// Numbas version: exam_results_page_options
{"name": "Binomial Expansion 1", "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", "d2", "e1", "e2", "f1", "f3", "f2", "g1", "g3", "g2", "a_coeff1", "a_coeff2", "a_coeff3", "a_coeff4", "a_coeff5", "b_coeff1", "b_coeff2", "b_coeff3", "b_coeff4", "b_coeff5", "c_bin1", "c_bin2", "c_bin3", "c_bin4", "d_bin2", "d_bin3", "d_bin4", "d_bin5", "e_bin2", "e_bin3", "e_bin4", "e_bin5", "f_bin2", "f_bin3", "f_bin4", "f_bin5", "g_bin2", "g_bin3", "g_bin4", "g_bin5"], "name": "Binomial Expansion 1", "tags": [], "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 $(1+x)^2 = \\simplify{comb(2,0)}*1^{2-0}*x^{(0)} + \\simplify{comb(2,1)}*1^{2-1}*x^1 + \\simplify{comb(2,2)}*1^{2-2}*x^2 = 1+2x+x^2$</p>", "rulesets": {}, "parts": [{"notallowed": {"message": "", "showStrings": false, "strings": [")^"], "partialCredit": 0}, "variableReplacements": [], "prompt": "<p>$(1+x)^{\\var{a1}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "1+{a_coeff1}x+{a_coeff2}x^2 +{a_coeff3}x^3 + {a_coeff4}x^4 + {a_coeff5}x^5", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"notallowed": {"message": "", "showStrings": false, "strings": [")^"], "partialCredit": 0}, "variableReplacements": [], "prompt": "<p>$(1+x)^{\\var{b1}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "1+{b_coeff1}x+{b_coeff2}x^2 +{b_coeff3}x^3 + {b_coeff4}x^4 + {b_coeff5}x^5", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"notallowed": {"message": "", "showStrings": false, "strings": [")^"], "partialCredit": 0}, "variableReplacements": [], "prompt": "<p>$(1+\\var{c2}x)^{\\var{c1}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "1+{c_bin1}{c2}x+{c_bin2}({c2}x)^2 +{c_bin3}({c2}x)^3 + {c_bin4}({c2}x)^4 ", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"notallowed": {"message": "", "showStrings": false, "strings": [")^"], "partialCredit": 0}, "variableReplacements": [], "prompt": "<p>$\\simplify{(1+{d2}x)^{{d1}}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "1+{d1}{d2}x+{d_bin2}({d2}x)^2 +{d_bin3}({d2}x)^3 + {d_bin4}({d2}x)^4 + {d_bin5}({d2}x)^5 ", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"notallowed": {"message": "", "showStrings": false, "strings": [")^"], "partialCredit": 0}, "variableReplacements": [], "prompt": "<p>$\\simplify{(1+{e2}x)^{{e1}}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "1+{e1}{e2}x+{e_bin2}({e2}x)^2 +{e_bin3}({e2}x)^3 + {e_bin4}({e2}x)^4 + {e_bin5}({e2}x)^5 ", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"notallowed": {"message": "", "showStrings": false, "strings": [")^"], "partialCredit": 0}, "variableReplacements": [], "prompt": "<p>$(1+\\frac{\\var{f3}}{2}x)^{{\\var{f1}}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "1+{f1}{f2}x+{f_bin2}({f2}x)^2 +{f_bin3}({f2}x)^3 + {f_bin4}({f2}x)^4 + {f_bin5}({f2}x)^5 ", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}, {"notallowed": {"message": "", "showStrings": false, "strings": [")^"], "partialCredit": 0}, "variableReplacements": [], "prompt": "<p>$(1-\\frac{\\var{1}}{\\var{g3}}x)^{{\\var{g1}}}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "1-{g1}{g2}x+{g_bin2}({g2}x)^2 -{g_bin3}({g2}x)^3 + {g_bin4}({g2}x)^4 -{g_bin5}({g2}x)^5 ", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "musthave": {"message": "", "showStrings": false, "strings": ["^2"], "partialCredit": 0}}], "statement": "<p>Expand the following</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"d_bin4": {"definition": "d1*(d1-1)*(d1-2)*(d1-3)/24", "templateType": "anything", "group": "Ungrouped variables", "name": "d_bin4", "description": ""}, "f1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "f2": {"definition": "f3/2", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "f3": {"definition": "random(1,3,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "f3", "description": ""}, "d_bin2": {"definition": "d1*(d1-1)/2", "templateType": "anything", "group": "Ungrouped variables", "name": "d_bin2", "description": ""}, "d_bin3": {"definition": "d1*(d1-1)*(d1-2)/6", "templateType": "anything", "group": "Ungrouped variables", "name": "d_bin3", "description": ""}, "c_bin1": {"definition": "c1", "templateType": "anything", "group": "Ungrouped variables", "name": "c_bin1", "description": ""}, "c_bin3": {"definition": "c1*(c1-1)*(c1-2)/6", "templateType": "anything", "group": "Ungrouped variables", "name": "c_bin3", "description": ""}, "c_bin2": {"definition": "c1*(c1-1)/2", "templateType": "anything", "group": "Ungrouped variables", "name": "c_bin2", "description": ""}, "c_bin4": {"definition": "c1*(c1-1)*(c1-2)*(c1-3)/24", "templateType": "anything", "group": "Ungrouped variables", "name": "c_bin4", "description": ""}, "b1": {"definition": "random(3..5 except a1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b_coeff5": {"definition": "b1*(b1-1)*(b1-2)*(b1-3)*(b1-4)/120", "templateType": "anything", "group": "Ungrouped variables", "name": "b_coeff5", "description": ""}, "d2": {"definition": "-1", "templateType": "anything", "group": "Ungrouped variables", "name": "d2", "description": ""}, "d1": {"definition": "random(3..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "f_bin4": {"definition": "f_bin3*(f1-3)/4", "templateType": "anything", "group": "Ungrouped variables", "name": "f_bin4", "description": ""}, "b_coeff3": {"definition": "b1*(b1-1)*(b1-2)/6", "templateType": "anything", "group": "Ungrouped variables", "name": "b_coeff3", "description": ""}, "a_coeff1": {"definition": "a1", "templateType": "anything", "group": "Ungrouped variables", "name": "a_coeff1", "description": ""}, "a_coeff3": {"definition": "a1*(a1-1)*(a1-2)/6", "templateType": "anything", "group": "Ungrouped variables", "name": "a_coeff3", "description": ""}, "a_coeff2": {"definition": "a1*(a1-1)/2", "templateType": "anything", "group": "Ungrouped variables", "name": "a_coeff2", "description": ""}, "a_coeff5": {"definition": "a1*(a1-1)*(a1-2)*(a1-3)*(a1-4)/120", "templateType": "anything", "group": "Ungrouped variables", "name": "a_coeff5", "description": ""}, "a_coeff4": {"definition": "a1*(a1-1)*(a1-2)*(a1-3)/24", "templateType": "anything", "group": "Ungrouped variables", "name": "a_coeff4", "description": ""}, "g_bin5": {"definition": "g_bin4*(g1-4)/5", "templateType": "anything", "group": "Ungrouped variables", "name": "g_bin5", "description": ""}, "g_bin4": {"definition": "g_bin3*(g1-3)/4", "templateType": "anything", "group": "Ungrouped variables", "name": "g_bin4", "description": ""}, "g_bin3": {"definition": "g_bin2*(g1-2)/3", "templateType": "anything", "group": "Ungrouped variables", "name": "g_bin3", "description": ""}, "g_bin2": {"definition": "g1*(g1-1)/2", "templateType": "anything", "group": "Ungrouped variables", "name": "g_bin2", "description": ""}, "b_coeff4": {"definition": "b1*(b1-1)*(b1-2)*(b1-3)/24", "templateType": "anything", "group": "Ungrouped variables", "name": "b_coeff4", "description": ""}, "f_bin3": {"definition": "f_bin2*(f1-2)/3", "templateType": "anything", "group": "Ungrouped variables", "name": "f_bin3", "description": ""}, "g3": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "g3", "description": ""}, "b_coeff1": {"definition": "b1", "templateType": "anything", "group": "Ungrouped variables", "name": "b_coeff1", "description": ""}, "b_coeff2": {"definition": "b1*(b1-1)/2", "templateType": "anything", "group": "Ungrouped variables", "name": "b_coeff2", "description": ""}, "f_bin5": {"definition": "f_bin4*(f1-4)/5", "templateType": "anything", "group": "Ungrouped variables", "name": "f_bin5", "description": ""}, "e_bin5": {"definition": "e_bin4*(e1-4)/5", "templateType": "anything", "group": "Ungrouped variables", "name": "e_bin5", "description": ""}, "e_bin4": {"definition": "e1*(e1-1)*(e1-2)*(e1-3)/24", "templateType": "anything", "group": "Ungrouped variables", "name": "e_bin4", "description": ""}, "e_bin3": {"definition": "e1*(e1-1)*(e1-2)/6", "templateType": "anything", "group": "Ungrouped variables", "name": "e_bin3", "description": ""}, "e_bin2": {"definition": "e1*(e1-1)/2", "templateType": "anything", "group": "Ungrouped variables", "name": "e_bin2", "description": ""}, "a1": {"definition": "random(3..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "c2": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "c1": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "e1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "e1", "description": ""}, "g2": {"definition": "1/g3", "templateType": 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