// Numbas version: exam_results_page_options
{"name": "Indefinite Integrals 1_2019 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p>Indefinite Integrals</p>", "variable_groups": [], "tags": [], "extensions": [], "preamble": {"css": "", "js": ""}, "rulesets": {}, "ungrouped_variables": ["a", "c", "b", "d", "f"], "name": "Indefinite Integrals 1_2019 (custom feedback)", "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Solve the following indefinite integrals, using $C$ to represent an unknown constant.</p>", "parts": [{"showPreview": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>$\\int(x^4-\\var{a}x^3+\\var{b}x-\\var{c})\\mathrm{dx}$</p>", "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "customMarkingAlgorithm": "", "unitTests": [], "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "type": "jme", "variableReplacements": [], "checkingAccuracy": 0.001, "marks": 1, "answer": "x^5/5-{a}x^4/4+{b}x^2/2-{c}x+C", "checkingType": "absdiff"}, {"showPreview": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>$\\int(u+\\var{d})(2u+\\var{f})\\mathrm{du}$</p>", "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "customMarkingAlgorithm": "malrules:\n  [\n    [\"(u^2/2+{d}*u)*(u^2+{f}*u)+C\", \"It looks like you integrated each term without multiplying out the expression. Try multiplying out first.\"]\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(sameVars);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty)", "unitTests": [], "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "type": "jme", "variableReplacements": [], "checkingAccuracy": 0.001, "marks": 1, "answer": "2u^3/3+u^2({f}+2{d})/2+{d}{f}u+C", "checkingType": "absdiff"}, {"showPreview": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>$\\int\\frac{\\sin(2x)}{\\sin(x)}\\mathrm{dx}$.</p>\n<p>Take care to include the brackets in the trigonometric expressions, i.e. write sin(x) rather than sinx.</p>", "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "customMarkingAlgorithm": "malrules:\n  [\n    [\"1/2cos(2x)/cos(x)+C\", \"It looks like you divided the integral of the top by the integral of the bottom. Integration doesn't work like this. Try using the trigonometric identity $\\sin(2x)=2\\sin(x)\\cos(x)$ first instead.\"]\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(sameVars);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty)", "unitTests": [], "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "type": "jme", "variableReplacements": [], "checkingAccuracy": 0.001, "marks": 1, "answer": "2sin(x) + C", "checkingType": "absdiff"}, {"showPreview": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>$\\int (\\frac{2}{x^4}+\\frac{3}{x}+1)\\mathrm{dx}$</p>", "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "customMarkingAlgorithm": "malrules:\n  [\n    [\"-2x^(-5)/5+3ln(x)+x+C\", \"Check the first term again. It looks like you have subtracted 1 from the power.\"],\n    [\"-2x^(-5)/5+ln(3x)+x+C\", \"The first two terms are incorrect. First term: It looks like you have subtracted 1 from the power. 2nd term: $\\\\frac{3}{x}=3\\\\left(\\\\frac{1}{x}\\\\right)$. What do you get when you integrate $\\\\frac{1}{x}$?\"],\n    [\"-2x^(-5)/5+3+x+C\", \"The first two terms are incorrect. First term: It looks like you have subtracted 1 from the power. 2nd term: $\\\\frac{3}{x}=3x^{-1}$. The power rule doesn't work if the power on the $x$ is $-1$.\"]\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(sameVars);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty) ", "unitTests": [], "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "type": "jme", "variableReplacements": [], "checkingAccuracy": 0.001, "marks": 1, "answer": "-2/3*1/x^3+3ln(x)+x+C", "checkingType": "absdiff"}, {"showPreview": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>$\\int(q^3+\\sqrt{q})\\mathrm{dq}$</p>", "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "customMarkingAlgorithm": "", "unitTests": [], "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "type": "jme", "variableReplacements": [], "checkingAccuracy": 0.001, "marks": 1, "answer": "q^4/4+2/3q^(3/2)+C", "checkingType": "absdiff"}, {"showPreview": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>$\\int(x^2-6+\\frac{x}{2})\\mathrm{dx}$</p>", "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "customMarkingAlgorithm": "", "unitTests": [], "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "type": "jme", "variableReplacements": [], "checkingAccuracy": 0.001, "marks": 1, "answer": "x^3/3-6x+x^2/4+C", "checkingType": "absdiff"}, {"showPreview": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>$\\int{(\\frac{3}{4}-2p+\\frac{4}{p^2}})\\mathrm{dp}$</p>", "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "customMarkingAlgorithm": "malrules:\n  [\n    [\"3/4p-p^2+4ln(p^2)+C\", \"Check the third term again. $\\\\int \\\\frac{1}{p} \\\\ dp = \\\\ln p$ but $\\\\int \\\\frac{1}{p^n} \\\\ dp$ for $n \\\\neq 1$ is not $\\\\ln(p^n)$. That is, if the power on $p$ under the line is anything other than $1$, the integral is not $\\\\ln$.\"]\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(sameVars);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty) ", "unitTests": [], "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "type": "jme", "variableReplacements": [], "checkingAccuracy": 0.001, "marks": 1, "answer": "3/4p-p^2-4/p+c", "checkingType": "absdiff"}, {"showPreview": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "<p>$\\int{(\\frac{1}{4}\\sqrt{x}-3\\sqrt{x^5})}\\mathrm{dx}$</p>", "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "customMarkingAlgorithm": "malrules:\n  [\n    [\"1/6x^(3/2)-2(x^5)^(3/2)+C\", \"Check the second term again. Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"]\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(sameVars);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty) ", "unitTests": [], "showCorrectAnswer": true, "scripts": {}, "failureRate": 1, "type": "jme", "variableReplacements": [], "checkingAccuracy": 0.001, "marks": 1, "answer": "1/6x^(3/2)-6/7x^(7/2)+c", "checkingType": "absdiff"}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Simple Indefinite Integrals</p>\n<p></p>"}, "variables": {"a": {"templateType": "anything", "name": "a", "description": "", "group": "Ungrouped variables", "definition": "random(2..9)"}, "c": {"templateType": "anything", "name": "c", "description": "", "group": "Ungrouped variables", "definition": "random(1..9 except a except b)"}, "d": {"templateType": "anything", "name": "d", "description": "", "group": "Ungrouped variables", "definition": "random(1..8)"}, "b": {"templateType": "anything", "name": "b", "description": "", "group": "Ungrouped variables", "definition": "random(2..9 except a)"}, "f": {"templateType": "anything", "name": "f", "description": "", "group": "Ungrouped variables", "definition": "random(1..8 except d)"}}, "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/"}]}