// Numbas version: exam_results_page_options
{"name": "MA1002 Integration Using Partial Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"a": {"description": "", "templateType": "anything", "name": "a", "group": "Ungrouped variables", "definition": "random(2..6)"}, "g": {"description": "", "templateType": "anything", "name": "g", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)"}, "f": {"description": "", "templateType": "anything", "name": "f", "group": "Ungrouped variables", "definition": "random(1..6 except c)"}, "h": {"description": "", "templateType": "anything", "name": "h", "group": "Ungrouped variables", "definition": "random(-3..3 except g except -g except 0)"}, "c": {"description": "", "templateType": "anything", "name": "c", "group": "Ungrouped variables", "definition": "random(1..5)"}, "d": {"description": "", "templateType": "anything", "name": "d", "group": "Ungrouped variables", "definition": "random(2..4 except b)"}, "b": {"description": "", "templateType": "anything", "name": "b", "group": "Ungrouped variables", "definition": "random(2..4)"}}, "variable_groups": [], "metadata": {"description": "<p>Integration using partial fractions</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"css": "", "js": ""}, "statement": "<p>Split the following into partial fractions and hence evaluate the integrals.</p>", "name": "MA1002 Integration Using Partial Fractions", "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "h"], "parts": [{"marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"marks": "5", "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "expectedvariablenames": [], "scripts": {}, "type": "jme", "showCorrectAnswer": false, "vsetrange": [0, 1], "checkingtype": "absdiff", "answer": "({a}{c}+1)/({f}+{c})ln(x-{c})+({a}{f}-1)/({c}+{f})ln(x+{f})", "vsetrangepoints": 5, "checkingaccuracy": 0.001, "showpreview": true}], "variableReplacements": [], "prompt": "<p>$\\int\\frac{1+\\var{a}x}{(x-\\var{c})(x+\\var{f})}\\mathrm{dx}$</p>\n<p>$=$[[0]]</p>\n<p>Express your answer in terms of the natural log, ln(x).&nbsp;</p>", "scripts": {}}, {"marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"marks": "5", "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "checkvariablenames": false, "expectedvariablenames": [], "scripts": {}, "type": "jme", "showCorrectAnswer": false, "vsetrange": [0, 1], "checkingtype": "absdiff", "answer": "{g}/({g}-{h})ln(x-{g})+{h}/({h}-{g})ln(x-{h})", "vsetrangepoints": 5, "checkingaccuracy": 0.001, "showpreview": true}], "variableReplacements": [], "prompt": "<p>$\\int\\frac{x}{\\simplify{x^2-{g+h}x+{g}{h}}}\\mathrm{dx}$</p>\n<p>$=$ [[0]]</p>", "scripts": {}}], "advice": "<p>First split into its partial fractions and then integrate</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": [], "tags": [], "rulesets": {}, "functions": {}, "type": "question", "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}]}]}], "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}]}