// Numbas version: exam_results_page_options
{"name": "Polar graph (geogebra) #2", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Polar graph (geogebra) #2", "tags": [], "metadata": {"description": "<p>This uses an embedded Geogebra graph of a polar function with random coefficients set by NUMBAS.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Look at the polar graphs below and try to choose the correct function from the list.</p>\n<p>Use the sliders to change the value of $\\theta$ and to trace the curve.</p>", "advice": "", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"f1": {"name": "f1", "group": "Ungrouped variables", "definition": "\"{a1}+{func1}({b1}*t)\"", "description": "", "templateType": "anything", "can_override": false}, "t": {"name": "t", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "f11d": {"name": "f11d", "group": "Ungrouped variables", "definition": "if(func1=\"sin\",expression(\"{a1+1}+cos({b1}*theta)\"),expression(\"{a1+2}+sin({b1}*theta)\"))", "description": "", "templateType": "anything", "can_override": false}, "f11a": {"name": "f11a", "group": "Ungrouped variables", "definition": "expression(\"{a1}\"+{func1}+\"({b1}*theta)\")", "description": "", "templateType": "anything", "can_override": false}, "func1": {"name": "func1", "group": "Ungrouped variables", "definition": "random(\"sin\",\"cos\")", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "defs1": {"name": "defs1", "group": "Ungrouped variables", "definition": "[\n  ['a',t],\n  ['f(t)',f1]\n]", "description": "", "templateType": "anything", "can_override": false}, "f22c": {"name": "f22c", "group": "Ungrouped variables", "definition": "expression(\"{a2}/(1-{b2}*cos(theta))\")", "description": "", "templateType": "anything", "can_override": false}, "f2": {"name": "f2", "group": "Ungrouped variables", "definition": "\"{a2}/(1+{b2}*cos(t))\"", "description": "", "templateType": "anything", "can_override": false}, "f22a": {"name": "f22a", "group": "Ungrouped variables", "definition": "expression(\"{a2}/(1+{b2}*cos(theta))\")", "description": "", "templateType": "anything", "can_override": false}, "f11c": {"name": "f11c", "group": "Ungrouped variables", "definition": "if(func1=\"sin\",expression(\"{a1}+cos({b1}*theta)\"),expression(\"{a1}+sin({a1+random(1,2)}*theta)\"))", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "random(0.2,0.5,0.8,0.9)", "description": "", "templateType": "anything", "can_override": false}, "f22d": {"name": "f22d", "group": "Ungrouped variables", "definition": "expression(\"{a2/(1-{b2})}/(1+{b2}*cos(theta))\")", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "", "templateType": "anything", "can_override": false}, "f22b": {"name": "f22b", "group": "Ungrouped variables", "definition": "expression(\"{a2/(1-{b2})}/(1+{b2}*sin(theta))\")", "description": "", "templateType": "anything", "can_override": false}, "defs2": {"name": "defs2", "group": "Ungrouped variables", "definition": "[\n  ['a',t],\n  ['f(t)',f2]\n]", "description": "", "templateType": "anything", "can_override": false}, "f11b": {"name": "f11b", "group": "Ungrouped variables", "definition": "expression(\"{a1}\"+{func1}+\"({b1+random(1,2)}*theta)\")", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "a2/(1-b2)<15 and a2/(1-b2)>2", "maxRuns": "200"}, "ungrouped_variables": ["t", "defs1", "f1", "a1", "b1", "func1", "f11a", "f11b", "f11c", "f11d", "f2", "a2", "defs2", "f22a", "f22b", "f22c", "f22d", "b2"], "variable_groups": [], "functions": {"geogebra": {"parameters": [], "type": "html", "language": "javascript", "definition": "{geogebra_base64('https://ggbm.at/AAngd6jz',200,400)}"}}, "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>{geogebra_applet('https://ggbm.at/AAngd6jz', defs1,[]&nbsp;)}</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>$r=\\simplify{{f11a}}$</p>", "<p>$r=\\simplify{{f11b}}$</p>", "<p>$r=\\simplify{{f11c}}$</p>", "<p>$r=\\simplify{{f11d}}$</p>"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"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>The graph below shows an ellipse.</p>\n<p>{geogebra_applet('https://ggbm.at/YtH99Gs6', defs2, [])}</p>\n<p>The equations look quite complicated; try to figure which options cannot be describing the shapes (i.e. use a process of elimination until you are left with the only possibility!)</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>$r=\\simplify{{f22a}}$</p>", "<p>$r=\\simplify{{f22b}}$</p>", "<p>$r=\\simplify{{f22c}}$</p>", "<p>$r=\\simplify{{f22d}}$</p>"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}]}], "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}