// Numbas version: exam_results_page_options
{"name": "T6Q12 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "T6Q12 (custom feedback)", "tags": [], "metadata": {"description": "<p>Partial differentiation question with customised feedback to catch some common errors.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>If $z=\\sin^{-1} \\frac{x}{y}$, find $\\frac{\\partial z}{\\partial x}$ and $\\frac{\\partial z}{\\partial y}$.</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>$\\frac{\\partial z}{\\partial x}=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n  [\n    [\"-1/sqrt(y^2-x^2)\", \"Check the rule for differentiating $\\\\sin^{-1} \\\\left( \\\\cdot \\\\right)$.\"],\n    [\"1/sqrt(y^2+x^2)\", \"Check the rule for differentiating $\\\\sin^{-1} \\\\left( \\\\cdot \\\\right)$.\"],\n    [\"y/(y^2+x^2)\", \"Check the rule for differentiating $\\\\sin^{-1} \\\\left( \\\\cdot \\\\right)$.\"]\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": "1/sqrt(y^2-x^2)", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}]}], "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>$\\frac{\\partial z}{\\partial y}=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n  [\n    [\"1/sqrt(1-(x/y)^2)\", \"Don't forget to multiply by the derivative of the top. Recall that $\\\\frac{\\\\partial}{\\\\partial y} \\\\left( \\\\sin^{-1} \\\\left( \\\\frac{y}{a} \\\\right) \\\\right) = \\\\frac{1}{\\\\sqrt{a^2-y^2}}$ but $\\\\frac{\\\\partial}{\\\\partial y} \\\\left( \\\\sin^{-1} \\\\left( \\\\frac{f(y)}{a} \\\\right) \\\\right) = \\\\frac{1}{\\\\sqrt{a^2-(f(y))^2}} \\\\cdot \\\\frac{\\\\partial}{\\\\partial y} \\\\left( f(y) \\\\right)$. i.e. $\\\\frac{1}{\\\\sqrt{(\\\\text{bottom})^2-(\\\\text{top})^2}} \\\\times \\\\left( \\\\text{derivative of the top} \\\\right)$\"],\n    [\"1/sqrt(y^2-x^2)\", \"There are two things to note here. Firstly, you are looking for the partial derivative with respect to $y$ here. Remember that, in the rule given on page 25 of the log tables for differentiating $\\\\sin^{-1} \\\\left( \\\\frac{x}{a} \\\\right)$, the $x$ is something to do with the variable, while $a$ is a number. Can you rewrite $\\\\sin^{-1} \\\\left( \\\\frac{x}{y} \\\\right)$ so that it looks like $\\\\sin^{-1} \\\\left( \\\\frac{\\\\text{something to do with } y}{\\\\text{a number}} \\\\right)$? Secondly, once you have written $\\\\sin^{-1} \\\\left( \\\\frac{x}{y} \\\\right)$ in this way, don't forget to multiply by the derivative of the top, i.e. the derivative will be $\\\\frac{1}{\\\\sqrt{(\\\\text{bottom})^2-(\\\\text{top})^2}} \\\\times \\\\left( \\\\text{derivative of the top} \\\\right)$.\"],\n    [\"-1/sqrt(y^2-x^2)*x/y^2\", \"You are looking for the partial derivative with respect to $y$ here. Remember that, in the rule given on page 25 of the log tables for differentiating $\\\\sin^{-1} \\\\left( \\\\frac{x}{a} \\\\right)$, the $x$ is something to do with the variable, while $a$ is a number. Can you rewrite $\\\\sin^{-1} \\\\left( \\\\frac{x}{y} \\\\right)$ so that it looks like $\\\\sin^{-1} \\\\left( \\\\frac{\\\\text{something to do with } y}{\\\\text{a number}} \\\\right)$?\"]\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": "-x/(y*sqrt(y^2-x^2))", "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": ""}, {"name": "y", "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/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}