// Numbas version: exam_results_page_options
{"name": "Binomial Expansion 7", "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", "a3", "b1", "b2", "b3", "b4"], "name": "Binomial Expansion 7", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Recall the Binomial Theorem, that is&nbsp;<img src=\"http://www.purplemath.com/modules/prob/binom01.gif\" width=\"200\" height=\"55\" border=\"0\" alt=\"(a + b)^n = sum[k=0,n][(n over k)a^(n-k)b^k]\"/>&nbsp; to find the binomial expansion in parts a) and c)<span color=\"#FFFFFF\" face=\"Arial\" size=\"1\" style=\"color: #ffffff; font-family: Arial; font-size: xx-small;\"></span></p>\n<p>For parts b) and d), substitute the appropriate value for x into your answer in parts a) and c) respectively.&nbsp;</p>", "rulesets": {}, "parts": [{"vsetrangepoints": 5, "prompt": "<p>Expand $(1-x)^{\\var{a1}}$ in ascending powers of x up to and including the term in $x^4$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "1-{a1}x+({a1}({a1}-1))x^2/2-({a1}({a1}-1)({a1}-2))x^3/6+{a1}({a1}-1)({a1}-2)({a1}-3)x^4/24", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"precisionType": "dp", "prompt": "<p>Hence approximate&nbsp;$(\\var{a3})^{\\var{a1}}$ to six decimal places&nbsp;</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "6", "maxValue": "1-{a1}{a2/100}+({a1}({a1}-1))({a2}/100)^2/2-({a1}({a1}-1)({a1}-2))({a2}/100)^3/6+{a1}({a1}-1)({a1}-2)({a1}-3)({a2}/100)^4/24", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "1-{a1}{a2}/100+({a1}({a1}-1))({a2}/100)^2/2-({a1}({a1}-1)({a1}-2))({a2}/100)^3/6+{a1}({a1}-1)({a1}-2)({a1}-3)({a2}/100)^4/24", "type": "numberentry", "showPrecisionHint": false}, {"vsetrangepoints": 5, "prompt": "<p>Expand $\\simplify{(1+{b4}x)^{b1}}$ in ascending powers of x up to and including the term in $x^3$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "1+{b1}{b4}x+({b1}({b1}-1))({b4}x)^2/2+({b1}({b1}-1)({b1}-2))({b4}x)^3/6", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"precisionType": "dp", "prompt": "<p>Hence approximate $(\\var{b3})^{\\var{b1}}$ to five decimal places</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "5", "maxValue": "1+{b1}{b4}({b2}/100)+({b1}({b1}-1))({b4}{b2}/100)^2/2+({b1}({b1}-1)({b1}-2))({b4}{b2}/100)^3/6", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "1+{b1}{b4}({b2}/100)+({b1}({b1}-1))({b4}{b2}/100)^2/2+({b1}({b1}-1)({b1}-2))({b4}{b2}/100)^3/6", "type": "numberentry", "showPrecisionHint": false}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"b4": {"definition": "random(-2..2 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "a1": {"definition": "random(5..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "1-({a2}/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "b1": {"definition": "random(5..10 except a1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(1..3 except a2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "1+b4*b2/100", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "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/"}]}