Calculating gradient and finding intercept from a geogebra graph.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "{app}
Find the gradient of the line.
Firstly draw a right angled 'step' from left to right. This triangle can be anywhere, but it is more helpful for it to have corners on the vertices (whole number points) of the graph and it is easier to calculate with postive numbers.
\n{app_advice}
\nBefore we start to calculate, notice that the line is {uod}, so the gradient will be {pon} and the line is {sos}, so the absolute value of the number will be {mol}.
Now find the coordinates of the places your triangle meets the line
$(x_1,y_1)=(\\var{ax},\\var{ay})$ and $(x_2,y_2)=(\\var{bx},\\var{by})$
\nWe need to compare the 'rise on the y-axis' to the 'run across the x-axis', we can say that:
\n$\\text{gradient} = \\frac{\\text{rise}}{\\text{run}}$
\nThis is equivalent to using the formula:
$ m = \\frac{y_2 - y_1}{x_2 - x_1} $
and substitute the coordinates of the vertices of the triangle:
$\\begin{split} &\\, m = \\frac{\\var{by} - \\var{ay}}{\\var{bx} - \\var{ax}} \\\\
&\\, = \\frac{\\var{by-ay}}{\\var{bx-ax}} \\\\
&\\, = \\var[fractionNumbers]{m} \\\\
\\end{split} $
if(m=abs(m),'positive','negative')
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$\\var[fractionNumbers]{m}$
Multiple choice - select the quadratic graph.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Which of the following is the graph $y=x^2$.
", "advice": "Use this link to find some resources to help you familiarise yourself with these graphs.
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", "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]]
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "\nTo solve an equation like
\n$\\displaystyle{\\frac{x+\\var{num1}}{\\var{num2}}+\\frac{x}{\\var{num3}}=\\var{num4}},$
\nthe first thing to deal with is the denominators of the fractions. In order to do that you multiply both sides of the equation by both denominators $\\var{num2}$ and $\\var{num3}$ (or their lowest common multiple to be slightly more efficient). This will give something equivalent to:
\n$\\displaystyle{\\var{num3 + num2} x+\\var{num3*num1} = \\var{num2*num3*num4}.}$
\nThen proceeding by subtracting $\\var{num3*num1} from both sides:
\n$\\displaystyle{\\var{num3 + num2} x = \\var{num2*num3*num4-num3*num1}.}$
\nAnd finally dividing by $\\var{num2+num3}$:
\n$\\displaystyle{x = \\frac{\\var{num2*num3*num4-num3*num1}}{\\var{num2+num3}}.}$
\n
Use this link to find resources to help you revise how to solve linear equations
Solve $\\displaystyle{\\frac{x+\\var{num1}}{\\var{num2}}+\\frac{x}{\\var{num3}}=\\var{num4}}$.
\n$x=$ [[0]]
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Calculate the derivative of $y=\\simplify{{a}x^{b}}$.
\n", "advice": "From the Table of Derivatives we see that a function of the form \\[ f(x)=kx^n \\] has a derivative \\[ \\frac{df}{dx} = knx^{n-1}. \\]
\nSo, for the function \\[ y=\\simplify{{a}x^{b}}, \\] the derivative is \\begin{split}\\frac{dy}{dx} &= (\\var{a}\\times\\var{b})x^{\\var{b}-1},\\\\ \\\\&= \\simplify{{a*b}x^{{b}-1}}.\\end{split}
\n\n
Use this link to find some resources which will help you revise this topic.
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", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Gap 0", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a*b}x^{{b}-1}", "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": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NA01 Money Calculation - Make Change", "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": "Calculate the change from a note given two costs.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "You buy a sandwich for {PriceS} and a drink for {PriceD}.
\nYou pay with a £5 bank note, what is the correct change in pounds?
", "advice": "| \n \n \nTo find the total cost of the sandwich and drink, add them together: \n{PriceS} $+$ {PriceD} $=$ {Sumtext} \nIf you pay with a £5 banknote, your change will be £5 minus the sum of the sandwich and drink: \n£5.00 $-$ {Sumtext} = {answertext} \n\nUse this link to find some resources which will help you revise this topic. \n | \n
£[[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": "5-PS-PD", "maxValue": "5-PS-PD", "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": "NA02 Dosage calculation 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": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "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
", "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": "d/t", "maxValue": "d/t", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "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": "NA04 Inequalities (understanding notation)", "extensions": ["chemistry", "geogebra", "jsxgraph", "codewords", "permutations", "polynomials", "quantities", "random_person", "stats", "visjs"], "custom_part_types": [{"source": {"pk": 28, "author": {"name": "Marie Nicholson", "pk": 1799}, "edit_page": "/part_type/28/edit"}, "name": "True/False", "short_name": "true-false", "description": "The answer is either 'True' or 'False'
", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["True", "False"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n correct(),\n incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=correct_answer,\n correct(),\n incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"True\"", "help_url": "", "hint": "", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "Identify the truth value of an inequality (T/F) between two numbers
", "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": "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
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", "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]]
\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": "precround(c1, 1)", "maxValue": "precround(c1, 1)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(c1, 2)", "maxValue": "precround(c1, 2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(c1, dp)", "maxValue": "precround(c1, dp)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "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.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"discount": {"name": "discount", "group": "Ungrouped variables", "definition": "percentage*price/100", "description": "", "templateType": "anything", "can_override": false}, "pname": {"name": "pname", "group": "Ungrouped variables", "definition": "random(\"Adair\",\"Aya\",\"Bergen\",\"Dua\",\"Fadhili\",\"Harper\",\"Kaden\",\"Ola\",\"Pat\",\"Skylar\",\"Wren\",\"Zendaya\")", "description": "Names.
", "templateType": "anything", "can_override": false}, "discountrounded": {"name": "discountrounded", "group": "Ungrouped variables", "definition": "precround(discount,2)", "description": "", "templateType": "anything", "can_override": false}, "price": {"name": "price", "group": "Ungrouped variables", "definition": "switch(\n item = \"TV\", random(170.99..1199.99), \n item = \"laptop\", random(200.99..799.99),\n item = \"smartphone\", random(100.99..799.99),\n item = \"PC\", random(200.99..969.99),\n item = \"gaming console\", random(80.99..349.99),\n random(110.99..649.99))\n", "description": "Price of an item.
", "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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", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NF06 Percentage increase", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "Calculate the percentage increase (as a percentage) given a number and the size of the increase.
", "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": "NF07 Percentage change (decrease then increase)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "Compound percentage change.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "The value of a car is initially {StartingPrice}. If the value decreases by {dec}%, and then increases by {inc}%, what is the final value?
\nGive your answer correct to two decimal places.
", "advice": "There is a {dec}% decrease in price. This means that price after the decrease will be {100-dec}% of the old price.
\n\\[\\frac{\\var{100-dec}}{100} \\times \\var{StartingPrice} = \\var{(100-dec)/100*StartingPrice}\\]
\nThen there is a {inc}% increase in price. This means the final price will be {100+inc}% of the price after the decrease.
\n\\[\\frac{\\var{100+inc}}{100} \\times \\var{(100-dec)/100*StartingPrice} = £\\var{dpformat((100+inc)/100*(100-dec)/100*StartingPrice,2)}\\]
\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": {"dec": {"name": "dec", "group": "Ungrouped variables", "definition": "random(1..50)", "description": "", "templateType": "anything", "can_override": false}, "inc": {"name": "inc", "group": "Ungrouped variables", "definition": "random(1..50)", "description": "", "templateType": "anything", "can_override": false}, "FinalPrice": {"name": "FinalPrice", "group": "Ungrouped variables", "definition": "StartingPrice*(1-dec/100)*(1+inc/100)", "description": "", "templateType": "anything", "can_override": false}, "StartingPrice": {"name": "StartingPrice", "group": "Ungrouped variables", "definition": "random(600..8000 # 10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["dec", "inc", "FinalPrice", "StartingPrice"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n£[[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": "FinalPrice", "maxValue": "FinalPrice", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "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": "NF11 One number as a percentage of another", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "Given the number of international students enrolled on a course of $n$ students, calculate the percentage of 'home' students.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "\n\n\n\n{num_students} of the {class_size} students enrolled on a course are international students. What percentage are 'home' students?
", "advice": "First work out the number of students who are not international. In this case it is {class_size} - {num_students} = {class_size-num_students} students.
\nThen write this as a fraction out of {class_size}. $ \\frac{\\var{class_size-num_students}} {\\var{class_size}} $
\nThen convert this to a percentage. You should put this fraction into your calculator and then multiply by 100:
\n$ \\frac{\\var{class_size-num_students}} {\\var{class_size}} \\times 100 = \\var{(class_size-num_students)/class_size*100}\\%$
\nUse this link to find resources to help you revise how to calculate percentages.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"num_students": {"name": "num_students", "group": "Ungrouped variables", "definition": "per*class_size/100\n", "description": "The number of students in the class who do speak a language other than English.
", "templateType": "anything", "can_override": false}, "class_size": {"name": "class_size", "group": "Ungrouped variables", "definition": "random(80..300)", "description": "", "templateType": "anything", "can_override": false}, "per": {"name": "per", "group": "Ungrouped variables", "definition": "random(5..90 except 50)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "num_students = precround(num_students,0) AND (num_students<>class_size/2 AND class_size<>100)", "maxRuns": 100}, "ungrouped_variables": ["num_students", "class_size", "per"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\var{class_size-num_students}\\%$", "$\\var{num_students*100/class_size}\\%$", "$\\var{num_students}\\%$", "$\\var{(class_size-num_students)/class_size*100}\\%$"], "matrix": [0, 0, 0, "1"], "distractors": ["Have you converted this to a percentage? Click on Reveal Answer and scroll down for Advice regarding this question.", "How many students do NOT speak a language other than English at home? Click on Reveal Answer and scroll down for Advice regarding this question.", "How many students do NOT speak a language other than English at home? Then convert this to a percentage. Click on Reveal Answer and scroll down for Advice regarding this question.", "Well done!"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "NU01 Convert Currency", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": [], "metadata": {"description": "Exchange rates.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "On a particular day, 1 Pound Sterling (£) is equivalent to {exchanget} United States Dollars (\\$). If you have \\$ {amount}, what does this equate to in Pound Sterling?
", "advice": "To convert Dollars (\\$) into Pounds (£) you will need to caculate:
\n\\begin{align}
\\frac{\\var{amount}}{\\var{exchange}} &= \\var{answer}\\\\
&= \\var{answert},
\\end{align}
ensuring to round off to the nearest penny.
\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": {"exchange": {"name": "exchange", "group": "Ungrouped variables", "definition": "random(0.9 .. 1.2#0.01)", "description": "Pound to dollar exchange rate.
", "templateType": "randrange", "can_override": false}, "amount": {"name": "amount", "group": "Ungrouped variables", "definition": "random(100 .. 1000#5)", "description": "Amount of dollars.
", "templateType": "randrange", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "amount/exchange", "description": "", "templateType": "anything", "can_override": false}, "answert": {"name": "answert", "group": "Ungrouped variables", "definition": "currency(answer,\"\u00a3\",\"p\")", "description": "", "templateType": "anything", "can_override": false}, "exchanget": {"name": "exchanget", "group": "Ungrouped variables", "definition": "dpformat(exchange,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["exchange", "amount", "answer", "answert", "exchanget"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "[[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": "answer", "maxValue": "answer", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "answert", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "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": "SD02 Interpret Pie Charts", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}], "tags": [], "metadata": {"description": "This question is about correctly interpreting pie charts.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "{geogebra_applet{\"https://www.geogebra.org/calculator/pmvumdrv\",[C: C,M: M]}}
\nThe Pie Chart above shows the responses to a question asked by someone trying to plan a social event for their workplace. It shows answers given to the question \"Where would you like to go for a staff social?\" with the options \"Meal\", \"Cinema\" and \"Games Cafe\".
", "advice": "A Pie chart of this type can only be used to make statements about the proportions of data in each category and does not provide information about the actual frequencies.
\nFor more information on Pie Charts follow this link.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"C": {"name": "C", "group": "Ungrouped variables", "definition": "random(60 .. 70#5)", "description": "", "templateType": "randrange", "can_override": false}, "M": {"name": "M", "group": "Ungrouped variables", "definition": "random(5 .. 25#5)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "C<>M", "maxRuns": 100}, "ungrouped_variables": ["C", "M"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "From the following comments which can you say are definitely true, definitely false and which do you not have enough information to know?
", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": true, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["50 people responded that they would like to go to the cinema.", "About one third of people said they wanted to go for a meal.", "Over half the people responding said they wanted to go to the Games Cafe."], "matrix": [[0, 0, "1"], [0, "1", 0], ["1", 0, 0]], "layout": {"type": "all", "expression": ""}, "answers": ["Definitely true.", "Definitely false.", "Not enough information to know."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SD03 Interpret Bar Chart", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Lauren Desoysa", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21504/"}], "tags": [], "metadata": {"description": "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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\nShe began at 9 am and finished at 7 pm.
\nThe line graph below shows her results.
\n{geogebra_applet{\"https://www.geogebra.org/classic/s4w7nmga\",[y1:y1,y3:y3,y4:y4,y6:y6]}}
", "advice": "a) You want to find the point on the graph with the greatest frequency. You can see that this is at 1pm when there were $\\var{y3}$ cars in the car park.
\nb) We find 11am on the $x$-axis and look vertically upwards until we find the point. From here we go horiztonally across to the $y$-axis to read the frequency. We can see that at 11am there were $\\var{y2}$ cars in the car park.
\nc) We want to find $\\var{number}$ on the $y$-axis and then look horiztonally across until we find the point. From here we move down to the $x$-axis to see at which time there were $\\var{number}$ cars in the car park. We can see this occured at $\\var{answerc}\\var{time}$.
\nd) We must find 6pm on the $x$-axis. This isn't marked on like the other times but we know it sits half way between 5pm and 7pm. From here we look vertically upwards until we meet the red line on our graph. Notice we don't have a point for this time, hence why this is an estimate. From here we move hortizontally across to the $y$-axis to find the frequency. At 6pm we estimate that there were $\\var{y56}$ cars in the car park.
\ne) We must find the frequency of cars at 1pm and at 3pm using the same steps as in part b. At 3pm there were $\\var{y4}$ cars in the car park and we subtract this from $\\var{y3}$ which is the number of cars in the car park at 1pm. Hence, $\\var{y3}-\\var{y4}=\\var{y3-y4}$.
\n", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"y6": {"name": "y6", "group": "Ungrouped variables", "definition": "random(10 .. 40#10)", "description": "Number of customers in supermarket at 7pm.
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", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["9 am", "11 am", "1 pm", "3 pm", "5 pm", "7 pm"], "matrix": [0, 0, "1", 0, 0, 0], "distractors": ["", "", "", "", "", ""]}, {"type": "numberentry", "useCustomName": true, "customName": "b)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "How many customers were in the supermarket at 11 am?
", "minValue": "y2", "maxValue": "y2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "c)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "At what time were there {number} customers in the supermarket?
\nIf your answer was 12pm you would just write 12 in the box.
", "minValue": "answerc", "maxValue": "answerc", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "d)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Estimate the number of customers in the supermarket at 6pm.
", "minValue": "y56", "maxValue": "y56", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "e)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "How many less customers were there in the supermarket at 3pm than 1pm?
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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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", "licence": "None specified"}, "statement": "Calculate the Mean from a list
", "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]]
This question provides a list of data to the student. They are asked to find the \"mode\".
", "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
The mode is the value that occurs the most often in the data.
\nTo find a mode, we can look at our sorted list:
\n$\\var{a_s[0]}, \\var{a_s[1]}, \\var{a_s[2]}, \\var{a_s[3]}, \\var{a_s[4]}, \\var{a_s[5]}, \\var{a_s[6]}, \\var{a_s[7]}, \\var{a_s[8]}, \\var{a_s[9]}, \\var{a_s[10]}, \\var{a_s[11]}, \\var{a_s[12]}, \\var{a_s[13]}, \\var{a_s[14]}, \\var{a_s[15]}, \\var{a_s[16]}, \\var{a_s[17]}, \\var{a_s[18]}, \\var{a_s[19]}$.
\nWe notice that $\\var{mode1}$ occurs the most ($\\var{modetimes[mode1]}$ times) so $\\var{mode1}$ is the mode.
\nUse this link to find some resources which will help you revise this topic.
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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
The median is the middle value. We need to sort the list in order:
\n\\[ \\var{a_s[0]}, \\quad \\var{a_s[1]}, \\quad \\var{a_s[2]}, \\quad \\var{a_s[3]}, \\quad \\var{a_s[4]}, \\quad \\var{a_s[5]}, \\quad \\var{a_s[6]}, \\quad \\var{a_s[7]}, \\quad \\var{a_s[8]}, \\quad \\var{a_s[9]}, \\quad \\var{a_s[10]}, \\quad \\var{a_s[11]}, \\quad \\var{a_s[12]}, \\quad \\var{a_s[13]}, \\quad \\var{a_s[14]}, \\quad \\var{a_s[15]}, \\quad \\var{a_s[16]}, \\quad \\var{a_s[17]}, \\quad \\var{a_s[18]}, \\quad \\var{a_s[19]} \\]
\nThere is an even number of responses, so there are two numbers in the middle (10th and 11th place). To find the median, we need to find the mean of these two numbers $\\var{a_s[9]}$ and $\\var{a_s[10]}$:
\n\\begin{align}
\\frac{\\var{a_s[9]} + \\var{a_s[10]}}{2} &= \\frac{\\var{a_s[9] + a_s[10]}}{2} \\\\
&= \\var{median} \\text{.}
\\end{align}
\n
Use this link to find some resources which will help you revise this topic.
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Here is a list of 20 random numbers:
\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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", "minValue": "range", "maxValue": "range", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SM09 Range and Interquartile Range", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Here are the ages of 7 people:
\n{a1}, {a2}, {a3}, {a4}, {a5}, {a6}, {a7}.
", "advice": "First we should order our list of ages from smallest to largest:
\n$\\var{list[0]}, \\var{list[1]}, \\var{list[2]}, \\var{list[3]}, \\var{list[4]}, \\var{list[5]}, \\var{list[6]}$.
\na)
\nTo find the range of ages we must subtract the smallest age from the largest age,
\n$\\var{max(list)} - \\var{min(list)} = \\var{range}$.
\nHence, the range is $\\var{range}$.
\nb)
\nTo calculate the interquartile range we subtract the lower quartile from the upper quartile.
\nTo calculate the lower quartile:
\nSince we have an odd number of ages we had one to the total and divide by 4,
\n$\\frac{7+1}{4} = \\frac{8}{4} = 2.$
\nSo we are looking for the $2^{nd}$ value in our list which is $\\var{lq}$.
\nHence the lower quartile is $\\var{lq}$.
\nTo find the upper quartile:
\nWe still add one to the number of ages because this number is odd and then we find $75$% of it,
\n$\\frac{3\\times(7+1)}{4} = \\frac{3\\times8}{4} = \\frac{24}{4} = 6.$
\nSo we are looking for the $6^{th}$ value in our list which is $\\var{uq}$.
\nHence the lower quartile is $\\var{uq}$.
\nNow we can calculate the interquartile range by subtracting the lower quartile from the upper quartile,
\n$\\var{uq}-\\var{lq} = \\var{iqr}.$
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "The scatter plot below shows the relationship between an employee’s height in centimetres and how long it takes them to walk to work in minutes.
\n| time (mins) | \n{drawgraph()} | \n
| \n | height (cm) | \n
The graph shows that there is a positive correlation between a person's height and how long it takes them to walk to work.
\nA postive correlation is a relationship between two variables where both variables move in the same diection.
\nThis tells us that as a person's height increases, the time it takes to walk to work increases.
\nUse this link to find some resources which will help you revise this topic
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\nFor any further information or questions please contact mash@sheffield.ac.uk
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