateType": "anything", "can_override": false}, "f30": {"name": "f30", "group": "Ungrouped variables", "definition": "f4+f5", "description": "<p>Sum of 4th &amp; 5th frequencies</p>", "templateType": "anything", "can_override": false}, "percentagea": {"name": "percentagea", "group": "Ungrouped variables", "definition": "(f30/sum)*100", "description": "<p>Percentage over 30 mins</p>", "templateType": "anything", "can_override": false}, "percentage": {"name": "percentage", "group": "Ungrouped variables", "definition": "precround(percentagea,1)", "description": "<p>Percentage rounded to one decimal place</p>", "templateType": "anything", "can_override": false}, "percent40": {"name": "percent40", "group": "Ungrouped variables", "definition": "precround(((f5/sum)*100),1)", "description": "<p>Percentage over 40 mins</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["f1", "f2", "f3", "f4", "f5", "meana", "sum", "f1m", "f2m", "f3m", "f4m", "f5m", "freqmid", "mean", "f30", "percentagea", "percentage", "percent40"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "a)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Using a calculator, calculate an estimate for the mean delay time. Give your answer to two decimal places.</p>", "minValue": "mean", "maxValue": "mean", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "b)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What percentage of delays were over 30 minutes? Give your answer to one decimal place.</p>", "minValue": "percentage", "maxValue": "percentage", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": true, "customName": "c)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The train company propose that they should only offer the 50% discount if the train is delayed for over 40 minutes.</p>\n<p>If you were the manager of the train company would you agree? Type yes or no into the box and think about the reasons for your answer.</p>", "answer": "yes", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "yes", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM11 Linear Interpolation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>This frequence table stores data about the lengths of some plants:</p>\n<table style=\"width: 285px;\">\n<tbody>\n<tr>\n<td style=\"width: 163.625px; text-align: left;\"><strong>Length ($x$ cm)</strong></td>\n<td style=\"width: 88.375px; text-align: left;\"><strong>Frequency</strong></td>\n</tr>\n<tr>\n<td style=\"width: 163.625px; text-align: left;\">10 &lt; $x$ $\\leq$ 20</td>\n<td style=\"width: 88.375px; text-align: left;\">{f1}</td>\n</tr>\n<tr>\n<td style=\"width: 163.625px; text-align: left;\">20 &lt; $x$ $\\leq$ 30</td>\n<td style=\"width: 88.375px; text-align: left;\">{f2}</td>\n</tr>\n<tr>\n<td style=\"width: 163.625px; text-align: left;\">30 &lt; $x$ $\\leq$ 40</td>\n<td style=\"width: 88.375px; text-align: left;\">{f3}</td>\n</tr>\n<tr>\n<td style=\"width: 163.625px; text-align: left;\">40 &lt; $x$ $\\leq$ 50</td>\n<td style=\"width: 88.375px; text-align: left;\">{f4}</td>\n</tr>\n</tbody>\n</table>", "advice": "<p><strong>a)</strong></p>\n<p>To find the median we must find the middle value. To do this we sum the frequencies and divide the result by 2:</p>\n<p>$\\frac{\\var{f1}+\\var{f2}+\\var{f3}+\\var{f4}}{2} = \\frac{\\var{total}}{2} = \\var{middle1}$.</p>\n<p>Hence we must find value number $\\var{middle1}$, we can do this by totalling the cumulative frequency in the table below.</p>\n<table style=\"height: 235px;\" width=\"966\">\n<tbody>\n<tr style=\"height: 46px;\">\n<td style=\"width: 176.25px; height: 14px; text-align: left;\">\n<p><strong>Length $x$ cm</strong></p>\n</td>\n<td style=\"width: 165.375px; height: 14px; text-align: left;\"><strong>Frequency</strong></td>\n<td style=\"width: 575.375px; height: 14px; text-align: left;\"><strong>Cumulative Frequency</strong></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 176.25px; text-align: left; height: 18px;\"><strong>1.</strong> 10 &lt; $x$ $\\leq$ 20</td>\n<td style=\"width: 165.375px; height: 18px; text-align: left;\">{f1}</td>\n<td style=\"width: 575.375px; height: 18px; text-align: left;\">$\\var{f1}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 176.25px; text-align: left; height: 18px;\"><strong>2.</strong> 20 &lt; $x$ $\\leq$ 30</td>\n<td style=\"width: 165.375px; height: 18px; text-align: left;\">{f2}</td>\n<td style=\"width: 575.375px; height: 18px; text-align: left;\">$\\var{f1}+\\var{f2}=\\var{cf2}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 176.25px; text-align: left; height: 18px;\"><strong>3.</strong> 30 &lt; $x$ $\\leq$ 40&nbsp;</td>\n<td style=\"width: 165.375px; height: 18px; text-align: left;\">{f3}</td>\n<td style=\"width: 575.375px; height: 18px; text-align: left;\">$\\var{f1}+\\var{f2} +\\var{f3} =\\var{cf3}$</td>\n</tr>\n<tr style=\"height: 10px;\">\n<td style=\"width: 176.25px; text-align: left; height: 10px;\"><strong>4.</strong> 40 &lt; $x$ $\\leq$ 50</td>\n<td style=\"width: 165.375px; height: 10px; text-align: left;\">{f4}</td>\n<td style=\"width: 575.375px; height: 10px; text-align: left;\">$\\var{f1}+\\var{f2} +\\var{f3} + \\var{f4} =\\var{total}$</td>\n</tr>\n</tbody>\n</table>\n<p>You can see value number $\\var{middle1}$ lies in interval number $\\var{interval1}$ hence this is the median class interval for the time taken.</p>\n<p>We can estimate the median by using interpolation:</p>\n<p>$$<br/>\\text{Estimate of median} = \\text{class start value} + \\frac{\\text{position in class}}{\\text{frequency in class}}\\times \\text{class width}<br/>$$</p>\n<p>In this case this is $\\var{lower1}+\\frac{\\var{middle1}-\\var{cf11}}{\\var{fint1}}\\times 10 =\\var{lower1}+\\var{interpolation1}=\\var{median1}.$</p>\n<p>(Note: that sometimes it is convenient to use $(\\var{total} + 1)/2 = \\var{middle2}$ as the way to work out the median position. The distinction does not really matter as this is an estimated value and often the decision is made based on which is the most convenient to calculate). This question has been written so that both answers will be marked correctly.</p>\n<p><strong>b)</strong></p>\n<p>To calculate the $i^{th}$ quartile ($Q_i$) we must use the following formula:</p>\n<p>$Q_i = l + \\frac{\\frac{iN}{4}-F}{f}\\times h,$</p>\n<p>where:</p>\n<p>$l$ = lower limit of the interval in which $Q_i$ lies;</p>\n<p>$N$ = Total number of observations;</p>\n<p>$F$ = Cumulative frequency of class previous to the $i^{th}$ quartile class;<br/><br/>$f$ = Frequency of $i^{th}$ quartile class.</p>\n<p>Since we want to calculate the lower quartile, $i=1$.</p>\n<p>If we calculate $\\frac{iN}{4} = \\frac{\\var{total}}{4} = \\var{quarter}$, we can see in the table from part <strong>a)</strong> that the lower quartile will be in interval number $\\var{intervallq}$. This means that $F = \\var{fprev}$ and $f = \\var{frequency}$.</p>\n<p>Hence,&nbsp;</p>\n<p>$Q_1 = \\var{lowerlq} + \\frac{\\var{quarter} - \\var{Fprev}}{\\var{frequency}} \\times 10 = \\var{lowerlq} + \\frac{\\var{quarter-Fprev}}{\\var{frequency}} \\times 10 = \\var{lowerlq} + \\var{((quarter-Fprev)/frequency)*10} = \\var{lq}.$&nbsp;<br/><br/>So, The lower quartile is $\\var{lqround}$ to two decimal places.</p>\n<p></p>\n<p><strong>c)&nbsp;</strong></p>\n<p>To calculate the upper quartile we use the same formula as in part <strong>b) </strong>but this time $i=3$. So, $\\frac{iN}{4} = \\frac{\\var{3*total}}{4} = \\var{3*quarter}$, we can see in the table from part <strong>a)</strong> that the lower quartile will be in interval number $\\var{intervaluq}$. This means that $F = \\var{ufprev}$ and $f = \\var{ufrequency}$.</p>\n<p>Hence,&nbsp;</p>\n<p>$Q_3 = \\var{upperlq} + \\frac{\\var{3*quarter} - \\var{uFprev}}{\\var{ufrequency}} \\times 10 = \\var{upperlq} + \\frac{\\var{3*quarter-uFprev}}{\\var{ufrequency}} \\times 10 = \\var{upperlq} + \\var{((3*quarter-uFprev)/ufrequency)*10} = \\var{uq}.$&nbsp;<br/><br/>So, The lower quartile is $\\var{uqround}$ to two decimal places.</p>\n<p><strong>d)</strong></p>\n<p>To calculate the interquartile range we subtract the lower quartile from the upper quartile.</p>\n<p>Hence,&nbsp;</p>\n<p>$IQR = Q_3 - Q_1 = \\var{uq}-\\var{lq}=\\var{iqr}$.</p>\n<p>So the interquartile range rounded to two decimal places is $\\var{iqrround}$.</p>\n<p></p>\n<p style=\"text-align: center;\"><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/first-steps#mean,-median-and-mode\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": 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"preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Upuli Wickramaarachchi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23527/"}], "tags": [], "metadata": {"description": "<p>Tests understanding of scatter plots and related concepts.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><span style=\"font-weight: 400;\">The scatter plot below shows the relationship between an employee&rsquo;s height in centimetres and how long it takes them to walk to work in minutes.</span></p>\n<table>\n<tbody>\n<tr>\n<td>time (mins)</td>\n<td>{drawgraph()}</td>\n</tr>\n<tr>\n<td></td>\n<td style=\"text-align: center;\">height (cm)</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p></p>\n<p></p>", "advice": "<p>The graph shows that there is a positive correlation between a person's height and how long it takes them to walk to work.</p>\n<p>A postive correlation is a relationship between two variables where both variables move in the same diection.</p>\n<p>This tells us that as a person's height increases, the time it takes to walk to work increases.</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/next-steps#Introduction%20to%20correlation\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"slope": {"name": "slope", "group": "Regression variables", "definition": "(6*sumxy-sumx*sumy)/(6*sumxx-(sumx)^2)", "description": "<p>s</p>", "templateType": "anything", "can_override": false}, "timemax": 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