// Numbas version: exam_results_page_options
{"name": "Simon's copy of Binomial series for Natural exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Simon's copy of Binomial series for Natural exponent", "statement": "<p>Given the expression \\((\\var{a}+\\var{b}x)^{\\var{n}}\\)</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"c": {"definition": "comb({n},{k})*{a}^({n}-{k})*{b}^{k}", "name": "c", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "a": {"definition": "random(2..10#1)", "name": "a", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}, "b": {"definition": "random(2..12#1)", "name": "b", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}, "n": {"definition": "random(4..9#1)", "name": "n", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}, "k": {"definition": "random(2..{n}-1)", "name": "k", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "rulesets": {}, "ungrouped_variables": ["a", "b", "n", "c", "k"], "preamble": {"css": "", "js": ""}, "tags": [], "functions": {}, "advice": "<p>The binomial series expansion for an expression of the form \\((a+bx)^n\\) where \\(n\\) is a Natural number is given by:</p>\n<p style=\"padding-left: 30px;\">\\((a+bx)^n=\\tbinom{n}{0}(a)^n(bx)^{0}+\\tbinom{n}{1}(a)^{n-1}(bx)^{1}+\\tbinom{n}{2}(a)^{n-2}(bx)^{2}+...\\tbinom{n}{k}(a)^{n-k}(bx)^{k}+...\\tbinom{n}{n}(a)^{0}(bx)^{n}\\)</p>\n<p>In this example &nbsp;\\(n=\\var{n}\\), \\(a=\\var{a}\\) &nbsp;and &nbsp;\\(b=\\var{b}\\).</p>\n<p></p>\n<p>Since we only require the coefficient of&nbsp;\\(x^{\\var{k}}\\), we just require the term where&nbsp;\\(k=\\var{k}\\).</p>\n<p>So the coefficient of \\(x^{\\var{k}}\\) is given by \\(\\tbinom{\\var{n}}{\\var{k}}\\times\\var{a}^{\\var{n}-\\var{k}}\\times\\var{b}^{\\var{k}}=\\var{c}\\).</p>\n<p style=\"padding-left: 30px;\"></p>", "parts": [{"showFeedbackIcon": true, "gaps": [{"maxValue": "{c}", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "minValue": "{c}", "allowFractions": true, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "type": "numberentry", "variableReplacements": [], "showCorrectAnswer": true, "unitTests": [], "marks": 1, "scripts": {}, "variableReplacementStrategy": "originalfirst", "mustBeReduced": false}], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "prompt": "<p>By using the binomial series expansion, calculate the coefficient of \\(x^{\\var{k}}\\) &nbsp;[[0]]</p>", "sortAnswers": false, "showCorrectAnswer": true, "unitTests": [], "marks": 0, "type": "gapfill", "variableReplacements": [], "scripts": {}}], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>Binomial series for Natural exponent</p>"}, "extensions": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}