// Numbas version: exam_results_page_options
{"name": "Factorising  Quadratics of form  $\\displaystyle{x ^ 2 + bx + c}$", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Factorising  Quadratics of form  $\\displaystyle{x ^ 2 + bx + c}$", "tags": [], "metadata": {"description": "<p>Algebra: &nbsp;Quadratic Factorisation.</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Coefficient of squared term is 1.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p><strong>Factorise</strong> the following quadratic expression into <strong>linear factors</strong>.</p>\n<p>That is, write it as&nbsp;a product of the form&nbsp;$(ax+b)(cx+d)$ where $a$, $b$, $c$&nbsp;and $d$ are real numbers.</p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-6..6 except 0)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-6..6 except 0 except-a)", "description": "", "templateType": "anything"}, "linear": {"name": "linear", "group": "Ungrouped variables", "definition": "a+b", "description": "", "templateType": "anything"}, "const": {"name": "const", "group": "Ungrouped variables", "definition": "a*b", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": "127"}, "ungrouped_variables": ["a", "b", "linear", "const"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{x^2+{linear}x+{const}}$ =&nbsp;[[0]].</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>", "stepsPenalty": "2", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>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 $d=ab$.</p>\n<p></p>\n<p>In the case of&nbsp;$\\simplify{x^2+{linear}x+{const}}$ we ask</p>\n<p style=\"text-align: center;\"><em>what two numbers add to give $\\var{linear}$ and multiply to give $\\var{const}$?&nbsp;</em></p>\n<p style=\"text-align: left;\">Therefore the numbers must be $\\var{a}$ and $\\var{b}$, that is&nbsp;</p>\n<p style=\"text-align: center;\">$\\simplify{x^2+{linear}x+{const}}=(\\simplify{x+{a}})(\\simplify{x+{b}}).$</p>\n<p style=\"text-align: left;\">You can check this by expanding the binomial product.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "(x+{a})(x+{b})", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "musthave": {"strings": ["(", ")"], "showStrings": false, "partialCredit": 0, "message": "<p>Ensure you factorise the expression.</p>"}, "notallowed": {"strings": ["xx", "x^2", "x**2"], "showStrings": false, "partialCredit": 0, "message": "<p>Ensure you factorise the expression.</p>"}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}