Marks":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 numbers to 1 significant figure ($30$, $20$, $6$).","code":"M"},{"id":"p2","marks":1,"description":"Method to calculate $\\frac{600}{6}$.","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 100.","code":"A"}],"finalAnswers":["100"],"generatedAt":"2026-05-06T15:43:55.755Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"one_significant_figure","label":"Round then estimate","steps":[{"type":"text","order":0,"title":"Round each number","content":"To estimate, replace each number with a nearby value that is easy to calculate with. Round each number to **1 significant figure**: $28.4$ becomes $30$, $21.05$ becomes $20$, and $5.9$ becomes $6$. This earns the rounding method mark (M1).","highlights":[{"text":"Work out an estimate for the value of $\\frac{28.4 \\times 21.05}{5.9}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\frac{\\htmlData{anchor=originalNum}{28.4\\times21.05}}{\\htmlData{anchor=originalDen}{5.9}}$"},{"latex":"$$\\frac{\\htmlData{anchor=roundedNum}{30\\times20}}{\\htmlData{anchor=roundedDen}{6}}$"},{"latex":"$$\\frac{\\htmlData{anchor=calcNum}{600}}{\\htmlData{anchor=calcDen}{6}}$"},{"latex":"$$\\htmlData{anchor=answer}{100}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"originalNum"},{"color":"amber","style":"text-color","anchor":"roundedNum"},{"color":"sky","style":"text-color","anchor":"originalDen"},{"color":"amber","style":"text-color","anchor":"roundedDen"},{"color":"orange","style":"text-color","anchor":"calcNum"},{"color":"green","style":"text-color","anchor":"answer"}],"connections":[{"to":"roundedNum","from":"originalNum","color":"sky","label":"round to 1 s.f."},{"to":"roundedDen","from":"originalDen","color":"sky","label":"round to 1 s.f."},{"to":"calcNum","from":"roundedNum","color":"orange","label":"multiply"},{"to":"answer","from":"calcNum","color":"green","label":"divide"}]},"order":1,"title":"Substitute rounded values","description":"Round each number to 1 significant figure, then complete the estimate. The calculation 30 x 20 / 6 = 600 / 6 earns M1; the final answer 100 earns A1."}]}],"generatedAt":"2026-07-21T04:01:46.790Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"93fb3124-7ee5-48bb-9ab1-337661e00e77","revisionId":"8a8a8ac2-1428-403f-8b20-c72760da6fef","questionNumber":"4","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Estimating","calculatorUse":null,"parts":[{"id":"49ce52c3-db11-4506-9453-22705435448e","label":"0","content":"Work out an estimate for the value of $\\frac{7.4 + 23.05}{0.196}$","markscheme":"- Rounds numbers to appropriate values: $7$, $23$ (or $20$), and $0.2$ M1\n- Performs addition and division: $\\frac{30}{0.2}$ M1\n- Final answer of $150$ (or $135$ if using $20$) A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Rounds denominator to $0.2$.","code":"B"},{"id":"p2","marks":1,"description":"Adds rounded numerator values (e.g., $7 + 23 = 30$).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 150 or 135.","code":"A"}],"finalAnswers":["150","135"],"generatedAt":"2026-05-06T15:43:55.755Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"round_and_estimate","label":"Round then estimate","steps":[{"type":"text","order":0,"title":"Round to easy values","content":"For a

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