// Numbas version: exam_results_page_options
{"name": "Differentiate by Power rule 1 [L7 Randomised]", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [{"name": "Q2 group", "variables": ["d1", "d2", "e1", "e2", "f1"]}, {"name": "Q3  group", "variables": ["g1", "g2", "h1", "h2", "i1"]}], "advice": "<p>Apply&nbsp;the rule:</p>\n<p style=\"padding-left: 30px;\">\\(y=ax^n\\,\\,\\,then\\,\\,\\,\\frac{dy}{dx}=nax^{n-1}\\)</p>\n<p>In this example</p>\n<p style=\"padding-left: 30px;\">\\(f(x)=\\var{a1}x^{\\var{a2}}+\\var{b1}x^{\\var{b2}}+\\var{c1}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{dx}=\\var{a2}*\\var{a1}x^{\\var{a2}-1}+\\var{b2}*\\var{b1}x^{\\var{b2}-1}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{dy}{dx}=\\simplify{{a2}*{a1}x^{{a2}-1}+{b2}*{b1}x^{{b2}-1}}\\)</p>", "tags": ["L7"], "parts": [{"customMarkingAlgorithm": "", "marks": 0, "sortAnswers": false, "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "gaps": [{"customMarkingAlgorithm": "", "expectedVariableNames": [], "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "marks": 1, "answer": "{a1}*{a2}*x^{{a2}-1}+{b1}*{b2}*x^{{b2}-1}", "type": "jme", "showFeedbackIcon": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "showPreview": true, "vsetRange": [0, 1], "failureRate": 1, "extendBaseMarkingAlgorithm": true, "unitTests": [], "checkVariableNames": false}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>\\(f(x)=\\var{a1}x^{\\var{a2}}+\\var{b1}x^{\\var{b2}}+\\var{c1}\\)</p>\n<p></p>\n<p>\\(\\frac{df}{dx}=\\)&nbsp;[[0]]</p>", "unitTests": [], "extendBaseMarkingAlgorithm": true}, {"customMarkingAlgorithm": "", "marks": 0, "sortAnswers": false, "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "gaps": [{"customMarkingAlgorithm": "", "expectedVariableNames": [], "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "marks": 1, "answer": "{d1}*{d2}*x^{{d2}-1}+{e1}*{e2}*x^{{e2}-1}", "type": "jme", "showFeedbackIcon": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "showPreview": true, "vsetRange": [0, 1], "failureRate": 1, "extendBaseMarkingAlgorithm": true, "unitTests": [], "checkVariableNames": false}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>\\(f(x)=\\var{d1}x^{\\var{d2}}+\\var{e1}x^{\\var{e2}}+\\var{f1}\\)</p>\n<p></p>\n<p>\\(\\frac{df}{dx}=\\)&nbsp;[[0]]</p>", "unitTests": [], "extendBaseMarkingAlgorithm": true}, {"customMarkingAlgorithm": "", "marks": 0, "sortAnswers": false, "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "gaps": [{"customMarkingAlgorithm": "", "expectedVariableNames": [], "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "marks": 1, "answer": "{g1}*{g2}*x^{{g2}-1}+{h1}*{h2}*x^{{h2}-1}", "type": "jme", "showFeedbackIcon": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "showPreview": true, "vsetRange": [0, 1], "failureRate": 1, "extendBaseMarkingAlgorithm": true, "unitTests": [], "checkVariableNames": false}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>\\(f(x)=\\var{g1}x^{\\var{g2}}+\\var{h1}x^{\\var{h2}}+\\var{i1}\\)</p>\n<p>\\(\\frac{df}{dx}=\\)&nbsp;[[0]]</p>", "unitTests": [], "extendBaseMarkingAlgorithm": true}], "name": "Differentiate by Power rule 1 [L7 Randomised]", "metadata": {"description": "<p>Power rule</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"js": "", "css": ""}, "functions": {}, "variables": {"g2": {"description": "", "name": "g2", "templateType": "randrange", "definition": "random(9..5#1)", "group": "Q3  group"}, "g1": {"description": "", "name": "g1", "templateType": "randrange", "definition": "random(2..9#1)", "group": "Q3  group"}, "a2": {"description": "", "name": "a2", "templateType": "randrange", "definition": "random(5..12#1)", "group": "Ungrouped variables"}, "c1": {"description": "", "name": "c1", "templateType": "randrange", "definition": "random(3..18#1)", "group": "Ungrouped variables"}, "f1": {"description": "", "name": "f1", "templateType": "randrange", "definition": "random(4..19#1)", "group": "Q2 group"}, "a1": {"description": "", "name": "a1", "templateType": "randrange", "definition": "random(2..10#1)", "group": "Ungrouped variables"}, "d2": {"description": "", "name": "d2", "templateType": "randrange", "definition": "random(7..5#1)", "group": "Q2 group"}, "b1": {"description": "", "name": "b1", "templateType": "randrange", "definition": "random(2..14#1)", "group": "Ungrouped variables"}, "h2": {"description": "", "name": "h2", "templateType": "randrange", "definition": "random(4..2#1)", "group": "Q3  group"}, "e2": {"description": "", "name": "e2", "templateType": "randrange", "definition": "random(4..2#1)", "group": "Q2 group"}, "b2": {"description": "", "name": "b2", "templateType": "randrange", "definition": "random(1..5#1)", "group": "Ungrouped variables"}, "i1": {"description": "", "name": "i1", "templateType": "randrange", "definition": "random(30..1#1)", "group": "Q3  group"}, "h1": {"description": "", "name": "h1", "templateType": "randrange", "definition": "random(6..14#1)", "group": "Q3  group"}, "d1": {"description": "", "name": "d1", "templateType": "randrange", "definition": "random(5..14#1)", "group": "Q2 group"}, "e1": {"description": "", "name": "e1", "templateType": "randrange", "definition": "random(3..9#1)", "group": "Q2 group"}}, "rulesets": {}, "statement": "<p>Differentiate the function:</p>\n<p style=\"padding-left: 30px;\">\\(f(x)=\\var{a1}x^{\\var{a2}}+\\var{b1}x^{\\var{b2}}+\\var{c1}\\)</p>", "ungrouped_variables": ["a1", "a2", "b1", "b2", "c1"], "extensions": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Abbi Mullins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2466/"}, {"name": "Matthew James Sykes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2582/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Abbi Mullins", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2466/"}, {"name": "Matthew James Sykes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2582/"}]}