// Numbas version: exam_results_page_options
{"name": "1.3.1.5 Simplify an expression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.3.1.5 Simplify an expression", "tags": [], "metadata": {"description": "<p>Simplify, if possible,<br />(a) $\\frac{2}{3}x^2 + \\frac{x^2}{3}$, (b) $0.5x^2 + \\frac{3}{4}x^2 - \\frac{11}{2}x$,&nbsp;(c) $3x^3 - 11x + 3yx + 11$, and (d) $-4\\alpha x^2 + \\beta x^2$ where $\\alpha$ and $\\beta$ are constants.</p>\n<p>The numbers and letters are all randomised.</p>\n<p>Part of HELM Book 1.3</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Note: After you have answered these questions, choose \"reveal answers\" and compare your answers to check that you have entered the most simplified forms of the expressions.</p>", "advice": "<p>$\\var{q5expr}=\\var{q5ans}$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"vars": {"name": "vars", "group": "Ungrouped variables", "definition": "shuffle(['a','b','c','d','f','g','h','k','m','n','p','q','r','s','t','u','v','w','x','y','z'])", "description": "", "templateType": "anything", "can_override": false}, "q5den": {"name": "q5den", "group": "question 5", "definition": "[random(2..6),random(2,4,5,8)]", "description": "", "templateType": "anything", "can_override": false}, "q5num": {"name": "q5num", "group": "question 5", "definition": "flatten([repeat(random(1..11 except q5den),3),[random(1..q5den[1]-1)]])", "description": "", "templateType": "anything", "can_override": false}, "q5ints": {"name": "q5ints", "group": "question 5", "definition": "repeat(random(-20..20 except [-1,0,1]),4)", "description": "", "templateType": "anything", "can_override": false}, "q5exprs": {"name": "q5exprs", "group": "question 5", "definition": "[ expression(\"(\"+q5num[0]+\"/\"+q5den[0]+\")*\"+vars[7]+\"^2+\"+\n  \"(\"+vars[7]+\"^2)/\"+q5den[0]),\n  expression(q5den[0] + \".\" + q5den[1]+\"*\"+vars[7]+\"^2+(\"+\n    q5num[0] + \".\" + q5num[1]+\")*\"+vars[7]+\"^2+(\"+\n    q5num[2] + \".\" + q5num[3] +\")*\"+vars[7] ),\n  expression(q5ints[0]+\"*\"+vars[7]+\"^2+\"+q5ints[1]+\"*\"+vars[7]+\"+\"+\n    q5ints[0]+\"*\"+vars[8]+\"*\"+vars[7]+\"+(-1)*\"+q5ints[1]  ),\n  expression(q5ints[0]+ \"*\\alpha \" + vars[7]+\"^2+\"+q5ints[1]+\"*\\beta \"+vars[7]+\"^2\")\n  ]", "description": "<p>1) (a/b)x^2+(x^2)/c (a,b,c &gt;0)</p>\n<p>2) dx^2+(a/b)x^2+(e/f)x (a,b,c,d,e &gt; 0)</p>\n<p>3) ax^2+bx+cyx-d (a,b,c,d are not 1 or -1)</p>\n<p>4) a.alpha.x^2+b.beta.x^2 (a and b are not 1 or -1)</p>", "templateType": "anything", "can_override": false}, "q5idx": {"name": "q5idx", "group": "question 5", "definition": "random(0..3)", "description": "<p>random(0..3)</p>", "templateType": "anything", "can_override": false}, "q5expr": {"name": "q5expr", "group": "question 5", "definition": "simplify(q5exprs[q5idx],[\"basic\",\"simplifyFractions\",\"unitFactor\"])", "description": "", "templateType": "anything", "can_override": false}, "q5ans": {"name": "q5ans", "group": "question 5", "definition": "simplify([ expression(\n      eval(expression(\"(\"+q5num[0]+\"/\"+q5den[0]+\") + (1/\"+q5den[0]+\")\"))+\n      \"*\"+ vars[7]+\"^2\"),\n  simplify(q5expr,\"all\"),\n  expression(q5ints[0]+\"*\"+vars[7]+\"^2+\"+q5ints[1]+\"*\"+vars[7]+\"+\"+\n    q5ints[0]+\"*\"+vars[8]+\"*\"+vars[7]+\"+(-1)*\"+q5ints[1]  ),\n  expression(\"(\"+q5ints[0]+ \"*\\alpha\" + \"+\"+q5ints[1]+\"*\\beta)*\"+vars[7]+\"^2\")\n  ][q5idx],[\"all\"])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["vars"], "variable_groups": [{"name": "question 5", "variables": ["q5den", "q5num", "q5ints", "q5exprs", "q5idx", "q5expr", "q5ans"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify, if possible: $\\var{q5expr}$ <span data-jme-visible=\"q5idx=3\">where $\\alpha$ and $\\beta$ are constants.</span></p>\n<p><span data-jme-visible=\"q5idx=3\">(Type alpha to enter $\\alpha$ and beta to enter $\\beta$.)</span></p>", "answer": "{q5ans}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "((`+-($n)`?*alpha + `+-($n)`?*beta) * $v^2) `|  // alpha +/- beta\n(((rational:$n `| decimal:$n `| `+-$n)*$v^2)`? + // v^2\n((decimal:$n `| `+-$n)*v)`? + // v\n($n*$v*$v)`? + // two variables\n($n)`?)  // constant term", "partialCredit": 0, "message": "You need to collect all like terms.", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}