// Numbas version: exam_results_page_options
{"name": "Sigma notation intro 4 - swap index", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Sigma notation intro 4 - swap index", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Students seem to struggle with Sigma notation, this is a simple question to ensure they&nbsp;understand the index can change without affecting the sum.</p>"}, "extensions": [], "type": "question", "statement": "<p>The following question is testing whether you understand the Sigma notation used in mathematics.</p>", "preamble": {"js": "", "css": ""}, "variable_groups": [], "functions": {}, "variables": {"f2": {"name": "f2", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random([latex('f'),latex('g'),latex('h'),latex('\\\\sin'),latex('\\\\cos'),latex('\\\\tan'),latex('\\\\log'),latex('\\\\ln')])"}, "index2": {"name": "index2", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random([latex('i'),latex('k'),latex('j'),latex('n'),latex('m')] except index)"}, "index": {"name": "index", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(latex('i'),latex('j'),latex('k'),latex('t'),latex('r'),latex('s'),latex('n'),latex('m'))"}}, "tags": [], "parts": [{"variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>The expression \\[\\sum_{\\var{index2}=a}^b\\var{f2}(\\var{index2})\\] is equivalent to which of the following?</p>\n<p>[[0]]</p>", "scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "gaps": [{"distractors": ["", "", ""], "matrix": ["1", 0, 0], "displayColumns": "1", "type": "1_n_2", "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "choices": ["<p>$\\displaystyle\\sum_{\\var{index}=a}^b\\var{f2}(\\var{index})$</p>", "<p>$\\displaystyle\\sum_{\\var{index}=a}^b\\var{f2}(\\var{index2})$</p>", "<p>$\\displaystyle&nbsp;\\sum_{\\var{index2}=a}^b\\var{f2}(\\var{index})$</p>"], "displayType": "radiogroup", "variableReplacements": [], "showFeedbackIcon": true, "minMarks": 0, "showCorrectAnswer": true, "shuffleChoices": true, "scripts": {}, "marks": 0}], "variableReplacementStrategy": "originalfirst", "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["index", "index2", "f2"], "rulesets": {}, "advice": "<p>Sigma notation is used to represent a sum.</p>\n<p></p>\n<p>The index is just a dummy variable, it is just a placeholder, swapping it for a different symbol has no affect on the actual sum, that is \\[\\sum_{\\var{index2}=a}^b\\var{f2}(\\var{index2})=\\sum_{\\var{index}=a}^b\\var{f2}(\\var{index}).\\]</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/"}]}