// Numbas version: exam_results_page_options
{"name": "Algebra: Solving quadratics by factorising. shorter", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Algebra: Solving quadratics by factorising. shorter", "statement": "<p>Solve the quadratic equations by factorising. Enter answers in&nbsp;<strong>ASCENDING ORDER.</strong></p>", "functions": {}, "variables": {"c": {"description": "", "templateType": "anything", "name": "c", "definition": "vector([1]+[1]+[1]+[1]+[1])", "group": "Ungrouped variables"}, "solmin": {"description": "", "templateType": "anything", "name": "solmin", "definition": "vector([min(-d[0]/c[0],-b[0]/a[0])]+[min(-d[1]/c[1],-b[1]/a[1])]+[min(-d[2]/c[2],-b[2]/a[2])]+[min(-d[3]/c[3],-b[3]/a[3])]+[min(-d[4]/c[4],-b[4]/a[4])])", "group": "Ungrouped variables"}, "d": {"description": "", "templateType": "anything", "name": "d", "definition": "vector([random(1..3)]+[random(2..3)]+[random(1..3)]+[random(-2..-4)]+[random(3..6)])", "group": "Ungrouped variables"}, "solmax": {"description": "", "templateType": "anything", "name": "solmax", "definition": "vector([max(-d[0]/c[0],-b[0]/a[0])]+[max(-d[1]/c[1],-b[1]/a[1])]+[max(-d[2]/c[2],-b[2]/a[2])]+[max(-d[3]/c[3],-b[3]/a[3])]+[max(-d[4]/c[4],-b[4]/a[4])])", "group": "Ungrouped variables"}, "b": 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"customMarkingAlgorithm": "", "answerSimplification": "std", "musthave": {"showStrings": false, "message": "", "strings": [")("], "partialCredit": 0}, "vsetRange": [0, 1], "useCustomName": false, "checkingAccuracy": 0.001, "checkingType": "absdiff", "notallowed": {"showStrings": false, "message": "", "strings": ["x^2", "x*x", "x x", "x(", "x*("], "partialCredit": 0}}, {"adaptiveMarkingPenalty": 0, "variableReplacements": [], "type": "matrix", "marks": 1, "showFeedbackIcon": true, "scripts": {}, "numRows": "2", "allowResize": false, "correctAnswerFractions": true, "customMarkingAlgorithm": "", "useCustomName": false, "allowFractions": true, "variableReplacementStrategy": "originalfirst", "markPerCell": false, "customName": "", "showCorrectAnswer": true, "numColumns": "1", "extendBaseMarkingAlgorithm": true, "unitTests": [], "correctAnswer": "matrix([{solmin[0]}],[{solmax[0]}])", "tolerance": 0}], "sortAnswers": false, "customMarkingAlgorithm": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Factorise $\\simplify{{a[0]*c[0]}x^2+{a[0]*d[0]+b[0]*c[0]}x+ {b[0]*d[0]}}$.&nbsp;[[0]]</p>\n<p>Hence solve $\\simplify{{a[0]*c[0]}x^2+{a[0]*d[0]+b[0]*c[0]}x+ {b[0]*d[0]}}=0$.</p>\n<p>[[1]]</p>"}, {"adaptiveMarkingPenalty": 0, "variableReplacements": [], "type": "gapfill", "marks": 0, "showFeedbackIcon": true, "scripts": {}, "gaps": [{"variableReplacements": [], "type": "jme", "marks": "1", "showFeedbackIcon": true, "answer": "({a[1]}x+{b[1]})({c[1]}x+{d[1]})", "valuegenerators": [{"name": "x", "value": ""}], "scripts": {}, "checkVariableNames": false, "failureRate": 1, "vsetRangePoints": 5, "customName": "", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "adaptiveMarkingPenalty": 0, "showPreview": true, "customMarkingAlgorithm": "", 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"originalfirst", "customName": "", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Factorise $\\simplify{{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}}$.&nbsp;[[0]]</p>\n<p>Hence solve $\\simplify{{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}}=0$.</p>\n<p>[[1]]</p>"}], "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "advice": "<p>See 3.3 and 3.5 for factorising. See 4.1 and 4.2 for how to use factorising to solve quadratics.</p>", "ungrouped_variables": ["a", "b", "c", "d", "solmax", "solmin"], "extensions": [], "metadata": {"description": "<p>Some quadratics are to be solved by factorising</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}