// Numbas version: exam_results_page_options
{"name": "Algebra: Quadratics, multiplying out brackets", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "answer": "{a[0]*c[0]}x^2+{a[0]*d[0]+b[0]*c[0]}x+ {b[0]*d[0]}", "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "unitTests": [], "type": "jme", "marks": "1", "checkVariableNames": false, "vsetRange": [0, 1], "checkingType": "absdiff", "failureRate": 1, "vsetRangePoints": 5, "showPreview": true, "expectedVariableNames": [], "showFeedbackIcon": true, "checkingAccuracy": 0.001, "prompt": "<p>Multiply out and simplify $\\simplify{({a[0]}x+{b[0]})({c[0]}x+{d[0]})}$</p>"}, {"extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "answer": "{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}", "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "unitTests": [], "type": "jme", "marks": "1", "checkVariableNames": false, "vsetRange": [0, 1], "checkingType": "absdiff", "failureRate": 1, "vsetRangePoints": 5, "showPreview": true, "expectedVariableNames": [], "showFeedbackIcon": true, "checkingAccuracy": 0.001, "prompt": "<p>Multiply out and simplify $\\simplify{({a[1]}x+{b[1]})({c[1]}x+{d[1]})}$</p>"}, {"extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "answer": "{a[2]*c[2]}x^2+{a[2]*d[2]+b[2]*c[2]}x+ {b[2]*d[2]}", "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "unitTests": [], "type": "jme", "marks": "1", "checkVariableNames": false, "vsetRange": [0, 1], "checkingType": "absdiff", "failureRate": 1, "vsetRangePoints": 5, "showPreview": true, "expectedVariableNames": [], "showFeedbackIcon": true, "checkingAccuracy": 0.001, "prompt": "<p>Multiply out and simplify $\\simplify{({a[2]}x+{b[2]})({c[2]}x+{d[2]})}$</p>"}, {"extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "answer": "{a[3]*c[3]}x^2+{a[3]*d[3]+b[3]*c[3]}x+ {b[3]*d[3]}", "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "unitTests": [], "type": "jme", "marks": "1", "checkVariableNames": false, "vsetRange": [0, 1], "checkingType": "absdiff", "failureRate": 1, "vsetRangePoints": 5, "showPreview": true, "expectedVariableNames": [], "showFeedbackIcon": true, "checkingAccuracy": 0.001, "prompt": "<p>Multiply out and simplify $\\simplify{({a[3]}x+{b[3]})({c[3]}x+{d[3]})}$</p>"}, {"extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "answer": "{a[4]*c[4]}x^2+{a[4]*abs(d[4])+b[4]*c[4]}x+ {b[4]*abs(d[4])}", "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "unitTests": [], "type": "jme", "marks": "1", "checkVariableNames": false, "vsetRange": [0, 1], "checkingType": "absdiff", "failureRate": 1, "vsetRangePoints": 5, "showPreview": true, "expectedVariableNames": [], "showFeedbackIcon": true, "checkingAccuracy": 0.001, "prompt": "<p>Multiply out and simplify $\\simplify{({a[4]}x+{b[4]})({c[4]}x+{abs(d[4])})}$</p>"}], "ungrouped_variables": ["a", "b", "c", "d"], "extensions": [], "metadata": {"description": "<p>Expressions of the form (ax+b)(cx+d) are to be multiplied out and simplified.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {}, "variables": {"b": {"name": "b", "description": "", "group": "Ungrouped variables", "definition": "shuffle([-5,-4,-3,-2,2,3,4,5])", "templateType": "anything"}, "a": {"name": "a", "description": "", "group": "Ungrouped variables", "definition": "[1,1]+shuffle([2,3,4])", "templateType": "anything"}, "d": {"name": "d", "description": "", "group": "Ungrouped variables", "definition": "shuffle([-5,-4,-3,-2,2,3,4,5])", "templateType": "anything"}, "c": {"name": "c", "description": "", "group": "Ungrouped variables", "definition": "vector([1]+[1]+[1]+[1]+[random(-3..3 except [0,1])])", "templateType": "anything"}}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "name": "Algebra: Quadratics, multiplying out brackets", "tags": [], "advice": "<p>See Lecture 2.1 and Workshop 2.2 work the rules or patterns about how multiplication and addition interact.</p>\n<p></p>\n<p>(a)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;$\\simplify{(x+{b[0]})(x+{d[0]})}$</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $=\\simplify[basic, unitFactor]{&nbsp; x^2+{d[0]}x + {b[0]}x + {c[0]*d[0]}&nbsp; }$</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $=\\simplify[basic, unitFactor]{&nbsp; x^2+{b[0]+d[0]}x + {c[0]*d[0]}&nbsp; }$</p>", "statement": "<p>This is a non-calculator question.</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "type": "question", "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/"}]}