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{"name": "grant's copy of Algebra: Solving quadratics by completing the square", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "gaps": [{"failureRate": 1, "checkingType": "absdiff", "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "notallowed": {"showStrings": false, "partialCredit": 0, "strings": ["x^2", "x*x", "x x", "x(", "x*("], "message": "<p>Input your answer in the form $(x+a)^2+b$.</p>"}, "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "showPreview": true, "checkingAccuracy": 0.001, "showFeedbackIcon": true, "marks": "1", "answerSimplification": "std", "expectedVariableNames": [], "musthave": {"showStrings": false, "partialCredit": 0, "strings": ["(", ")", "^"], "message": "<p>please input in the form $(x+a)^2+b$</p>"}, "unitTests": [], "answer": "(x+{a[0]})^2+{b[0]}", "type": "jme"}, {"variableReplacementStrategy": "originalfirst", "allowResize": true, "correctAnswerFractions": false, "numRows": 1, "tolerance": 0, "correctAnswer": "matrix([{xmin[0]},{xmax[0]}])", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "allowFractions": false, "marks": 1, "markPerCell": false, "extendBaseMarkingAlgorithm": true, "numColumns": 1, "unitTests": [], "type": "matrix"}, {"variableReplacementStrategy": "originalfirst", "allowResize": true, "correctAnswerFractions": false, "numRows": 1, "tolerance": 0, "correctAnswer": "matrix([{xmin[3]}])", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "allowFractions": false, "marks": 1, "markPerCell": false, "extendBaseMarkingAlgorithm": true, "numColumns": 1, "unitTests": [], "type": "matrix"}], "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>Complete the square on $\\simplify{x^2+{2*a[0]}x+ {a[0]^2+b[0]}}$ [[0]]</p>\n<p>Hence solve&nbsp;$\\simplify{x^2+{2*a[0]}x+ {a[0]^2+b[0]}} = \\var{fx[0]}$ [[1]]</p>\n<p>Also solve&nbsp;$\\simplify{x^2+{2*a[0]}x+ {a[0]^2+b[0]}} = \\var{fx[3]}$ [[2]]</p>", "unitTests": [], "type": "gapfill"}, {"variableReplacementStrategy": "originalfirst", "sortAnswers": false, "gaps": [{"failureRate": 1, "checkingType": "absdiff", "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "notallowed": {"showStrings": false, "partialCredit": 0, "strings": ["x^2", "x*x", "x x", "x(", "x*("], "message": "<p>Input your answer in the form $(x+a)^2+b$.</p>"}, "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "showPreview": true, "checkingAccuracy": 0.001, "showFeedbackIcon": true, "marks": "1", "answerSimplification": "std", "expectedVariableNames": [], "musthave": {"showStrings": false, "partialCredit": 0, "strings": ["(", ")", "^"], "message": "<p>please input in the form $(x+a)^2+b$</p>"}, "unitTests": [], "answer": "(x+{a[1]})^2+{b[1]}", "type": "jme"}, {"variableReplacementStrategy": "originalfirst", "allowResize": true, "correctAnswerFractions": false, "numRows": 1, "tolerance": 0, "correctAnswer": "matrix([{xmin[4]},{xmax[4]}])", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "allowFractions": false, "marks": 1, "markPerCell": false, "extendBaseMarkingAlgorithm": true, "numColumns": 1, "unitTests": [], "type": "matrix"}, {"variableReplacementStrategy": "originalfirst", "allowResize": true, "correctAnswerFractions": false, "numRows": 1, "tolerance": 0, "correctAnswer": "matrix([{xmin[5]},{xmax[5]}])", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "allowFractions": false, "marks": 1, "markPerCell": false, "extendBaseMarkingAlgorithm": true, "numColumns": 1, "unitTests": [], "type": "matrix"}], "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 0, "extendBaseMarkingAlgorithm": true, "prompt": "<p>Complete the square on $\\simplify{x^2+{2*a[1]}x+ {a[1]^2+b[1]}}$ [[0]]</p>\n<p>Hence solve&nbsp;$\\simplify{x^2+{2*a[1]}x+ {a[1]^2+b[1]}} = \\var{fx[4]}$ [[1]]</p>\n<p>Also solve&nbsp;$\\simplify{x^2+{2*a[1]}x+ {a[1]^2+b[1]}} = \\var{fx[5]}$ [[2]]</p>", "unitTests": [], "type": "gapfill"}], "preamble": {"js": "", "css": ""}, "tags": [], "functions": {}, "name": "grant's copy of Algebra: Solving quadratics by completing the square", "ungrouped_variables": ["a", "b", "shift", "xmin", "xmax", "fx"], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.</p>"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "<p>See Lecture 5.4 for examples of me completing the square.</p>", "statement": "<p>Solve these equations by completing the square. If there is more than one answer increase the number of <strong>COLUMNS&nbsp;</strong>and enter your answers in&nbsp;<strong>ASCENDING ORDER</strong>.</p>", "variables": {"xmax": {"group": "Ungrouped variables", "name": "xmax", "templateType": "anything", "description": "", "definition": "vector([-a[0]]+[-a[0]]+[-a[0]]+[-a[0]]+[-a[1]]+[-a[1]]+[-a[1]]+[-a[1]])+shift"}, "shift": {"group": "Ungrouped variables", "name": "shift", "templateType": "anything", "description": "", "definition": "vector(shuffle(1..9#4)+[0]+shuffle(1..9#4)+[0])"}, "fx": {"group": "Ungrouped variables", "name": "fx", "templateType": "anything", "description": "", "definition": "vector([(xmax[0]+a[0])^2+b[0]]+[(xmax[1]+a[0])^2+b[0]]+[(xmax[2]+a[0])^2+b[0]]+[(xmax[3]+a[0])^2+b[0]]+[(xmax[4]+a[1])^2+b[1]]+[(xmax[5]+a[1])^2+b[1]]+[(xmax[6]+a[1])^2+b[1]]+[(xmax[7]+a[1])^2+b[1]])"}, "b": {"group": "Ungrouped variables", "name": "b", "templateType": "anything", "description": "", "definition": "vector([random(-10..25)] + [random(-10..25)] + [random(-10..25)] + [random(-10..25)] + [random(-10..25)] )"}, "a": {"group": "Ungrouped variables", "name": "a", "templateType": "anything", "description": "", "definition": "vector([random(1..5)]+[random(-1..-5)]+[random(-1..-5)]+[random(-1..-5)]+[random(1..5)])"}, "xmin": {"group": "Ungrouped variables", "name": "xmin", "templateType": "anything", "description": "", "definition": "vector([-a[0]]+[-a[0]]+[-a[0]]+[-a[0]]+[-a[1]]+[-a[1]]+[-a[1]]+[-a[1]])-shift"}}, "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/"}]}