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{"name": "Algebra: binomial expansion, coefficient of particular term, calculator", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Algebra: binomial expansion, coefficient of particular term, calculator", "tags": [], "metadata": {"description": "<p>Expression of the (a+bx)^n is given and a couple of coefficients are asked for.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>This is a calculator question. Note that the numbers in this question will be quite large.</p>\n<p>-----------------------------------------------</p>", "advice": "<p>See ??</p>", "rulesets": {}, "extensions": [], "variables": {"k2": {"name": "k2", "group": "Ungrouped variables", "definition": "random(3..{n}-3)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..9 except a)*-1", "description": "", "templateType": "anything"}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "comb(n,k2)*a^(n-k2)*b^k2", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(3..{n}-3)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "comb(n,k)*a^(n-k)*b^k", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(7..12)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "mod(k-k2,2)<>0", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "n", "k", "k2", "c", "c2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate the coefficient of $x^{\\var{k}}$ if you multiply out the expression $\\simplify{({a} + {b}x)^{n}}$</p>\n<p></p>\n<p>The coefficient of \\(x^{\\var{k}}\\) is&nbsp;&nbsp;[[0]]</p>\n<p></p>\n<p>How about the coefficient of $x^{\\var{k2}}$? [[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{c}", "maxValue": "{c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": "50", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": false, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{c2}", "maxValue": "{c2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": "50", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "contributors": [{"name": "Angharad Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/315/"}, {"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Angharad Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/315/"}, {"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}