// Numbas version: exam_results_page_options
{"name": "SIT190 - Week 6 - Quiz -Short", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Musa's copy of 3 Degrees to radians", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}], "tags": [], "metadata": {"description": "<p>Converting Degrees to Radians</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Convert the following to radians (use \"pi\" for $\\pi$):</p>", "advice": "<p>To convert degrees to radians: multiply by $\\pi$ and divide by 180.</p>", "rulesets": {}, "variables": {"a6": {"name": "a6", "group": "Ungrouped variables", "definition": "radians(d61+(d62/60))", "description": "", "templateType": "anything"}, "d41": {"name": "d41", "group": "Ungrouped variables", "definition": "random(15..37)", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "radians(d1)", "description": "", "templateType": "anything"}, "d62": {"name": "d62", "group": "Ungrouped variables", "definition": "random(32..47)", "description": "", "templateType": "anything"}, "d42": {"name": "d42", "group": "Ungrouped variables", "definition": "random(40..55)", "description": "", "templateType": "anything"}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "radians(d3)", "description": "", "templateType": "anything"}, "d61": {"name": "d61", "group": "Ungrouped variables", "definition": "random(101..114)", "description": "", "templateType": "anything"}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "random(65..87#0.01)", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "radians(d2)", "description": "", "templateType": "anything"}, "d52": {"name": "d52", "group": "Ungrouped variables", "definition": "random(15..27)", "description": "", "templateType": "anything"}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "random(30,45,60,90,120,180,270)", "description": "", "templateType": "anything"}, "d3": {"name": "d3", "group": "Ungrouped variables", "definition": "random(15,20,25,35,40,50,55,65,70,75,80,85,90,110,130,140)", "description": "", "templateType": "anything"}, "a5": {"name": "a5", "group": "Ungrouped variables", "definition": "radians(d51+(d52/60))", "description": "", "templateType": "anything"}, "a4": {"name": "a4", "group": "Ungrouped variables", "definition": "radians(d41+(d42/60))", "description": "", "templateType": "anything"}, "d51": {"name": "d51", "group": "Ungrouped variables", "definition": "random(62..75)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["d1", "d2", "d3", "d41", "d42", "d51", "d52", "d61", "d62", "a1", "a2", "a3", "a4", "a5", "a6"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\var{d1}^{\\circ}$ =&nbsp;[[0]] radians</p>\n<p></p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>To convert to radians divide by 180 and multiply by&nbsp;$\\pi$</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{d1/180}pi", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\var{d3}^{\\circ}$&nbsp;=&nbsp;[[0]] radians</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{d3/180}pi", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}]}, {"name": "Musa's copy of 3 Radians to Degrees", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}], "tags": [], "metadata": {"description": "<p>Converting Radians to Degrees</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Convert the following to degrees:</p>\n<p>Round your answer to 2 decimal places.</p>", "advice": "<p>To convert radians to degrees: multiply by $\\pi$ and divide by 180.</p>\n<p>$\\frac{\\var{d1}&nbsp;\\times&nbsp;180&nbsp; }{\\pi} = \\var{a1}$</p>", "rulesets": {}, "variables": {"a4": {"name": "a4", "group": "Ungrouped variables", "definition": "degrees(pi*(d4/5))", "description": "", "templateType": "anything"}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "random(1.025..2.925#0.025 except[2,2.5,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2.1,2.2,2.3,2.4,2.6,2.7,2.8,2.9])", "description": "", "templateType": "anything"}, "d4": {"name": "d4", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything"}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "random(0.05..0.95)", "description": "", "templateType": "anything"}, "d5": {"name": "d5", "group": "Ungrouped variables", "definition": "random(6..9)", "description": "", "templateType": "anything"}, "d3": {"name": "d3", "group": "Ungrouped variables", "definition": "random(4.025..5.925#0.005 except[4,4.5,4.1,4.2,4.3,4.4,4.5,4.6,4.7,4.8,4.9,5.1,5.2,5.3,5.4,5.6,5.7,5.8,5.9])", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "degrees(d2)", "description": "", "templateType": "anything"}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "degrees(d3)", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "degrees(d1)", "description": "", "templateType": "anything"}, "a5": {"name": "a5", "group": "Ungrouped variables", "definition": "degrees(pi*(d5/5))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["d1", "d2", "d3", "d4", "d5", "a1", "a2", "a3", "a4", "a5"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\var{d1}$ radians=&nbsp;[[0]]&nbsp;$^{\\circ}$</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{a1}", "maxValue": "{a1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\frac{\\var{d4}\\pi}{5}$ radians=&nbsp;[[0]]&nbsp;$^{\\circ}$&nbsp;</p>\n<p></p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "{a4}", "maxValue": "{a4}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}]}, {"name": "Musa's copy of 3 Right-angled triangles", "extensions": [], "custom_part_types": [], "resources": [["question-resources/PictureTriangle_0.png", "/srv/numbas/media/question-resources/PictureTriangle_0.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}], "tags": [], "metadata": {"description": "<p>Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Using the right-angled triangle pictured below (not to scale), find the specified side lengths or angles using trigonometry and the given values. If this topic is new to you, clike Reveal answers for the first time and click Advice.</strong></p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/PictureTriangle_0.png\" width=\"387\" height=\"265\"/></p>\n<p style=\"text-align: left;\">Before starting, check that your calculator is in degrees mode by verifying that $\\cos{60} = \\frac{1}{2}$.</p>\n<p style=\"text-align: left;\">(If your calculator does not give this answer, press SHIFT $\\rightarrow$ SETUP $\\rightarrow$ 3 to enter degrees mode if using a Casio $fx$ model calculator, otherwise refer to your calculator's manual.)</p>", "advice": "<p>Each angle on a triangle is connected to two sides and is facing another.</p>\n<p>The longest side of the triangle is always the <strong>hypotenuse</strong>.&nbsp;</p>\n<p>The other side that makes the angle is called the <strong>adjacent</strong>.</p>\n<p>The final side not connected in any way to the angle is called the&nbsp;<strong>opposite</strong>.</p>\n<p>(Note&nbsp;that we only call the longest side the hypotenuse if we have a <strong>right-angled triangle</strong>. We <strong>cannot</strong> apply SOHCAHTOA or Pythagoras' Theorem to triangles which are not right-angled, so we would use the sine or cosine rules instead.)<strong>&nbsp;</strong></p>\n<p>For example, using the image below, you can see which side is denoted by each term from the highlighted angle's perspective.</p>\n<p><img width=\"312\" height=\"211\" src=\"resources/question-resources/triangle_2.png\"/></p>\n<p></p>\n<p></p>\n<p></p>\n<p>One of the ways you can approach this style of question is by using SOHCAHTOA.</p>\n<p>This can be written more visually as</p>\n<h4>\\[\\text{S}^\\text{O}_\\text{H}\\space\\text{C}^\\text{A}_\\text{H}\\space\\text{T}^\\text{O}_\\text{A}\\]</h4>\n<p>It represents each trigonometric function and what they are equivalent to.</p>\n<p>Written out in full, we would have:</p>\n<p><b>SIN:&nbsp;</b>opposite / hypotenuse</p>\n<p><b>COS:&nbsp;</b>adjacent /&nbsp;hypotenuse</p>\n<p><b>TAN:&nbsp;</b>opposite / adjacent</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p>For example, $\\sin$ is represented by the first S.</p>\n<p>If we were given an angle, say of $30^\\circ$,</p>\n<p>$\\sin(30^\\circ)=\\frac{\\text{opposite}}{\\text{hypotenuse}}$</p>\n<p>Evaluating&nbsp;$\\sin(30^\\circ)=\\frac{1}{2}$, we now know that $\\frac{\\text{opposite}}{\\text{hypotenuse}}=\\frac{1}{2}$</p>\n<p>If we were given one of these sides, we would then be able to work out the other one by multiplying accordingly.</p>\n<p></p>\n<p></p>\n<p></p>\n<p>Similarly if we were given two sides, and told to work out a specific angle, we could.</p>\n<p>Referring to the image above, suppose we want to find the highlighted angle and we are given that the hypotenuse is equal to $5$ units, and the adjacent is $4$ units.</p>\n<p>We would determine from SOHCAHTOA that we need to use&nbsp;<strong>cos</strong> since we have the values for&nbsp;<strong>A</strong>&nbsp;and&nbsp;<strong>H</strong>.</p>\n<p>So, $\\cos(x)=\\frac{4}{5}$</p>\n<p>Hence, $x=\\cos^{-1}(\\frac{4}{5})=36.87^\\circ$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"fa": {"name": "fa", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "fa_1": {"name": "fa_1", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "repeat(random(3..10),9)", "description": "", "templateType": "anything", "can_override": false}, "fh": {"name": "fh", "group": "Ungrouped variables", "definition": "random(6..10)", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "shuffle([25,30,40,50,60,70])", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "repeat(random(3..10),9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "x", "fa", "fh", "fa_1", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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>Find sin/cos/tan of angle x in triangle (use \"sqrt\" for square root)</p>\n<p>$a=\\var{a[6]}$</p>\n<p>$b=\\var{b[6]}$</p>\n<p>$\\sin(x) =$ [[0]],&nbsp; $\\cos(x) =$[[1]],&nbsp;$\\tan(x) =$ [[2]]</p>\n<p></p>", "stepsPenalty": 0, "steps": [{"type": "information", "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>use the definitaions of $\\sin, \\cos$ and $\\tan$</p>"}], "gaps": [{"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": "{b[6]/sqrt(({a[6]}^2)+({b[6]}^2))}", "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": []}, {"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": "{a[6]/sqrt(({a[6]}^2)+({b[6]}^2))}", "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": []}, {"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": "{b[6]/a[6]}", "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": []}], "sortAnswers": false}, {"type": "gapfill", "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>$x=\\var{x[4]}^\\circ$</p>\n<p>$y=$&nbsp;[[0]]$^\\circ$</p>", "stepsPenalty": 0, "steps": [{"type": "information", "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>For this question, use the principle that the&nbsp;interior angles in any triangle always add up to $180^\\circ$</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "90-{x[4]}", "maxValue": "90-{x[4]}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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>$c=\\var{a[0]}$</p>\n<p>$x=\\var{x[0]}^\\circ$</p>\n<p>$a=$&nbsp;[[0]]&nbsp; (Give your answer to <strong>two decimal places</strong>)</p>", "stepsPenalty": 0, "steps": [{"type": "information", "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>Use CAH to answer this question as you know the values of the side adjacent to the angle and the hypotenuse.</p>\n<p>Cos(x)=a/c</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a[0]}cos({x[0]}pi/180)", "maxValue": "{a[0]}cos({x[0]}pi/180)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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>$c=\\var{fh}$</p>\n<p>$a=\\var{fa}$</p>\n<p>$x=$&nbsp;[[0]]$^\\circ$&nbsp;&nbsp; (Give your answer to <strong>two decimal places</strong>)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "arccos({fa}/{fh})*(180/pi)", "maxValue": "arccos({fa}/{fh})*(180/pi)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Musa's copy of 3 Geometry: trig on unit circle, short", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [["question-resources/Unit_circle.png", "/srv/numbas/media/question-resources/Unit_circle.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}], "tags": [], "metadata": {"description": "<p>$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.&nbsp; Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.) Also find values and <span class=\"prompt content-area\"><span>sign of cos/tan/sin(x).</span></span></p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"angle": {"name": "angle", "group": "Ungrouped variables", "definition": "[a]+shuffle([-a,180+a])+shuffle([360-a,180-a,90-a])", "description": "<p>The slope of the line.</p>", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "[cos(angle[0]/180*pi),\ncos(angle[1]/180*pi),\ncos(angle[3]/180*pi)]", "description": "<p>The y-intercept.</p>", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "[sin(angle[0]/180*pi),\nsin(angle[1]/180*pi),\nsin(angle[3]/180*pi)]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random([13,14,15,16,17,-4,-5,-6,22,24,25])*10+random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "An": {"name": "An", "group": "Ungrouped variables", "definition": "random(0,30,45,60,90)", "description": "", "templateType": "anything", "can_override": false}, "index": {"name": "index", "group": "Ungrouped variables", "definition": "random(0..8)", "description": "", "templateType": "anything", "can_override": false}, "teta": {"name": "teta", "group": "Ungrouped variables", "definition": "[0,30,45,60,90,120,135,150,180]", "description": "", "templateType": "anything", "can_override": false}, "x_v": {"name": "x_v", "group": "Ungrouped variables", "definition": "[1,0.87,0.71,0.5,0,-0.50,-0.71,-0.87,-1]", "description": "", "templateType": "anything", "can_override": false}, "y_v": {"name": "y_v", "group": "Ungrouped variables", "definition": "[0,0.5,0.71,0.87,1,0.87,0.71,0.50,0]", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "random(0,3)", "description": "", "templateType": "anything", "can_override": false}, "tsct": {"name": "tsct", "group": "Ungrouped variables", "definition": "[[1,\"+\",\"+\",\"+\"],[2,\"+\",\"-\",\"-\"],[3,\"-\",\"-\",\"+\"],[4,\"-\",\"+\",\"-\"]]", "description": "", "templateType": "anything", "can_override": false}, "x_a": {"name": "x_a", "group": "Ungrouped variables", "definition": "random(1..359)", "description": "", "templateType": "anything", "can_override": false}, "sx_a": {"name": "sx_a", "group": "Ungrouped variables", "definition": "sin(x_a*pi/180)", "description": "", "templateType": "anything", "can_override": false}, "cx_a": {"name": "cx_a", "group": "Ungrouped variables", "definition": "cos(x_a*pi/180)", "description": "", "templateType": "anything", "can_override": false}, "tx_a": {"name": "tx_a", "group": "Ungrouped variables", "definition": "tan(x_a*pi/180)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "angle", "x", "y", "An", "index", "teta", "x_v", "y_v", "q", "tsct", "x_a", "sx_a", "cx_a", "tx_a"], "variable_groups": [], "functions": {"dragpointa": {"parameters": [["x0", "number"], ["y0", "number"]], "type": "html", "language": "javascript", "definition": "// set up the board\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-1.2,1.2,1.2,-1.2],grid:true,labels:true});\nvar board = div.board;\n\n\n//plot circle of radius 1 centred at origin\nboard.create('functiongraph',\n         [function(x){ return Math.sqrt(1-x*x)},-1,1]);\nboard.create('functiongraph',\n         [function(x){ return -1*Math.sqrt(1-x*x)},-1,1]);\n\n\n\nvar a = board.create('point',[x0,y0],{size:3});\na.setProperty({fixed:true});\n\n//var b = board.create('point',[-0.2,0],{size:3});\n//var c = board.create('point',[0.2,0],{size:3});\n//var d = board.create('point',[0.4,0],{size:3});\n\n//b.on('drag',function(){\n//  var x0 = Numbas.math.niceNumber(b.X());\n//  var y0 = Numbas.math.niceNumber(b.Y());\n//  Numbas.exam.currentQuestion.parts[0].gaps[2].display.studentAnswer(y0);\n//  Numbas.exam.currentQuestion.parts[0].gaps[3].display.studentAnswer(x0);\n//});\n//c.on('drag',function(){\n//  var x0 = Numbas.math.niceNumber(c.X());\n//  var y0 = Numbas.math.niceNumber(c.Y());\n//  Numbas.exam.currentQuestion.parts[0].gaps[6].display.studentAnswer(y0);\n//  Numbas.exam.currentQuestion.parts[0].gaps[7].display.studentAnswer(x0);\n//});\n//d.on('drag',function(){\n//  var x0 = Numbas.math.niceNumber(d.X());\n//  var y0 = Numbas.math.niceNumber(d.Y());\n//  Numbas.exam.currentQuestion.parts[0].gaps[6].display.studentAnswer(y0);\n//  Numbas.exam.currentQuestion.parts[0].gaps[7].display.studentAnswer(x0);\n//});\n\nreturn div;\n\n\n"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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>{dragpointa(x[0],y[0])}</p>\n<p></p>\n<p>Use the diagram above to&nbsp;determine $\\sin(\\var{angle[0]}^{\\circ})$ and $\\cos(\\var{angle[0]}^{\\circ})$. To get to point $A$, we started at $(1,0)$ and rotated by $\\var{angle[0]}^{\\circ}$.&nbsp;If you hover the mouse over the point $A$, you will be shown its coordinates.</p>\n<p>Give your answer to 2 d.p..</p>\n<p>$\\sin(\\var{angle[0]}^{\\circ}) =$ [[0]]</p>\n<p>$\\cos(\\var{angle[0]}^{\\circ}) =$ [[1]]</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(y[0],2)", "maxValue": "precround(y[0],2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(x[0],2)", "maxValue": "precround(x[0],2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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><img src=\"resources/question-resources/Unit_circle.png\" width=\"298\" height=\"264\"/></p>\n<p>Find the point $(x,y)$ on the unit circle when A= {teta[index]}$^\\circ$</p>\n<p>(Give your answers to <strong>two decimal places</strong>):</p>\n<p>$x$ = [[0]]&nbsp;</p>\n<p>$y$ = [[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x_v[index]}", "maxValue": "{x_v[index]}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{y_v[index]}", "maxValue": "{y_v[index]}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}, {"name": "Ria Rushin Joseph", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19976/"}], "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [["question-resources/PictureTriangle_0.png", "/srv/numbas/media/question-resources/PictureTriangle_0.png"], ["question-resources/Unit_circle.png", "/srv/numbas/media/question-resources/Unit_circle.png"]]}