// Numbas version: finer_feedback_settings {"type": "exam", "percentPass": 0, "showstudentname": true, "timing": {"timedwarning": {"message": "", "action": "none"}, "allowPause": true, "timeout": {"message": "", "action": "none"}}, "name": "Eukleides extension", "feedback": {"showactualmark": true, "showanswerstate": true, "allowrevealanswer": true, "showtotalmark": true, "intro": "", "advicethreshold": 0, "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "metadata": {"description": "A couple of questions demonstrating the use of the Eukleides extension to create geometrical drawings.", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "duration": 0, "question_groups": [{"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Group", "questions": [{"name": "Dividing equilateral triangles equally", "extensions": ["eukleides", "random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "preventleave": false, "showfrontpage": false, "showresultspage": "never"}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "rulesets": {}, "statement": "", "parts": [{"type": "numberentry", "variableReplacements": [], "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "allowFractions": false, "scripts": {}, "showCorrectAnswer": true, "useCustomName": false, "showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "customName": "", "mustBeReducedPC": 0, "showFractionHint": true, "correctAnswerStyle": "plain", "prompt": "

Each of the equilateral triangles has been split into triangles of equal area.

\n

{max_width(40,shearer_diagram)}

\n

What is the missing length?

", "maxValue": "len_shearer", "marks": 1, "minValue": "len_shearer"}], "tags": [], "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Three equilateral triangles are divided equally into 3, 4 and 5 parts respectively. Calculate the distance between two marked points.

Based on a puzzle by Catriona Shearer, shared on Twitter.

"}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "variables": {"q": {"name": "q", "group": "Ungrouped variables", "definition": "x(equilateral(30)[1])", "description": "", "templateType": "anything"}, "base": {"name": "base", "group": "Ungrouped variables", "definition": "random(1..7)*30", "description": "", "templateType": "anything"}, "len_shearer": {"name": "len_shearer", "group": "Ungrouped variables", "definition": "base*(1/2+2/3*4/5)", "description": "", "templateType": "anything"}, "shearer_diagram": {"name": "shearer_diagram", "group": "Ungrouped variables", "definition": "// Based on https://twitter.com/Cshearer41/status/1115917680027021312\neukleides(\"Catriona Shearer puzzle\",[\nlet(\n [a,b,c],equilateral(30)\n, [c,b,d],equilateral(c,b)\n, [d,b,f],equilateral(d,b)\n, a1, b+2/3*(c-b)\n, a2, a+1/2*(b-a)\n, b1, b+3/4*(d-b)\n, b2, b+2/3*(c-b)\n, b3, b+1/2*(b1-b)\n, c1, b+4/5*(f-b)\n, c2, b+3/4*(d-b)\n, c3, b+2/3*(c1-b)\n, c4, b+1/2*(c2-b)\n, [\n a..b..c\n , b..c..d\n , d..b..f\n , (a..a1..a2) color1 open\n , (c..b1..b2..b3) color2 open\n , (d..c1..c2..c3..c4) color3 open\n , ((c..d)+vector(0,2)) arrows size(10) label(base)\n , ((c3..a2)+vector(0,-2)) arrows size(10) label(\"?\")\n ] * size(20) font(\"sans\")\n)\n],[\"base\":base])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "ungrouped_variables": ["base", "shearer_diagram", "len_shearer", "q"], "type": "exam"}, {"name": "Problem solving in GCSE mathematics q 37", "extensions": ["eukleides", "quantities", "random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "rulesets": {}, "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "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.

"}, "advice": "", "tags": [], "parts": [{"showFeedbackIcon": true, "unitTests": [], "gaps": [{"showFeedbackIcon": true, "variableReplacements": [], "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "customName": "", "showPrecisionHint": false, "type": "numberentry", "precisionPartialCredit": 0, "unitTests": [], "precisionType": "sigfig", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "precision": "3", "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "strictPrecision": false, "allowFractions": false, "scripts": {}, "customMarkingAlgorithm": "", "maxValue": "x", "showCorrectAnswer": true, "minValue": "x"}, {"showFeedbackIcon": true, "variableReplacements": [], "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "customName": "", "showPrecisionHint": false, "type": "numberentry", "precisionPartialCredit": 0, "unitTests": [], "precisionType": "sigfig", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "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": "

The following diagram shows all of the given information.

\n

{name} begins at $A$, moves to $B$ and then $C$.

\n

{max_height(40,max_width(30,hint_diagram))}

", "useCustomName": false, "variableReplacementStrategy": "originalfirst"}], "stepsPenalty": 0, "marks": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "type": "gapfill", "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "prompt": "

{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.

\n

If {they} {if(neutral,'wish','wishes')} to return directly to {their} starting point, on what bearing should {they} walk, and for what distance?

\n

Walk for [[0]] km on a bearing of [[1]] degrees.

\n

Give your answer to 3 significant figures.

", "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 ]) 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": "", "group": "Ungrouped variables", "name": "solved_diagram"}, "theta": {"templateType": "anything", "definition": "degrees(arcsin(5sin(abc)/x))", "description": "", "group": "Ungrouped variables", "name": "theta"}, "their": {"templateType": "anything", "definition": "person['pronouns']['their']", "description": "", "group": "Ungrouped variables", "name": "their"}, "length_2": {"templateType": "anything", "definition": "random(3..6)", "description": "", "group": "Ungrouped variables", "name": "length_2"}, "x": {"templateType": "anything", "definition": "sqrt(4^2+5^2-2*4*5*cos(abc))", "description": "", "group": "Ungrouped variables", "name": "x"}, "h1": {"templateType": "anything", "definition": "random(70..100#5)", "description": "", "group": "Ungrouped variables", "name": "h1"}, "person": {"templateType": "anything", "definition": "random_person()", "description": "", "group": "Ungrouped variables", "name": "person"}, "name": {"templateType": "anything", "definition": "person[\"name\"]", "description": "", "group": "Ungrouped variables", "name": "name"}, "abc": {"templateType": "anything", "definition": "radians(180+h1-h2)", "description": "", "group": "Ungrouped variables", "name": "abc"}}, "functions": {}, "preamble": {"js": "", "css": ""}, "statement": "", "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question"}]}], "navigation": {"browse": true, "showfrontpage": false, "showresultspage": "oncompletion", "preventleave": false, "onleave": {"message": "", "action": "none"}, "startpassword": "", "reverse": true, "allowregen": true}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "extensions": ["eukleides", "quantities", "random_person"], "custom_part_types": [], "resources": []}