// Numbas version: exam_results_page_options
{"name": "Quadratic Function Fourier Series", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "", "preamble": {"js": "function dragpoint_board() {\n  var scope = question.scope;\n\n  JXG.Options.text.display = 'internal';\n  \n  var t = scope.variables.t.value;\n  var c = scope.variables.c.value;\n  var a = scope.variables.a.value;\n  \n  var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',{boundingBox:[-3*t,a*t*t + 10,3*t,-a*t], axis:true, grid:false, title:{\n        text: \"\"}});\n \n $(question.display.html).find('#dragpoint').append(div);\n  \n var board = div.board;\n      \n  var graph = board.create('curve',\n                       [function(x){ return x;},\n                        function(x){ return a*x*x;},\n                        -t, t],{strokeWidth:1,strokeColor:'blue'}\n                    );\n  var graph = board.create('curve',\n                       [function(x){ return x+2*t;},\n                        function(x){ return a*x*x;},\n                        -t, t],{strokeWidth:1,strokeColor:'blue'}\n                    );\n  var graph = board.create('curve',\n                       [function(x){ return x-2*t;},\n                        function(x){ return a*x*x;},\n                        -t, t],{strokeWidth:1,strokeColor:'blue'}\n                    );\n  \n  \n}\n\nquestion.signals.on('HTMLAttached',function() {\n  dragpoint_board();\n});", "css": "table#values th {\n  background: none;\n  text-align: center;\n}"}, "extensions": ["jsxgraph"], "functions": {}, "rulesets": {"std": ["all", "fractionNumbers"]}, "variables": {"t": {"name": "t", "description": "", "definition": "random(2..10#2)", "group": "Ungrouped variables", "templateType": "anything"}, "a": {"name": "a", "description": "", "definition": "random(1,2,3,4)", "group": "Ungrouped variables", "templateType": "anything"}, "shift": {"name": "shift", "description": "", "definition": "random(-t/2..t/2 except 0)", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"name": "c", "description": "", "definition": "random(4..12#1 except t)", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "<div id=\"dragpoint\"><strong></strong></div>\n<p></p>\n<p>State&nbsp;the&nbsp;time period of the function.</p>\n<p>T = [[0]]</p>", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "maxValue": "2*t", "scripts": {}, "marks": 1, "allowFractions": false, "variableReplacements": [], "showCorrectAnswer": true, "correctAnswerFraction": false, "showFeedbackIcon": true, "type": "numberentry", "minValue": "2*t", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"]}], "variableReplacements": []}, {"variableReplacementStrategy": "originalfirst", "mustBeReduced": true, "maxValue": "{{2*t^2*a}/6}", "scripts": {}, "marks": 1, "allowFractions": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "prompt": "<p>State&nbsp;the value of $a_0$.</p>", "showFeedbackIcon": true, "type": "numberentry", "minValue": "{{2*t^2*a}/6}", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "correctAnswerFraction": false}, {"variableReplacementStrategy": "originalfirst", "checkingtype": "absdiff", "scripts": {}, "marks": 1, "expectedvariablenames": [], "answer": "{4*a*t^2}*(-1)^n/(pi^2*n^2)", "variableReplacements": [], "vsetrange": [0, 1], "showCorrectAnswer": true, "prompt": "<p>State the value of $a_n$.</p>", "showFeedbackIcon": true, "vsetrangepoints": 5, "type": "jme", "checkingaccuracy": 0.001, "showpreview": true, "checkvariablenames": false}, {"variableReplacementStrategy": "originalfirst", "checkingtype": "absdiff", "scripts": {}, "marks": 1, "expectedvariablenames": [], "answer": "0", "variableReplacements": [], "vsetrange": [0, 1], "showCorrectAnswer": true, "prompt": "<p>State&nbsp;the value of $b_n$.</p>", "showFeedbackIcon": true, "vsetrangepoints": 5, "type": "jme", "checkingaccuracy": 0.001, "showpreview": true, "checkvariablenames": false}], "variable_groups": [], "name": "Quadratic Function Fourier Series", "statement": "<p>Calculate the Fourier Series of the function $f(x) = \\simplify{{a}x^2}$.</p>", "tags": [], "metadata": {"description": "<p>Widget Sales</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "ungrouped_variables": ["t", "c", "shift", "a"], "type": "question", "contributors": [{"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}]}]}], "contributors": [{"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}]}