// Numbas version: exam_results_page_options
{"name": "Integration: Integral of a graph. Version I", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "functions": {"plotpoly": {"parameters": [["n", "number"], ["r1", "number"], ["r2", "number"], ["a", "number"]], "type": "html", "language": "javascript", "definition": "// This function creates the board and sets it up, then returns an\n// HTML div tag containing the board.\n\n//Put in your values of x here\n\nvar x_min = -4;\nvar x_max = 4;\nvar y_min = -10;\nvar y_max = 10;\n\n\n// First, make the JSXGraph board.\n// The function provided by the JSXGraph extension wraps the board up in \n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n//{boundingBox: [-8,10,8,-10],\n {boundingBox: [x_min,y_max,x_max,y_min],                                           \n axis: false,\n showNavigation: false,\n grid: true\n});\n\n\n\n\n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\nvar board = div.board; \n\n// create the x-axis.\nvar xaxis = board.create('line',[[0,0],[1,0]], { strokeColor: 'black', fixed: true});\nvar xticks = board.create('ticks',[xaxis,1],{\n  drawLabels: false,\n  label: {offset: [-4, -10]},\n  minorTicks: 0\n});\n\n// create the y-axis\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nvar yticks = board.create('ticks',[yaxis,1],{\ndrawLabels: false,\nlabel: {offset: [-20, 0]},\nminorTicks: 0\n});\n\n\n // PUT YOUR FUNCTION HERE\n\nb=(r1+r2)/2;\nc=r1*r2;\n\nd2=(Math.floor(Math.random()*2)*2 - 1);    //This produces -1 or 1 with 50% odds\nd3=(Math.floor(Math.random()*2)*2 - 1)*2;  //This produces -2 or 2 with 50% odds\nd4=(Math.floor(Math.random()*2)*2 - 1)*3;  //This produces -3 or 3 with 50% odds\nd5=(Math.floor(Math.random()*2)*2 - 1);    //This produces -1 or 1 with 50% odds\n\nif(n==1)\n  board.create('functiongraph',[function(x){ return a*(x+r1)*(x+r2);},x_min,x_max]);\nelse if (n==2)\n  board.create('functiongraph',[function(x){ return a*(x*x*x/3 + x*x*b + c*x)+d2;},x_min,x_max]);\nelse if (n==3)\n  board.create('functiongraph',[function(x){ return -a*(x*x*x/3 + x*x*b + c*x)+d3;},x_min,x_max]);\nelse if (n==4)\n    board.create('functiongraph',[function(x){ return a*(x*x*x/3 + x*x*(b-1) + c*x)+d4;},x_min,x_max]);\nelse if (n==5)\n    board.create('functiongraph',[function(x){ return -a*(x*x*x/3 + x*x*b + (c-1)*x)+d5;},x_min,x_max]);\n\nreturn div;"}}, "advice": "", "ungrouped_variables": ["root1", "root2", "a"], "parts": [{"variableReplacements": [], "scripts": {}, "distractors": ["", "", "", ""], "marks": 0, "unitTests": [], "displayType": "radiogroup", "type": "1_n_2", "showFeedbackIcon": true, "maxMarks": "2", "matrix": ["2", "0", 0, 0], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "shuffleChoices": true, "prompt": "<p>Here is a graph of $f$.</p>\n<p>{plotpoly(1,{root1},{root2},{a})}</p>\n<p>Which of the graphs below could be the graph of an&nbsp;integral of $f$.</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p>", "displayColumns": 0, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "minMarks": 0, "choices": ["<p>{plotpoly(2,{root1},{root2},{a})}</p>", "<p>{plotpoly(3,{root1},{root2},{a})}</p>", "<p>{plotpoly(4,{root1},{root2},{a})}</p>", "<p>{plotpoly(5,{root1},{root2},{a})}</p>"]}], "preamble": {"css": "", "js": ""}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": ["jsxgraph"], "variables": {"a": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "a", "definition": "random(1,-1)"}, "root2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "root2", "definition": "root1 - random(2..4 #0.5)"}, "root1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "root1", "definition": "random(1..3 #0.5)"}}, "statement": "", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>A graph is drawn. A student is to identify the derivative of this graph from four other graphs.</p>\n<p>Version I. Graph is&nbsp;quadratic</p>\n<p>Version II. Graph is&nbsp;horizontal</p>\n<p>Version III. Graph is&nbsp;cubic</p>\n<p>Version IV. Graph is sinusoidal</p>"}, "rulesets": {}, "name": "Integration: Integral of a graph. Version I", "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}