// Numbas version: exam_results_page_options
{"name": "CA2 Block 2 Q5 2019", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "tags": [], "extensions": [], "name": "CA2 Block 2 Q5 2019", "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Perform the following integration, using&nbsp;the letter $C$ to represent any unknown constants.</p>", "parts": [{"unitTests": [], "variableReplacementStrategy": "originalfirst", "checkingAccuracy": 0.001, "showCorrectAnswer": true, "marks": "2", "prompt": "<p>$\\int \\cos (\\var{c}x+2) \\&nbsp;dx$.</p>\n<p></p>", "checkingType": "absdiff", "checkVariableNames": false, "vsetRangePoints": 5, "showPreview": true, "showFeedbackIcon": true, "scripts": {}, "type": "jme", "vsetRange": [0, 1], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "answer": "(1/{c})*sin({c}x+2)+C", "expectedVariableNames": [], "failureRate": 1, "customMarkingAlgorithm": "malrules:\n  [\n    [\"(1/{c})*sin({c}x+2)\", \"Almost there! Did you forget to include the integration constant?\",0.9],\n    [\"-{c}*sin({c}x+2)+C\", \"It looks like you differentiated rather than integrating.\",0],\n    [\"-{c}*sin({c}x+2)\", \"It looks like you differentiated rather than integrating.\",0],\n    [\"-(1/{c})*sin({c}x+2)+C\", \"Double check the rule for integrating $\\\\cos(x)$.\",0],\n    [\"-(1/{c})*sin({c}x+2)\", \"Double check the rule for integrating $\\\\cos(x)$.\",0],\n    [\"{c}*sin({c}x+2)+C\", \"It looks like you have multiplied by the number in front of $x$. Did you mean to do this?\",0],\n    [\"{c}*sin({c}x+2)\", \"It looks like you have multiplied by the number in front of $x$. Did you mean to do this?\",0],\n    [\"sin({c}x+2)+C\",\"Did you forget to divide by the number in front of $x$?\",0],\n    [\"sin({c}x+2)\",\"Did you forget to divide by the number in front of $x$?\",0]\n  ]\n\n\nparsed_malrules: \n    map(\n        [\"expr\":parse(x[0]),\"feedback\":x[1],\"credit\":x[2]],\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(matched_malrules[0][1][\"credit\"],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)"}], "variables": {"b": {"group": "Ungrouped variables", "name": "b", "definition": "random(1..8 except a)", "description": "", "templateType": "anything"}, "c": {"group": "Ungrouped variables", "name": "c", "definition": "random(2..20)", "description": "", "templateType": "anything"}, "a": {"group": "Ungrouped variables", "name": "a", "definition": "random(2..6)", "description": "", "templateType": "anything"}}, "metadata": {"description": "<p>Integration by susbtitution. Use the letter C for the constant.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "<p>integration by Susbtitution</p>", "ungrouped_variables": ["c", "b", "a"], "type": "question", "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}