// Numbas version: exam_results_page_options
{"name": "Simon's copy of Summation notation 2", "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 Summation notation 2", "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"x1": {"name": "x1", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(1..30#1)", "description": ""}, "x5": {"name": "x5", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(2..10#1)", "description": ""}, "x6": {"name": "x6", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(5..20#1)", "description": ""}, "x4": {"name": "x4", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(5..15#1)", "description": ""}, "x2": {"name": "x2", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(10..20#1)", "description": ""}, "x3": {"name": "x3", "group": "Ungrouped variables", "templateType": "randrange", "definition": "random(2..10#1)", "description": ""}}, "ungrouped_variables": ["x2", "x3", "x1", "x6", "x4", "x5"], "variable_groups": [], "statement": "<p>Six adults spent {x1}, {x2}, {x3}, {x4}, {x5} and {x6} euros on lottery tickets last month. Let $y$ denote last month's lottery ticket expenses for an adult.</p>", "advice": "<p>The symbol $\\Sigma$ means 'sum of' or 'total'.</p>\n<p><strong>(a)</strong></p>\n<p>$\\sum y&nbsp; $ means add up the&nbsp;$y$ values.&nbsp; &nbsp; &nbsp;</p>\n<p>$\\var{x1}+\\var{x2}+\\var{x3}+\\var{x4}+\\var{x5}+\\var{x6}=\\var{x1+x2+x3+x4+x5+x6}$</p>\n<p><strong>(b)</strong></p>\n<p>$(\\sum y)^2 &nbsp;$&nbsp; means add up the $y$ values and then square your answer.&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>\n<p>&nbsp;Using your answer in part (a),&nbsp; $\\var{x1+x2+x3+x4+x5+x6}^2=\\var{(x1+x2+x3+x4+x5+x6)^2}$<br/><strong></strong></p>\n<p><strong>(c)</strong></p>\n<p>$\\sum y^2 &nbsp;$ means square each of the $y$ values then add them up.&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>\n<p>$\\var{x1}^2+\\var{x2}^2+\\var{x3}^2+\\var{x4}^2+\\var{x5}^2+\\var{x6}^2=\\var{x1^2}+\\var{x2^2}+\\var{x3^2}+\\var{x4^2}+\\var{x5^2}+\\var{x6^2}=\\var{x1^2+x2^2+x3^2+x4^2+x5^2+x6^2}$</p>\n<p>Note this does not give the same answer as the calculation in (b)!</p>\n<p></p>", "extensions": [], "tags": [], "rulesets": {}, "metadata": {"description": "<p>Summation Notation</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"marks": 0, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "variableReplacements": [], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "variableReplacements": [], "correctAnswerFraction": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "maxValue": "{x1}+{x2}+{x3}+{x4}+{x5}+{x6}", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "showCorrectAnswer": true, "scripts": {}, "minValue": "{x1}+{x2}+{x3}+{x4}+{x5}+{x6}", "unitTests": [], "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false}, {"notationStyles": ["plain", "en", "si-en"], "marks": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "variableReplacements": [], "correctAnswerFraction": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "maxValue": "({x1}+{x2}+{x3}+{x4}+{x5}+{x6})^2", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "showCorrectAnswer": true, "scripts": {}, "minValue": "({x1}+{x2}+{x3}+{x4}+{x5}+{x6})^2", "unitTests": [], "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false}, {"notationStyles": ["plain", "en", "si-en"], "marks": "2", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "variableReplacements": [], "correctAnswerFraction": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "maxValue": "{x1}^2+{x2}^2+{x3}^2+{x4}^2+{x5}^2+{x6}^2", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "showCorrectAnswer": true, "scripts": {}, "minValue": "{x1}^2+{x2}^2+{x3}^2+{x4}^2+{x5}^2+{x6}^2", "unitTests": [], "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false}], "sortAnswers": false, "prompt": "<p>Find</p>\n<p><strong>(a)</strong></p>\n<p>$\\sum y = $ &nbsp;[[0]]</p>\n<p><strong>(b)</strong></p>\n<p>$(\\sum y)^2 = $ [[1]]</p>\n<p><strong>(c)</strong></p>\n<p>$\\sum y^2 = $ [[2]]</p>"}], "functions": {}, "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}