// Numbas version: exam_results_page_options
{"name": "Factorise the quadratic expression - Refresh", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "rulesets": {}, "variables": {"a": {"name": "a", "description": "<p>x-coefficient in first factor</p>", "definition": "random(-5 .. 5#1)", "templateType": "randrange", "group": "Ungrouped variables"}, "b": {"name": "b", "description": "<p>constant in first factor</p>", "definition": "random(-5 .. 5#1)", "templateType": "randrange", "group": "Ungrouped variables"}, "d": {"name": "d", "description": "<p>constant in second factor</p>", "definition": "random(-5 .. 5#1)", "templateType": "randrange", "group": "Ungrouped variables"}, "c": {"name": "c", "description": "<p>x-coefficient in second factor</p>", "definition": "random(-5 .. 5#1)", "templateType": "randrange", "group": "Ungrouped variables"}}, "ungrouped_variables": ["a", "b", "c", "d"], "functions": {}, "variable_groups": [], "name": "Factorise the quadratic expression - Refresh", "variablesTest": {"maxRuns": 100, "condition": "(b/a <> d/c)\nand \n(a <> 0)\nand\n(b <> 0)\nand\n(c <> 0)\nand\n(d <> 0)\nand\n(gcd(a,b) = 1)\nand\n(gcd(c,d) = 1)"}, "advice": "<p>The first step is to find two numbers that add together to give $\\var{a*d+c*b}$ and multiply to give $\\var{a*c} \\times \\var{b*d} = \\var{a*b*c*d}$.</p>\n<p></p>\n<p>These are $\\var{a*d}$ and $\\var{c*b}$.</p>\n<p></p>\n<p>We split the $x$-term using $\\simplify{{a + b}x = {a} x + {b} x}$ and work as follows:</p>\n<p>\\[\\begin{aligned}\\simplify{{a*c}x^2 + {a*d + c*b} x + {b*d}} &amp;= \\simplify{{a*c}x^2 + {a*d} x + {c*b} x + {c*d}} \\\\ &amp;= \\simplify{{a} x({c} x + {d}) + {b}({c}x + {d})} \\\\ &amp;= \\simplify{({a}x + {b})({c}x + {d})}\\end{aligned}\\]</p>", "metadata": {"description": "<p>Testing factorisation of quadratics.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Factorise the following quadratic.</p>", "extensions": [], "tags": [], "parts": [{"checkVariableNames": false, "musthave": {"message": "", "strings": ["(", ")"], "showStrings": false, "partialCredit": 0}, "customMarkingAlgorithm": "", "marks": "2", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPreview": true, "valuegenerators": [{"name": "x", "value": ""}], "extendBaseMarkingAlgorithm": true, "customName": "", "answer": "({a}x+{b})({c}x+{d})", "adaptiveMarkingPenalty": 0, "prompt": "<p>$\\simplify{{a*c}x^2 + {a*d + c*b}x + {b*d}}$</p>", "notallowed": {"message": "", "strings": ["^"], "showStrings": false, "partialCredit": 0}, "showFeedbackIcon": true, "failureRate": 1, "unitTests": [], "vsetRangePoints": 5, "useCustomName": false, "type": "jme", "checkingType": "absdiff", "checkingAccuracy": 0.001, "vsetRange": [0, 1], "showCorrectAnswer": true}], "contributors": [{"name": "Andrew Stacey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Maria Pickett", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3492/"}]}]}], "contributors": [{"name": "Andrew Stacey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Maria Pickett", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3492/"}]}