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{"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": [{"rulesets": {}, "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Taken from question 37 of the book <i>Problem Solving in GCSE Mathematics</i> by Daniel Griller.</p><p>Given bearings and lengths of two straight lines, work out the bearing and distance back to the starting point.</p><p>A Eukleides diagram shows the setup visually.<br></p>"}, "advice": "", "tags": [], "parts": [{"showFeedbackIcon": true, "unitTests": [], "gaps": [{"showFeedbackIcon": true, "variableReplacements": [], "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, 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"precision": "3", "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "strictPrecision": false, "allowFractions": false, "scripts": {}, "customMarkingAlgorithm": "", "maxValue": "bearing", "showCorrectAnswer": true, "minValue": "bearing"}], "steps": [{"showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "customName": "", "type": "information", "scripts": {}, "unitTests": [], "variableReplacements": [], "prompt": "<p>The following diagram shows all of the given information.</p>\n<p>{name} begins at $A$, moves to $B$ and then $C$.</p>\n<p>{max_height(40,max_width(30,hint_diagram))}</p>", "useCustomName": false, "variableReplacementStrategy": "originalfirst"}], "stepsPenalty": 0, "marks": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "type": "gapfill", "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "prompt": "<p>{name} walks on a bearing of {deg(h1)} for 4 km, then turns and walks on a bearing of {deg(h2)} for {length_2} km.</p>\n<p>If {they} {if(neutral,'wish','wishes')} to return directly to {their} starting point, on what bearing should {they} walk, and for what distance?</p>\n<p>Walk for [[0]] km on a bearing of [[1]] degrees.</p>\n<p>Give your answer to 3 significant figures.</p>", "useCustomName": false, "variableReplacementStrategy": "originalfirst"}], "ungrouped_variables": ["solved_diagram", "h1", "h2", "person", "name", "they", "neutral", "their", "abc", "x", "theta", "bearing", "hint_diagram", "length_2"], "variables": {"bearing": {"templateType": "anything", "definition": "180+h1+theta", "description": "", "group": "Ungrouped variables", "name": "bearing"}, "hint_diagram": {"templateType": "anything", "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": "", "group": "Ungrouped variables", "name": "hint_diagram"}, "neutral": {"templateType": "anything", "definition": "person['gender']='neutral'", "description": "", "group": "Ungrouped variables", "name": "neutral"}, "they": {"templateType": "anything", "definition": "person['pronouns']['they']", "description": "", "group": "Ungrouped variables", "name": "they"}, "h2": {"templateType": "anything", "definition": "180+random(10..30#5)", "description": "", "group": "Ungrouped variables", "name": "h2"}, "solved_diagram": {"templateType": "anything", "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      ]) 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