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{"name": "Graphing: circles - simple recognition of radius and centre", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"type": "question", "advice": "<p>The equation of a circle with&nbsp;radius $r$ and&nbsp;centre $(a,b)$ is $(x-a)^2+(y-b)^2=r^2$.</p>\n<ul>\n<li>This means the top of the circle will be at the point $(a,b+r)$.</li>\n<li>This means the bottom&nbsp;of the circle will be at the point $(a,b-r)$.</li>\n<li>This means the far left&nbsp;of the circle will be at the point $(a-r,b)$.</li>\n<li>This means the far right&nbsp;of the circle will be at the point $(a+r,b)$.</li>\n</ul>", "tags": ["circles", "graphing"], "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "name": "Graphing: circles - simple recognition of radius and centre", "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>You are given the equation $\\simplify{(x-{a})^2+(y-{b})^2={rs}}$.</p>", "variables": {"b": {"name": "b", "definition": "random(-12..12 except 0)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "r": {"name": "r", "definition": "random(1..12)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "rs": {"name": "rs", "definition": "r^2", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a": {"name": "a", "definition": "random(-12..12)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "ungrouped_variables": ["a", "b", "r", "rs"], "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "marks": 0, "scripts": {}, "type": "gapfill", "prompt": "<p>The equation $\\simplify{(x-{a})^2+(y-{b})^2={rs}}$ is the equation of a circle with radius&nbsp;[[0]]&nbsp; centred at the point $\\large($ [[1]],&nbsp;[[2]]$\\large)$.&nbsp;</p>", "gaps": [{"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{r}", "marks": 1, "maxValue": "{r}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{a}", "marks": 1, "maxValue": "{a}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{b}", "marks": 1, "maxValue": "{b}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}]}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "marks": 0, "scripts": {}, "type": "gapfill", "prompt": "<p>The above information allows us to find four points of the circle easily:</p>\n<ul>\n<li>The top of the circle is at the point&nbsp;$\\large($[[0]],&nbsp;[[1]]$\\large)$</li>\n<li>The bottom&nbsp;of the circle is at the point&nbsp;$\\large($[[2]],&nbsp;[[3]]$\\large)$</li>\n<li>The far left&nbsp;of the circle is at the point&nbsp;$\\large($[[4]],&nbsp;[[5]]$\\large)$</li>\n<li>The far right&nbsp;of the circle is at the point&nbsp;$\\large($[[6]],&nbsp;[[7]]$\\large)$</li>\n</ul>", "gaps": [{"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{a}", "marks": 1, "maxValue": "{a}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{b+r}", "marks": 1, "maxValue": "{b+r}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{a}", "marks": 1, "maxValue": "{a}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{b-r}", "marks": 1, "maxValue": "{b-r}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{a-r}", "marks": 1, "maxValue": "{a-r}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{b}", "marks": 1, "maxValue": "{b}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{a+r}", "marks": 1, "maxValue": "{a+r}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}, {"showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "numberentry", "minValue": "{b}", "marks": 1, "maxValue": "{b}", "correctAnswerFraction": false, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}]}], "preamble": {"css": "", "js": ""}, "functions": {}, "extensions": [], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "<p>Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$&nbsp;</p>"}, "rulesets": {}, "showQuestionGroupNames": false, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}