// Numbas version: finer_feedback_settings
{"name": "Construct the region satisfied by three inequalities", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Construct the region satisfied by three inequalities", "tags": [], "metadata": {"description": "<p>The student is shown a set of axes with three lines. They must move the lines so they match the given inequalities, then move a point inside the region satisfied by the inequalities.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>On the grid, identify the region that satisfies all these inequalities.</p>\n<p>\\begin{align}<br/>y &amp;\\gt \\var{y1}<br/>&amp;<br/>x+y &amp;\\lt \\var{y3}<br/>&amp;<br/>y &amp;\\lt \\simplify{{m2}x}<br/>\\end{align}</p>", "advice": "<p>The diagram should look like this:</p>\n<p>{correct_board}</p>", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"g": {"name": "g", "group": "Ungrouped variables", "definition": "jessiecode(600,600,[-bound,bound,bound,-bound],\"\"\"\n  a1 = point(-1,1) <<name: 'a1', snapToGrid: true, withLabel: false>>;\n  a2 = point(1,2) <<name: 'a2', snapToGrid: true, withLabel: false>>;\n  a = line(a1,a2) <<name: 'a', snapToGrid: true, dash: 2, fixed: true, strokeColor: 'black'>>;\n\n  b1 = point(-1,2) <<name: 'b1', snapToGrid: true, withLabel: false>>;\n  b2 = point(1,3) <<name: 'b2', snapToGrid: true, withLabel: false>>;\n  b = line(b1,b2) <<name: 'b', snapToGrid: true, dash: 2, fixed: true, strokeColor: 'black'>>;\n  \n  c1 = point(-1,3) <<name: 'c1', snapToGrid: true, withLabel: false>>;\n  c2 = point(1,4) <<name: 'c2', snapToGrid: true, withLabel: false>>;\n  c = line(c1,c2) <<name: 'c', snapToGrid: true, dash: 2, fixed: true, strokeColor: 'black'>>;\n  \n  p1 = intersection(a,b) <<visible: false>>;\n  p2 = intersection(a,c) <<visible: false>>;\n  p3 = intersection(b,c) <<visible: false>>;\n  \n  // polygon(p1,p2,p3) <<name: 'p'>>;\n  \n  region = point(-0.5,0.5) <<name: 'A', fillColor: 'blue', size: 6>>;\n\"\"\")", "description": "<p>The graph to show to the student.</p>", "templateType": "anything", "can_override": false}, "bound": {"name": "bound", "group": "Ungrouped variables", "definition": "7", "description": "", "templateType": "anything", "can_override": false}, "correct_lines": {"name": "correct_lines", "group": "Ungrouped variables", "definition": "[\n  [0,m2],\n  [y1,0],\n  [y3,-1]\n]", "description": "<p>Parameters for the inequalities, in the form <code>[y-intercept, slope]</code>.</p>", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "random(0,1,2)", "description": "<p>The height of the horizontal line.</p>", "templateType": "anything", "can_override": false}, "m2": {"name": "m2", "group": "Ungrouped variables", "definition": "random(1,2,3)", "description": "<p>The graidnet of the line through the origin.</p>", "templateType": "anything", "can_override": false}, "y3": {"name": "y3", "group": "Ungrouped variables", "definition": "random(4,5,6)", "description": "<p>The y-intercept of the diagonal line</p>", "templateType": "anything", "can_override": false}, "correct_board": {"name": "correct_board", "group": "Ungrouped variables", "definition": "jessiecode(600,600,[-bound,bound,bound,-bound],\"\"\"\n  a1 = point(-1,{y1}) <<name: 'a1', snapToGrid: true, withLabel: false, fixed: true>>;\n  a2 = point(1,{y1}) <<name: 'a2', snapToGrid: true, withLabel: false, fixed: true>>;\n  a = line(a1,a2) <<name: 'a', snapToGrid: true, dash: 2, fixed: true, strokeColor: 'black'>>;\n\n  b1 = point(0,{y3}) <<name: 'b1', snapToGrid: true, withLabel: false, fixed: true>>;\n  b2 = point({y3},0) <<name: 'b2', snapToGrid: true, withLabel: false, fixed: true>>;\n  b = line(b1,b2) <<name: 'b', snapToGrid: true, dash: 2, fixed: true, strokeColor: 'black'>>;\n  \n  c1 = point(0,0) <<name: 'c1', snapToGrid: true, withLabel: false, fixed: true>>;\n  c2 = point(1,{m2}) <<name: 'c2', snapToGrid: true, withLabel: false, fixed: true>>;\n  c = line(c1,c2) <<name: 'c', snapToGrid: true, dash: 2, fixed: true, strokeColor: 'black'>>;\n  \n  p1 = intersection(a,b) <<visible: false>>;\n  p2 = intersection(a,c) <<visible: false>>;\n  p3 = intersection(b,c) <<visible: false>>;\n  \n  // polygon(p1,p2,p3) <<name: 'p'>>;\n  \n  region = incenter(p1,p2,p3) <<name: 'A', fillColor: 'blue', size: 6, fixed: true>>;\n\"\"\")", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["bound", "g", "correct_lines", "y1", "m2", "y3", "correct_board"], "variable_groups": [], "functions": {"get_lines": {"parameters": [], "type": "list", "language": "javascript", "definition": "var board = scope.getVariable('g').board;\nvar lines = ['a','b','c'].map(function(x) { return board.elementsByName[x]; });\nvar line_props = lines.map(function(l) { return [l.getRise(), l.getSlope()]; });\nreturn Numbas.jme.wrapValue(line_props);"}, "get_region_point": {"parameters": [], "type": "vector", "language": "javascript", "definition": "var board = scope.getVariable('g').board;\nvar p = board.elementsByName['A'];\nreturn [p.X(),p.Y()];"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "extension", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"constructor": {"script": "this.marks = 5;", "order": "after"}}, "customMarkingAlgorithm": "student_lines: get_lines()\n\nstudent_point: get_region_point()\n\npoint_in_shaded_region:\n  let([x,y],student_point, all([y>y1, x+y<y3, y<m2*x]))\n\nlines_in_right_places:\n  set(student_lines)=set(correct_lines)\n\nmark:\n  if(lines_in_right_places,\n    add_credit(3/5,\"You have drawn the inequalities correctly.\");\n    if(point_in_shaded_region,\n      add_credit(2/5,\"You have moved point A inside the correct region.\"),\n      negative_feedback(\"Point A is not in the correct region.\")\n    )\n  ,\n    negative_feedback(\"You have not drawn the inequalities correctly.\");false\n  )\n\ninterpreted_answer: lines", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{g}</p>\n<p>Drag the points to move the lines around, and then move point A inside the region satisfied by the inequalities.</p>"}], "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": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Kate Henderson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/808/"}, {"name": "Aamir Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4537/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Kate Henderson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/808/"}, {"name": "Aamir Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4537/"}]}