// Numbas version: finer_feedback_settings
{"name": "2.6.7 Circle inequality no 2", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "2.6.7 Circle inequality no 2", "tags": [], "metadata": {"description": "<p>Given a circle centre and radius, write an appropriate inequality for the region either inside or outside the circle.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>State an inequality that describes the points that lie <span data-jme-visible=\"idx=1\">inside</span> <span data-jme-visible=\"idx=0\">outside</span> the circle of radius $\\var{radius}$ with centre $(\\var{centrex}, \\var{centrey})$.</p>", "advice": "<p><span data-jme-visible=\"idx=0\">The points outside the circle are the points that are further from the centre than the distance of the radius.&nbsp;</span></p>\n<p><span data-jme-visible=\"idx=1\">The points inside the circle are the points that are closer to the centre than the distance of the radius.&nbsp;</span></p>\n<p>Thus, putting the centre coordinates and the radius into the circle equation and then writing the inequality gives:</p>\n<p>$\\var{inequality}$</p>\n<p>The diagram shows the area that satisfies the inequality shaded in cyan.</p>\n<p>{correctgraph}</p>", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"centrex": {"name": "centrex", "group": "The inequality", "definition": "random(-9..9)", "description": "", "templateType": "anything", "can_override": false}, "centrey": {"name": "centrey", "group": "The inequality", "definition": "random(-9..9)", "description": "", "templateType": "anything", "can_override": false}, "radiussquared": {"name": "radiussquared", "group": "The inequality", "definition": "weighted_random([[random([1,4,9,16,25,36,49,64,81]),0.8],[random(1..99),0.2]])", "description": "", "templateType": "anything", "can_override": false}, "radius": {"name": "radius", "group": "The inequality", "definition": "simplify(expression(\"sqrt(\"+radiussquared+\")\"),\"sqrtSquare\")", "description": "", "templateType": "anything", "can_override": false}, "inequality": {"name": "inequality", "group": "The inequality", "definition": "simplify(expression(\"(x-\"+centrex+\")^2+(y-\"+centrey+\")^2\"+if(idx=0,\">\",\"<\")+radiussquared),\"all\")", "description": "", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "The inequality", "definition": "random(0,1)", "description": "<p>Selector</p>\n<p>0 =&gt; &gt;</p>\n<p>1 =&gt; &lt;</p>", "templateType": "anything", "can_override": false}, "correctgraph": {"name": "correctgraph", "group": "The graph", "definition": "jessiecode(\n  400,400,[{xmin},{ymax},{xmax},{ymin}],\"incolor={incolor};outcolor={outcolor};xmin={xmin};ymin={ymin};xmax={xmax};ymax={ymax};R={radius};Cx={centrex};Cy={centrey};\"+safe(\n  \"\"\"\n    p=polygon([xmin,ymin],[xmin,ymax],[xmax,ymax],[xmax,ymin]) <<color:outcolor>>;\n    C=point(Cx,Cy) <<id:'C', color:'blue', name:'', snapToGrid: true>>;\n    C1=circle(C,R) <<id:'C1',fillcolor:incolor, fillOpacity: 0.8, strokeOpacity:0.3 >>;\n  \"\"\"),\n  [\n    \"axis\": true,\n  ]\n)  ", "description": "", "templateType": "anything", "can_override": false}, "xmax": {"name": "xmax", "group": "The graph", "definition": "if(xmaxtemp-xmin > ymaxtemp-ymin,xmaxtemp,xmin+ymaxtemp-ymin)", "description": "", "templateType": "anything", "can_override": false}, "xmin": {"name": "xmin", "group": "The graph", "definition": "min(-1,centrex-ceil(eval(radius))-1)", "description": "", "templateType": "anything", "can_override": false}, "ymax": {"name": "ymax", "group": "The graph", "definition": "if(ymaxtemp-ymin > xmaxtemp-xmin,ymaxtemp,ymin+xmaxtemp-xmin)", "description": "", "templateType": "anything", "can_override": false}, "ymin": {"name": "ymin", "group": "The graph", "definition": "min(-1,centrey-ceil(eval(radius))-1)", "description": "", "templateType": "anything", "can_override": false}, "xmaxtemp": {"name": "xmaxtemp", "group": "The graph", "definition": "max(1,centrex+ceil(eval(radius))+1)", "description": "", "templateType": "anything", "can_override": false}, "ymaxtemp": {"name": "ymaxtemp", "group": "The graph", "definition": "max(1,centrey+ceil(eval(radius))+1)", "description": "", "templateType": "anything", "can_override": false}, "incolor": {"name": "incolor", "group": "The graph", "definition": "if(idx=0,\"\\'white\\'\",\"\\'cyan\\'\")", "description": "", "templateType": "anything", "can_override": false}, "outcolor": {"name": "outcolor", "group": "The graph", "definition": "if(idx=0,\"\\'cyan\\'\",\"\\'none\\'\")", "description": "", "templateType": "anything", "can_override": false}, "studentgraph": {"name": "studentgraph", "group": "The graph", "definition": "jessiecode(\n  400,400,[{xmin},{ymax},{xmax},{ymin}],\"incolor={incolor};outcolor={outcolor};xmin={xmin};ymin={ymin};xmax={xmax};ymax={ymax};R={radius};Cx={centrex};Cy={centrey};\"+safe(\n  \"\"\"\n    p=polygon([xmin,ymin],[xmin,ymax],[xmax,ymax],[xmax,ymin]) <<color:outcolor>>;\n    C=point(Cx,Cy) <<id:'C', color:'blue', name:'', snapToGrid: true>>;\n    C1=circle(C,R) <<id:'C1',fillcolor:incolor, fillOpacity: 0.8, strokeOpacity:0.3 >>;\n  \"\"\"),\n  [\n    \"axis\": true,\n  ]\n)  ", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "The inequality", "variables": ["centrex", "centrey", "radiussquared", "inequality", "radius", "idx"]}, {"name": "The graph", "variables": ["correctgraph", "xmin", "ymin", "xmaxtemp", "xmax", "ymaxtemp", "ymax", "incolor", "outcolor", "studentgraph"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{inequality}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "resources": []}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}