// Numbas version: exam_results_page_options {"name": "Rates", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["person", "number", "integer", "unit", "thing"], "name": "Rates", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "
{person} {thing[0]} {number} {thing[2]} per {integer} {unit}s. This is equivalent to {thing[1]} [[0]] {thing[2]} per {unit}.
\nNote: 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)
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "The word 'per' can be replaced with the operation of division.
\nThese questions are very similar to equivalent fractions.
\n\nSuppose you are told 'Daniel eats 61 berries per 3 hours'. The following three methods are equivalent but might appear different.
\nA {vehicle} travels {distance} km per {amount} L of petrol.
\n\nHow many kilometres can be travelled by using {niceamount} L? [[1]] km
\nHow many litres of petrol are needed to travel {nicedistance} km? [[0]] L
\n\n
Note: 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)
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Just like a fraction, we can multiply or divide both sides of the rate by any number (except 0).
\n\nSuppose you have 'a motorbike travels 245 km per 13 L of petrol'. Note, this can be written as 245 km / 13 L.
\nTo determine kilometres per 20 L, first determine how many kilometres per 1 L, and then multiply by 20. That is,
\n245 km / 13 L = $\\frac{345}{13}$ km/L = $\\frac{345}{13}\\times 20$ km / 20 L.
\nTo determine litres per 50 km, first determine how many litres per 1 km, and then multiply by 50. That is,
\n245 km / 13 L = 1 km / $\\frac{13}{245}$ L = 50 km / $\\frac{13}{245}\\times 50$ L.
\n\nNote, 245 km per 13 L could also be written as 13 L / 245 km. It might be simpler to do the second question this way:
\nTo determine litres per 50 km, first determine how many litres per 1 km, and then multiply by 50. That is,
\n13 L / 245 km = $\\frac{13}{245}$ L / km = $\\frac{13}{245}\\times 50$ L / 50 km.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{amount}*{nicedistance}/{distance}", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{distance}/{amount}*{niceamount}", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "A rate of {num1} {firstunit[0]}s / {num2} {secondunit[0]}s is equivalent to [[0]] {firstunit[1]}s / {secondunit[1]}.
\n\nNote: 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)
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Just like a fraction, we can multiply or divide both sides of the rate by any number (except 0). Do one thing at a time to avoid making a mistake.
\n\nFor example, suppose we need to convert 24 milliseconds / 4 litres into an equivalent rate in minutes / kilolitre. We need to do the following steps:
\nSo our final answer is 0.1 minutes / litre.
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"}, "amount": {"definition": "if(vehicle='car',random(35..60),if(vehicle='motorbike',random(11..20)))", "templateType": "anything", "group": "fuel", "name": "amount", "description": ""}, "person": {"definition": "Random(['Aaron', 'Alex', 'Ben', 'Claire', 'Charlotte', 'Daniel', 'Deb', 'Ethan', 'Elizabeth', 'Grace', 'Hunter', 'Julia', 'Isaac', 'Xavier', 'Victoria', 'Sophie', 'Abbey', 'Annie', 'Noah'])", "templateType": "anything", "group": "Ungrouped variables", "name": "person", "description": ""}, "niceamount": {"definition": "random(list(10..50#5) except amount)", "templateType": "anything", "group": "fuel", "name": "niceamount", "description": ""}, "nicedistance": {"definition": "random(list(50..200#10))", "templateType": "anything", "group": "fuel", "name": "nicedistance", "description": ""}, "vehicle": {"definition": "random(['car','motorbike'])", "templateType": "anything", "group": "fuel", "name": "vehicle", "description": ""}, "integer": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "integer", "description": ""}, "secondunit": {"definition": "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])))))", "templateType": "anything", "group": "part c", "name": "secondunit", "description": ""}, "seed": {"definition": "shuffle(['cap','time','mass','distance'])[0..2]", "templateType": "anything", "group": "part c", "name": "seed", "description": ""}, "unit": {"definition": "random(['hour', 'minute', 'day', 'month'])", "templateType": "anything", "group": "Ungrouped variables", "name": "unit", "description": ""}}, "metadata": {"description": "Unit rates and converting rates.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "contributors": [{"name": "Nigel Atkins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/275/"}]}]}], "contributors": [{"name": "Nigel Atkins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/275/"}]}