// Numbas version: exam_results_page_options
{"name": "Sheet 2 Q1 - product rule with custom feedback", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Sheet 2 Q1 - product rule with custom feedback", "tags": [], "metadata": {"description": "Product rule question with feedback given for anticipated student errors.", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Use the <strong>product rule</strong> to differentiate the function&nbsp;$y=2t^2 \\cos (2t)$.</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "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>$\\displaystyle \\frac{dy}{dt}= $ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "malrules:\n  [\n    [\"4t*cos(2t)+2t^2*sin(2t)\", \"You're on the right track, but it looks like you have made a couple of mistakes. First, double check that you have correctly differentiated $\\\\cos(\\\\cdot)$. Next, note that while the log tables give the rule for $\\\\cos(\\\\textbf{$x$})$ or $\\\\cos(\\\\textbf{$t$})$, here you have $\\\\cos(\\\\color{red}{\\\\textbf{$2$}}t)$. What extra step do you need to correctly differentiate this?\"],\n    [\"4t*cos(2t)-2t^2*sin(2t)\", \"Almost there! Note that while the log tables give the rule for $\\\\cos(\\\\textbf{$x$})$ or $\\\\cos(\\\\textbf{$t$})$, here you have $\\\\cos(\\\\color{red}{\\\\textbf{$2$}}t)$. What extra step do you need to correctly differentiate this?\"],\n    [\"4t*cos(2t)+4t^2*sin(2t)\", \"Almost there! Double check that you have correctly differentiated $\\\\cos(\\\\cdot)$ - in particular, note the signs.\"],\n    [\"4t*cos(2t)-4t^2*sin(t)\", \"Very close. Remember, the angle of a trig. function never changes when you differentiate!\"],\n    [\"4t*cos(2t)+4t^2*sin(t)\", \"You're on the right track, but need to watch a couple of things. First, remember that the angle of a trig. function never changes when you differentiate. Next, double check that you have correctly differentiated $\\\\cos(\\\\cdot)$.\"],\n    [\"4t*cos(2t)+2t^2*sin(t)\", \"You're on the right track, but need to watch a couple of things. First, remember that the angle of a trig. function never changes when you differentiate. Next, double check that you have correctly differentiated $\\\\cos(\\\\cdot)$. Finally, note that while the log tables give the rule for $\\\\cos(\\\\textbf{$x$})$ or $\\\\cos(\\\\textbf{$t$})$, here you have $\\\\cos(\\\\color{red}{\\\\textbf{$2$}}t)$. What extra step do you need to correctly differentiate this?\"],\n    [\"4t*cos(2t)-2t^2*sin(t)\", \"You're on the right track, but need to watch a couple of things. First, remember that the angle of a trig. function never changes when you differentiate. Also, note that while the log tables give the rule for $\\\\cos(\\\\textbf{$x$})$ or $\\\\cos(\\\\textbf{$t$})$, here you have $\\\\cos(\\\\color{red}{\\\\textbf{$2$}}t)$. What extra step do you need to correctly differentiate this?\"],\n    [\"-8t*sin(2t)\", \"The function you need to differentiate is $2t^2 \\\\times \\\\cos(2t)$ i.e. one function of $t$ multiplied by another function of $t$. Therefore, you need the product rule.\"],\n    [\"8t*sin(2t)\", \"The function you need to differentiate is $2t^2 \\\\times \\\\cos(2t)$ i.e. one function of $t$ multiplied by another function of $t$. Therefore, you need the product rule.\"],\n    [\"4t*sin(2t)\", \"The function you need to differentiate is $2t^2 \\\\times \\\\cos(2t)$ i.e. one function of $t$ multiplied by another function of $t$. Therefore, you need the product rule.\"],\n    [\"-4t*sin(2t)\", \"The function you need to differentiate is $2t^2 \\\\times \\\\cos(2t)$ i.e. one function of $t$ multiplied by another function of $t$. Therefore, you need the product rule.\"]\n  ]\n\nparsed_malrules: \n    map(\n        [\"expr\":parse(x[0]),\"feedback\":x[1]],\n        x,\n        malrules\n    )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n    map(\n        len(filter(not x ,x,map(\n            try(\n                resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n                message,\n                false\n            ),\n            vars,\n            vset\n        )))<settings[\"failureRate\"],\n        malrule,\n        parsed_malrules\n    )\n\nmatched_malrules:\n  filter(x[0],x,zip(agree_malrules,parsed_malrules))\n  \nmalrule_feedback:\n    assert(numericallyCorrect,\n        assert(len(matched_malrules)=0,\n            set_credit(0,matched_malrules[0][1][\"feedback\"])\n        )\n    )\n\nmark:\n    apply(studentExpr);\n    apply(unexpectedVariables);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty)", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "4t*cos(2t)-4t^2*sin(2t)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "t", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}