// Numbas version: exam_results_page_options
{"name": "Expansion of two brackets: Linear 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Expansion of two brackets: Linear 2", "tags": ["algebra", "algebraic manipulation", "expansion of brackets", "expansion of the product of two linear terms"], "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": 1.0, "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      ", "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": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "maxlength": {"length": 17.0, "message": "<p>Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.</p>", "partialcredit": 0.0}, "answer": "{a*c}x^2+{b*c+a*d}x+{b*d}", "marks": 2.0, "type": "jme", "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": 0.0}}], "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          ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "extensions": [], "statement": "<p>Expand the following to give a quadratic in $x$.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(-5..5 except 0)", "name": "a"}, "c": {"definition": "random(-5..5 except 0)", "name": "c"}, "b": {"definition": "random(-9..9 except [0,a])", "name": "b"}, "d": {"definition": "random(-9..9 except [0,c])", "name": "d"}}, "metadata": {"notes": "\n    \t\t<p><strong>15/08/2012:</strong></p>\n    \t\t                <p>Added tags.</p>\n    \t\t                <p>Added description.</p>\n    \t\t", "description": "<p>Expand $(ax+b)(cx+d)$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}