// Numbas version: exam_results_page_options
{"name": "Maths 1 Week 9 Assessed", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", ""], "questions": [{"name": "Differentiation. True/False 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Paul Howes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/632/"}, {"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}], "tags": [], "metadata": {"description": "Multi choice question week 3", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>See ??</p>", "rulesets": {}, "variables": {"statements": {"name": "statements", "group": "do not change these", "definition": "map(if(rand[j]=1,\n    statements_true[j],\n    statements_false[j]),j,0..n-1)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "change these", "definition": "random(6..9)", "description": "", "templateType": "anything"}, "max_mark": {"name": "max_mark", "group": "change these", "definition": "4", "description": "", "templateType": "anything"}, "statements_false": {"name": "statements_false", "group": "change these", "definition": "[\"$\\\\frac{df}{dt} = \\\\cos(x)$\",\n\"$\\\\frac{dg}{dx} = -\\\\sin(t)$ \",\n\"$\\\\frac{df}{dx} = df \\\\div dx$ \",\n\"The derivative of $\\\\frac{1}{x^5}$ is $\\\\frac{1}{5x^4}$\",\n\"The derivative of $x^5 \\\\sin(x)$ is $5x^4 \\\\cos(x)$ \",\n\"$x^5 = 5x^4$\",\n\"The derivative of $\\\\sqrt{x}$ is determined by re-writing it as $x^{-2}$\"\n]", "description": "<p><br />\"The derivative of $x^2 \\\\sin(x)$ is $2x \\\\cos(x)$ \",<br />\"When adding up a geometric series using the reasoning from lectures, you re-write the original sum underneath but in reverse order\",<br />\"$f'(0)=0$\",<br />\"$g'(0)=-1$\",<br />\"The derivative of $\\\\sqrt{x}$ is explicitly stated in the formula sheet\"<br />]</p>", "templateType": "anything"}, "statements_true": {"name": "statements_true", "group": "change these", "definition": "[\"$\\\\frac{df}{dx} = \\\\cos(x)$\",\n\"$\\\\frac{dg}{dt} = -\\\\sin(t)$ \",\n\"$\\\\frac{df}{dx}$ should not be treated like a fraction\",\n\"The derivative of $\\\\frac{1}{x^5}$ is determined by re-writing it as $x^{-5}$\",\n\"The derivative of $x^5 \\\\sin(x)$ is not $5x^4 \\\\cos(x)$ \",\n\"The derivative of $x^3$ is $3x^2$\",\n\"The derivative of $\\\\sqrt{x}$ is determined by re-writing it as $x^{\\\\frac{1}{2}}$\"\n]\n ", "description": "<p><br />\"The derivative of $\\\\sqrt{x}$ is not explicitly stated in the formula sheet\"<br />]</p>", "templateType": "anything"}, "b": {"name": "b", "group": "change these", "definition": "random(10..18)+random(1..9)/10", "description": "", "templateType": "anything"}, "rand": {"name": "rand", "group": "do not change these", "definition": "repeat(if(random(-2..2)>0,1,0),n-1)+[if(random(0..5)=5,1,0)]", "description": "", "templateType": "anything"}, "error": {"name": "error", "group": "change these", "definition": "1/2", "description": "<p>what proportion of total marks should be lost for each error. e.g. 1/2 would mean a single error costs half of all marks available. 1/3 would mean each error costs a third of all marks.</p>", "templateType": "anything"}, "marks": {"name": "marks", "group": "do not change these", "definition": "matrix(map(if(rand[j]=1,[max_mark/n,-max_mark*error+max_mark/n],[-max_mark*error+max_mark/n,max_mark/n]),j,0..n-1))\n\n", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "do not change these", "definition": "length(statements_true)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "change these", "definition": "random(3..7)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "change these", "variables": ["statements_true", "statements_false", "max_mark", "error", "a", "b", "c"]}, {"name": "do not change these", "variables": ["n", "rand", "statements", "marks"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>In the following,&nbsp;$f(x) = \\sin(x)$ and $g(t) = \\cos(t)$.&nbsp; Which of the following are true and which are false?&nbsp;&nbsp;</p>\n<p></p>\n<p>If you are unsure of something,&nbsp;find out the answer instead of guessing.&nbsp;<strong>Each error will cost half of the marks available</strong>. If you are unable to find out, you are welcome to ask me for help or advice.</p>", "minMarks": 0, "maxMarks": "0", "minAnswers": "{n}", "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": false, "choices": "{statements}", "matrix": "{marks}", "layout": {"type": "all", "expression": ""}, "answers": ["<p>True</p>", "<p>False</p>"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Differentiation: standard derivatives, multiple terms, complicated coefficients, randomised", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}], "tags": [], "metadata": {"description": "<p>Standard derivatives asked for (e.g. $x^n$, $1/x^n$, $\\sqrt(x)$, $\\ln(x)$, $\\sin(x)$, etc.) .&nbsp;&nbsp;</p>", "licence": "None specified"}, "statement": "", "advice": "<p>See 10.1, 10.2, 10.4 and 10.5.</p>", "rulesets": {}, "variables": {"f": {"name": "f", "group": "functions", "definition": "[\n  [\"(1*\",\")\"],\n  [\"(\",\")^\"+n1],\n  [\"(\",\")^\"+n2],\n  [\"1/(\",\")\"],\n  [\"1/((\",\")^\"+n3+\")\"],\n  [\"sqrt(\",\")\"],\n  [\"sin(\",\")\"],\n  [\"cos(\",\")\"],\n  [\"e^(\",\")\"],\n  [\"ln(\",\")\"]\n ]", "description": "", "templateType": "anything"}, "f0": {"name": "f0", "group": "functions", "definition": "map(expression(a[j]+\"*\"+f[rand[j]][0]+var+ f[rand[j]][1]),j,0..8)", "description": "", "templateType": "anything"}, "n3": {"name": "n3", "group": "coeffs etc", "definition": "random(2..5)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "coeffs etc", "definition": "shuffle(map(random(-2..-9),j,0..8)+[0.25,0.2,0.75,0.8,0.1,0.6,2/3])", "description": "", "templateType": "anything"}, "n1": {"name": "n1", "group": "coeffs etc", "definition": "random(2..3)", "description": "", "templateType": "anything"}, "n2": {"name": "n2", "group": "coeffs etc", "definition": "random(7..9)", "description": "", "templateType": "anything"}, "f'": {"name": "f'", "group": "functions", "definition": "[\n  [\"(1*(\",\"^0))\"],\n  [n1+\"*(\",\")^\"+(n1-1)],\n  [n2+\"*(\",\")^\"+(n2-1)],\n  [\"-1/((\",\")^2)\"],\n  [\"-\"+n3+\"/((\",\")^\"+(n3+1)+\")\"],\n  [\"0.5/(sqrt(\",\"))\"],\n  [\"cos(\",\")\"],\n  [\"-sin(\",\")\"],\n  [\"e^(\",\")\"],\n  [\"1/(\",\")\"]\n ]", "description": "", "templateType": "anything"}, "rand": {"name": "rand", "group": "Ungrouped variables", "definition": "shuffle(0..9)", "description": "<p>[<br />0[\"(\"+b0[0]+\"*\",\")\"],<br />1[\"(\",\")^\"+n1],<br />2[\"(\",\")^\"+n2],<br />3[\"1/(\",\")\"],<br />4[\"1/((\",\")^\"+n3+\")\"],<br />5[\"sqrt(\",\")\"],<br />6[\"sin(\",\")\"],<br />7[\"cos(\",\")\"],<br />8[\"e^(\",\")\"],<br />9[\"ln(\",\")\"]<br /> ]</p>\n<p></p>\n<p>don't use 0 for product rule</p>", "templateType": "anything"}, "var": {"name": "var", "group": "coeffs etc", "definition": "random(['x','z','t','p','s','r','w'])", "description": "", "templateType": "anything"}, "f0'": {"name": "f0'", "group": "functions", "definition": "map(expression(a[j]+\"*\"+f'[rand[j]][0]+var+ f'[rand[j]][1]),j,0..8)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["rand"], "variable_groups": [{"name": "coeffs etc", "variables": ["var", "n1", "n2", "n3", "a"]}, {"name": "functions", "variables": ["f", "f'", "f0", "f0'"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Differentiate the following with respect to $\\simplify{{expression(var)}}$.</p>\n<p></p>\n<p>$\\simplify[fractionNumbers, all]{{f0[0]}+{f0[1]}}$. [[0]]</p>\n<p>$\\simplify[fractionNumbers, all]{{f0[2]}+{f0[3]}+{f0[4]}}$. [[1]]</p>\n<p>$\\simplify[fractionNumbers, all]{{f0[5]}+{f0[6]}+{f0[7]}+{f0[8]}}$. [[2]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0'[0]}+{f0'[1]}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0'[2]}+{f0'[3]}+{f0'[4]}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0'[5]}+{f0'[6]}+{f0'[7]}+{f0'[8]}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}], "sortAnswers": false}]}, {"name": "Algebra: exponential to linear form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Paul Howes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/632/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "<p>See ??</p>", "rulesets": {}, "variables": {"vari": {"name": "vari", "group": "Ungrouped variables", "definition": "shuffle(['q','r','s','t','v','w','M','K','L','Z'])", "description": "", "templateType": "anything"}, "powera": {"name": "powera", "group": "part a", "definition": "random(2/3, 3/2, 3/5, 5/3, 0.5, 1/3)", "description": "", "templateType": "anything"}, "ca": {"name": "ca", "group": "part a", "definition": "siground(e^intercepta,2)", "description": "", "templateType": "anything"}, "grada": {"name": "grada", "group": "part a", "definition": "powera", "description": "", "templateType": "anything"}, "intercepta": {"name": "intercepta", "group": "part a", "definition": "random([-4,-3,-2,2,3,4]) + random(1..9)*0.1", "description": "", "templateType": "anything"}, "qa": {"name": "qa", "group": "part a", "definition": "expression('{vari[0]} = C {vari[1]}^(gamma)')", "description": "", "templateType": "anything"}, "v0": {"name": "v0", "group": "part a", "definition": "expression('{vari[0]}')", "description": "", "templateType": "anything"}, "v1": {"name": "v1", "group": "part a", "definition": "expression('{vari[1]}')", "description": "", "templateType": "anything"}, "ansa": {"name": "ansa", "group": "part a", "definition": "expression('gamma*x + ln(C)')", "description": "", "templateType": "anything"}, "ansa2": {"name": "ansa2", "group": "part a", "definition": "expression('{ca}*{vari[1]}^({powera})')", "description": "", "templateType": "anything"}, "v2": {"name": "v2", "group": "part b", "definition": "expression('{vari[2]}')", "description": "", "templateType": "anything"}, "v3": {"name": "v3", "group": "part b", "definition": "expression('{vari[3]}')", "description": "", "templateType": "anything"}, "qb": {"name": "qb", "group": "part b", "definition": "expression('{vari[2]} = A *e^(B*{vari[3]})')", "description": "", "templateType": "anything"}, "interceptb": {"name": "interceptb", "group": "part b", "definition": "random([-4,-3,-2,2,3,4]) + random(1..9)*0.1", "description": "", "templateType": "anything"}, "gradb": {"name": "gradb", "group": "part b", "definition": "random(55..99)/10*random([1,-1])", "description": "", "templateType": "anything"}, "ansb": {"name": "ansb", "group": "part b", "definition": "expression('B*x + ln(A)')", "description": "", "templateType": "anything"}, "ansb2": {"name": "ansb2", "group": "part b", "definition": "expression('{A} *e^({gradb}*{vari[3]})')", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "part b", "definition": "siground(e^interceptb,2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["vari"], "variable_groups": [{"name": "part a", "variables": ["powera", "v0", "v1", "qa", "grada", "intercepta", "ca", "ansa", "ansa2"]}, {"name": "part b", "variables": ["v2", "v3", "qb", "gradb", "interceptb", "A", "ansb", "ansb2"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>We are investigating the relationship between the variables $\\simplify{{v0}}$ and $\\simplify{{v1}}$ experimentally.</p>\n<p>We know that they are related via the equation $\\simplify{{qa}}$, where $\\gamma$ and $C$ are constants to be determined.</p>\n<p>This is done by plotting $\\simplify{y = ln({v0})}$ against $\\simplify{x = ln({v1})}$; we should get a straight line.</p>\n<p></p>\n<p>1. Write&nbsp;$y$ in terms of $x$, $\\gamma$ and $C$.&nbsp; To enter \"$\\gamma$\" you type \"gamma\". Use * to indicate multiplication.</p>\n<p>$y =$ [[0]]</p>\n<p></p>\n<p>2. (Calculator). When plotting $y$ against $x$, we get a straight line with gradient $\\simplify[fractionNumbers]{{grada}}$ and $y$-intercept $\\var{intercepta}$.&nbsp; Hence write $\\simplify{{v0}}$&nbsp;in terms of $\\simplify{{v1}}$. $C$ should be provided to 2 s.f..&nbsp;</p>\n<p>$\\simplify{{v0}} = $ [[1]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ansa}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ansa2}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>We are investigating the relationship between the variables $\\simplify{{v2}}$ and $\\simplify{{v3}}$ experimentally.</p>\n<p>We know that they are related via the equation $\\simplify{{qb}}$, where $A$ and $B$ are constants to be determined.</p>\n<p>This is done by plotting $\\simplify{y = ln({v2})}$ against $\\simplify{x = {v3}}$; we should get a straight line.</p>\n<p></p>\n<p>1. Write&nbsp;$y$ in terms of $x$, $A$ and $B$.&nbsp;Use * to indicate multiplication.</p>\n<p>$y =$ [[0]]</p>\n<p></p>\n<p>2. (Calculator). When plotting $y$ against $x$, we get a straight line with gradient $\\simplify{{gradb}}$ and $y$-intercept $\\var{interceptb}$.&nbsp; Hence write $\\simplify{{v2}}$&nbsp;in terms of $\\simplify{{v3}}$.&nbsp;Constants&nbsp;should be provided to 2 s.f..&nbsp;</p>\n<p>$\\simplify{{v2}} = $ [[1]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ansb}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ansb2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Integration. True/False", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Paul Howes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/632/"}, {"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}], "tags": [], "metadata": {"description": "Multi choice question week 3", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>See ??</p>", "rulesets": {}, "variables": {"statements": {"name": "statements", "group": "do not change these", "definition": "map(if(rand[j]=1,\n    statements_true[j],\n    statements_false[j]),j,0..n-1)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "change these", "definition": "random(6..9)", "description": "", "templateType": "anything"}, "max_mark": {"name": "max_mark", "group": "change these", "definition": "4", "description": "", "templateType": "anything"}, "statements_false": {"name": "statements_false", "group": "change these", "definition": "[\"$\\\\displaystyle \\\\int f(x) = \\\\cos(x)+c$\",\n  random([\"$\\\\displaystyle \\\\int \\\\sin(x) \\\\, dx = \\\\cos(x)$\",\n      \"$\\\\displaystyle \\\\int f(x) \\\\, dx = \\\\cos(x)+c$\"]),\n  \"$\\\\displaystyle \\\\int g(t) = -\\\\sin(t)+c$\",\n  random([\"$\\\\displaystyle \\\\int g(t) \\\\, dt = -\\\\sin(x)+c$\",\n      \"$\\\\displaystyle \\\\int \\\\cos(t) \\\\, dx = -\\\\sin(t)+c$\"]),\n  \"When integrating, there is no way to check your answer.\",\n  \"You include $+c$ when integrating because it is just a random rule you have to memorise.\",\n  \"The integral of $\\\\frac{1}{x}$ is determined by re-writing it as $x^{-1}$\"  \n]", "description": "", "templateType": "anything"}, "statements_true": {"name": "statements_true", "group": "change these", "definition": "[\"$\\\\displaystyle \\\\int f(x) \\\\, dx = -\\\\cos(x)+c$\",\n  \"$\\\\displaystyle \\\\int \\\\sin(x) \\\\, dx = -\\\\cos(x)+c$\",\n  \"$\\\\displaystyle \\\\int g(t) \\\\, dt = \\\\sin(t)+c$\",\n  \"$\\\\displaystyle \\\\int \\\\cos(t) \\\\, dt = \\\\sin(t)+c$\",\n  \"When integrating, you should check your answer by differentiating your answer.\",\n  \"The constant of integration summarises the possibility that you can add any number to the function.\",\n  \"The integral of $\\\\frac{1}{x}$ is $\\\\ln(x) + c$\"\n]\n ", "description": "<p><br /> \"<br /><br /><br /><br /><br /> \"To calculate changes in position using areas in a velocity-time graph, you need to think about when the object is moving forwards or backwards\",<br /> \"$\\\\sec(x) = \\\\frac{1}{\\\\cos(x)}$\",<br /> \"$\\\\csc(x) = \\\\frac{1}{\\\\sin(x)}$\" <br /> ]</p>", "templateType": "anything"}, "b": {"name": "b", "group": "change these", "definition": "random(10..18)+random(1..9)/10", "description": "", "templateType": "anything"}, "rand": {"name": "rand", "group": "do not change these", "definition": "repeat(if(random(-2..2)>0,1,0),n-1)+[if(random(0..5)=5,1,0)]", "description": "", "templateType": "anything"}, "error": {"name": "error", "group": "change these", "definition": "1/2", "description": "<p>what proportion of total marks should be lost for each error. e.g. 1/2 would mean a single error costs half of all marks available. 1/3 would mean each error costs a third of all marks.</p>", "templateType": "anything"}, "marks": {"name": "marks", "group": "do not change these", "definition": "matrix(map(if(rand[j]=1,[max_mark/n,-max_mark*error+max_mark/n],[-max_mark*error+max_mark/n,max_mark/n]),j,0..n-1))\n\n", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "do not change these", "definition": "length(statements_true)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "change these", "definition": "random(3..7)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "change these", "variables": ["statements_true", "statements_false", "max_mark", "error", "a", "b", "c"]}, {"name": "do not change these", "variables": ["n", "rand", "statements", "marks"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>In the following,&nbsp;$f(x) = \\sin(x)$ and $g(t) = \\cos(t)$.&nbsp; Which of the following are true and which are false?&nbsp;&nbsp;</p>\n<p></p>\n<p>If you are unsure of something,&nbsp;find out the answer instead of guessing.&nbsp;<strong>Each error will cost half of the marks available</strong>. If you are unable to find out, you are welcome to ask me for help or advice.</p>", "minMarks": 0, "maxMarks": "0", "minAnswers": "{n}", "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": false, "choices": "{statements}", "matrix": "{marks}", "layout": {"type": "all", "expression": ""}, "answers": ["<p>True</p>", "<p>False</p>"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Integration: standard integrals, multiple simple terms, randomised", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}], "tags": [], "metadata": {"description": "<p>Standard simple integrals asked for (1/x, sin(x), cos(x), x^2, x, e^x)</p>", "licence": "None specified"}, "statement": "", "advice": "<p>See&nbsp;??</p>", "rulesets": {}, "variables": {"a": {"name": "a", "group": "coeffs etc", "definition": "shuffle(repeat(random(2..9),5) + [-1,-1,1,random(-1,1)])", "description": "", "templateType": "anything"}, "var": {"name": "var", "group": "coeffs etc", "definition": "random(['x','z','t','p','s','r','w'])", "description": "", "templateType": "anything"}, "f0": {"name": "f0", "group": "functions", "definition": "map(expression(a[j]+\"*\"+f[rand[j]][0]+var+ f[rand[j]][1]),j,0..8)", "description": "", "templateType": "anything"}, "n2": {"name": "n2", "group": "coeffs etc", "definition": "2", "description": "", "templateType": "anything"}, "n3": {"name": "n3", "group": "coeffs etc", "definition": "random(2..5)", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "functions", "definition": "[\n  [\"(1*\",\")\"],\n  [\"(\",\")^\"+n1],\n  [\"(\",\")^\"+n2],\n  [\"1/(\",\")\"],\n  [\"1/((\",\")^\"+n3+\")\"],\n  [\"sqrt(\",\")\"],\n  [\"sin(\",\")\"],\n  [\"cos(\",\")\"],\n  [\"e^(\",\")\"],\n  [\"ln(\",\")\"]\n ]", "description": "", "templateType": "anything"}, "rand": {"name": "rand", "group": "Ungrouped variables", "definition": "shuffle([1,2,random(6..7),8,9])+shuffle([6,7,1,random(8,9)])", "description": "<p>[<br />0[\"(\"+b0[0]+\"*\",\")\"],<br />1[\"(\",\")^\"+n1],<br />2[\"(\",\")^\"+n2],<br />3[\"1/(\",\")\"],<br />4[\"1/((\",\")^\"+n3+\")\"],<br />5[\"sqrt(\",\")\"],<br />6[\"sin(\",\")\"],<br />7[\"cos(\",\")\"],<br />8[\"e^(\",\")\"],<br />9[\"ln(\",\")\"]<br /> ]</p>\n<p></p>\n<p>don't use 0 for product rule</p>", "templateType": "anything"}, "f'": {"name": "f'", "group": "functions", "definition": "[\n  [\"(1*(\",\"^0))\"],\n  [n1+\"*(\",\")^\"+(n1-1)],\n  [n2+\"*(\",\")^\"+(n2-1)],\n  [\"-1/((\",\")^2)\"],\n  [\"-\"+n3+\"/((\",\")^\"+(n3+1)+\")\"],\n  [\"0.5/(sqrt(\",\"))\"],\n  [\"cos(\",\")\"],\n  [\"-sin(\",\")\"],\n  [\"e^(\",\")\"],\n  [\"1/(\",\")\"]\n ]", "description": "", "templateType": "anything"}, "f0'": {"name": "f0'", "group": "functions", "definition": "map(expression(a[j]+\"*\"+f'[rand[j]][0]+var+ f'[rand[j]][1]),j,0..8)", "description": "", "templateType": "anything"}, "n1": {"name": "n1", "group": "coeffs etc", "definition": "1", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["rand"], "variable_groups": [{"name": "coeffs etc", "variables": ["var", "n1", "n2", "n3", "a"]}, {"name": "functions", "variables": ["f", "f'", "f0", "f0'"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Integrate the following with respect to&nbsp;$\\simplify{{expression(var)}}$.</p>\n<p></p>\n<p>$\\simplify{{f0'[0]}+{f0'[1]}}$.</p>\n<p>[[0]]</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p>$\\simplify{{f0'[2]}+{f0'[3]}+{f0'[4]}}$.</p>\n<p>[[1]]</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p>$\\simplify{{f0'[5]}+{f0'[6]}+{f0'[7]}+{f0'[8]}}$.</p>\n<p>[[2]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0[0]}+{f0[1]}+c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0[2]}+{f0[3]}+{f0[4]}+c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0[5]}+{f0[6]}+{f0[7]}+{f0[8]}+c", "showPreview": true, "checkingType": "absdiff", 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