ide 3000 by 10","style":"solid"}]},"order":2,"title":"Divide for estimate","description":"Divide the rounded numerator by the rounded denominator. The final estimated value earns A1."}]}],"generatedAt":"2026-07-20T16:39:42.640Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":42,"sampleSize":31}},{"id":"1106d965-dcef-45ac-bdef-2ef0d4c3e5c3","revisionId":"cb710d4c-b914-44a4-b4c7-947903599dbb","questionNumber":"2","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Estimating","calculatorUse":null,"parts":[{"id":"5453b2fb-b696-4f7b-b145-372f807d191c","label":"0","content":"Work out an estimate for the value of $\\frac{41.2 \\times 19.8}{0.49}$","markscheme":"- Rounds numbers to 1 significant figure: $40$, $20$, and $0.5$ M1\n- Performs calculation: $\\frac{40 \\times 20}{0.5} = \\frac{800}{0.5}$ M1\n- Final answer of $1600$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Rounds numbers to 1 significant figure ($40$, $20$, $0.5$).","code":"M"},{"id":"p2","marks":1,"description":"Correctly divides by $0.5$ (equivalent to multiplying by 2).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 1600.","code":"A"}],"finalAnswers":["1600"],"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 to one figure","content":"For an estimate, round each number to **1 significant figure** (the first non-zero digit):\n\n$$41.2\\approx40,\\qquad19.8\\approx20,\\qquad0.49\\approx0.5$$\n\nThis rounding earns the first mark.","highlights":[{"text":"Work out an estimate","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\frac{41.2\\times19.8}{0.49}\\approx\\frac{\\htmlData{anchor=rounded}{\\color{@sky}{40\\times20}}}{\\color{@amber}{0.5}}"},{"latex":"\\frac{\\htmlData{anchor=product}{\\color{@sky}{800}}}{\\color{@amber}{0.5}}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"rounded"},{"color":"sky","style":"text-color-with-background","anchor":"product"}],"connections":[{"to":"product","from":"rounded","color":"sky","label":"multiply"}]},"order":1,"title":"Substitute the estimates","description":"Put the rounded values into the original calculation. This substitution and multiplication earn the second mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=whole_fraction}{\\frac{800}{0.5}}"},{"latex":"\\htmlData{anchor=final_answer}{1600}"}],"highlights":[{"color":"sky","style":"text-color","anchor":"whole_fraction"},{"color":"green","style":"text-color-with-background","anchor":"final_answer"}],"connections":[{"to":"final_answer","from":"whole_fraction","color":"green","label":"divide","style":"solid"}]},"order":2,"title":"Divide by one half","description":"Now divide 800 by 0.5: 800 ÷ 0.5 = 1600. The final estimate is 1600, earning the final mark."}]}],"generatedAt":"2026-07-21T03:59:08.344Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"0e46e4d3-4920-4daf-9f89-bdade37a39b0","revisionId":"ed929698-6a10-4cd3-9e84-c792f5a18959","questionNumber":"3","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Estimating","calculatorUse":null,"parts":[{"id":"fd216f01-9c67-41ae-82bb-b74399e08741","label":"0","content":"Work out an estimate for the value of $\\frac{28.4 \\times 21.05}{5.9}$","markscheme":"- Rounds numbers to 1 significant figure: $30$, $20$, and $6$ M1\n- Performs calculation: $\\frac{30 \\times 20}{6} = \\frac{600}{6}$ M1\n- Final answer of $100$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Rounds numbe

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