// Numbas version: exam_results_page_options
{"name": "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": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d"], "name": "Expansion of two brackets: Linear 2 positive coefficients", "tags": ["algebra", "algebraic manipulation", "expansion of brackets", "expansion of the product of two linear terms", "Rebel", "REBEL", "rebel", "rebelmaths"], "advice": "\n  <p>Using the method given by Show steps we have:</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>&nbsp;</p>\n  ", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepsPenalty": 1, "prompt": "\n      <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>You can click on Show steps for more information, but you will lose one mark if you do so.</p>\n      ", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"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>", "showStrings": false, "strings": ["("], "partialCredit": 0}, "variableReplacements": [], "expectedvariablenames": [], "maxlength": {"length": 17, "message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "partialCredit": 0}, "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "musthave": {"message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "showStrings": false, "strings": ["x^2"], "partialCredit": 0}, "scripts": {}, "answer": "{a*c}x^2+{b*c+a*d}x+{b*d}", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "answersimplification": "std"}], "steps": [{"prompt": "\n          <p>There are many ways to expand an expression such as $(ax+b)(cx+d)$.</p>\n          <p>One way:</p>\n          <p>\\[\\begin{eqnarray*} (ax+b)(cx+d)&amp;=&amp;ax(cx+d)+b(cx+d)\\\\&amp;=&amp;acx^2+adx+bcx+bd\\\\&amp;=&amp;acx^2+(ad+bc)x+bd\\end{eqnarray*}\\]</p>\n          ", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "extensions": [], "statement": "<p>Expand the following to give a quadratic in $x$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..9 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..9 except [0,c])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "<p>Expand $(ax+b)(cx+d)$.</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}