9 questions: Expanding out expressions such $(ax+b)(cx+d)$ etc.
", "licence": "Creative Commons Attribution 4.0 International"}, "percentPass": 0, "question_groups": [{"pickQuestions": 1, "name": "Group", "pickingStrategy": "all-ordered", "questions": [{"name": "Michael's copy of Expansion of two brackets: Linear 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "showQuestionGroupNames": false, "type": "question", "functions": {}, "metadata": {"description": "Expand $ax(cx+d)$ and expand $(rx+s)(px)$
", "notes": "\n \t\t \t\t15/08/2012:
\n \t\t \t\tAdded tags.
\n \t\t \t\tAdded description.
\n \t\t \n \t\t", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"b": {"name": "b", "definition": 0.0}, "b1": {"name": "b1", "definition": "random(-9..9 except [0,c])"}, "c1": {"name": "c1", "definition": "random(-5..5 except 0)"}, "a1": {"name": "a1", "definition": "random(-5..5 except [0,a])"}, "c": {"name": "c", "definition": "random(-5..5 except 0)"}, "a": {"name": "a", "definition": "random(-5..5 except 0)"}, "d": {"name": "d", "definition": "random(-9..9 except [0,c])"}}, "variable_groups": [], "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [], "pickQuestions": 0}], "parts": [{"gaps": [{"notallowed": {"partialcredit": 0.0, "message": "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 $a,\\;b,\\;c$.
", "showstrings": false, "strings": ["("]}, "answersimplification": "std", "type": "jme", "vsetrangepoints": 5.0, "vsetrange": [0.0, 1.0], "checkingtype": "absdiff", "maxlength": {"partialcredit": 0.0, "length": 13.0, "message": "Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.
"}, "checkingaccuracy": 0.001, "answer": "{a*c}x^2+{a*d}x", "marks": 1.0}, {"notallowed": {"partialcredit": 0.0, "message": "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 $a,\\;b,\\;c$.
", "showstrings": false, "strings": ["("]}, "answersimplification": "std", "type": "jme", "vsetrangepoints": 5.0, "vsetrange": [0.0, 1.0], "checkingtype": "absdiff", "maxlength": {"partialcredit": 0.0, "length": 13.0, "message": "Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.
"}, "checkingaccuracy": 0.001, "answer": "{a1*c1}*x^2+{b1*c1}*x", "marks": 1.0}], "type": "gapfill", "prompt": "\n$\\simplify[std]{({a}x)({c}x+{d})}=\\;$[[0]].
\n$\\simplify[std]{({a1}x+{b1})({c1}x)}=\\;$[[1]].
\nYour answers should be quadratics in $x$ and should not include any brackets.
\nYou can click on Show steps to get more information, but you will lose one mark if you do so.
\n ", "stepspenalty": 1.0, "steps": [{"prompt": "\\[ax(cx+d)=acx^2+adx\\]
", "type": "information", "marks": 0.0}], "marks": 0.0}], "progress": "ready", "tags": ["algebra", "algebraic manipulation", "expansion of brackets", "expansion of the product of two linear terms"], "statement": "Expand the following to give quadratics in $x$.
", "advice": "\n1. Using the method given by Show steps we have:
\n\\[\\simplify[std]{ {a}x*({c}x+{d})}=\\simplify[std]{{a*c}x^2+{a*d}x}\\]
\n2.
\n\\[\\simplify[std]{ ({a1}x+{b1})*({c1}x)}=\\simplify[std]{{a1*c1}x^2+{b1*c1}x}\\]
\n\n
\n "}, {"name": "Michael's copy of Expansion of two brackets: Linear 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "functions": {}, "showQuestionGroupNames": false, "metadata": {"notes": "\n \t\t
15/08/2012:
\n \t\tAdded tags.
\n \t\tAdded description.
\n \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "Expand $(ax+b)(cx+d)$.
"}, "progress": "ready", "question_groups": [{"name": "", "questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0}], "tags": ["algebra", "algebraic manipulation", "expansion of brackets", "expansion of the product of two linear terms"], "statement": "Expand the following to give a quadratic in $x$.
", "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"gaps": [{"maxlength": {"message": "Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.
", "partialcredit": 0.0, "length": 17.0}, "marks": 2.0, "answer": "{a*c}x^2+{b*c+a*d}x+{b*d}", "notallowed": {"message": "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 $a,\\;b,\\;c$.
", "strings": ["("], "showstrings": false, "partialcredit": 0.0}, "vsetrangepoints": 5.0, "answersimplification": "std", "vsetrange": [0.0, 1.0], "type": "jme", "musthave": {"message": "Input your answer as a quadratic in $x$, in the form $ax^2+bx+c$ for appropriate integers $a,\\;b,\\;c$.
", "strings": ["x^2"], "showstrings": false, "partialcredit": 0.0}, "checkingaccuracy": 0.001, "checkingtype": "absdiff"}], "prompt": "\n$\\simplify[std]{({a}x+{b})({c}x+{d})}=\\;$[[0]].
\nYour answer should be a quadratic in $x$ and should not include any brackets.
\nYou can click on Show steps for more information, but you will lose one mark if you do so.
\n ", "stepspenalty": 1.0, "steps": [{"prompt": "\nThere are many ways to expand an expression such as $(ax+b)(cx+d)$.
\nOne way:
\n\\[\\begin{eqnarray*} (ax+b)(cx+d)&=&ax(cx+d)+b(cx+d)\\\\&=&acx^2+adx+bcx+bd\\\\&=&acx^2+(ad+bc)x+bd\\end{eqnarray*}\\]
\n ", "type": "information", "marks": 0.0}], "type": "gapfill", "marks": 0.0}], "variables": {"c": {"name": "c", "definition": "random(-5..5 except 0)"}, "a": {"name": "a", "definition": "random(-5..5 except 0)"}, "d": {"name": "d", "definition": "random(-9..9 except [0,c])"}, "b": {"name": "b", "definition": "random(-9..9 except [0,a])"}}, "type": "question", "variable_groups": [], "advice": "\nUsing the method given by Show steps we have:
\n\\[\\begin{eqnarray*}\\simplify[std]{ ({a}x+{b})({c}x+{d})}&=&\\simplify[std]{{a}x*({c}x+{d})+{b}({c}x+{d})}\\\\&=&\\simplify[std]{{a*c}x^2+{a*d}x+{b*c}x+{b*d}}\\\\&=&\\simplify[std]{{a*c}x^2+{(a*d+b*c)}x+{b*d}}\\end{eqnarray*}\\]
\n\n "}, {"name": "Michael's copy of Expansion of two brackets: Linear and Quadratic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "advice": "\n
Using the method given by Show steps:
\n\\[\\begin{eqnarray*}\\simplify[std]{ ({p}w+{q})({a}w^2+{b}w+{c})}&=&\\simplify[std]{{p}w*({a}w^2+{b}w+{c})+{q}({a}w^2+{b}w+{c})}\\\\&=&\\simplify[std]{{a*p}w^3+{b*p}w^2+{c*p}w+{a*q}w^2+{q*b}w+{c*q}}\\\\&=&\\simplify[std]{{a*p}w^3+{(a*q+b*p)}w^2+{b*q+c*p}w+{c*q}}\\end{eqnarray*}\\]
\n\n ", "variable_groups": [], "metadata": {"description": "
Expand $(pw+q)(aw^2+bw+c)$.
", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"variableReplacements": [], "useCustomName": false, "prompt": "\n$\\simplify[std]{({p}w+{q})({a}w^2+{b}w+{c})}=\\;$[[0]].
\nYour answer should be a cubic in $w$ and should not include any brackets.
\nYou can click on Show steps for more information, but you will lose one mark if you do so.
\n ", "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "stepsPenalty": 1, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "steps": [{"variableReplacements": [], "useCustomName": false, "prompt": "\nOne way to expand this is as follows:
\n$(pw+q)(aw^2+bw+c)=pw (aw^2+bw+c) +q(aw^2+bw+c)$ etc..
\nOr as $(pw+q)(aw^2+bw+c)=(aw^2+bw+c)(pw+q)$ we can expand it as:
\n$(aw^2+bw+c)(pw+q)=aw^2(pw+q)+bw(pw+q)+c(pw+q)$
\n ", "scripts": {}, "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "marks": 0, "type": "information", "customName": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "unitTests": []}], "marks": 0, "type": "gapfill", "customName": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "sortAnswers": false, "gaps": [{"variableReplacements": [], "useCustomName": false, "answerSimplification": "std", "extendBaseMarkingAlgorithm": true, "checkingType": "absdiff", "showFeedbackIcon": true, "showPreview": true, "checkingAccuracy": 0.001, "type": "jme", "valuegenerators": [{"value": "", "name": "w"}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "notallowed": {"message": "Do not include brackets in your answer. Input your answer as a cubic in $w$, in the form $aw^3+bw^2+cw+d$ for appropriate integers $a,\\;b,\\;c,\\;d$.
", "strings": ["(", "ww", "w*w"], "partialCredit": 0, "showStrings": false}, "answer": "{a*p}w^3+{a*q+p*b}w^2+{q*b+c*p}w+{c*q}", "failureRate": 1, "scripts": {}, "adaptiveMarkingPenalty": 0, "checkVariableNames": false, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "vsetRange": [0, 1], "marks": 2, "customName": "", "unitTests": []}]}], "tags": [], "ungrouped_variables": ["d", "a", "p", "c", "q", "b"], "variables": {"q": {"description": "", "templateType": "anything", "name": "q", "group": "Ungrouped variables", "definition": "random(-3..3 except [0,b,d])"}, "b": {"description": "", "templateType": "anything", "name": "b", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,a])"}, "a": {"description": "", "templateType": "anything", "name": "a", "group": "Ungrouped variables", "definition": "random(1..5)"}, "p": {"description": "", "templateType": "anything", "name": "p", "group": "Ungrouped variables", "definition": "random(1..3 except [a,c])"}, "c": {"description": "", "templateType": "anything", "name": "c", "group": "Ungrouped variables", "definition": "random(2..5)"}, "d": {"description": "", "templateType": "anything", "name": "d", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,c])"}}, "functions": {}, "statement": "Expand the following to give a cubic in $w$.
"}, {"name": "Michael's copy of Expansion of two brackets: Quadratic and Linear", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "tags": ["algebra", "algebraic manipulation", "expansion of a quadratic and linear term", "expansion of brackets"], "statement": "Expand the following to give a cubic in $z$.
", "showQuestionGroupNames": false, "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "variable_groups": [], "variables": {"b": {"name": "b", "definition": "random(-9..9 except [0,a])"}, "c": {"name": "c", "definition": "random(2..5)"}, "a": {"name": "a", "definition": "random(1..5)"}, "d": {"name": "d", "definition": "random(-9..9 except [0,c])"}, "q": {"name": "q", "definition": "random(-3..3 except [0,b,d])"}, "p": {"name": "p", "definition": "random(1..3 except [a,c])"}}, "type": "question", "functions": {}, "parts": [{"gaps": [{"checkingaccuracy": 0.001, "checkingtype": "absdiff", "vsetrange": [0.0, 1.0], "type": "jme", "vsetrangepoints": 5.0, "answersimplification": "std", "answer": "{a*p}z^3+{a*q+p*b}z^2+{q*b+c*p}z+{c*q}", "notallowed": {"message": "Do not include brackets in your answer. Input your answer as a cubic in $z$, in the form $az^3+bz^2+cz+d$ for appropriate integers $a,\\;b,\\;c,\\;d$.
", "showstrings": false, "strings": ["(", "zz", "z*z"], "partialcredit": 0.0}, "marks": 2.0}], "type": "gapfill", "prompt": "\n$\\simplify[std]{({a}z^2+{b}z+{c})({p}z+{q})}=\\;$[[0]].
\nYour answer should be a cubic in $z$ and should not include any brackets.
\nYou can click on Show steps for more information, but you will lose one mark if you do so.
\n ", "stepspenalty": 1.0, "steps": [{"type": "information", "prompt": "\nOne way to expand this is as follows:
\n$(az^2+bz+c)(pz+q)=az^2(pz+q)+bz*(pz+q)+c(pz+q)$ etc..
\n ", "marks": 0.0}], "marks": 0.0}], "progress": "ready", "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "pickQuestions": 0, "questions": []}], "advice": "\nUsing the method given by Show steps:
\n\\[\\begin{eqnarray*}\\simplify[std]{ ({a}z^2+{b}z+{c})({p}z+{q})}&=&\\simplify[std]{{a}z^2*({p}z+{q})+{b}*z*({p}z+{d})+{c}({p}z+{q})}\\\\&=&\\simplify[std]{{a*p}z^3+{a*q}z^2+{b*p}z^2+{b*d}z+{c*p}z+{c*q}}\\\\&=&\\simplify[std]{{a*p}z^3+{(a*q+b*p)}z^2+{b*d+c*p}z+{c*q}}\\end{eqnarray*}\\]
\n\n ", "metadata": {"description": "
Expand $(az^2+bz+c)(pz+q)$.
", "notes": "\n \t\t \t\t16/08/2012:
\n \t\t \t\tAdded tags.
\n \t\t \t\tAdded description.
\n \t\t \n \t\t", "licence": "Creative Commons Attribution 4.0 International"}}, {"name": "Michael's copy of Expansion of two brackets: Quadratic and Quadratic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "tags": ["algebra", "algebraic manipulation", "expansion of brackets", "expansion of two quadratic terms"], "statement": "Expand the following to give a quartic in $z$.
", "showQuestionGroupNames": false, "rulesets": {"std": ["all", "!noLeadingMinus", "!collectNumbers"]}, "variable_groups": [], "variables": {"m": {"name": "m", "definition": "random(1..4 except a)"}, "b": {"name": "b", "definition": "random(-9..9 except [0,a])"}, "c": {"name": "c", "definition": "random(2..5)"}, "a": {"name": "a", "definition": "random(1..5)"}, "d": {"name": "d", "definition": "random(-9..9 except [0,c])"}, "q": {"name": "q", "definition": "random(-3..3 except 0)"}, "p": {"name": "p", "definition": "random(-3..3 except 0)"}}, "type": "question", "functions": {}, "parts": [{"gaps": [{"checkingaccuracy": 0.001, "checkingtype": "absdiff", "vsetrange": [0.0, 1.0], "maxlength": {"message": "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 $f$.
", "length": 31.0, "partialcredit": 0.0}, "type": "jme", "vsetrangepoints": 5.0, "answersimplification": "std", "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}", "notallowed": {"message": "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 $f$.
", "showstrings": false, "strings": ["(", "zz", "z*z"], "partialcredit": 0.0}, "marks": 2.0}], "type": "gapfill", "prompt": "\n$\\simplify[std]{({a}z^2+{b}z+{c})({m}*z^2+{p}z+{q})}=\\;$[[0]].
\nYour answer should be a quartic (degree 4 polynomial) in $z$ and should not include any brackets.
\nYou can click on Show steps for more information, but you will lose one mark if you do so.
\n ", "stepspenalty": 1.0, "steps": [{"type": "information", "prompt": "\nOne way to expand this is as follows:
\n$(az^2+bz+c)(dz^2+pz+q)=az^2(dz^2+pz+q)+bz(dz^2+pz+q)+c(dz^2+pz+q)$ etc..
\n ", "marks": 0.0}], "marks": 0.0}], "progress": "ready", "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "pickQuestions": 0, "questions": []}], "advice": "\nUsing the method given by Show steps:
\n\\[\\begin{eqnarray*}\\simplify[std]{ ({a}z^2+{b}z+{c})({m}z^2+{p}z+{q})}&=&\\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})}\\\\&=&\\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}}\\\\&=&\\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*}\\]
\n\n ", "metadata": {"description": "
Expand $(az^2+bz+c)(dz^2+pz+q)$.
", "notes": "\n \t\t17/08/2012:
\n \t\tAdded tags.
\n \t\tAdded description.
\n \t\tChecked calculation.
\n \t\t", "licence": "Creative Commons Attribution 4.0 International"}}, {"name": "Michael's copy of Verschil van twee veeltermproducten", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Johan Maertens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1301/"}], "functions": {}, "metadata": {"description": "Simplify $(ax+b)(cx+d)-(ax+d)(cx+b)$. Answer is a multiple of $x$.
", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"js": "", "css": ""}, "tags": [], "statement": "Werk uit en herleid.
", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["c", "a", "d", "b"], "variables": {"c": {"templateType": "anything", "description": "", "name": "c", "definition": "random(-6..6 except [0,a])", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "description": "", "name": "a", "definition": "random(-6..6 except 0)", "group": "Ungrouped variables"}, "d": {"templateType": "anything", "description": "", "name": "d", "definition": "random(1..9 except c)", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "description": "", "name": "b", "definition": "random(1..9 except a)", "group": "Ungrouped variables"}}, "type": "question", "variable_groups": [], "advice": "\nExpanding the brackets we have:
\n\\[\\begin{eqnarray*}\\simplify[std]{({a}x+{b})({c}x+{d})-({a}x+{d})({c}x+{b})}&=&(\\simplify[std]{{a*c}x^2+{b*c+a*d}x+{b*d}})-(\\simplify[std]{{a*c}x^2+{b*a+c*d}x+{b*d}})\\\\&=&\\simplify[std]{{b*c+a*d}x-{b*a+c*d}x}\\\\&=&\\var{(a-c)*(d-b)}x\\end{eqnarray*}\\]
\n ", "parts": [{"scripts": {}, "gaps": [{"scripts": {}, "vsetrange": [0, 1], "vsetrangepoints": 5, "showFeedbackIcon": true, "showpreview": true, "variableReplacementStrategy": "originalfirst", "checkingtype": "absdiff", "maxlength": {"message": "Je kan de veelterm korter schrijven.
", "length": 6, "partialCredit": 0}, "marks": 2, "answer": "{(a-c)*(d-b)}*x", "notallowed": {"strings": ["("], "message": "Geen haken gebruiken!
", "showStrings": false, "partialCredit": 0}, "checkvariablenames": false, "answersimplification": "std", "variableReplacements": [], "showCorrectAnswer": true, "type": "jme", "checkingaccuracy": 0.001, "expectedvariablenames": []}], "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "prompt": "$\\simplify[std]{({a}x+{b})({c}x+{d})-({a}x+{d})({c}x+{b})}=\\;$[[0]]
"}]}, {"name": "Michael's copy of Simplify Algebraic Expressions: 2 unknowns", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}], "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "showQuestionGroupNames": false, "type": "question", "functions": {}, "metadata": {"description": "Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.
", "notes": "\n \t\t \t\t18/08/2012:
\n \t\t \t\tAdded tags.
\n \t\t \t\tAdded description.
\n \t\t \n \t\t", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"b": {"name": "b", "definition": "random(1..9 except a)"}, "c": {"name": "c", "definition": "random(-6..6 except [0,a])"}, "d": {"name": "d", "definition": "random(1..9 except [c,b])"}, "a": {"name": "a", "definition": "random(-6..6 except 0)"}}, "variable_groups": [], "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [], "pickQuestions": 0}], "parts": [{"gaps": [{"notallowed": {"partialcredit": 0.0, "message": "Do not include brackets in your answer.
", "showstrings": false, "strings": ["("]}, "answersimplification": "std", "type": "jme", "vsetrangepoints": 5.0, "vsetrange": [0.0, 1.0], "checkingtype": "absdiff", "maxlength": {"partialcredit": 0.0, "length": 7.0, "message": "You can simplify the expression further.
"}, "checkingaccuracy": 0.001, "answer": "{(a-c)*(d-b)}*x*y", "marks": 2.0}], "prompt": "\nSimplify:
\n$\\simplify[std]{({a}x+{b}y)({c}x+{d}y)-({a}x+{d}y)({c}x+{b}y)}=\\;$[[0]]
\nDo not include brackets in your answer.
\nInput $xy$ as $x*y$.
\n ", "type": "gapfill", "marks": 0.0}], "progress": "ready", "tags": ["algebra", "algebraic manipulation", "expanding brackets", "simplification", "simplifying an expression"], "statement": "Simplify the following expression.
", "advice": "\nExpanding the brackets we have:
\n\\[\\begin{eqnarray*}\\simplify[std]{({a}x+{b}y)({c}x+{d}y)-({a}x+{d}y)({c}x+{b}y)}&=&(\\simplify[std]{{a*c}x^2+{b*c+a*d}x*y+{b*d}y^2})-(\\simplify[std]{{a*c}x^2+{b*a+c*d}x*y+{b*d}y^2})\\\\&=&\\simplify[std]{{b*c+a*d}x*y-{b*a+c*d}x*y}\\\\&=&\\var{(a-c)*(d-b)}xy\\end{eqnarray*}\\]
\n "}, {"name": "Michael's copy of Johan's copy of Simplify Expression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Johan Maertens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1301/"}], "tags": ["algebra", "algebraic manipulation", "simplification", "simplify an expression"], "statement": "Express the following expression as $ax+by$ for suitable integers $a$ and $b$.
", "showQuestionGroupNames": false, "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "variable_groups": [], "variables": {"a2": {"name": "a2", "definition": "random(-5..5 except [0,1,-1])"}, "b1": {"name": "b1", "definition": "random(-9..9 except 0)"}, "b": {"name": "b", "definition": "random(1..6)"}, "c": {"name": "c", "definition": "random(-5..5 except 0)"}, "a": {"name": "a", "definition": "random(-6..6 except [0,1,-1])"}, "b2": {"name": "b2", "definition": "random(-9..9 except [0,a,a1])"}, "f": {"name": "f", "definition": "a*b+a1+a2*b2"}, "c2": {"name": "c2", "definition": "random(-9..9 except 0)"}, "a1": {"name": "a1", "definition": "random(-9..9 except [0,a,-a])"}, "d": {"name": "d", "definition": "a*c+b1+a2*c2"}}, "type": "question", "functions": {}, "parts": [{"gaps": [{"checkingaccuracy": 0.001, "checkingtype": "absdiff", "vsetrange": [0.0, 1.0], "maxlength": {"message": "Collect together all $x$ and $y$ terms and input your answer in the form $ax+by$ for suitable values of $a$ and $b$.
", "length": 14.0, "partialcredit": 0.0}, "type": "jme", "vsetrangepoints": 5.0, "answersimplification": "std", "answer": "{f}x+{d}y", "notallowed": {"message": "Do not include brackets in your answer. Collect together all $x$ and $y$ terms and input your answer in the form $ax+by$ for suitable values of $a$ and $b$.
", "showstrings": false, "strings": ["("], "partialcredit": 0.0}, "marks": 1.0}], "type": "gapfill", "prompt": "\nSimplify $f(x,y)=\\simplify[std]{{a}({b}x+{c}y)+{a1}x+{b1}y+{a2}({b2}x+{c2}y)}$
\n$f(x,y)=\\;$[[0]]
\nDo not include brackets in your answer.
\n ", "marks": 0.0}], "progress": "ready", "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [], "pickQuestions": 0}], "advice": "\n\\[\\begin{eqnarray*}f(x,y)&=&\\simplify[std]{{a}({b}x+{c}y)+{a1}x+{b1}y+{a2}({b2}x+{c2}y)}\\\\&=&\\simplify[std]{{a*b}x+{a*c}y+{a1}x+{b1}y+{a2*b2}x+{a2*c2}y}\\\\&=&\\simplify[std]{{a*b}x+{a1}x+{a2*b2}x+{a*c}y+{b1}y+{a2*c2}y}\\\\&=&\\simplify[std]{({a*b}+{a1}+{a2*b2})x+({a*c}+{b1}+{a2*c2})y}\\\\&=&\\simplify[std]{{a*b+a1+a2*b2}x+{a*c+b1+a2*c2}y}\\end{eqnarray*}\\]
\n\n ", "metadata": {"description": "
Express a sum of linear terms in $x$ and $y$ as a single linear term in $x$ and $y$.
", "licence": "Creative Commons Attribution 4.0 International", "notes": "\n \t\t17/08/2012:
\n \t\tAdded tags.
\n \t\tAdded description.
\n \t\tChecked calculations.OK.
\n \t\t"}}]}], "showQuestionGroupNames": false, "navigation": {"showresultspage": "oncompletion", "showfrontpage": false, "allowregen": true, "preventleave": false, "browse": true, "onleave": {"action": "none", "message": ""}, "startpassword": "", "reverse": true}, "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "Owen Jepps", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1195/"}], "extensions": [], "custom_part_types": [], "resources": []}