$\\simplify{{a[0]*c[0]}x^2+{a[0]*d[0]+b[0]*c[0]}x+ {b[0]*d[0]}} = $ [[0]]
", "scripts": {}, "customMarkingAlgorithm": "", "sortAnswers": false}, {"unitTests": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "gaps": [{"vsetRange": [0, 1], "unitTests": [], "checkingType": "absdiff", "failureRate": 1, "marks": "1", "showPreview": true, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "notallowed": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["x^2", "x*x", "x x", "x(", "x*("]}, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "answer": "({a[1]}x+{b[1]})({c[1]}x+{d[1]})", "type": "jme", "scripts": {}, "customMarkingAlgorithm": "", "expectedVariableNames": [], "answerSimplification": "std"}], "variableReplacements": [], "type": "gapfill", "prompt": "$\\simplify{{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}} = $ [[0]]
", "scripts": {}, "customMarkingAlgorithm": "", "sortAnswers": false}, {"unitTests": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "gaps": [{"vsetRange": [0, 1], "unitTests": [], "checkingType": "absdiff", "failureRate": 1, "marks": "1", "showPreview": true, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "notallowed": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["x^2", "x*x", "x x", "x(", "x*("]}, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "answer": "({a[2]}x+{b[2]})({c[2]}x+{d[2]})", "type": "jme", "scripts": {}, "customMarkingAlgorithm": "", "expectedVariableNames": [], "answerSimplification": "std"}], "variableReplacements": [], "type": "gapfill", "prompt": "$\\simplify{{a[2]*c[2]}x^2+{a[2]*d[2]+b[2]*c[2]}x+ {b[2]*d[2]}} = $ [[0]]
", "scripts": {}, "customMarkingAlgorithm": "", "sortAnswers": false}, {"unitTests": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "gaps": [{"vsetRange": [0, 1], "unitTests": [], "checkingType": "absdiff", "failureRate": 1, "marks": "1", "showPreview": true, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "notallowed": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["x^2", "x*x", "x x", "x(", "x*("]}, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "answer": "({a[3]}x+{b[3]})({c[3]}x+{d[3]})", "type": "jme", "scripts": {}, "customMarkingAlgorithm": "", "expectedVariableNames": [], "answerSimplification": "std"}], "variableReplacements": [], "type": "gapfill", "prompt": "$\\simplify{{a[3]*c[3]}x^2+{a[3]*d[3]+b[3]*c[3]}x+ {b[3]*d[3]}} = $ [[0]]
", "scripts": {}, "customMarkingAlgorithm": "", "sortAnswers": false}, {"unitTests": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "gaps": [{"vsetRange": [0, 1], "unitTests": [], "checkingType": "absdiff", "failureRate": 1, "marks": "1", "showPreview": true, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "checkVariableNames": false, "checkingAccuracy": 0.001, "notallowed": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["x^2", "x*x", "x x", "x(", "x*("]}, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "answer": "({a[4]}x+{b[4]})({c[4]}x+{d[4]})", "type": "jme", "scripts": {}, "customMarkingAlgorithm": "", "expectedVariableNames": [], "answerSimplification": "std"}], "variableReplacements": [], "type": "gapfill", "prompt": "$\\simplify{{a[4]*c[4]}x^2+{a[4]*d[4]+b[4]*c[4]}x+ {b[4]*d[4]}} = $ [[0]]
", "scripts": {}, "customMarkingAlgorithm": "", "sortAnswers": false}], "statement": "Factorise the following quadratics
\nx^2 - x -6
", "variables": {"d": {"description": "", "definition": "vector([random(1..3)]+[random(2..3)]+[random(1..3)]+[random(-2..-4)]+[random(3..6)])", "group": "Ungrouped variables", "name": "d", "templateType": "anything"}, "c": {"description": "", "definition": "vector([1]+[1]+[1]+[1]+[1])", "group": "Ungrouped variables", "name": "c", "templateType": "anything"}, "a": {"description": "", "definition": "vector([1]+[random(2..4)]+[1]+[1]+[random(3..4)])", "group": "Ungrouped variables", "name": "a", "templateType": "anything"}, "b": {"description": "", "definition": "vector([random(1..5)] + [random(1..5)] + [random(-1..-5)] + [random(-1..-5)] + [random(2..5)] )", "group": "Ungrouped variables", "name": "b", "templateType": "anything"}}, "tags": [], "functions": {}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": [], "metadata": {"description": "Several quadratics are given and students are asked to factorise them.
", "licence": "Creative Commons Attribution 4.0 International"}, "name": "rema's copy of Algebra: Factorising quadratics", "preamble": {"js": "", "css": ""}, "advice": "See Lecture 5.4 for examples of me factorising.
", "ungrouped_variables": ["a", "b", "c", "d"], "variable_groups": [], "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "rema Nath", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2545/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "rema Nath", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2545/"}]}