// Numbas version: exam_results_page_options
{"name": "Percentages", "feedback": {"allowrevealanswer": true, "showtotalmark": true, "advicethreshold": 0, "intro": "", "feedbackmessages": [], "showanswerstate": true, "showactualmark": true}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "duration": 0, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "metadata": {"description": "<p>Calculating percentages, VAT, Profit, Loss</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Q 0.5 Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "tags": ["rebel", "REBEL", "Rebel", "rebelmaths", "teame"], "metadata": {"description": "<p>Introduction to percentage</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Solve the following correct to 1 decimal place:</p>", "advice": "<p>Click on the link below and watch the video on how to calculate a percentage.</p>\n<p><a href=\"https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/percent-intro-pre-alg/v/taking-a-percentage-example\" target=\"_blank\">Example of how to calculate percentages</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"per1": {"name": "per1", "group": "Ungrouped variables", "definition": "shuffle(3..10)[0..2]", "description": "", "templateType": "anything", "can_override": false}, "per4": {"name": "per4", "group": "Ungrouped variables", "definition": "random(15..35#5)", "description": "", "templateType": "anything", "can_override": false}, "num2": {"name": "num2", "group": "Ungrouped variables", "definition": "random(510..690#10)", "description": "", "templateType": "anything", "can_override": false}, "num5": {"name": "num5", "group": "Ungrouped variables", "definition": "random(8..14)*per1[1]", "description": "", "templateType": "anything", "can_override": false}, "per3": {"name": "per3", "group": "Ungrouped variables", "definition": "shuffle(1..2)[0..2]", "description": "", "templateType": "anything", "can_override": false}, "num3": {"name": "num3", "group": "Ungrouped variables", "definition": "random(11..15#0.5)*per4", "description": "", "templateType": "anything", "can_override": false}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "per1[0]*0.01*num1[0]", "description": "", "templateType": "anything", "can_override": false}, "num1": {"name": "num1", "group": "Ungrouped variables", "definition": "shuffle(110..250#10)[0..2]", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "(num3/per4)*per3[0]", "description": "", "templateType": "anything", "can_override": false}, "ans5": {"name": "ans5", "group": "Ungrouped variables", "definition": "(num5/per1[1])*100", "description": "", "templateType": "anything", "can_override": false}, "ans4": {"name": "ans4", "group": "Ungrouped variables", "definition": "(num1[1]/per3[1])*100", "description": "", "templateType": "anything", "can_override": false}, "per2": {"name": "per2", "group": "Ungrouped variables", "definition": "shuffle(12..35)[0..2]", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "per2[0]*0.01*num2", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["num1", "per1", "ans1", "num2", "per2", "ans2", "num3", "ans3", "per3", "per4", "ans4", "ans5", "num5"], "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>i) Find $\\var{per1[0]}$% of $\\var{num1[0]}$</p>\n<p>[[0]]</p>\n<p>ii) Find $\\var{per2[0]}$% of $\\var{num2}$</p>\n<p>[[1]]</p>\n<p>iii) $\\var{per4}$% of a number is $\\var{num3}$. What is&nbsp;$\\var{per3[0]}$% of the number?</p>\n<p>[[2]]</p>\n<p>iv) $\\var{per3[1]}$% of a number is $\\var{num1[1]}$. What is the number?</p>\n<p>[[3]]</p>\n<p>v) $\\var{per1[1]}$% of a number is $\\var{num5}$. What is the number?</p>\n<p>[[4]]</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": "{ans1}", "maxValue": "{ans1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "{ans2}", "maxValue": "{ans2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans3}", "maxValue": "{ans3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "{ans4}", "maxValue": "{ans4}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "{ans5}", "maxValue": "{ans5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "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}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Q1 percentages", "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/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "ans"], "tags": ["Percentage", "percentage", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>Divide {a} by {b} to get 1%, and multipy by {c} to get {c}% of the number.</p>\n<p>As seen below:</p>\n<p>$(\\frac{\\var{a}}{\\var{b}}) \\times \\var{c} = \\var{ans}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": "1", "vsetrangepoints": 5, "prompt": "<p>If $\\var{b}$% of a number is $\\var{a}$, what is $\\var{c}$% of this number?</p>", "expectedvariablenames": [], "checkingaccuracy": "2", "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>If $\\var{b}$% of a number is $\\var{a}$</p>\n<p>Find 1% of the number first, then calculate $\\var{c}$% of the number!!</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "{ans}", "marks": "2", "checkvariablenames": false, "checkingtype": "dp", "type": "jme"}], "statement": "<p>Calculate the following to 2 decimal places:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "(random(1.1..3.5 except[2,3]))*b", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(3..b-3)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(10..90#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "ans": {"definition": "{a}/{b}*{c} ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}}, "metadata": {"description": "<p>Percentages</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": []}]}, {"name": "Q2 Basic Percentages", "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/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "ans"], "tags": ["rebel", "Rebel", "REBEL", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>Divide {a} by {b} to get 1%, and multipy by {c} to get {c}% of the number.</p>\n<p>As seen below:</p>\n<p>$(\\frac{\\var{a}}{\\var{b}}) \\times \\var{c} = \\var{ans}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": "1", "vsetrangepoints": 5, "prompt": "<p>If $\\var{b}$% of a number is $\\var{a}$, what is $\\var{c}$% of this number?</p>", "expectedvariablenames": [], "checkingaccuracy": "2", "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>If $\\var{b}$% of a number is $\\var{a}$</p>\n<p>Find 1% of the number first, then calculate $\\var{c}$% of the number!!</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "{ans}", "marks": "2", "checkvariablenames": false, "checkingtype": "dp", "type": "jme"}], "statement": "<p>Calculate the following to 2 decimal places:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..10)*b", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(b..95)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(10..50#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "ans": {"definition": "{a}/{b}*{c} ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}}, "metadata": {"description": "<p>Basic Percentages Question</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": []}]}, {"name": " Q 3 VAT", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "tags": ["rebel", "REBEL", "Rebel", "rebelmaths", "teame", "VAT"], "metadata": {"description": "<p>Finding the cost including VAT</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following to the nearest cent:</p>", "advice": "<p>First we need to find&nbsp;$\\var{VAT}$% of&nbsp;$&euro;\\var{a}$. To do this we need to multiply $&euro;\\var{a}$ by $\\var{VAT}$ and divide by 100. The easiest way is to&nbsp;multiply $&euro;\\var{a}$ by $\\frac{\\var{VAT}}{100}$. This is the amount of VAT that must be paid. Add this on to the original cost priceto find the total selling price including VAT.</p>\n<p>$&euro;\\var{a} \\times \\var{newVAT1} = &euro;\\var{ans}$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(50..100)", "description": "", "templateType": "anything", "can_override": false}, "word": {"name": "word", "group": "Ungrouped variables", "definition": "random([\"cost\",\"selling\"])", "description": "", "templateType": "anything", "can_override": false}, "newVAT": {"name": "newVAT", "group": "Ungrouped variables", "definition": "100+{VAT}", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "{a}*{newVAT1}", "description": "", "templateType": "anything", "can_override": false}, "newVAT1": {"name": "newVAT1", "group": "Ungrouped variables", "definition": "{newVAT}/100", "description": "", "templateType": "anything", "can_override": false}, "VAT": {"name": "VAT", "group": "Ungrouped variables", "definition": "random(21..23)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["word", "a", "VAT", "ans", "newVAT", "newVAT1"], "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>The cost&nbsp;price of an item was &euro;$\\var{a}$ before VAT. What was the price including VAT at $\\var{VAT}$%?</p>\n<p>&euro;[[0]]</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>VAT is Value Added Tax. It must be added to the price. First we need to find out how much the VAT is. Find&nbsp;$\\var{VAT}$% of&nbsp;$&euro;\\var{a}$. Add this to the cost price.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans}", "maxValue": "{ans}", "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": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Q 4 Profit, Loss and Percentages", "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/"}], "functions": {}, "ungrouped_variables": ["a", "profit", "loss", "ansone", "aprofit", "aloss", "anstwo"], "tags": ["loss", "profit", "Rebel", "REBEL", "rebel", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p><strong>Cost price = 100%</strong></p>\n<p><em>Part 1:</em></p>\n<p>If sold at a profit of $\\var{profit}$%, then</p>\n<p>Selling price = $\\var{aprofit}$%</p>\n<p>$\\var{a}&nbsp;\\times (\\frac{\\var{aprofit}}{100}) = \\var{ansone}$</p>\n<p></p>\n<p>Part 2 :</p>\n<p>If sold at a loss of $\\var{loss}$%, then</p>\n<p>Selling price = $\\var{aloss}$%</p>\n<p>$\\var{a} \\times (\\frac{\\var{aloss}}{100}) = \\var{anstwo}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Sold at a profit of $\\var{profit}$%?</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>A profit of $\\var{profit}$% means that the seller made an extra&nbsp;$\\var{profit}$% of the cost price on the sale. So first we need to find that&nbsp;$\\var{profit}$% of the cost price.</p>\n<p>Then we add that on to&nbsp;$&euro;\\var{a}$ to find the selling price including the&nbsp;$\\var{profit}$% profit.</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": true, "minValue": "{ansone}", "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>Sold at a loss of $\\var{loss}$%?</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>A loss&nbsp;of $\\var{loss&nbsp;}$% means that the seller lost&nbsp;$\\var{loss&nbsp;}$% of the original cost price on the sale. So first we need to find that&nbsp;$\\var{loss&nbsp;}$% of the cost price.</p>\n<p>Then we subtract&nbsp;that from&nbsp;$&euro;\\var{a}$ to find the selling price including the&nbsp;$\\var{loss&nbsp;}$% loss.</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": "{anstwo}", "strictPrecision": true, "minValue": "{anstwo}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>The cost&nbsp;price of an item was &euro;{dpformat(a,2)}. To the nearest cent, what was the selling price if the item was:</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(40..150#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "loss": {"definition": "random(5..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "loss", "description": ""}, "anstwo": {"definition": "{a}*({aloss}/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "anstwo", "description": ""}, "ansone": {"definition": "{a}*({aprofit}/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ansone", "description": ""}, "profit": {"definition": "random(10..30)", "templateType": "anything", "group": "Ungrouped variables", "name": "profit", "description": ""}, "aloss": {"definition": "100 - {loss}", "templateType": "anything", "group": "Ungrouped variables", "name": "aloss", "description": ""}, "aprofit": {"definition": "100 + {profit}\n", "templateType": "anything", "group": "Ungrouped variables", "name": "aprofit", "description": ""}}, "metadata": {"description": "<p>Profit and Loss, Percentages</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": []}]}, {"name": "Q5  VAT", "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/"}], "functions": {}, "ungrouped_variables": ["VAT", "VATnew", "price", "ansone", "anstwo", "VATa", "VATnewa"], "tags": ["Rebel", "REBEL", "rebel", "rebelmaths", "teame", "VAT"], "preamble": {"css": "", "js": ""}, "advice": "<p>Price including VAT of $\\var{VAT}$% = $\\var{VATa}$%</p>\n<p><em>Part 1:</em></p>\n<p>To get price before VAT (100%), divide by $\\var{VATa}$% (or multiply by $\\frac{100}{\\var{VATa}}$)</p>\n<p>$(&euro;\\var{price} \\div (\\frac{\\var{VATa}}{100}))&nbsp; = &euro;\\var{ansone}$</p>\n<p><em>Part 2:</em></p>\n<p>First get the price before VAT, the answer from&nbsp;part 1</p>\n<p>Then, multiply by $\\var{VATnewa}$%, (or multiply by $\\frac{\\var{VATnewa}}{100})$</p>\n<p>$\\var{ansone} \\times (\\frac{\\var{VATnewa}}{100}) = &euro;\\var{anstwo}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>What is the price before VAT, to the nearest cent?</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The price includes VAT already, so the $\\var{VAT}$% has already been added on. So the price is 100% +&nbsp;$\\var{VAT}$%. We need to find 1% first and then 100%. Note if the answer is eg. 24 you need to enter 24.00.</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": true, "minValue": "{ansone}", "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>What will the new price be&nbsp;if the VAT rate changes to $\\var{VATnew}$%?</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Start with the price before VAT (answer to part a) and add on the new VAT.</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": "{anstwo}", "strictPrecision": true, "minValue": "{anstwo}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>The price of an item including VAT at $\\var{VAT}$% is &euro;$\\var{price}$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"anstwo": {"definition": "ansone*(1+({VATnew}/100))", "templateType": "anything", "group": "Ungrouped variables", "name": "anstwo", "description": ""}, "ansone": {"definition": "{price}/({VATa}/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ansone", "description": ""}, "price": {"definition": "random(80..250)*(1+(VAT/100))", "templateType": "anything", "group": "Ungrouped variables", "name": "price", "description": ""}, "VATnewa": {"definition": "100 + {VATnew}", "templateType": "anything", "group": "Ungrouped variables", "name": "VATnewa", "description": ""}, "VATa": {"definition": "100+{VAT}", "templateType": "anything", "group": "Ungrouped variables", "name": "VATa", "description": ""}, "VATnew": {"definition": "random(20..24 except VAT)", "templateType": "anything", "group": "Ungrouped variables", "name": "VATnew", "description": ""}, "VAT": {"definition": "random(13,21,22,23)", "templateType": "anything", "group": "Ungrouped variables", "name": "VAT", "description": ""}}, "metadata": {"description": "<p>VAT</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": []}]}, {"name": "Q7 Profit and Loss", "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/"}], "functions": {}, "ungrouped_variables": ["a", "profit", "loss", "ansone", "aprofit", "aloss", "anstwo"], "tags": ["cost", "loss", "profit", "Rebel", "REBEL", "rebel", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p><strong>Selling price = 100%</strong></p>\n<p><em>Part 1:</em></p>\n<p>If sold at a profit of $\\var{profit}$%, then</p>\n<p>Cost price = $\\var{aprofit}$%</p>\n<p>$&euro;\\var{a}&nbsp;\\times (\\frac{100}{\\var{aprofit}}) = &euro;\\var{ansone}$</p>\n<p>Then round this to two deicmal places.</p>\n<p></p>\n<p>Part 2 :</p>\n<p>If sold at a loss of $\\var{loss}$%, then</p>\n<p>Cost price = $\\var{aloss}$%</p>\n<p>$&euro;\\var{a}&nbsp;\\times (\\frac{100}{\\var{aloss}}) = &euro;\\var{anstwo}$</p>\n<p>Then round this to two deicmal places.</p>\n<p></p>\n<p></p>\n<p><strong>Note:</strong></p>\n<p>This question might require an awkward long division. If you are having problems with getting a correct answer you may need to work up to 5 or 6 decimal places in your long division.</p>\n<p>Here is a reminder video about doing long division:</p>\n<p><a href=\"https://www.khanacademy.org/math/arithmetic/multiplication-division/long_division/v/dividing-by-a-two-digit-number\">Long Division</a></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>There had been&nbsp;a profit of $\\var{profit}$% on the first item?</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The selling price already includes the $\\var{profit}$% profit so it is 100% +&nbsp;$\\var{profit}$%. Find 1% and then 100%.</p>\n<p>Note this question might require an awkward long division. If you are having problems with getting a correct answer you may need to work up to 5 or 6 decimal places in your long division.</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, "showPrecisionHint": false, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>There had been a loss of $\\var{loss}$% on the second item?</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Now the loss has already been taken into account so the selling price is 100% - $\\var{loss}$%. Find 1% and then 100%.</p>\n<p>Again, note this question might require an awkward long division. If you are having problems with getting a correct answer you may need to work up to 5 or 6 decimal places in your long division.</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": "{anstwo}", "strictPrecision": false, "minValue": "{anstwo}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "showPrecisionHint": false, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>The selling price of two items was &euro;$\\var{a}$ each. To the nearest cent, what was the cost price of each&nbsp;if:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(40..150#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "loss": {"definition": "random(5..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "loss", "description": ""}, "anstwo": {"definition": "{a}*(100/{aloss})", "templateType": "anything", "group": "Ungrouped variables", "name": "anstwo", "description": ""}, "ansone": {"definition": "{a}*(100/{aprofit})", "templateType": "anything", "group": "Ungrouped variables", "name": "ansone", "description": ""}, "profit": {"definition": "random(10..30)", "templateType": "anything", "group": "Ungrouped variables", "name": "profit", "description": ""}, "aloss": {"definition": "100 - {loss}", "templateType": "anything", "group": "Ungrouped variables", "name": "aloss", "description": ""}, "aprofit": {"definition": "100 + {profit}\n", "templateType": "anything", "group": "Ungrouped variables", "name": "aprofit", "description": ""}}, "metadata": {"description": "<p>Cost price, selling price, profit and loss</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": []}]}, {"name": "Q8 VAT", "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/"}], "functions": {}, "ungrouped_variables": ["VAT", "VATnew", "price", "ansone", "anstwo", "VATa", "VATnewa"], "tags": ["Rebel", "REBEL", "rebel", "rebelmaths", "teame", "VAT"], "preamble": {"css": "", "js": ""}, "advice": "<p>Price including VAT of $\\var{VAT}$% = $\\var{VATa}$%</p>\n<p>First get the price before VAT by,&nbsp;$(\\var{price} \\div \\frac{\\var{VATa}}{100})$</p>\n<p>Then, multiply by $\\var{VATnewa}$%, (or multiply by $\\frac{\\var{VATnewa}}{100})$</p>\n<p><strong>$(\\var{price} \\div \\frac{\\var{VATa}}{100}) \\times \\frac{\\var{VATnewa}}{100} = \\var{anstwo}$</strong></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>What is&nbsp;the price if the VAT rate changes to $\\var{VATnew}$%?</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The price already includes VAT so it is 100% + $\\var{VAT}$%. We need to find 1% and then 100% to find the original price. Now the new VAT rate is applied and added on.</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": "{anstwo}", "strictPrecision": true, "minValue": "{anstwo}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>The price of an item including VAT at $\\var{VAT}$% is &euro;$\\var{price}$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"anstwo": {"definition": "ansone*(1+({VATnew}/100))", "templateType": "anything", "group": "Ungrouped variables", "name": "anstwo", "description": ""}, "ansone": {"definition": "random(110..220#10)", "templateType": "anything", "group": "Ungrouped variables", "name": "ansone", "description": ""}, "price": {"definition": "ansone*(VATa/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "price", "description": ""}, "VATnewa": {"definition": "100 + {VATnew}", "templateType": "anything", "group": "Ungrouped variables", "name": "VATnewa", "description": ""}, "VATa": {"definition": "100+{VAT}", "templateType": "anything", "group": "Ungrouped variables", "name": "VATa", "description": ""}, "VATnew": {"definition": "random(20..26 except VAT)", "templateType": "anything", "group": "Ungrouped variables", "name": "VATnew", "description": ""}, "VAT": {"definition": "random(13.5,21,21.5,22,22.5,23)", "templateType": "anything", "group": "Ungrouped variables", "name": "VAT", "description": ""}}, "metadata": {"description": "<p>What is the change in price if the VAT changes</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": []}]}, {"name": "Q11 Selling price given cost and profit", "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/"}], "functions": {}, "ungrouped_variables": ["item", "price", "profit", "ans", "profita"], "tags": ["cost", "percentages", "profit", "rebel", "Rebel", "REBEL", "rebelmaths", "teame"], "advice": "<p>Cost price = 100%</p>\n<p>selling price = $\\var{profita}$%</p>\n<p>Selling price = $\\frac{\\var{price}}{100}&nbsp;\\times \\var{profita}$</p>\n<p><strong>$&euro;\\var{price}&nbsp;\\times \\frac{\\var{profita}}{100} = &euro;\\var{ans}$</strong></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>$\\var{item}$ which costs &euro;$\\var{price}$ was sold at a profit of $\\var{profit}$%. What was the selling price, to the nearest cent?</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": 0, "maxValue": "{ans}", "minValue": "{ans}", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>A profit of $\\var{profit}$% means that the seller made an extra&nbsp;$\\var{profit}$% of the cost price on the sale. So first we need to find that&nbsp;$\\var{profit}$% of the cost price.</p>\n<p>Then we add that on to&nbsp;$&euro;\\var{a}$ to find the selling price including the&nbsp;$\\var{profit}$% profit.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "<p>Calculate the Selling Price</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"profit": {"definition": "random(10..15#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "profit", "description": ""}, "item": {"definition": "random('A computer','An article','A Laptop', 'An insurance policy', 'A second-hand car')", "templateType": "anything", "group": "Ungrouped variables", "name": "item", "description": ""}, "price": {"definition": "random(1000..2000#100)", "templateType": "anything", "group": "Ungrouped variables", "name": "price", "description": ""}, "profita": {"definition": "100 + {profit}", "templateType": "anything", "group": "Ungrouped variables", "name": "profita", "description": ""}, "ans": {"definition": "{price}*({profita}/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}}, "metadata": {"description": "<p>Given the cost and profit, find the selling price</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": []}]}, {"name": "Q12 Prive including VAT", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "tags": ["rebelmaths", "teame", "VAT"], "metadata": {"description": "<p>Including VAT</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following to the nearest cent:</p>", "advice": "<p>The selling price of an item before VAT is equal to 100%, and the selling price including VAT of&nbsp;$\\var{VAT}$% has to equal&nbsp;$\\var{newVAT}$%.</p>\n<p>Therefore to get the selling price including VAT, divide by <strong>100</strong> and multiply by $\\var{newVAT}$, or simply multiply by $\\var{newVAT1}$ as seen below:</p>\n<p><em>$&euro;\\var{a} \\times \\var{newVAT1} = &euro;\\var{ans}$</em></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(90..140)", "description": "", "templateType": "anything", "can_override": false}, "newVAT": {"name": "newVAT", "group": "Ungrouped variables", "definition": "100+{VAT}", "description": "", "templateType": "anything", "can_override": false}, "newVAT1": {"name": "newVAT1", "group": "Ungrouped variables", "definition": "{newVAT}/100", "description": "", "templateType": "anything", "can_override": false}, "VAT": {"name": "VAT", "group": "Ungrouped variables", "definition": "random(18.5..24.5)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "{a}*{newVAT1}", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "VAT", "ans", "newVAT", "newVAT1"], "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>The&nbsp;selling price of an item was &euro;$\\var{a}$ before VAT. What was the price if the rate of VAT was $\\var{VAT}$%?</p>\n<p>&euro;[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans}", "maxValue": "{ans}", "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}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Q13 VAT", "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/"}], "functions": {}, "ungrouped_variables": ["VAT", "VATnew", "price", "ans", "VATa", "VATnewa"], "tags": ["rebel", "Rebel", "REBEL", "rebelmaths", "teame", "VAT"], "preamble": {"css": "", "js": ""}, "advice": "<p>Price including VAT of $\\var{VAT}$% = $\\var{price}$% (Total Vat $= \\var{VATa}$%)</p>\n<p>First get 1%, then multipy by 100 to get 100% or price before VAT.</p>\n<p>Then, multiply by $\\var{VATnewa}$%, (or multiply by $\\frac{\\var{VATnewa}}{100})$</p>\n<p><strong>$(\\var{price} \\div \\frac{\\var{VATa}}{100})$</strong></p>\n<p><strong>Or</strong></p>\n<p><strong>$\\var{price} \\times \\frac{100}{\\var{VATa}}&nbsp; = \\var{ans}$</strong></p>\n<p></p>\n<p><strong>Note:</strong></p>\n<p>This question might require an awkward long division. If you are having problems with getting a correct answer you may need to work up to 5 or 6 decimal places in your long division.</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>What was the price&nbsp;before VAT?</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The price includes VAT already, so the $\\var{VAT}$% has already been added on. So the price is 100% +&nbsp;$\\var{VAT}$%. We need to find 1% first and then 100%.</p>\n<p>Note, this question might require an awkward long division. If you are having problems with getting a correct answer you may need to work up to 5 or 6 decimal places in your long division.</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": "{ans}", "strictPrecision": true, "minValue": "{ans}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": false, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>The selling price of an item&nbsp;was &euro;$\\var{price}$ including VAT at $\\var{VAT}$%.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"price": {"definition": "random(80..250#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "price", "description": ""}, "VATnewa": {"definition": "100 + {VATnew}", "templateType": "anything", "group": "Ungrouped variables", "name": "VATnewa", "description": ""}, "VATa": {"definition": "100+{VAT}", "templateType": "anything", "group": "Ungrouped variables", "name": "VATa", "description": ""}, "ans": {"definition": "{price}/({VATa}/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}, "VATnew": {"definition": "random(20..24 except VAT)", "templateType": "anything", "group": "Ungrouped variables", "name": "VATnew", "description": ""}, "VAT": {"definition": "random(13.5,21,21.5,22,22.5,23)", "templateType": "anything", "group": "Ungrouped variables", "name": "VAT", "description": ""}}, "metadata": {"description": "<p>Find the exVAT price</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": []}]}, {"name": "Q14 Price Excluding VAT", "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/"}], "functions": {}, "ungrouped_variables": ["VAT", "VATnew", "price", "ans", "VATa", "VATnewa", "word"], "tags": ["Rebel", "REBEL", "rebel", "rebelmaths", "teame", "VAT"], "preamble": {"css": "", "js": ""}, "advice": "<p>Price including VAT of $\\var{VAT}$% = $&euro;\\var{price}$ (Total Vat $= \\var{VATa}$%)</p>\n<p>First get 1%, then multipy by 100 to get 100% or price before VAT.</p>\n<p>Then, multiply by $\\var{VATnewa}$%, (or multiply by $\\frac{\\var{VATnewa}}{100})$</p>\n<p><strong>$(&euro;\\var{price} \\div \\frac{\\var{VATa}}{100})$</strong></p>\n<p><strong>Or</strong></p>\n<p><strong>$&euro;\\var{price} \\times \\frac{100}{\\var{VATa}}&nbsp; = &euro;\\var{ans}$</strong></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>What was the bill before VAT?</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The price includes VAT already, so the $\\var{VAT}$% has already been added on. So the price is 100% +&nbsp;$\\var{VAT}$%. We need to find 1% first and then 100%.</p>\n<p>Note, this question might require an awkward long division. If you are having problems with getting a correct answer you may need to work up to 5 or 6 decimal places in your long division.</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": "{ans}", "strictPrecision": false, "minValue": "{ans}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": false, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>$\\var{word}$&nbsp;bill was &euro;{dpformat(price,2)}. This&nbsp;includes VAT at $\\var{VAT}$%.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"word": {"definition": "random([\"A mobile phone\",\"A car service\",\"An internet\",\" A resturant\"])", "templateType": "anything", "group": "Ungrouped variables", "name": "word", "description": ""}, "price": {"definition": "random(40..85#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "price", "description": ""}, "VATnewa": {"definition": "100 + {VATnew}", "templateType": "anything", "group": "Ungrouped variables", "name": "VATnewa", "description": ""}, "VATa": {"definition": "100+{VAT}", "templateType": "anything", "group": "Ungrouped variables", "name": "VATa", "description": ""}, "ans": {"definition": "{price}/({VATa}/100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}, "VATnew": {"definition": "random(20..24 except VAT)", "templateType": "anything", "group": "Ungrouped variables", "name": "VATnew", "description": ""}, "VAT": {"definition": "random(13.5,21,21.5,22,22.5,23)", "templateType": "anything", "group": "Ungrouped variables", "name": "VAT", "description": ""}}, "metadata": {"description": "<p>Finding the exVAT price</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": []}]}, {"name": "Q15 Simple Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "tags": ["percentage", "Percentage", "rebelmaths", "teame"], "metadata": {"description": "<p>Simple Percentages</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>$\\var{name1}$ spends $\\var{rent}$% of her wages on rent. She saves $\\var{save}$% of what is left in a $\\var{acc}$ account.</p>", "advice": "<p>Calculate how much rent is first:</p>\n<p>$&euro;\\var{wage} \\times \\frac{\\var{rent}}{100} = &euro;\\var{wage1}$</p>\n<p>Next caluculate the saving, after the rent is subtracted:</p>\n<p>$(&euro;\\var{wage} - &euro;\\var{wage1}) \\times \\frac{\\var{save}}{100} = &euro;\\var{wage2}$</p>\n<p>Spending money per week:</p>\n<p>$&euro;\\var{wage} - (&euro;\\var{wage1} + &euro;\\var{wage2}) = &euro;\\var{ans}$</p>\n<p>Rounding to two decimal places we get $&euro;\\var{ans_dec}$.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"wage": {"name": "wage", "group": "Ungrouped variables", "definition": "random(400..550#5)", "description": "", "templateType": "anything", "can_override": false}, "save": {"name": "save", "group": "Ungrouped variables", "definition": "random(10..25#5 except rent)", "description": "", "templateType": "anything", "can_override": false}, "name1": {"name": "name1", "group": "Ungrouped variables", "definition": "  random([\"Mary\",\"Kate\",\"Sinead\",\"Niamh\"])", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "{wage}-({wage1}+{wage2})", "description": "", "templateType": "anything", "can_override": false}, "wage1": {"name": "wage1", "group": "Ungrouped variables", "definition": "({wage}*({rent}/100))", "description": "", "templateType": "anything", "can_override": false}, "wage2": {"name": "wage2", "group": "Ungrouped variables", "definition": "({wage}-{wage1})*({save}/100)", "description": "", "templateType": "anything", "can_override": false}, "acc": {"name": "acc", "group": "Ungrouped variables", "definition": "random([\"current\",\"savings\",\"deposit\"])", "description": "", "templateType": "anything", "can_override": false}, "rent": {"name": "rent", "group": "Ungrouped variables", "definition": "random(25..50#5)", "description": "", "templateType": "anything", "can_override": false}, "ans_dec": {"name": "ans_dec", "group": "Ungrouped variables", "definition": "precround(ans,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["rent", "save", "wage", "wage1", "acc", "wage2", "name1", "ans", "ans_dec"], "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>If $\\var{name1}$'s weekly wage is $&euro;\\var{wage}$, how much spending money does she have per week?</p>\n<p>&euro;[[0]]</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>Find out how much the rent is.</p>\n<p>Take this away from her wage.</p>\n<p>She saves $\\var{save}$% of what is left.</p>\n<p>Everything left over is spending money.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans}", "maxValue": "{ans}", "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"}]}], "contributors": [{"name": "Deirdre Casey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/681/"}], "extensions": [], "custom_part_types": [], "resources": []}