// Numbas version: finer_feedback_settings
{"name": "Q3 Ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["numberone", "numbertwo", "ans", "lent", "width", "area", "numberthree", "numberthreea", "numberfour", "numberfoura", "numberfive", "numberfivea", "numberfiveb", "ansone", "anstwo", "ansthree", "num1", "num2", "num3", "a1", "a2", "a3"], "name": "Q3 Ratios", "tags": ["ratio", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p></p>\n<p><em>Part 1:</em></p>\n<p>Add the three ratios together, which gives $15$</p>\n<p>Therefore $1$ is equal to $\\frac{180}{15}$degrees (12degrees)</p>\n<p>&nbsp;Multiply each ratio by 18 to find the value of each angle in degrees</p>\n<p>$12&nbsp;\\times \\var{num1}$</p>\n<p>$12&nbsp;\\times&nbsp;\\var{num2}$</p>\n<p>$12&nbsp;\\times&nbsp;\\var{num3}$</p>\n<p></p>\n<p><em>Part 2:</em></p>\n<p>Add the three ratios together, which gives $10$</p>\n<p>Therefore $1$ is equal to $\\frac{180}{10}$degrees (18degrees)</p>\n<p>&nbsp;Multiply each ratio by 18 to find the value of each angle in degrees</p>\n<p>$18 \\times \\var{numberthree}\\frac{1}{\\var{numberthreea}}$</p>\n<p>$18 \\times&nbsp;\\var{numberfour}\\frac{1}{\\var{numberfoura}}$</p>\n<p>$18 \\times&nbsp;\\var{numberfive}\\frac{\\var{numberfiveb}}{\\var{numberfivea}}$</p>\n<p><em></em></p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>If the angles of a triangle are in the ratio $\\var{num1}:\\var{num2}:\\var{num3}$.</p>\n<p></p>\n<p>Find the angles in degrees.</p>\n<p>[[0]]degrees</p>\n<p>[[1]]degrees</p>\n<p>[[2]]degrees</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>There are 180 degrees in a triangle.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{a1}", "minValue": "{a1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a2}", "minValue": "{a2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a3}", "minValue": "{a3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>If the angles of a triangle are in the ratio $\\var{numberthree}\\frac{1}{\\var{numberthreea}}:\\var{numberfour}\\frac{1}{\\var{numberfoura}}:\\var{numberfive}\\simplify{{numberfiveb}/{numberfivea}}$.</p>\n<p></p>\n<p>Find the angles in degrees.</p>\n<p>[[0]]degrees</p>\n<p>[[1]]degrees</p>\n<p>[[2]]degrees</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Convert the fraction into top heavy fractions. Simplify this ratio into integers like in Q1 (c). Now continue as in part (a) above.</p>\n<p>Or, alternatively add the fractions in fraction form.</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": "{ansone}", "strictPrecision": false, "minValue": "{ansone}", "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": "{anstwo}", "strictPrecision": false, "minValue": "{anstwo}", "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": "{ansthree}", "strictPrecision": false, "minValue": "{ansthree}", "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 shape questions, correct to 2 decimal places.</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"num1": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "7", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "15-(num1+num2)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "numberfivea": {"definition": "{numberthreea}*{numberfoura}", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfivea", "description": ""}, "ans": {"definition": "({area}-1)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}, "numberone": {"definition": "random(2..25)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberone", "description": ""}, "anstwo": {"definition": "18*({numberfour} + (1/{numberfoura}))", "templateType": "anything", "group": "Ungrouped variables", "name": "anstwo", "description": ""}, "ansone": {"definition": "18*({numberthree} + (1/{numberthreea}))", "templateType": "anything", "group": "Ungrouped variables", "name": "ansone", "description": ""}, "area": {"definition": "lent*width", "templateType": "anything", "group": "Ungrouped variables", "name": "area", "description": ""}, "numberfour": {"definition": "random(2..4 except {numberthree})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfour", "description": ""}, "numberthree": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberthree", "description": ""}, "width": {"definition": "1-{numbertwo}/100", "templateType": "anything", "group": "Ungrouped variables", "name": "width", "description": ""}, "numberfiveb": {"definition": "{numberfivea}-({numberthreea}+{numberfoura})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfiveb", "description": ""}, "numberthreea": {"definition": "random(2..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberthreea", "description": ""}, "numberfoura": {"definition": "random(2..8 except {numberthreea})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfoura", "description": ""}, "a1": {"definition": "12*num1", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "12*num3", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "12*num2", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "lent": {"definition": "1+{numberone}/100", "templateType": "anything", "group": "Ungrouped variables", "name": "lent", "description": ""}, "ansthree": {"definition": "18*({numberfive} + ({numberfiveb}/{numberfivea}))", "templateType": "anything", "group": "Ungrouped variables", "name": "ansthree", "description": ""}, "numberfive": {"definition": "random(2..4 except {numberthree} except {numberfour})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfive", "description": ""}, "numbertwo": {"definition": "random(2..25 except {numberone})", "templateType": "anything", "group": "Ungrouped variables", "name": "numbertwo", "description": ""}}, "metadata": {"description": "<p>Ratio Questions</p>\n<p>rebel</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/"}]}