// Numbas version: finer_feedback_settings
{"name": "Error & Approximation", "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>Error, percentage error and approximation.</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "None specified"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Q1 (Percentage Error)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["material", "est", "lent", "ans1", "name1", "est1", "est2", "cost", "ans2", "att", "ans3", "game", "item"], "tags": ["rebelmaths"], "advice": "<p>Part 1:</p>\n<p>Percentage error:</p>\n<p>$abs(\\frac{\\var{est} - \\var{lent}}{\\var{lent}}) \\times 100 = \\var{ans1}$%</p>\n<p>Part 2:</p>\n<p>Percentage error:</p>\n<p>$abs(\\frac{\\var{est1} - \\var{cost}}{\\var{cost}}) \\times 100 = \\var{ans2}$%</p>\n<p>Part 3:</p>\n<p>Percentage error:</p>\n<p>$abs(\\frac{\\var{est2} - \\var{att}}{\\var{att}}) \\times 100 = \\var{ans3}$%</p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>The length of a $\\var{material}$ bar&nbsp;was estimated to be $\\var{est}$ cm. If the true length was $\\var{lent}$ cm, calculate the percentage error.</p>\n<p>[[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "1", "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>First find out how wrong the guess was (the error). This is the difference between the guess and the true value. We always use the positive number.</p>\n<p>Find what percentage this is of the true value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<p>The&nbsp;estimate to repair&nbsp;a&nbsp;$\\var{item}$ was $&euro;\\var{est1}$. If the final cost was $&euro;\\var{cost}$, calculate the percentage error.</p>\n<p>[[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "1", "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>The&nbsp;attendance&nbsp;at a&nbsp;$\\var{game}$ match was estimated to be $&euro;\\var{est2}$ people. If the actual attendance was $&euro;\\var{att}$, calculate the percentage error.</p>\n<p>[[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "1", "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>&nbsp;<em>Calculate the following&nbsp;correct to one decimal place:</em></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"material": {"definition": "random('copper','brass','metal','steel')", "templateType": "anything", "group": "Ungrouped variables", "name": "material", "description": ""}, "lent": {"definition": "random((est-8)..(est+8) except[est,(est-1),est-2,est-3,(est+1),(est+2),(est+3)])", "templateType": "anything", "group": "Ungrouped variables", "name": "lent", "description": ""}, "ans1": {"definition": "(abs(est-lent)/lent)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "(abs(est1 - cost)/ cost)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "(abs(est2 - att)/ att)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "att": {"definition": "random(est2-500..est2+1000#20 except[est2,est2-20,est2-40,est2-60,est2-80,est2+20,est2+40,est2+60,est2+80,est2+100,est2-100])", "templateType": "anything", "group": "Ungrouped variables", "name": "att", "description": ""}, "item": {"definition": "random('car','motorbike','computer','van')", "templateType": "anything", "group": "Ungrouped variables", "name": "item", "description": ""}, "game": {"definition": "random('tennis','football','soccer','hurling')", "templateType": "anything", "group": "Ungrouped variables", "name": "game", "description": ""}, "cost": {"definition": "random(est1-50..est1+50#10 except[est1,est1-10,est1+10])", "templateType": "anything", "group": "Ungrouped variables", "name": "cost", "description": ""}, "est": {"definition": "random(30..70#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "est", "description": ""}, "est2": {"definition": "random(5000..10000#500)", "templateType": "anything", "group": "Ungrouped variables", "name": "est2", "description": ""}, "name1": {"definition": "random('Susan','Rose','Lisa','Karen','Kate','Vicky')", "templateType": "anything", "group": "Ungrouped variables", "name": "name1", "description": ""}, "est1": {"definition": "random(500..700#50)", "templateType": "anything", "group": "Ungrouped variables", "name": "est1", "description": ""}}, "metadata": {"description": "<p>Percentage Error</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q2 (Percentage Error with adding and Subtracting)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["num1", "num2", "num3", "ans", "num1a", "num2a", "num3a", "ans1"], "tags": ["rebelmaths"], "advice": "<p>part 1</p>\n<p>$ABS(\\frac{(\\var{num3} - (\\var{num1} + \\var{num2}))}{(\\var{num1} + \\var{num2})}) \\times 100 = \\var{ans}$</p>\n<p>part 2</p>\n<p>$ABS(\\frac{(\\var{num3a} - (\\var{num1a} - \\var{num2a}))}{(\\var{num1a} - \\var{num2a})}) \\times 100 = \\var{ans1}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>The answer to $\\var{num1} + \\var{num2}$ was given as $\\var{num3}$.</p>\n<p>What was the percentage error?</p>\n<p>[[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans}", "minValue": "{ans}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>You need to find accurte answer. Work your division up to 5&nbsp;decimals places to be sure you have the accuracy required.</p>\n<p>Work this video to recap how to divide decimals by decimals.</p>\n<p><a href=\"http://www.virtualnerd.com/pre-algebra/rational-numbers/decimal-operations/decimal-examples/divide-decimals-example\">Video</a></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<p>The answer to $\\var{num1a} - \\var{num2a}$ was given as $\\var{num3a}$.</p>\n<p>What was the percentage error?</p>\n<p>[[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following&nbsp;correct to two&nbsp;decimal places.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"num2a": {"definition": "random(6.1..8.9#0.01 except 7 except 8)", "templateType": "anything", "group": "Ungrouped variables", "name": "num2a", "description": ""}, "num1": {"definition": "random(2.8..4#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "random(1.8..3.5#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "precround(num1,1)+ precround(num2,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "ans1": {"definition": "(abs(num3a-(num1a-num2a))/(num1a-num2a))*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "num1a": {"definition": "random(11.1..14.9#0.01 except 12 except 13 except 14)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1a", "description": ""}, "num3a": {"definition": "precround(num1a,1)- precround(num2a,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3a", "description": ""}, "ans": {"definition": "(abs(num3-(num1+num2))/(num1+num2))*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}}, "metadata": {"description": "<p>Percentage Error</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q3 (Percentage error in rounding to 1 significant figure)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["num1", "num2", "num3", "ans", "num4"], "tags": ["rebelmaths"], "advice": "<p>$ABS(\\frac{(\\var{num4} - (\\frac{\\var{num1}&nbsp;\\times \\var{num2}}{\\var{num3}}))}{(\\frac{\\var{num1}&nbsp;\\times \\var{num2}}{\\var{num3}})}) \\times 100 = \\var{ans}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Calculate&nbsp;the percentage error, correct to one decimal place?</p>\n<p>[[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "1", "maxValue": "{ans}", "minValue": "{ans}", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>You need to find an accurate answer. Work your division up to 4 decimal places to be sure you have &nbsp;the accuracy required. Then figure out how wrong the guess was. Find the absolute value ( or positive value) of this error and find out what percentage that is of the correct value.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "<p>A person used $\\var{num4}$ as an approximation for&nbsp;$\\frac{\\var{num1}&nbsp;\\times \\var{num2}}{\\var{num3}}$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"num4": {"definition": "(precround(num1,0)* precround(num2,0))/ precround(num3,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num4", "description": ""}, "num3": {"definition": "random(0.5..1.5#0.01 except 1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "num1": {"definition": "random(84.01..90.99#0.01 except[84.5,85,85.5,85,86.5,87,87.5,88,88.5,89,89.5])", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "random(2.01..3.49#0.01 except 2.5 except 3 except 3.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "ans": {"definition": "(abs(num4-((num1*num2)/num3))/((num1*num2)/num3))*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}}, "metadata": {"description": "<p>Perventage Error</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q4 (Percentage error when estimating total cost of shop items)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["place", "num", "name", "ans1", "name1", "est1", "est2", "ans2", "price"], "tags": ["rebelmaths"], "advice": "<p>Part 1:</p>\n<p>$\\var{name}$ ignores the cent part and estimates:</p>\n<p>$ Estimate = &euro;\\var{est1}$</p>\n<p>Percentage error:</p>\n<p>$abs(\\frac{\\var{est1} - \\var{price}}{\\var{price}}) \\times 100 = \\var{ans1}$%</p>\n<p>Part 2:</p>\n<p>$\\var{name1}$&nbsp;rounds to the nearest euro&nbsp;and estimates:</p>\n<p>$ Estimate = &euro; \\var{est2}$</p>\n<p>Percentage error:</p>\n<p>$abs(\\frac{\\var{est2} - \\var{price}}{\\var{price}}) \\times 100 = \\var{ans2}$%</p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>$\\var{name}$ estimates the total cost by ignoring the cent part in the cost of each item. Calculate the percentage error in her&nbsp;estimate.</p>\n<p>[[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "1", "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>You need to figure out both the guess and the correct value</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"prompt": "<p>$\\var{name1}$ estimates the total cost by rounding the cost of each item to the nearest euro. Calculate the percentage error in his estimate.</p>\n<p>[[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "1", "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Four items in a $\\var{place}$ cost &euro;{dpformat(num[0],2)},&nbsp;&euro;{dpformat(num[1],2)}, &euro;{dpformat(num[2],2)} and &euro;{dpformat(num[3],2)}.&nbsp;</p>\n<p><em>Calculate correct to one decimal place:</em></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"name": {"definition": "random('Robert','John','Liam','Karl','Victor')", "templateType": "anything", "group": "Ungrouped variables", "name": "name", "description": ""}, "ans1": {"definition": "(abs(est1-price)/price)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "price": {"definition": "num[0]+num[1]+num[2]+num[3]", "templateType": "anything", "group": "Ungrouped variables", "name": "price", "description": ""}, "num": {"definition": "shuffle(3.5..14.5#0.05)[0..4]", "templateType": "anything", "group": "Ungrouped variables", "name": "num", "description": ""}, "place": {"definition": "random('shop','supermarket','corner shop')", "templateType": "anything", "group": "Ungrouped variables", "name": "place", "description": ""}, "est1": {"definition": "floor(num[0])+floor(num[1])+floor(num[2])+floor(num[3])", "templateType": "anything", "group": "Ungrouped variables", "name": "est1", "description": ""}, "est2": {"definition": "precround(num[0],0)+precround(num[1],0)+precround(num[2],0)+precround(num[3],0)", "templateType": "anything", "group": "Ungrouped variables", "name": "est2", "description": ""}, "name1": {"definition": "random('Susan','Rose','Lisa','Karen','Kate','Vicky')", "templateType": "anything", "group": "Ungrouped variables", "name": "name1", "description": ""}, "ans2": {"definition": "(abs(est2-price)/price)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}}, "metadata": {"description": "<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q5 percentage error", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["num", "ans2", "ans1", "ans3"], "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>Part 1:</p>\n<p>Exact relationship formula:</p>\n<p>$((\\frac{9}{5}) \\times \\var{num}) + 32 = \\var{ans1}$degrees</p>\n<p>Part 2:</p>\n<p>Approximate relationship formula::</p>\n<p>$(\\var{num} + 15) \\times 2= \\var{ans2}$degrees</p>\n<p>Part 3:</p>\n<p>Percentage error:</p>\n<p>$abs(\\frac{\\var{ans2} - \\var{ans1}}{\\var{ans1}}) \\times 100 = \\var{ans3}$%</p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>Find the value of F when C is $\\var{num}$ degrees using the exact relationship formula.</p>\n<p>[[0]]degrees</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Find the value of F when C is $\\var{num}$ degrees using the approximate relationship formula.</p>\n<p>[[0]]degrees</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": false, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Calculate the percentage error in using the approximate relationship formula, correct to one decimal place.</p>\n<p>[[0]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "strictPrecision": false, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>The exact relationship between Celsius and Fahrenheit is: <strong>$F = \\frac{9}{5}C + 32$</strong>. An approximate relationship between&nbsp;Celsius and Fahrenheit&nbsp;is given by the follow rule:</p>\n<p><strong>To find F, add 15 to C and double your answer.</strong></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "(num*(9/5))+32", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "(num+15)*2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "num": {"definition": "random(10..35#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "num", "description": ""}, "ans3": {"definition": "(abs(ans2 - ans1)/ ans1)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}}, "metadata": {"description": "<p>(Calculating estimate and actual value of temperature using given formulas, and hence finding the percentage error)</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q6 (Calculate the minimum and maximum approximations of an estimate)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["est", "shop", "ans1", "num", "per", "ans2"], "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>First calculate $\\var{num}$% of the estimate $\\var{est}$</p>\n<p>$\\frac{\\var{num}}{100} \\times \\var{est} = &euro;\\var{per}$</p>\n<p>Part 1:</p>\n<p>Cheapest possible cost</p>\n<p>$&euro;\\var{est} - &euro;\\var{per} = &euro;\\var{ans1}$</p>\n<p>Part 2:</p>\n<p>Dearest possible cost</p>\n<p>$&euro;\\var{est}&nbsp;+ &euro;\\var{per} = &euro;\\var{ans2}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Calculate the cheapest and dearest possible costs, if an estimate of $&euro;\\var{est}$ is given for a particular repair.</p>\n<p>Cheapest:&nbsp;&nbsp;&nbsp; &euro;[[0]]</p>\n<p>Dearest:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &euro;[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Find the percentage of the estimate. The actual cost must be in the range $\\var{est}$ +/-&nbsp;$\\var{num}$%.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": true, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>$\\var{shop}$&nbsp;guarantees that the actual cost of repairs will not be more than $\\var{num}$% different from any estimate.</p>\n<p><em>Calculate correct to two decimal place.</em></p>\n<p><strong>&nbsp;</strong></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"shop": {"definition": "random('A garage','A PC repair shop','A Phone-shop',' An eletronics-shop','An engineering shop')", "templateType": "anything", "group": "Ungrouped variables", "name": "shop", "description": ""}, "est": {"definition": "random(300..500#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "est", "description": ""}, "ans1": {"definition": "est-per", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "est+per", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "per": {"definition": "(est*num)/100", "templateType": "anything", "group": "Ungrouped variables", "name": "per", "description": ""}, "num": {"definition": "random(3..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "num", "description": ""}}, "metadata": {"description": "<p><strong></strong>(Calculate the minimum and maximum approximations of an estimate)</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q7 (Calculate the estimate, actual and from these the percentage error)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {"tens": {"definition": "random(35..80#0.01)", "type": "number", "language": "jme", "parameters": []}, "hun": {"definition": "random(301..599)", "type": "number", "language": "jme", "parameters": []}, "sin": {"definition": "random(3..8#0.01)", "type": "number", "language": "jme", "parameters": []}, "hun1": {"definition": "random(400..600)", "type": "number", "language": "jme", "parameters": []}}, "ungrouped_variables": ["num1", "num2", "num3", "num4", "num5", "num7", "num6", "num8", "num9", "num10", "num11", "num12", "num13", "num14", "num15", "num16", "num17", "num18", "num19", "num20", "num21", "ans11", "ans21", "ans31", "ans41", "ans51", "ans61", "ans12", "ans22", "ans32", "ans42", "ans52", "ans62", "ans13", "ans23", "ans33", "ans43", "ans53", "ans63"], "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>When rounding off a number to one significant place, round to the left most figure of the number, like below;</p>\n<p>$367 = 400$</p>\n<p>$38 = 40$</p>\n<p>$71 = 70$</p>\n<p>$3.79 = 4$</p>\n<p>$65.13 = 70$</p>\n<p>$215 = 200$</p>\n<p></p>\n<p><em>Part 1:</em></p>\n<p>Estimate value with each number rounded to one significant place:</p>\n<p>$\\frac{(\\var{num1}&nbsp;\\times \\var{num2})}{(\\var{num3} \\times \\var{num4})}$&nbsp;</p>\n<p>Round numbers to one significant number:</p>\n<p>$\\var{num1} = ${siground(num1,1)}</p>\n<p>$\\var{num2} = ${siground(num2,1)}</p>\n<p>$\\var{num3} = ${siground(num3,1)}</p>\n<p>$\\var{num4} = ${siground(num4,1)}</p>\n<p>Answer:</p>\n<p>$= \\var{ans11}$</p>\n<p></p>\n<p><em>Part 2:</em></p>\n<p>Actual value:</p>\n<p>$\\frac{(\\var{num1} \\times \\var{num2})}{(\\var{num3} \\times \\var{num4})} = \\var{ans12}$</p>\n<p></p>\n<p><em>Part 3:</em></p>\n<p>Percentage error:</p>\n<p>$abs(\\frac{\\var{ans12} - \\var{ans11}}{\\var{ans11}}) \\times 100 = \\var{ans13}$%</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\frac{\\var{num1} \\times \\var{num2}}{\\var{num3} \\times \\var{num4}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;&nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}", "minValue": "{ans11}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}", "minValue": "{ans12}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans13}+1", "strictPrecision": false, "minValue": "{ans13}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num5}&nbsp;+ \\var{num6}}{\\var{num7}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;&nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans23}+1", "strictPrecision": false, "minValue": "{ans23}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num8} \\times \\var{num9}}{\\var{num10}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans33}+1", "strictPrecision": false, "minValue": "{ans33}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num11}&nbsp;- \\var{num12}}{\\var{num13}&nbsp;+ \\var{num14}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans41}", "minValue": "{ans41}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans42}", "minValue": "{ans42}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans43}+1", "strictPrecision": false, "minValue": "{ans43}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num15}&nbsp;- \\var{num16}}{\\var{num17}&nbsp;+ \\var{num18}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans51}", "minValue": "{ans51}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans52}", "minValue": "{ans52}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans53}+1", "strictPrecision": false, "minValue": "{ans53}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num19}^2 \\times \\var{num20}}{\\var{num21}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans61}", "minValue": "{ans61}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans62}", "minValue": "{ans62}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans63}+1", "strictPrecision": false, "minValue": "{ans63}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>By rounding each number correct to one significant figure, estimate the answer to each of the problems given below. Then use your calculator to accurately evaluate each of them.</p>\n<p>Calculate the percentage error in using the estimate, correct to one decimal place.</p>\n<p><strong>&nbsp;</strong></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"num4": {"definition": "random(35..80 except num3)", "templateType": "anything", "group": "Ungrouped variables", "name": "num4", "description": ""}, "num5": {"definition": "random(120..140#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "num5", "description": ""}, "num6": {"definition": "random(20..30#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "num6", "description": ""}, "num7": {"definition": "tens()", "templateType": "anything", "group": "Ungrouped variables", "name": "num7", "description": ""}, "num1": {"definition": "hun()", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "hun1() ", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "precround(tens(),0)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "num8": {"definition": "precround(tens(),1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num8", "description": ""}, "num9": {"definition": "random(55..65#0.1 except num8 except 60)", "templateType": "anything", "group": "Ungrouped variables", "name": "num9", "description": ""}, "ans23": {"definition": "(abs(ans21 - ans22)/ ans22)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23", "description": ""}, "ans22": {"definition": "(num5+num6)/(num7)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "(siground(num5,1)+siground(num6,1))/siground(num7,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "ans63": {"definition": "(abs(ans61 - ans62)/ ans62)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans63", "description": ""}, "ans62": {"definition": "(num19^2*num20)/(num21)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans62", "description": ""}, "ans61": {"definition": "((siground(num19,1)^2)*siground(num20,1))/siground(num21,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans61", "description": ""}, "ans41": {"definition": "(siground(num11,1)-siground(num12,1))/(siground(num13,1)+siground(num14,1))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans41", "description": ""}, "ans43": {"definition": "(abs(ans41 - ans42)/ ans42)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans43", "description": ""}, "ans42": {"definition": "(num11-num12)/(num13+num14)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans42", "description": ""}, "num21": {"definition": "random(800.1..899#0.2)", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "num20": {"definition": "tens()", "templateType": "anything", "group": "Ungrouped variables", "name": "num20", "description": ""}, "ans12": {"definition": "(num1*num2)/(num3*num4)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans13": {"definition": "(abs(ans11 - ans12)/ ans12)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13", "description": ""}, "ans11": {"definition": "(siground(num1,1)*siground(num2,1))/(siground(num3,1)*siground(num4,1))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans31": {"definition": "(siground(num8,1)*siground(num9,1))/siground(num10,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "(num8*num9)/(num10)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans33": {"definition": "(abs(ans31 - ans32)/ ans32)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33", "description": ""}, "ans52": {"definition": "(num15-num16)/(num17+num18)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans52", "description": ""}, "ans53": {"definition": "(abs(ans51 - ans52)/ ans52)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans53", "description": ""}, "ans51": {"definition": "(siground(num15,1)-siground(num16,1))/(siground(num17,1)+siground(num18,1))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans51", "description": ""}, "num16": {"definition": "random(201..299)", "templateType": "anything", "group": "Ungrouped variables", "name": "num16", "description": ""}, "num17": {"definition": "random(41..59 except 50)", "templateType": "anything", "group": "Ungrouped variables", "name": "num17", "description": ""}, "num14": {"definition": "random(11..25#0.01 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num14", "description": ""}, "num15": {"definition": "hun()", "templateType": "anything", "group": "Ungrouped variables", "name": "num15", "description": ""}, "num12": {"definition": "sin()", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num13": {"definition": "random(3.5..5.5#0.01 except num12)", "templateType": "anything", "group": "Ungrouped variables", "name": "num13", "description": ""}, "num10": {"definition": "random(15..30#0.1 except num8)", "templateType": "anything", "group": "Ungrouped variables", "name": "num10", "description": ""}, "num11": {"definition": "precround(tens(),1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "num18": {"definition": "random(201..299 except num16)", "templateType": "anything", "group": "Ungrouped variables", "name": "num18", "description": ""}, "num19": {"definition": "sin()", "templateType": "anything", "group": "Ungrouped variables", "name": "num19", "description": ""}}, "metadata": {"description": "<p>(Calculate the estimate, actual and from these the percentage error)</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q8 (Calculate the estimate, actual and the percentage error from these)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {"tens": {"definition": "random(35..80#0.01)", "type": "number", "language": "jme", "parameters": []}, "hun": {"definition": "random(301..599)", "type": "number", "language": "jme", "parameters": []}, "sin": {"definition": "random(3..8#0.01)", "type": "number", "language": "jme", "parameters": []}, "hun1": {"definition": "random(400..600)", "type": "number", "language": "jme", "parameters": []}}, "ungrouped_variables": ["num1", "num2", "num3", "num4", "num5", "num7", "num6", "num8", "num9", "num10", "num11", "num12", "num13", "num14", "num15", "num16", "num17", "num18", "num19", "num20", "num21", "ans11", "ans21", "ans31", "ans41", "ans51", "ans61", "ans12", "ans22", "ans32", "ans42", "ans52", "ans62", "ans13", "ans23", "ans33", "ans43", "ans53", "ans63"], "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>When rounding off a number to two&nbsp;significant place, round to the left 2 most figure of the number, like below;</p>\n<p>$367 = 370$</p>\n<p>$381 = 380$</p>\n<p>$715 = 720$</p>\n<p>$3.79 = 3.8$</p>\n<p>$65.13 = 65$</p>\n<p>$215 = 220$</p>\n<p></p>\n<p><em>Part 1:</em></p>\n<p>Estimate value with each number rounded to one significant place:</p>\n<p>$\\frac{(\\var{num1}&nbsp;\\times \\var{num2})}{(\\var{num3} \\times \\var{num4})}$&nbsp;</p>\n<p>Round numbers to one significant number:</p>\n<p>$\\var{num1} = ${siground(num1,2)}</p>\n<p>$\\var{num2} = ${siground(num2,2)}</p>\n<p>$\\var{num3} = ${siground(num3,2)}</p>\n<p>$\\var{num4} = ${siground(num4,2)}</p>\n<p>Answer:</p>\n<p>$= \\var{ans11}$</p>\n<p></p>\n<p><em>Part 2:</em></p>\n<p>Actual value:</p>\n<p>$\\frac{(\\var{num1} \\times \\var{num2})}{(\\var{num3} \\times \\var{num4})} = \\var{ans12}$</p>\n<p></p>\n<p><em>Part 3:</em></p>\n<p>Percentage error:</p>\n<p>$abs(\\frac{\\var{ans12} - \\var{ans11}}{\\var{ans11}}) \\times 100 = \\var{ans13}$%</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\frac{\\var{num1} -&nbsp;\\var{num2}}{\\var{num3}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;&nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}", "strictPrecision": false, "minValue": "{ans11}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}", "strictPrecision": false, "minValue": "{ans12}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans13}+1", "strictPrecision": false, "minValue": "{ans13}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num5}&nbsp;+ \\var{num6}}{\\var{num7}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;&nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "strictPrecision": false, "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "strictPrecision": false, "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans23}+1", "strictPrecision": false, "minValue": "{ans23}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num8} \\times \\var{num9}}{\\var{num10}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "strictPrecision": false, "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "strictPrecision": false, "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans33}+1", "strictPrecision": false, "minValue": "{ans33}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num11} \\times \\var{num12}}{\\var{num13}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans41}", "strictPrecision": false, "minValue": "{ans41}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans42}", "strictPrecision": false, "minValue": "{ans42}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans43}+1", "strictPrecision": false, "minValue": "{ans43}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>By rounding each number correct to two&nbsp;significant figure, estimate the answer to each of the problems given below. Then use your calculator to accurately evaluate each of them.</p>\n<p>Calculate the percentage error in using the estimate, correct to two&nbsp;decimal place.</p>\n<p><strong>&nbsp;</strong></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"num4": {"definition": "random(35..80 except num3)", "templateType": "anything", "group": "Ungrouped variables", "name": "num4", "description": ""}, "num5": {"definition": "random(120..170)", "templateType": "anything", "group": "Ungrouped variables", "name": "num5", "description": ""}, "num6": {"definition": "random(201..279)", "templateType": "anything", "group": "Ungrouped variables", "name": "num6", "description": ""}, "num7": {"definition": "random(61.5..89.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "num7", "description": ""}, "num1": {"definition": "random(33.1..36.9#0.1 except 34 except 35 except 36)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "random(23.1..26.9#0.01 except 34 except 35 except 36)", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "random(0.0011..0.0199#0.0001)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "num8": {"definition": "random(7..9#0.005)", "templateType": "anything", "group": "Ungrouped variables", "name": "num8", "description": ""}, "num9": {"definition": "random(21.05..35#0.005)", "templateType": "anything", "group": "Ungrouped variables", "name": "num9", "description": ""}, "ans23": {"definition": "(abs(ans21 - ans22)/ ans22)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23", "description": ""}, "ans22": {"definition": "(num5+num6)/(num7)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "(siground(num5,2)+siground(num6,2))/siground(num7,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "ans63": {"definition": "(abs(ans61 - ans62)/ ans62)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans63", "description": ""}, "ans62": {"definition": "(num19^2*num20)/(num21)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans62", "description": ""}, "ans61": {"definition": "((siground(num19,1)^2)*siground(num20,1))/siground(num21,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans61", "description": ""}, "ans41": {"definition": "(siground(num11,2)*siground(num12,2))/(siground(num13,2))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans41", "description": ""}, "ans43": {"definition": "(abs(ans41 - ans42)/ ans42)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans43", "description": ""}, "ans42": {"definition": "(num11*num12)/(num13)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans42", "description": ""}, "num21": {"definition": "random(800.1..899#0.2)", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "num20": {"definition": "tens()", "templateType": "anything", "group": "Ungrouped variables", "name": "num20", "description": ""}, "ans12": {"definition": "(num1-num2)/(num3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans13": {"definition": "(abs(ans11 - ans12)/ ans12)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13", "description": ""}, "ans11": {"definition": "(siground(num1,2)-siground(num2,2))/(siground(num3,2))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans31": {"definition": "(siground(num8,2)*siground(num9,2))/siground(num10,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "(num8*num9)/(num10)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans33": {"definition": "(abs(ans31 - ans32)/ ans32)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33", "description": ""}, "ans52": {"definition": "(num15-num16)/(num17+num18)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans52", "description": ""}, "ans53": {"definition": "(abs(ans51 - ans52)/ ans52)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans53", "description": ""}, "ans51": {"definition": "(siground(num15,1)-siground(num16,1))/(siground(num17,1)+siground(num18,1))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans51", "description": ""}, "num16": {"definition": "random(201..299)", "templateType": "anything", "group": "Ungrouped variables", "name": "num16", "description": ""}, "num17": {"definition": "random(41..59 except 50)", "templateType": "anything", "group": "Ungrouped variables", "name": "num17", "description": ""}, "num14": {"definition": "random(11..25#0.01 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num14", "description": ""}, "num15": {"definition": "hun()", "templateType": "anything", "group": "Ungrouped variables", "name": "num15", "description": ""}, "num12": {"definition": "random(16.5..24.5#0.05)", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num13": {"definition": "random(18.1..27.9#0.05 except num12)", "templateType": "anything", "group": "Ungrouped variables", "name": "num13", "description": ""}, "num10": {"definition": "random(12..19#0.05)", "templateType": "anything", "group": "Ungrouped variables", "name": "num10", "description": ""}, "num11": {"definition": "random(401..499 except 410 except 420 except 430 except 440 except 450 except 460 except 470 except 480 except 490)", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "num18": {"definition": "random(201..299 except num16)", "templateType": "anything", "group": "Ungrouped variables", "name": "num18", "description": ""}, "num19": {"definition": "sin()", "templateType": "anything", "group": "Ungrouped variables", "name": "num19", "description": ""}}, "metadata": {"description": "<p>(Calculate the estimate, actual and the percentage error from these)</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Deirdre Casey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/681/"}], "extensions": [], "custom_part_types": [], "resources": []}