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Mel makes.","markscheme":"- Calculate the change in value: $325600 - 352000 = -26400$ M1\n- Use the percentage change formula: $\\frac{26400}{352000} \\times 100$ M1\n- Final answer of 7.5% A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates the loss amount (£26,400).","code":"M"},{"id":"p2","marks":1,"description":"Divides the loss by the original price (£352,000).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 7.5.","code":"A"}],"finalAnswers":["7.5"],"generatedAt":"2026-05-07T01:43:33.169Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"percentage_loss","label":"Percentage loss","steps":[{"type":"text","order":0,"title":"Find the change","content":"The change is **selling price minus buying price**:\n\n$$325600-352000=-26400$$\n\nThe negative sign shows a loss. The loss itself is therefore $26400$. This earns the first M1 mark for calculating the change in value.","highlights":[{"text":"Calculate the percentage loss Mel makes.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{percentage loss}=\\htmlData{anchor=formula}{\\color{@sky}{\\frac{26400}{352000}\\times100}}"},{"latex":"\\text{percentage loss}=\\htmlData{anchor=decimal}{\\color{@sky}{0.075\\times100}}"},{"latex":"\\text{percentage loss}=\\htmlData{anchor=answer}{\\color{@green}{7.5\\%\\text{ loss}}}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"formula"},{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"decimal","from":"formula","color":"sky","label":"divide","style":"solid"}]},"order":1,"title":"Use original price","description":"Dividing the loss by the original price and multiplying by 100 earns the second M1. The final answer, 7.5% loss, earns A1."}]}],"generatedAt":"2026-07-21T03:56:47.430Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":53},"walkthroughVideo":null},{"id":"c0fe0f74-1974-4371-9cb6-bd3c9ae1e453","revisionId":"652c7824-b3a9-406d-9308-00da67cab488","questionNumber":"3","questionType":"LA","specification":"","difficultyBand":"medium","tier":null,"totalMarks":3,"sourceTitle":"Percentage Change","calculatorUse":null,"isCalculation":true,"parts":[{"id":"dc9d010f-11b9-4c62-8b14-051fb8432d6c","label":"0","content":"Last year Geri's council tax bill was £1815\n\nThis year she has to pay £1906 for her council tax.\n\nWork out the percentage increase in her council tax bill.\n\nGive your answer to 1 decimal place.","markscheme":"- Calculate the increase: $1906 - 1815 = 91$ M1\n- Calculate percentage: $\\frac{91}{1815} \\times 100 = 5.01377...$ M1\n- Round to 1 decimal place: 5.0% A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates the increase in tax (£91).","code":"M"},{"id":"p2","marks":1,"description":"Divides the increase by the original bill (£1815).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 5.0 (to 1 d.p.).","code":"A"}],"finalAnswers":["5.0"],"generatedAt":"2026-05-07T01:43:33.169Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"percentage_increase","label":"Percentage increase","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{increase}=\\htmlData{anchor=subtraction}{\\color{@sky}{1906-1815}}$"},{"latex":"$$\\text{increase}=\\htmlData{anchor=increase_result}{\\color{@green}{91}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"subtraction"},{"color":"green","style":"text-color-with-background","anchor":"increase_result"}],"connections":[{"to":"increase_result","from":"subtraction","color":"sky","label":"subtract"}]},"order":0,"title":"Find the increase","description":"Subtract last year's bill from this year's bill. This correct subtraction earns the first method mark (M1)."},{"type":"text","order":1,"title":"Use the original bill","content":"For a percentage increase, divide the increase by the **original** amount. Here, the original amount is last year's bill, $£1815$. Then multiply by $100$ to convert the result to a percentage.","highlights":[{"text":"Last year Geri's council tax bill was £1815","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{percentage increase}=\\htmlData{anchor=formula}{\\color{@orange}{\\dfrac{\\text{increase}}{\\text{original amount}}\\times 100}}$"},{"latex":"$$\\text{percentage increase}=\\htmlData{anchor=substitution}{\\color{@green}{\\dfrac{91}{1815}\\times 100}}$"},{"latex":"$$\\text{percentage increase}=\\color{@sky}{5.01377\\ldots\\%}$"}],"highlights":[{"color":"orange","style":"text-color","anchor":"formula"},{"color":"green","style":"text-color","anchor":"substitution"}],"connections":[{"to":"substitution","from":"formula","color":"orange","label":"substitute"}]},"order":2,"title":"Calculate the percentage","description":"Substituting the increase and original bill into the percentage-increase formula earns the second method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{percentage increase}=\\htmlData{anchor=unrounded}{\\color{@sky}{5.01377\\ldots\\%}}$"},{"latex":"$$\\boxed{\\text{percentage increase}=\\htmlData{anchor=rounded}{\\color{@green}{5.0\\%}}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"unrounded"},{"color":"green","style":"text-color","anchor":"rounded"}],"connections":[{"to":"rounded","from":"unrounded","color":"green","label":"round to 1 decimal place","style":"solid"}]},"order":3,"title":"Round the answer","description":"The question asks for one decimal place. The hundredths digit is 1, so the tenths digit stays unchanged; this earns the accuracy mark (A1)."}]}],"generatedAt":"2026-07-20T16:32:21.877Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":56},"walkthroughVideo":null}],"subjectCode":"igcse_maths__cie","summaries":[{"id":"61bdae87-69d9-400e-a849-f3614a5f09ef","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"86b74992-959b-46aa-9078-36351a13a3d6","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"c0fe0f74-1974-4371-9cb6-bd3c9ae1e453","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"2a24afd1-e695-4f02-83bf-c807aa126adb","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"94e8933a-0403-40fb-af1d-2566480f3238","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"6a5e6c36-4606-4a61-b54e-7ae905438c68","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"3a2eab83-cd65-4c6e-8a3f-24f642893462","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"47c4225d-9a70-4d4f-ae04-c2e68e2f28dd","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"4bdfea9d-e72a-40ea-b162-1d9019a30570","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"090917f4-34a9-449c-a0c0-60f80fe4a1de","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"f2405e53-20f4-4ae8-aa89-c4da95a654c9","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"55874878-cded-40b0-b390-b560f2fccf37","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"ab590872-483f-4eb4-a04d-e03c53dc0c5c","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"02da1f72-d40a-49e1-a99b-3a2251ce310c","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true}],"title":"Percentage Change","topicId":"c5227842-5c08-4222-afc5-c0a7f7ab34f2","topicSidebar":"$L3a","topicSlug":"grade-3-3-7-percentage-change","topicTitle":"Percentage Change"}]}],"$L3b","$L3c"]}]