// Numbas version: exam_results_page_options
{"name": "Q9 - Coordinate geometry: line and parabola", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "values", "v1", "m", "yc", "x1", "x2", "x3", "x4", "x5", "y1", "y2", "y3", "y4", "y5", "m2", "yc2"], "name": "Q9 - Coordinate geometry: line and parabola", "tags": ["graph", "interactive", "Jsxgraph", "jsxgraph", "plot", "quadratic"], "advice": "<div id=\"showgraph\"></div>", "rulesets": {"std": ["all", "fractionNumbers"]}, "parts": [{"prompt": "<p>What is the (a) slope and (b) the y-axis intercept of the following line:</p>\n<p>$\\simplify{y={m}x+{yc}}$</p>\n<p>Slope = &nbsp;[[0]]&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; y-intercept =&nbsp; [[1]]</p>\n<p></p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "m", "minValue": "m", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "yc", "minValue": "yc", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Which of the following points are on the line&nbsp;&nbsp; $ y=\\simplify{{m2}*x + {yc2}}$&nbsp;&nbsp; ?</p>", "matrix": [0, 0, 0, "1", 0], "shuffleChoices": true, "marks": 0, "variableReplacements": [], "choices": ["<p>({x1},{y1})</p>", "<p>({x2},{y2})</p>", "<p>({x3},{y3})</p>", "<p>({x4},{y4})</p>", "<p>({x5},{y5})</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "distractors": ["", "", "", "", ""], "displayColumns": 0, "showCorrectAnswer": false, "type": "1_n_2", "minMarks": 0}, {"prompt": "<p>Fill in the table of values for the following curve: \\[y=\\simplify[std]{{a}x^2+{c}}\\]</p>\n<p></p>\n<p></p>\n<table id=\"values\" border=\"1\">\n<thead>\n<tr><th>$x$</th><th>$-3$</th><th>$-2$</th><th>$-1$</th><th>$0$</th><th>$1$</th><th>$2$</th><th>$3$</th></tr>\n</thead>\n<tbody>\n<tr><th>$y$</th>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>[[2]]</td>\n<td>[[3]]</td>\n<td>[[4]]</td>\n<td>[[5]]</td>\n<td>[[6]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "scripts": {}, "answer": "{a}*9+{c}", "marks": 0.5, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "scripts": {}, "answer": "{a}*4+{c}", "marks": 0.5, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "scripts": {}, "answer": "{a}*1+{c}", "marks": 0.5, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "scripts": {}, "answer": "{c}", "marks": 0.5, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "scripts": {}, "answer": "{a}*1+{c}", "marks": 0.5, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "scripts": {}, "answer": "{a}*4+{c}", "marks": 0.5, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "scripts": {}, "answer": "{a}*9+{c}", "marks": 0.5, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<div id=\"dragpoint\"></div>\n<p>Slide the points to the correct $y$ values to show the graph of the curve in part (c).</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{values[0]}", "minValue": "{values[0]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "0.2", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{values[1]}", "minValue": "{values[1]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "0.2", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{values[2]}", "minValue": "{values[2]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "0.2", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{values[3]}", "minValue": "{values[3]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "0.3", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{values[4]}", "minValue": "{values[4]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "0.2", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{values[5]}", "minValue": "{values[5]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "0.2", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{values[6]}", "minValue": "{values[6]}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "0.2", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Complete the following.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "table#values th {\n  background: none;\n  text-align: center;\n}", "js": "\nfunction dragpoint_board() {\n\n  var scope = question.scope; \n  var a = scope.variables.a.value;\n\n  var c = scope.variables.c.value;\n  var maxy = Math.max(Math.abs(a*9+c),Math.abs(c));\n  \n  var div = Numbas.extensions.jsxgraph.makeBoard('250px','400px',{boundingBox:[-5,maxy+2,5,-maxy-2],grid:true});\n  $(question.display.html).find('#dragpoint').append(div);\n  \n  var board = div.board;\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 = 7;\n  var points = [];\n  \n  \n  // this function sets up the i^th point\n  function make_point(i) {\n    \n    // calculate initial coordinates\n    var x = i-(num_points-1)/2;\n    \n    // create an invisible vertical line for the point to slide along\n    var line = board.create('line',[[x,0],[x,1]],{visible: false});\n    \n    // create the point\n    var point = points[i] = board.create(\n      'glider',\n      [i-(num_points-1)/2,-maxy-1,line],\n      {\n        name:'',\n        size:2,\n        snapSizeY: 0.1,  // the point will snap to y-coordinates which are multiples of 0.1\n        snapToGrid: true\n      }\n    );\n    \n    // the contents of the input box for this point\n    var studentAnswer = question.parts[3].gaps[i].display.studentAnswer;\n    \n    //Here I have commented out the functions which connect the student input to the graph and the filling in of the answer fields\n    //when the student drags the points on the graph.\n    \n    // watch the student's input and reposition the point when it changes.    \n   // ko.computed(function() {\n     // y = evaluate(studentAnswer());\n      //if(!(isNaN(y)) && board.mode!=board.BOARD_MODE_DRAG) {\n      //  point.moveTo([x,y],100);\n     // }\n   // });\n    \n    // when the student drags the point, update the gapfill input\n   point.on('drag',function(){\n   var y = Numbas.math.niceNumber(point.Y());\n    studentAnswer(y);\n    });\n    \n  }\n  \n  // create each point\n  for(var i=0;i<num_points;i++) {\n    make_point(i);\n  }\n  \n  // create the parabola\n  var parabool = board.create('spline',points,{strokeWidth:3,strokeColor:'red'});\n}\n//function showgraph(){\n//  var scope = question.scope; \n//  var a = scope.variables.a.value;\n//  var v1=[];\n \n//  var c = scope.variables.c.value;\n//  var maxy = Math.max(Math.abs(a*9+c),Math.abs(c));\n  \n//  var div = Numbas.extensions.jsxgraph.makeBoard('250px','400px',{boundingBox:[-5,maxy+3,5,-maxy-3],grid:true});\n//  $(question.display.html).find('#showgraph').append(div);\n  \n//  var board = div.board;\n//   for(var i=-3;i<4;i++){\n//    v1[i+3]=board.create('point', [i,a*Math.pow(i,2)+c], {size: 4, name: ''});\n//   }\n//  var parab = board.create('spline',v1,{strokeWidth:3,strokeColor:'blue'});\n//}\n\nquestion.signals.on('HTMLAttached',function() {\n  dragpoint_board();\n // showgraph();\n}); "}, "variables": {"a": {"definition": "random(-2,-1,-0.5,0.5,1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-4..4 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "x1": {"definition": "random(-5..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "x1", "description": ""}, "y1": {"definition": "m2*x1+yc2+random(-2,-1,1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "y1", "description": ""}, "yc2": {"definition": "random(1..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "yc2", "description": ""}, "yc": {"definition": "random(-5..5 except [0,m])", "templateType": "anything", "group": "Ungrouped variables", "name": "yc", "description": ""}, "m": {"definition": "random(-2,-1.5,-1,-0.5,0.5,1,1.5,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "v1": {"definition": "map([x-3,values[x]],x,0..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "v1", "description": ""}, "values": {"definition": "map({a*x^2+c},x,-3..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "values", "description": ""}, "m2": {"definition": "random(-3,-2,2,3,4,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "m2", "description": ""}, "x2": {"definition": "random(-5..5 except x1)", "templateType": "anything", "group": "Ungrouped variables", "name": "x2", "description": ""}, "x3": {"definition": "random(-5..5 except [x1,x2])", "templateType": "anything", "group": "Ungrouped variables", "name": "x3", "description": ""}, "y3": {"definition": "m2*x3+yc2+random(-2,-1,1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "y3", "description": ""}, "y2": {"definition": "m2*x2+yc2+random(-2,-1,1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "y2", "description": ""}, "y5": {"definition": "m2*x5+yc2+random(-2,-1,1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "y5", "description": ""}, "y4": {"definition": "m2*x4+yc2", "templateType": "anything", "group": "Ungrouped variables", "name": "y4", "description": ""}, "x4": {"definition": "random(-5..5 except[x1,x2,x3])", "templateType": "anything", "group": "Ungrouped variables", "name": "x4", "description": ""}, "x5": {"definition": "random(-5..5 except[x1,x2,x3,x4])", "templateType": "anything", "group": "Ungrouped variables", "name": "x5", "description": ""}}, "metadata": {"notes": "<p>Removed graph from advice.</p>", "description": "<p>Compute a table of values for a quadratic function. Calculate the slope and intercept of a line.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}]}]}], "contributors": [{"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}]}