// Numbas version: exam_results_page_options
{"name": "Percentage question 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Percentage question 3", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>This question will help you appreciate how % works in some in real life situations like % yield, mixture recipes and excess in formulae. You can then apply your knowledge to more real life examples.</p>\n<p>Answer the following three question parts. Please enter your answers as a decimal, not a fraction. Give your answer to two decimal places (only round your final answer, use the exact values on your calculator when working out any intermediate steps).</p>\n<p>If you would like to see how to do this question, click on 'Reveal answers' at the bottom of the page.</p>", "advice": "<p>You need to be aware of units in your answers. A later quiz will explore this in more detail. Read each question carefully to ensure you provide your answer in the requested units. If in doubt just input the number you have calculated.</p>\n<p>Many pharmaceutical calculations are rounded to two decimal places so we will expect answers to two decimal places unless otherwise stated. Round carefully.</p>\n<p><span style=\"text-decoration: underline;\"><strong>Part a</strong></span></p>\n<p>The fraction of yield is \\[ \\frac{Actual\\space yield}{Theoretical\\space yield}\\]</p>\n<p>Perecentage yield is calculated by coverting this fraction to a percentage by multipying by 100. Check earlier questions if you don't appreciate why this is</p>\n<p>So the equation to use is \\[Percentage\\space yield = 100 \\times \\frac{Actual\\space yield}{Theoretical\\space yield}\\]</p>\n<p>The units for Actual and Theoretical yields are both grams so we don't need to consolidate units</p>\n<p>So $ Percentage\\space yield = 100 \\times \\frac{\\var{actual}}{\\var{theoretical}}$</p>\n<p style=\"padding-left: 40px;\"><span style=\"text-decoration: underline;\"><strong>Part b</strong></span></p>\n<p style=\"padding-left: 40px;\">The formula tells us we need 10% Concentrated Compound Gentian Infusion BP to make up 100% of Alkaline Gentian Mixture BP as Potable water is used to <em><strong>make up to</strong> </em>100%.</p>\n<p style=\"padding-left: 40px;\">So we just need to work out 10% of {volume} millilitres</p>\n<p style=\"padding-left: 40px;\">If the answer we want is called $y$ we can use the equation</p>\n<p style=\"padding-left: 40px;\">$ \\frac{y}{\\var{volume}} = \\frac{10}{100}$</p>\n<p style=\"padding-left: 40px;\">Rearrange the equation to</p>\n<p style=\"padding-left: 40px;\">$y = {\\var{volume}}\\times \\frac{10}{100}$</p>\n<p></p>\n<p><span style=\"text-decoration: underline;\"><strong>Part c</strong></span></p>\n<p>You are asked to make {cream} grams Dithranol {percent}% Cream using Dithranol Powder and Emulsifing Ointment extemporaneously. To take into account some loss when transferring into the final container you need to make {excess}% excess. How many grams of Dithranol Powder should you use in total?</p>\n<p>There are several ways to work this out. I would approach it this way. I can use the numbers with changing units as everone is in grams.</p>\n<p>For <strong>{cream}</strong> grams Dithranol <strong>{percent}</strong> % Cream we would need $ \\frac {\\var{cream} \\times \\var{percent}}{100}$ grams of Dithranol Powder.</p>\n<p>We need to make <strong>{excess}</strong>% more to ensure we enough when transferring to the final container so need to use $ (100 + \\var{excess})$ % of the amount of Dithranol Powder above.</p>\n<p>Converting this to an equation $Amount \\space of \\space powder = \\frac {(100 + \\var{excess})\\times \\var{cream} \\times \\var{percent}}{100}$ grams.&nbsp;</p>\n<p>Take care to work out the bracketed sum first <em>remember BODMAS</em></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"actual": {"name": "actual", "group": "Ungrouped variables", "definition": "random(8 .. 12#0.1)", "description": "<p>The actual yield</p>", "templateType": "randrange", "can_override": false}, "theoretical": {"name": "theoretical", "group": "Ungrouped variables", "definition": "random(4 .. 7.9#0.1)", "description": "<p>The theoretical yield</p>", "templateType": "randrange", "can_override": false}, "cream": {"name": "cream", "group": "Ungrouped variables", "definition": "random(150 .. 500#50)", "description": "<p>Total weight of cream</p>", "templateType": "randrange", "can_override": false}, "percent": {"name": "percent", "group": "Ungrouped variables", "definition": "random(0.1 .. 2#0.1)", "description": "<p>% dithranol in cream</p>", "templateType": "randrange", "can_override": false}, "excess": {"name": "excess", "group": "Ungrouped variables", "definition": "random(5 .. 10#1)", "description": "<p>Excess % used to cover loss</p>", "templateType": "randrange", "can_override": false}, "volume": {"name": "volume", "group": "Ungrouped variables", "definition": "random(150 .. 500#20)", "description": "<p>Volume of mixture to make</p>", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["actual", "theoretical", "cream", "percent", "excess", "volume"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Copper oxide reacts with sulfuric acid to make copper sulfate and water. In an experiment, {actual} grams of dry copper sulfate crystals are made. If the theoretical yield is {theoretical} grams, calculate the percentage yield of copper sulfate.</p>", "minValue": "100*{actual}/{theoretical}", "maxValue": "100*{actual}/{theoretical}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct number of decimal places.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The formula for Alkaline Gentian Mixture BP is&nbsp;</p>\n<table style=\"width: 456px; height: 112px;\" height=\"151\">\n<tbody>\n<tr style=\"height: 28px;\">\n<td style=\"width: 345.099px; height: 28px; text-align: left;\">Concentrated Compound Gentian Infusion BP</td>\n<td style=\"width: 77.9119px; height: 28px;\">10%</td>\n</tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 345.099px; height: 28px; text-align: left;\">Sodium Bicarbonate BP</td>\n<td style=\"width: 77.9119px; height: 28px;\">5%</td>\n</tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 345.099px; height: 28px; text-align: left;\">Double Strength Chloroform Water BP</td>\n<td style=\"width: 77.9119px; height: 28px;\">50%</td>\n</tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 345.099px; height: 28px; text-align: left;\">Potable water</td>\n<td style=\"width: 77.9119px; height: 28px;\">to 100%</td>\n</tr>\n</tbody>\n</table>\n<p>How many mls of Concentrated Compound Gentian Infusion BP would you use to make {volume} mls of Alkaline Gentian Mixture BP</p>", "minValue": "{volume}*0.1", "maxValue": "{volume}*0.1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct number of decimal places.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>You are asked to make {cream} g Dithranol {percent} % Cream using Dithranol Powder and Emulsifing Ointment extemporaneously. To take into account some loss when transferring into the final container you need to make {excess} % excess. How many grams of Dithranol Powder should you use in total?</p>", "minValue": "{cream}*(100+{excess})*{percent}/100", "maxValue": "{cream}*(100+{excess})*{percent}/100", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct number of decimal places.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Bob Morris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4834/"}]}]}], "contributors": [{"name": "Bob Morris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4834/"}]}