// Numbas version: finer_feedback_settings
{"name": "Lucy's copy of Factoring Quadratics 2  $ax^2+bx+c$      4 questions READY", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": [], "name": "Lucy's copy of Factoring Quadratics 2  $ax^2+bx+c$      4 questions READY", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>A worked example using the quadratic&nbsp;expression&nbsp;from Part a: &nbsp;<strong>$\\simplify{{f1}x^2+{f2}x+{f3}}$</strong></p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\">When the coefficient of&nbsp;$x^2$ is not $1$ in a quadratic expression such as this one it is a little more complicated.</p>\n<p style=\"text-align: left;\">We must produce a pair of brackets &nbsp;<strong>$(ax+c)(bx+d)$</strong> which multiply out to give&nbsp;<strong>$\\simplify{{f1}x^2+{f2}x+{f3}}$</strong></p>\n<p style=\"text-align: left;\">Therefore we must&nbsp;find:</p>\n<p style=\"text-align: left;\"><strong>the two factors, a and b, &nbsp;of the coefficent of the $x^2$&nbsp;term in the quadratic, &nbsp;</strong>($\\var{f1}$ in this example ) AND</p>\n<p style=\"text-align: left;\"><strong>the two factors, c&nbsp;and d, &nbsp;of the constant term in the quadratic, &nbsp;(</strong>$\\var{f3}$ in this example),</p>\n<p style=\"text-align: left;\">such that&nbsp;<strong>$(ax+c)(bx+d)$ =&nbsp;$\\simplify{{f1}x^2+{f2}x+{f3}}$</strong></p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\">Here we use&nbsp;$\\var{a}$ and $\\var{b}$ as the factors of&nbsp;$\\var{f1}$ &nbsp;and&nbsp;$\\var{c}$ and $\\var{d}$&nbsp;as the factors of&nbsp;$\\var{f3}$</p>\n<p style=\"text-align: left;\">and we must now combine them correctly such that<strong>&nbsp;$(ax+c)(bx+d)$</strong> =&nbsp;<strong>$\\simplify{{f1}x^2+{f2}x+{f3}}$</strong></p>\n<p style=\"text-align: left;\">The correct combination is: &nbsp;<strong>$\\simplify{({a}x+{c})({b}x+{d})}$</strong></p>\n<p style=\"text-align: left;\">These brackets, when multiplied out, will give the original quadratic&nbsp;expression&nbsp;<strong>$\\simplify{{f1}x^2+{f2}x+{f3}}$</strong></p>\n<p style=\"text-align: left;\">Try it!</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\"></p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\simplify{{f1}x^2+{f2}*x+{f3}}$</p>\n<p>$=$[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>The answer must be factorised.</p>", "showStrings": true, "strings": ["x^"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({a}x+{c})({b}x+{d})", "marks": "2", "checkvariablenames": true, "checkingtype": "reldiff", "type": "jme", "musthave": {"message": "<p>The answer must be factorised.</p>", "showStrings": true, "strings": ["(", ")"], "partialCredit": 0}}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\simplify{{f12}x^2+{f22}*x+{f32}}$</p>\n<p>$=$[[0]]&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>The answer must be factorised.</p>", "showStrings": true, "strings": ["x^"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({a2}x+{c2})({b2}x+{d2})", "marks": "2", "checkvariablenames": true, "checkingtype": "reldiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\simplify{{f13}x^2+{f23}*x+{f33}}$</p>\n<p>$=$[[0]]&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>The answer must be factorised.</p>", "showStrings": true, "strings": ["x^"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({a3}x+{c3})({b3}x+{d3})", "marks": "2", "checkvariablenames": true, "checkingtype": "reldiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\simplify{{f14}x^2+{f24}*x+{f34}}$</p>\n<p>$=$[[0]]&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>The answer must be factorised.</p>", "showStrings": true, "strings": ["x^"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({a4}x+{c4})({b4}x+{d4})", "marks": "3", "checkvariablenames": true, "checkingtype": "reldiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p><strong>Express each of&nbsp;the following quadratic&nbsp;expressions as the product of&nbsp;two linear factors of&nbsp;the form $(ax+c)(bx+d)$.</strong></p>", "variable_groups": [{"variables": ["a", "b", "c", "d", "f1", "f2", "f3"], "name": "Part a"}, {"variables": ["a2", "b2", "c2", "d2", "f12", "f22", "f32"], "name": "Part b"}, {"variables": ["a3", "b3", "c3", "d3", "f13", "f23", "f33"], "name": "Part c"}, {"variables": ["a4", "b4", "c4", "d4", "f14", "f24", "f34"], "name": "Part d"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"f1": {"definition": "a*b", "templateType": "anything", "group": "Part a", "name": "f1", "description": ""}, "f2": {"definition": "(b*c)+(a*d)", "templateType": "anything", "group": "Part a", "name": "f2", "description": ""}, "f3": {"definition": "c*d", "templateType": "anything", "group": "Part a", "name": "f3", "description": ""}, "b4": {"definition": "random(1..4 except a4)", "templateType": "anything", "group": "Part d", "name": "b4", "description": ""}, "b2": {"definition": "random(2,3)", "templateType": "anything", "group": "Part b", "name": "b2", "description": ""}, "b3": {"definition": "random(2..3)", "templateType": "anything", "group": "Part c", "name": "b3", "description": ""}, "d4": {"definition": "random(-6..6 except 0)", "templateType": "anything", "group": "Part d", "name": "d4", "description": ""}, "d2": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Part b", "name": "d2", "description": ""}, "d3": {"definition": "random(-8..8 except 0)", "templateType": "anything", "group": "Part c", "name": "d3", "description": ""}, "f23": {"definition": "(b3*c3)+(a3*d3)", "templateType": "anything", "group": "Part c", "name": "f23", "description": ""}, "f22": {"definition": "(b2*c2)+(a2*d2)", "templateType": "anything", "group": "Part b", "name": "f22", "description": ""}, "f24": {"definition": "(b4*c4)+(a4*d4)", "templateType": "anything", "group": "Part d", "name": "f24", "description": ""}, "a3": {"definition": "random(1..3)", "templateType": "anything", "group": "Part c", "name": "a3", "description": ""}, "a2": {"definition": "random(1,2)", "templateType": "anything", "group": "Part b", "name": "a2", "description": ""}, "a4": {"definition": "2", "templateType": "anything", "group": "Part d", "name": "a4", "description": ""}, "c3": {"definition": "random(-10..10)", "templateType": "anything", "group": "Part c", "name": "c3", "description": ""}, "c2": {"definition": "random(-4..4 except 0)", "templateType": "anything", "group": "Part b", "name": "c2", "description": ""}, "c4": {"definition": "0", "templateType": "anything", "group": "Part d", "name": "c4", "description": ""}, "a": {"definition": "random(2,3)", "templateType": "anything", "group": "Part a", "name": "a", "description": ""}, "c": {"definition": "random(-1,1 )", "templateType": "anything", "group": "Part a", "name": "c", "description": ""}, "b": {"definition": "1", "templateType": "anything", "group": "Part a", "name": "b", "description": ""}, "d": {"definition": "-c", "templateType": "anything", "group": "Part a", "name": "d", "description": ""}, "f32": {"definition": "c2*d2", "templateType": "anything", "group": "Part b", "name": "f32", "description": ""}, "f33": {"definition": "c3*d3", "templateType": "anything", "group": "Part c", "name": "f33", "description": ""}, "f34": {"definition": "c4*d4", "templateType": "anything", "group": "Part d", "name": "f34", "description": ""}, "f12": {"definition": "a2*b2", "templateType": "anything", "group": "Part b", "name": "f12", "description": ""}, "f13": {"definition": "a3*b3", "templateType": "anything", "group": "Part c", "name": "f13", "description": ""}, "f14": {"definition": "a4*b4", "templateType": "anything", "group": "Part d", "name": "f14", "description": ""}}, "metadata": {"description": "<p>Factorising basic quadratics.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Lucy Hadfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/110/"}]}]}], "contributors": [{"name": "Lucy Hadfield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/110/"}]}