od mark; obtaining 225 earns the final accuracy mark."}]}],"generatedAt":"2026-07-21T04:11:50.210Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"1441f2d6-a3a1-4e59-b600-f9bf17eb9f09","revisionId":"9ddb8d80-cc33-4567-8727-3324e12078eb","questionNumber":"6","questionType":"LA","specification":"","difficulty":1,"difficultyBand":null,"totalMarks":3,"sourceTitle":"Estimating","calculatorUse":null,"parts":[{"id":"e724a84b-c9c1-4c6f-8d65-c9194ada154f","label":"0","content":"Work out an estimate for the value of $\\frac{18.3 + 62.8}{0.13}$","markscheme":"- Rounds numbers: $20$, $60$, and $0.1$ M1\n- Performs calculation: $\\frac{80}{0.1}$ M1\n- Final answer of $800$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Rounds denominator to $0.1$.","code":"B"},{"id":"p2","marks":1,"description":"Adds rounded numerator values ($20 + 60 = 80$).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 800.","code":"A"}],"finalAnswers":["800"],"generatedAt":"2026-05-06T15:43:55.755Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"round_then_divide","label":"Round then divide","steps":[{"type":"text","order":0,"title":"Round each number","content":"Round each number to one significant figure: $18.3\\to20$, $62.8\\to60$ and $0.13\\to0.1$.\n\nExaminer: rounding to $20$, $60$ and $0.1$ earns M1.","highlights":[{"text":"Work out an estimate","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\frac{\\htmlData{anchor=originalnumerator}{\\color{@sky}{18.3+62.8}}}{\\htmlData{anchor=originaldenominator}{\\color{@orange}{0.13}}}"},{"latex":"\\frac{\\htmlData{anchor=roundednumerator}{\\color{@sky}{20+60}}}{\\htmlData{anchor=roundeddenominator}{\\color{@orange}{0.1}}}"},{"latex":"\\frac{\\htmlData{anchor=estimate}{\\color{@green}{80}}}{0.1}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"roundednumerator"},{"color":"orange","style":"text-color-with-background","anchor":"roundeddenominator"},{"color":"green","style":"text-color-with-background","anchor":"estimate"}],"connections":[{"to":"roundednumerator","from":"originalnumerator","color":"sky","label":"round values","style":"solid"},{"to":"roundeddenominator","from":"originaldenominator","color":"orange","label":"round","style":"solid"},{"to":"estimate","from":"roundednumerator","color":"green","label":"add","style":"solid"}]},"order":1,"title":"Substitute rounded values","description":"Replace each original number with a sensible rounded value, then add the numerator. Examiner: obtaining 80 divided by 0.1 earns M1."},{"type":"text","order":2,"title":"Divide by one tenth","content":"Dividing by $0.1$ is the same as multiplying by $10$, so $$\\frac{80}{0.1}=800.$$ \n\nThis is an **estimate**, because the original numbers were rounded. Examiner: the final answer $800$ earns A1."}]}],"generatedAt":"2026-07-21T04:10:35.118Z","modelVersion":"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":

Estimating Questions

Estimating Questions

Estimating Questions

Estimating Questions