// Numbas version: exam_results_page_options
{"name": "Joe's copy of  Expand product of 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}, "variable_groups": [], "advice": "<p>For part a)</p>\n<p>\\[\\begin{eqnarray*}\\simplify[std]{ ({a}x+{b})({c}x+{d})}&amp;=&amp;\\simplify[std]{{a}x*({c}x+{d})+{b}({c}x+{d})}\\\\&amp;=&amp;\\simplify[std]{{a*c}x^2+{a*d}x+{b*c}x+{b*d}}\\\\&amp;=&amp;\\simplify[std]{{a*c}x^2+{(a*d+b*c)}x+{b*d}}\\end{eqnarray*}\\]</p>\n<p></p>\n<p>For part b)</p>\n<p>\\[\\begin{eqnarray*}\\simplify[std]{ ({s}x+{t})({u}x+{v})}&amp;=&amp;\\simplify[std]{{s}x*({u}x+{v})+{t}({u}x+{d})}\\\\&amp;=&amp;\\simplify[std]{{s*u}x^2+{s*v}x+{t*u}x+{t*v}}\\\\&amp;=&amp;\\simplify[std]{{s*u}x^2+{(s*v+t*u)}x+{t*v}}\\end{eqnarray*}\\]</p>\n<p>&nbsp;</p>", "ungrouped_variables": ["a", "c", "b", "d", "s", "u", "t", "v"], "metadata": {"description": "<p>These questions will help you expand double set of brackets- &nbsp;$(ax+b)(cx+d)$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Expand the following to give a quadratic in $x$.</p>", "extensions": [], "name": "Joe's copy of  Expand product of brackets", "tags": [], "parts": [{"marks": 0, "sortAnswers": false, "prompt": "<p>$\\simplify[std]{({a}x+{b})({c}x+{d})}=\\;$[[0]].</p>\n<p>Your answer should be a quadratic in $x$ and should not include any brackets.</p>\n<p></p>", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "gaps": [{"musthave": {"strings": ["x^2"], "partialCredit": 0, "showStrings": false, "message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>"}, "checkingType": "absdiff", "expectedVariableNames": [], "maxlength": {"partialCredit": 0, "length": "0", "message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>"}, "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "vsetRange": [0, 1], "showCorrectAnswer": true, "checkVariableNames": false, "answer": "{a*c}x^2+{b*c+a*d}x+{b*d}", "marks": 2, "notallowed": {"strings": ["("], "partialCredit": 0, "showStrings": false, "message": "<p>Do not include brackets in your answer. Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>"}, "answerSimplification": "std", "showFeedbackIcon": true, "failureRate": 1, "unitTests": [], "type": "jme", "showPreview": true, "customMarkingAlgorithm": ""}], "unitTests": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacements": []}, {"marks": 0, "sortAnswers": false, "prompt": "<p>$\\simplify[std]{({s}x-{t})({u}x-{v})}=\\;$[[0]]</p>\n<p>Your answer should be a quadratic in $x$ and should not include any brackets.</p>\n<p></p>", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "gaps": [{"answer": "{s*u}x^2-{t*u+s*v}x+{t*v}", "marks": "2", "expectedVariableNames": [], "checkingAccuracy": 0.001, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "answerSimplification": "std", "showFeedbackIcon": true, "failureRate": 1, "vsetRangePoints": 5, "showPreview": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "checkVariableNames": false, "scripts": {}, "type": "jme", "vsetRange": [0, 1], "musthave": {"strings": ["x^2"], "partialCredit": 0, "showStrings": false, "message": ""}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacements": []}], "unitTests": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacements": []}], "functions": {}, "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "variables": {"a": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "a", "definition": "random(-5..5 except 0)"}, "b": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "b", "definition": "random(-9..9 except [0,a])"}, "u": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "u", "definition": "random(-10..10 except 0)"}, "s": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s", "definition": "random(-10..10 except 0)"}, "v": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "v", "definition": "random(11..20 except [0,u])"}, "d": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "d", "definition": "random(-9..9 except [0,c])"}, "c": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c", "definition": "random(-5..5 except 0)"}, "t": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "t", "definition": "random(11..20 except [0,s])"}}, "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "emma rand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/115/"}, {"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}]}]}], "contributors": [{"name": "emma rand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/115/"}, {"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}]}