// Numbas version: exam_results_page_options {"name": "Binomial Expansion", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "

Recall the binomial theorem \"(a and use this to answer each part

\n

For example, if we want to know the coefficient of the $x^i$ term in $(a+bx)^n$ then we look at the binomial theorem and can see that the coefficient will be $\\simplify{comb(n, i)}*a^{(n-i)}*b^i$

", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "variables": {"c5": {"definition": "c3/c4", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c5"}, "f4": {"definition": "random(2..5 except f3 except e4)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "f4"}, "d2": {"definition": "floor(2d1/3)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "d2"}, "g3": {"definition": "random([2,4,5] except g1)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "g3"}, "f3": {"definition": "random(2..5 except e3)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "f3"}, "e5": {"definition": "e3/e4", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "e5"}, "c1": {"definition": "random(2..6)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c1"}, "g2": {"definition": "random(1,3)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "g2"}, "d1": {"definition": "random(3..6)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "d1"}, "f5": {"definition": "f3/f4", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "f5"}, "f1": {"definition": "random(3..6)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "f1"}, "g5": {"definition": "floor(2g4/3)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "g5"}, "f2": {"definition": "floor(2f1/3)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "f2"}, "e1": {"definition": "random(3..6)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "e1"}, "c2": {"definition": "floor(c1/2)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c2"}, "d4": {"definition": "random(2..5 except d3 except c4)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "d4"}, "h4": {"definition": "random(2..6)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "h4"}, "d3": {"definition": "random(2..5 except c3)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "d3"}, "c3": {"definition": "random(2..5)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c3"}, "h1": {"definition": "random(2..5)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "h1"}, "e4": {"definition": "random(2..5 except e3 except d4)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "e4"}, "c4": {"definition": "random(2..5 except c3)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c4"}, "h3": {"definition": "random([2,4,5] except h1)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "h3"}, "g4": {"definition": "random(2..6)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "g4"}, "e3": {"definition": "random(2..5 except d3)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "e3"}, "h2": {"definition": "random(1,3)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "h2"}, "h5": {"definition": "floor(h4/2)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "h5"}, "g1": {"definition": "random(2..5)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "g1"}, "e2": {"definition": "floor(e1/2)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "e2"}, "d5": {"definition": "d3/d4", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "d5"}}, "parts": [{"mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to the correct precision.", "prompt": "

$(\\var{c4}+\\var{c3}x)^{\\var{c1}}$     $[x^{\\var{c2}}]$

", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "({c4}^{c1})*(comb({c1},{c2}))*({c5}^{c2})", "allowFractions": false, "strictPrecision": true, "customMarkingAlgorithm": "", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "precision": 0, "showPrecisionHint": false, "showFeedbackIcon": true, "scripts": {}, "marks": 1, "precisionPartialCredit": 0, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "minValue": "({c4}^{c1})*(comb({c1},{c2}))*({c5}^{c2})", "showCorrectAnswer": true}, {"mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to the correct precision.", "prompt": "

$(\\var{d4}+\\var{d3}x)^{\\var{d1}}$     $[x^{\\var{d2}}]$

", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "({d4}^{d1})*(comb({d1},{d2}))*({d5}^{d2})", "allowFractions": false, "strictPrecision": true, "customMarkingAlgorithm": "", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "precision": 0, "showPrecisionHint": false, "showFeedbackIcon": true, "scripts": {}, "marks": 1, "precisionPartialCredit": 0, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "minValue": "({d4}^{d1})*(comb({d1},{d2}))*({d5}^{d2})", "showCorrectAnswer": true}, {"mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to the correct precision.", "prompt": "

$(\\var{e4}-\\var{e3}x)^{\\var{e1}}$     $[x^{\\var{e2}}]$

", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "({e4}^{e1})*(comb({e1},{e2}))*((-{e5})^{e2})", "allowFractions": false, "strictPrecision": true, "customMarkingAlgorithm": "", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "precision": 0, "showPrecisionHint": false, "showFeedbackIcon": true, "scripts": {}, "marks": 1, "precisionPartialCredit": 0, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "minValue": "({e4}^{e1})*(comb({e1},{e2}))*((-{e5})^{e2})", "showCorrectAnswer": true}, {"mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to the correct precision.", "prompt": "

$(\\var{f4}-\\var{f3}x)^{\\var{f1}}$     $[x^{\\var{f2}}]$

", "precisionType": "dp", "extendBaseMarkingAlgorithm": true, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "maxValue": "({f4}^{f1})*(comb({f1},{f2}))*({f5}^{f2})*((-1)^{f2})", "allowFractions": false, "strictPrecision": true, "customMarkingAlgorithm": "", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "numberentry", "precision": 0, "showPrecisionHint": false, "showFeedbackIcon": true, "scripts": {}, "marks": 1, "precisionPartialCredit": 0, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "minValue": "({f4}^{f1})*(comb({f1},{f2}))*({f5}^{f2})*((-1)^{f2})", "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": true, "mustBeReduced": false, "showFeedbackIcon": true, "mustBeReducedPC": 0, "prompt": "

$(\\frac{1}{\\var{g1}}+\\frac{\\var{g2}}{\\var{g3}}x)^\\var{g4}$     $[x^\\var{g5}]$

", "minValue": "((1/{g1})^{g4})*(comb({g4},{g5}))*(({g1}*{g2}/{g3})^{g5})", "marks": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "maxValue": "((1/{g1})^{g4})*(comb({g4},{g5}))*(({g1}*{g2}/{g3})^{g5})", "type": "numberentry", "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": true, "mustBeReduced": false, "showFeedbackIcon": true, "mustBeReducedPC": 0, "prompt": "

$(\\frac{1}{\\var{h1}}-\\frac{\\var{h2}}{\\var{h3}}x)^\\var{h4}$     $[x^\\var{h5}]$

", "minValue": "((1/{h1})^{h4})*(comb({h4},{h5}))*(({h1}*{h2}*(-1)/{h3})^{h5})", "marks": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "maxValue": "((1/{h1})^{h4})*(comb({h4},{h5}))*(({h1}*{h2}*(-1)/{h3})^{h5})", "type": "numberentry", "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "showCorrectAnswer": true}], "name": "Binomial Expansion", "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "rulesets": {}, "variable_groups": [], "ungrouped_variables": ["c1", "c2", "c3", "c4", "c5", "d2", "d1", "d3", "d4", "d5", "e1", "e2", "e3", "e4", "e5", "f1", "f2", "f3", "f4", "f5", "g1", "g2", "g3", "g4", "g5", "h1", "h2", "h3", "h4", "h5"], "preamble": {"js": "", "css": ""}, "extensions": [], "statement": "

Find the coefficient of the term indicated in the square brackets in the expansion of each of the following expressions below

", "type": "question", "contributors": [{"name": "Matthew Mears", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1688/"}]}]}], "contributors": [{"name": "Matthew Mears", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1688/"}]}