// Numbas version: exam_results_page_options
{"name": "Binomial Expansion 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a1", "a2", "b1", "b2", "c1", "c2", "c3", "d1", "d2", "d3", "e1", "e2", "e3", "f1", "f2", "f3", "g1", "g2", "g3"], "name": "Binomial Expansion 3", "tags": [], "preamble": {"css": "", "js": ""}, "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>", "rulesets": {}, "parts": [{"prompt": "<p>$(1+x)^{\\var{a1}}$ &nbsp; &nbsp; $[x^{\\var{a2}}]$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "comb({a1},{a2})", "minValue": "comb({a1},{a2})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$(1+x)^{\\var{b1}}$ &nbsp; &nbsp; $[x^{\\var{b2}}]$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "comb({b1},{b2})", "minValue": "comb({b1},{b2})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$(1+\\var{c3}x)^{\\var{c1}}$ &nbsp; &nbsp; $[x^{\\var{c2}}]$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "comb({c1},{c2})*({c3}^{c2})", "minValue": "comb({c1},{c2})*({c3}^{c2})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$(1-\\var{d3}x)^{\\var{d1}}$ &nbsp; &nbsp; $[x^{\\var{d2}}]$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((-1)^{d2})*(comb({d1},{d2}))*({d3}^{d2})", "minValue": "((-1)^{d2})*(comb({d1},{d2}))*({d3}^{d2})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$(1+\\var{e3}x)^{\\var{e1}}$ &nbsp; &nbsp; $[x^{\\var{e2}}]$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "comb({e1},{e2})*({e3}^{e2})", "minValue": "comb({e1},{e2})*({e3}^{e2})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$(1-\\var{f3}x)^{\\var{f1}}$ &nbsp; &nbsp; $[x^{\\var{f2}}]$</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((-1)^{f2})*(comb({f1},{f2}))*({f3}^{f2})", "minValue": "((-1)^{f2})*(comb({f1},{f2}))*({f3}^{f2})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$(1+\\frac{1}{\\var{g3}}x)^{\\var{g1}}$ &nbsp; &nbsp; $[x^{\\var{g2}}]$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "comb({g1},{g2})*((1/{g3})^{g2})", "minValue": "comb({g1},{g2})*((1/{g3})^{g2})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Find the coefficient of the term indicated in the square brackets in the expansion of each of the following expressions below</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"f1": {"definition": "random(2..9 except c1 except b1 except a1 except d1 except e1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "f2": {"definition": "floor(f1/2)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "f3": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}, "g3": {"definition": "random(2..5 except 3)", "templateType": "anything", "group": "Ungrouped variables", "name": "g3", "description": ""}, "g2": {"definition": "floor(2g1/3)", "templateType": "anything", "group": "Ungrouped variables", "name": "g2", "description": ""}, "g1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "g1", "description": ""}, "e1": {"definition": "random(2..9 except c1 except b1 except a1 except d1)", "templateType": "anything", "group": "Ungrouped variables", "name": "e1", "description": ""}, "a1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a2": {"definition": "floor(a1/2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "b1": {"definition": "random(2..9 except a1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "floor(2b1/3)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "c3": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "c2": {"definition": "floor(c1/2)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "c1": {"definition": "random(2..9 except b1 except a1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "e2": {"definition": "floor(2e1/3)", "templateType": "anything", "group": "Ungrouped variables", "name": "e2", "description": ""}, "d2": {"definition": "floor(2d1/3+1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "d3": {"definition": "random(2..5 except c3)", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "e3": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "e3", "description": ""}, "d1": {"definition": "random(2..9 except c1 except b1 except a1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}