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{"percentPass": 0, "name": "MA1002 First Real Exam", "feedback": {"showactualmark": true, "showanswerstate": true, "advicethreshold": 0, "intro": "", "feedbackmessages": [], "allowrevealanswer": true, "showtotalmark": true}, "metadata": {"description": "<p>First Real Exam on Wednesday 1st March 2017</p>", "licence": "None specified"}, "showQuestionGroupNames": false, "duration": 3000, "navigation": {"reverse": true, "showresultspage": "oncompletion", "allowregen": true, "showfrontpage": true, "onleave": {"message": "", "action": "none"}, "preventleave": true, "browse": true}, "timing": {"timeout": {"message": "<p>Yuor time has run out. You will get credit for the work you have done so far.</p>", "action": "warn"}, "allowPause": true, "timedwarning": {"message": "<p>Warning, your time will run out in five minutes.&nbsp;</p>", "action": "warn"}}, "showstudentname": true, "question_groups": [{"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Group", "questions": [{"name": "MA1002 Antiderivatives", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "preamble": {"css": "", "js": ""}, "parts": [{"marks": "2", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "vsetrangepoints": 5, "checkingtype": "absdiff", "expectedvariablenames": [], "variableReplacements": [], "type": "jme", "checkvariablenames": false, "prompt": "<p>$f(x) = \\var{a}x - \\var{b}$</p>", "variableReplacementStrategy": "originalfirst", "showpreview": true, "answer": "{a}x^2/2-{b}x+C", "vsetrange": [0, 1], "scripts": {}, "showCorrectAnswer": false}, {"marks": "2", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "vsetrangepoints": 5, "checkingtype": "absdiff", "expectedvariablenames": [], "variableReplacements": [], "type": "jme", "checkvariablenames": false, "prompt": "<p>$f(x) = \\frac{1}{\\var{c}}+ \\frac{2}{\\var{d}}x^2 - \\frac{3}{\\var{f}}x^3$</p>", "variableReplacementStrategy": "originalfirst", "showpreview": true, "answer": "1/{c}x+2/(3{d})x^3-3x^4/(4{f})+C", "vsetrange": [0, 1], "scripts": {}, "showCorrectAnswer": false}, {"marks": "2", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "vsetrangepoints": 5, "checkingtype": "absdiff", "expectedvariablenames": [], "variableReplacements": [], "type": "jme", "checkvariablenames": false, "prompt": "<p>$f(x) = e^\\var{g}$</p>", "variableReplacementStrategy": "originalfirst", "showpreview": true, "answer": "e^{g}x+C", "vsetrange": [0, 1], "scripts": {}, "showCorrectAnswer": false}, {"marks": "2", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "vsetrangepoints": 5, "checkingtype": "absdiff", "expectedvariablenames": [], "variableReplacements": [], "type": "jme", "checkvariablenames": false, "prompt": "<p>$f(x) = e^{\\var{g}x}$</p>", "variableReplacementStrategy": "originalfirst", "showpreview": true, "answer": "e^({g}x)/{g}+C", "vsetrange": [0, 1], "scripts": {}, "showCorrectAnswer": false}], "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>Find the most general antiderivatives of the functions. Use the letter C to represent an unknown constant.&nbsp;</p>", "ungrouped_variables": ["a", "c", "b", "d", "g", "f"], "advice": "<p>Don't forget to include the unknown constant C.</p>", "metadata": {"description": "<p>Antiderivatives</p>\n<p>rebel&nbsp;</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {}, "rulesets": {}, "variable_groups": [], "variables": {"f": {"definition": "random(4,5,7,8)", "templateType": "anything", "name": "f", "group": "Ungrouped variables", "description": ""}, "b": {"definition": "random(1..9 except a)", "templateType": "anything", "name": "b", "group": "Ungrouped variables", "description": ""}, "a": {"definition": "2*random(2..4)", "templateType": "anything", "name": "a", "group": "Ungrouped variables", "description": ""}, "d": {"definition": "random(3,5,7)", "templateType": "anything", "name": "d", "group": "Ungrouped variables", "description": ""}, "g": {"definition": "random(2..5)", "templateType": "anything", "name": "g", "group": "Ungrouped variables", "description": ""}, "c": {"definition": "random(2..4)", "templateType": "anything", "name": "c", "group": "Ungrouped variables", "description": ""}}, "type": "question"}, {"name": "MA1002 Integration by Substitution", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "preamble": {"css": "", "js": ""}, "parts": [{"type": "gapfill", "marks": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "gaps": [{"answer": "(({a[0]}*(x^2)+{b[0]})^({m[0]}+1))/(2*{a[0]}*({m[0]}+1))+C", "marks": "2", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "vsetrangepoints": 5, "checkingtype": "absdiff", "answersimplification": "all", "notallowed": {"partialCredit": 0, "message": "<p>Input all numbers as integers or fractions and not as decimals.</p>", "showStrings": false, "strings": ["."]}, "type": "jme", "showpreview": true, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "variableReplacements": [], "vsetrange": [0, 1], "scripts": {}, "showCorrectAnswer": false}, {"marks": 1, "showFeedbackIcon": true, "checkingaccuracy": 0.001, "vsetrangepoints": 5, "checkingtype": "absdiff", "answersimplification": "all", "showCorrectAnswer": false, "type": "jme", "showpreview": true, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "variableReplacements": [], "vsetrange": [0, 1], "scripts": {}, "answer": "2{a[0]}x"}, {"marks": "1", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "vsetrangepoints": 5, "checkingtype": "absdiff", "answersimplification": "all", "showCorrectAnswer": false, "type": "jme", "showpreview": true, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "variableReplacements": [], "vsetrange": [0, 1], "scripts": {}, "answer": "du/(2{a[0]}x)"}, {"marks": 1, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "scripts": {}, "allowFractions": true, "correctAnswerFraction": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "minValue": "1/(2{a[0]})", "variableReplacements": [], "mustBeReducedPC": 0, "showCorrectAnswer": false, "maxValue": "1/(2{a[0]})", "notationStyles": ["plain", "en", "si-en"]}, {"marks": "1", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "vsetrangepoints": 5, "checkingtype": "absdiff", "answersimplification": "all", "showCorrectAnswer": false, "type": "jme", "showpreview": true, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "variableReplacements": [], "vsetrange": [0, 1], "scripts": {}, "answer": "u^({m[0]}+1)/({m[0]}+1)"}], "prompt": "<p>$I=\\simplify[std]{Int( x*({a[0]}x^2+{b[0]})^{m[0]},x)}$</p>\n<p></p>\n<p>Use $u=\\simplify[std]{{a[0]}x^2+{b[0]}}$ as your substitution.</p>\n<p>$\\frac{du}{dx}=$&nbsp;[[1]]</p>\n<p>$dx=$&nbsp;[[2]]</p>\n<p>Substituting back into the original equation for $dx$ and pulling out constants gives</p>\n<p>$I=$[[3]]$\\simplify[std]{Int(u^{m[0]},u)}$</p>\n<p>The next step is to integrate.</p>\n<p>$\\simplify{Int(u^{m[0]},u)}=$&nbsp;[[4]]</p>\n<p>Putting all of these results together, we get the final answer of:</p>\n<p>[[0]]</p>", "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true}], "ungrouped_variables": ["a", "b", "m"], "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p><strong>Integrate the following by substitution.</strong></p>\n<p>Don't forget the constant of integration ($C$).</p>", "tags": [], "advice": "<p>This problem is best solved by using substitution. <br/>Note that if we let $u=\\simplify[std]{{a[0]} * (x ^ 2) + {b[0]}}$ then $du=\\simplify[std]{(2*{a[0]} * x)*dx }$<br/>Hence we can replace $xdx$ by $\\frac{1}{2*\\var{a[0]}}du$.</p>\n<p>Hence the integral becomes:</p>\n<p>\\[\\begin{eqnarray*} I&amp;=&amp;\\simplify[std]{Int((1/(2{a[0]}))u^{m[0]},u)}\\\\ &amp;=&amp;\\simplify[all]{(1/(2{a[0]}))u^{m[0]+1}/{m[0]+1}+C}\\\\ &amp;=&amp; \\simplify[all]{({a[0]} * (x ^ 2) + {b[0]})^{m[0]+1}/(2{a[0]}*({m[0]}+1))+C} \\end{eqnarray*}\\]</p>\n<p><b>A Useful Result</b><br/>This example can be generalised. <br/>Suppose \\[I = \\int\\; f'(x)g(f(x))\\;dx\\]<br/>The using the substitution $u=f(x)$ we find that $du=f'(x)\\;dx$ and so using the same method as above:<br/>\\[I = \\int g(u)\\;du \\]<br/>And if we can find this simpler integral in terms of $u$ we can replace $u$ by $f(x)$ and get the result in terms of $x$.</p>", "metadata": {"description": "<p>Step by step solving for integration by substitution</p>", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "variable_groups": [], "variables": {"a": {"definition": "repeat(random(1..5),5)", "templateType": "anything", "description": "", "name": "a", "group": "Ungrouped variables"}, "m": {"definition": "repeat(random(4..9),5)", "templateType": "anything", "description": "", "name": "m", "group": "Ungrouped variables"}, "b": {"definition": "repeat(random(-9..9 except 0),5)", "templateType": "anything", "description": "", "name": "b", "group": "Ungrouped variables"}}, "type": "question"}, {"name": "MA1002 Integration by substitution 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "variables": {"b": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b", "definition": "random(1..8 except a)"}, "c": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "c", "definition": "random(1..9)"}, "a": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "a", "definition": "random(2..6)"}}, "statement": "<p>Evaluate the following indefinite integrals using integration by substitution. Use the letter C to represent any unknown constants.</p>", "preamble": {"css": "", "js": ""}, "parts": [{"variableReplacements": [], "showFeedbackIcon": true, "checkvariablenames": false, "prompt": "<p>$\\int e^x\\sqrt{1+e^x}\\mathrm{dx}$</p>", "checkingaccuracy": 0.001, "showpreview": true, "answer": "2(1+e^x)^(3/2)/3+C", "scripts": {}, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "type": "jme", "checkingtype": "absdiff", "showCorrectAnswer": false, "vsetrange": [0, 1], "marks": "2", "expectedvariablenames": []}, {"variableReplacements": [], "showFeedbackIcon": true, "checkvariablenames": false, "prompt": "<p>$\\int\\frac{\\mathrm{dx}}{\\var{a}x+\\var{b}}$.</p>\n<p>Answer in terms of the natural log, represented by ln( ).</p>", "checkingaccuracy": 0.001, "showpreview": true, "answer": "1/{a}ln({a}x+{b})+C", "scripts": {}, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "type": "jme", "checkingtype": "absdiff", "showCorrectAnswer": false, "vsetrange": [0, 1], "marks": "2", "expectedvariablenames": []}, {"variableReplacements": [], "showFeedbackIcon": true, "checkvariablenames": false, "prompt": "<p>$\\int \\frac{x \\mathrm{dx}}{\\var{c}+x^2}$.</p>\n<p>Answer in terms of the natural log, represented by ln( ).</p>", "checkingaccuracy": 0.001, "showpreview": true, "answer": "ln({c}+x^2)/2+C", "scripts": {}, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "type": "jme", "checkingtype": "absdiff", "showCorrectAnswer": false, "vsetrange": [0, 1], "marks": "2", "expectedvariablenames": []}], "metadata": {"description": "<p>Integration by susbtitution, no hint given</p>", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "<p>integration by Susbtitution</p>", "ungrouped_variables": ["c", "b", "a"], "tags": [], "functions": {}, "rulesets": {}, "type": "question"}, {"name": "MA1002 using fractions (simple operations)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "statement": "<p>These are basic questions to help you practice adding, subtracting, multiplying and dividing fractions.</p>\n<p>Attempt the questions&nbsp;without a calculator.</p>\n<p>Give your answer as a <em><strong>fraction.</strong></em></p>", "functions": {}, "metadata": {"description": "<p>This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.</p>\n<p>All of these can be done without a calculator.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "rulesets": {}, "advice": "<p>When<strong> adding/subtracting</strong> fractions, you must first find a <em>common denominator</em> between the fractions. If they already have the same denominator then you only need to worry about adding/subtracting the numerators and dividing the result by the common denominator.</p>\n<p>For example:<br/>To find a common denominator of $\\frac{2}{5} + \\frac{7}{15}$, the most obvious would be $15$, because $5\\times3=15$. Therefore, you must multiply both sides of the fraction&nbsp;$\\frac{2}{5}$ by $3$ to obtain a new fraction $\\frac{6}{15}$. This is known as 'scaling up'.<br/>Now you can add the two fractions together (by adding the numerators) because they have the same denominator:<br/>$\\frac{6}{15}+\\frac{7}{15}=\\frac{13}{15}$.</p>\n<p>The same applies with&nbsp;subtraction as well as addition.</p>\n<p></p>\n<p>When <strong>multiplying</strong> fractions, you can simply multiply the two numerators and divide this by the multiplication of the two denominators.</p>\n<p>For example:<br/>$\\frac{a}{b}\\times\\frac{c}{d}$ = $\\frac{a\\times{c}}{b\\times{d}}$</p>\n<p></p>\n<p>When <strong>dividing</strong> fractions, you firstly need to reciprocate (flip) <i>the second fraction</i>, then multiply the numerators and denominators as you would a normal multiplication question.</p>\n<p>For example:<br/>$\\frac{a}{b} \\div \\frac{c}{d}$ would be flipped to become&nbsp;$\\frac{a}{b} \\div \\frac{d}{c}$ and then treated as a normal multiplication question (as explained above).</p>", "tags": [], "parts": [{"showCorrectAnswer": false, "correctAnswerFraction": true, "allowFractions": true, "prompt": "<p>What is the answer to $\\frac{\\var{a}}{\\var{b}} \\times \\frac{\\var{c}}{\\var{b}}$?</p>", "marks": "1", "showFeedbackIcon": true, "minValue": "(a*c)/(b*b)", "mustBeReducedPC": 0, "type": "numberentry", "steps": [{"showCorrectAnswer": false, "correctAnswerFraction": false, "maxValue": "a*c", "allowFractions": false, "prompt": "<p>Multiply the numerators</p>", "marks": 1, "showFeedbackIcon": true, "minValue": "a*c", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerStyle": "plain"}, {"showCorrectAnswer": false, "correctAnswerFraction": false, "maxValue": "b*b", "allowFractions": false, "prompt": "<p>Multiply the denominators</p>", "marks": 1, "showFeedbackIcon": true, "minValue": "b*b", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerStyle": "plain"}, {"showCorrectAnswer": false, "correctAnswerFraction": true, "maxValue": "(a*c)/(b*b)", "allowFractions": true, "prompt": "<p>Put into a fraction, with the new numerator over the new denominator</p>", "marks": 1, "showFeedbackIcon": true, "minValue": "(a*c)/(b*b)", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerStyle": "plain"}], "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "maxValue": "(a*c)/(b*b)", "variableReplacements": [], "correctAnswerStyle": "plain", "stepsPenalty": 0}, {"showCorrectAnswer": false, "correctAnswerFraction": true, "allowFractions": true, "prompt": "<p>What is the answer to $\\frac{\\var{d}}{\\var{f}} \\div \\frac{\\var{g}}{\\var{f}}$?</p>", "marks": "1", "showFeedbackIcon": true, "minValue": "d/g", "mustBeReducedPC": 0, "type": "numberentry", "steps": [{"showCorrectAnswer": false, "correctAnswerFraction": true, "maxValue": "f/g", "allowFractions": true, "prompt": "<p>Flip the second fraction e.g. $a/b$ becomes $b/a$</p>", "marks": 1, "showFeedbackIcon": true, "minValue": "f/g", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerStyle": "plain"}, {"showCorrectAnswer": false, "correctAnswerFraction": true, "maxValue": "(d*f)/(g*f)", "allowFractions": true, "prompt": "<p>Multiply the fractions as you would with a normal multiplication question using the flipped fraction above as the new second fraction</p>", "marks": 1, "showFeedbackIcon": true, "minValue": "(d*f)/(g*f)", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerStyle": "plain"}], "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "maxValue": "d/g", "variableReplacements": [], "correctAnswerStyle": "plain", "stepsPenalty": 0}, {"showCorrectAnswer": false, "correctAnswerFraction": true, "allowFractions": true, "prompt": "<p>What is the answer to $\\frac{\\var{h}}{\\var{j}} + \\frac{\\var{k}}{\\var{j}}$?</p>", "marks": "1", "showFeedbackIcon": true, "minValue": "(h+k)/j", "mustBeReducedPC": 0, "type": "numberentry", "steps": [{"showCorrectAnswer": true, "scripts": {}, "prompt": "<p>Check to see if the denominators are the same. If they are, you only need to add the numerators together and leave the denominator as it is for the final answer.</p>", "variableReplacementStrategy": "originalfirst", "marks": 0, "type": "information", "showFeedbackIcon": true, "variableReplacements": []}, {"showCorrectAnswer": false, "correctAnswerFraction": false, "maxValue": "h+k", "allowFractions": true, "prompt": "<p>Add the numerators</p>", "marks": 1, "showFeedbackIcon": true, "minValue": "h+k", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerStyle": "plain"}, {"showCorrectAnswer": false, "correctAnswerFraction": true, "maxValue": "(h+k)/j", "allowFractions": true, "prompt": "<p>Write as a fraction over the similar denominator; cancel down if you can.</p>", "marks": 1, "showFeedbackIcon": true, "minValue": "(h+k)/j", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerStyle": "plain"}], "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "maxValue": "(h+k)/j", "variableReplacements": [], "correctAnswerStyle": "plain", "stepsPenalty": 0}, {"showCorrectAnswer": false, "correctAnswerFraction": true, "allowFractions": true, "prompt": "<p>What is the answer to $\\frac{\\var{l}}{\\var{m}} - \\frac{\\var{n}}{\\var{m}}$?</p>", "marks": "1", "showFeedbackIcon": true, "minValue": "(l-n)/m", "mustBeReducedPC": 0, "type": "numberentry", "steps": [{"showCorrectAnswer": true, "scripts": {}, "prompt": "<p>Check to see if the denominators are the same. If they are, you only need to subtract the numerators and leave the denominator as it is.</p>", "variableReplacementStrategy": "originalfirst", "marks": 0, "type": "information", "showFeedbackIcon": true, "variableReplacements": []}, {"showCorrectAnswer": false, "correctAnswerFraction": false, "maxValue": "(l-n)", "allowFractions": false, "prompt": "<p>Subtract the numerators</p>", "marks": 1, "showFeedbackIcon": true, "minValue": "(l-n)", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerStyle": "plain"}, {"showCorrectAnswer": false, "correctAnswerFraction": true, "maxValue": "(l-n)/m", "allowFractions": true, "prompt": "<p>Create a fraction with the original denominator; cancel down if you can.</p>", "marks": 1, "showFeedbackIcon": true, "minValue": "(l-n)/m", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerStyle": "plain"}], "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "maxValue": "(l-n)/m", "variableReplacements": [], "correctAnswerStyle": "plain", "stepsPenalty": 0}, {"showCorrectAnswer": false, "correctAnswerFraction": true, "allowFractions": true, "prompt": "<p>What is the answer to $\\frac{\\var{o}}{\\var{p}} \\times \\frac{\\var{q}}{\\var{r}}$?</p>", "marks": "1", "showFeedbackIcon": true, "minValue": "(o*q)/(p*r)", "mustBeReducedPC": 0, "type": "numberentry", "steps": [{"showCorrectAnswer": true, "scripts": {}, "prompt": "<p>Multiply the numerators to make the top of the fraction</p>\n<p>Multiply the denominators to make the bottom of the fraction</p>\n<p>Cancel down if you can</p>", "variableReplacementStrategy": 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"en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "maxValue": "(s*v)/(u*t)", "variableReplacements": [], "correctAnswerStyle": "plain", "stepsPenalty": "0"}, {"showCorrectAnswer": false, "correctAnswerFraction": true, "allowFractions": true, "prompt": "<p>What is the answer to $\\frac{\\var{w}}{\\var{x}} + \\frac{\\var{y}}{\\var{z}}$?</p>", "marks": "1", "showFeedbackIcon": true, "minValue": "((w*z)+(y*x))/(x*z)", "mustBeReducedPC": 0, "type": "numberentry", "steps": [{"showCorrectAnswer": true, "scripts": {}, "prompt": "<p>Check to see if the denominators are the same</p>\n<p>If they are not - multiply each fraction up to equivalent fractions with <em>equal denominators</em></p>\n<p>Once they are equal add the numerators and put over the equal denominator</p>\n<p>Cancel down if needed</p>", "variableReplacementStrategy": "originalfirst", "marks": 0, "type": "information", "showFeedbackIcon": true, "variableReplacements": []}], "mustBeReduced": false, 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