// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Expansion of two brackets: Linear 2 positive coefficients", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Expand $(ax+b)(cx+d)$.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "name": "Simon's copy of Expansion of two brackets: Linear 2 positive coefficients", "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"sortAnswers": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "gaps": [{"answer": "{a*c}x^2+{b*c+a*d}x+{b*d}", "scripts": {}, "variableReplacements": [], "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "vsetRange": [0, 1], "checkingType": "absdiff", "type": "jme", "notallowed": {"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>", "strings": ["(", ")"]}, "expectedVariableNames": [], "marks": 2, "showPreview": true, "maxlength": {"length": 17, "partialCredit": 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>"}, "checkVariableNames": false, "showCorrectAnswer": true, "musthave": {"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>", "strings": ["x^2"]}, "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "answerSimplification": "std", "unitTests": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "failureRate": 1}], "variableReplacements": [], "customMarkingAlgorithm": "", "steps": [{"variableReplacements": [], "prompt": "<p>There are many ways to expand an expression such as $(ax+b)(cx+d)$.</p>\n<p>One method is sometimes referred to as FOIL,&nbsp;a mnemonic to help us remember which terms to multiply with one another:</p>\n<p><strong>F</strong>irst&nbsp; &nbsp; $ax \\times cx$</p>\n<p><strong>O</strong>utside&nbsp; &nbsp; $ax \\times d$</p>\n<p><strong>I</strong>nside&nbsp; &nbsp; $b \\times cx$</p>\n<p><strong>L</strong>ast&nbsp; &nbsp; $b \\times d$</p>\n<p>We then add these together and simplify by collecting like terms.</p>", "unitTests": [], "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "information", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 0}], "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>", "unitTests": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "stepsPenalty": "0", "type": "gapfill", "showCorrectAnswer": true, "marks": 0}], "variable_groups": [], "ungrouped_variables": ["a", "c", "b", "d"], "extensions": [], "tags": [], "statement": "<p>Expand the following to give a quadratic in $x$.</p>", "advice": "<p>There are many ways to expand an expression such as $(ax+b)(cx+d)$.</p>\n<p>One method is sometimes referred to as FOIL,&nbsp;a mnemonic to help us remember which terms to multiply with one another:</p>\n<p><strong>F</strong>irst&nbsp; &nbsp; $ax \\times cx$</p>\n<p><strong>O</strong>utside&nbsp; &nbsp; $ax \\times d$</p>\n<p><strong>I</strong>nside&nbsp; &nbsp; $b \\times cx$</p>\n<p><strong>L</strong>ast&nbsp; &nbsp; $b \\times d$</p>\n<p>We then add these together and simplify by collecting like terms.</p>\n<p></p>\n<p></p>\n<p>\\[\\begin{eqnarray*}\\simplify[std]{ ({a}x+{b})({c}x+{d})}&amp;=&amp;(\\var{a}x\\times\\var{c}x)+(\\var{a}x\\times\\var{d})+(\\var{b}\\times\\var{c}x)+(\\var{b}\\times\\var{d})\\\\&amp;=&amp;(\\var{a*c}x^2)+(\\var{a*d}x)+(\\var{b*c}x)+(\\var{b*d})\\\\&amp;=&amp;\\simplify[std]{{a*c}x^2+{(a*d+b*c)}x+{b*d}}\\end{eqnarray*}\\]</p>\n<p>&nbsp;</p>", "functions": {}, "variables": {"d": {"description": "", "group": "Ungrouped variables", "name": "d", "definition": "random(2..9 except [0,c])", "templateType": "anything"}, "c": {"description": "", "group": "Ungrouped variables", "name": "c", "definition": "random(2..5 except 0 except a)", "templateType": "anything"}, "a": {"description": "", "group": "Ungrouped variables", "name": "a", "definition": "random(2..5)", "templateType": "anything"}, "b": {"description": "", "group": "Ungrouped variables", "name": "b", "definition": "random(1..9 except a)", "templateType": "anything"}}, "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}