// Numbas version: exam_results_page_options
{"name": "Fourier Sketching (-3 to 3)", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": "200", "condition": ""}, "advice": "<p>The correct graph is shown below.</p>\n<p>{graph(a,b,c)}</p>", "preamble": {"js": "function dragpoint_board() {\n  var scope = question.scope;\n  \n  var a = scope.variables.a.value;\n  var b = scope.variables.b.value;\n  var c = scope.variables.c.value;\n\n  \n  var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-3.3,13.5,3.3,-13.5],grid:true,withLabel:true});\n  $(question.display.html).find('#dragpoint').append(div);\n\n  var board = div.board;\n  \n// ceeate axis labels\n  \n   var label1 = board.create('point',[3.1,0.2],{name:'X',size:-1});\n   label1.setProperty({fixed:true});\n   var label2 = board.create('point',[0,14.3],{name:'y',size:-1});\n   label2.setProperty({fixed:true});\n  \n    \n    \n  //create draggable points\n\n\n    var line0 = board.create('line',[[-3,0],[-3,4]],{visible: false});\n    var np0 = board.create('glider',[-3,8,line0],\n      {\n        name:'A',\n        size:3\n      }\n    );\n\n    var line1 = board.create('line',[[0,0],[0,4]],{visible: false});\n    var np1 = board.create('glider',[-1,8,line1],\n      {\n        name:'B',\n        size:3\n      }\n    );\n  \n    var line2 = board.create('line',[[0,0],[0,4]],{visible: false});\n    var np2 = board.create('glider',[0,6,line2],\n      {\n        name:'C',\n        size:3,\n      }\n    );\n \n   var line3 = board.create('line',[[3,0],[3,4]],{visible: false});\n    var np3 = board.create('glider',[0,6,line3],\n      {\n        name:'D',\n        size:3,\n      }\n    );\n  \n  \n  //shorthand to evaluate a mathematical expression to a number\n  function evaluate(expression) {\n    try {\n      var val = Numbas.jme.evaluate(expression,question.scope);\n      return Numbas.jme.unwrapValue(val);\n    }\n    catch(e) {\n      // if there's an error, return no number\n      return NaN;\n    }\n  }\n  \n  // set up points array\n  var num_points = 4;\n  var points = [np0, np1, np2, np3];\n  \n  \n  // this function sets up the i^th point\n  function make_point(i) {\n    \n   var point = points[i];\n    \n    var x=point[0];\n    var y=point[1];\n    \n    // the contents of the input box for this point\n    var xstudentAnswer =  question.parts[0].gaps[i].display.studentAnswer;\n\n    \n    // when the student drags the point, update the gapfill input\n    point.on('drag',function(){\n      var x = Numbas.math.niceNumber(point.X());\n      var y = Numbas.math.niceNumber(point.Y());\n      if(i < 2)\n      {\n      var diff = y-(a);\n      xstudentAnswer(diff);\n      }\n      if (i===2)\n        {\n      var diff = y-(c);\n      xstudentAnswer(diff);\n      }\n      if (i===3)\n        {\n      var diff = y-(b*3+c);\n      xstudentAnswer(diff);\n      }\n    });\n    \n  }\n  \n  // create each point\n  for(var i=0;i<num_points;i++) {\n    make_point(i);\n  }\n     \n  \n  // create the parabola\n  var parabool = board.create('line',[np0,np1],{straightFirst:false, straightLast:false, strokeWidth:2,strokeColor:'blue'});\n  var parabool = board.create('line',[np2, np3],{straightFirst:false, straightLast:false, strokeWidth:2,strokeColor:'blue'});\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": {"graph": {"type": "html", "language": "javascript", "parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "definition": "// set up the board\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-3.3,13.5,3.3,-13.5],grid:true,withLabel:true,ticks:false});\n\nvar board = div.board;\n\nvar d = board.create('point',[3.1,0],{size:-1,name:'x'});\nd.setProperty({fixed:true});\nvar f = board.create('point',[0,14],{size:-1,name:'y'});\nf.setProperty({fixed:true});\nvar e = board.create('point',[-3,a],{size:3,name:'A'});\ne.setProperty({fixed:true});\nvar g = board.create('point',[0,a],{size:3,name:'B'});\ng.setProperty({fixed:true});\nvar e = board.create('point',[0,c],{size:3,name:'C'});\ne.setProperty({fixed:true});\nvar h = board.create('point',[3,c + b*3],{size:3,name:'D'});\nh.setProperty({fixed:true});\n\nboard.create('functiongraph',[function(x){ return a;},-3,0],{strokeColor:'blue',strokeWidth:2});\nboard.create('functiongraph',[function(x){ return c + b*x;},0,3],{strokeColor:'blue',strokeWidth:2});\n\nreturn div;"}}, "rulesets": {}, "variables": {"b": {"name": "b", "description": "", "definition": "random(-3..3 except 0)", "group": "Ungrouped variables", "templateType": "anything"}, "a": {"name": "a", "description": "", "definition": "random(-12..12)", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"name": "c", "description": "", "definition": "random(-4..4)", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "<div id=\"dragpoint\"></div>", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "maxValue": "0.2", "scripts": {}, "marks": "1", "allowFractions": false, "variableReplacements": [], "showCorrectAnswer": true, "correctAnswerFraction": false, "showFeedbackIcon": false, "type": "numberentry", "minValue": "-0.2", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"]}, {"variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "maxValue": "0.2", "scripts": {}, "marks": "1", "allowFractions": false, "variableReplacements": [], "showCorrectAnswer": true, "correctAnswerFraction": false, "showFeedbackIcon": false, "type": "numberentry", "minValue": "-0.2", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"]}, {"variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "maxValue": "0.2", "scripts": {}, "marks": "1", "allowFractions": false, "variableReplacements": [], "showCorrectAnswer": true, "correctAnswerFraction": false, "showFeedbackIcon": false, "type": "numberentry", "minValue": "- 0.2", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"]}, {"variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "maxValue": "0.2", "scripts": {}, "marks": "1", "allowFractions": false, "variableReplacements": [], "showCorrectAnswer": true, "correctAnswerFraction": false, "showFeedbackIcon": false, "type": "numberentry", "minValue": "- 0.2", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"]}], "variableReplacements": []}], "variable_groups": [], "name": "Fourier Sketching (-3 to 3)", "statement": "<p style=\"text-align: center;\"></p>\n<p>By dragging the points A, B, and C, construct the graph of the function</p>\n<p>$ f(x) = \\left\\{ \\begin{array}{cl} \\var{a}\\;\\;\\;\\;\\;\\;\\;\\;\\; &nbsp;-3 &lt; x &lt; 0 \\\\ \\simplify{{b}x + {c}} \\;\\;\\;\\;\\; \\; \\; 0&lt;x&lt;3.\\end{array}\\right.$</p>\n<p>Note that in order to be marked correct, the points need to be within 0.2 of their correct $y$-values.</p>\n<p>Also note that you have to drag each of the points in order to be able to submit your answer.</p>", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "ungrouped_variables": ["a", "b", "c"], "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/"}]}