// Numbas version: exam_results_page_options
{"name": "Q1 Circle mensuration problems", "extensions": [], "custom_part_types": [], "resources": [["question-resources/circle-sector-area.gif", "/srv/numbas/media/question-resources/circle-sector-area.gif"], ["question-resources/circle-segment-area.gif", "/srv/numbas/media/question-resources/circle-segment-area.gif"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"circle": {"definition": "\n      var c = document.createElement('canvas');\n        $(c).attr('width',600).attr('height',450);\n        var context = c.getContext('2d');\n        \n        //fill in rectangle with a light shade\n        context.fillStyle = '#eee';\n        context.beginPath();\n        context.arc(200, 200, 150, 50, Math.PI*2, true); \n        context.closePath();\n        context.fill();\n       \n        //draw labels\n        context.fillStyle = '#000';\n        context.font = '20px sans-serif';\n        var wstring = 'Perimeter ='+ p +'m';\n        var tw = context.measureText(wstring).width;\n//        console.log(tw);\n        context.fillText(wstring,60,38);\n        \n        var hstring = 'r';\n        var hw = context.measureText(hstring).width;\n        context.save();\n        context.translate(30,200);\n        context.rotate(-2*Math.PI);\n        context.fillText(hstring,70,-5);\n\n        var hstring = '____________';\n        var hw = context.measureText(hstring).width;\n        context.save();\n        context.translate(30,200);\n        context.rotate(2*Math.PI);\n        context.fillText(hstring,-10,-200);\n        \n        return c;\n      ", "type": "html", "language": "javascript", "parameters": [["p", "number"]]}, "ang": {"definition": "var c = document.createElement('canvas');\n$(c).attr('width',300).attr('height',300);\nvar ctx = c.getContext('2d');\n\nvar angle = Math.PI *((a-(Math.PI/2))/180);  // == 45 degrees\nvar cx = 150;\nvar cy = 150;\nvar radius = 100;\n\nangle-=Math.PI/2;\nctx.lineWidth = 2;\nctx.strokeStyle = 'red';\n\n// draw the red line at the desired angle\nctx.beginPath();\nctx.moveTo(cx, cy);\nctx.arc(cx, cy, radius, angle, angle);\nctx.stroke();\n\n// draw the bulls-eyed circle\nctx.beginPath();\nctx.strokeStyle = 'black';\nctx.arc(cx, cy, radius, 0, Math.PI * 2);\nctx.moveTo(cx - radius, cy);\nctx.lineTo(cx + radius, cy);\nctx.moveTo(cx, cy - radius);\nctx.lineTo(cx, cy + radius);\nctx.stroke();\n\n\n\nreturn c;", "type": "html", "language": "javascript", "parameters": [["a", "number"]]}, "circle1": {"definition": "\n      var c = document.createElement('canvas');\n        $(c).attr('width',600).attr('height',450);\n        var context = c.getContext('2d');\n        \n        //fill in rectangle with a light shade\n        context.fillStyle = '#eee';\n        context.beginPath();\n        context.arc(200, 200, 150, 50, Math.PI*2, true); \n        context.closePath();\n        context.fill();\n       \n        //draw labels\n        context.fillStyle = '#000';\n        context.font = '20px sans-serif';\n        var wstring = 'Area ='+ p +'m^2';\n        var tw = context.measureText(wstring).width;\n//        console.log(tw);\n        context.fillText(wstring,60,38);\n        \n        var hstring = 'r';\n        var hw = context.measureText(hstring).width;\n        context.save();\n        context.translate(30,200);\n        context.rotate(-2*Math.PI);\n        context.fillText(hstring,70,-5);\n\n        var hstring = '____________';\n        var hw = context.measureText(hstring).width;\n        context.save();\n        context.translate(30,200);\n        context.rotate(2*Math.PI);\n        context.fillText(hstring,-10,-200);\n        \n        return c;\n      ", "type": "html", "language": "javascript", "parameters": [["p", "number"]]}}, "ungrouped_variables": ["r", "area1", "ans1", "area12", "per2", "per22", "ans2", "ans3", "ans4", "sect", "rad", "ans5", "rds", "ans6", "sect1", "ans7", "ans8", "area5", "circ6"], "name": "Q1 Circle mensuration problems", "tags": ["area of a circle", "area of a sector", "canvas", "Circle", "circle", "function", "graphic", "Perimeter", "perimeter", "rebelmaths", "Sector", "sector", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>part&nbsp;1</p>\n<p>Formula for perimeter of circle.</p>\n<p>Perimeter = $2 \\times \\pi \\times r$</p>\n<p>radius(r) = &nbsp;$\\frac{\\text{Perimeter}}{2 \\times pi} = \\var{ans7}m$</p>\n<p></p>\n<p>part&nbsp;2</p>\n<p>Formula for area&nbsp;of circle.</p>\n<p>Area&nbsp;=&nbsp;$\\pi r^2$</p>\n<p>radius(r)=&nbsp;$\\sqrt\\frac{(\\text{area})}{pi}&nbsp;= \\var{ans8}m$</p>\n<p></p>\n<p>part 3</p>\n<p>Formula for area&nbsp;of circle.</p>\n<p>Area&nbsp;=&nbsp;$\\pi r^2$</p>\n<p>radius(r)= $\\sqrt\\frac{(\\text{area})}{pi}$</p>\n<p></p>\n<p>Formula for perimeter of circle.</p>\n<p>Perimeter = $2 \\times \\pi \\times r$</p>\n<p>$2 \\times \\pi \\times r[0] = \\var{ans1}m$</p>\n<p></p>\n<p>Part 4</p>\n<p>Formula for perimeter of circle.</p>\n<p>Perimeter = $2 \\times \\pi \\times r$</p>\n<p>Therefore;</p>\n<p>radius(r)= $\\frac{(\\text{perimter})}{2 \\times \\pi}$</p>\n<p>$\\frac{\\var{per22}}{2 \\times \\pi} = \\var{r[1]}m$</p>\n<p></p>\n<p>Formula for area&nbsp;of circle.</p>\n<p>Area&nbsp;=&nbsp;$\\pi r^2$</p>\n<p>$\\pi \\times&nbsp;\\var{r[1]}^2 = \\var{ans2}m^2$</p>\n<p></p>\n<p>Part&nbsp;5</p>\n<p>$\\frac{\\pi \\times \\var{r[2]}}{2} + 2 \\times \\var{r[2]} = \\var{ans3}$</p>\n<p>$\\frac{\\pi \\times \\var{r[2]}^2}{4} = \\var{ans4}$</p>\n<p></p>\n<p>Part&nbsp;6</p>\n<p><img src=\"resources/question-resources/circle-sector-area.gif\" width=\"247\" height=\"148\"/><img src=\"resources/question-resources/circle-segment-area.gif\" width=\"140\" height=\"145\"/></p>\n<p>where theta is in radians.</p>\n<p>$\\frac{\\var{rds}}{2} \\times \\var{rad}^2= \\var{ans5}$</p>\n<p>$\\frac{1}{2} \\times (\\var{rds} - sin(\\var{rds})) \\times \\var{rad}^2= \\var{ans6}$</p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>{circle(circ6)}</p>\n<p>The length of the circumference of a circle is $\\var{circ6}m$. Find the length of the radius of the circle.</p>\n<p>[[0]]&nbsp;$m$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans8}", "strictPrecision": false, "minValue": "{ans8}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>{circle1(area5)}</p>\n<p>The area of a&nbsp;circle&nbsp;is&nbsp;$\\var{area5}m^2$. Find&nbsp;the radius&nbsp;of the circle?</p>\n<p>[[0]]m</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans7}", "strictPrecision": false, "minValue": "{ans7}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>{circle1(area12)}</p>\n<p>This circle&nbsp;has an area of $\\var{area12}m^2$. Calculate the perimeter of this circle?</p>\n<p>[[0]]m</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>First you need to find the radius of this circle.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>{circle(per22)}</p>\n<p>Calculate the area of a&nbsp;circle which has a&nbsp;perimeter of $\\var{per22}m^2$.</p>\n<p>[[0]]&nbsp;$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>First you need to find the radius of this circle.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": false, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>A steel plate is in the shape of a quadrant of a circle and has a radius of $\\var{r[2]}$m. Calculate&nbsp;the perimeter of this plate and the area of the segment.</p>\n<p>Perimeter =&nbsp;[[0]]m</p>\n<p>Area =&nbsp;[[1]]$m^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Remember the formula for the area of a sector uses radian measure for the angle.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "strictPrecision": false, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans4}", "strictPrecision": false, "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>{ang(sect1)}</p>\n<p>A sector of a circle makes an angle of $\\var{sect}$ degrees at the centre and has a radius of $\\var{rad}cm$. Calculate the area of the sector and the area of the segment.</p>\n<p>The angle is the obtuse&nbsp;angle between the positive x-axis&nbsp;line, (3 o'clock point) and the red line, in an anti-clockwise motion.</p>\n<p>Area of sector =&nbsp;[[0]]$cm^2$</p>\n<p>Area of segment =&nbsp;[[1]]$cm^2$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The following diagrams should help to explain the question.</p>\n<p><img src=\"resources/question-resources/circle-sector-area.gif\" width=\"282\" height=\"169\"/><img src=\"resources/question-resources/circle-segment-area.gif\" width=\"237\" height=\"246\"/></p>\n<p>where theta is in radians.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans5}", "strictPrecision": false, "minValue": "{ans5}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans6}", "strictPrecision": false, "minValue": "{ans6}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Solve the following to <strong>two decimal places</strong>.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans8": {"definition": "circ6/(2 * pi)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans8", "description": ""}, "rad": {"definition": "random(4..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "rad", "description": ""}, "rds": {"definition": "precround(radians(sect),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "rds", "description": ""}, "sect1": {"definition": "(180-sect)+270", "templateType": "anything", "group": "Ungrouped variables", "name": "sect1", "description": ""}, "per22": {"definition": "precround(per2,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "per22", "description": ""}, "ans1": {"definition": "2*pi*r[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "pi*(r[1]^2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "(pi*r[2])/2 + 2*r[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "(pi*(r[2]^2))/4", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "ans5": {"definition": "(rds/2)*rad^2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5", "description": ""}, "ans6": {"definition": "0.5*(rds-sin(rds))*rad^2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans6", "description": ""}, "ans7": {"definition": "sqrt(area5/(pi))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans7", "description": ""}, "per2": {"definition": "2*pi*r[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "per2", "description": ""}, "circ6": {"definition": "random(120..160)", "templateType": "anything", "group": "Ungrouped variables", "name": "circ6", "description": ""}, "r": {"definition": "shuffle(3..7#0.1)[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "sect": {"definition": "random(95..170)", "templateType": "anything", "group": "Ungrouped variables", "name": "sect", "description": ""}, "area5": {"definition": "random(1500..2000)", "templateType": "anything", "group": "Ungrouped variables", "name": "area5", "description": ""}, "area12": {"definition": "precround(area1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "area12", "description": ""}, "area1": {"definition": "pi*(r[0]^2)", "templateType": "anything", "group": "Ungrouped variables", "name": "area1", "description": ""}}, "metadata": {"description": "<p>Circumference and area of a circle</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}