// Numbas version: finer_feedback_settings
{"name": "Binomial Expansion 5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a1", "b1", "c1", "c2", "d1", "d3", "d2", "a2", "b2", "a3", "b3", "c3", "c4", "d4", "e1", "e2", "e3", "e4", "f1", "f2", "f3", "f4", "n1", "n2", "n3", "n4"], "name": "Binomial Expansion 5", "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>Alternatively, take out a factor of $a^n$ and recall the formula for $(1+\\frac{b}{a}x)^n$ to find the expansion as in part f)</p>", "rulesets": {}, "parts": [{"notallowed": {"message": "", "showStrings": false, "strings": [")^"], "partialCredit": 0}, "vsetrangepoints": 5, "prompt": "<p>$(\\var{c3}-\\var{c2}x)^{\\var{c1}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "({c3})^{c1}(1-{c1}{c4}x+{c1}{c1-1}/2 ({c4}x)^2 -{c1}{c1-1}{c1-2}/6 ({c4}x)^3)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"notallowed": {"message": "", "showStrings": false, "strings": [")^"], "partialCredit": 0}, "vsetrangepoints": 5, "prompt": "<p>$(\\var{a3}+\\var{a2}x)^{\\var{a1}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "({a3})^{a1}(1+{a1}{a2}x+{a1}{a1-1}/2 ({a2}x)^2 +{a1}{a1-1}{a1-2}/6 ({a2}x)^3) ", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"vsetrangepoints": 5, "prompt": "<p>$(\\var{d4}+\\frac{\\var{d3}}{2}x)^{{\\var{d1}}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "{d4}^{d1}+{d1}{d4}^({d1}-1){d3}/2x+{d1}{d1-1}/2 {d4}^({d1}-2)({d3}/2x)^2 +{d1}{d1-1}{d1-2}/6 {d4}^({d1}-3)({d3}/2x)^3", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"vsetrangepoints": 5, "prompt": "<p>$(\\var{e2}x+\\var{e3})^{{\\var{e1}}}$</p>", "expectedvariablenames": [], "checkingaccuracy": "0.01", "vsetrange": ["0.1", 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "({e3})^{e1}+{e1}{e2}({e3})^({e1}-1)(x)+{e1}{e1-1}/2({e3})^({e1}-2) ({e2}(x))^2 +{e1}{e1-1}{e1-2}/6 ({e3})^({e1}-3)({e2}(x))^3 ", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"vsetrangepoints": 5, "prompt": "<p>$\\simplify{({f2}x-{f3})^{{f1}}}$</p>", "expectedvariablenames": [], "checkingaccuracy": "0.01", "vsetrange": ["0.1", 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "(-{f3})^{f1}+{f1}{f2}(-{f3})^({f1}-1)(x)+{f1}{f1-1}/2 (-{f3})^({f1}-2)({f2}(x))^2 +{f1}{f1-1}{f1-2}/6(-{f3})^({f1}-3) ({f2}(x))^3", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"vsetrangepoints": 5, "prompt": "<p>$(\\var{n4}+\\frac{\\var{n3}}{3}x)^{{\\var{n1}}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "{n4}^{n1}(1+{n1}{n2}x+{n1}{n1-1}/2 ({n2}x)^2 +{n1}{n1-1}{n1-2}/6 ({n2}x)^3)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}], "statement": "<p>Expand each of the following in ascending powers of x, up to and including the term in $x^3$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"f1": {"definition": "random(2..9 except e1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "f2": {"definition": "random(1..3 except e2)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "f3": {"definition": "random(2..4 except f2)", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}, "f4": {"definition": "f2/f3", "templateType": "anything", "group": "Ungrouped variables", "name": "f4", "description": ""}, "b1": {"definition": "random(3..5 except a1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, 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"Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "c3": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "c3", "description": ""}, "e4": {"definition": "e2/e3", "templateType": "anything", "group": "Ungrouped variables", "name": "e4", "description": ""}, "c1": {"definition": "random(3..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "e1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "e1", "description": ""}, "e3": {"definition": "random(2..3 except e2)", "templateType": "anything", "group": "Ungrouped variables", "name": "e3", "description": ""}, "c4": {"definition": "c2/c3", "templateType": "anything", "group": "Ungrouped variables", "name": "c4", "description": ""}, "n1": {"definition": "random(3..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "n2": {"definition": "n3/(3n4)", "templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}, "n3": {"definition": "random(2,4,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "n3", "description": ""}, "n4": {"definition": "random(2..5 except n3)", "templateType": "anything", "group": "Ungrouped variables", "name": "n4", "description": ""}, "c2": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "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/"}]}