on":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"478c7a7d-1b6e-456a-b23d-04bfbf0c4fe4","revisionId":"0384e8e5-3fdc-4194-bcdf-78f1054fb877","questionNumber":"7","questionType":"LA","specification":"","difficulty":2,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Estimating","calculatorUse":null,"parts":[{"id":"2ede5c3e-3387-4a50-969f-c0c6193e2ef2","label":"0","content":"Work out an estimate for the value of $\\frac{21.75 + \\sqrt{98.1}}{0.192}$","markscheme":"- Rounds numbers: $20$, $\\sqrt{100}$, and $0.2$ M1\n- Simplifies numerator: $20 + 10 = 30$ M1\n- Final answer: $\\frac{30}{0.2} = 150$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Rounds $\\sqrt{98.1}$ to $\\sqrt{100}$ or $10$.","code":"B"},{"id":"p2","marks":1,"description":"Method to calculate $\\frac{30}{0.2}$.","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 150.","code":"A"}],"finalAnswers":["150"],"generatedAt":"2026-05-06T15:43:55.755Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"round_then_calculate","label":"Round then calculate","steps":[{"type":"text","order":0,"title":"Round each value","content":"Because this asks for an **estimate**, replace each number with a nearby value that is easy to calculate with:\n\n- $21.75\\approx20$\n- $98.1\\approx100$, so $\\sqrt{98.1}\\approx\\sqrt{100}$\n- $0.192\\approx0.2$\n\nChoosing $100$ is especially helpful because it is a square number: its square root is an integer. This rounding earns the first method mark (M1).","highlights":[{"text":"Work out an estimate for the value of $\\frac{21.75 + \\sqrt{98.1}}{0.192}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\sqrt{\\htmlData{anchor=rootinput}{\\color{@sky}{100}}}=\\htmlData{anchor=rootresult}{\\color{@green}{10}}"},{"latex":"\\htmlData{anchor=twenty}{\\color{@sky}{20}}+\\htmlData{anchor=ten}{\\color{@green}{10}}=\\htmlData{anchor=total}{\\color{@orange}{30}}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"rootinput"},{"color":"green","style":"text-color","anchor":"rootresult"},{"color":"orange","style":"text-color","anchor":"total"}]},"order":1,"title":"Simplify the numerator","description":"Evaluate the square root, then add the two estimated terms in the numerator. Examiner annotation: 20 + 10 = 30 earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\frac{\\htmlData{anchor=top}{\\color{@orange}{30}}}{\\htmlData{anchor=bottom}{\\color{@sky}{0.2}}}=\\htmlData{anchor=result}{\\color{@green}{150}}"},{"text":"Examiner annotation: 30 divided by 0.2 = 150 earns A1."}]},"order":2,"title":"Divide the estimate","description":"Use the rounded denominator, 0.2, to finish the calculation."}]}],"generatedAt":"2026-07-21T03:14:18.432Z","modelVersion":"gpt-5.6-terra","explanationVersion":"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

Estimating Questions

Estimating Questions

Estimating Questions

Estimating Questions