// Numbas version: exam_results_page_options {"name": "Clare's copy of Factorising a monic quadratic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"variableReplacements": [], "stepsPenalty": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "steps": [{"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "prompt": "

Since \$(x+a)(x+b)=x^2+(a+b)x+ab\$, when we are factorising a quadratic, such as \$x^2+cx+d\$, we must find the numbers \$a\$ and \$b\$ such that \$c=a+b\$ and \$d=ab\$.

\n

\n

In the case of \$\\simplify{x^2+{linear}x+{const}}\$ we ask

\n

what two numbers add to give \$\\var{linear}\$ and multiply to give \$\\var{const}\$?

\n

Therefore the numbers must be \$\\var{a}\$ and \$\\var{b}\$, that is

\n

\$\\simplify{x^2+{linear}x+{const}}=(\\simplify{x+{a}})(\\simplify{x+{b}}).\$

\n

You can check this by expanding the binomial product.

", "marks": 0, "type": "information"}], "prompt": "

\$\\simplify{x^2+{linear}x+{const}}\$ = [[0]].

\n

\n

\n

\n

", "marks": 0, "gaps": [{"checkingaccuracy": 0.001, "vsetrangepoints": 5, "scripts": {}, "showCorrectAnswer": true, "checkingtype": "absdiff", "showpreview": true, "marks": 1, "answer": "(x+{a})(x+{b})", "variableReplacements": [], "expectedvariablenames": ["x"], "variableReplacementStrategy": "originalfirst", "notallowed": {"message": "

Ensure you factorise the expression.

", "showStrings": false, "strings": ["xx", "x^2", "x**2"], "partialCredit": 0}, "musthave": {"message": "

Ensure you factorise the expression.

", "showStrings": false, "strings": ["(", ")"], "partialCredit": 0}, "answersimplification": "all", "checkvariablenames": true, "vsetrange": [0, 1], "type": "jme"}], "type": "gapfill"}], "name": "Clare's copy of Factorising a monic quadratic", "variables": {"a": {"definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "name": "a", "group": "Ungrouped variables"}, "const": {"definition": "a*b", "description": "", "templateType": "anything", "name": "const", "group": "Ungrouped variables"}, "linear": {"definition": "a+b", "description": "", "templateType": "anything", "name": "linear", "group": "Ungrouped variables"}, "b": {"definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "name": "b", "group": "Ungrouped variables"}}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": "127"}, "tags": ["binomial", "factorisation", "Factorisation", "factorising", "factors", "Factors", "monic", "quadratic", "quadratics"], "statement": "

Factorise the following into linear factors. That is, write the quadratic as a product of terms that look like \$ax+b\$ where \$a\$ and \$b\$ are real numbers.

", "preamble": {"js": "", "css": ""}, "question_groups": [{"pickingStrategy": "all-ordered", "pickQuestions": 0, "name": "", "questions": []}], "variable_groups": [], "ungrouped_variables": ["a", "b", "linear", "const"], "advice": "", "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "functions": {}, "showQuestionGroupNames": false, "type": "question", "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}