// Numbas version: exam_results_page_options
{"name": "T6Q6 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "T6Q6 (custom feedback)", "tags": [], "metadata": {"description": "<p>Product rule differentiation question with customised feedback to catch some common errors.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Find $\\displaystyle \\frac{dy}{dx}$ if $y=\\sin x \\cos (x^2+4)$.</p>", "advice": "", "rulesets": {}, "extensions": [], "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>$\\displaystyle \\frac{dy}{dx}=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n  [\n    [\"(cos(x^3+4x))^2-2x*(sin(x^3+4x))^2\", \"$\\\\sin A \\\\sin B \\\\neq \\\\sin^2 (AB).$ To see this, try entering $\\\\sin \\\\left(\\\\frac{\\\\pi}{2} \\\\right) \\\\times \\\\sin \\\\left( 2 \\\\right)$ into your calculator and compare to the answer you get if you enter $\\\\left( \\\\sin \\\\left( \\\\frac{\\\\pi}{2} \\\\times 2 \\\\right) \\\\right)^2$ into your calculator. Similarly $\\\\cos A \\\\cos B \\\\neq \\\\cos^2 (AB)$.\"],\n    [\"cos(x^3+4x)-2x*sin(x^3+4x)\", \"$\\\\sin A \\\\sin B \\\\neq \\\\sin (AB).$ To see this, try entering $\\\\sin \\\\left(\\\\frac{\\\\pi}{2} \\\\right) \\\\times \\\\sin \\\\left( 2 \\\\right)$ into your calculator and compare to the answer you get if you enter $\\\\sin \\\\left( \\\\frac{\\\\pi}{2} \\\\times 2 \\\\right)$ into your calculator. Similarly $\\\\cos A \\\\cos B \\\\neq \\\\cos (AB)$.\"],\n    [\"-2x*cos(x)*sin(x^2+4)\", \"Don't forget the product rule! Remember, you need the product rule whenever you have one function of $x$ multiplied by another function of $x$.\"],\n    [\"cos(x)*cos(x^2+4)-sin(x)*sin(x^2+4)\", \"On the right track. Don't forget the derivative of $\\\\cos$ (angle) is $-\\\\sin$ (the same angle) $\\\\times$ (derivative of the angle).\"],\n    [\"cos(x)*cos(x^2+4)-sin(x)*sin(2x)\", \"Be careful when differentiating $\\\\cos(x^2+4)$. Remember the angle never changes when you differentiate a trigonometric function. Instead, the derivative of $\\\\cos$ (angle) is $-\\\\sin$ (the same angle) $\\\\times$ (derivative of the angle).\"]\n    ]\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(sameVars);\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": "-2x*sin(x)*sin(x^2+4)+cos(x)*cos(x^2+4)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "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/"}]}