// Numbas version: exam_results_page_options
{"name": "Sheet 2 Q8 Chain 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 Q8 Chain Rule with custom feedback", "tags": [], "metadata": {"description": "Chain rule question with feedback given for anticipated student errors.", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Find the slope of the tangent to the curve $f(t)=\\ln (\\cos t)$ when $\\displaystyle t=\\frac{\\pi}{4}$.</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>First, find the derivative:</p>\n<p>$f'(t) = $ [[0]]</p>\n<p></p>\n<p>Next, find the slope of the tangent when $\\displaystyle t = \\frac{\\pi}{4}$:</p>\n<p>Slope = [[1]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n  [\n    [\"1/t*cos(t)-ln(sin(t))\", \"Note that the function you need to differentiate is $3 \\\\ln(\\\\cos t)$ not $3 \\\\ln \\\\times \\\\cos t$. This is not a product and so we do not need the product rule.\"],\n    [\"1/t*cos(t)+ln(sin(t))\", \"Note that the function you need to differentiate is $3 \\\\ln(\\\\cos t)$ not $\\\\ln \\\\times \\\\cos t$. This is not a product and so we do not need the product rule.\"],\n    [\"1/cos(t)\", \"You have used the correct basic rule for the natural log. However, when you are differentiating $\\\\ln(\\\\color{red}{f(t)})$ rather than just $\\\\ln(t)$, what extra step do you need to include?\"],\n    [\"sin(t)/cos(t)\", \"You are almost there. Double check the rule for differentiating $\\\\cos t$.\"]\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": "-sin(t)/cos(t)", "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": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n  [\n    [\"-0.013708642\", \"It looks like you have your calculator set to degrees rather than radians.\"],\n    [\"-3.016702834\", \"Note that the function you need to differentiate is $3 \\\\ln(\\\\cos t)$ not $3 \\\\ln \\\\times \\\\cos t$. This is not a product and so we do not need the product rule. Also, make sure your calculator is in radians and not degrees.\"],\n    [\"5.562942681\", \"Note that the function you need to differentiate is $3 \\\\ln(\\\\cos t)$ not $3 \\\\ln \\\\times \\\\cos t$. This is not a product and so we do not need the product rule. Also, make sure your calculator is in radians and not degrees.\"],\n    [\"0.553742725\", \"Note that the function you need to differentiate is $3 \\\\ln(\\\\cos t)$ not $3 \\\\ln \\\\times \\\\cos t$. This is not a product and so we do not need the product rule.\"],\n    [\"1.246889906\", \"Note that the function you need to differentiate is $3 \\\\ln(\\\\cos t)$ not $3 \\\\ln \\\\times \\\\cos t$. This is not a product and so we do not need the product rule.\"],\n    [\"sqrt(2)\", \"You have used the correct basic rule for the natural log. However, when you are differentiating $\\\\ln(\\\\color{red}{f(t)})$ rather than just $\\\\ln(t)$, what extra step do you need to include?\"],\n    [\"1.000093959\", \"You have used the correct basic rule for the natural log. However, when you are differentiating $\\\\ln(\\\\color{red}{f(t)})$ rather than just $\\\\ln(t)$, what extra step do you need to include? Also, make sure your calculator is set to radians rather than degrees.\"],\n    [\"0.013708642\", \"You are almost there. Double check the rule for differentiating $\\\\cos t$. Also, make sure your calculator is set to radians rather than degrees.\"],\n    [\"1\", \"You are almost there. Double check the rule for differentiating $\\\\cos t$.\"]\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": "-1", "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": []}], "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/"}]}