// Numbas version: exam_results_page_options
{"name": "Integration Using Partial Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "preamble": {"css": "", "js": ""}, "metadata": {"description": "<p>Integration using partial fractions</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": [], "functions": {}, "tags": [], "variables": {"f": {"description": "", "definition": "random(1..6 except c)", "name": "f", "group": "Ungrouped variables", "templateType": "anything"}, "g": {"description": "", "definition": "random(-3..3 except 0)", "name": "g", "group": "Ungrouped variables", "templateType": "anything"}, "a": {"description": "", "definition": "random(2..6)", "name": "a", "group": "Ungrouped variables", "templateType": "anything"}, "d": {"description": "", "definition": "random(2..4 except b)", "name": "d", "group": "Ungrouped variables", "templateType": "anything"}, "b": {"description": "", "definition": "random(2..4)", "name": "b", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"description": "", "definition": "random(1..5)", "name": "c", "group": "Ungrouped variables", "templateType": "anything"}, "h": {"description": "", "definition": "random(-3..3 except g except -g except 0)", "name": "h", "group": "Ungrouped variables", "templateType": "anything"}}, "name": "Integration Using Partial Fractions", "parts": [{"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>", "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}, "gaps": [{"checkingaccuracy": 0.001, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showpreview": true, "checkvariablenames": false, "showCorrectAnswer": true, "answer": "({a}{c}+1)/({f}+{c})ln(x-{c})+({a}{f}-1)/({c}+{f})ln(x+{f})", "scripts": {}, "vsetrange": [0, 1], "vsetrangepoints": 5, "marks": 1, "checkingtype": "absdiff", "type": "jme", "expectedvariablenames": [], "showFeedbackIcon": true}]}, {"prompt": "<p>$\\int\\frac{x}{\\simplify{x^2-{g+h}x+{g}{h}}}\\mathrm{dx}$</p>\n<p>$=$ [[0]]</p>", "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}, "gaps": [{"checkingaccuracy": 0.001, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showpreview": true, "checkvariablenames": false, "showCorrectAnswer": true, "answer": "{g}/({g}-{h})ln(x-{g})+{h}/({h}-{g})ln(x-{h})", "scripts": {}, "vsetrange": [0, 1], "vsetrangepoints": 5, "marks": 1, "checkingtype": "absdiff", "type": "jme", "expectedvariablenames": [], "showFeedbackIcon": true}]}], "variable_groups": [], "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "h"], "advice": "<p>First split into its partial fractions and then integrate</p>", "statement": "<p>Split the following into partial fractions and hence evaluate the integrals.</p>", "type": "question", "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}]}]}], "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}]}