sion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"8acdfb34-d2c3-4d01-88e9-2a02f48f6fe3","revisionId":"204bf5db-790e-4627-9aaa-2e70cf44e557","questionNumber":"8","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Estimating","calculatorUse":null,"parts":[{"id":"df202d9b-1c99-4cd1-848d-e2fdef1995c0","label":"0","content":"Work out an estimate for the value of $\\frac{8.3 \\times 18.7}{0.52}$","markscheme":"- Rounds numbers: $8$, $20$, and $0.5$ M1\n- Performs calculation: $\\frac{160}{0.5}$ M1\n- Final answer of $320$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Rounds numbers to 1 significant figure ($8$, $20$, $0.5$).","code":"M"},{"id":"p2","marks":1,"description":"Method to multiply $8 \\times 20$ and divide by $0.5$.","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 320.","code":"A"}],"finalAnswers":["320"],"generatedAt":"2026-05-06T15:43:55.755Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"round_and_calculate","label":"Round then calculate","steps":[{"type":"text","order":0,"title":"Round each number","content":"For an estimate, replace each number with a nearby, easy-to-use number. Rounding to **one significant figure** gives\n\n$$8.3\\approx 8,\\qquad 18.7\\approx 20,\\qquad 0.52\\approx 0.5$$\n\nThis earns the first M1 mark: the three required rounded values are correct.","highlights":[{"text":"Work out an estimate for the value of $\\frac{8.3 \\times 18.7}{0.52}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\frac{\\htmlData{anchor=num}{\\color{@sky}{8\\times20}}}{0.5}"},{"latex":"\\frac{\\htmlData{anchor=num2}{\\color{@sky}{160}}}{0.5}"},{"text":"This gives the second M1 mark: the rounded calculation is 160 divided by 0.5."}],"highlights":[{"color":"sky","style":"text-color","anchor":"num"},{"color":"sky","style":"text-color","anchor":"num2"}],"connections":[{"to":"num2","from":"num","color":"sky","label":"multiply"}]},"order":1,"title":"Substitute rounded values","description":"Put the rounded values into the original fraction, then multiply only the numerator."},{"type":"text","order":2,"title":"Divide to estimate","content":"Now divide the numerator by the denominator:\n\n$$\\frac{160}{0.5}=320$$\n\nThe final estimate is $320$. Reaching $320$ earns the A1 mark."}]}],"generatedAt":"2026-07-21T04:13:07.739Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"52035651-b070-4185-8a94-c6c05ac9d730","revisionId":"3ea540f1-a909-40b5-be3b-97affefe10e6","questionNumber":"9","questionType":"LA","specification":"Eddie and Ellen use a calculator to work out $\\frac{431.1}{14.3 + 3.8^2}$\n\nEddie's answer is 1.5\n\nEllen's answer is 15\n\nOne of those answers is correct.","difficulty":2,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Estimating","calculatorUse":null,"parts":[{"id":"38455511-0b20-447f-bb06-d94ef38ea9e2","label":"0","content":"Use approximations to find out which answer is correct.","markscheme":"- Rounds numbers to 1 significant figure: $400$, $10$ (or $14$), and $4$ M1\n- Performs calculation: $\\frac{400}{14 + 16} = \\frac{400}{30} \\approx 13.3$ M1\n- Concludes Ellen is correct A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Rounds values to 1 significant figure (e.g., $400$, $10$ or $14$, $4$).","code":"M"},{"id":"p2","marks":1,"description":"Calculates an estimate (e.g., $\\frac{400}{30}$ or $\\frac{400}{26}$).","code":"M"},{"id":"p3","marks":1,"description":"Identifies Ellen as the correct person based on the estimate.","code":"A"}],"finalAnswers":["Ellen"],"generatedAt":"2026-05-06T15:43:55.755Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"estimate","label":"Estimate the calculation","steps":[{"type":

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