// Numbas version: exam_results_page_options {"name": "Placing a point on a number line (21 bars multiple of pi/3)", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"c": {"templateType": "randrange", "definition": "random(-30..30#1)", "description": "

This is three times the multiple of pi.

", "group": "Ungrouped variables", "name": "c"}, "l": {"templateType": "anything", "definition": "floor(c*22/21)", "description": "

This is the left hand endpoint of the numberline.

", "group": "Ungrouped variables", "name": "l"}, "r": {"templateType": "anything", "definition": "l+1", "description": "

This is the right hand endpoint of the numberline.

", "group": "Ungrouped variables", "name": "r"}, "a": {"templateType": "anything", "definition": "(c*22/21-floor(c*22/21))*21", "description": "

This is the distance along the number line.

", "group": "Ungrouped variables", "name": "a"}}, "statement": "

This question asks you to place a point on a number line.

", "parts": [{"prompt": "

Using the approximation $\\displaystyle \\pi\\simeq\\dfrac{22}{7}$, place the point $\\displaystyle A=\\var[fractionNumbers]{c/3}\\pi$ on the number line below by dragging it.

\n

Note that the line starts at the number $\\displaystyle \\var{l}$ and finishes at the number $\\displaystyle \\var{r}$. In addition please disregard the numbers that appear when you drag the point $A$, these refer to an invisible grid that enables the program to calculate where you drag the point to.

\n

The point should finish up on a vertical bar, the vertical position of the point does not matter and your answer will default to the nearest vertical bar.

\n

{dragpoint()}

", "marks": 0, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "minValue": "a-0.5", "showCorrectAnswer": true, "type": "numberentry", "mustBeReducedPC": 0, "maxValue": "a+0.5", "correctAnswerFraction": false, "mustBeReduced": false, "correctAnswerStyle": "plain", "marks": 1, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "allowFractions": false}], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "showCorrectAnswer": true}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

This question asks you to place a point on a number line. The number is a multiple of pi.

"}, "variablesTest": {"maxRuns": "100", "condition": "c<>-3 and c<>0 and c<>3 and floor(c*22/21)<>c*22/21"}, "tags": [], "extensions": ["jsxgraph"], "functions": {"dragpointafter": {"type": "html", "parameters": [], "definition": "// set up the board\n\nJXG.Options.text.fontSize = 15; \n\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','150px',{boundingBox:[-1.5,3,22.5,-3],axis:false,showNavigation:false});\nvar board = div.board;\n\nvar l1 = board.create('line',[[0,0],[21,0]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l2 = board.create('line',[[1,-1],[1,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l3 = board.create('line',[[2,-1],[2,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l4 = board.create('line',[[3,-1],[3,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l5 = board.create('line',[[4,-1],[4,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l6 = board.create('line',[[5,-1],[5,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l7 = board.create('line',[[6,-1],[6,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l8 = board.create('line',[[7,-1],[7,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l9 = board.create('line',[[8,-1],[8,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l10 = board.create('line',[[9,-1],[9,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l11 = board.create('line',[[10,-1],[10,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l12 = board.create('line',[[11,-1],[11,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l13 = board.create('line',[[12,-1],[12,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l14 = board.create('line',[[13,-1],[13,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l15 = board.create('line',[[14,-1],[14,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l16 = board.create('line',[[15,-1],[15,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l17 = board.create('line',[[16,-1],[16,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l18 = board.create('line',[[17,-1],[17,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l19 = board.create('line',[[18,-1],[18,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l20 = board.create('line',[[19,-1],[19,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l21 = board.create('line',[[20,-1],[20,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\n\nvar a1 = board.create('line',[[0,0],[0.5,0.5]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar a2 = board.create('line',[[0,0],[0.5,-0.5]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar a3 = board.create('line',[[21,0],[20.5,0.5]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar a4 = board.create('line',[[21,0],[20.5,-0.5]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\n\nvar l = Numbas.jme.unwrapValue(scope.variables.l);\nvar r = Numbas.jme.unwrapValue(scope.variables.r);\n\nvar b = board.create('point',[-1.7,-0.4],{size:-1,name:l});\nb.setProperty({fixed:true});\nvar c = board.create('point',[20.7,-0.4],{size:-1,name:r});\nc.setProperty({fixed:true});\n\n\nvar a = Numbas.jme.unwrapValue(scope.variables.a);\n\nvar a = board.create('point',[a,0],{size:5});\na.setProperty({fixed:true});\n\nreturn div;", "language": "javascript"}, "dragpoint": {"type": "html", "parameters": [], "definition": "// set up the board\n\nJXG.Options.text.fontSize = 15; \n\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','150px',{boundingBox:[-1.5,3,22.5,-3],axis:false,showNavigation:false});\nvar board = div.board;\n\nvar l1 = board.create('line',[[0,0],[21,0]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l2 = board.create('line',[[1,-1],[1,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l3 = board.create('line',[[2,-1],[2,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l4 = board.create('line',[[3,-1],[3,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l5 = board.create('line',[[4,-1],[4,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l6 = board.create('line',[[5,-1],[5,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l7 = board.create('line',[[6,-1],[6,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l8 = board.create('line',[[7,-1],[7,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l9 = board.create('line',[[8,-1],[8,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l10 = board.create('line',[[9,-1],[9,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l11 = board.create('line',[[10,-1],[10,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l12 = board.create('line',[[11,-1],[11,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l13 = board.create('line',[[12,-1],[12,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l14 = board.create('line',[[13,-1],[13,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l15 = board.create('line',[[14,-1],[14,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l16 = board.create('line',[[15,-1],[15,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l17 = board.create('line',[[16,-1],[16,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l18 = board.create('line',[[17,-1],[17,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l19 = board.create('line',[[18,-1],[18,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l20 = board.create('line',[[19,-1],[19,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar l21 = board.create('line',[[20,-1],[20,1]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\n\nvar a1 = board.create('line',[[0,0],[0.5,0.5]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar a2 = board.create('line',[[0,0],[0.5,-0.5]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar a3 = board.create('line',[[21,0],[20.5,0.5]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar a4 = board.create('line',[[21,0],[20.5,-0.5]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\n\nvar l = Numbas.jme.unwrapValue(scope.variables.l);\nvar r = Numbas.jme.unwrapValue(scope.variables.r);\n\nvar b = board.create('point',[-1.7,-0.4],{size:-1,name:l});\nb.setProperty({fixed:true});\nvar c = board.create('point',[20.7,-0.4],{size:-1,name:r});\nc.setProperty({fixed:true});\n\nvar a = board.create('point',[10.5,2],{size:5});\n\na.on('drag',function(){\n Numbas.exam.currentQuestion.parts[0].gaps[0].display.studentAnswer(a.X()); \n});\n\nreturn div;", "language": "javascript"}}, "preamble": {"css": "", "js": ""}, "variable_groups": [], "advice": "

Since each bar represents $\\displaystyle \\dfrac{\\var{r}-(\\var{l})}{21}=\\var[fractionNumbers]{(r-l)/21}$ and since the number $\\displaystyle A=\\var[fractionNumbers]{c/3}\\pi\\simeq \\var[fractionNumbers]{c/3}\\times \\dfrac{22}{7}=\\var[fractionNumbers]{c*22/21}$ lies $\\displaystyle A-(\\var{l})\\simeq\\var[fractionNumbers]{l+a/21}-(\\var{l})=\\var[fractionNumbers]{a/21}=\\var[fractionNumbers]{a}\\times \\dfrac{1}{21}$ from $\\displaystyle \\var{l}$, the number $\\displaystyle A=\\var[fractionNumbers]{c/3}\\pi$ lies approximately $\\displaystyle \\var[fractionNumbers]{a}$ bars from the left as shown below.

\n

{dragpointafter()}

", "rulesets": {}, "name": "Placing a point on a number line (21 bars multiple of pi/3)", "ungrouped_variables": ["l", "r", "a", "c"], "type": "question", "contributors": [{"name": "Anthony Brown", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/799/"}]}]}], "contributors": [{"name": "Anthony Brown", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/799/"}]}