// Numbas version: exam_results_page_options {"name": "Placing a point on a number line (20 bars multiple of sqrt{2}/2)", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"showfrontpage": false, "preventleave": false, "allowregen": true}, "question_groups": [{"questions": [{"ungrouped_variables": ["l", "r", "a", "c", "b"], "advice": "

Since each bar represents $\\displaystyle \\dfrac{\\var{r}-(\\var{l})}{20}=\\var[fractionNumbers]{(r-l)/20}$ and since the number $\\displaystyle A=\\var[fractionNumbers]{c}\\sqrt{2}\\simeq \\var[fractionNumbers]{c}\\times 1.4=\\var[fractionNumbers]{c*1.4}$ lies $\\displaystyle A-(\\var{l})\\simeq\\var[fractionNumbers]{l+a/10}-(\\var{l})=\\var[fractionNumbers]{a*((r-l)/20)}=\\var{a}\\times \\var[fractionNumbers]{(r-l)/20}$ from $\\displaystyle \\var{l}$, the number $\\displaystyle A=\\var[fractionNumbers]{c}\\sqrt{2}$ lies approximately $\\displaystyle \\var{a}$ bars from the left as shown below.

\n

{dragpointafter()}

", "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "

Using the approximation $\\sqrt{2}\\simeq 1.4$, place the point $\\displaystyle A=\\var[fractionNumbers]{c}\\sqrt{2}$ 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, "showFeedbackIcon": true, "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "marks": 1, "type": "numberentry", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "variableReplacements": [], "maxValue": "a+0.5", "scripts": {}, "showFeedbackIcon": true, "mustBeReduced": false, "minValue": "a-0.5", "allowFractions": false, "mustBeReducedPC": 0, "showCorrectAnswer": true}], "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true}], "contributors": [{"name": "Anthony Brown", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/799/"}], "tags": [], "type": "question", "preamble": {"js": "", "css": ""}, "functions": {"dragpointafter": {"type": "html", "language": "javascript", "definition": "// set up the board\n\nJXG.Options.text.fontSize = 15; \n\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','150px',{boundingBox:[-1.5,3,21.5,-3],axis:false,showNavigation:false});\nvar board = div.board;\n\nvar l1 = board.create('line',[[0,0],[20,0]], \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});\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',[[20,0],[19.5,0.5]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar a4 = board.create('line',[[20,0],[19.5,-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',[-1.5,-0.4],{size:-1,name:l});\nb.setProperty({fixed:true});\nvar c = board.create('point',[19.7,-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;", "parameters": []}, "dragpoint": {"type": "html", "language": "javascript", "definition": "// set up the board\n\nJXG.Options.text.fontSize = 15; \n\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','150px',{boundingBox:[-1.5,3,21.5,-3],axis:false,showNavigation:false});\nvar board = div.board;\n\nvar l1 = board.create('line',[[0,0],[20,0]], \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});\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',[[20,0],[19.5,0.5]], \n {straightFirst:false, straightLast:false, strokeWidth:2,fixed:true});\nvar a4 = board.create('line',[[20,0],[19.5,-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',[-1.5,-0.4],{size:-1,name:l});\nb.setProperty({fixed:true});\nvar c = board.create('point',[19.7,-0.4],{size:-1,name:r});\nc.setProperty({fixed:true});\n\nvar a = board.create('point',[10,2],{size:5});\n\na.on('drag',function(){\n Numbas.exam.currentQuestion.parts[0].gaps[0].display.studentAnswer(a.X()); \n});\n\nreturn div;", "parameters": []}}, "metadata": {"description": "

This question asks you to place a point on a number line. The number is a multiple of sqrt{2}/2.

", "licence": "Creative Commons Attribution 4.0 International"}, "name": "Placing a point on a number line (20 bars multiple of sqrt{2}/2)", "variables": {"c": {"description": "

This is the multiple of sqrt{2}.

", "templateType": "randrange", "name": "c", "definition": "random(-10..10#0.5)", "group": "Ungrouped variables"}, "b": {"description": "

This is the integer part of the distance from the left hand endpoint.

", "templateType": "anything", "name": "b", "definition": "random(0,1)", "group": "Ungrouped variables"}, "l": {"description": "

This is the left hand endpoint of the numberline.

", "templateType": "anything", "name": "l", "definition": "floor(c*1.4)-b", "group": "Ungrouped variables"}, "r": {"description": "

This is the right hand endpoint of the numberline.

", "templateType": "anything", "name": "r", "definition": "l+2", "group": "Ungrouped variables"}, "a": {"description": "

This is the distance along the number line.

", "templateType": "anything", "name": "a", "definition": "10*b+(c*1.4-floor(c*1.4))*10", "group": "Ungrouped variables"}}, "variable_groups": [], "statement": "

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

", "rulesets": {}, "extensions": ["jsxgraph"], "variablesTest": {"maxRuns": "100", "condition": "c<>-1 and c<>0 and c<>1 and (floor(1.4*c)<>1.4*c or b>0)"}}], "pickingStrategy": "all-ordered"}], "contributors": [{"name": "Anthony Brown", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/799/"}]}