// Numbas version: finer_feedback_settings
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"if(seed[0]='cap',random([\"millilitre\",\"kilolitre\",1000000],[\"millilitre\",\"megalitre\",1000000000]),\nif(seed[0]='mass',random([\"gram\",\"tonne\",1000000],[\"milligram\",\"tonne\",1000000000],[\"milligram\",\"kilogram\",1000000]),\nif(seed[0]='time',random([\"millisecond\",\"hour\",3600000],[\"minute\",\"day\",1440],[\"second\",\"day\",86400],[\"millisecond\",\"day\",24*3600000]),\nif(seed[0]='distance',random([\"millimetre\",\"kilometre\", 1000000], [\"centimetre\", \"kilometre\",100000],[\"millimetre\",\"metre\",1000]),'error'))))", "description": "", "templateType": "anything", "can_override": false}, "num1": {"name": "num1", "group": "part c", "definition": "random(5..45)", "description": "", "templateType": "anything", "can_override": false}, "num2": {"name": "num2", "group": "part c", "definition": "random(5..45 except num1)", "description": "", "templateType": "anything", "can_override": false}, "distance": {"name": "distance", "group": "fuel", "definition": 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"if(seed[1]='cap',random([\"millilitre\",\"kilolitre\",1000000],[\"millilitre\",\"megalitre\",1000000000]),\nif(seed[1]='mass',random([\"gram\",\"tonne\",1000000],[\"milligram\",\"tonne\",1000000000],[\"milligram\",\"kilogram\",1000000]),\nif(seed[1]='time',random([\"millisecond\",\"hour\",3600000],[\"minute\",\"day\",1440],[\"second\",\"day\",86400],[\"millisecond\",\"day\",24*3600000]),\nif(seed[1]='distance',random([\"millimetre\",\"kilometre\", 1000000], [\"centimetre\", \"kilometre\",100000],[\"millimetre\",\"metre\",1000]),'error'))))", "description": "", "templateType": "anything", "can_override": false}, "seed": {"name": "seed", "group": "part c", "definition": "shuffle(['cap','time','mass','distance'])[0..2]", "description": "", "templateType": "anything", "can_override": false}, "unit": {"name": "unit", "group": "Ungrouped variables", "definition": "random(['hour', 'minute', 'day', 'month'])", "description": "", "templateType": "anything", "can_override": false}, "temp": {"name": "temp", "group": "part c", "definition": "num1*secondunit[2]/(num2*firstunit[2])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["person", "number", "integer", "unit", "thing"], "variable_groups": [{"name": "fuel", "variables": ["vehicle", "distance", "amount", "nicedistance", "niceamount"]}, {"name": "part c", "variables": ["firstunit", "seed", "secondunit", "num1", "num2", "temp"]}], "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": "<p>{person} {thing[0]} {number} {thing[2]} per {integer} {unit}s. This is equivalent to {thing[1]} [[0]]&nbsp;{thing[2]} per {unit}.</p>\n<p><strong>Note:</strong>&nbsp;If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)</p>", "stepsPenalty": 0, "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": "<p><em>The word 'per' can be replaced with the operation of division.</em></p>\n<p>These questions are very similar to equivalent fractions.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Suppose you are told 'Daniel eats 61 berries per 3 hours'. The following three methods are equivalent but might appear different.</p>\n<ol>\n<li>We are given 61 berries / 3 hours. Divide both sides of the rate by 3 (so that we are dealing with 'per hour' not 'per 3 hours'). This gives 61/3 berries/hour.</li>\n<li><br/>\\[\\text{61 berries/3 hours}=\\frac{61\\text{ berries}}{3 \\text{ hours}}=\\frac{61}{3}\\frac{\\text{berries}}{\\text{hour}}=\\frac{61}{3} \\,\\text{berries/hour}.\\]</li>\n<li><br/>\\[\\text{61 berries/3 hours}=\\frac{61\\text{ berries}}{3 \\text{ hours}}=\\frac{61\\text{ berries }\\div 3}{3 \\text{ hours }\\div 3}=\\frac{61\\div 3\\text{ berries }}{1 \\text{ hour }}=\\frac{61}{3} \\,\\text{berries/hour}.\\]</li>\n</ol>\n<p></p>"}], "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": "{number}/{integer}", "maxValue": "{number}/{integer}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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": "<p>A {vehicle} travels {distance} km per {amount} L of petrol. &nbsp;</p>\n<p></p>\n<p>How many kilometres can be travelled by using {niceamount} L?&nbsp;[[1]] km</p>\n<p>How many litres of petrol are needed to travel {nicedistance} km?&nbsp;[[0]] L</p>\n<p><strong></strong></p>\n<p><strong>Note:</strong>&nbsp;If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)</p>", "stepsPenalty": 0, "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": "<p><em>Just like a fraction, we can multiply or divide both sides of the rate by any number (except 0).</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>Suppose you have 'a motorbike travels 245 km per 13 L of petrol'. Note, this can be&nbsp;written as 245 km / 13 L.</p>\n<p>To determine kilometres per 20 L, first determine how many kilometres per 1 L, and then multiply by 20. That is,&nbsp;</p>\n<p style=\"text-align: center;\">245 km / 13 &nbsp;L &nbsp;= $\\frac{345}{13}$ km/L = &nbsp;$\\frac{345}{13}\\times 20$ km / 20 L.</p>\n<p>To determine litres per 50 km, first determine how many litres per 1 km, and then multiply by 50. That is,</p>\n<p style=\"text-align: center;\">245 km / 13 L = 1 km / $\\frac{13}{245}$ L = 50 km / $\\frac{13}{245}\\times 50$ L.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Note,&nbsp;245 km per 13 L could also be written as 13 L / 245 km.&nbsp;It might be simpler to do the second question this way:</p>\n<p>&nbsp;To determine litres per 50 km, first determine how many litres per 1 km, and then multiply by 50. That is,</p>\n<p style=\"text-align: center;\">13 L / 245 km = $\\frac{13}{245}$ L / km =&nbsp;$\\frac{13}{245}\\times 50$ L / 50 km.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{amount}*{nicedistance}/{distance}", "answerSimplification": "all", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{distance}/{amount}*{niceamount}", "answerSimplification": "all", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"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": "<p>A&nbsp;rate of {num1} {firstunit[0]}s / {num2} {secondunit[0]}s is equivalent to [[0]]&nbsp;{firstunit[1]}s / {secondunit[1]}.</p>\n<p></p>\n<p><strong>Note:</strong>&nbsp;If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)</p>", "stepsPenalty": 0, "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": "<p><strong></strong><em>Just like a fraction, we can multiply or divide both sides of the rate by any number (except 0).&nbsp;</em><em>Do one thing at a time to avoid making a mistake.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>For example, suppose we need to convert 24 milliseconds / 4 litres into an equivalent rate in minutes / kilolitre. We need to do the following steps:</p>\n<ol>\n<li>convert milliseconds to minutes,</li>\n<li>convert litres to kilolitres,</li>\n<li>make it per kilolitre.&nbsp;</li>\n</ol>\n<p></p>\n<hr/>\n<p></p>\n<ol>\n<li>There are 60,000 milliseconds in a minute so to convert from millisecond to minutes we divide the milliseconds by 60,000. We now have 0.0004 minutes / 4 litres.</li>\n<li>There are 1,000 litres in a kilolitre so to convert from litres to kilolitres, you need to divide the litres by 1,000. We now have&nbsp;0.0004 minutes / 0.004 litres.&nbsp;</li>\n<li>To make it per litre we recall that 0.0004 minutes / 0.004 litres <g class=\"gr_ gr_1763 gr-alert gr_gramm Grammar multiReplace\" id=\"1763\" data-gr-id=\"1763\">is</g> equivalent to&nbsp;0.0004/0.004 minutes / litre (this is the same as dividing both sides by 0.004).&nbsp;</li>\n</ol>\n<p>So our final answer is 0.1 minutes / litre.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{num1}*{secondunit[2]}/({num2}*{firstunit[2]})", "answerSimplification": "all", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}