// Numbas version: finer_feedback_settings
{"name": "Integration by substitution 2 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["c", "b", "a"], "functions": {}, "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Integration by susbtitution, no hint given</p>"}, "extensions": [], "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"type": "jme", "checkingAccuracy": 0.001, "marks": 1, "vsetRangePoints": 5, "answer": "2(1+e^x)^(3/2)/3+C", "unitTests": [], "showFeedbackIcon": true, "expectedVariableNames": [], "prompt": "<p>$\\int e^x \\sqrt{1+e^x} \\ dx$</p>", "customMarkingAlgorithm": "malrules:\n  [\n    [\"2/3*(1+e^x)^(3/2)\", \"Almost there! Did you forget to include the integration constant?\"],\n    [\"e^x+2/3*e^(3x/2)\", \"$\\\\sqrt{1+e^x} \\\\neq \\\\sqrt{1}+\\\\sqrt{e^x}$. Hint: Try substitution.\"],\n    [\"e^x+2/3*e^(3x/2)+C\", \"$\\\\sqrt{1+e^x} \\\\neq \\\\sqrt{1}+\\\\sqrt{e^x}$. Hint: Try substitution.\"],\n    [\"2/3*(u)^(3/2)\", \"Don't forget to fill back in for $u$. You must give your answer in terms of the original variable i.e. in terms of $x$.\"],\n    [\"2/3*(u)^(3/2)+C\", \"Don't forget to fill back in for $u$. You must give your answer in terms of the original variable i.e. in terms of $x$.\"],\n    [\"3/2*(1+e^x)^(3/2)\", \"You have multiplied by the new power rather than dividing by it.\"],\n    [\"3/2*(1+e^x)^(3/2)+C\", \"You have multiplied by the new power rather than dividing by it.\"],\n    [\"3/2*u^(3/2)+C\", \"You have multiplied by the new power rather than dividing by it.\"],\n    [\"3/2*u^(3/2)\", \"You have multiplied by the new power rather than dividing by it.\"],\n    [\"e^x*sqrt(x+e^x)+C\",\"You cannot simply integrate individual terms that are multiplied together. Hint: Try substitution.\"],\n    [\"e^x*sqrt(x+e^x)\",\"You cannot simply integrate individual terms that are multiplied together. Hint: Try substitution.\"],\n    [\"u^(1/2)+C\",\"You have not actually integrated anything. You simply substituted for $1+e^x$.\"],\n    [\"u^(1/2)\",\"You have not actually integrated anything. You simply substituted for $1+e^x$.\"],\n    [\"(1+e^x)^(1/2)+C\",\"You have not actually integrated anything. You simply substituted for $1+e^x$ and then subbed back in again.\"],\n    [\"(1+e^x)^(1/2)\",\"You have not actually integrated anything. You simply substituted for $1+e^x$ and then subbed back in again.\"]\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(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty)", "checkVariableNames": false, "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "vsetRange": [0, 1], "showPreview": true, "extendBaseMarkingAlgorithm": true}, {"type": "jme", "checkingAccuracy": 0.001, "marks": 1, "vsetRangePoints": 5, "answer": "1/{a}ln({a}x+{b})+C", "unitTests": [], "showFeedbackIcon": true, "expectedVariableNames": [], "prompt": "<p>$\\int\\frac{dx}{\\var{a}x+\\var{b}}$.</p>\n<p>Answer in terms of the natural log, represented by ln( ).</p>", "customMarkingAlgorithm": "malrules:\n  [\n    [\"1/{a}ln({a}x+{b})\", \"Almost there! Did you forget to include the integration constant?\"],\n    [\"ln({a}x+{b})\", \"Did  you remember to divide by the number in front of $x$? If you used substitution, double check the relationship between $du$ and $dx$.\"],\n    [\"ln({a}x+{b})+C\", \"Did  you remember to divide by the number in front of $x$? If you used substitution, double check the relationship between $du$ and $dx$.\"],\n    [\"{a}*ln({a}x+{b})\", \"You have multiplied by the number in front of $x$ rather than dividing by it. If you used substitution, double check the relationship between $du$ and $dx$.\"],\n    [\"{a}*ln({a}x+{b})+C\", \"You have multiplied by the number in front of $x$ rather than dividing by it. If you used substitution, double check the relationship between $du$ and $dx$.\"]\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(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty)", "checkVariableNames": false, "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "vsetRange": [0, 1], "showPreview": true, "extendBaseMarkingAlgorithm": true}, {"type": "jme", "checkingAccuracy": 0.001, "marks": 1, "vsetRangePoints": 5, "answer": "ln({c}+x^2)/2+C", "unitTests": [], "showFeedbackIcon": true, "expectedVariableNames": [], "prompt": "<p>$\\int \\frac{x \\ dx}{\\var{c}+x^2}$.</p>\n<p>Answer in terms of the natural log, represented by ln( ).</p>", "customMarkingAlgorithm": "malrules:\n  [\n    [\"ln({c}+x^2)/2\", \"Almost there! Did you forget to include the integration constant?\"],\n    [\"1/2*ln(u)\", \"Don't forget to fill back in for $u$. You must give your answer in terms of the original variable i.e. in terms of $x$.\"],\n    [\"1/2*ln(u)+C\", \"Don't forget to fill back in for $u$. You must give your answer in terms of the original variable i.e. in terms of $x$.\"],\n    [\"ln(u)+C\", \"Double check the relationship between $du$ and $dx$. Did you sub in correctly here?\"],\n    [\"ln(u)\", \"Double check the relationship between $du$ and $dx$. Did you sub in correctly here?\"],\n    [\"ln({c}+x^2)+C\", \"Double check the relationship between $du$ and $dx$. Did you sub in correctly here?\"],\n    [\"ln({c}+x^2)\", \"Double check the relationship between $du$ and $dx$. Did you sub in correctly here?\"],\n    [\"1/(2({c}+x^2))\",\"You have not actually integrated anything. You simply substituted for ${c}+x^2$ and then subbed back in again.\"],\n    [\"1/(2({c}+x^2))+C\",\"You have not actually integrated anything. You simply substituted for ${c}+x^2$ and then subbed back in again.\"],\n    [\"1/(2u)\",\"You have not actually integrated anything. You simply substituted for ${c}+x^2$.\"],\n    [\"1/(2u)+C\",\"You have not actually integrated anything. You simply substituted for ${c}+x^2$.\"]\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(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty)", "checkVariableNames": false, "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "vsetRange": [0, 1], "showPreview": true, "extendBaseMarkingAlgorithm": true}], "name": "Integration by substitution 2 (custom feedback)", "advice": "<p>integration by Susbtitution</p>", "rulesets": {}, "statement": "<p>Evaluate the following indefinite integrals using integration by substitution. Use the letter C to represent any unknown constants.</p>", "variable_groups": [], "variables": {"c": {"description": "", "templateType": "anything", "name": "c", "definition": "random(1..9)", "group": "Ungrouped variables"}, "a": {"description": "", "templateType": "anything", "name": "a", "definition": "random(2..6)", "group": "Ungrouped variables"}, "b": {"description": "", "templateType": "anything", "name": "b", "definition": "random(1..8 except a)", "group": "Ungrouped variables"}}, "type": "question", "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}, {"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}], "resources": []}]}], "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}, {"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}