// Numbas version: exam_results_page_options
{"name": "Musa's copy of Expand brackets and collect like terms 3", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Musa's copy of Expand brackets and collect like terms 3", "tags": [], "metadata": {"description": "<p>Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>For each expression below,&nbsp;collect like terms&nbsp;and expand brackets.</p>\n<p><em>The <code>*</code> symbol is required between algebraic symbols, e.g. $5ab^2$ should be written </em><code>5*a*b^2</code><em>.</em></p>", "advice": "<p>When simplifying expressions, only terms of the same type or like terms can be added together.</p>\n<p>Algebraic symbols or letters can be added together provided that they are raised to the same power. For example, we can add $x^2+x^2=2x^2$, but we cannot collect both $x^2$ and $x$ into one term.</p>\n<h4>a)</h4>\n<p>\\[&nbsp;<br/>\\begin{align}<br/>\\var{c[0]}x+\\var{c[1]}x+\\var{c[2]}x&amp;=(\\var{c[0]}+\\var{c[1]}+\\var{c[2]})x\\\\<br/>&amp;=\\simplify{({c[0]}+{c[1]}+{c[2]})}x<br/>\\end{align}<br/>\\]</p>\n<h4>b)</h4>\n<p>\\[&nbsp;<br/>\\begin{align}<br/>\\var{a[1]}x^2+\\var{a[2]}x^2+\\var{a[3]}x+\\var{a[4]}x +\\var{a[0]}&amp;=(\\var{a[1]}+\\var{a[2]})x^2+(\\var{a[3]}+\\var{a[4]})x +\\var{a[0]}\\\\<br/>&amp;=\\simplify{({a[1]}+{a[2]})}x^2+\\simplify{({a[3]}+{a[4]})}x+\\var{a[0]}<br/>\\end{align}<br/>\\]</p>\n<h4>c)</h4>\n<p>\\[&nbsp;<br/>\\begin{align}<br/>\\var{b[0]}y^5+\\var{b[1]}y^5+\\var{b[2]}y^5+\\var{b[4]}y^5+\\var{b[3]}y^5&amp;=(\\var{b[0]}+\\var{b[1]}+\\var{b[2]}+\\var{b[4]}+\\var{b[3]})y^5\\\\<br/>&amp;=\\simplify{({b[1]}+{b[2]}+{b[3]}+{b[4]}+{b[0]})}y^5<br/>\\end{align}<br/>\\]</p>\n<h4>d)</h4>\n<p>\\[&nbsp;<br/>\\begin{align}<br/>\\var{d[0]}ab+\\var{d[1]}abc+\\var{d[2]}a+\\var{d[3]}b+\\var{d[4]}c+\\var{d[5]}abc<br/>&amp;=(\\var{d[1]}+\\var{d[5]})abc+\\var{d[0]}ab+\\var{d[2]}a+\\var{d[3]}b+\\var{d[4]}c\\\\<br/>&amp;=\\simplify{{d[1]}+{d[5]}}abc+\\var{d[0]}ab+\\var{d[2]}a+\\var{d[3]}b+\\var{d[4]}c<br/>\\end{align}<br/>\\]</p>\n<h4>e)</h4>\n<p>\\[&nbsp;<br/>\\begin{align}<br/>\\var{f[0]}a^2b+\\var{f[1]}ab^2+\\var{f[2]}ab+\\var{f[3]}a^2b+\\var{f[4]}ab^2<br/>&amp;=(\\var{f[0]}+\\var{f[3]})a^2b+(\\var{f[1]}+\\var{f[4]})ab^2+\\var{f[2]}ab\\\\<br/>&amp;=\\simplify{{f[0]}+{f[3]}}a^2b+\\simplify{{f[1]}+{f[4]}}ab^2+\\var{f[2]}ab<br/>\\end{align}<br/>\\]</p>\n<h4>f)</h4>\n<p>\\[<br/>\\begin{align}<br/>\\var{g[0]}(\\var{g[1]}x+\\var{g[2]}y)+\\var{g[4]}x+\\var{g[5]}y<br/>&amp;=(\\var{g[0]}\\times \\var{g[1]}+\\var{g[4]})x+(\\var{g[0]} \\times\\var{g[2]}+\\var{g[5]})y\\\\<br/>&amp;=(\\simplify{{g[0]}*{g[1]}}+\\var{g[4]})x+(\\simplify{{g[0]}*{g[2]}}+\\var{g[5]})y\\\\<br/>&amp;=\\simplify{{g[0]}*{g[1]}+{g[4]}}x+\\simplify{{g[0]}*{g[2]}+{g[5]}}y<br/>\\end{align}<br/>\\]</p>\n<h4>g)</h4>\n<p>\\[&nbsp;<br/>\\begin{align}<br/>\\var{h[0]}x(\\var{h[1]}x+\\var{h[2]}z)+\\var{h[3]}x+\\var{h[6]}z+\\var{h[4]}x^2+\\var{h[5]}z^2<br/>&amp;=(\\simplify[]{{h[0]}{h[1]}}+\\var{h[4]})x^2+(\\simplify[]{{h[0]}{h[2]}})zx+\\var{h[3]}x+\\var{h[5]}z^2+\\var{h[6]}z\\\\<br/>&amp;=(\\simplify{{h[0]}{h[1]}}+\\var{h[4]})x^2+(\\simplify[]{{h[0]}{h[2]}})zx+\\var{h[3]}x+\\var{h[5]}z^2+\\var{h[6]}z\\\\<br/>&amp;=\\simplify{{h[0]}*{h[1]}+{h[4]}}x^2+\\simplify{{h[0]}*{h[2]}}zx+\\simplify{{h[3]}x+{h[5]}}z^2+\\var{h[6]}z<br/>\\end{align}<br/>\\]</p>\n<h4>h)</h4>\n<p>\\[&nbsp;<br/>\\begin{align}<br/>\\var{j[0]}(\\var{j[1]}x-\\var{j[2]}y)+\\var{j[3]}(\\var{j[4]}x-\\var{j[5]}y)+\\var{j[6]}(\\var{j[7]}x-\\var{j[8]}y)<br/>&amp;= (\\simplify[]{{j[0]}{j[1]}}+\\simplify[]{{j[3]}{j[4]}}+\\simplify[]{{j[6]}{j[7]}})x-(\\simplify[]{{j[0]}{j[2]}}+\\simplify[]{{j[3]}{j[5]}}+\\simplify[]{{j[6]}{j[8]}})y\\\\<br/>&amp;= (\\simplify{{j[0]}{j[1]}}+\\simplify{{j[3]}{j[4]}}+\\simplify{{j[6]}{j[7]}})x-(\\simplify{{j[0]}{j[2]}}+\\simplify{{j[3]}{j[5]}}+\\simplify{{j[6]}{j[8]}})y\\\\<br/>&amp;= \\simplify{({j[0]}*{j[1]}+{j[4]*j[3]}+{j[6]}*{j[7]})x}-\\simplify{({j[0]}*{j[2]}+{j[5]}{j[3]}+{j[6]}*{j[8]})y}<br/>\\end{align}<br/>\\]</p>\n<h4></h4>", "rulesets": {}, "extensions": ["stats"], "variables": {"c": {"name": "c", "group": "Part a", "definition": "repeat(random(2..10),5)", "description": "", "templateType": "anything"}, "c1": {"name": "c1", "group": "B group", "definition": "random(2..5)*2", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "B group", "definition": "random(2..10 except a1)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Part a", "definition": "repeat(random(2..33),6)", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "Part a", "definition": "repeat(random(2..20),7)", "description": "", "templateType": "anything"}, "j": {"name": "j", "group": "Part a", "definition": "repeat(random(2..20),9)", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "Part a", "definition": "repeat(random(2..20),7)", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "B group", "definition": "random(5..10)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Part a", "definition": "repeat(random(5..15),5)", "description": "<p>random variables for part 1</p>", "templateType": "anything"}, "b": {"name": "b", "group": "Part a", "definition": "repeat(random(2..10),5)", "description": "", "templateType": "anything"}, "g": {"name": "g", "group": "Part a", "definition": "repeat(random(2..15),7)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "B group", "variables": ["a1", "b1", "c1"]}, {"name": "Part a", "variables": ["a", "b", "c", "d", "f", "g", "h", "j"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\var{c[0]}x+\\var{c[1]}x+\\var{c[2]}x=$ [[0]]<em></em></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "({c[1]}+{c[0]}+{c[2]})x", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "maxlength": {"length": "0", "partialCredit": 0, "message": "<p>You must collect like terms&nbsp;to fully simplify.</p>"}, "mustmatchpattern": {"pattern": "$n*x", "partialCredit": 0, "message": "You haven't simplified: you still have two or more like terms that should be collected together.", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p><br/>$\\var{a[1]}x^2+\\var{a[2]}x^2+\\var{a[3]}x+\\var{a[4]}x +\\var{a[0]}=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "({a[1]}+{a[2]})x^2+({a[3]}+{a[4]})x+{a[0]}", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "$n*x^2 + $n*x + $n", "partialCredit": 0, "message": "You haven't simplified: you still have two or more like terms that should be collected together.", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\var{g[0]}(\\var{g[1]}x+\\var{g[2]}y)=$&nbsp;[[0]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "({g[0]}{g[1]})x+({g[0]}{g[2]})y", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "maxlength": {"length": "0", "partialCredit": 0, "message": "<p>You must condense your answer to fully simplify. *'s are not needed to indicate multiplication here.</p>"}, "mustmatchpattern": {"pattern": "$n*x+$n*y", "partialCredit": 0, "message": "You haven't simplified: you still have two or more like terms that should be collected together.", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Solve for&nbsp; $x$:</p>\n<p>$\\var{j[6]+1} x&nbsp; + \\var{j[7]}= \\var{j[0]}$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "({j[0]-j[7]})/({j[6]}+1)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "maxlength": {"length": "0", "partialCredit": 0, "message": "<p>You must condense your answer to fully simplify. *'s are not needed to indicate multiplication here.</p>"}, "mustmatchpattern": {"pattern": "`+-$n/$n", "partialCredit": 0, "message": "You haven't simplified: you still have two or more like terms that should be collected together.", "nameToCompare": ""}, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Solve for&nbsp; $x$:</p>\n<p>$\\var{j[5]+1} x&nbsp; + \\var{j[6]}a= \\var{j[2]}$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "({j[2]}-{j[6]}a)/({j[5]}+1)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "maxlength": {"length": "0", "partialCredit": 0, "message": "<p>You must condense your answer to fully simplify. *'s are not needed to indicate multiplication here.</p>"}, "valuegenerators": [{"name": "a", "value": ""}]}], "sortAnswers": false}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}, {"name": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}, {"name": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}