// Numbas version: exam_results_page_options {"name": "radial survey", "extensions": [], "custom_part_types": [], "resources": [["question-resources/radial_survey_1.png", "/srv/numbas/media/question-resources/radial_survey_1.png"], ["question-resources/radial_survey_2.png", "/srv/numbas/media/question-resources/radial_survey_2.png"], ["question-resources/radial_survey_3.png", "/srv/numbas/media/question-resources/radial_survey_3.png"], ["question-resources/radial_survey_4.png", "/srv/numbas/media/question-resources/radial_survey_4.png"], ["question-resources/radial_survey_5.png", "/srv/numbas/media/question-resources/radial_survey_5.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "radial survey", "tags": [], "metadata": {"description": "

Students are shown one of 5 different radial surveys and asked to answer one of 8 questions about it.

2 questions ask for the length of a side.

2 questions ask for the value of an angle.

2 questions ask for the area of a triangle.

1 question asks for the land area, and 1 question asks for the land perimeter.

The values are hard coded. In cases where your choice of precision affects your answer, a range of answers is accepted, and a comment is made in the advice to that effect.

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

The diagram from a radial survey is shown.

{image('resources/question-resources/'+image)}

not to scale

", "advice": "

{advice}

", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"question_array": {"name": "question_array", "group": "Ungrouped variables", "definition": "[\"What is the distance from B to C, in {units}?
Give your answer rounded to 1 decimal place.\",\n \"What is the distance from D to B, in {units}?
Give your answer rounded to 1 decimal place.\",\n \"What is the area of the land inside triangle OBC, in {units}\\$^2\\$?
{if(image_no=3,'Give your answer rounded to 2 decimal places','Give your answer rounded to the nearest whole number.')}\",\n \"What is the area of the land inside triangle OBD, in {units}\\$^2\\$?
{if(image_no=3,'Give your answer rounded to 2 decimal places','Give your answer rounded to the nearest whole number.')}\",\n \"What is the area of the land, in {units}\\$^2\\$?
{if(image_no=3,'Give your answer rounded to 1 decimal place','Give your answer rounded to the nearest whole number.')}\",\n \"What is the perimeter of the land, in {units}?
{if(image_no=3,'Give your answer rounded to 1 decimal place','Give your answer rounded to the nearest whole number.')}\",\n \"What is the value of angle OBD in degrees?
Give your answer rounded to the nearest degree.\",\n \"What is the value of angle ODB in degrees?
Give your answer rounded to the nearest degree.\"\n]", "description": "", "templateType": "anything", "can_override": false}, "question_no": {"name": "question_no", "group": "Ungrouped variables", "definition": "random(0..7)", "description": "", "templateType": "anything", "can_override": false}, "question": {"name": "question", "group": "Ungrouped variables", "definition": "question_array[question_no]", "description": "", "templateType": "anything", "can_override": false}, "image_no": {"name": "image_no", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "image": {"name": "image", "group": "Ungrouped variables", "definition": "\"radial_survey_\"+string(image_no)+\".png\"", "description": "", "templateType": "anything", "can_override": false}, "answer_array": {"name": "answer_array", "group": "Ungrouped variables", "definition": "[\n [719.8, 952.9, 106712, 42368, 218435, 2280, 9, 13\n ],\n [73.4, 121.8, 1969, 972, 4394, 349, 17, 13\n ],\n [3.5, 3.5, 1.73, 1.73, 5.1, 10.4, 30.0, 30.0\n ],\n [580.0, 675.6, 84000, 65818, 306181, 2248, 29,31\n ],\n [323.8, 503.5, 22630, 46203, 234836, 2153, 75,22\n ]\n ]", "description": "

answers to each question for each image

answer[image][question]

[\"What is the distance from B to C?\",
\"What is the distance from D to B?\",
\"What is the area of the land enclosed by the centre point, B and C?\",
\"What is the area of land enclosed by the centre point, B and D?\"
\"What is the area of the land?\",
\"What is the perimeter of the land?\",
]

", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "answer_array[image_no-1][question_no]", "description": "", "templateType": "anything", "can_override": false}, "advice_array": {"name": "advice_array", "group": "Ungrouped variables", "definition": "[\n [\"Use the cos rule: \\$(BC)^2 = 580^2 + 370^2 - 2 \\\\times 580 \\\\times 370 \\\\times \\\\cos(96\u00b0)\\$,
so \\$ BC = \\\\var{answer}\\$ m\",\n \"Use the cos rule: \\$(BD)^2 = 580^2 + 390^2 - 2 \\\\times 580 \\\\times 390 \\\\times \\\\cos(158\u00b0)\\$,
so \\$ BD = \\\\var{answer}\\$ m\",\n \"Calculate the area: \\$A = 0.5 \\\\times 580 \\\\times 370 \\\\times \\\\sin(96\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n \"Calculate the area: \\$A = 0.5 \\\\times 580 \\\\times 390 \\\\times \\\\sin(158\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n \"Calculate the area of each triangle and add them: \" +\n \"
\\$A = 0.5 \\\\times 580 \\\\times 370 \\\\times \\\\sin(96\u00b0) + \\$\" +\n \"\\$0.5 \\\\times 580 \\\\times 390 \\\\times \\\\sin(158\u00b0) + \\$\" +\n \"\\$0.5 \\\\times 370 \\\\times 390 \\\\times \\\\sin(106\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n \"Calculate the length of each side using the cosine rule, and add them: \" +\n \"
Perimeter = \\$\\\\sqrt{(580^2 + 370^2 - 2 \\\\times 580 \\\\times 370 \\\\times \\\\cos(96\u00b0))} +\\$\" +\n \"\\$\\\\sqrt{(580^2 + 390^2 - 2 \\\\times 580 \\\\times 390 \\\\times \\\\cos(158\u00b0))} +\\$\" + \n \"\\$\\\\sqrt{(370^2 + 390^2 - 2 \\\\times 370 \\\\times 390 \\\\times \\\\cos(106\u00b0))} = \\\\var{answer} \\$ m\",\n \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n \"
\\$(BD)^2 = 580^2 + 390^2 - 2 \\\\times 580 \\\\times 390 \\\\times \\\\cos(158\u00b0)\\$,
so \\$BD = \\\\var{precround(cosrule_side(580,390,radians(158)),1)}\\$\" +\n \"
\\$\\\\frac\\{390\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(158\u00b0)\\}\\$,
so Angle OBD $= \\\\var{answer}\\$\u00b0\",\n \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n \"
\\$(BD)^2 = 580^2 + 390^2 - 2 \\\\times 580 \\\\times 390 \\\\times \\\\cos(158\u00b0)\\$,
so \\$BD = \\\\var{precround(cosrule_side(580,390,radians(158)),1)}\\$\" +\n \"
\\$\\\\frac\\{580\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(158\u00b0)\\}\\$,
so Angle OBD $= \\\\var{answer}\\$\u00b0\"\n ],\n [\"Use the cos rule: \\$(BC)^2 = 54^2 + 86^2 - 2 \\\\times 54 \\\\times 86 \\\\times \\\\cos(58\u00b0)\\$,
so \\$ BC = \\\\var{answer}\\$ m\",\n \"Use the cos rule: \\$(BD)^2 = 72^2 + 54^2 - 2 \\\\times 72 \\\\times 54 \\\\times \\\\cos(150\u00b0)\\$,
so \\$ BD = \\\\var{answer}\\$ m\",\n \"Calculate the area: \\$A = 0.5 \\\\times 54 \\\\times 86 \\\\times \\\\sin(58\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n \"Calculate the area: \\$A = 0.5 \\\\times 54 \\\\times 72 \\\\times \\\\sin(150\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n \"Calculate the area of each triangle and add them: \" +\n \"
\\$A = 0.5 \\\\times 54 \\\\times 86 \\\\times \\\\sin(58\u00b0) + \\$\" +\n \"\\$0.5 \\\\times 54 \\\\times 72 \\\\times \\\\sin(150\u00b0) + \\$\" +\n \"\\$0.5 \\\\times 86 \\\\times 72 \\\\times \\\\sin(152\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\"+\n \"
Your answer might have varied slightly (e.g. you might have got 4394 or 4395 for your answer), due to rounding.\",\n \"Calculate the length of each side using the cosine rule, and add them: \" +\n \"
Perimeter = \\$\\\\sqrt{(54^2 + 86^2 - 2 \\\\times 54 \\\\times 86 \\\\times \\\\cos(58\u00b0))} +\\$\" +\n \"\\$\\\\sqrt{(72^2 + 54^2 - 2 \\\\times 72 \\\\times 54 \\\\times \\\\cos(150\u00b0))} + \\$\" + \n \"\\$\\\\sqrt{(72^2 + 86^2 - 2 \\\\times 72 \\\\times 86 \\\\times \\\\cos(152\u00b0))} = \\\\var{answer} \\$ m\",\n \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n \"
\\$(BD)^2 = 72^2 + 54^2 - 2 \\\\times 72 \\\\times 54 \\\\times \\\\cos(150\u00b0)\\$,
so \\$BD = \\\\var{precround(cosrule_side(72,54,radians(150)),1)}\\$\" +\n \"
\\$\\\\frac\\{72\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(150\u00b0)\\}\\$,
so Angle OBD $= \\\\var{answer}\\\u00b0$\",\n \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n \"
\\$(BD)^2 = 72^2 + 54^2 - 2 \\\\times 72 \\\\times 54 \\\\times \\\\cos(150\u00b0)\\$,
so \\$BD = \\\\var{precround(cosrule_side(72,54,radians(150)),1)}\\$\" +\n \"
\\$\\\\frac\\{54\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(150\u00b0)\\}\\$,
so Angle OBD $= \\\\var{answer}\\\u00b0$\"\n ],\n [\"Use the cos rule: \\$(BC)^2 = 2^2 + 2^2 - 2 \\\\times 2 \\\\times 2 \\\\times \\\\cos(120\u00b0)\\$,
so \\$ BC = \\\\var{answer}\\$ km\",\n \"Use the cos rule: \\$(BD)^2 = 2^2 + 2^2 - 2 \\\\times 2 \\\\times 2 \\\\times \\\\cos(120\u00b0)\\$,
so \\$ BD = \\\\var{answer}\\$ km\",\n \"Calculate the area: \\$A = 0.5 \\\\times 2 \\\\times 2 \\\\times \\\\sin(120\u00b0) = \\\\var{answer}\\$ km\\$^2\\$\",\n \"Calculate the area: \\$A = 0.5 \\\\times 2 \\\\times 2 \\\\times \\\\sin(120\u00b0) = \\\\var{answer}\\$ km\\$^2\\$\",\n \"Calculate the area of each triangle and add them: \" +\n \"
\\$A = 3 \\\\times 0.5 \\\\times 2 \\\\times 2 \\\\times \\\\sin(120\u00b0) = \\\\var{answer}\\$ km\\$^2\\$\",\n \"Calculate the length of each side using the cosine rule, and add them: \" +\n \"
Perimeter \\$= 3 \\\\times \\\\sqrt{(2^2 + 2^2 - 2 \\\\times 2 \\\\times 2 \\\\times \\\\cos(120\u00b0))} = \\\\var{answer} \\$ km\"+\n \"
Your answer might have varied slightly (e.g. you might have got 10.4 or 10.5 for your answer), due to rounding.\",\n \"Since triangle OBD is isosceles, angle OBD = \\$\\\\frac\\{1\\}\\{2\\} (180\u00b0 - 120\u00b0) = 30\u00b0 \\$\",\n \"Since triangle OBD is isosceles, angle OBD = \\$\\\\frac\\{1\\}\\{2\\} (180\u00b0 - 120\u00b0) = 30\u00b0 \\$\"\n ],\n [\"Use the cos rule: \\$(BC)^2 = 400^2 + 420^2 - 2 \\\\times 400 \\\\times 420 \\\\times \\\\cos(90\u00b0)\\$,
so \\$ BC = \\\\var{answer}\\$ m\",\n \"Use the cos rule: \\$(BD)^2 = 380^2 + 400^2 - 2 \\\\times 380 \\\\times 400 \\\\times \\\\cos(120\u00b0)\\$,
so \\$ BD = \\\\var{answer}\\$ m\",\n \"Calculate the area: \\$A = 0.5 \\\\times 400 \\\\times 420 \\\\times \\\\sin(90\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n \"Calculate the area: \\$A = 0.5 \\\\times 400 \\\\times 380 \\\\times \\\\sin(120\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n \"Calculate the area of each triangle and add them: \" +\n \"
\\$A = 0.5 \\\\times 400 \\\\times 420 \\\\times \\\\sin(90\u00b0) + \\$\" +\n \"\\$0.5 \\\\times 400 \\\\times 380 \\\\times \\\\sin(120\u00b0) + \\$\" +\n \"\\$0.5 \\\\times 420 \\\\times 430 \\\\times \\\\sin(56\u00b0) + \\$\" + \n \"\\$0.5 \\\\times 430 \\\\times 380 \\\\times \\\\sin(94\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n \"Calculate the length of each side using the cosine rule, and add them: \" +\n \"
Perimeter = \\$\\\\sqrt{(400^2 + 420^2 - 2 \\\\times 400 \\\\times 420 \\\\times \\\\cos(90\u00b0))} + \\$\" +\n \"\\$\\\\sqrt{(380^2 + 400^2 - 2 \\\\times 380 \\\\times 400 \\\\times \\\\cos(120\u00b0))} + \\$\" + \n \"\\$\\\\sqrt{(380^2 + 430^2 - 2 \\\\times 380 \\\\times 430 \\\\times \\\\cos(94\u00b0))} + \\$\" + \n \"\\$\\\\sqrt{(430^2 + 420^2 - 2 \\\\times 430 \\\\times 420 \\\\times \\\\cos(56\u00b0))} = \\\\var{answer} \\$ m\",\n \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n \"
\\$(BD)^2 = 380^2 + 400^2 - 2 \\\\times 380 \\\\times 400 \\\\times \\\\cos(120\u00b0)\\$,
so \\$BD = \\\\var{precround(cosrule_side(380,400,radians(120)),1)}\\$\" +\n \"
\\$\\\\frac\\{380\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(120\u00b0)\\}\\$,
so Angle OBD $= \\\\var{answer} \\$\u00b0\",\n \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n \"
\\$(BD)^2 = 380^2 + 400^2 - 2 \\\\times 380 \\\\times 400 \\\\times \\\\cos(120\u00b0)\\$,
so \\$BD = \\\\var{precround(cosrule_side(380,400,radians(120)),1)}\\$\" +\n \"
\\$\\\\frac\\{400\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(120\u00b0)\\}\\$,
so Angle OBD $= \\\\var{answer} \\$\u00b0\"\n ],\n [\"Use the cos rule: \\$(BC)^2 = 240^2 + 190^2 - 2 \\\\times 240 \\\\times 190 \\\\times \\\\cos(97\u00b0)\\$,
so \\$ BC = \\\\var{answer}\\$ m\",\n \"Use the cos rule: \\$(BD)^2 = 490^2 + 190^2 - 2 \\\\times 490 \\\\times 190 \\\\times \\\\cos(83\u00b0)\\$,
so \\$ BD = \\\\var{answer}\\$ m\",\n \"Calculate the area: \\$A = 0.5 \\\\times 240 \\\\times 190 \\\\times \\\\sin(97\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n \"Calculate the area: \\$A = 0.5 \\\\times 490 \\\\times 190 \\\\times \\\\sin(83\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\",\n \"Calculate the area of each triangle and add them: \" +\n \"
\\$A = 0.5 \\\\times 240 \\\\times 190 \\\\times \\\\sin(97\u00b0) + \\$\" +\n \"\\$0.5 \\\\times 490 \\\\times 190 \\\\times \\\\sin(83\u00b0) + \\$\" +\n \"\\$0.5 \\\\times 240 \\\\times 520 \\\\times \\\\sin(61\u00b0) + \\$\" + \n \"\\$0.5 \\\\times 520 \\\\times 490 \\\\times \\\\sin(119\u00b0) = \\\\var{answer}\\$ m\\$^2\\$\" ,\n \"Calculate the length of each side using the cosine rule, and add them: \" +\n \"
Perimeter = \\$\\\\sqrt{(240^2 + 190^2 - 2 \\\\times 240 \\\\times 190 \\\\times \\\\cos(97\u00b0))} +\\$\" +\n \"\\$\\\\sqrt{(490^2 + 190^2 - 2 \\\\times 490 \\\\times 190 \\\\times \\\\cos(83\u00b0))} +\\$\" + \n \"\\$\\\\sqrt{(490^2 + 520^2 - 2 \\\\times 490 \\\\times 520 \\\\times \\\\cos(119\u00b0))} +\\$\" + \n \"\\$\\\\sqrt{(520^2 + 240^2 - 2 \\\\times 520 \\\\times 240 \\\\times \\\\cos(61\u00b0))} = \\\\var{answer}\\$ m\",\n \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n \"
\\$(BD)^2 = 490^2 + 190^2 - 2 \\\\times 490 \\\\times 190 \\\\times \\\\cos(83\u00b0)\\$,
so \\$BD = \\\\var{precround(cosrule_side(490,190,radians(83)),1)}\\$\" +\n \"
\\$\\\\frac\\{490\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(83\u00b0)\\}\\$,
so Angle OBD $= \\\\var{answer}\\$\u00b0\",\n \"We need to do this in 2 steps: first we need to use the cosine rule to compute the length of side BD. Then we need to use the sine rule to compute angle OBD.\" + \n \"
\\$(BD)^2 = 490^2 + 190^2 - 2 \\\\times 490 \\\\times 190 \\\\times \\\\cos(83\u00b0)\\$,
so \\$BD = \\\\var{precround(cosrule_side(490,190,radians(83)),1)}\\$\" +\n \"
\\$\\\\frac\\{190\\}\\{\\\\angle OBD\\} = \\\\frac\\{BD\\}\\{\\\\cos(83\u00b0)\\}\\$,
so Angle OBD $= \\\\var{answer} \\$\u00b0\"\n ]\n ]", "description": "

worked answers to each question for each image

advice[image][question]

", "templateType": "anything", "can_override": false}, "advice": {"name": "advice", "group": "Ungrouped variables", "definition": "advice_array[image_no-1][question_no]", "description": "", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "Ungrouped variables", "definition": "area(490,190,radians(83))", "description": "", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "if(image_no=3,\"kilometres\",\"metres\")", "description": "", "templateType": "anything", "can_override": false}, "answer_array_max": {"name": "answer_array_max", "group": "Ungrouped variables", "definition": "[\n [719.8, 952.9, 106712, 42368, 218435, 2280, 9, 13\n ],\n [73.4, 121.8, 1969, 972, 4395, 349, 17, 13\n ],\n [3.5, 3.5, 1.73, 1.73, 5.2, 10.5, 30.0, 30.0\n ],\n [580.0, 675.6, 84000, 65818, 306181, 2248, 29,31\n ],\n [323.8, 503.5, 22630, 46203, 234836, 2153, 75,22\n ]\n ]", "description": "", "templateType": "anything", "can_override": false}, "answer_max": {"name": "answer_max", "group": "Ungrouped variables", "definition": "answer_array_max[image_no-1][question_no]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["question_array", "question_no", "question", "image_no", "image", "answer_array", "answer", "answer_array_max", "answer_max", "advice_array", "advice", "test", "units"], "variable_groups": [], "functions": {"cosrule_side": {"parameters": [["a", "number"], ["b", "number"], ["C", "number"]], "type": "number", "language": "javascript", "definition": "tmp=Math.pow(a,2) + Math.pow(b,2) - 2*a*b*Math.cos(C);\ntmp2 = Math.sqrt(tmp);\nreturn tmp2;"}, "area": {"parameters": [["a", "number"], ["b", "number"], ["C", "number"]], "type": "number", "language": "jme", "definition": "precround(0.5 * a * b * sin(C),1)"}, "sinerule_angle": {"parameters": [["a", "number"], ["b", "number"], ["angB", "number"]], "type": "number", "language": "javascript", "definition": "return Math.asin(a*Math.sin(angB)/b)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

{question}

", "minValue": "answer", "maxValue": "answer_max", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}