$\\simplify{{q[0]}} = $ [[0]]
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", "unitTests": [], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "statement": "Factorise the following quadratics.
\n----------------------------------------------------
", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["a", "b", "c", "d", "vari", "q", "ans"], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"b": {"description": "", "templateType": "anything", "name": "b", "group": "Ungrouped variables", "definition": "vector([random(1..5)] + [random(1..5)] + [random(-1..-5)] + [random(-1..-5)] + [random(2..5)] )"}, "ans": {"description": "", "templateType": "anything", "name": "ans", "group": "Ungrouped variables", "definition": "map(expression('({a[j]}*{vari[j]}+{b[j]})({c[j]}*{vari[j]}+{d[j]})'),j,0..4)"}, "c": {"description": "", "templateType": "anything", "name": "c", "group": "Ungrouped variables", "definition": "vector([1]+[1]+[1]+[1]+[1])"}, "a": {"description": "", "templateType": "anything", "name": "a", "group": "Ungrouped variables", "definition": "vector([1]+[random(2..4)]+[1]+[1]+[random(3..4)])"}, "vari": {"description": "", "templateType": "anything", "name": "vari", "group": "Ungrouped variables", "definition": "shuffle(['n','m','l','k','w'])"}, "q": {"description": "", "templateType": "anything", "name": "q", "group": "Ungrouped variables", "definition": "map(expression('{a[j]*c[j]}*{vari[j]}^2+{a[j]*d[j]+b[j]*c[j]}*{vari[j]}+ {b[j]*d[j]}'),j,0..4)"}, "d": {"description": "", "templateType": "anything", "name": "d", "group": "Ungrouped variables", "definition": "vector([random(1..3)]+[random(2..3)]+[random(1..3)]+[random(-2..-4)]+[random(3..6)])"}}, "functions": {}, "advice": "See 3.3 and 3.5 for examples and background. With practice, you shoud learn many of the common patterns that will help speed things up.
\nNote tha there might be more than one way to factorise some quadratics.
", "name": "Algebra: Factorising quadratics", "extensions": [], "metadata": {"description": "Several quadratics are given and students are asked to factorise them.
", "licence": "Creative Commons Attribution 4.0 International"}, "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}