// Numbas version: exam_results_page_options
{"name": "Binomial Expansion 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "ungrouped_variables": ["a1", "b1", "c1", "c2", "d1", "d3", "d2", "a2", "b2", "a3", "b3", "c3", "c4", "d4", "e1", "e2", "e3", "e4", "f1", "f2", "f3", "f4"], "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>Alternatively, take out a factor of $a^n$ and recall the formula for $(1+\\frac{b}{a}x)^n$ to find the expansion.</p>", "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"prompt": "<p>$(\\var{c3}-\\var{c2}x)^{\\var{c1}}$</p>", "notallowed": {"strings": [")^"], "message": "", "partialCredit": 0, "showStrings": false}, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "valuegenerators": [{"value": "", "name": "x"}], "customName": "", "answer": "({c3})^{c1}-{c1}{c2}({c3})^({c1}-1)x+{c1}{c1-1}/2 ({c3})^({c1}-2)*{c2}^2*x^2 -{c1}{c1-1}{c1-2}/6 ({c3})^({c1}-3)*{c2}^3x^3 + {c1}{c1-1}{c1-2}{c1-3}/24({c3})^({c1}-4)*{c2}^4x^4 - {c1}{c1-1}{c1-2}{c1-3}{c1-4}/120({c3})^({c1}-5)*{c2}^5x^5 ", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "musthave": {"strings": ["^2"], "message": "", "partialCredit": 0, "showStrings": false}, "failureRate": 1, "answerSimplification": "all,fractionnumbers"}], "tags": [], "statement": "<p>Using the binomial theorem, or otherwise, expand the following:</p>", "variables": {"d3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1,3,5)", "name": "d3"}, "f4": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "f2/f3", "name": "f4"}, "b1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(3..5 except a1)", "name": "b1"}, "c2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..4)", "name": "c2"}, "c4": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "c2/c3", "name": "c4"}, "b3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "1/b2", "name": "b3"}, "f3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1..3 except f2)", "name": "f3"}, "c3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..9 except c2)", "name": "c3"}, "a3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "1/a2", "name": "a3"}, "f1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5 except e1)", "name": "f1"}, "d1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(3..5)", "name": "d1"}, "d4": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5 except d3)", "name": "d4"}, "e4": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "e2/e3", "name": "e4"}, "c1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)", "name": "c1"}, "d2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "d3/(2d4)", "name": "d2"}, "b2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..4)", "name": "b2"}, "a2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..4)", "name": "a2"}, "e3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1..3 except e2)", "name": "e3"}, "e1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)", "name": "e1"}, "f2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1..3)", "name": "f2"}, "a1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(3..5)", "name": "a1"}, "e2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1..3)", "name": "e2"}}, "rulesets": {}, "functions": {}, "extensions": [], "name": "Binomial Expansion 2", "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/"}]}