// Numbas version: exam_results_page_options
{"name": "Solving Equations with Hidden Quadratics", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"solmax": {"description": "", "group": "Ungrouped variables", "name": "solmax", "definition": "max(-b/a,-d/c)", "templateType": "anything"}, "d": {"description": "", "group": "Ungrouped variables", "name": "d", "definition": "random(-5..5#1)", "templateType": "randrange"}, "solmax1": {"description": "", "group": "Ungrouped variables", "name": "solmax1", "definition": "if(solmax<0,\"no real solutions\",sqrt(solmax))", "templateType": "anything"}, "a": {"description": "", "group": "Ungrouped variables", "name": "a", "definition": "random(1..5#1)", "templateType": "randrange"}, "solmin": {"description": "", "group": "Ungrouped variables", "name": "solmin", "definition": "min(-b/a,-d/c)", "templateType": "anything"}, "solmin1": {"description": "", "group": "Ungrouped variables", "name": "solmin1", "definition": "if(solmin<0,\"no real solutions\",sqrt(solmin))", "templateType": "anything"}, "c": {"description": "", "group": "Ungrouped variables", "name": "c", "definition": "random(1..5#1)", "templateType": "randrange"}, "b": {"description": "", "group": "Ungrouped variables", "name": "b", "definition": "random(-5..5#1)", "templateType": "randrange"}}, "preamble": {"js": "", "css": ""}, "name": "Solving Equations with Hidden Quadratics", "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "solmax", "solmin", "solmax1", "solmin1"], "statement": "<p>Solve this equation by factorising. Enter answers in&nbsp;<strong>ASCENDING ORDER.</strong></p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "variable_groups": [], "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "tags": [], "metadata": {"description": "<p>Several quadratics are given and students are asked to complete the square.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"marks": 0, "type": "gapfill", "gaps": [{"vsetrangepoints": 5, "showFeedbackIcon": true, "checkingaccuracy": 0.0001, "variableReplacementStrategy": "originalfirst", "answer": "({a}x^2+{b})({c}x^2+{d})", "answersimplification": "std", "checkvariablenames": false, "marks": "1", "expectedvariablenames": [], "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": [")("], "partialCredit": 0}, "scripts": {}, "showCorrectAnswer": true, "notallowed": {"message": "", "showStrings": false, "strings": ["x^2", "x*x", "x x", "x(", "x*("], "partialCredit": 0}, "showpreview": true, "checkingtype": "absdiff", "vsetrange": [0, 1], "variableReplacements": []}, {"vsetrangepoints": 5, "showFeedbackIcon": true, "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "answer": "{solmin}", "checkvariablenames": false, "marks": 1, "expectedvariablenames": [], "type": "jme", "scripts": {}, "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "vsetrange": [0, 1], "variableReplacements": []}, {"vsetrangepoints": 5, "showFeedbackIcon": true, "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "answer": "{solmax}", "checkvariablenames": false, "marks": 1, "expectedvariablenames": [], "type": "jme", "scripts": {}, "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "vsetrange": [0, 1], "variableReplacements": []}, {"vsetrangepoints": 5, "showFeedbackIcon": true, "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "answer": "{solmin1}", "checkvariablenames": false, "marks": 1, "expectedvariablenames": [], "type": "jme", "scripts": {}, "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "vsetrange": [0, 1], "variableReplacements": []}, {"vsetrangepoints": 5, "showFeedbackIcon": true, "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "answer": "{solmax1}", "checkvariablenames": false, "marks": 1, "expectedvariablenames": [], "type": "jme", "scripts": {}, "showCorrectAnswer": true, "showpreview": true, "checkingtype": "absdiff", "vsetrange": [0, 1], "variableReplacements": []}], "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "<p>Factorise $\\simplify{{a*c}x^4+{a*d+b*c}x^2+ {b*d}}$.&nbsp;[[0]]</p>\n<p>Hence solve $\\simplify{{a*c}x^2+{a*d+b*c}x+ {b*d}}=0$.</p>\n<p>$x^2=$ [[1]] or [[2]]</p>\n<p>$x=$ [[3]] or [[4]]</p>", "variableReplacements": []}], "type": "question", "contributors": [{"name": "Katherine Tomlinson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1652/"}]}]}], "contributors": [{"name": "Katherine Tomlinson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1652/"}]}