view"},"explanation":{"methods":[{"id":"state_valid_assumption","label":"State a valid assumption","steps":[{"type":"text","order":1,"title":"State one assumption","content":"A valid assumption is: **shaking the bag mixed the beads thoroughly, so the second sample was representative of the whole bag.**\n\nThis earns **B1**. Another acceptable assumption would be that none of the black crosses rubbed off before the second sample was taken.","highlights":[{"text":"Write down any assumptions you have made.","location":"specification"}]}]}],"generatedAt":"2026-07-20T16:24:33.065Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":87}},{"id":"bade8d4e-15a2-4e03-9a4a-267bc59803d9","revisionId":"37e432e0-25c4-486e-9b81-a073c4151174","questionNumber":"2","questionType":"LA","specification":"Carlos wants to find an estimate for the number of ants in a colony.\n\nHe catches 60 ants from the colony and marks each one with a dye. He then returns the ants to the colony.\n\nA week later, Carlos catches another 60 ants. 8 of these ants are marked with the dye.","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Capture Recapture","calculatorUse":null,"parts":[{"id":"62a3cc84-4f11-43d0-8e69-59af53d10e5b","label":"","content":"Work out an estimate for the number of ants in the colony.\n\nWrite down an assumption you have made.","markscheme":"- Sets up ratio: $\\frac{60}{x} = \\frac{8}{60}$ M1\n- Calculates estimate: $60 \\times 7.5 = 450$ A1\n- States assumption: e.g., the dye stayed on all of the ants. B1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Sets up a correct proportion, e.g., $\\frac{60}{x} = \\frac{8}{60}$.","code":"M"},{"id":"p2","marks":1,"description":"Correct estimate of 450.","code":"A"},{"id":"p3","marks":1,"description":"States a valid assumption regarding the marks or the population.","code":"B"}],"finalAnswers":["450"],"generatedAt":"2026-05-06T15:23:48.190Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"capture_recapture","label":"Capture–recapture","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{estimated marked proportion}=\\frac{60}{x}"},{"latex":"\\frac{60}{x}=\\frac{8}{60}"}]},"order":1,"title":"Form the ratio","description":"Let x be the total number of ants in the colony. Estimate the marked proportion in the colony using the marked proportion in the second catch. Forming this proportion earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\frac{60}{x}=\\frac{8}{60}"},{"latex":"x=60\\times\\frac{60}{8}"},{"latex":"x=60\\times 7.5"},{"latex":"x=450"}]},"order":2,"title":"Calculate the estimate","description":"Rearrange the proportion to find the total colony size. So the estimated colony size is 450 ants. This earns A1."},{"type":"text","order":3,"title":"State an assumption","content":"Assume that the dye stayed on all the marked ants during the week. This earns B1."}]}],"generatedAt":"2026-07-20T16:23:35.712Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":66}},{"id":"0310a90f-ffe1-4a8f-bdcc-93495e529b48","revisionId":"79d27630-cdfe-4c44-a15e-3c2304b2d1f2","questionNumber":"3","questionType":"LA","specification":"Beth wants to estimate the number of frogs in a lake. She catches a sample of 80 frogs, marks them and puts them back in the lake. Later that day, in a second sample of 80 frogs, she finds that 10 of them are marked.","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Capture Recapture","calculatorUse":null,"parts":[{"id":"b4f25725-d0f2-4581-9b48-2ead79c250c9","label":"a","content":"Work out an estimate for the number of frogs in the lake.","markscheme":"- Sets up ratio: $\\frac{80}{x} = \\frac{10}{80}$ M1\n- Calculates $80 \\times 8 = 640$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"point

Capture Recapture

Question 2

Capture Recapture Questions

Capture Recapture

Question 2

Capture Recapture Questions