Substitute values into an algebraic expression and calculate the result.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Evaluate the following expression,
\n\\[\\simplify{p^{n}+{a}*r*t+{c}},\\]
\nwhen $p = \\var{pval}$, $r = \\var{rval}$, and $t = \\var{tval}$.
", "advice": "In order to evaluate $\\simplify{p^{n}+{a}*r*t+{c}},$ with the given values, $p = \\var{pval}$, $r = \\var{rval}$, and $t = \\var{tval}$, we replace each instance of that letter with its corresponding value and then apply the rules of BIDMAS:
\n\\[\\var{pval}^\\var{n}+\\var{a}\\times \\var{rval} \\times \\var{tval} + \\var{c}\\]
\nWhich gives the answer $\\var{ans}$.
\nFollow this link for more help on tackling these kind of questions.
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Rearrange the following equation, to make $y$ the subject:
\n\\[{cy -b = 3x}\\]
", "advice": "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 $c$:
\n\\begin{split} cy-b &= 3x \\\\ cy &= 3x + b \\\\ y &=\\frac{3x+b}{c} \\end{split}
\n\nUse this link to find some resources which will help you revise this topic.
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", "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": "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": "Solve linear equations with unkowns on both sides. Including brackets and fractions.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "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.
\n\n| \n | \n | \n |
| \n | \n | \n |
| $\\simplify{{m}w+{n}}$ | \n$=$ | \n$\\simplify{{p}w+{q}}$ | \n
| \n | \n | \n |
| $\\simplify[!cancelTerms,unitFactor]{{m}w-{n}-{p}w}$ | \n$=$ | \n$\\simplify[!cancelTerms,unitFactor]{{p}w+{q}-{p}w}$ | \n
| \n | \n | \n |
| $\\simplify{{m-p}w-{n}}$ | \n$=$ | \n$\\var{q}$ | \n
| \n | \n | \n |
| $\\var{m-p}w-\\var{n}+\\var{n}$ | \n$=$ | \n$\\var{q}+\\var{n}$ | \n
| \n | \n | \n |
| $\\var{m-p}w$ | \n$=$ | \n$\\var{q+n}$ | \n
| \n | \n | \n |
| $\\displaystyle{\\frac{\\var{m-p}w}{\\var{m-p}}}$ | \n$=$ | \n$\\displaystyle{\\frac{\\var{q+n}}{\\var{m-p}}}$ | \n
| \n | \n | \n |
| $w$ | \n$=$ | \n$\\displaystyle{\\simplify{{q+n}/{m-p}}} = \\var{precround(ansA,1)} \\text{ to 1 dp}$ | \n
Use this link to find resources to help you revise how to solve linear equations
Solve $\\simplify{({m}w-{n}) = {p}w+{q}}$
\n$w=$ [[0]]
", "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": "GM01 Area of a circle", "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": "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": "Finding the area of a circle when given the diameter of the circle.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Find the area of a circle with diameter $\\var{d}$ cm giving your answer to 1 decimal place.
\n{geogebra_applet('https://www.geogebra.org/m/ngcchpcj',[d: d])}
", "advice": "To calculate the area of a circle we want to use the formula \\[ A = \\pi r^2, \\]
\nwhere $r$ is the radius of the circle.
\nSo, if the diameter, d, is $\\var{d}$ cm, then the radius is, $r=\\frac{d}{2}=\\var{{d}/2}$ cm, then
\n\\[ \\begin{split} Area &\\,=\\var{{d}/2}^2 \\times \\pi \\text{ cm}^2 \\\\ &\\,= \\simplify[all, fractionNumbers]{{{{d}^2/4}}pi} \\text{ cm}^2 \\\\ &\\,= \\var{precround({d}^2/4*pi,1)} \\text{ cm}^2. \\end{split} \\]
\nUse this link to find some resources to help you revise how to calculate the area of a circle.
\n", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "random(6,8,10,12,14,16,18,20)", "description": "", "templateType": "anything", "can_override": true}, "t": {"name": "t", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["d", "t"], "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": "$Area=$ [[0]] $\\text{ cm}^2$
", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Gap 0", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "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": "", "useAlternativeFeedback": false, "answer": "precround({{d/2}}^2*pi,1)", "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": []}], "answer": "precround({{d/2}}^2*pi,1)", "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": "GM03 Volume of cylinder", "extensions": [], "custom_part_types": [], "resources": ["question-resources/sqbasedpyramid_sEpkGzO.svg", "question-resources/triangularprism.svg", "question-resources/cylinder.svg", "question-resources/cuboid.svg"], "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": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}, {"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": ["3D shapes", "cuboid", "Cylinder", "cylinder", "pyramid", "taxonomy", "triangular prism", "volume", "Volume", "volume of a cuboid", "volume of a cylinder", "volume of a pyramid", "volume of a triangular prism"], "metadata": {"description": "Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "For a cylinder, we first need to find the area of the circular face then multiply this area by the depth of the cylinder.
In this example the radius of the circular face is $\\mathrm{radius} = \\var{r7}m$ which can be used to calculate the area of the circular face.
\\begin{align}
\\mathrm{Area\\thinspace_\\bigcirc} &= \\pi \\times \\mathrm{radius}^2 \\\\
&= \\pi \\times \\var{r7}^2 \\\\
&= \\var{pi * (r7)^2}\\, \\mathrm{m}^2 \\,.
\\end{align}
Now that we have the area of the circular face ($\\mathrm{Area\\thinspace_\\bigcirc}$) we can multiply this by the $\\mathrm{depth} =\\var{w7}m\\thinspace$.
\n\\begin{align}
\\mathrm{Volume} &= \\mathrm{Area\\thinspace_\\bigcirc} \\times \\mathrm{depth} \\\\
&= \\var{pi*(r7)^2} \\times \\var{w7} \\\\
&= \\var{dpformat(pi*w7*(r7)^2, 5)} \\\\
&= \\var{dpformat(pi*w7*(r7)^2, 1)}\\, \\mathrm{m}^2\\,. \\quad \\text{1 d.p.}
\\end{align}
Use this link to find resources to help you revise how to calculate the volume of a cylinder.
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", "templateType": "anything", "can_override": false}, "w6": {"name": "w6", "group": "Triangular prism", "definition": "random(5..9#1)", "description": "Creates base of triangle.
", "templateType": "anything", "can_override": false}, "d8": {"name": "d8", "group": "Square based pyramid", "definition": "random(3..6#0.1)", "description": "One side of square base.
", "templateType": "anything", "can_override": false}, "h8": {"name": "h8", "group": "Square based pyramid", "definition": "random(3..7#1)", "description": "Height of pyramid.
", "templateType": "anything", "can_override": false}, "w7": {"name": "w7", "group": "Cylinder", "definition": "random(7..15#0.1)", "description": "Depth of cylinder.
", "templateType": "anything", "can_override": false}, "d6": {"name": "d6", "group": "Triangular prism", "definition": "random(9..15#0.1)", "description": "Depth of triangular prism.
", "templateType": "anything", "can_override": false}, "r7": {"name": "r7", "group": "Cylinder", "definition": "random(2..6#1)", "description": "Radius of the cylinder.
", "templateType": "anything", "can_override": false}, "h4": {"name": "h4", "group": "Cuboid ", "definition": "random(2..5#1 except d4)", "description": "Side of square in cuboid.
", "templateType": "anything", "can_override": false}, "w4": {"name": "w4", "group": "Cuboid ", "definition": "random(5.5..8#0.1)", "description": "Width of cuboid.
", "templateType": "anything", "can_override": false}, "w8": {"name": "w8", "group": "Square based pyramid", "definition": "random(3..7#1)", "description": "One side of square base.
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", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Cuboid ", "variables": ["w4", "d4", "h4"]}, {"name": "Triangular prism", "variables": ["w6", "h6", "d6"]}, {"name": "Cylinder", "variables": ["r7", "w7"]}, {"name": "Square based pyramid", "variables": ["h8", "w8", "d8"]}], "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": "Calculate the $\\mathrm{Volume}$ of the following cylinder.
\n\n$\\mathrm{Volume} =$[[0]] $\\mathrm{m}^3$. Round your answer to 1 decimal place.
", "stepsPenalty": "1", "steps": [{"type": "information", "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": "Volume of a cylinder:
\n\\begin{align}
\\mathrm{Volume} &= \\mathrm{Area\\thinspace_\\bigcirc} \\times \\mathrm{depth} \\\\
&= \\pi \\times \\mathrm{r}^2 \\times \\mathrm{depth}
\\end{align}
Whole number division in a context of number of tablets per day based on a tablet size and a daily prescribed amount.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "You prescribe a patient {p} milligrams (mg) per day of a particular drug. The drug is available in tablets of {t} milligrams (mg). How many tablets should you instruct the patient to take each day?
", "advice": "| \n \n \nSince each tablet is {t} mg of the necessary drug, we must prescribe enough tablets to add up to {p} milligrams. By dividing {p} by {t} we can find out how many {t} mg tablet make up {p} mg, which gives {answer}. \n | \n
Use this link to find some resources which will help you revise this topic.
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\n", "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": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA03 Dosage Calculation 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": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "Division resulting in decimals in the context of a dose per hour.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "You are required to give an infusion of a drug of {d}ml over {t}hours, what is the rate per hour?
\n(answer to 1 decimal place)
", "advice": "| \n \n \nIf there is {d}ml in {t} hours, then {d} should be divided by {t} to get {answert}ml per hour. \n\nMake use of the following resource(s) to revise if necessary: \nUse this link to find some resources which will help you revise this topic \nIf you were unsure how to round your answer then look at the following resource(s): \nUse this link to find some resources which will help you revise this topic \n | \n
[[0]] ml per hour
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "The symbol is a comparitor that $<$ says that the object to its left is less than the object to its right. Similarly, $>$ says the object to its left is greater than the object to its right.
\nIn each case the sentence can be read in two ways e.g. $a<b$ can be read as \"$a$ is less than $b$\" OR \"$b$ is greater than $a$\".
\nThe 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, $x>4$ and $x$ is a whole number means that $x$ could be $5,6,$... etc. Notably in the second case $x$ cannot be $4$.
\n\n
Use this link to find some resources which will help you revise this topic.
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\n\\(\\var{disp_values2[0]}\\var{disp_op2}\\var{disp_values2[1]}\\)
\n", "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": "Number sequences - find a missing number
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Find the missing number from the following sequence
\n\\[\\var{a}, \\var{a+d}, \\var{a+2*d}, \\var{a+3d}, ?, \\var{a+5d}, \\var{a+6d}, \\var{a+7d}, \\ldots\\]
", "advice": "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 Arithmetic Sequence.
\n\nUse this link to find some resources which will help you revise this topic.
", "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": "[[0]]
", "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": "NA06 Find factors of a number", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}, {"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": "Multiples, factors, lowest common multiples and highest common factors.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "Factors multiply together in pairs to give the original number (e.g., the factors of 10 are 1, 2, 5 and 10, because 1x10=10 and 2x5=10.
\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"ca2": {"name": "ca2", "group": "Ungrouped variables", "definition": "random(answers except ca1)", "description": "", "templateType": "anything", "can_override": false}, "ca1": {"name": "ca1", "group": "Ungrouped variables", "definition": "random(answers)", "description": "", "templateType": "anything", "can_override": false}, "hcf": {"name": "hcf", "group": "Ungrouped variables", "definition": "gcd(k,l)", "description": "", "templateType": "anything", "can_override": false}, "lcm4": {"name": "lcm4", "group": "Ungrouped variables", "definition": "lcm(p,q)", "description": "", "templateType": "anything", "can_override": false}, "lcm2": {"name": "lcm2", "group": "Ungrouped variables", "definition": "lcm(n,m)", "description": "", "templateType": "anything", "can_override": false}, "product": {"name": "product", "group": "Ungrouped variables", "definition": "a*b*c", 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"templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "random(6..24)", "description": "", "templateType": "anything", "can_override": false}, "wa2": {"name": "wa2", "group": "Ungrouped variables", "definition": "random(1..product except [a,b,c,a*b,a*c,b*c,1,product,wa1])", "description": "", "templateType": "anything", "can_override": false}, "wa1": {"name": "wa1", "group": "Ungrouped variables", "definition": "random(1..product except answers)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["hcf2", "lcm2", "a", "b", "c", "product", "answers", "wa1", "wa2", "ca1", "ca2", "d", "f", "g", "h", "j", "k", "l", "lcm", "m", "n", "hcf", "p", "q", "hcf3", "lcm4"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, 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", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": "0", "warningType": "warn", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$\\var{ca1}$
", "$\\var{ca2}$
", "$\\var{wa1}$
", "$\\var{wa2}$
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Evaluate the following expression:
", "advice": "BIDMAS stands for:
\nBrackets
\nIndices
\nDivision
\nMultiplication
\nAddition
\nSubtraction
\n\nAnd 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.
\nFirst 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:
\n\\[\\var{a}-\\var{b} \\times \\var{c}\\]
\n\\[=\\var{a}-\\var{b*c}\\]
\n\\[=\\var{a-b*c}\\]
\nUse this link to find some resources which will help you revise this topic.
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\n$\\var{a}-\\var{b} \\times\\var{c}$
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Evaluate the following expression:
", "advice": "BIDMAS stands for:
\nBrackets
\nIndices
\nDivision
\nMultiplication
\nAddition
\nSubtraction
\n\nAnd 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.
\nFirst 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:
\n\n\\[\\var{h}-\\var{a2*b2} \\div \\var{b2}\\]
\n\\[=\\var{h}-\\var{a2}\\]
\n\\[=\\var{h-a2}\\]
\nUse this link to find some resources which will help you revise this topic.
", "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": "$\\var{h}-\\var{a2*b2} \\div \\var{b2}$
", "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": "Applying the order of operators.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "To calculate the following expression you press a sequence of buttons on your calculator.
\n\\begin{align}\\frac{\\var{num}}{\\var{a}\\times\\var{b}}\\end{align}
\nWhich of the following would give the WRONG answer?
\n", "advice": "BIDMAS stands for:
\nBrackets
\nIndices
\nDivision
\nMultiplication
\nAddition
\nSubtraction
\nThis 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.
\nUse this link to find some resources which will help you revise this topic.
", "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": "Calculations with negative numbers.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Calculate $\\var{x}+(\\var{y})$.
", "advice": "When you add a negative number that is the same as subtracting the number so
\n\\[\\var{x}+(\\var{y})=\\var{x}-\\var{-y}=\\var{x+y}.\\]
\nUse this link to find some resources which will help you revise this topic.
", "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": "Calculations with negative numbers.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Calculate $\\var{x}-(\\var{y})$.
", "advice": "When you subtract a negative number that is the same as adding the number so
\n\\[\\var{x}-(\\var{y})=\\var{x}+\\var{-y}=\\var{x-y}\\]
\nUse this link to find some resources which will help you revise this topic.
", "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": "Calculations with negative numbers.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Calculate $\\var{x}\\times(\\var{y})$.
", "advice": "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
\n\\[\\var{x}\\times(\\var{y})=-(\\var{x}\\times\\var{-y})=\\var{x*y}.\\]
\nUse this link to find some resources which will help you revise this topic.
", "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": "Calculations with negative numbers.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Calculate $(\\var{x})\\times(\\var{y})$.
", "advice": "Multiplying two negative numbers gives a positive so we just calculate the multiplication as if both numbers were positive. This means we have
\n\\[(\\var{x})\\times(\\var{y})=\\var{-x}\\times\\var{-y}=\\var{x*y}.\\]
\nUse this link to find some resources which will help you revise this topic.
", "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": "Calculations with negative numbers.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Calculate $(\\var{x})\\div(\\var{y})$.
", "advice": "When we divide two numbers the rule is,
\nIn this calculation we have
\n\\[(\\var{x})\\div(\\var{y})=\\var{x/y}.\\]
\nUse this link to find some resources which will help you revise this topic.
", "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": "Proportional calculation in context.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "If {n1} adult cinema tickets cost £{n1price}, how much would it cost for {n2} adults to buy tickets to the cinema?
", "advice": "If {n1} tickets cost £{n1price} then we can calculate that one ticket costs
\n\\[£\\var{n1price}\\div\\var{n1}=£\\var{price}.\\]
\nThis means that {n2} tickets cost $\\var{n2}\\times£\\var{price}=£\\var{n2price}$
\n\nUse this link to find some resources which will help you revise this topic.
", "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": "£[[0]]
", "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": "Round numbers to a given number of decimal places.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "We can approximate numbers by rounding.
\nRound $\\var{c1}$ to a given number of decimal places.
", "advice": "The first thing to do when we are rounding numbers is to identify the last digit we are keeping.
\nWhen you're asked to round your answer to a number of decimal places, you need to decide whether to keep the last 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 when the next digit is 5 or more.
\nTo write it down in steps:
\nIt 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 move along to the left side until we find a digit less than 9.
\nTo round a number to a given number $n$ of decimal places, we look at the $n$th digit after the decimal point.
\nWe have $\\var{c1}$.
\ni)
\nWe 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 updown to get $\\var{precround(c1, 1)}$.
\nii)
\nThe second digit after the decimal point is $\\var{cdig[3]}$. It is followed by $\\var{cdig[2]}$ so we round updown to get $\\var{precround(c1, 2)}$.
\niii)
\nThe 3rd decimal place is $\\var{cdig[2]}$, followed by $\\var{cdig[1]}$. We get $\\var{precround(c1, 3)}$. The 4th decimal place is $\\var{cdig[1]}$, followed by $\\var{cdig[0]}$. We get $\\var{precround(c1, 4)}$.
\nUse this link to find some resources which will help you revise this topic
\n", "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": "Random number with 5 decimal places.
", "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": "Number of decimal places to round.
", "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": "i) $\\var{c1}$ rounded to 1 decimal place is: [[0]]
\nii) $\\var{c1}$ rounded to 2 decimal places is: [[1]]
\niii) $\\var{c1}$ rounded to {dp} decimal places is: [[2]]
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "The first thing to do when we are rounding numbers is to identify the last digit we are keeping.
\nWhen you're asked to round your answer to a number of significant figures, you need to decide whether to keep the last digit 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 when the next digit is 5 or more.
\nTo write it down in steps:
\nIt 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 move along to the left side until we find a digit less than 9.
\nThe last digit we need to keep will depend on how many zeros there are. We don't consider leading zeros to be significant,
i.e. 0.03 and 0.3 both have 1 significant figure (but 0.30 has two significant figures, since the second zero isn't a 'leading' zero).
i)
\nWe round $\\var{d1}$ to 1 significant figure. The first non-zero digit is $\\var{ddig[5]}$. The following digit is $\\var{ddig[4]}$ so we round updown to get $\\var{dpformat(siground(d1, 1), 0)}$.
\nii)
\nWe round $\\var{d1}$ to {sf} significant figures. The first non-zero digit is $\\var{ddig[5]}$. The second following digit is $\\var{ddig[4]}$, the third following digit is $\\var{ddig[3]}$ and the fourth following digit is $\\var{ddig[2]}$. The digit following the last digit we are keeping is $\\var{ddig[3]}$$\\var{ddig[2]}$$\\var{ddig[1]}$, so we round to get $\\var{sigformat(d1, sf)}$. These are our {sf} significant figures.
\n\nUse this link to find some resources which will help you revise this topic.
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\ni) $\\var{d1}$ rounded to 1 significant figure is: [[0]]
\nii) $\\var{d1}$ rounded to {sf} significant figures is: [[1]]
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "The first thing to do when we are rounding numbers is to identify the last digit we are keeping.
\nWhen you're asked to round your answer to a number of significant figures, you need to decide whether to keep the last digit 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 when the next digit is 5 or more.
\nTo write it down in steps:
\nIt 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 move along to the left side until we find a digit less than 9.
\nThe last digit we need to keep will depend on how many zeros there are. We don't consider leading zeros to be significant,
i.e. 0.03 and 0.3 both have 1 significant figure (but 0.30 has two significant figures, since the second zero isn't a 'leading' zero).
i)
\nWe round $\\var{e1}$ to 1 significant figure. The first non-zero digit is $\\var{edig[4]}$, followed by $\\var{edig[3]}$. This is lower than 5 so we round downmore than 5 so we round up to get $\\var{sigformat(e1,1)}$.
\nii)
\nWe round $\\var{e1}$ to {sf} significant figures. The first non-zero digit is $\\var{edig[4]}$. The second following digit is $\\var{edig[3]}$, the third following digit is $\\var{edig[2]}$ and the fourth following digit is $\\var{edig[1]}$. The digit following the last digit we are keeping is $\\var{edig[2]}$$\\var{edig[1]}$$\\var{edig[0]}$, so we round to get $\\var{sigformat(e1, sf)}$. These are our {sf} significant figures.
\n\nUse this link to find some resources which will help you revise this topic.
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\niii) $\\var{e1}$ rounded to 1 significant figure is: [[0]]
\niv) $\\var{e1}$ rounded to {sf} significant figures is: [[1]]
", "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": "siground(e1, 1)", "maxValue": "siground(e1, 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": "siground(e1, sf)", "maxValue": "siground(e1, sf)", "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": "NF05 Percentage decrease", "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", "discount", "percentages", "taxonomy"], "metadata": {"description": "Given a student discount, calculate a discounted price.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "{pname} is buying a new {item}. The price of the model he picked is £{price}. On a website with discounts for students, he found a voucher for a discount of {percentage}%.
", "advice": "There are multiple methods to approach this problem. The first method involves working out the discounted price as a percentage of the original, while the second method calculates the value of the discount and subtracts that from the listed price.
\nThere is a {percentage}% decrease in price. This means that the new price will be {100-percentage}% of the old price.
\n\\[\\begin{align} \\frac{\\var{100-percentage}}{100} \\times \\var{price} &= \\var{dpformat((100-percentage)/100*price,4)} \\\\&= \\var{dpformat((100-percentage)/100*price, 2)}\\text{.} \\end{align}\\]
\nOr, using the multiplier method,
\n\\[\\begin{align} \\var{(100-percentage)/100} \\times \\var{price} &= \\var{dpformat((100-percentage)/100*price,4)}\\\\&= \\var{dpformat((100-percentage)/100*price, 2)}\\text{.} \\end{align}\\]
\nWhen we are talking about money, it is usually assumed that we will round the answer to 2 decimal places.
\nWe find the discount first. This is
\n\\[\\frac{\\var{percentage}}{100} \\times \\var{price} = \\var{dpformat((percentage)/100*price,4)}\\text{.}\\]
\nOr using a decimal multiplier,
\n\\[\\var{(percentage)/100} \\times \\var{price} = \\var{dpformat((percentage)/100*price,4)}\\text{.}\\]
\nThen we subtract the discount from the original price to get the new price:
\n\\[ \\var{price} - \\var{dpformat(discount,2)} = \\var{dpformat(price - discount, 2)}\\text{.} \\]
\n\nUse this link to find some resources which will help you revise this topic.
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", "templateType": "anything", "can_override": false}, "item": {"name": "item", "group": "Ungrouped variables", "definition": "random(\"TV\", \"laptop\", \"smartphone\", \"PC\", \"gaming console\", \"fridge\")", "description": "The bought item.
", "templateType": "anything", "can_override": false}, "percentage": {"name": "percentage", "group": "Ungrouped variables", "definition": "random(5..40 #5)", "description": "Discount percentage.
", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "1000"}, "ungrouped_variables": ["item", "pname", "price", "percentage", "discount", "discountrounded"], "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": "What will the discounted price of the {item} be?
\nRound your answer to the nearest penny.
\n£ [[0]]
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "What is the percentage increase in a class of {total} if {additional} more are added to it?
\nGive your answer to 2 decimal places.
", "advice": "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
\n\\[ \\frac{\\var{additional}}{\\var{total}}\\times100\\%=\\var{dpformat(additional/total,4)}\\times 100\\%=\\var{dpformat(percentage,2)}\\%\\]
\n\nUse this link to find some resources which will help you revise this topic.
", "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": "[[0]]%
", "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": "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": "Find a percentage of an amount.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "What is {x}% of {y}?
", "advice": "Taking {x}% of {y} is calculated by multiplying,
\n\\[\\frac{\\var{x}}{100}\\times\\var{y}.\\]
\nFor 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,
\\[\\var{x/10}\\times10\\%\\times \\var{y}=\\var{x/10}\\times\\var{y*0.1}=\\var{x/100*y}.\\]
Use this link to find some resources which will help you revise this topic.
", "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": "Calculate one number as percentage of another.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "To find the percentage of a number we can use the formula:
\n\\[ \\text{New value } = \\text{Original value } \\times \\text{Percentage in decimal form} \\]
\nFirstly, to convert a percentage into decimal form we need to divide by $100$:
\n\\[ \\var{p} \\% = \\var{p/100} \\]
\nTherefore,
\n\\[ \\begin{split} \\var{p} \\% \\,\\text{ of } \\var{og} &\\,= \\var{og} \\times \\var{p/100} \\\\ &\\,= \\var{ans} \\end{split} \\]
\n\nUse this link to find resources to help you revise how to work out percentages.
\n", "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": "Find {p}% of {og}
", "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": "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": "Convert a fraction into a decimal.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Write $\\frac{\\var{x}}{\\var{y}}$ as a decimal. Round your answer to 3 decimal places.
", "advice": "You can calculate the decimals by hand using long division of $\\var{x}.000$ divided by $\\var{y}$.
\nIn some cases you may be able to simplify the fraction to something that you know the decimal for.
\nUse this link to find some resources which will help you revise this topic.
", "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": "NF23 Equivalent Ratios", "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": "Picking a ratio out of a list that is not equivalent to the others.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Which of the following ratios is not equivalent to the others?
", "advice": "The key to this question is understanding how to simplify ratios. In this case all the ratios simplify to $\\var{a}:\\var{b}$ except for $\\var{6*a}:\\var{7*b}$.
\n\nFor more help with this topic have a look at the resources here.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2 .. 6#1)", "description": "", "templateType": "randrange", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "a+1", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "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": ["$\\var{a}:\\var{b}$", "$\\var{2*a}:\\var{2*b}$", "$\\var{3*a}:\\var{3*b}$", "$\\var{5*a}:\\var{5*b}$", "$\\var{6*a}:\\var{7*b}$"], "matrix": [0, 0, 0, 0, "1"], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF24 Dividing amounts in ratios", "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": "Dividing amounts in ratios
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "The ratio of ethanol to water is {a}:{b} for an experiment. If I have {volWater}ml of water, how much ethanol do I need?
", "advice": "If there is a ratio of {a}:{b} for ethanol:water then that means for every {b}ml of water we need {a}ml of ethanol.
\nIn our experiment there is {volwater}ml of water so to find the amount of ethanol we divide by {b} and then multiply by {a}.
\n\\[\\var{volwater}\\text{ml}\\times\\frac{\\var{a}}{\\var{b}}=\\var{volwater*a/b}\\text{ml}\\]
Use this link to find some resources which will help you revise this topic.
[[0]]ml
", "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": "volwater/b*a", "maxValue": "volwater/b*a", "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": "NU03 Convert Units - volume - l to ml", "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": "Simple unit conversion with metric units.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Express {liquid} litres ($l$) in millilitres ($ml$).
", "advice": "There are $1000ml$ in $1l$. To work out the conversion: $\\var{liquid}*1000 = \\var{answer}$.
\n\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"liquid": {"name": "liquid", "group": "Ungrouped variables", "definition": "random(1 .. 6#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "liquid*1000", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["liquid", "answer"], "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": "[[0]]$ml$
", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "answer", "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": "answer", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NU04 Convert Units - volume - ml to l", "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": "Metric Unit conversion - division by 1000.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Express {liquid} millilitres ($ml$) in litres ($l$). Give your answer to 3 decimal places.
", "advice": "There are $1000ml$ in $1l$. To work out the conversion: $\\frac{\\var{liquid}}{1000} = \\var{answer}$.
\n\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"liquid": {"name": "liquid", "group": "Ungrouped variables", "definition": "random(100 .. 5200#1)", "description": "", "templateType": "randrange", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "liquid/1000", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["liquid", "answer"], "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": "[[0]]$l$
", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "answer", "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": "answer", "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"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NU05 Convert Units - metric prefixes - milligrams to grams", "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": "Using prefixes (milli) in this case.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Express {x} milligrams ($mg$) in grams ($g$). Give your answer to 3 decimal places.
", "advice": "There are $1000mg$ in $1g$. To work out the conversion: $\\frac{\\var{x}}{1000} = \\var{answer}$.
\n\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(100 .. 5200#1)", "description": "", "templateType": "randrange", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "x/1000", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "answer"], "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": "[[0]]$g$
", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "answer", "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": "answer", "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"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NU06 Convert Units - metric prefixes - milligrams to micrograms", "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": "Using prefixes - milli and micro.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Express {x} milligrams ($mg$) in micrograms ($\\mu g$).
", "advice": "There are $1000\\mu g$ in $1mg$. To work out the conversion: $\\var{x}*1000 = \\var{answer}$.
\n\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(0.1 .. 2#0.001)", "description": "", "templateType": "randrange", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "x*1000", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "answer"], "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": "[[0]]$\\mu g$
", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "answer", "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": "answer", "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"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NU07 Convert Units - metric prefixes - micrograms to milligrams", "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": "convert from micrograms to milligrams.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Express {x} micrograms ($\\mu g$) in milligrams ($mg$). Give your answer to 3 decimal places.
", "advice": "There are $1000\\mu g$ in $1mg$. To work out the conversion: $\\frac{\\var{x}}{1000} = \\var{answer}$.
\n\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(100 .. 5200#1)", "description": "", "templateType": "randrange", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "x/1000", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "answer"], "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": "[[0]]$mg$
", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "answer", "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": "answer", "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"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NU08 Convert Units - Volume - ml to cubic cm", "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": "\"Convert\" from millilitres to cubic centimeters.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Express {x} millilitres ($ml$) in cubic centimetres ($cm^3$).
", "advice": "$1 ml$ is the same measurement of volume as $1 cm^3$ so there is nothing to do to convert except change the units.
\n\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(100 .. 5200#1)", "description": "", "templateType": "randrange", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "x", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "answer"], "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": "[[0]]$cm^3$
", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "answer", "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": "answer", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NU09 Convert Units - Length - Inches to cm", "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": "convert from inches to cm.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Given that $1$ $inch$ is approximately $2.54$ $cm$. How long is a $\\var{x}$ inch ruler in $cm$?
", "advice": "The information given in the question tells you to use a conversion factor of $2.54$. So you must multiply $\\var{x}$ by $2.54$ to find the length of the ruler in $cm$.
\n\nUse this link to find some resources which will help you revise this topic.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(5 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "x*2.54", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "answer"], "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": "[[0]]$cm$.
\nGive your answer to 2 decimal places.
", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "answer", "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": "answer", "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": "SD01 Choosing a suitable chart", "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/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": [], "metadata": {"description": "This question is about identifying what types of charts or visual representations of data you can use for different data sets.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "This question is about recognising what types of charts or visual representations of data you can use with what types of data sets.
", "advice": "There are many different types of visual representations of data and sometimes there will be a choice of what you use.
\n\n", "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_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": "The table shows different names of charts on the left hand side and different descriptions of data sets along the top.
\nPair up each description with the chart that would be most suitable.
", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["Scatter plot", "Histogram", "Bar Chart"], "matrix": [["1", 0, 0], [0, "0", "1"], [0, "1", "0"]], "layout": {"type": "all", "expression": ""}, "answers": ["Two continuous variables plotted against each other to investigate their relationship.", "Non-numerical categories and the frequencies of each category.", "A continuous variable such as \"height in $cm$\" grouped into intervals showingthe frequency of the data in each interval."]}], "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": "Reading a value from a simple bar chart.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "The bar heights give the values of the spend.
Each company has two bars, the left one for last year (in red) and the right one for this year (in purple).
Isolate last years spend by looking at the the bars on the right side, and choose the tallest bar, corresponding to the highest value.
Use this link to find some resources which will help you revise this topic.
", "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": "new y values after the transformation
", "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": "the (random) original y values which relate to the x values
", "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": "vertical shift
", "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": "horizontal shift
", "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": "new transformed x values
", "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": "original x values
", "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": "\n
What was the maximum spend by a single company last year?
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "A random sample of 20 residents from Newcastle were asked about the number of times they went to see a play at the theatre last year.
\nHere is the list of their answers:
\n| $\\var{a[0]}$ | \n$\\var{a[1]}$ | \n$\\var{a[2]}$ | \n$\\var{a[3]}$ | \n$\\var{a[4]}$ | \n$\\var{a[5]}$ | \n$\\var{a[6]}$ | \n$\\var{a[7]}$ | \n$\\var{a[8]}$ | \n$\\var{a[9]}$ | \n
| $\\var{a[10]}$ | \n$\\var{a[11]}$ | \n$\\var{a[12]}$ | \n$\\var{a[13]}$ | \n$\\var{a[14]}$ | \n$\\var{a[15]}$ | \n$\\var{a[16]}$ | \n$\\var{a[17]}$ | \n$\\var{a[18]}$ | \n$\\var{a[19]}$ | \n
Range is the difference between the highest and the lowest value in the data.
\nTo find this, we subtract the lowest value from the highest value:
\n\\[ \\var{max(a)} - \\var{min(a)} = \\var{range} \\text{.}\\]
\n\nUse this link to find some resources which will help you revise this topic.
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", "advice": "The MEAN is the sum, divided by the number of values summed i.e.
$\\frac{\\var{list[0]} + \\var{list[1]} + \\var{list[2]} + \\var{list[3]} + \\var{list[4]}}{5}$
use your calculator to find
\nmean = $\\var{mean}$.
\n\nUse this link to find some resources which will help you revise this topic.
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{list}
Calculate the mean: [[0]]
Thank you for completing the Skills Audit for Maths and Stats. Hopefully it has been useful in directing you to resources and services that can support your studies. The Skills Audit for Maths and Stats will remain open to you throughout the academic year and you can always revisit it again later.
\nFor any further information or questions please contact mash@sheffield.ac.uk
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