![\"Parallelogram\"](\"https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif\")
You have 5 minutes left, please check you have completed all sections
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", "action": "warn"}}, "question_groups": [{"pickingStrategy": "all-ordered", "name": "Group", "pickQuestions": 1, "questions": [{"name": "john's copy of Calculate the areas of polygons", "extensions": [], "custom_part_types": [], "resources": [["question-resources/trapezium.svg", "/srv/numbas/media/question-resources/trapezium.svg"], ["question-resources/trangle.svg", "/srv/numbas/media/question-resources/trangle.svg"], ["question-resources/parallelogram.svg", "/srv/numbas/media/question-resources/parallelogram.svg"], ["question-resources/Parallelogram_area_animated.gif", "/srv/numbas/media/question-resources/Parallelogram_area_animated.gif"], ["question-resources/rectangle_zISmvoz.svg", "/srv/numbas/media/question-resources/rectangle_zISmvoz.svg"], ["question-resources/hardertrapezium_8GqMwOo.svg", "/srv/numbas/media/question-resources/hardertrapezium_8GqMwOo.svg"], ["question-resources/Trap_advice.svg", "/srv/numbas/media/question-resources/Trap_advice.svg"], ["question-resources/Triangle_advice_lD6eKvD.svg", "/srv/numbas/media/question-resources/Triangle_advice_lD6eKvD.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "john halder", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1736/"}], "preamble": {"js": "", "css": ""}, "functions": {}, "ungrouped_variables": [], "statement": "Calculate the area of the following shapes.
", "variables": {"h5": {"description": "Height of the trapezium.
", "definition": "random(2..5#0.1)", "templateType": "anything", "group": "'Harder' trapezium", "name": "h5"}, "w5a": {"description": "The top parallel side in the trapezium.
", "definition": "random(5..6.5#0.1)", "templateType": "anything", "group": "'Harder' trapezium", "name": "w5a"}, "wh11": {"description": "The product of the two terms, w1 and h1, such that a condition can be satisfied.
", "definition": "precround(w1*h1,3)", "templateType": "anything", "group": "Parallelogram", "name": "wh11"}, "wh11dp": {"description": "The product of the two terms, w1 and h1, to one decimal place such that a condition can be satisfied.
", "definition": "precround(w1*h1, 1)", "templateType": "anything", "group": "Parallelogram", "name": "wh11dp"}, "wabh5dp": {"description": "The Area of a trapezium using the three terms, w5a, w5b and h5 to one decimal place, such that a condition can be satisfied.
", "definition": "precround((w5a+w5b)*(h5)/2, 1)", "templateType": "anything", "group": "'Harder' trapezium", "name": "wabh5dp"}, "wh00": {"description": "The product of the two terms, w0 and h0, such that a condition can be satisfied.
", "definition": "precround(w0*h0,3)", "templateType": "anything", "group": "Rectangle", "name": "wh00"}, "h2": {"description": "Height of the triangle.
", "definition": "random(1..4.5#0.1)", "templateType": "anything", "group": "Triangle", "name": "h2"}, "h1": {"description": "The height of the parallelogram
", "definition": "random(1..4.5#0.1)", "templateType": "anything", "group": "Parallelogram", "name": "h1"}, "wabh5": {"description": "The Area of a trapezium using the three terms, w5a, w5b and h5, such that a condition can be satisfied.
", "definition": "precround((w5a+w5b)*(h5)/2, 5)", "templateType": "anything", "group": "'Harder' trapezium", "name": "wabh5"}, "wh22": {"description": "The Area of a triangle using the two terms, w2 and h2, such that a condition can be satisfied.
", "definition": "precround(0.5*w2*h2,4)", "templateType": "anything", "group": "Triangle", "name": "wh22"}, "w0": {"description": "Width of the rectangle.
", "definition": "random(5..10#0.1)", "templateType": "anything", "group": "Rectangle", "name": "w0"}, "w1": {"description": "The width of the parallelogram.
", "definition": "random(5..10#0.1)", "templateType": "anything", "group": "Parallelogram", "name": "w1"}, "w2": {"description": "Base of the triangle.
", "definition": "random(5..10#0.1)", "templateType": "anything", "group": "Triangle", "name": "w2"}, "wh00dp": {"description": "The product of the two terms, w0 and h0, to one decimal place, such that a condition can be satisfied.
", "definition": "precround(w0*h0,1)", "templateType": "anything", "group": "Rectangle", "name": "wh00dp"}, "wh22dp": {"description": "The Area of a triangle using the two terms, w2 and h2 to one decimal place, such that a condition can be satisfied.
", "definition": "precround(0.5*w2*h2, 1)", "templateType": "anything", "group": "Triangle", "name": "wh22dp"}, "h0": {"description": "Height of the rectangle.
", "definition": "random(1..5#0.1)", "templateType": "anything", "group": "Rectangle", "name": "h0"}, "w5b": {"description": "The bottom parallel side in the trapezium.
", "definition": "random(7.5..10#0.1)", "templateType": "anything", "group": "'Harder' trapezium", "name": "w5b"}}, "advice": "a)
\nThe area of a rectangle is calculated using the formula
\n\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}\\text{.}\\]
\nWe have a base of $\\var{w0}$m and a height $\\var{h0}$m, therefore
\n\\begin{align}
\\mathrm{Area} &= \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\var{w0} \\times \\var{h0} \\\\ &= \\var{w0*h0} \\\\
&= \\var{dpformat(w0*h0,1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}
\\begin{align}
\\mathrm{Area} &= \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\var{w0} \\times \\var{h0} \\\\
&= \\var{dpformat(w0*h0,1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}
b)
\nThe parallelogram is just a slanted rectangle:
\n\n
Therefore, the area of a parallelogram is calculated using the formula
\n\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}.\\]
\nWe have a base $\\var{w1}$m and perpendicular height $\\var{h1}$m.
\n\\begin{align}
\\mathrm{Area} &= \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\var{w1} \\times \\var{h1} \\\\ &= \\var{{w1}{h1}}\\, \\mathrm{m}^2 \\\\
&= \\var{dpformat({w1}{h1},1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}
\\begin{align}
\\mathrm{Area} &= \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\var{w1} \\times \\var{h1} \\\\
&= \\var{dpformat({w1}{h1},1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}
The area of a triangle is calculated using the formula
\n\\[\\mathrm{Area} = \\frac{\\mathrm{base} \\times \\mathrm{height}}{2}.\\]
\nNote that the triangle is half of a rectangle:
\n\nOur triangle has a base $\\var{w2}$m and a height $\\var{h2}$m, therefore
\n\\begin{align} \\mathrm{Area} &= \\frac{1}{2} \\times \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\frac{1}{2} \\times \\var{w2} \\times \\var{h2} \\\\
&= \\var{0.5*w2*h2}\\, \\mathrm{m}^2 \\\\
&= \\var{dpformat(0.5*w2*h2, 1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}
\\begin{align} \\mathrm{Area} &= \\frac{1}{2} \\times \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\frac{1}{2} \\times \\var{w2} \\times \\var{h2} \\\\
&= \\var{dpformat(0.5*w2*h2, 1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.} \\\\
\\end{align}
d)
\n\nA trapezium can be interpreted as half of a parallelogram, this is shown below:
\n\nAs we only want the area of one half of this shape, the area is half of
\n\\[\\mathrm{area} = (a+b) \\times \\mathrm{height}\\text{,}\\]
\nwith ${a} = \\var{w5a}$m, ${b} = \\var{w5b}$m, and height $\\var{h5}$m.
\n\\begin{align}
\\mathrm{Area} &= \\frac{(a+b)}{2} \\times \\mathrm{height} \\\\
&= \\frac{(\\var{w5a}+\\var{w5b})}{2} \\times \\var{h5} \\\\
&= \\var{(w5a+w5b)*0.5} \\times \\var{h5} \\\\
&= \\var{(w5a+w5b)*(h5)/2}\\, \\mathrm{m}^2 \\\\
&= \\var{dpformat((w5a+w5b)*(h5)/2, 1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.}
\\end{align}
\\begin{align}
\\mathrm{Area} &= \\frac{(a+b)}{2} \\times \\mathrm{height} \\\\
&= \\frac{(\\var{w5a}+\\var{w5b})}{2} \\times \\var{h5} \\\\
&= \\var{(w5a+w5b)*0.5} \\times \\var{h5} \\\\
&= \\var{dpformat((w5a+w5b)*(h5)/2, 1)}\\, \\mathrm{m}^2 \\quad \\text{to 1 d.p.}
\\end{align}
This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.
\nThe shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.
\nAuthor of gif: Picknick
https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
The area of the rectangle is [[0]] $\\mathrm{m^2}$. Round your answer to 1 decimal place.
", "marks": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "stepsPenalty": "1", "steps": [{"marks": 0, "type": "information", "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "The formula for the area of a rectangle is:
\n\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}.\\]
", "variableReplacements": []}], "variableReplacements": []}, {"gaps": [{"maxValue": "{h1}*{w1} + 0.01", "precisionType": "dp", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{h1}*{w1} - 0.01", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "precision": "1", "precisionMessage": "You have not given your answer to the correct precision.", "marks": "2", "correctAnswerFraction": false, "type": "numberentry", "precisionPartialCredit": 0, "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "strictPrecision": false, "showCorrectAnswer": true}], "type": "gapfill", "prompt": "\nThe area of the parallelogram is [[0]] $\\mathrm{m^2}$. Round your answer to 1 decimal place.
", "marks": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "stepsPenalty": "1", "steps": [{"marks": 0, "type": "information", "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "The formula for the area of a parallelogram is:
\n\\[\\mathrm{Area} = \\mathrm{base} \\times \\mathrm{height}.\\]
", "variableReplacements": []}], "variableReplacements": []}, {"gaps": [{"maxValue": "{w2}{h2}*0.5 + 0.01", "precisionType": "dp", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{w2}{h2}*0.5 - 0.01", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "precision": "1", "precisionMessage": "You have not given your answer to the correct precision.", "marks": "2", "correctAnswerFraction": false, "type": "numberentry", "precisionPartialCredit": 0, "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "strictPrecision": false, "showCorrectAnswer": true}], "type": "gapfill", "prompt": "\nThe area of the triangle is [[0]] $\\mathrm{m^2}$ Round your answer to 1 decimal place.
", "marks": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "stepsPenalty": "1", "steps": [{"marks": 0, "type": "information", "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "The formula for the area of a triangle is:
\n\\[\\mathrm{Area} = \\frac{\\mathrm{base} \\times \\mathrm{height}}{2}.\\]
", "variableReplacements": []}], "variableReplacements": []}, {"gaps": [{"maxValue": "0.5{w5a+w5b}{h5} + 0.01", "precisionType": "dp", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "0.5{w5a+w5b}{h5} - 0.01", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "precision": "1", "precisionMessage": "You have not given your answer to the correct precision.", "marks": "2", "correctAnswerFraction": false, "type": "numberentry", "precisionPartialCredit": 0, "scripts": {}, "showPrecisionHint": false, "variableReplacements": [], "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "strictPrecision": false, "showCorrectAnswer": true}], "type": "gapfill", "prompt": "\nThe area of the trapezium is [[0]] $\\mathrm{m^2}$. Round your answer to 1 decimal place.
", "marks": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "stepsPenalty": "1", "steps": [{"marks": 0, "type": "information", "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "The formula for the area of a trapezium is:
\n\\[\\mathrm{Area} = \\frac{(a+b)}{2}\\times \\mathrm{height}.\\]
", "variableReplacements": []}], "variableReplacements": []}], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question"}, {"name": "Converting units of length (km/m/miles)", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}], "variable_groups": [], "variables": {"miles": {"templateType": "anything", "definition": "km*km_to_miles", "description": "", "name": "miles", "group": "Ungrouped variables"}, "location": {"templateType": "anything", "definition": "random('Boston', 'Edinburgh', 'Great Welsh', 'London')", "description": "", "name": "location", "group": "Ungrouped variables"}, "km_to_miles": {"templateType": "anything", "definition": "0.62", "description": "conversion rate km to miles
", "name": "km_to_miles", "group": "Ungrouped variables"}, "person": {"templateType": "anything", "definition": "random_person()", "description": "", "name": "person", "group": "Ungrouped variables"}, "km": {"templateType": "anything", "definition": "random(24..28#2)", "description": "", "name": "km", "group": "Ungrouped variables"}}, "type": "question", "parts": [{"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "variableReplacements": [], "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "scripts": {}, "minValue": "km*1000", "maxValue": "km*1000", "marks": 1, "variableReplacements": []}], "prompt": "The week before the event, {person['name']} goes on a final training run. An app on {person['pronouns']['their']} phone tells {person['pronouns']['them']} that {person['pronouns']['they']} ran $\\var{km}$ km.
\nWhat was the length of {person['pronouns']['their']} training run in metres?
\n[[0]] metres.
\n\n"}, {"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "variableReplacements": [], "gaps": [{"correctAnswerFraction": false, "precisionType": "dp", "type": "numberentry", "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "showCorrectAnswer": true, "precisionPartialCredit": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "scripts": {}, "strictPrecision": false, "maxValue": "miles+0.5", "precision": 0, "marks": 1, "mustBeReduced": false, "variableReplacements": [], "minValue": "miles-0.5", "mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to the correct precision."}], "prompt": "
Use the approximate conversion, $1$ kilometre = $0.62$ miles, to find the length of {person['pronouns']['their']} training run in miles.
\n[[0]] miles. Round your answer to the nearest mile.
"}, {"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "variableReplacements": [], "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "scripts": {}, "minValue": "42-0.5", "maxValue": "42+0.5", "marks": 1, "variableReplacements": []}], "prompt": "{person['name']} knows that the {location} Marathon is 26 miles. Use the conversion rate in part b) to find the approximate length in km.
\n[[0]] km round your answer to the nearest km
"}], "advice": "{person['name']}'s training run is $\\var{km}$ km long.
\nTo convert $\\var{km}$ km into metres, we multiply $\\var{km}$ by $1000$.
\n\\[\\var{km}\\times1000= \\var{km*1000}\\text{ metres.}\\]
\n\nTo convert $\\var{km}$ km into miles, we multiply $\\var{km}$ by the conversion rate given: $0.62$.
\n\\[\\begin{align}
\\var{km}\\times\\frac{5}{8}&= \\var{miles}\\\\
&=\\var{dpformat(miles,0)}\\text{ miles, rounded to the nearest integer.}
\\end{align}\\]
The {location} Marathon is $26$ miles long. To convert to km we multiply by the inverse of the conversion rate given in part b):
\n\\[ 26 \\times \\frac{1}{0.62} = 42\\text{ miles, rounded to the nearest integer.} \\]
\n", "tags": ["taxonomy"], "preamble": {"js": "", "css": ""}, "rulesets": {}, "functions": {}, "ungrouped_variables": ["km_to_miles", "km", "miles", "person", "location"], "statement": "
{person['name']} is training for the {location} Marathon.
", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Convert from km to metres and miles, and miles to km.
"}, "variablesTest": {"condition": "", "maxRuns": 100}}, {"name": "Fractions and Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Breanne Chryst", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1658/"}], "statement": "\nConvert the following fractions and percentages as directed.
\n", "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "functions": {}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "advice": "", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "This question will help you practice converting between fractions and percentages
"}, "parts": [{"variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "gapfill", "scripts": {}, "gaps": [{"strictPrecision": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "marks": 1, "allowFractions": false, "showPrecisionHint": true, "variableReplacements": [], "precisionType": "dp", "correctAnswerStyle": "plain", "precision": "2", "precisionPartialCredit": 0, "maxValue": "a/100", "mustBeReduced": false, "minValue": "a/100", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0}, {"strictPrecision": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "marks": 1, "allowFractions": false, "showPrecisionHint": true, "variableReplacements": [], "precisionType": "dp", "correctAnswerStyle": "plain", "precision": "2", "precisionPartialCredit": 0, "maxValue": "b/100", "mustBeReduced": false, "minValue": "b/100", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0}, {"strictPrecision": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "marks": 1, "allowFractions": false, "showPrecisionHint": true, "variableReplacements": [], "precisionType": "dp", "correctAnswerStyle": "plain", "precision": "2", "precisionPartialCredit": 0, "maxValue": "c/100", "mustBeReduced": false, "minValue": "c/100", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0}, {"strictPrecision": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "marks": 1, "allowFractions": false, "showPrecisionHint": true, "variableReplacements": [], "precisionType": "dp", "correctAnswerStyle": "plain", "precision": "2", "precisionPartialCredit": 0, "maxValue": "d/100", "mustBeReduced": false, "minValue": "d/100", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0}], "marks": 0, "prompt": "Insert a fraction that has the same value as the following percentages:
\n$\\var{a}$ % = [[0]]
\n$\\var{b}$ % = [[1]]
\n$\\var{c}$ % = [[2]]
\n$\\var{d}$ % = [[3]]
"}, {"variableReplacements": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "gapfill", "scripts": {}, "gaps": [{"strictPrecision": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "marks": 1, "allowFractions": false, "showPrecisionHint": true, "variableReplacements": [], "precisionType": "dp", "correctAnswerStyle": "plain", "precision": "2", "precisionPartialCredit": 0, "maxValue": "(f/g)*100", "mustBeReduced": false, "minValue": "(f/g)*100", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0}, {"strictPrecision": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "marks": 1, "allowFractions": false, "showPrecisionHint": true, "variableReplacements": [], "precisionType": "dp", "correctAnswerStyle": "plain", "precision": "2", "precisionPartialCredit": 0, "maxValue": "(h/j)*100", "mustBeReduced": false, "minValue": "(h/j)*100", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0}, {"strictPrecision": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "marks": 1, "allowFractions": false, "showPrecisionHint": true, "variableReplacements": [], "precisionType": "dp", "correctAnswerStyle": "plain", "precision": "2", "precisionPartialCredit": 0, "maxValue": "(k/l)*100", "mustBeReduced": false, "minValue": "(k/l)*100", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0}, {"strictPrecision": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "numberentry", "scripts": {}, "marks": 1, "allowFractions": false, "showPrecisionHint": true, "variableReplacements": [], "precisionType": "dp", "correctAnswerStyle": "plain", "precision": "2", "precisionPartialCredit": 0, "maxValue": "(m/n)*100", "mustBeReduced": false, "minValue": "(m/n)*100", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0}], "marks": 0, "prompt": "Insert the correct percentage for each of these fractions
\n$\\frac{\\var{f}}{\\var{g}}$ = [[0]]
\n$\\frac{\\var{h}}{\\var{j}}$ = [[1]]
\n$\\frac{\\var{k}}{\\var{l}}$ = [[2]]
\n$\\frac{\\var{m}}{\\var{n}}$ = [[3]]
"}], "variables": {"f": {"name": "f", "group": "Ungrouped variables", "definition": "random(1..g-1)", "templateType": "anything", "description": ""}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random([2,4,5,10,20,25,50,100])", "templateType": "anything", "description": ""}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(0..l-1#4 except 0)", "templateType": "anything", "description": ""}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(0..100#10 except [0,100])", "templateType": "anything", "description": ""}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(0..j-1#2 except 0)", "templateType": "anything", "description": ""}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(0..100 except [0,100])", "templateType": "anything", "description": ""}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(1..n)", "templateType": "anything", "description": ""}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random([3,6,9])", "templateType": "anything", "description": ""}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "random([4,5,10,20,25,40,50,100,200])", "templateType": "anything", "description": ""}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(0..100#5 except [0,100])", "templateType": "anything", "description": ""}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(1..200)", "templateType": "anything", "description": ""}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "random([8,16,20,40,80,100,200,400])", "templateType": "anything", "description": ""}}, "rulesets": {}, "type": "question"}, {"name": "Percentages and ratios - box of chocolates", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}], "type": "question", "statement": "A family receive a box of chocolates as a gift. There are five different kinds of chocolate inside: plain, nut, caramel, dark and coconut.
\nThe box contains equal numbers of each kind of chocolate..
", "advice": "100% represents the whole box of chocolates. As there are 5 different kinds of chocolate in the box and they are all represented equally, to calculate the percentage chocolates which are caramel, divide 100 by 5.
\nCaramel chocolate = $\\displaystyle\\frac{100}{5}$ = $20$% of the box.
\n\n\nb)
\nThe original number of chocolates in the box is stated. We worked out above that each type of chocolate makes up 20% of the box, so we need to work out 20% of {chocs}.
\nTo do this, either divide {chocs} by 100 and mulitply by 20, OR multiply {chocs} by 0.2. The two methods will give the same result.
\nMethod 1: $\\displaystyle\\frac{\\var{chocs}}{100}$ x $20$ = $\\var{type}$;
\nOR
\nMethod 2: $\\var{chocs}$ x $0.2$ = $\\var{type}$.
\n\n\nc)
\nThere are now {type} fewer chocolates in the box, but the remaining chocolates now represent 100% of the box. There are now only 4 types of chocolate in it and there is still equal representation inside the box.
\nUse the method from part a) to find out the equal share of each chocolate type.
\nEach type = $\\displaystyle\\frac{100}{4}$ = $25$% of the box.
\n\n\nd)
\ni)
\nThe first section asks you to compare plain chocolate and dark chocolate. It states that there are {p} plain chocolates and {d} dark chocolates left in the box.
\nInsert the numbers of each into the gaps.
\nPlain $\\var{p}$ : $\\var{d}$ Dark
\nFrom this, we should look to see if this answer can be simplified down. To do this, we need to find the greatest common divisor of $\\var{p}$ and $\\var{d}$.
\nThe greatest common divisor is $\\var{gcd}$.
\nUsing this value to simplify down the ratio by dividing each term by the value, the final answer is
\nPlain $\\var{ratio_plain}$ : $\\var{ratio_dark}$ Dark.
\nThis states that for every {ratio_plain} plain {if(ratio_plain=1,\"chocolate\",\"chocolates\")}, there {if(ratio_dark=1,\"is\",\"are\")} {ratio_dark} dark {if(ratio_dark=1,\"chocolate\",\"chocolates\")}.
\nTherefore, it is not possible to simplify further and the final answer is
\nPlain $\\var{p}$ : $\\var{d}$ Dark.
\nThis states that for every {p} plain {if(p=1,\"chocolate\",\"chocolates\")}, there {if(d=1,\"is\",\"are\")}{d} dark {if(d=1,\"chocolate\",\"chocolates\")}.
\n\nii)
\nThe second section asks you to compare coconut chocolates and the rest of the box. It states that there are {c} coconut chocolates. To calculate the number of chocolates in the rest of the box, add together the stated amounts of plain, dark and nutty chocolates:
\n$\\var{p}+\\var{d}+\\var{n}$ = $\\var{rob}$.
\nInsert these two figures into the gaps.
\nCoconut $\\var{c}$ : $\\var{rob}$ Other chocolates
\nFrom this, we should look to see if this answer can be simplified down. To do this, we need to find the greatest common divisor of $\\var{c}$ and $\\var{rob}$.
\nThe greatest common divisor is $\\var{gcd2}$.
\nUsing this value to simplify down the ratio by dividing each term by the value, the final answer is
\nCoconut $\\var{ratio_coconut}$ : $\\var{ratio_rest}$ Other chocolates.
\nThis states that for every {ratio_coconut} coconut {if(ratio_coconut=1,\"chocolate\",\"chocolates\")}, there {if(ratio_rest=1,\"is\",\"are\")} {ratio_rest} other {if(ratio_rest=1,\"chocolate\",\"chocolates\")} in the box.
\nTherefore, it is not possible to simplify further and the final answer is
\nCoconut $\\var{c}$ : $\\var{rob}$ Other chocolates.
\nThis states that for every {c} coconut {if(c=1,\"chocolate\",\"chocolates\")}, there {if(rob=1,\"is\",\"are\")} {rob} other {if(rob=1,\"chocolate\",\"chocolates\")} in the box.
", "variables": {"ratio_dark": {"templateType": "anything", "name": "ratio_dark", "definition": "d/gcd(p,d)", "description": "Number of dark chocolates in ratio of plain to dark.
", "group": "Ungrouped variables"}, "ratio_rest": {"templateType": "anything", "name": "ratio_rest", "definition": "rob/gcd(c, rob)", "description": "Number of 'rest of box' chocolates in ratio of coconut to rest of box.
", "group": "Ungrouped variables"}, "d": {"templateType": "anything", "name": "d", "definition": "random(1..3)*p", "description": "Number of dark chocolates on day 3.
", "group": "Ungrouped variables"}, "gcd2": {"templateType": "anything", "name": "gcd2", "definition": "gcd(c,rob)", "description": "", "group": "Ungrouped variables"}, "type": {"templateType": "anything", "name": "type", "definition": "chocs/5", "description": "Number of each type of chocolate in the box.
", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "name": "c", "definition": "random(1..14 except 7 except 11 except 13)", "description": "Number of coconut chocolates on day 3.
", "group": "Ungrouped variables"}, "chocs": {"templateType": "randrange", "name": "chocs", "definition": "random(70..95#5)", "description": "Total number of chocolates in the box before eating.
", "group": "Ungrouped variables"}, "rob": {"templateType": "anything", "name": "rob", "definition": "p+n+d", "description": "Sum of the rest of the box excluding coconut.
", "group": "Ungrouped variables"}, "p": {"templateType": "anything", "name": "p", "definition": "random(2..5)", "description": "Number of plain chocolates on day 3.
", "group": "Ungrouped variables"}, "ratio_plain": {"templateType": "anything", "name": "ratio_plain", "definition": "p/gcd(p,d)", "description": "Number of plain chocolates in ratio of plain to dark.
", "group": "Ungrouped variables"}, "prob": {"templateType": "anything", "name": "prob", "definition": "precround({n/{a},2)", "description": "Probability that a nutty chocolate is selected from the box on day 3.
", "group": "Ungrouped variables"}, "gcd": {"templateType": "anything", "name": "gcd", "definition": "gcd(p,d)", "description": "", "group": "Ungrouped variables"}, "n": {"templateType": "anything", "name": "n", "definition": "random(1..14 except 7 except 11 except 13)", "description": "Number of nutty chocolates on day 3.
", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "name": "a", "definition": "p+n+d+c", "description": "Number of chocolates in the box on day 3.
", "group": "Ungrouped variables"}, "perc": {"templateType": "anything", "name": "perc", "definition": "100*(prob)", "description": "Percentage version of probability.
", "group": "Ungrouped variables"}, "minusc": {"templateType": "anything", "name": "minusc", "definition": "{chocs-type}", "description": "Number of chocolates in the box minus caramel.
", "group": "Ungrouped variables"}, "ratio_coconut": {"templateType": "anything", "name": "ratio_coconut", "definition": "c/gcd(c, rob)", "description": "Number of coconut chocolates in ratio of coconut to rest of box.
", "group": "Ungrouped variables"}}, "functions": {}, "tags": ["percentages", "ratios", "Ratios", "taxonomy"], "variable_groups": [], "parts": [{"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "20", "showFeedbackIcon": true, "minValue": "20", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "What percentage of the box of chocolates is represented by the caramel chocolates?
\nCaramel chocolate = [[0]] % of the box.
", "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "type", "showFeedbackIcon": true, "minValue": "type", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "If there were $\\var{chocs}$ chocolates in the box originally, how many of each kind were there?
\nThere are [[0]] of each type of chocolate in the box.
\n", "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "25", "showFeedbackIcon": true, "minValue": "25", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "Caramel flavoured chocolate is the family favourite, and so all of these chocolates are eaten first, and none of the other kinds are touched.
\nWhat percentage of the remaining chocolates are plain?
\nPlain chocolates = [[0]]% of the box.
", "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ratio_plain", "showFeedbackIcon": true, "minValue": "ratio_plain", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ratio_dark", "showFeedbackIcon": true, "minValue": "ratio_dark", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ratio_coconut", "showFeedbackIcon": true, "minValue": "ratio_coconut", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ratio_rest", "showFeedbackIcon": true, "minValue": "ratio_rest", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "Over the next few days, the remaining chocolates in the box are slowly devoured so that by day three, all that remain are:
\n$\\var{p}$ plain chocolates, $\\var{n}$ nutty chocolates, $\\var{c}$ coconut chocolates and $\\var{d}$ dark chocolates.
\n\ni) What is the ratio of plain to dark chocolates? Give your answer in its simplest form.
\nPlain [[0]] : [[1]] Dark
\n\nii) What is the ratio of coconut chocolates to the rest of the box? Give your answer in its simplest form.
\nCoconut [[2]] : [[3]] Rest of the box
\n", "type": "gapfill"}], "ungrouped_variables": ["chocs", "type", "p", "n", "d", "c", "rob", "prob", "a", "perc", "minusc", "ratio_plain", "ratio_dark", "ratio_coconut", "ratio_rest", "gcd", "gcd2"], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "A simple situational question about a box of chocolates, asking how many of each type there are, what percentage of the box they represent, the probability of picking one and ratios of different types.
"}, "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "", "maxRuns": 100}}, {"name": "Rounding and estimating calculations - painting a room", "extensions": ["random_person"], "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/"}], "type": "question", "statement": "{person['name']} just bought a new house. {capitalise(pronouns['their'])} new bedroom's wall and ceiling are currently painted white, but {pronouns['they']} would like to paint these {colour}.
\nThe dimensions of the floor are $\\var{length}\\,\\mathrm{m} \\times \\var{width}\\,\\mathrm{m}$ and the room is $\\var{height}\\,\\mathrm{m}$ high.
\n{person['name']} want{verbs} to know how much paint to buy so {pronouns['they']} can paint all four walls and the ceiling {colour}.
", "variablesTest": {"condition": "mod(rall,15)<>0", "maxRuns": 100}, "variables": {"buckets": {"description": "", "name": "buckets", "group": "Calculations", "templateType": "anything", "definition": "ceil(rall/bucket_area)"}, "bucket_area": {"description": "The area that can be painted with one bucket of paint.
", "name": "bucket_area", "group": "Calculations", "templateType": "anything", "definition": "15"}, "colour": {"description": "", "name": "colour", "group": "Random bits", "templateType": "anything", "definition": "random(\"green\", \"red\", \"orange\", \"yellow\", \"blue\", \"purple\", \"pink\")"}, "width": {"description": "", "name": "width", "group": "Random bits", "templateType": "anything", "definition": "random(2.50..5.00 #0.1) + random(0.01..0.09 #0.01)"}, "w": {"description": "", "name": "w", "group": "Calculations", "templateType": "anything", "definition": "ceil(width)"}, "verbs": {"description": "", "name": "verbs", "group": "Person", "templateType": "anything", "definition": "if(person['gender']='neutral','','s')"}, "height": {"description": "", "name": "height", "group": "Random bits", "templateType": "anything", "definition": "random(2.10..2.70 #0.1) + random(0.01..0.09 #0.01)"}, "h": {"description": "", "name": "h", "group": "Calculations", "templateType": "anything", "definition": "ceil(height)"}, "rall": {"description": "", "name": "rall", "group": "Calculations", "templateType": "anything", "definition": "rceiling + rwall1*2 + rwall2*2"}, "pronouns": {"description": "", "name": "pronouns", "group": "Person", "templateType": "anything", "definition": "person['pronouns']"}, "length": {"description": "", "name": "length", "group": "Random bits", "templateType": "anything", "definition": "random(3.50..8.00 #0.1) + random(0.01..0.09 #0.01)"}, "person": {"description": "", "name": "person", "group": "Person", "templateType": "anything", "definition": "random_person()"}, "rwall1": {"description": "", "name": "rwall1", "group": "Calculations", "templateType": "anything", "definition": "l*h"}, "rwall2": {"description": "", "name": "rwall2", "group": "Calculations", "templateType": "anything", "definition": "w*h"}, "rceiling": {"description": "", "name": "rceiling", "group": "Calculations", "templateType": "anything", "definition": "w*l"}, "l": {"description": "", "name": "l", "group": "Calculations", "templateType": "anything", "definition": "ceil(length)"}}, "functions": {}, "tags": ["random names", "taxonomy"], "variable_groups": [{"name": "Random bits", "variables": ["colour", "height", "width", "length"]}, {"name": "Person", "variables": ["person", "pronouns", "verbs"]}, {"name": "Calculations", "variables": ["h", "w", "l", "rwall1", "rwall2", "rceiling", "rall", "bucket_area", "buckets"]}], "parts": [{"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"scripts": {}, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "choices": ["Overestimate and therefore we round each measurement up.
", "Underestimate and therefore we round each measurement down.
"], "showFeedbackIcon": true, "shuffleChoices": false, "displayColumns": "1", "variableReplacements": [], "marks": 0, "matrix": ["1", 0], "showCorrectAnswer": true, "maxMarks": 0, "type": "1_n_2"}], "showFeedbackIcon": true, "prompt": "Is it better to overestimate or underestimate in this situation?
\n[[0]]
", "marks": 0}, {"showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "rall", "showFeedbackIcon": true, "minValue": "rall", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "stepsPenalty": 0, "prompt": "Rounding each measurement to the nearest metre, estimate the whole area to be painted {colour}.
\n[[0]] m2
\n", "steps": [{"scripts": {}, "variableReplacements": [], "type": "information", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "
The room is {length}m long, {width}m wide, and {height}m high.
\nRound each measurement in the direction you decided on above.
", "marks": 0}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ceil(length)", "showFeedbackIcon": true, "prompt": "Round the length to the nearest metre.
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", "minValue": "ceil(width)", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "0.1", "showCorrectAnswer": true}, {"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "maxValue": "ceil(height)", "showFeedbackIcon": true, "prompt": "Round the height to the nearest metre.
", "minValue": "ceil(height)", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "0.1", "showCorrectAnswer": true}], "marks": 0}, {"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "buckets", "showFeedbackIcon": true, "minValue": "buckets", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "One bucket of {colour} paint is enough to paint an area of 15m2. How many buckets should {person['name']} buy to ensure {pronouns['they']} {if(person['gender']='neutral','have','has')} enough paint?
\n[[0]]
", "marks": 0}], "ungrouped_variables": [], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Estimate the number of buckets of paint to buy, by rounding measurements of a room up to the nearest metre and estimating the total area.
"}, "preamble": {"css": "", "js": ""}, "advice": "It is much better to have spare paint than not to have enough of it. So it is better to overestimate the area.
\nTherefore, we round each measurement up.
\nWe round each of our measurements up to the nearest whole metre:
\nLength: $\\var{length}\\,\\mathrm{m} \\approx \\var{l}\\,\\mathrm{m}$.
\nWidth: $\\var{width}\\,\\mathrm{m} \\approx \\var{w}\\,\\mathrm{m}$.
\nHeight: $\\var{height}\\,\\mathrm{m} \\approx \\var{h}\\,\\mathrm{m}$.
\nThe total area consists of five areas: two walls of $\\var{l}\\,\\text{m} \\times \\var{h}\\,\\text{m}$ (length by height); two walls of $\\var{w}\\,\\text{m} \\times \\var{h}\\,\\text{m}$ (width by height); and a ceiling of $\\var{l}\\,\\text{m} \\times \\var{w}\\,\\text{m}$ (length by width).
\n\\[ \\begin{align}
\\var{l}\\,\\text{m} \\times \\var{h}\\,\\text{m} &= \\var{l*h}\\,\\text{m}^2
\\\\ \\var{w}\\,\\text{m} \\times \\var{h}\\,\\text{m} &= \\var{w*h}\\,\\text{m}^2
\\\\ \\var{l}\\,\\text{m} \\times \\var{w}\\,\\text{m} &= \\var{l*w}\\,\\text{m}^2
\\end{align}\\]
Therefore, the total area {person['name']} needs to paint is
\n\\[ \\var{2*l*h} + \\var{2*w*h} + \\var{l*w} \\,\\mathrm{m}^2 = \\var{rall}\\,\\mathrm{m}^2 \\text{.} \\]
\nThe exact number of buckets needed is
\n\\[\\var{rall}\\,\\text{m}^2 \\div 15\\,\\text{m}^2 = \\var{rall/15} \\text{.}\\]
\n{person['name']} can only buy a whole number of buckets, so {pronouns['they']} need{verbs} to decide between {buckets-1} and {buckets} paint buckets. As it is better to buy more paint than not buy enough, {pronouns['they']} should buy {buckets} buckets of {colour} paint.
"}, {"name": "Mathematical formulae - Volume", "extensions": [], "custom_part_types": [], "resources": [["question-resources/sqbasedpyramid_sEpkGzO.svg", "/srv/numbas/media/question-resources/sqbasedpyramid_sEpkGzO.svg"], ["question-resources/triangularprism.svg", "/srv/numbas/media/question-resources/triangularprism.svg"], ["question-resources/cylinder.svg", "/srv/numbas/media/question-resources/cylinder.svg"], ["question-resources/cuboid.svg", "/srv/numbas/media/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/"}], "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": "Calculate the volumes of the following shapes.
", "advice": "a)
\nFor a cuboid, we first need to find out the area of one of the faces then multiply this area by the depth of the object.
In this example you can choose either of the faces. To make the calculations easier I am going to choose the face with $\\mathrm{base} = \\var{d4}m$ and $\\mathrm{height}= \\var{h4}m\\thinspace$.
\\begin{align}
\\mathrm{Area\\thinspace_\\square} &= \\mathrm{base} \\times \\mathrm{height} \\\\
&= \\var{h4} \\times \\var{d4} \\\\
&= \\var{h4*d4}\\, \\mathrm{m}^2\\,.
\\end{align}
Now that we have the area of the face ($\\mathrm{Area\\thinspace_\\square}$) we can multiply this by the $\\mathrm{depth} = \\var{w4}m$ to calculate the volume of the object.
\n\\begin{align}
\\mathrm{Volume} &= \\mathrm{Area\\thinspace_\\square} \\times \\mathrm{depth} \\\\
&= \\var{h4*d4} \\times \\var{w4} \\\\
&= \\var{h4*d4*w4}\\, \\mathrm{m}^3\\,.
\\end{align}
b)
\nFor a triangular prism, we first need to find the area of one of the faces then multiply this area by the depth of the prism.
In this example the easiest way to calculate the volume is to take the area of the triangular face first with $\\mathrm{base} = \\var{w6}m$ and $\\mathrm{height} = \\var{h6}m\\thinspace$.
\\begin{align}
\\mathrm{Area\\thinspace_\\triangle} &= \\frac{\\mathrm{base} \\times \\mathrm{height}}{2} \\\\
&= \\frac{\\var{w6} \\times \\var{h6}}{2} \\\\
&= \\var{0.5*w6*h6}\\, \\mathrm{m}^2\\,.
\\end{align}
Now that we have the area of the triangular face ($\\mathrm{Area\\thinspace_\\triangle}$) we can multiply this by the $\\mathrm{depth} = \\var{d6}m\\thinspace$.
\n\\begin{align}
\\mathrm{Volume} &= \\mathrm{Area\\thinspace_\\triangle} \\times \\mathrm{depth} \\\\
&= \\var{w6*h6} \\times \\var{d6} \\\\
&= \\var{w6*h6*d6}\\, \\mathrm{m}^2\\,.
\\end{align}
c)
\nFor 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}
d)
For a rectangular-based pyramid, we first need to calculate the area of the base and multiply this area by $\\frac{1}{3}$ the height of the pyramid.
In this example the area of the base can be calculated from the $\\mathrm{width}= \\var{w8}m$ and $\\mathrm{length} = \\var{d8}m\\thinspace$.
\\begin{align}
\\mathrm{Area\\thinspace_\\boxdot} &= \\mathrm{width} \\times \\mathrm{length} \\\\
&= \\var{w8} \\times \\var{d8} \\\\
&= \\var{w8*d8}\\, \\mathrm{m}^2\\,.
\\end{align}
Now that we have the area of the base we can multiply this by the $\\frac{1}{3} \\mathrm{height}$ where $\\mathrm{height} = \\var{h8}m\\thinspace$.
\n\\begin{align}
\\mathrm{Volume} &= \\mathrm{Area\\thinspace_\\boxdot} \\times \\frac{1}{3} \\mathrm{height} \\\\
&= \\var{w8*d8} \\times \\var{dpformat(1/3*h8,5)}\\\\
&= \\var{dpformat(w8*d8*h8*1/3,5)}\\\\
&= \\var{dpformat(w8*d8*h8*1/3,1)}\\, \\mathrm{m}^3\\,. \\quad \\text{1 d.p.}
\\end{align}
Side of square in cuboid.
", "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.
", "templateType": "anything", "can_override": false}, "h6": {"name": "h6", "group": "Triangular prism", "definition": "random(2..5#1)", "description": "Height of traingle.
", "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 cuboid.
\n\n$\\mathrm{Volume} =$[[0]] $\\mathrm{m}^3$.
", "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 cuboid:
\n\\begin{align}
\\mathrm{Volume} &= \\mathrm{Area\\thinspace_\\square} \\times \\mathrm{depth} \\\\
&= \\mathrm{base} \\times \\mathrm{height} \\times \\mathrm{depth}
\\end{align}
Calculate the $\\mathrm{Volume}$ of the following triangular prism.
\n\n$\\mathrm{Volume} =$[[0]]$\\mathrm{m}^3$.
", "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 triangular prism:
\n\\begin{align}
\\mathrm{Volume} &= \\mathrm{Area\\thinspace_\\triangle} \\times \\mathrm{depth} \\\\
&= \\frac{\\mathrm{base} \\times \\mathrm{height}}{2} \\times \\mathrm{depth}
\\end{align}
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}
Calculate the $\\mathrm{Volume}$ of the following pyramid.
\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 square-based pyramid:
\n\\begin{align}
\\mathrm{Volume} &= \\mathrm{Area\\thinspace_\\boxdot} \\times \\frac{1}{3}\\mathrm{height} \\\\
&= \\mathrm{width} \\times \\mathrm{length} \\times \\frac{1}{3}\\mathrm{height}
\\end{align}
Probability someone goes to see Star Wars
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", "definition": "random(100..180 #20)", "group": "Ungrouped variables"}}, "functions": {}, "statement": "There are four films being shown in a cinema on a particular day.
\nThe probability that a person buys a ticket to see each film, denoted $P(\\text{Film})$, is given in the table below.
\n| Film | \n$P(\\text{Film})$ | \nGenre | \n
| Forgotten Game | \n$\\var{Avatar}$ | \nSci-Fi | \n
| The Diamond Valley | \n$\\var{SW}$ | \nSci-Fi | \n
| School of Return | \n$\\var{NYSM}$ | \nThriller | \n
| The Silk's Nobody | \n$\\var{TIJ}$ | \nCrime | \n
$\\var{no_people}$ people each buy a ticket at the cinema to see a film of their own choosing during the day.
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", "minValue": "{no_people}*({Avatar}+{SW})", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "ungrouped_variables": ["Avatar", "SW", "NYSM", "TIJ", "no_people"], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.
"}, "preamble": {"css": "", "js": ""}, "advice": "If we are given the probability of an event occurring in a single trial then we can calculate the expected number of times that this event would occur in a larger number of trials.
\nTo do this, we multiply the probability of the event occurring in a single trial by the total number of trials:
\n\\[\\text{Expected number of times an event occurs} = \\text{Probability of event} \\times \\text{Number of trials}.\\]
\nWe are given the probabilities that someone buys a ticket to see each film in the table below.
\n| Film | \n$P(\\text{Film})$ | \nGenre | \n
| Forgotten Game | \n$\\var{Avatar}$ | \nSci-Fi | \n
| The Diamond Valley | \n$\\var{SW}$ | \nSci-Fi | \n
| School of Return | \n$\\var{NYSM}$ | \nThriller | \n
| The Silk's Nobody | \n$\\var{TIJ}$ | \nCrime | \n
We are also told that $\\var{no_people}$ people each buy a ticket at the cinema to see a film of their own choosing during this day.
\nTo calculate the expected number of people who bought tickets to see one of these films we multiply the probability that a person buys a ticket for that film by how many people bought tickets for a film at the cinema.
\nSo the expected number of people who bought tickets to see Forgotten Game is
\n\\[
\\var{Avatar} \\times \\var{no_people} = \\var{{Avatar}*{no_people}}.
\\]
We are now asked to calculate the expected number of people who bought tickets to see a Sci-Fi film.
\nFrom the table above we can see that there are two films which belong to the Sci-Fi genre: Forgotten Game and The Diamond Valley.
\nFirstly, we need to calculate the probability that a person buys a ticket to see a Sci-Fi film, which we will denote $P(\\text{Sci-Fi})$.
\nSince the probability that a person buys a ticket to see each film is different, it would be incorrect to say that the probability that a person buys a ticket to see a Sci-Fi film is
\n\\[\\displaystyle\\frac{2}{4} = \\displaystyle\\frac{1}{2}.\\]
\nInstead we must recognise that the probability that a person buys a ticket to see a Sci-Fi film is the probability that a person buys a ticket to see either Forgotten or The Diamond Valley.
\nTherefore to calculate this probability, we add the probabilities of a person buying a ticket to see each of these films:
\n\\[
\\begin{align}
P(\\text{Sci-Fi}) &= P(\\text{Forgotten Game})+P(\\text{The Diamond Valley})\\\\
&= \\var{Avatar}+\\var{SW}\\\\
&= \\var{Avatar+SW}.
\\end{align}
\\]
Then the expected number of people who bought tickets to see a Sci-Fi film is
\n\\[
\\var{Avatar+SW} \\times \\var{no_people} = \\var{({Avatar+SW})*{no_people}}.
\\]
Calculate the mean, median, mode and range of the following data.
\n$\\var{a1}, \\var{a2}, \\var{a3}, \\var{a4}, \\var{a5}, \\var{a6}, \\var{a7}, \\var{a8}, \\var{a9}$ .
", "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Exam covering questions on the Errorsr part of the SOEE5154M Maths course.
\nTopics covered are calculating the mean, median, mode and standard deviation.
\nrebelmaths
\n$\\text{mean}=\\;\\;$[[0]]
\nEnter decimal answers to 1 decimal places.
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", "showFeedbackIcon": true, "variableReplacements": []}, {"variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "scripts": {}, "gaps": [{"variableReplacementStrategy": "originalfirst", "type": "jme", "answer": "{a2-a3}", "variableReplacements": [], "marks": 2, "checkingaccuracy": 0.01, "vsetrangepoints": 5, "answersimplification": "std", "vsetrange": [0, 1], "showFeedbackIcon": true, "showpreview": true, "scripts": {}, "showCorrectAnswer": true, "checkingtype": "absdiff", "checkvariablenames": false, "expectedvariablenames": []}], "showCorrectAnswer": true, "prompt": "$\\text{range}=\\;\\;$[[0]]
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\nMedian: middle value
\nMode: most common value
\nRange: Highest value - lowest value
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