// Numbas version: exam_results_page_options
{"name": "grant's copy of Algebra: Solving quadratics by factorising", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "tags": [], "functions": {}, "name": "grant's copy of Algebra: Solving quadratics by factorising", "ungrouped_variables": ["a", "b", "c", "d", "solmax", "solmin"], "advice": "<p>See Lecture 5.4 for examples of me&nbsp;factorising.</p>", "variable_groups": [], "metadata": {"description": "<p>Some quadratics are to be solved by factorising</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "gaps": [{"failureRate": 1, "checkingType": "absdiff", "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showPreview": true, "showCorrectAnswer": true, "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "notallowed": {"showStrings": false, "partialCredit": 0, "strings": ["x^2", "x*x", "x x", "x(", "x*("], "message": ""}, "checkingAccuracy": 0.0001, "showFeedbackIcon": true, "marks": "1", "answerSimplification": "std", "expectedVariableNames": [], "musthave": {"showStrings": false, "partialCredit": 0, "strings": [")("], "message": ""}, "unitTests": [], "answer": "({a[0]}x+{b[0]})({c[0]}x+{d[0]})", "type": "jme"}, {"variableReplacementStrategy": "originalfirst", "markPerCell": false, "correctAnswerFractions": true, "numRows": 1, "tolerance": 0, "correctAnswer": "matrix([{solmin[0]},{solmax[0]}])", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "allowFractions": true, "allowResize": false, "marks": 1, "extendBaseMarkingAlgorithm": true, "numColumns": "2", "unitTests": [], "type": "matrix"}], "showFeedbackIcon": true, "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "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 $\\simplify{{a[0]*c[0]}x^2+{a[0]*d[0]+b[0]*c[0]}x+ {b[0]*d[0]}}=0$. [[1]]</p>", "unitTests": [], "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "gaps": [{"failureRate": 1, "checkingType": "absdiff", "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showPreview": true, "showCorrectAnswer": true, "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "notallowed": {"showStrings": false, "partialCredit": 0, "strings": ["x^2", "x*x", "x x", "x(", "x*("], "message": ""}, "checkingAccuracy": 0.0001, "showFeedbackIcon": true, "marks": "1", "answerSimplification": "std", "expectedVariableNames": [], "musthave": {"showStrings": false, "partialCredit": 0, "strings": [")("], "message": ""}, "unitTests": [], "answer": "({a[1]}x+{b[1]})({c[1]}x+{d[1]})", "type": "jme"}, {"variableReplacementStrategy": "originalfirst", "markPerCell": false, "correctAnswerFractions": true, "numRows": 1, "tolerance": 0, "correctAnswer": "matrix([{solmin[1]},{solmax[1]}])", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "allowFractions": true, "allowResize": false, "marks": 1, "extendBaseMarkingAlgorithm": true, "numColumns": "2", "unitTests": [], "type": "matrix"}], "showFeedbackIcon": true, "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "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 $\\simplify{{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}}=0$. [[1]]</p>", "unitTests": [], "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "gaps": [{"failureRate": 1, "checkingType": "absdiff", "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showPreview": true, "showCorrectAnswer": true, "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "notallowed": {"showStrings": false, "partialCredit": 0, "strings": ["x^2", "x*x", "x x", "x(", "x*("], "message": ""}, "checkingAccuracy": 0.0001, "showFeedbackIcon": true, "marks": "1", "answerSimplification": "std", "expectedVariableNames": [], "musthave": {"showStrings": false, "partialCredit": 0, "strings": [")("], "message": ""}, "unitTests": [], "answer": "({a[2]}x+{b[2]})({c[2]}x+{d[2]})", "type": "jme"}, {"variableReplacementStrategy": "originalfirst", "markPerCell": false, "correctAnswerFractions": true, "numRows": 1, "tolerance": 0, "correctAnswer": "matrix([{solmin[2]},{solmax[2]}])", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "allowFractions": true, "allowResize": false, "marks": 1, "extendBaseMarkingAlgorithm": true, "numColumns": "2", "unitTests": [], "type": "matrix"}], "showFeedbackIcon": true, "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "prompt": "<p>Factorise $\\simplify{{a[2]*c[2]}x^2+{a[2]*d[2]+b[2]*c[2]}x+ {b[2]*d[2]}}$.&nbsp;[[0]]</p>\n<p>Hence solve $\\simplify{{a[2]*c[2]}x^2+{a[2]*d[2]+b[2]*c[2]}x+ {b[2]*d[2]}}=0$. [[1]]</p>", "unitTests": [], "showCorrectAnswer": true}], "statement": "<p>Solve the quadratic equations by factorising. Enter answers in&nbsp;<strong>ASCENDING ORDER.</strong></p>", "variables": {"c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "vector([1]+[1]+[1]+[1]+[1])", "name": "c", "description": ""}, "solmin": {"group": "Ungrouped variables", "templateType": "anything", "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])])", "name": "solmin", "description": ""}, "solmax": {"group": "Ungrouped variables", "templateType": "anything", "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])])", "name": "solmax", "description": ""}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "vector([random(1..5)] + [random(1..5)] + [random(-1..-5)] + [random(-1..-5)] + [random(2..5)] )", "name": "b", "description": ""}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "vector([1]+[random(2..4)]+[1]+[1]+[random(3..4)])", "name": "a", "description": ""}, "d": {"group": "Ungrouped variables", "templateType": "anything", "definition": "vector([random(1..3)]+[random(2..3)]+[random(1..3)]+[random(-2..-4)]+[random(3..6)])", "name": "d", "description": ""}}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "grant smith", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2569/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "grant smith", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2569/"}]}