// 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": [{"extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "statement": "<p>Expand the following:</p>", "functions": {}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"c_bin1": {"templateType": "anything", "name": "c_bin1", "description": "", "group": "Ungrouped variables", "definition": "c1"}, "e2": {"templateType": "anything", "name": "e2", "description": "", "group": "Ungrouped variables", "definition": "random(-4..-2)"}, "g_bin5": {"templateType": "anything", "name": "g_bin5", "description": "", "group": "Ungrouped variables", "definition": "g_bin4*(g1-4)/5"}, "b_coeff4": {"templateType": "anything", "name": "b_coeff4", "description": "", "group": "Ungrouped variables", "definition": "b1*(b1-1)*(b1-2)*(b1-3)/24"}, "d_bin2": {"templateType": "anything", "name": "d_bin2", "description": "", "group": "Ungrouped variables", "definition": "d1*(d1-1)/2"}, "f_bin4": {"templateType": "anything", "name": "f_bin4", "description": "", "group": "Ungrouped variables", "definition": "f_bin3*(f1-3)/4"}, "c1": {"templateType": "anything", "name": "c1", "description": "", "group": "Ungrouped variables", "definition": "random(2..4)"}, "a1": {"templateType": "anything", "name": "a1", "description": "", "group": "Ungrouped variables", "definition": "random(3..5)"}, "c_bin3": {"templateType": "anything", "name": "c_bin3", "description": "", "group": "Ungrouped variables", "definition": "c1*(c1-1)*(c1-2)/6"}, "a_coeff3": {"templateType": "anything", "name": "a_coeff3", "description": "", "group": "Ungrouped variables", "definition": "a1*(a1-1)*(a1-2)/6"}, "g_bin2": {"templateType": "anything", "name": "g_bin2", "description": "", "group": "Ungrouped variables", "definition": "g1*(g1-1)/2"}, "b_coeff5": {"templateType": "anything", "name": "b_coeff5", "description": "", "group": "Ungrouped variables", "definition": "b1*(b1-1)*(b1-2)*(b1-3)*(b1-4)/120"}, "g3": {"templateType": "anything", "name": "g3", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)"}, "a_coeff5": {"templateType": "anything", "name": "a_coeff5", "description": "", "group": "Ungrouped variables", "definition": "a1*(a1-1)*(a1-2)*(a1-3)*(a1-4)/120"}, "c_bin4": {"templateType": "anything", "name": "c_bin4", "description": "", "group": "Ungrouped variables", "definition": "c1*(c1-1)*(c1-2)*(c1-3)/24"}, "b_coeff2": {"templateType": "anything", "name": "b_coeff2", "description": "", "group": "Ungrouped variables", "definition": "b1*(b1-1)/2"}, "b_coeff1": {"templateType": "anything", "name": "b_coeff1", "description": "", "group": "Ungrouped variables", "definition": "b1"}, "f3": {"templateType": "anything", "name": "f3", "description": "", "group": "Ungrouped variables", "definition": "random(1,3,5)"}, "d_bin5": {"templateType": "anything", "name": "d_bin5", "description": "", "group": "Ungrouped variables", "definition": "d_bin4*(d1-4)/5"}, "g1": {"templateType": "anything", "name": "g1", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)"}, "c_bin2": {"templateType": "anything", "name": "c_bin2", "description": "", "group": "Ungrouped variables", "definition": "c1*(c1-1)/2"}, "g_bin3": {"templateType": "anything", "name": "g_bin3", "description": "", "group": "Ungrouped variables", "definition": "g_bin2*(g1-2)/3"}, "e1": {"templateType": "anything", "name": "e1", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)"}, "f_bin5": {"templateType": "anything", "name": "f_bin5", "description": "", "group": "Ungrouped variables", "definition": "f_bin4*(f1-4)/5"}, "d_bin4": {"templateType": "anything", "name": "d_bin4", "description": "", "group": "Ungrouped variables", "definition": "d1*(d1-1)*(d1-2)*(d1-3)/24"}, "b_coeff3": {"templateType": "anything", "name": "b_coeff3", "description": "", "group": "Ungrouped variables", "definition": "b1*(b1-1)*(b1-2)/6"}, "g2": {"templateType": "anything", "name": "g2", "description": "", "group": "Ungrouped variables", "definition": "1/g3"}, "e_bin3": {"templateType": "anything", "name": "e_bin3", "description": "", "group": "Ungrouped variables", "definition": "e1*(e1-1)*(e1-2)/6"}, "a_coeff1": {"templateType": "anything", "name": "a_coeff1", "description": "", "group": "Ungrouped variables", "definition": "a1"}, "f_bin2": {"templateType": "anything", "name": "f_bin2", "description": "", "group": "Ungrouped variables", "definition": "f1*(f1-1)/2"}, "e_bin4": {"templateType": "anything", "name": "e_bin4", "description": "", "group": "Ungrouped variables", "definition": "e1*(e1-1)*(e1-2)*(e1-3)/24"}, "b1": {"templateType": "anything", "name": "b1", "description": "", "group": "Ungrouped variables", "definition": "random(3..5 except a1)"}, "d2": {"templateType": "anything", "name": "d2", "description": "", "group": "Ungrouped variables", "definition": "-1"}, "f2": {"templateType": "anything", "name": "f2", "description": "", "group": "Ungrouped variables", "definition": "f3/2"}, "g_bin4": {"templateType": "anything", "name": "g_bin4", "description": "", "group": "Ungrouped variables", "definition": "g_bin3*(g1-3)/4"}, "d1": {"templateType": "anything", "name": "d1", "description": "", "group": "Ungrouped variables", "definition": "random(3..5)"}, "c2": {"templateType": "anything", "name": "c2", "description": "", "group": "Ungrouped variables", "definition": "random(2..4)"}, "a_coeff4": {"templateType": "anything", "name": "a_coeff4", "description": "", "group": "Ungrouped variables", "definition": "a1*(a1-1)*(a1-2)*(a1-3)/24"}, "e_bin5": {"templateType": "anything", "name": "e_bin5", "description": "", "group": "Ungrouped variables", "definition": "e_bin4*(e1-4)/5"}, "d_bin3": {"templateType": "anything", "name": "d_bin3", "description": "", "group": "Ungrouped variables", "definition": "d1*(d1-1)*(d1-2)/6"}, "f_bin3": {"templateType": "anything", "name": "f_bin3", "description": "", "group": "Ungrouped variables", "definition": "f_bin2*(f1-2)/3"}, "a_coeff2": {"templateType": "anything", "name": "a_coeff2", "description": "", "group": "Ungrouped variables", "definition": "a1*(a1-1)/2"}, "f1": {"templateType": "anything", "name": "f1", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)"}, "e_bin2": {"templateType": "anything", "name": "e_bin2", "description": "", "group": "Ungrouped variables", "definition": "e1*(e1-1)/2"}}, "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"], "tags": [], "preamble": {"js": "", "css": ""}, "variable_groups": [], "advice": "<p>Recall the binomial theorem:&nbsp;<img width=\"182\" height=\"50\" alt=\"(a + b)^n = sum[k=0,n][(n over k)a^(n-k)b^k]\" src=\"http://www.purplemath.com/modules/prob/binom01.gif\" border=\"0\"/>&nbsp;and use this to answer each part.<span style=\"color: #ffffff; font-family: Arial; font-size: xx-small;\" size=\"1\" face=\"Arial\" color=\"#FFFFFF\"></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>", "name": "Binomial Expansion 1", "parts": [{"showCorrectAnswer": true, "marks": 1, "variableReplacements": [], "valuegenerators": [{"value": "", "name": "x"}], "notallowed": {"partialCredit": 0, "strings": [")^"], "showStrings": false, "message": ""}, "answerSimplification": "all,fractionnumbers", "useCustomName": false, "scripts": {}, "customName": "", "type": "jme", "checkingType": "absdiff", "musthave": {"partialCredit": 0, "strings": ["^2"], "showStrings": false, "message": ""}, "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "vsetRange": [0, 1], "showPreview": true, "checkingAccuracy": 0.001, "prompt": "<p>$(1+\\var{c2}x)^{\\var{c1}}$</p>", "failureRate": 1, "answer": "1+{c_bin1}{c2}x+{c_bin2}*{c2}^2x^2 +{c_bin3}*{c2}^3x^3 + {c_bin4}*{c2}^4x^4 ", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": []}, {"showCorrectAnswer": true, "marks": 1, "variableReplacements": [], "valuegenerators": [{"value": "", "name": "x"}], "notallowed": {"partialCredit": 0, "strings": [")^"], "showStrings": false, "message": ""}, "answerSimplification": "all,fractionnumbers", "useCustomName": false, "scripts": {}, "customName": "", "type": "jme", "checkingType": "absdiff", "musthave": {"partialCredit": 0, "strings": ["^2"], "showStrings": false, "message": ""}, "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "vsetRange": [0, 1], "showPreview": true, "checkingAccuracy": 0.001, "prompt": "<p>$\\simplify{(1+{d2}x)^{{d1}}}$</p>", "failureRate": 1, "answer": "1+{d1}{d2}x+{d_bin2}*{d2}^2x^2 +{d_bin3}*{d2}^3x^3 + {d_bin4}{d2}^4x^4 + {d_bin5}*{d2}^5x^5 ", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": []}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}