// Numbas version: exam_results_page_options
{"name": "Rectangle enlargements", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Ratio of sides of rectangles</p>\n<p>rebel</p>\n<p>rebelmaths</p>"}, "tags": [], "ungrouped_variables": ["numberone", "numbertwo", "ans", "lent", "width", "area", "numberthree", "numberthreea", "numberfour", "numberfoura", "numberfive", "numberfivea", "numberfiveb", "ansone", "anstwo", "ansthree", "num1", "num2", "num3", "a1", "a2", "a3", "sf"], "variable_groups": [], "variables": {"lent": {"definition": "1+{numberone}/100", "name": "lent", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "numbertwo": {"definition": "random(2..25 except {numberone})", "name": "numbertwo", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "num2": {"definition": "7", "name": "num2", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "ans": {"definition": "({area}-1)*100", "name": "ans", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "numberfivea": {"definition": "{numberthreea}*{numberfoura}", "name": "numberfivea", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a1": {"definition": "12*num1", "name": "a1", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "numberfive": {"definition": "random(2..4 except {numberthree} except {numberfour})", "name": "numberfive", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "sf": {"definition": "random(2,9)", "name": "sf", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a3": {"definition": "12*num3", "name": "a3", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "numberfiveb": {"definition": "{numberfivea}-({numberthreea}+{numberfoura})", "name": "numberfiveb", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "ansone": {"definition": "18*({numberthree} + (1/{numberthreea}))", "name": "ansone", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "num3": {"definition": "15-(num1+num2)", "name": "num3", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "numberthree": {"definition": "random(2..4)", "name": "numberthree", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "ansthree": {"definition": "18*({numberfive} + ({numberfiveb}/{numberfivea}))", "name": "ansthree", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "numberone": {"definition": "random(2..25)", "name": "numberone", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a2": {"definition": "12*num2", "name": "a2", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "numberthreea": {"definition": "random(2..8)", "name": "numberthreea", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "numberfoura": {"definition": "random(2..8 except {numberthreea})", "name": "numberfoura", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "width": {"definition": "1-{numbertwo}/100", "name": "width", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "numberfour": {"definition": "random(2..4 except {numberthree})", "name": "numberfour", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "anstwo": {"definition": "18*({numberfour} + (1/{numberfoura}))", "name": "anstwo", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "num1": {"definition": "random(2..6)", "name": "num1", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "area": {"definition": "lent*width", "name": "area", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "name": "Rectangle enlargements", "parts": [{"showCorrectAnswer": true, "steps": [{"customMarkingAlgorithm": "", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "marks": 0, "unitTests": [], "showFeedbackIcon": true, "prompt": "<p>Suppose the original rectangle has length $l$ and width $w$. This has area $w\\times l$.</p>\n<p>The new rectangle has length $\\var{sf}l$ and width $\\var{sf}w$. What is it's area? How does this relate to the original rectangle?</p>\n<p></p>", "type": "information", "variableReplacementStrategy": "originalfirst", "scripts": {}}], "showFeedbackIcon": true, "unitTests": [], "scripts": {}, "gaps": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{sf^2}", "unitTests": [], "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "minValue": "{sf^2}", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "mustBeReduced": false, "marks": 1, "mustBeReducedPC": 0, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "allowFractions": false, "type": "numberentry"}], "type": "gapfill", "customMarkingAlgorithm": "", "prompt": "<p>The length and width of a rectangle&nbsp;are both mutiplied by&nbsp;$\\var{sf}$&nbsp;</p>\n<p>What&nbsp;must&nbsp;we multiply the old area by to find the new area?</p>\n<p><em></em></p>\n<p><em>&nbsp;[[0]]</em></p>", "marks": 0, "stepsPenalty": 0, "sortAnswers": false, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"showCorrectAnswer": true, "steps": [{"customMarkingAlgorithm": "", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "marks": 0, "unitTests": [], "showFeedbackIcon": true, "prompt": "<p>Suppose the original rectangle has length $l$ and width $w$. This has area $w\\times l$.</p>\n<p>The new rectangle has length $l\\times(1+\\var{numberone/100})$ and width $w\\times(1-\\var{numbertwo/100})$. What is it's area? How does this relate to the original rectangle?</p>", "type": "information", "variableReplacementStrategy": "originalfirst", "scripts": {}}], "showFeedbackIcon": true, "unitTests": [], "scripts": {}, "gaps": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{area}", "unitTests": [], "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "minValue": "{area}", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "mustBeReduced": false, "marks": 1, "mustBeReducedPC": 0, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "allowFractions": false, "type": "numberentry"}], "type": "gapfill", "customMarkingAlgorithm": "", "prompt": "<p>The length of a rectangle is increased by $\\var{numberone}$% while the width is decreased by $\\var{numbertwo}$%.</p>\n<p>What must we multiply the old area by to find the new area?</p>\n<p><em>[[0]]</em></p>", "marks": 0, "stepsPenalty": 0, "sortAnswers": false, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}], "rulesets": {}, "preamble": {"css": "", "js": ""}, "statement": "<p></p>\n<p></p>", "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "advice": "<p><strong>(a)</strong></p>\n<p>Suppose the original rectangle has length $l$ and width $w$. This has area $w\\times l$.</p>\n<p>The new rectangle has length $\\var{sf}l$ and width $\\var{sf}w$.&nbsp;</p>\n<p>Therefore it has area&nbsp;$\\var{sf}w \\times \\var{sf}l = \\var{sf}^2\\times w \\times l$, which is $\\var{sf^2}$ times the original area.</p>\n<p></p>\n<p>In general:</p>\n<p>-if we enlarge a 2-d shape by scale factor $k$, its area will be multiplied by $k^2$</p>\n<p>-if we enlarge a 3-d shape by scale factor $k$, its&nbsp;volume will be multiplied by $k^3$</p>\n<p></p>\n<p><strong>(</strong><strong>b)</strong></p>\n<p><strong></strong>An increase in length of $\\var{numberone}$%, is the same as multiplying the length by $\\var{lent}$</p>\n<p>An decrease in width of $\\var{numbertwo}$%, is the same as multiplying the width by $\\var{width}$</p>\n<p>Therefore the new area will be&nbsp;$\\var{width}w \\times \\var{lent}l =&nbsp;\\var{width*lent}\\times w \\times l$</p>\n<p></p>", "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/"}]}]}], "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/"}]}