// Numbas version: finer_feedback_settings
{"name": "Problem solving in GCSE mathematics q 37", "extensions": ["eukleides", "random_person", "quantities"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Problem solving in GCSE mathematics q 37", "tags": [], "metadata": {"description": "
Taken from question 37 of the book Problem Solving in GCSE Mathematics by Daniel Griller.
Given bearings and lengths of two straight lines, work out the bearing and distance back to the starting point.
A Eukleides diagram shows the setup visually.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "extensions": ["eukleides", "quantities", "random_person"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"bearing": {"name": "bearing", "group": "Ungrouped variables", "definition": "180+h1+theta", "description": "", "templateType": "anything", "can_override": false}, "hint_diagram": {"name": "hint_diagram", "group": "Ungrouped variables", "definition": "eukleides(\"Bearings between A, B and C\",[\n let(\n ana, deg(heading_1)\n , anb, deg(heading_2)\n , a, origin\n , b, point(4,deg(90)-ana)\n , c, point(length_2,deg(90)-anb)+(b-a)\n , m, (a+vector(0,1))\n , n, (b+vector(0,1))\n , p, (c+vector(0,1.5)) \n , [\n (a..b..c)\n , (a..b) label(\"4\")\n , (b..c) label(length_2+\"\")\n , (a..c) label(\"x\",deg(180)) italic\n , (a..m) arrow\n , (b..n) arrow\n , (c..p) arrow\n , ([\n a label(\"A\",deg(180))\n , b label(\"B\")\n , c label(\"C\",deg(-90))\n , m label(\"M\",deg(90),0.1)\n , n label(\"N\",deg(90),0.1)\n , p label(\"P\",deg(90),0.1)\n ]) italic\n , angle(b,a,m) label(ana)\n , angle(c,b,n) label(anb)\n , b\n , c\n ])\n],[\"heading_1\": h1, \"heading_2\": h2, \"length_2\": 5])\n", "description": "", "templateType": "anything", "can_override": false}, "neutral": {"name": "neutral", "group": "Ungrouped variables", "definition": "person['gender']='neutral'", "description": "", "templateType": "anything", "can_override": false}, "they": {"name": "they", "group": "Ungrouped variables", "definition": "person['pronouns']['they']", "description": "", "templateType": "anything", "can_override": false}, "h2": {"name": "h2", "group": "Ungrouped variables", "definition": "180+random(10..30#5)", "description": "", "templateType": "anything", "can_override": false}, "solved_diagram": {"name": "solved_diagram", "group": "Ungrouped variables", "definition": "eukleides(\"Bearings between A, B and C\",[\n let(\n ana, deg(heading_1)\n , anb, deg(heading_2)\n , a, origin\n , b, point(4,deg(90)-ana)\n , c, point(length_2,deg(90)-anb)+(b-a)\n , m, (a+vector(0,1))\n , n, (b+vector(0,1))\n , p, (c+vector(0,1.5)) \n , [\n (a..b..c)\n , (a..b) label(\"4\")\n , (b..c) label(length_2+\"\")\n , (a..c) label(\"x\",deg(180)) italic\n , (a..m) arrow\n , (b..n) arrow\n , (c..p) arrow\n , ([\n a label(\"A\",deg(180))\n , b label(\"B\")\n , c label(\"C\",deg(-90))\n , m label(\"M\",deg(90),0.1)\n , n label(\"N\",deg(90),0.1)\n , p label(\"P\",deg(90),0.1)\n ]) italic\n , angle(b,a,m) label(ana)\n , angle(c,b,n) label(anb)\n , angle(c,a,b) label(\"\u03b8\") italic\n , angle(n,b,a) label(deg(180)-ana)\n , angle(a,b,c) label(deg(180)+ana-anb)\n , b\n , c\n ])\n],[\"heading_1\": h1, \"heading_2\": h2])", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "degrees(arcsin(5sin(abc)/x))", "description": "", "templateType": "anything", "can_override": false}, "their": {"name": "their", "group": "Ungrouped variables", "definition": "person['pronouns']['their']", "description": "", "templateType": "anything", "can_override": false}, "length_2": {"name": "length_2", "group": "Ungrouped variables", "definition": "random(3..6)", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "sqrt(4^2+5^2-2*4*5*cos(abc))", "description": "", "templateType": "anything", "can_override": false}, "h1": {"name": "h1", "group": "Ungrouped variables", "definition": "random(70..100#5)", "description": "", "templateType": "anything", "can_override": false}, "person": {"name": "person", "group": "Ungrouped variables", "definition": "random_person()", "description": "", "templateType": "anything", "can_override": false}, "pname": {"name": "pname", "group": "Ungrouped variables", "definition": "person[\"name\"]", "description": "", "templateType": "anything", "can_override": false}, "abc": {"name": "abc", "group": "Ungrouped variables", "definition": "radians(180+h1-h2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["solved_diagram", "h1", "h2", "person", "pname", "they", "neutral", "their", "abc", "x", "theta", "bearing", "hint_diagram", "length_2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "{pname} walks on a bearing of {deg(h1)} for 4 km, then turns and walks on a bearing of {deg(h2)} for {length_2} km.
\nIf {they} {if(neutral,'wish','wishes')} to return directly to {their} starting point, on what bearing should {they} walk, and for what distance?
\nWalk for [[0]] km on a bearing of [[1]] degrees.
\nGive your answer to 3 significant figures.
", "stepsPenalty": 0, "steps": [{"type": "information", "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": "The following diagram shows all of the given information.
\n{pname} begins at $A$, moves to $B$ and then $C$.
\n{max_height(40,max_width(30,hint_diagram))}
"}], "gaps": [{"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, "minValue": "x", "maxValue": "x", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "minValue": "bearing", "maxValue": "bearing", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "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", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}], "resources": []}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}]}