// Numbas version: exam_results_page_options
{"name": "Sigma notation intro 2 - functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variable_groups": [], "tags": [], "name": "Sigma notation intro 2 - functions", "functions": {}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.</p>"}, "ungrouped_variables": ["a", "b", "f", "index"], "parts": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "gapfill", "prompt": "<p>The expression \\[\\sum_{\\var{index}=\\var{a}}^{\\var{b}}\\var{f}(\\var{index})\\] is equivalent to which of the following?</p>\n<p>[[0]]</p>", "variableReplacements": [], "gaps": [{"distractors": ["", "", ""], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "displayColumns": "1", "type": "1_n_2", "showCorrectAnswer": true, "showFeedbackIcon": true, "maxMarks": 0, "scripts": {}, "marks": 0, "displayType": "radiogroup", "shuffleChoices": true, "choices": ["<p>$\\var{f}(\\var{a})+\\var{f}(\\var{a+1})+\\var{f}(\\var{a+2})+\\ldots + \\var{f}(\\var{b-2})+ \\var{f}(\\var{b-1})+ \\var{f}(\\var{b})$</p>", "<p>$\\var{f}(\\var{index})+\\var{f}(\\var{index})+\\var{f}(\\var{index})+\\ldots + \\var{f}(\\var{index})+ \\var{f}(\\var{index})+ \\var{f}(\\var{index})$</p>", "<p>$\\var{a}+\\var{a+1}+\\var{a+2}+\\ldots + \\var{b-2}+ \\var{b-1}+ \\var{b}$</p>"], "matrix": ["1", 0, 0], "minMarks": 0}], "marks": 0}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"description": "", "templateType": "anything", "definition": "random(0..10)", "name": "a", "group": "Ungrouped variables"}, "b": {"description": "", "templateType": "anything", "definition": "a+random(50..79)", "name": "b", "group": "Ungrouped variables"}, "f": {"description": "", "templateType": "anything", "definition": "random(latex('f'),latex('g'),latex('h'),latex('\\\\sin'),latex('\\\\cos'),latex('\\\\tan'),latex('\\\\log'),latex('\\\\ln'))", "name": "f", "group": "Ungrouped variables"}, "index": {"description": "", "templateType": "anything", "definition": "random(latex('i'),latex('j'),latex('k'),latex('t'),latex('r'),latex('s'),latex('n'),latex('m'))", "name": "index", "group": "Ungrouped variables"}}, "extensions": [], "type": "question", "preamble": {"js": "", "css": ""}, "advice": "<p>Sigma notation is used to represent a sum.</p>\n<p>In this sum, we are adding up a bunch of terms that look like $\\var{f}(\\var{index})$ each for a different value of the index $\\var{index}$. Notice the sum starts with $\\var{index}=\\var{a}$ and ends with $\\var{index}=\\var{b}$, therefore, \\[\\sum_{\\var{index}=\\var{a}}^{\\var{b}}\\var{f}(\\var{index})=\\var{f}(\\var{a})+\\var{f}(\\var{a+1})+\\var{f}(\\var{a+2})+\\ldots + \\var{f}(\\var{b-2})+ \\var{f}(\\var{b-1})+ \\var{f}(\\var{b}).\\]</p>", "statement": "<p>The following question is testing whether you understand the Sigma notation used in mathematics.</p>", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}