// Numbas version: exam_results_page_options {"name": "T6Q11 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"variableReplacements": [], "type": "gapfill", "prompt": "

$\\frac{dy}{dx}=$ [[0]]

", "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacements": [], "checkVariableNames": false, "showPreview": true, "type": "jme", "scripts": {}, "vsetRangePoints": 5, "customMarkingAlgorithm": "malrules:\n [\n [\"x^2*e^(x^2-1)\", \"You cannot use the power rule when there is a variable in the power. What other rule could you use here? Look at page 25 of the log tables if you need to.\"],\n [\"e^(x^2)\", \"Don't forget to multiply by the derivative of the power. Remember, $\\\\frac{d}{dx} \\\\left( e^x \\\\right) = e^x$ but $\\\\frac{d}{dx} \\\\left( e^{f(x)} \\\\right) = e^{f(x)} \\\\cdot f'(x)$.\"],\n [\"2x*e^(x^2-1)\", \"Remember, the power on the exponential function never changes when you differentiate.\"],\n [\"e^(2x)\", \"Remember, the power on the exponential function never changes when you differentiate.\"]\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 )))$\\frac{d^2 y}{dx^2}=$ [[0]]

", "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacements": [], "checkVariableNames": false, "showPreview": true, "type": "jme", "scripts": {}, "vsetRangePoints": 5, "customMarkingAlgorithm": "malrules:\n [\n [\"4x*e^(x^2)\", \"Don't forget to use the product rule! The first derivative is one function of $x$ multiplied by another function of $x$ and so, to find the second derivative, you need the product rule.\"],\n [\"2e^(x^2)+2x*e^(2x)\", \"Remember: the power on the exponential function never changes when you differentiate.\"],\n [\"2e^(x^2)+2x*e^(x^2)\", \"Almost there! When differentiating $e^{x^2}$, don't forget to multiply by the derivative of the power. Remember, $\\\\frac{d}{dx} \\\\left( e^x \\\\right) = e^x$ but $\\\\frac{d}{dx} \\\\left( e^{f(x)} \\\\right) = e^{f(x)} \\\\cdot f'(x)$.\"],\n [\"2e^(2x)\", \"There are two things to note here. Firstly, don't forget to use the product rule! The first derivative is one function of $x$ multiplied by another function of $x$ and so, to find the second derivative, you need the product rule. Also, remember: the power on the exponential function never changes when you differentiate.\"],\n [\"2e^(x^2)\", \"Don't forget to use the product rule! The first derivative is one function of $x$ multiplied by another function of $x$ and so, to find the second derivative, you need the product rule.\"]\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 )))$\\frac{1}{2} \\frac{d^2 y}{dx^2} + \\frac{dy}{dx}=$ [[0]]

", "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"variableReplacements": [], "checkVariableNames": false, "showPreview": true, "type": "jme", "scripts": {}, "vsetRangePoints": 5, "customMarkingAlgorithm": "", "checkingAccuracy": 0.001, "vsetRange": [0, 1], "unitTests": [], "marks": 1, "showCorrectAnswer": true, "expectedVariableNames": [], "checkingType": "absdiff", "answer": "e^(x^2)*(2x^2+2x+1)", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "failureRate": 1, "variableReplacementStrategy": "originalfirst"}], "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst"}], "metadata": {"description": "

Differentiation question with customised feedback to catch some common errors.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": [], "variable_groups": [], "variables": {}, "advice": "", "statement": "

If $y=e^{x^2}$, find $\\frac{1}{2} \\frac{d^2 y}{dx^2} + \\frac{dy}{dx}$.

", "name": "T6Q11 (custom feedback)", "tags": [], "rulesets": {}, "extensions": [], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "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/"}]}