// Numbas version: exam_results_page_options
{"name": "Converting units of volume (cc/cm^3/litres/m^3)", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"unitTests": [], "type": "gapfill", "prompt": "<p>{person['name']} applies to find out how much the insurance for the car would cost, but is required to state the engine size in litres.&nbsp;</p>\n<p>What is the engine size in litres?</p>\n<p>&nbsp;[[0]] litres.&nbsp;</p>\n<p><em></em></p>", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "sortAnswers": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "correctAnswerFraction": false, "unitTests": [], "type": "numberentry", "marks": 1, "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "maxValue": "litres", "mustBeReducedPC": 0, "mustBeReduced": false, "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "minValue": "litres"}], "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0}, {"unitTests": [], "type": "gapfill", "prompt": "<p>The specification of a second car gives the engine size in m$^3$. In order for {person['name']} to make a comparison {person['pronouns']['they']} convert{s} the engine size of the first car to&nbsp;cubic metres.</p>\n<p>What is the engine size of the first car in units of m$^3$?</p>\n<p>[[0]]m$^3$ &nbsp; &nbsp; &nbsp;<em><small>Give your answer to 4 decimal places</small></em></p>", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "sortAnswers": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"correctAnswerFraction": false, "unitTests": [], "type": "numberentry", "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "mustBeReduced": false, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "precision": "4", "precisionPartialCredit": 0, "maxValue": "metres_cubed", "showCorrectAnswer": true, "marks": "1", "allowFractions": false, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": false, "variableReplacements": [], "minValue": "metres_cubed", "scripts": {}, "showFeedbackIcon": true}], "scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0}], "variables": {"cc": {"name": "cc", "definition": "random(1200..3000#200)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "person": {"name": "person", "definition": "random_person()", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "metres_cubed": {"name": "metres_cubed", "definition": "cc*(10^-6)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "litres": {"name": "litres", "definition": "cc/1000", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "s": {"name": "s", "definition": "if(person['gender']='neutral','','s')", "templateType": "anything", "group": "Ungrouped variables", "description": ""}}, "statement": "<p>{person['name']} is looking to buy a car.&nbsp;{capitalise(person['pronouns']['they'])} find{s} one advertised with an engine size of $\\var{cc}$cc.&nbsp;</p>\n<p>{person['name']} recognises&nbsp;that 'cc' stands for units of cubic centimetres (cm$^3$)&nbsp;and&nbsp;knows the following conversions:</p>\n<table border=\"1\" cellpadding=\"5\">\n<tbody>\n<tr>\n<td style=\"text-align: left;\">$1$ m</td>\n<td style=\"text-align: left;\">$100$ cm</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$1$ litre</td>\n<td style=\"text-align: left;\">$1000\\,\\text{cm}^3$&nbsp;</td>\n</tr>\n</tbody>\n</table>", "ungrouped_variables": ["person", "litres", "cc", "s", "metres_cubed"], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "preamble": {"js": "", "css": ""}, "rulesets": {}, "extensions": ["random_person"], "metadata": {"description": "<p>Convert figures for car engine sizes between cc (cm^3), litres, and m^3.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "<h4>a)</h4>\n<p>The&nbsp;advertised engine size is $\\var{cc}$ cubic centimetres.&nbsp;To convert cubic centimetres to litres, we&nbsp;divide by $1000$.&nbsp;</p>\n<p>\\[\\var{cc}\\div 1000= \\var{litres}\\text{ litres.}\\]</p>\n<h4>b)</h4>\n<p>In order to convert to cubic metres, we first note that&nbsp;</p>\n<p>\\[ 1 \\text{cm} = 0.01&nbsp;\\text{m.} \\]</p>\n<p>An example of a volume of&nbsp;$1\\text{cm}^3$ is&nbsp;a&nbsp;cube with $1$cm sides. Converting each side into metres,</p>\n<p>\\begin{align}<br/>1\\text{cm}^3 &amp;= 1\\text{cm}\\times1\\text{cm}\\times1\\text{cm} \\\\<br/>&amp;= 0.01\\text{m}\\times0.01\\text{m}\\times0.01\\text{m} \\\\<br/>&amp;= 0.000001\\text{m}^3 \\text{.}<br/>\\end{align}</p>\n<p>Therefore $\\var{cc}\\text{cm}^3$ is&nbsp;</p>\n<p>\\[ \\var{cc} \\times 0.000001 = \\var{metres_cubed}\\text{m}^3\\text{.} \\]</p>", "variable_groups": [], "name": "Converting units of volume (cc/cm^3/litres/m^3)", "functions": {}, "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}]}