// Numbas version: exam_results_page_options
{"name": "Partial Fractions - simplifying to one fraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a1", "a2", "b1", "b2", "b3", "c1", "c2", "c3", "ct", "d1", "d2", "d3", "dt1", "dt2"], "name": "Partial Fractions - simplifying to one fraction", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"vsetrangepoints": 5, "prompt": "<p>$\\frac{1}{x} + \\frac{1}{\\var{a1}x+\\var{a2}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "(({a1}+1)x+{a2})/({a1}x^2+{a2}x)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": ["x^2"], "partialCredit": 0}}, {"vsetrangepoints": 5, "prompt": "<p>$\\simplify{{b1}x} + \\simplify{{b2}/(x+{b3})}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({b1}x^2+{b1}*{b3}x+{b2})/(x+{b3})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": ["x^2"], "partialCredit": 0}}, {"vsetrangepoints": 5, "prompt": "<p>$\\simplify{(x-{c1})/(x-{c2})}+\\simplify{({ct})/(x-{c3})}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "(x^2-({c1}+{c3}-{ct})x+{c1}*{c3}-{c2}*{ct})/(x^2-({c2}+{c3})x+{c2}*{c3})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": ["x^2"], "partialCredit": 0}}, {"vsetrangepoints": 5, "prompt": "<p>$\\simplify{{dt1}/(x-{d1})} + \\simplify{{dt2}/((x-{d2})(x-{d3}))}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({dt1}x^2-({dt1}*{d2}+{dt1}*{d3}-{dt2})x+({dt1}*{d2}*{d3}-{dt2}*{d1}))/(x^3-({d1}+{d2}+{d3})x^2+({d1}*{d2}+{d2}*{d3}+{d1}*{d3})x-({d1}*{d2}*{d3}))", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": ["x^3", "x^2"], "partialCredit": 0}}], "statement": "<p>Express each of these as a single fraction in its simplest form.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a2": {"definition": "random(2..5 except a1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "c1": {"definition": "random(-4..4 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "b1": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(2..5 except b1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(-3..3 except 0 except b2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "c3": {"definition": "random(-5..5 except 0 except c1 except c2)", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "dt2": {"definition": "random(1..5 except dt1)", "templateType": "anything", "group": "Ungrouped variables", "name": "dt2", "description": ""}, "dt1": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "dt1", "description": ""}, "d1": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "d2": {"definition": "random(-5..5 except d1 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "d3": {"definition": "random(-5..5 except 0 except d1 except d2)", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "c2": {"definition": "random(-5..5 except 0 except c1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "ct": {"definition": "random(1..6 except [c1,c2,c3])", "templateType": "anything", "group": "Ungrouped variables", "name": "ct", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}