// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Q7 Track shape problems", "extensions": [], "custom_part_types": [], "resources": [["question-resources/area-of-a-equilateral-triangle-formula_RlGhwyD.png", "area-of-a-equilateral-triangle-formula_RlGhwyD.png"], ["question-resources/115650640143b203406ae67.jpg", "115650640143b203406ae67.jpg"], ["question-resources/display-illustration.jpg", "display-illustration.jpg"], ["question-resources/pfig1.jpg", "pfig1.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "ungrouped_variables": ["size", "size2", "size3", "ans11", "ans12", "ans21", "ans22", "ans31", "ans32"], "variables": {"ans22": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "ans22", "definition": "((pi*(size[1]/2)^2)/2)+(size[1]^2)+((sqrt(3)/4)*size[1]^2)"}, "size2": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "size2", "definition": "random(45..70)"}, "size3": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "size3", "definition": "random(25..40)"}, "ans12": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "ans12", "definition": "(pi*(size[0]/2)^2)+(size[0]^2)"}, "ans32": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "ans32", "definition": "(pi*(size3/2)^2)+(size2*size3)"}, "size": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "size", "definition": "shuffle(25..77#0.2)[0..2]"}, "ans11": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "ans11", "definition": "(2*pi*(size[0]/2))+(2*size[0])"}, "ans21": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "ans21", "definition": "(pi*(size[1]/2))+(2*size[1])+(2*size[1])"}, "ans31": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "ans31", "definition": "(2*pi*(size3/2))+(2*size2)"}}, "parts": [{"prompt": "<p><img src=\"resources/question-resources/115650640143b203406ae67.jpg\" width=\"244\" height=\"148\"/></p>\n<p>The figure above shows a running track which is made up of a square of side $\\var{size[0]}$ metres and a semi-circle on each end.</p>\n<p>(i) Calculate the perimeter of the running track.</p>\n<p>[[0]]m</p>\n<p>(ii) Calculate the area enclosed by the running track.</p>\n<p>[[1]]m$^2$</p>", "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "showPrecisionHint": false, "unitTests": [], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "scripts": {}, "precision": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{ans11}", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "minValue": "{ans11}", "extendBaseMarkingAlgorithm": true}, {"correctAnswerFraction": false, "mustBeReduced": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "showPrecisionHint": false, "unitTests": [], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "scripts": {}, "precision": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{ans12}", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "minValue": "{ans12}", "extendBaseMarkingAlgorithm": true}], "showCorrectAnswer": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"prompt": "<p><img src=\"resources/question-resources/display-illustration.jpg\" width=\"345\" height=\"190\"/></p>\n<p>The figure above is made up of a square of side $\\var{size[1]}$ metres and a semi-circle on one&nbsp;end and an equilateral triangle on the other end.</p>\n<p>(i) Calculate the perimeter of the figure.</p>\n<p>[[0]]m</p>\n<p>(ii) Calculate the area&nbsp;of the figure. Note the area of an equilateral triangle with side length $a$ is given by $A =\\frac{\\sqrt{3}}{4}&nbsp;a^2$</p>\n<p>[[1]]m$^2$</p>", "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "showPrecisionHint": false, "unitTests": [], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "scripts": {}, "precision": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{ans21}", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "minValue": "{ans21}", "extendBaseMarkingAlgorithm": true}, {"correctAnswerFraction": false, "mustBeReduced": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "showPrecisionHint": false, "unitTests": [], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "scripts": {}, "precision": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{ans22}", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "minValue": "{ans22}", "extendBaseMarkingAlgorithm": true}], "showCorrectAnswer": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "sortAnswers": false}, {"prompt": "<p><img src=\"resources/question-resources/pfig1.jpg\"/></p>\n<p>The figure above shows a running track which is made up of a rectangle&nbsp;of length&nbsp;$\\var{size2}$ m and width $\\var{size3}$ m&nbsp; and a semi-circle on each end.</p>\n<p>(i) Calculate the perimeter of the running track.</p>\n<p>[[0]]m</p>\n<p>(ii) Calculate the area enclosed by the running track.</p>\n<p>[[1]]m$^2$</p>", "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "showPrecisionHint": false, "unitTests": [], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "scripts": {}, "precision": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{ans31}", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "minValue": "{ans31}", "extendBaseMarkingAlgorithm": true}, {"correctAnswerFraction": false, "mustBeReduced": false, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "showPrecisionHint": false, "unitTests": [], "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "scripts": {}, "precision": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{ans32}", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "minValue": "{ans32}", "extendBaseMarkingAlgorithm": true}], "showCorrectAnswer": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "sortAnswers": false}], "variablesTest": {"condition": "", "maxRuns": 100}, "name": "Simon's copy of Q7 Track shape problems", "variable_groups": [], "functions": {}, "advice": "<p><strong>(a)</strong></p>\n<p>Perimeter = 2 semicircles + 2 straight lines = $(2 \\times \\pi \\times \\frac{\\var{size[0]}}{2}) + (2 \\times \\var{size[0]}) = \\var{precround(ans11,2)}$m</p>\n<p>Area = 2 semicircles + 1 square = 1 circle + 1 square = $(\\pi \\times (\\frac{\\var{size[0]}}{2})^2) + (\\var{size[0]}^2) = \\var{precround(ans12,2)}$m$^2$</p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>Perimeter = 1 semicircle + 4 straight lines =&nbsp; $(\\pi \\times \\frac{\\var{size[1]}}{2}) + (2 \\times \\var{size[1]}) + (2 \\times \\var{size[1]})&nbsp;= \\var{precround(ans21,2)}$m</p>\n<p>The area of an equilateral triangle with side length $a$ is given by $A =\\frac{\\sqrt{3}}{4}&nbsp;a^2$</p>\n<p>Area = 1 semicircle + 1 square + 1&nbsp;triangle = $\\frac{(\\pi \\times (\\frac{\\var{size[1]}}{2})^2)}{2} + (\\var{size[1]}^2) +(\\frac{\\sqrt(3)}{4} \\times (\\var{size[1]}^2)) = \\var{precround(ans22,2)}$m$^2$</p>\n<p></p>\n<p><strong>(c)</strong></p>\n<p>Perimeter = 2 semicircles + 2 straight lines =&nbsp; $(2 \\times \\pi \\times \\frac{\\var{size3}}{2}) + (2 \\times \\var{size2}) = \\var{precround(ans31,2)}$m</p>\n<p>Area = 2 semicircles + 1 rectangle = 1 circle + 1 rectangle = $(\\pi \\times (\\frac{\\var{size3}}{2})^2) + (\\var{size2} \\times \\var{size3}) = \\var{precround(ans32,2)}$m$^2$</p>", "preamble": {"css": "", "js": ""}, "statement": "<p>Solve the following questions to 2 decimal places:</p>", "tags": [], "metadata": {"description": "<p>Area and perimeter of compound shapes</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": [], "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}], "resources": ["question-resources/area-of-a-equilateral-triangle-formula_RlGhwyD.png", "question-resources/115650640143b203406ae67.jpg", "question-resources/display-illustration.jpg", "question-resources/pfig1.jpg"]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}