// Numbas version: finer_feedback_settings
{"name": "MG Two-person compass directions (7)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Compass_Ben_150.png", "/srv/numbas/media/question-resources/Compass_Ben_150.png"], ["question-resources/Compass_Ben_200.png", "/srv/numbas/media/question-resources/Compass_Ben_200.png"], ["question-resources/compass_Isaac_225.png", "/srv/numbas/media/question-resources/compass_Isaac_225.png"], ["question-resources/Compass_Ben_Isaac_250.png", "/srv/numbas/media/question-resources/Compass_Ben_Isaac_250.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "MG Two-person compass directions (7)", "tags": ["LANTITE", "Western Sydney MESH"], "metadata": {"description": "<p>Used for LANTITE preparation (Australia). MG = Measurement &amp; Geometry strand.&nbsp;Two people walk away from a central flagpole, in different directions.&nbsp;The multiple choice question asks for the angle between them. There are seven potential scenarios.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>{name1}, {name2} and {name3} are all standing next to a flagpole.</p>\n<p>{direc1}</p>\n<p>{direc2}</p>\n<p>{name3} turns to look at {name1}. Then {name3} turns in a clockwise direction until&nbsp;{pronoun}&nbsp;is looking at {name2}.&nbsp;</p>", "advice": "<p>The example below shows one way of approaching these kinds of questions. Read it through and see if you can then apply the reasoning to the given problem.</p>\n<p><strong>Sample question:</strong></p>\n<p><em>Isaac,&nbsp;Ben and&nbsp;Madi are all standing next to a flagpole.</em></p>\n<p><em>Isaac&nbsp;walks 25 metres in a southerly direction, then turns and walks 25 metres in a westerly direction, then stops.</em><br/><em>Ben&nbsp;walks&nbsp;10 metres in an easterly direction, then turns and walks 10 metres in a southerly direction, then stops.</em></p>\n<p><em>Madi&nbsp;turns to look at Isaac. Then&nbsp;Madi turns in a clockwise direction until&nbsp;she&nbsp;is looking at Ben.</em></p>\n<p><em>How many degrees did&nbsp;Madi turn through between looking at&nbsp;Isaac and looking at Ben?</em></p>\n<p><strong>Solution:</strong></p>\n<p>Imagine that the flagpole is at the centre of the compass rose below.</p>\n<p>The solid yellow lines show the path that Isaac took - south and then west. Effectively, Isaac has travelled in a south-westerly direction because both sections of his walk were the same length (25 metres each).</p>\n<p><img src=\"resources/question-resources/compass_Isaac_225.png\"/></p>\n<p>The solid red lines on the diagram below show the path that Ben took -&nbsp;east and then south. Effectively, Ben has travelled in a south-easterly direction because both sections of his walk were the same length (10 metres each).</p>\n<p><img src=\"resources/question-resources/Compass_Ben_200.png\"/></p>\n<p>Now imagine that Madi is at the centre of the compass rose. She looks first at Isaac, then turns clockwise to look at Ben (see the curved black arrow). It does not matter that Ben and Isaac travelled different distances. We are interested in the angle between them.</p>\n<p><img src=\"resources/question-resources/Compass_Ben_Isaac_250.png\"/></p>\n<p>How many degrees has she turned through? In this case, she has turned through 3 x 90 degrees.</p>\n<p>Madi turned through 270 degrees between looking at&nbsp;Isaac and looking at Ben.</p>\n<p><sup>Images adapted from&nbsp;<a href=\"https://en.wikipedia.org/wiki/File:Compass_rose_simple.svg\">https://en.wikipedia.org/wiki/File:Compass_rose_simple.svg</a></sup></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "json_decode(safe(\"[\\n{\\n\\\"dir1\\\":\\\"Tim walks 35 metres in a northerly direction, then turns and walks 35 metres in a westerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Mick walks 25 metres in a southerly direction, then turns and walks 25 metres in a westerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Tim\\\",\\n\\\"n2\\\":\\\"Mick\\\",\\n\\\"n3\\\":\\\"Luke\\\",\\n\\\"pnoun\\\":\\\"he\\\",\\n\\\"answer\\\":270,\\n\\\"wrong1\\\":\\\"90\\\",\\n\\\"wrong2\\\":\\\"180\\\",\\n\\\"wrong3\\\":\\\"45\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Angie walks 25 metres in a northerly direction, then turns and walks 25 metres in an easterly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Jake walks 30 metres in a westerly direction, then turns and walks 30 metres in a southerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Angie\\\",\\n\\\"n2\\\":\\\"Jake\\\",\\n\\\"n3\\\":\\\"Liam\\\",\\n\\\"pnoun\\\":\\\"he\\\",\\n\\\"answer\\\":180,\\n\\\"wrong1\\\":\\\"90\\\",\\n\\\"wrong2\\\":\\\"270\\\",\\n\\\"wrong3\\\":\\\"45\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Brad walks 15 metres in an easterly direction, then turns and walks 15 metres in a southerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Subah walks 20 metres in a southerly direction, then turns and walks 20 metres in a westerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Brad\\\",\\n\\\"n2\\\":\\\"Subah\\\",\\n\\\"n3\\\":\\\"Lisa\\\",\\n\\\"pnoun\\\":\\\"she\\\",\\n\\\"answer\\\":90,\\n\\\"wrong1\\\":\\\"180\\\",\\n\\\"wrong2\\\":\\\"270\\\",\\n\\\"wrong3\\\":\\\"135\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Maria walks 20 metres in an easterly direction, then turns and walks 20 metres in a northerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Tony walks 30 metres in a westerly direction, then turns and walks 30 metres in a northerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Maria\\\",\\n\\\"n2\\\":\\\"Tony\\\",\\n\\\"n3\\\":\\\"Lara\\\",\\n\\\"pnoun\\\":\\\"she\\\",\\n\\\"answer\\\":270,\\n\\\"wrong1\\\":\\\"180\\\",\\n\\\"wrong2\\\":\\\"90\\\",\\n\\\"wrong3\\\":\\\"135\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Sue walks 35 metres in an easterly direction, then turns and walks 35 metres in a southerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Mark walks 15 metres in an easterly direction, then turns and walks 15 metres in a northerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Sue\\\",\\n\\\"n2\\\":\\\"Mark\\\",\\n\\\"n3\\\":\\\"Lily\\\",\\n\\\"pnoun\\\":\\\"she\\\",\\n\\\"answer\\\":270,\\n\\\"wrong1\\\":\\\"180\\\",\\n\\\"wrong2\\\":\\\"90\\\",\\n\\\"wrong3\\\":\\\"135\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Will walks 45 metres in a northerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"Hana walks 15 metres in a westerly direction, then turns and walks 15 metres in a southerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Will\\\",\\n\\\"n2\\\":\\\"Hana\\\",\\n\\\"n3\\\":\\\"Li\\\",\\n\\\"pnoun\\\":\\\"she\\\",\\n\\\"answer\\\":225,\\n\\\"wrong1\\\":\\\"180\\\",\\n\\\"wrong2\\\":\\\"90\\\",\\n\\\"wrong3\\\":\\\"135\\\"\\n},\\n{\\n\\\"dir1\\\":\\\"Sara walks 20 metres in a westerly direction, then stops.\\\",\\n\\\"dir2\\\":\\\"John walks 40 metres in a southerly direction, then turns and walks 40 metres in a westerly direction, then stops.\\\",\\n\\\"n1\\\":\\\"Sara\\\",\\n\\\"n2\\\":\\\"John\\\",\\n\\\"n3\\\":\\\"Laz\\\",\\n\\\"pnoun\\\":\\\"he\\\",\\n\\\"answer\\\":315,\\n\\\"wrong1\\\":\\\"45\\\",\\n\\\"wrong2\\\":\\\"270\\\",\\n\\\"wrong3\\\":\\\"135\\\"\\n}\\n]\"))", "description": "<p>The list of all possible directions, and the number of degrees between the two people (the answer).</p>", "templateType": "json", "can_override": false}, "direc1": {"name": "direc1", "group": "Ungrouped variables", "definition": "scenario[\"dir1\"]", "description": "<p>The directions and distances that name1 walks for the chosen scenario.</p>", "templateType": "anything", "can_override": false}, "index": {"name": "index", "group": "Ungrouped variables", "definition": "random(0 .. 6#1)", "description": "<p>The index which selects the scenario for the question.</p>", "templateType": "randrange", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "scenarios[index]", "description": "<p>The selected scenario for the question.</p>", "templateType": "anything", "can_override": false}, "direc2": {"name": "direc2", "group": "Ungrouped variables", "definition": "scenario[\"dir2\"]", "description": "<p>The directions and distances that name2 walks for the chosen scenario.</p>", "templateType": "anything", "can_override": false}, "degrees": {"name": "degrees", "group": "Ungrouped variables", "definition": "scenario[\"answer\"]", "description": "<p>The correct answer in degrees for the chosen scenario.</p>", "templateType": "anything", "can_override": false}, "option2": {"name": "option2", "group": "Ungrouped variables", "definition": "scenario[\"wrong1\"]", "description": "<p>The first wrong answer (distractor).</p>", "templateType": "anything", "can_override": false}, "option3": {"name": "option3", "group": "Ungrouped variables", "definition": "scenario[\"wrong2\"]", "description": "<p>The second wrong answer (distractor).</p>", "templateType": 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"<p>The name of the second person.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "index", "scenario", "name1", "name2", "name3", "pronoun", "direc1", "direc2", "degrees", "option2", "option3", "option4"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How many degrees did {name3} turn through between looking at {name1}&nbsp;and looking at {name2}?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{degrees}", "{option2}", "{option3}", "{option4}"], "matrix": ["1", 0, 0, 0], "distractors": ["Well done - you are correct!", "Read the question carefully and try again.", "Read the question carefully and try again.", "Read the question carefully and try again."]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}]}], "contributors": [{"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}]}