// Numbas version: exam_results_page_options
{"name": "Factorise the quadratic expression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "extensions": [], "variablesTest": {"condition": "a <> b\na <> 0\nb <> 0", "maxRuns": 100}, "name": "Factorise the quadratic expression", "ungrouped_variables": ["a", "b"], "metadata": {"description": "<p>Testing factorisation of quadratics.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "<p>The first step is to find two numbers that add together to give $\\var{a+b}$ and multiply to give $\\var{a*b}$.</p>\n<p></p>\n<p>These are $\\var{a}$ and $\\var{b}$.</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{x^2 + {a + b} x + {a*b}} &amp;= \\simplify{x^2 + {a} x + {b} x + {a*b}} \\\\ &amp;= \\simplify{x(x + {a}) + {b}(x + {a})} \\\\ &amp;= \\simplify{(x + {b})(x + {a})}\\end{aligned}\\]</p>", "statement": "<p>Factorise the following quadratic.</p>", "preamble": {"js": "", "css": ""}, "parts": [{"answer": "(x+{a})(x+{b})", "variableReplacementStrategy": "originalfirst", "vsetrange": [0, 1], "showFeedbackIcon": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "scripts": {}, "expectedvariablenames": [], "type": "jme", "musthave": {"strings": ["(", ")"], "partialCredit": 0, "message": "", "showStrings": false}, "vsetrangepoints": 5, "variableReplacements": [], "prompt": "<p>$\\simplify{x^2 + {a + b}x + {a*b}}$</p>", "checkvariablenames": false, "showpreview": true, "notallowed": {"strings": ["^"], "partialCredit": 0, "message": "", "showStrings": false}, "marks": "2", "showCorrectAnswer": true}], "tags": [], "variable_groups": [], "functions": {}, "variables": {"a": {"description": "<p>One of the factors.</p>", "definition": "random(-9..9#1)", "group": "Ungrouped variables", "templateType": "randrange", "name": "a"}, "b": {"description": "<p>The second factor.</p>", "definition": "random(-9..9#1)", "group": "Ungrouped variables", "templateType": "randrange", "name": "b"}}, "type": "question", "contributors": [{"name": "Andrew Stacey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1605/"}]}]}], "contributors": [{"name": "Andrew Stacey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1605/"}]}