// Numbas version: exam_results_page_options
{"name": "Binomial Expansion 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"e5": {"templateType": "anything", "name": "e5", "description": "", "definition": "e3/e4", "group": "Ungrouped variables"}, "d3": {"templateType": "anything", "name": "d3", "description": "", "definition": "random(2..5 except c3)", "group": "Ungrouped variables"}, "f4": {"templateType": "anything", "name": "f4", "description": "", "definition": "random(2..5 except f3 except e4)", "group": "Ungrouped variables"}, "c4": {"templateType": "anything", "name": "c4", "description": "", "definition": "random(2..5 except c3)", "group": "Ungrouped variables"}, "d2": {"templateType": "anything", "name": "d2", "description": "", "definition": "floor(2d1/3)", "group": "Ungrouped variables"}, "e2": {"templateType": "anything", "name": "e2", "description": "", "definition": "floor(e1/2)", "group": "Ungrouped variables"}, "h1": {"templateType": "anything", "name": "h1", "description": "", "definition": "random(2..5)", "group": "Ungrouped variables"}, "h4": {"templateType": "anything", "name": "h4", "description": "", "definition": "random(2..6)", "group": "Ungrouped variables"}, "h3": {"templateType": "anything", "name": "h3", "description": "", "definition": "random([2,4,5] except h1)", "group": "Ungrouped variables"}, "c2": {"templateType": "anything", "name": "c2", "description": "", "definition": "floor(c1/2)", "group": "Ungrouped variables"}, "f5": {"templateType": "anything", "name": "f5", "description": "", "definition": "f3/f4", "group": "Ungrouped variables"}, "g5": {"templateType": "anything", "name": "g5", "description": "", "definition": "floor(2g4/3)", "group": "Ungrouped variables"}, "g4": {"templateType": "anything", "name": "g4", "description": "", "definition": "random(2..6)", "group": "Ungrouped variables"}, "c1": {"templateType": "anything", "name": "c1", "description": "", "definition": "random(2..6)", "group": "Ungrouped variables"}, "f2": {"templateType": "anything", "name": "f2", "description": "", "definition": "floor(2f1/3)", "group": "Ungrouped variables"}, "d5": {"templateType": "anything", "name": "d5", "description": "", "definition": "d3/d4", "group": "Ungrouped variables"}, "h2": {"templateType": "anything", "name": "h2", "description": "", "definition": "random(1,3)", "group": "Ungrouped variables"}, "c3": {"templateType": "anything", "name": "c3", "description": "", "definition": "random(2..5)", "group": "Ungrouped variables"}, "h5": {"templateType": "anything", "name": "h5", "description": "", "definition": "floor(h4/2)", "group": "Ungrouped variables"}, "d1": {"templateType": "anything", "name": "d1", "description": "", "definition": "random(3..6)", "group": "Ungrouped variables"}, "f3": {"templateType": "anything", "name": "f3", "description": "", "definition": "random(2..5 except e3)", "group": "Ungrouped variables"}, "d4": {"templateType": "anything", "name": "d4", "description": "", "definition": "random(2..5 except d3 except c4)", "group": "Ungrouped variables"}, "e3": {"templateType": "anything", "name": "e3", "description": "", "definition": "random(2..5 except d3)", "group": "Ungrouped variables"}, "e4": {"templateType": "anything", "name": "e4", "description": "", "definition": "random(2..5 except e3 except d4)", "group": "Ungrouped variables"}, "g2": {"templateType": "anything", "name": "g2", "description": "", "definition": "random(1,3)", "group": "Ungrouped variables"}, "e1": {"templateType": "anything", "name": "e1", "description": "", "definition": "random(3..6)", "group": "Ungrouped variables"}, "c5": {"templateType": "anything", "name": "c5", "description": "", "definition": "c3/c4", "group": "Ungrouped variables"}, "g3": {"templateType": "anything", "name": "g3", "description": "", "definition": "random([2,4,5] except g1)", "group": "Ungrouped variables"}, "g1": {"templateType": "anything", "name": "g1", "description": "", "definition": "random(2..5)", "group": "Ungrouped variables"}, "f1": {"templateType": "anything", "name": "f1", "description": "", "definition": "random(3..6)", "group": "Ungrouped variables"}}, "statement": "<p>Find the coefficient of the term indicated in the square brackets in the expansion of each of the following expressions below</p>", "name": "Binomial Expansion 4", "parts": [{"marks": 1, "showCorrectAnswer": true, "precision": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "integerPartialCredit": 0, "minValue": "({c4}^{c1})*(comb({c1},{c2}))*({c5}^{c2})", "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "precisionType": "dp", "scripts": {}, "strictPrecision": true, "type": "numberentry", "maxValue": "({c4}^{c1})*(comb({c1},{c2}))*({c5}^{c2})", "allowFractions": false, "prompt": "<p>$(\\var{c4}+\\var{c3}x)^{\\var{c1}}$ &nbsp; &nbsp; $[x^{\\var{c2}}]$</p>", "precisionPartialCredit": 0, "correctAnswerFraction": false, "variableReplacements": []}, {"marks": 1, "showCorrectAnswer": true, "precision": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "integerPartialCredit": 0, "minValue": "({d4}^{d1})*(comb({d1},{d2}))*({d5}^{d2})", "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "precisionType": "dp", "scripts": {}, "strictPrecision": true, "type": "numberentry", "maxValue": "({d4}^{d1})*(comb({d1},{d2}))*({d5}^{d2})", "allowFractions": false, "prompt": "<p>$(\\var{d4}+\\var{d3}x)^{\\var{d1}}$ &nbsp; &nbsp; $[x^{\\var{d2}}]$</p>", "precisionPartialCredit": 0, "correctAnswerFraction": false, "variableReplacements": []}, {"marks": 1, "showCorrectAnswer": true, "precision": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "integerPartialCredit": 0, "minValue": "({e4}^{e1})*(comb({e1},{e2}))*((-{e5})^{e2})", "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "precisionType": "dp", "scripts": {}, "strictPrecision": true, "type": "numberentry", "maxValue": "({e4}^{e1})*(comb({e1},{e2}))*((-{e5})^{e2})", "allowFractions": false, "prompt": "<p>$(\\var{e4}-\\var{e3}x)^{\\var{e1}}$ &nbsp; &nbsp; $[x^{\\var{e2}}]$</p>", "precisionPartialCredit": 0, "correctAnswerFraction": false, "variableReplacements": []}, {"marks": 1, "showCorrectAnswer": true, "precision": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "integerPartialCredit": 0, "minValue": "({f4}^{f1})*(comb({f1},{f2}))*({f5}^{f2})*((-1)^{f2})", "variableReplacementStrategy": "originalfirst", "showPrecisionHint": false, "precisionType": "dp", "scripts": {}, "strictPrecision": true, "type": "numberentry", "maxValue": "({f4}^{f1})*(comb({f1},{f2}))*({f5}^{f2})*((-1)^{f2})", "allowFractions": false, "prompt": "<p>$(\\var{f4}-\\var{f3}x)^{\\var{f1}}$ &nbsp; &nbsp; $[x^{\\var{f2}}]$</p>", "precisionPartialCredit": 0, "correctAnswerFraction": false, "variableReplacements": []}, {"marks": 1, "prompt": "<p>$(\\frac{1}{\\var{g1}}+\\frac{\\var{g2}}{\\var{g3}}x)^\\var{g4}$ &nbsp; &nbsp; $[x^\\var{g5}]$</p>", "variableReplacementStrategy": "originalfirst", "minValue": "((1/{g1})^{g4})*(comb({g4},{g5}))*(({g1}*{g2}/{g3})^{g5})", "showPrecisionHint": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "((1/{g1})^{g4})*(comb({g4},{g5}))*(({g1}*{g2}/{g3})^{g5})", "allowFractions": true, "correctAnswerFraction": true, "variableReplacements": []}, {"marks": 1, "prompt": "<p>$(\\frac{1}{\\var{h1}}-\\frac{\\var{h2}}{\\var{h3}}x)^\\var{h4}$ &nbsp; &nbsp; $[x^\\var{h5}]$</p>", "variableReplacementStrategy": "originalfirst", "minValue": "((1/{h1})^{h4})*(comb({h4},{h5}))*(({h1}*{h2}*(-1)/{h3})^{h5})", "showPrecisionHint": false, "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "maxValue": "((1/{h1})^{h4})*(comb({h4},{h5}))*(({h1}*{h2}*(-1)/{h3})^{h5})", "allowFractions": true, "correctAnswerFraction": true, "variableReplacements": []}], "functions": {}, "rulesets": {}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "tags": [], "question_groups": [{"name": "", "pickQuestions": 0, "questions": [], "pickingStrategy": "all-ordered"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["c1", "c2", "c3", "c4", "c5", "d2", "d1", "d3", "d4", "d5", "e1", "e2", "e3", "e4", "e5", "f1", "f2", "f3", "f4", "f5", "g1", "g2", "g3", "g4", "g5", "h1", "h2", "h3", "h4", "h5"], "advice": "<p>Recall the binomial theorem&nbsp;<img src=\"http://www.purplemath.com/modules/prob/binom01.gif\" width=\"182\" height=\"50\" border=\"0\" alt=\"(a + b)^n = sum[k=0,n][(n over k)a^(n-k)b^k]\"/>&nbsp;and use this to answer each part<span color=\"#FFFFFF\" face=\"Arial\" size=\"1\" style=\"color: #ffffff; font-family: Arial; font-size: xx-small;\"></span></p>\n<p>For example, if we want to know the coefficient of the $x^i$ term in $(a+bx)^n$ then we look at the binomial theorem and can see that the coefficient will be $\\simplify{comb(n, i)}*a^{(n-i)}*b^i$</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "", "notes": ""}, "showQuestionGroupNames": false, "type": "question", "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}