// Numbas version: finer_feedback_settings {"name": "WP Math 11 Midterm", "metadata": {"description": "

Contains some questions from mini-tests which should be changed.

", "licence": "None specified"}, "duration": 0, "percentPass": "0", "showQuestionGroupNames": false, "shuffleQuestionGroups": true, "showstudentname": false, "question_groups": [{"name": "Problems slope/grade/tangent", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "E Slopes/tan/grade problems", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "K W", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3194/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

A farmer needs to ensure proper drainage in a 400-meter long field with a required elevation drop of 2 meters to prevent waterlogging.

Determine the angle of elevation of the ramp (round to the nearest degree). [[0]]

Express the slope of the ramp as a percentage. [[1]]

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The tangent ratio of a wheelchair ramp is 5/12.

Determine the angle of elevation of the ramp (round to the nearest degree). [[0]]

Express the slope of the ramp as a percentage. [[1]]

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A homeowner is paving a new driveway that needs to ascend 2 feet from the street to the garage. With a desired slope of 1/6 for ease of access.

How long will the driveway be from the street to the garage?

[[0]]

A 4 km section of the Trans-Canada Highway (Hwy 1) through the Fraser Valley has a constant grade of 2%. Calculate the change in elevation (in meters) for vehicles traveling this section of the highway.

[[0]]

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "4000*0.02", "maxValue": "4000*0.02", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Trigonometry", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "K's copy of Trigonometry: Right angled: Find approx side lengths", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [["question-resources/undefined_YwBJcjH", "/srv/numbas/media/question-resources/undefined_YwBJcjH"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "K W", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3194/"}], "tags": ["epphys", "JSXgraph", "Jsxgraph", "jsxgraph", "triangle", "Triangle", "trig", "Trigonometry", "trigonometry"], "metadata": {"description": "

A right-angled triangle is displayed either pointing left or right with one of the other angles and one of the sides given. Use SOH CAH TOA to find the side indicated with an x.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "

Based on the sides that we have and are interested in we use

$\\sin \\theta = \\dfrac{\\text{opposite}}{\\text{hypotenuse}}$ $\\cos \\theta = \\dfrac{\\text{adjacent}}{\\text{hypotenuse}}$ $\\tan \\theta = \\dfrac{\\text{opposite}}{\\text{adjacent}}$

and substitute in the values that we have

$\\sin \\var{anglelist[0]}^\\circ = \\dfrac{\\var{v}}{\\var{d}}$. $\\cos \\var{anglelist[0]}^\\circ = \\dfrac{\\var{h}}{\\var{d}}$. $\\tan \\var{anglelist[0]}^\\circ= \\dfrac{\\var{v}}{\\var{h}}$. $\\sin \\var{anglelist[0]}^\\circ = \\dfrac{\\var{h}}{\\var{d}}$. $\\cos \\var{anglelist[0]}^\\circ = \\dfrac{\\var{v}}{\\var{d}}$. $\\tan \\var{anglelist[0]}^\\circ= \\dfrac{\\var{h}}{\\var{v}}$.

To solve this equation for $x$ we multiply both sides of the equation by the denominator. To solve this equation for $x$ we multiply both sides of the equation by the denominator and then divide both sides of the equation by the trig term.

$x=\\dfrac{\\var{h}}{\\cos \\var{anglelist[0]}^\\circ}$ $x=\\var{d}\\cos \\var{anglelist[0]}^\\circ$ $x=\\dfrac{\\var{v}}{\\sin \\var{anglelist[0]}^\\circ}$ $x=\\dfrac{\\var{v}}{\\tan \\var{anglelist[0]}^\\circ}$ $x=\\var{d}\\sin \\var{anglelist[0]}^\\circ$ $x=\\var{h}\\tan \\var{anglelist[0]}^\\circ$

$x=\\dfrac{\\var{h}}{\\sin \\var{anglelist[0]}^\\circ}$ $x=\\var{d}\\sin \\var{anglelist[0]}^\\circ$ $x=\\dfrac{\\var{v}}{\\cos \\var{anglelist[0]}^\\circ}$ $x=\\var{v}\\tan \\var{anglelist[0]}^\\circ$ $x=\\var{d}\\cos \\var{anglelist[0]}^\\circ$ $x=\\dfrac{\\var{h}}{\\tan \\var{anglelist[0]}^\\circ}$

A calculator (in degrees mode) evaluates this as $\\var{ans}\\ldots$ which we round to one decimal place as $\\var{precround(ans,1)}$

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"deltax": {"name": "deltax", "group": "Ungrouped variables", "definition": "precround(-12+2*triples[1]/triples[0],4)", "description": "", "templateType": "anything", "can_override": false}, "thetaans": {"name": "thetaans", "group": "Ungrouped variables", "definition": "if(vec1=[0,1,2], h/cos(rsang),\nif(vec1=[0,2,1], d*cos(rsang),\nif(vec1=[1,0,2], v/sin(rsang),\nif(vec1=[1,2,0], v/tan(rsang),\nif(vec1=[2,0,1], d*sin(rsang),\nif(vec1=[2,1,0], h*tan(rsang),\n'error'))))))", "description": "

answer using theta (lower angle in diagram)

", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "if(anglelist[1]=3, thetaans, phians)", "description": "

I think I just calculated the answer two different ways

", "templateType": "anything", "can_override": false}, "display_angles1": {"name": "display_angles1", "group": "Ungrouped variables", "definition": "display_angles[1]", "description": "", "templateType": "anything", "can_override": false}, "rsang": {"name": "rsang", "group": "Ungrouped variables", "definition": "smallest_angle*pi/180", "description": "

radians smallest angle

", "templateType": "anything", "can_override": false}, "display_angles": {"name": "display_angles", "group": "Ungrouped variables", "definition": "if(anglelist[1]=3,[smallest_angle,''],['',complement])", "description": "

used in jsxgraph

", "templateType": "anything", "can_override": false}, "display_angles0": {"name": "display_angles0", "group": "Ungrouped variables", "definition": "display_angles[0]", "description": "", "templateType": "anything", "can_override": false}, "vec1": {"name": "vec1", "group": "Ungrouped variables", "definition": "shuffle([0,1,2])", "description": "

shuffles which edge is shortest

", "templateType": "anything", "can_override": false}, "triples": {"name": "triples", "group": "Ungrouped variables", "definition": "random([[3, 4, 5], [5, 12, 13], [7, 24, 25], [8, 15, 17], [9, 40, 41], [11, 60, 61], [12, 35, 37], [16, 63, 65], [20, 21, 29], [20, 99, 101], [24, 143, 145], [28, 45, 53], [33, 56, 65], [36, 77, 85], [39, 80, 89], [44, 117, 125], [48, 55, 73], [51, 140, 149], [52, 165, 173], [57, 176, 185], [60, 91, 109], [60, 221, 229], [65, 72, 97], [68, 285, 293], [69, 260, 269], [75, 308, 317], [76, 357, 365], [84, 187, 205], [84, 437, 445], [85, 132, 157], [87, 416, 425], [88, 105, 137], [92, 525, 533], [93, 476, 485], [95, 168, 193], [96, 247, 265], [100, 621, 629], [104, 153, 185], [105, 208, 233], [105, 608, 617], [111, 680, 689], [115, 252, 277], [119, 120, 169], [120, 209, 241], [120, 391, 409], [132, 475, 493], [133, 156, 205], [135, 352, 377], [136, 273, 305], [140, 171, 221], [145, 408, 433], [152, 345, 377], [155, 468, 493], [156, 667, 685], [160, 231, 281], [161, 240, 289], [165, 532, 557], [168, 425, 457], [168, 775, 793], [175, 288, 337], [180, 299, 349], [184, 513, 545], [185, 672, 697], [189, 340, 389], [195, 748, 773], [200, 609, 641], [203, 396, 445], [204, 253, 325], [205, 828, 853], [207, 224, 305], [215, 912, 937], [216, 713, 745], [217, 456, 505], [220, 459, 509], [225, 272, 353], [228, 325, 397], [231, 520, 569], [232, 825, 857], [240, 551, 601], [248, 945, 977], [252, 275, 373], [259, 660, 709], [260, 651, 701], [261, 380, 461], [273, 736, 785], [276, 493, 565], [279, 440, 521], [280, 351, 449], [280, 759, 809], [287, 816, 865], [297, 304, 425], [300, 589, 661], [301, 900, 949], [308, 435, 533], [315, 572, 653], [319, 360, 481], [333, 644, 725], [336, 377, 505], [336, 527, 625], [341, 420, 541], [348, 805, 877], [364, 627, 725], [368, 465, 593], [369, 800, 881], [372, 925, 997], [385, 552, 673], [387, 884, 965], [396, 403, 565], [400, 561, 689], [407, 624, 745], [420, 851, 949], [429, 460, 629], [429, 700, 821], [432, 665, 793], [451, 780, 901], [455, 528, 697], [464, 777, 905], [468, 595, 757], [473, 864, 985], [481, 600, 769], [504, 703, 865], [533, 756, 925], [540, 629, 829], [555, 572, 797], [580, 741, 941], [615, 728, 953], [616, 663, 905], [696, 697, 985]])\n", "description": "

Some the following were too skinny and so were removed.

use https://www.mathsisfun.com/numbers/pythagorean-triples.html

random([[3,4,5], [5,12,13], [7,24,25], [8,15,17], [9,40,41],
[11,60,61], [12,35,37], [13,84,85], [15,112,113], [16,63,65],
[19,180,181], [20,21,29], [20,99,101],
[23,264,265], [24,143,145], [25,312,313], [27,364,365], [28,45,53],
[28,195,197], [31,480,481], [32,255,257], [33,56,65],
[33,544,545], [35,612,613], [36,77,85], [36,323,325], [37,684,685],
[39,80,89], [40,399,401], [41,840,841], [43,924,925],
[44,117,125], [44,483,485], [48,55,73], [48,575,577], [51,140,149],
[52,165,173], [52,675,677], [56,783,785], [57,176,185], [60,91,109],
[60,221,229], [60,899,901], [65,72,97], [68,285,293], [69,260,269],
[75,308,317], [76,357,365], [84,187,205], [84,437,445], [85,132,157],
[87,416,425], [88,105,137], [92,525,533], [93,476,485], [95,168,193],
[96,247,265], [100,621,629], [104,153,185], [105,208,233], [105,608,617],
[108,725,733], [111,680,689], [115,252,277], [116,837,845], [119,120,169],
[120,209,241], [120,391,409], [123,836,845], [129,920,929],
[132,475,493], [133,156,205], [135,352,377], [136,273,305], [140,171,221],
[145,408,433], [152,345,377], [155,468,493], [156,667,685], [160,231,281],
[161,240,289], [165,532,557], [168,425,457], [168,775,793], [175,288,337],
[180,299,349], [184,513,545], [185,672,697], [189,340,389], [195,748,773],
[200,609,641], [203,396,445], [204,253,325], [205,828,853], [207,224,305],
[215,912,937], [216,713,745], [217,456,505], [220,459,509], [225,272,353],
[228,325,397], [231,520,569], [232,825,857], [240,551,601], [248,945,977],
[252,275,373], [259,660,709], [260,651,701], [261,380,461], [273,736,785],
[276,493,565], [279,440,521], [280,351,449], [280,759,809], [287,816,865],
[297,304,425], [300,589,661], [301,900,949], [308,435,533], [315,572,653],
[319,360,481], [333,644,725], [336,377,505], [336,527,625], [341,420,541],
[348,805,877], [364,627,725], [368,465,593], [369,800,881], [372,925,997],
[385,552,673], [387,884,965], [396,403,565], [400,561,689], [407,624,745],
[420,851,949], [429,460,629], [429,700,821], [432,665,793], [451,780,901],
[455,528,697], [464,777,905], [468,595,757], [473,864,985], [481,600,769],
[504,703,865], [533,756,925], [540,629,829], [555,572,797], [580,741,941],
[615,728,953], [616,663,905], [696,697,985]])

", "templateType": "anything", "can_override": false}, "tritop": {"name": "tritop", "group": "Ungrouped variables", "definition": "precround(triples[0]*scale,4)/2", "description": "

top of triangle for jsxgraph, keeping same ratios.

", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "if(vec1[2]=1,triples[2],if(vec1[2]=0,'','$x$'))", "description": "

diagonal length in triangle

so always integer and scale by k for more randomness.

", "templateType": "anything", "can_override": false}, "anglelist": {"name": "anglelist", "group": "Ungrouped variables", "definition": "random([smallest_angle,3,'$\\\\theta$'],[complement,4,'$\\\\phi$'])", "description": "

[precround(180*arctan(triples[0]/triples[1])/pi,0),90-precround(180*arctan(triples[0]/triples[1])/pi,0)]

", "templateType": "anything", "can_override": false}, "smallest_angle": {"name": "smallest_angle", "group": "Ungrouped variables", "definition": "precround(180*arctan(triples[0]/triples[1])/pi,0)", "description": "", "templateType": "anything", "can_override": false}, "phians": {"name": "phians", "group": "Ungrouped variables", "definition": "if(vec1=[0,1,2], h/sin(rcang),\nif(vec1=[0,2,1], d*sin(rcang),\nif(vec1=[1,0,2], v/cos(rcang),\nif(vec1=[1,2,0], v*tan(rcang),\nif(vec1=[2,0,1], d*cos(rcang),\nif(vec1=[2,1,0], h/tan(rcang),\n'error'))))))", "description": "

ans using phi (upper angle in diagram)

", "templateType": "anything", "can_override": false}, "scale": {"name": "scale", "group": "Ungrouped variables", "definition": "24/triples[1]", "description": "", "templateType": "anything", "can_override": false}, "rcang": {"name": "rcang", "group": "Ungrouped variables", "definition": "complement*pi/180", "description": "

radians complement angle

", "templateType": "anything", "can_override": false}, "switcharoo": {"name": "switcharoo", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "

determines which orientation the triangle is displayed as

", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "if(vec1[1]=1,triples[1],if(vec1[1]=0,'','$x$'))", "description": "

horizontal length in triangle

", "templateType": "anything", "can_override": false}, "complement": {"name": "complement", "group": "Ungrouped variables", "definition": "90-smallest_angle", "description": "", "templateType": "anything", "can_override": false}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "if(vec1[0]=1,triples[0],if(vec1[0]=0,'','$x$'))", "description": "

vertical length in triangle

", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["triples", "vec1", "v", "h", "d", "scale", "tritop", "deltax", "switcharoo", "smallest_angle", "complement", "anglelist", "display_angles", "display_angles0", "display_angles1", "rsang", "rcang", "ans", "thetaans", "phians"], "variable_groups": [], "functions": {"otherway": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-17,17,14,-14],grid:false,axis:false});\nvar board = div.board;\n\n//Doesn't look like you need this\nJXG.Options.text.useMathJax = true;\n\n// get the height of the triangle\nTT = Numbas.jme.unwrapValue(scope.variables.tritop);\ndx = Numbas.jme.unwrapValue(scope.variables.deltax);\nh = Numbas.jme.unwrapValue(scope.variables.h);\nv = Numbas.jme.unwrapValue(scope.variables.v);\nd = Numbas.jme.unwrapValue(scope.variables.d);\ntheta = Numbas.jme.unwrapValue(scope.variables.display_angles0);\nphi = Numbas.jme.unwrapValue(scope.variables.display_angles1);\n\n// create the horizontal line\nvar hor = board.create('line',[[-12,-TT],[12,-TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the vertical line\nvar vert = board.create('line',[[-12,-TT],[-12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the diagonal line\nvar vert = board.create('line',[[12,-TT],[-12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the box for right angle\nboard.create('line',[[(-12+0.1*TT),-TT],[(-12+0.1*TT),-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\nboard.create('line',[[(-12+0.1*TT),-TT*0.9],[-12,-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//label the angle theta\nif (theta == '') {\n} else {\nboard.create('text',[5.5,-4*TT/5,\n function() { \n return theta + \"\\u00B0\";\n }], {fontSize:20,fixed: true});\n}\n\n//label the angle phi\nif (phi == '') {\n} else {\nboard.create('text',[-11.5,3*TT/5,\n function() { \n return phi + \"\\u00B0\";\n }], {fontSize:20,fixed: true});\n}\n\n//display the side lengths\nvar vtext= board.create('text',[-15,0,v], {fontSize:20,fixed: true});\nvar htext= board.create('text',[-2,-TT-1,h], {fontSize:20,fixed: true});\nvar dtext= board.create('text',[-2,TT/2+0.3,d], {fontSize:20,fixed: true});\n\n//can't figure out how to rotate text. http://jsxgraph.uni-bayreuth.de/wiki/index.php/Texts_and_Transformations suggests the following\n//var tRot = board.create('transform', [Math.PI/2, 13,0], {type:'rotate'}); \n//tRot.bindTo(vtext);\n\n\n\n\nreturn div;\n\n"}, "triangle": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-13,13,17,-17],grid:false,axis:false});\nvar board = div.board;\n\n//Doesn't look like you need this\nJXG.Options.text.useMathJax = true;\n\n// get the height of the triangle\nTT = Numbas.jme.unwrapValue(scope.variables.tritop);\ndx = Numbas.jme.unwrapValue(scope.variables.deltax);\nh = Numbas.jme.unwrapValue(scope.variables.h);\nv = Numbas.jme.unwrapValue(scope.variables.v);\nd = Numbas.jme.unwrapValue(scope.variables.d);\ntheta = Numbas.jme.unwrapValue(scope.variables.display_angles0);\nphi = Numbas.jme.unwrapValue(scope.variables.display_angles1);\n\n// create the horizontal line\nvar hor = board.create('line',[[-12,-TT],[12,-TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the vertical line\nvar vert = board.create('line',[[12,-TT],[12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the diagonal line\nvar vert = board.create('line',[[-12,-TT],[12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the box for right angle\nboard.create('line',[[(12-0.1*TT),-TT],[(12-0.1*TT),-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\nboard.create('line',[[(12-0.1*TT),-TT*0.9],[12,-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//label the angle theta\nif (theta == '') {\n} else {\nboard.create('text',[-7.2,-4*TT/5,\n function() { \n return theta + \"\\u00B0\";\n }], {fontSize:20,fixed: true});\n}\n\n//label the angle phi\nif (phi == ''){\n} else {\n board.create('text',[9.6,3*TT/5,\n function() { \n return phi + \"\\u00B0\";\n }], {fontSize:20,fixed: true});\n}\n \n//display the side lengths\nvar vtext= board.create('text',[12.5,0,v], {fontSize:20,fixed: true});\nvar htext= board.create('text',[0,-TT-1,h], {fontSize:20,fixed: true});\nvar dtext= board.create('text',[0,TT/2+0.3,d], {fontSize:20,fixed: true});\n\n//can't figure out how to rotate text. http://jsxgraph.uni-bayreuth.de/wiki/index.php/Texts_and_Transformations suggests the following\n//var tRot = board.create('transform', [Math.PI/2, 13,0], {type:'rotate'}); \n//tRot.bindTo(vtext);\n\n\n\n\nreturn div;\n\n"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Given the triangle described below, the value of $x$ is [[0]] to 1 decimal place.

{if(switcharoo=0,triangle(),otherway())}

You have not given your answer to the correct precision.

", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "K's copy of Trigonometry: Right angled: Finding trig ratios", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [["question-resources/undefined_YwBJcjH", "/srv/numbas/media/question-resources/undefined_YwBJcjH"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "K W", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3194/"}], "tags": ["epphys", "JSXgraph", "Jsxgraph", "jsxgraph", "trig", "Trigonometry", "trigonometry"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"anglelist": {"name": "anglelist", "group": "Ungrouped variables", "definition": "random(['$\\\\theta$',3],['$\\\\phi$',4])", "description": "", "templateType": "anything", "can_override": false}, "ans1num": {"name": "ans1num", "group": "Ungrouped variables", "definition": "if((anglelist[1]=3 and ratio[1]=0) or (anglelist[1]=4 and ratio[1]=1),v,\n if((anglelist[1]=3 and ratio[1]=1) or (anglelist[1]=4 and ratio[1]=0),h,\n if(anglelist[1]=3 and ratio[1]=2 ,v,\n if(anglelist[1]=4 and ratio[1]=2 ,h,'error'))))", "description": "", "templateType": "anything", "can_override": false}, "scale": {"name": "scale", "group": "Ungrouped variables", "definition": "24/h", "description": "", "templateType": "anything", "can_override": false}, "triples": {"name": "triples", "group": "Ungrouped variables", "definition": "random([[3, 4, 5], [5, 12, 13], [7, 24, 25], [8, 15, 17], [9, 40, 41], [11, 60, 61], [12, 35, 37], [16, 63, 65], [20, 21, 29], [20, 99, 101], [24, 143, 145], [28, 45, 53], [33, 56, 65], [36, 77, 85], [39, 80, 89], [44, 117, 125], [48, 55, 73], [51, 140, 149], [52, 165, 173], [57, 176, 185], [60, 91, 109], [60, 221, 229], [65, 72, 97], [68, 285, 293], [69, 260, 269], [75, 308, 317], [76, 357, 365], [84, 187, 205], [84, 437, 445], [85, 132, 157], [87, 416, 425], [88, 105, 137], [92, 525, 533], [93, 476, 485], [95, 168, 193], [96, 247, 265], [100, 621, 629], [104, 153, 185], [105, 208, 233], [105, 608, 617], [111, 680, 689], [115, 252, 277], [119, 120, 169], [120, 209, 241], [120, 391, 409], [132, 475, 493], [133, 156, 205], [135, 352, 377], [136, 273, 305], [140, 171, 221], [145, 408, 433], [152, 345, 377], [155, 468, 493], [156, 667, 685], [160, 231, 281], [161, 240, 289], [165, 532, 557], [168, 425, 457], [168, 775, 793], [175, 288, 337], [180, 299, 349], [184, 513, 545], [185, 672, 697], [189, 340, 389], [195, 748, 773], [200, 609, 641], [203, 396, 445], [204, 253, 325], [205, 828, 853], [207, 224, 305], [215, 912, 937], [216, 713, 745], [217, 456, 505], [220, 459, 509], [225, 272, 353], [228, 325, 397], [231, 520, 569], [232, 825, 857], [240, 551, 601], [248, 945, 977], [252, 275, 373], [259, 660, 709], [260, 651, 701], [261, 380, 461], [273, 736, 785], [276, 493, 565], [279, 440, 521], [280, 351, 449], [280, 759, 809], [287, 816, 865], [297, 304, 425], [300, 589, 661], [301, 900, 949], [308, 435, 533], [315, 572, 653], [319, 360, 481], [333, 644, 725], [336, 377, 505], [336, 527, 625], [341, 420, 541], [348, 805, 877], [364, 627, 725], [368, 465, 593], [369, 800, 881], [372, 925, 997], [385, 552, 673], [387, 884, 965], [396, 403, 565], [400, 561, 689], [407, 624, 745], [420, 851, 949], [429, 460, 629], [429, 700, 821], [432, 665, 793], [451, 780, 901], [455, 528, 697], [464, 777, 905], [468, 595, 757], [473, 864, 985], [481, 600, 769], [504, 703, 865], [533, 756, 925], [540, 629, 829], [555, 572, 797], [580, 741, 941], [615, 728, 953], [616, 663, 905], [696, 697, 985]])\n", "description": "

Some the following were too skinny and so were removed.

random([[3,4,5], [5,12,13], [7,24,25], [8,15,17], [9,40,41],
[11,60,61], [12,35,37], [13,84,85], [15,112,113], [16,63,65],
[19,180,181], [20,21,29], [20,99,101],
[23,264,265], [24,143,145], [25,312,313], [27,364,365], [28,45,53],
[28,195,197], [31,480,481], [32,255,257], [33,56,65],
[33,544,545], [35,612,613], [36,77,85], [36,323,325], [37,684,685],
[39,80,89], [40,399,401], [41,840,841], [43,924,925],
[44,117,125], [44,483,485], [48,55,73], [48,575,577], [51,140,149],
[52,165,173], [52,675,677], [56,783,785], [57,176,185], [60,91,109],
[60,221,229], [60,899,901], [65,72,97], [68,285,293], [69,260,269],
[75,308,317], [76,357,365], [84,187,205], [84,437,445], [85,132,157],
[87,416,425], [88,105,137], [92,525,533], [93,476,485], [95,168,193],
[96,247,265], [100,621,629], [104,153,185], [105,208,233], [105,608,617],
[108,725,733], [111,680,689], [115,252,277], [116,837,845], [119,120,169],
[120,209,241], [120,391,409], [123,836,845], [129,920,929],
[132,475,493], [133,156,205], [135,352,377], [136,273,305], [140,171,221],
[145,408,433], [152,345,377], [155,468,493], [156,667,685], [160,231,281],
[161,240,289], [165,532,557], [168,425,457], [168,775,793], [175,288,337],
[180,299,349], [184,513,545], [185,672,697], [189,340,389], [195,748,773],
[200,609,641], [203,396,445], [204,253,325], [205,828,853], [207,224,305],
[215,912,937], [216,713,745], [217,456,505], [220,459,509], [225,272,353],
[228,325,397], [231,520,569], [232,825,857], [240,551,601], [248,945,977],
[252,275,373], [259,660,709], [260,651,701], [261,380,461], [273,736,785],
[276,493,565], [279,440,521], [280,351,449], [280,759,809], [287,816,865],
[297,304,425], [300,589,661], [301,900,949], [308,435,533], [315,572,653],
[319,360,481], [333,644,725], [336,377,505], [336,527,625], [341,420,541],
[348,805,877], [364,627,725], [368,465,593], [369,800,881], [372,925,997],
[385,552,673], [387,884,965], [396,403,565], [400,561,689], [407,624,745],
[420,851,949], [429,460,629], [429,700,821], [432,665,793], [451,780,901],
[455,528,697], [464,777,905], [468,595,757], [473,864,985], [481,600,769],
[504,703,865], [533,756,925], [540,629,829], [555,572,797], [580,741,941],
[615,728,953], [616,663,905], [696,697,985]])

", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "triples[2]", "description": "

use https://www.mathsisfun.com/numbers/pythagorean-triples.html

so always integer and scale by k for more randomness.

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top of triangle for jsxgraph, keeping same ratios.

", "templateType": "anything", "can_override": false}, "switcharoo": {"name": "switcharoo", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["triples", "v", "h", "d", "anglelist", "angle", "ratio", "question", "ans1num", "ans1den", "scale", "tritop", "deltax", "switcharoo"], "variable_groups": [], "functions": {"otherway": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-17,17,14,-14],grid:false,axis:false});\nvar board = div.board;\n\n//Doesn't look like you need this\nJXG.Options.text.useMathJax = true;\n\n// get the height of the triangle\nTT = Numbas.jme.unwrapValue(scope.variables.tritop);\ndx = Numbas.jme.unwrapValue(scope.variables.deltax);\nh = Numbas.jme.unwrapValue(scope.variables.h);\nv = Numbas.jme.unwrapValue(scope.variables.v);\nd = Numbas.jme.unwrapValue(scope.variables.d);\n\n\n// create the horizontal line\nvar hor = board.create('line',[[-12,-TT],[12,-TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the vertical line\nvar vert = board.create('line',[[-12,-TT],[-12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the diagonal line\nvar vert = board.create('line',[[12,-TT],[-12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the box for right angle\nboard.create('line',[[(-12+0.1*TT),-TT],[(-12+0.1*TT),-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\nboard.create('line',[[(-12+0.1*TT),-TT*0.9],[-12,-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//these are the guides for angle label\n//var p1 = board.create('point', [-12*6/10, -6*TT/10]);\n//var p2 = board.create('point', [-12*6/10, -TT]);\n//var p3 = board.create('point', [12, 3*TT/5]);\n//var p4 = board.create('point', [12*6/10, 3*TT/5]);\n\n\n//label the angle theta\nboard.create('text',[+6.2,-4*TT/5,\n function() { \n return '$\\\\theta$';\n }], {fontSize:20,fixed: true});\n\n//label the angle phi\nboard.create('text',[-11,3*TT/5,\n function() { \n return '$\\\\phi$';\n }], {fontSize:20,fixed: true});\n\n\n//display the side lengths\nvar vtext= board.create('text',[-16,0,1*v+' m'], {fontSize:20,fixed: true});\nvar htext= board.create('text',[-2,-TT-1,1*h+' m'], {fontSize:20,fixed: true});\nvar dtext= board.create('text',[-2,TT/2+0.3,1*d+' m'], {fontSize:20,fixed: true});\n\n//can't figure out how to rotate text. http://jsxgraph.uni-bayreuth.de/wiki/index.php/Texts_and_Transformations suggests the following\n//var tRot = board.create('transform', [Math.PI/2, 13,0], {type:'rotate'}); \n//tRot.bindTo(vtext);\n\n\n\n\nreturn div;\n\n"}, "triangle": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-13,13,17,-17],grid:false,axis:false});\nvar board = div.board;\n\n//Doesn't look like you need this\nJXG.Options.text.useMathJax = true;\n\n// get the height of the triangle\nTT = Numbas.jme.unwrapValue(scope.variables.tritop);\ndx = Numbas.jme.unwrapValue(scope.variables.deltax);\nh = Numbas.jme.unwrapValue(scope.variables.h);\nv = Numbas.jme.unwrapValue(scope.variables.v);\nd = Numbas.jme.unwrapValue(scope.variables.d);\n\n\n// create the horizontal line\nvar hor = board.create('line',[[-12,-TT],[12,-TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the vertical line\nvar vert = board.create('line',[[12,-TT],[12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the diagonal line\nvar vert = board.create('line',[[-12,-TT],[12,TT/1]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the box for right angle\nboard.create('line',[[(12-0.1*TT),-TT],[(12-0.1*TT),-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\nboard.create('line',[[(12-0.1*TT),-TT*0.9],[12,-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//these are the guides for angle label\n//var p1 = board.create('point', [-12*6/10, -6*TT/10]);\n//var p2 = board.create('point', [-12*6/10, -TT]);\n//var p3 = board.create('point', [12, 3*TT/5]);\n//var p4 = board.create('point', [12*6/10, 3*TT/5]);\n\n\n//label the angle theta\nboard.create('text',[-7.2,-4*TT/5,\n function() { \n return '$\\\\theta$';\n }], {fontSize:20,fixed: true});\n\n//label the angle phi\nboard.create('text',[9.6,3*TT/5,\n function() { \n return '$\\\\phi$';\n }], {fontSize:20,fixed: true});\n\n\n//display the side lengths\nvar vtext= board.create('text',[12.5,0,v+' m'], {fontSize:20,fixed: true});\nvar htext= board.create('text',[0,-TT-1,h+' m'], {fontSize:20,fixed: true});\nvar dtext= board.create('text',[0,TT/2+0.3,d+' m'], {fontSize:20,fixed: true});\n\n//can't figure out how to rotate text. http://jsxgraph.uni-bayreuth.de/wiki/index.php/Texts_and_Transformations suggests the following\n//var tRot = board.create('transform', [Math.PI/2, 13,0], {type:'rotate'}); \n//tRot.bindTo(vtext);\n\n\n\n\nreturn div;\n\n"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

{if(switcharoo=0,triangle(),otherway())}

Given the triangle described above, the value of {question} is [[0]].

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{t1}

What was the highest total sales for one type?

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What was the biggest increase in sales for one type?

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{t1}

Which flavors are <25% of peoples favorite?

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Which flavor is the most popular?

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{t1}

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What was the first month were Toronto's average temperature was below 0?

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What month was hottest in Vancouver?

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What was Toronto's coldest month?

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Each day, Jack records the hours he spent going for walks. Here are the results after 7 days.

$3.5, 2, 1.5, 1.5, 3, 1.5, 2$

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What is the mean of this data set?

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What is the mode of this data set?

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The average rent for a survey of 1500 victoria residents was 2150$ a month.

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Which option below describes the average rent in the survey?

Which option below describes the residents of victoria in the survey?

Which option below describes the 1500 people who answered the survey?

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Solve the following slope related question.

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A hill has a slope of $\\frac{\\var{rise}}{\\var{run}}$ and rises a distance of {meters} m. Given the available information, determine the hill's horizontal distance.

Answer: [[0]]

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