// Numbas version: exam_results_page_options
{"name": "Expansion of two brackets: Quadratic and Quadratic ", "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: Quadratic and Quadratic ", "tags": ["algebra", "algebraic manipulation", "expansion of brackets", "expansion of two quadratic terms"], "advice": "\n  <p>Using the method given by Show steps:</p>\n  <p>\\[\\begin{eqnarray*}\\simplify[std]{ ({a}z^2+{b}z+{c})({m}z^2+{p}z+{q})}&amp;=&amp;\\simplify[std]{{a}z^2*({m}z^2+{p}z+{q})+{b}*z*({m}z^2+{p}z+{q})+{c}({m}z^2+{p}z+{q})}\\\\&amp;=&amp;\\simplify[std]{{a*m}z^4+{a*p}z^3+{a*q}z^2+{b*m}z^3+{b*p}z^2+{b*q}z+{c*m}z^2+{c*p}z+{c*q}}\\\\&amp;=&amp;\\simplify[std]{{a*m}z^4+{a*p+m*b}z^3+{(a*q+c*m+b*p)}z^2+{b*q+c*p}z+{c*q}}\\end{eqnarray*}\\]</p>\n  <p>&nbsp;</p>\n  ", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepspenalty": 1.0, "prompt": "\n      <p>$\\simplify[std]{({a}z^2+{b}z+{c})({m}*z^2+{p}z+{q})}=\\;$[[0]].</p>\n      <p>Your answer should be a quartic (degree 4 polynomial) in $z$ 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 quartic in $z$, in the form $az^4+bz^3+cz^2+dz+f$ for appropriate integers $a,\\;b,\\;c,\\;d$ and $f$.</p>", "showstrings": false, "strings": ["(", "zz", "z*z"], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "{a*m}z^4+{a*p+b*m}z^3+{a*q+p*b+c*m}z^2+{q*b+c*p}z+{c*q}", "type": "jme", "maxlength": {"length": 31.0, "message": "<p>Input our answer as a quartic polynomial with all terms cllected together in the form $az^4+bz^3+cz^2+dz+f$ for appropriate integers $a,\\;b,\\;c,\\;d$ and $f$.</p>", "partialcredit": 0.0}}], "steps": [{"prompt": "\n          <p>One way to expand this is as follows:</p>\n          <p>$(az^2+bz+c)(dz^2+pz+q)=az^2(dz^2+pz+q)+bz(dz^2+pz+q)+c(dz^2+pz+q)$ etc..</p>\n          ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "extensions": [], "statement": "<p>Expand the following to give a quartic in $z$.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(1..5)", "name": "a"}, "c": {"definition": "random(2..5)", "name": "c"}, "b": {"definition": "random(-9..9 except [0,a])", "name": "b"}, "d": {"definition": "random(-9..9 except [0,c])", "name": "d"}, "m": {"definition": "random(1..4 except a)", "name": "m"}, "q": {"definition": "random(-3..3 except 0)", "name": "q"}, "p": {"definition": "random(-3..3 except 0)", "name": "p"}}, "metadata": {"notes": "\n    \t\t<p><strong>17/08/2012:</strong></p>\n    \t\t        <p>Added tags.</p>\n    \t\t        <p>Added description.</p>\n    \t\t        <p>Checked calculation.</p>\n    \t\t", "description": "<p>Expand $(az^2+bz+c)(dz^2+pz+q)$.</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/"}]}