Without using a calculator, evaluate each of the following:
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", "minValue": "a", "maxValue": "a", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "b)", "marks": "0.5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "$\\var{d} - (\\var{f})$
", "minValue": "d-f", "maxValue": "d-f", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "c)", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "$\\frac{\\var{a1}}{\\var{b1}}+\\frac{\\var{a2}}{\\var{b2}}$
", "minValue": "(a1*b2+a2*b1)/(b1*b2)", "maxValue": "(a1*b2+a2*b1)/(b1*b2)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "d)", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "$(\\var{s1} \\frac{\\var{r1}}{\\var{r2}}+\\var{s2}\\frac{\\var{t1}}{\\var{t2}}) \\div \\frac{\\var{p1}}{\\var{p2}}$ [Please give your answer as a fraction]
", "minValue": "(s1*r2*t2*p2+sign(s1)*r1*t2*p2+s2*t2*r2*p2+sign(s2)*t1*r2*p2)/(p1*r2*t2)", "maxValue": "(s1*r2*t2*p2+sign(s1)*r1*t2*p2+s2*t2*r2*p2+sign(s2)*t1*r2*p2)/(p1*r2*t2)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "70", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}]}, {"name": "Percentages 2020", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "David Goulding", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2365/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "For each of the following questions, round your answer to given number of decimal places or significant figures as requested in the question.
", "advice": "", "rulesets": {}, "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(10 .. 55#5)", "description": "", "templateType": "randrange"}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(2 .. 6#0.5)", "description": "", "templateType": "randrange"}, "p1": {"name": "p1", "group": "Ungrouped variables", "definition": "random(10..30)", "description": "", "templateType": "anything"}, "p2": {"name": "p2", "group": "Ungrouped variables", "definition": "random(110..195)", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(24000 .. 30000#500)", "description": "", "templateType": "randrange"}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(49001..50000)", "description": "", "templateType": "anything"}, "ci": {"name": "ci", "group": "Ungrouped variables", "definition": "random(300..370)", "description": "", "templateType": "anything"}, "t1": {"name": "t1", "group": "Ungrouped variables", "definition": "random(3..7)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y", "p1", "p2", "b1", "s1", "ci", "t1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "Part a)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Express $\\var{x}$ minutes as a percentage of $\\var{y}$ hours. Round your answer to 2 decimal places. Note: you should not enter the '%' sign as part of your answer.
", "minValue": "(x/(y*60))*100", "maxValue": "(x/(y*60))*100", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "Express $\\var{x}$ minutes as a fraction of $\\var{y}$ hours - write the fraction in its simplest form.
", "minValue": "x/(y*60)", "maxValue": "x/(y*60)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "70", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Find $\\var{p1}$% of $\\var{p2}$. Round the result to first decimal place.
", "minValue": "(p2/100)*p1", "maxValue": "(p2/100)*p1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "In January 2021, a trader bought Bitcoin for €$\\var{b1}$ and sold it in April for €$\\var{s1}$. Calculate the percentage profit they made on the transaction. Round the result to 4th significant figure. Note: you should not enter the '%' sign as part of your answer.
", "minValue": "((s1-b1)/(b1))*100", "maxValue": "((s1-b1)/(b1))*100", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "4", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "An insurance company charges a customer €$\\var{ci}$ for their car insurance. The price includes government insurance premium tax of $\\var{t1}$%. Calculate the cost before the tax was added. Round the value to the nearest cent.
", "minValue": "(ci/(100+t1))*100", "maxValue": "(ci/(100+t1))*100", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Ratios and proportions - A", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "David Goulding", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2365/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "Abigail went on holiday to Perth, Australia in January 2020.
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", "minValue": "s1/a1", "maxValue": "s1/a1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "b)", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "After returning from her holiday, she exchanged her remaining Australian dollars at the bank and received €$\\var{r1}$. If the exchange rate when she got back was €1 = AU\\$ $\\var{t2}$, how many AU\\$ did she return with? Round your answer to the nearest dollar. Note: you should not enter the '\\$' symbol in your answer.
", "minValue": "r1*t2", "maxValue": "r1*t2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}]}, {"name": "Ratios and proportions - B", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "David Goulding", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2365/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "A piña colada cocktail recipe contains $\\var{dr1}$, $\\var{dr2}$, $\\var{dr3}$ and $\\var{dr4}$ in the ratio $2 \\frac{1}{2}:1 \\frac{1}{2}:1 \\frac{1}{2}:\\frac{1}{2}$.
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\n\n$\\var{dr2}$: [[0]]
\n\n\n$\\var{dr3}$: [[1]]
\n\n$\\var{dr4}$: [[2]]
\n", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "1.5*d1/2.5", "maxValue": "1.5*d1/2.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "1.5*d1/2.5", "maxValue": "1.5*d1/2.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "0.5*d1/2.5", "maxValue": "0.5*d1/2.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}]}, {"name": "College arrivals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "David Goulding", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2365/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "$\\var{p1}$% of MTU students use public transportation. Of those who use public transportation, $\\var{p2}$% arrive to college on time. Of those who do not use public transportation, $\\var{p3}$% arrive on time.
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