// Numbas version: finer_feedback_settings
{"name": "Percentages - Test Yourself", "feedback": {"allowrevealanswer": true, "showtotalmark": true, "advicethreshold": 0, "intro": "", "feedbackmessages": [], "showanswerstate": true, "showactualmark": true, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "duration": 0, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "metadata": {"description": "<p>This activity has a variety of percentage questions all designed to be done without a calculator.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Percentages - Quick Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "g", "f", "h", "j", "k", "l", "m", "n"], "tags": [], "advice": "<p>Work out your quick percentages first: &nbsp;50%, 25%, 10%, 5% and 1%</p>\n<p>Add or subtract combinations of these to get the required amount.</p>", "rulesets": {}, "parts": [{"prompt": "<p>What is $\\var{a}\\text{%}$ of $\\var{b}$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(a/100)*b", "minValue": "(a/100)*b", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{c}\\text{%}$ of $\\var{d}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(c/100)*d", "minValue": "(c/100)*d", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{g}\\text{%}$ of $\\var{f}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(g/100)*f", "minValue": "(g/100)*f", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{h}\\text{%}$ of $\\var{j}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(h/100)*j", "minValue": "(h/100)*j", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{k}\\text{%}$ of $\\var{l}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(k/100)*l", "minValue": "(k/100)*l", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>What is $\\var{m}\\text{%}$ of $\\var{n}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(m/100)*n", "minValue": "(m/100)*n", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>These questions are asking you to use a non-calculator method to work out a percentage amount of a value.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(0..100#5 except 0) //a multiple of 5%", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(0..100#5 except 0) //a multiple of 5%", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(100..1000#20) //a multiple of 20 betwen 100 and 1000", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(100..1000#20) //a multiple of 20 betwen 100 and 1000", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(0..100#5 except 0) //a multiple of 5%", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(100..1000#20) //a multiple of 20 betwen 100 and 1000", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(1..99) //select a random percentage", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(1..99) //select a random percentage", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(100..1000#20)", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(1..99) //select a random percentage", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(100..1000#20)", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random(100..1000)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"notes": "<p>They are to be done without a calculator, and increase in difficulty.</p>", "description": "<p>These questions are asking you to use a non-calculator method to work out a percentage amount of a value.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Percentages- Percentage Increases and Decreases", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": 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"variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Subtract your previous answer from $\\var{h}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-j/100)*h", "minValue": "(1-j/100)*h", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "2", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>Increase&nbsp;$\\var{k}$ by $\\var{l}\\text{%}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1+l/100)*k", "minValue": "(1+l/100)*k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out $\\var{l}\\text{%}$ of $\\var{k}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(l/100)*k", "minValue": "(l/100)*k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Add&nbsp;your previous answer to&nbsp;$\\var{k}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-l/100)*k", "minValue": "(1-l/100)*k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "2", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": 0, "prompt": "<p>Decrease $\\var{m}$ by $\\var{n}\\text{%}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-n/100)*m", "minValue": "(1-n/100)*m", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out $\\var{n}\\text{%}$ of $\\var{m}$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(n/100)*m", "minValue": "(n/100)*m", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Subtract your previous answer from $\\var{m}$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(1-n/100)*m", "minValue": "(1-n/100)*m", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "2", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Here you need to work out percentage increases and decreases using non-calculator methods.</p>\n<p>If you get stuck you can select \"Show Steps\" which will take you through how to answer the question.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(100..1000#20)  //random number between 100 and 1000 that is divisible by 20", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(100..1000#20)  //random number between 100 and 1000 that is divisible by 20", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(0..100#5) //A random percentage between 0 and 100 that is divisble by 5", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(0..100#5) //A random percentage between 0 and 100 that is divisble by 5", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(0..100#5) //A random percentage between 0 and 100 that is divisble by 5", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(100..1000#20)  //random number between 100 and 1000 that is divisible by 20", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(100..1000#20)  //random number between 100 and 1000 that is divisible by 20", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(100..1000#10) // random number between 100 and 1000 that is divisble by 10", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(0..100#5) //A random percentage between 0 and 100 that is divisble by 5", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(100..1000#10) // random number between 100 and 1000 that is divisble by 10", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(0..100) //random number between 1 and 100", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random(0..100) //random number between 1 and 100", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"notes": "", "description": "<p>Non-calculator percentage increase and decrease calculations.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Percentages - One Amount as a Percentage of Another", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "tags": [], "advice": "<p>Write it as a fraction - the small amount over the larger amount.</p>\n<p>If the denominator is not a factor of 100 then cancel the fraction down till it is a factor of 100.</p>\n<p>Once the denominator is a factor of 100 multiply the fraction up so that the denominator is 100.</p>\n<p>The percentage is the value of the numerator.</p>", "rulesets": {}, "parts": [{"stepsPenalty": "2", "prompt": "<p>What percentage of $\\var{a}$ is $\\var{b}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(b/a)*100", "minValue": "(b/a)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by writing it as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "b/a", "minValue": "b/a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the fraction up so that the denominator is equal to 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(b/a)*((100/a)/(100/a))", "minValue": "(b/a)*((100/a)/(100/a))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The value of the numerator is the percentage.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(b/a)*100", "minValue": "(b/a)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>What percentage of $\\var{c}$ is $\\var{d}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(d/c)*100", "minValue": "(d/c)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by writing it as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "d/c", "minValue": "d/c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the fraction up so that the denominator is equal to 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(d/c)*((100/c)/(100/c))", "minValue": "(d/c)*((100/c)/(100/c))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The value of the numerator is the percentage.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(d/c)*100", "minValue": "(d/c)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{j}$ is what percengage of $\\var{h}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(j/h)*100", "minValue": "(j/h)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by writing it as a fraction.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "j/h", "minValue": "j/h", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply the fraction up so that the denominator is equal to 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(j/h)*((100/h)/(100/h))", "minValue": "(j/h)*((100/h)/(100/h))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The value of the numerator is the percentage.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(j/h)*100", "minValue": "(j/h)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "3", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{f}$ is what percentage of $\\var{g}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(f/g)*100", "minValue": "(f/g)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by making it a fraction</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "f/g", "minValue": "f/g", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Then cancel the fraction&nbsp;down so that the denominator is a factor of 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(f/4)/(g/4)", "minValue": "(f/4)/(g/4)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply up the fraction so that the denominator is 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(f*(100/g))/(g*(100/g))", "minValue": "(f*(100/g))/(g*(100/g))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The percentage is the value of the numerator.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(f/g)*100", "minValue": "(f/g)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{k}$ is what percentage of $\\var{l}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(k/l)*100", "minValue": "(k/l)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by making it a fraction</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "k/l", "minValue": "k/l", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Then cancel the fraction&nbsp;down so that the denominator is a factor of 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(k/3)/(l/3)", "minValue": "(k/3)/(l/3)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply up the fraction so that the denominator is 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(k*(100/l))/(l*(100/l))", "minValue": "(k*(100/l))/(l*(100/l))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The percentage is the value of the numerator.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(k/l)*100", "minValue": "(k/l)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "2", "prompt": "<p>$\\var{m}$ is what percentage of $\\var{n}$?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(m/n)*100", "minValue": "(m/n)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Start by making it a fraction</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "m/n", "minValue": "m/n", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Then cancel the fraction&nbsp;down so that the denominator is a factor of 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(m/7)/(n/7)", "minValue": "(m/7)/(n/7)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Multiply up the fraction so that the denominator is 100.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(m*(100/n))/(m*(100/n))", "minValue": "(m*(100/n))/(n*(100/n))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>The percentage is the value of the numerator.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(m/n)*100", "minValue": "(m/n)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>For each of the following questions work out one value as a percentage of the other. You are&nbsp;expected to do this without the help of a calculator.</p>\n<p>You can click reveal steps to show you how to solve each question. You will lose marks for revealing steps.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random([5,10,20,25,50,100]) //random value that is a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random([5,10,20,25,50,100]) //random value that is a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..a-1) //random number that is less than the value of a", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..c-1) //random number that is less than the value of c", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(20,40,80) //random number from list", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(4..g-1#4) // a random number less than f that is divisible by 4", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random([5,10,20,25,50,100,200]) //random value that is a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(3..l-1#3)  //random number less than l that is divisible by 3", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(1..h-1) //random number that is less than the value of h", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(7..n-1#7)  //random number that is divisble by 7 and less than n", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(15,30,60,75,150)  //a random number that divides by 3 to give a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random(35,70,140,175,350)  //random number that when divided by 7 gives a factor of 100", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"notes": "", "description": "<p>This question asks you to work out one value as a percentage of another. &nbsp;You are expected to do these without the help of a calculator.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Percentages - Non-Calculator Worded Questions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "aa", "bb", "cc", "dd", "ee", "ff", "gg", "hh", "ii", "jj"], "tags": [], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "4", "prompt": "<p>The monthly budget for front of house is $\\var{a}$. &nbsp;If $\\var{b}\\text{%}$ is spent on flowers, how much is spent on flowers?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(b/100)*a", "minValue": "(b/100)*a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>First find 10%, 5% and 1%.</p>\n<p>Add together what you need to make up the required percentage.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>Out of $\\var{c}$ people $\\var{d}\\text{%}$ have have brown hair. &nbsp;How many people do not have brown hair?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((100-d)/100)*c", "minValue": "((100-d)/100)*c", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out what percentage of people do not have brown hair.</p>\n<p>Work out 50%, 25%, 10%, 5% and 1%.</p>\n<p>Combine together to get the correct percentage.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A jumper is priced at &pound;$\\var{f}$ in a sale there there is $\\var{g}\\text{%}$ off. &nbsp;What is the sale price of the jumper?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "f*(1-(g/100))", "minValue": "f*(1-(g/100))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out 50%, 25%, 10%, 5%, 1%.</p>\n<p>Find out the amount of money to be removed.</p>\n<p>Subtract to find the sale price.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>Pupils spend $\\var{l}$ hours a week in lessons. $\\var{m}$ hours a week are allocated to English, what percentage of the lessons&nbsp;is this?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(m/l)*100", "minValue": "(m/l)*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Write it as a fraction of&nbsp;what you want over the total amount.</p>\n<p>If you need to: cancel the fraction down so the denominator goes into 100.</p>\n<p>Multiply your fraction up so that the denominator is equal to 100.</p>\n<p>The percentage is the value of the numerator.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A television is reduced in price from $\\var{cc}$ by $\\var{dd}\\text{%}$. &nbsp;What is the new price of the television?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(cc)*(1-((dd)/100))", "minValue": "(cc)*(1-((dd)/100))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out the quick percentages.</p>\n<p>Combine to give the amount of the decrease.</p>\n<p>Take this value from the starting value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A market researcher wants to take a sample of $\\var{v}\\text{%}$ out of a group of applicants. &nbsp;If there are $\\var{w}$ in the group what is the minimum number of people they need in the sample?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "ceil((v/100)*w)", "minValue": "ceil((v/100)*w)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out the quick percentages.</p>\n<p>Combine till you have the percentage amount.</p>\n<p>Round up to the nearest person (you cannot have point something of a person).</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>In a small village $\\var{gg}$ people turn up to vote in the local election. &nbsp;If there are $\\var{hh}$ residents in the village what percentage of the village turned up to vote?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((gg)/(hh))*100", "minValue": "((gg)/(hh))*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Make a fraction of those that turned up over total number of people.</p>\n<p>If you need to: cancel down the fraction of that the denominator goes into 100.</p>\n<p>Multiplty up the fraction so that the denominator is equal to 100.</p>\n<p>The percentage is the value of the numerator.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A theatre sells ice ceam during the intervals of its show. &nbsp;Last night $\\var{x}$ ice creams were sold of which $\\var{y}\\text{%}$ of them were strawberry flavour. &nbsp;How many strawberry ice creams were sold?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(y/100)*x", "minValue": "(y/100)*x", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out the quick percentages.</p>\n<p>Combine to give the total number of strawberry ice creams sold.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>House prices are expected to increase next year by $\\var{z}\\text{%}$. &nbsp;If your house is currently worth &pound;$\\var{aa}$ how much will it be worth this time next year?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(aa)*(1+(z/100))", "minValue": "(aa)*(1+(z/100))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out the quick percentages.</p>\n<p>Combine to work out the amount to increase it by.</p>\n<p>Add to the starting value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A pupil scored $\\var{n}\\text{%}$ in a test. &nbsp;Later they scored $\\var{o}$ out of $\\var{p}$ in a second test. &nbsp;What is the difference in the percentage scores?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "abs(n-((o/p)*100))", "minValue": "abs(n-((o/p)*100))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Take the second score and turn it into a fraction.</p>\n<p>Cancel down if needed so the denominator divides into 100.</p>\n<p>Multiply up so that the denominator is 100.</p>\n<p>The numerator is the percentage value.</p>\n<p>Work out the difference between the two percentages.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>If there are currently 7 billion people on the planet and the population is expected to rise by $\\var{bb}\\text{%}$ over the next year, how many people will there be next year?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(7000000000)*(1+((bb)/100))", "minValue": "(7000000000)*(1+((bb)/100))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out the quick percentages.</p>\n<p>Combine to give the amount of the increase.</p>\n<p>Add to the starting value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>A resturant has two specials on its menu. &nbsp;Last night it sold $\\var{ee}$ specials in total of which $\\var{ff}$ were steak. &nbsp;What percentage of the specials were steak?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((ff)/(ee))*100", "minValue": "((ff)/(ee))*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Write as a fraction of steaks over total amount of specials.</p>\n<p>If you need to: cancel down so that 100 can be divided by the denominator.</p>\n<p>Mutilply the fraction up so that the denominator is 100.</p>\n<p>The percentage is the value of the numerator.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>Red, green and yellow balls are in a bag; of which $\\var{h}\\text{%}$ of the balls are red and&nbsp;$\\var{j}\\text{%}$ green. &nbsp;If there are $\\var{k}$ balls in the bag how many are yellow?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((100-h-j)/100)*k", "minValue": "((100-h-j)/100)*k", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Work out what percentage of the balls are yellow.</p>\n<p>Find the quick percentages.</p>\n<p>Combine to give the number of yellow balls.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "4", "prompt": "<p>The area of a circle is $\\var{ii}\\pi$. If a sector is cut out of the circle with area $\\var{jj}\\pi$ what percentage of the circle is the sector?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((jj)/(ii))*100", "minValue": "((jj)/(ii))*100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "steps": [{"prompt": "<p>Write a fraction of the area of the sector over the total area.</p>\n<p>If you need to: cancel the fraction down so that the denominator goes into 100.</p>\n<p>Multiply up so that the denominator is equal to 100.</p>\n<p>The percentage is the value of the numerator.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": "4", "showCorrectAnswer": false, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Each of the questions below check your understanding of the methods in the previous questions.</p>\n<p>You should be able to do these without a calculator.</p>\n<p>You can click show steps but you will lose all your marks for doing so.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"aa": {"definition": "random(80000..350000#1000)  // random price for house", "templateType": "anything", "group": "Ungrouped variables", "name": "aa", "description": ""}, "jj": {"definition": "random(6..ii-1#6) // random area of sector of circle", "templateType": "anything", "group": "Ungrouped variables", "name": "jj", "description": ""}, "cc": {"definition": "random(240..450#5) // random price of television", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "ii": {"definition": "random(12..144#12 except 84) // random number for total area of circle", "templateType": "anything", "group": "Ungrouped variables", "name": "ii", "description": ""}, "ee": {"definition": "random([5,10,20,25,50,200,100]) // random number of steak sales", "templateType": "anything", "group": "Ungrouped variables", "name": "ee", "description": ""}, "bb": {"definition": "random(1..10) // random percentage increase of population", "templateType": "anything", "group": "Ungrouped variables", "name": "bb", "description": ""}, "dd": {"definition": "random(5..30)  // random percentage decrease in cost of TV", "templateType": "anything", "group": "Ungrouped variables", "name": "dd", "description": ""}, "hh": {"definition": "random(300..1000#50)  // random number of residents in village", "templateType": "anything", "group": "Ungrouped variables", "name": "hh", "description": ""}, "ff": {"definition": "random(1..ee-1)  // random number of specials that were steak", "templateType": "anything", "group": "Ungrouped variables", "name": "ff", "description": ""}, "a": {"definition": "random(1000..15000#1000)  // random number of thousands between 1000 and 10000 for front of house takings", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "gg": {"definition": "random(0..hh-1#5) // random number of people who turned up to vote", "templateType": "anything", "group": "Ungrouped variables", "name": "gg", "description": ""}, "c": {"definition": "random(100..1000#50) // random number of students between 100 and 1000", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(5..15)  // random percentage of 5 to 15 spent on flowers", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(30..60) // random percentage between 30 and 60 of those that passed", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(5..35) // random percentage off the jumper", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(35..65#5) // random price of jumper", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(10..40) // random percentage less than 40 for red balls", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(100..50#50) // random number divisible by 50 total number of balls", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(10..40) // random percentage less than 40 for green balls", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random([5,6,8,10,12])  // random number of hours allocated to English", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random([20,25])  // random number from list for number of hours in lessons", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "o": {"definition": "random(18..p-1#6)  // random number for score", "templateType": "anything", "group": "Ungrouped variables", "name": "o", "description": ""}, "n": {"definition": "random(60..80)  // random percentage test score", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "random([0,1]) // random numbr of hours for a test to take", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random([20,24,25,30,50,60,75,120,150])  // random total of marks in a test", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(10..30#5)  // random percentage of extra time granted in the test", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(10..50#10) // random number of minutes for a test to take", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(10..50#10)  // random starting time for test - minutes", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(9,10)  // random starting time for test - hour", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "random(60..600#10)  // random number of people in the group", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "random(30..45)  // random percentage for sample size", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "y": {"definition": "random(20..80)  // random percentage of ice creams that were strawberry", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(20..300#10) // random number of ice creams sold", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "z": {"definition": "random(1..12) // random percentage increase for house prices", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}}, "metadata": {"notes": "", "description": "<p>These are worded questions on percentages. &nbsp;They can be done without a calculator.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Bonny Barkus", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/775/"}], "extensions": [], "custom_part_types": [], "resources": []}