Capture recapture – GCSE Maths

Higher · Grade 6

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Capture–recapture estimates a population: catch $M$ and tag them, release, catch $n$ later of which $m$ are tagged. Estimate $N=\frac{Mn}{m}$, assuming the tagged animals mixed in and the population did not change. Rearrange if $N$ is given and a different letter is missing.

Assumptions are marks: mixing, no tags falling off, no big births/deaths/migration between samples. An estimate is not an exact head-count — write it as a whole number of animals if that is the context, after the division.

Estimate $N=\frac{M\times n}{R}$ (tagged in first sample, size of second, tagged in second). Assume mixing, no tags lost, population closed. If tags leave, $R$ is too small and $N$ is too high.

Objectives

• Estimate a population from tagged animals in a second sample.
• Find how many tagged animals to expect in a sample.
• Write the tagged fraction, and recover how many were tagged first.

Key points

• Use the proportion $\frac{\text{tagged in first sample}}{\text{population}}=\frac{\text{tagged in second sample}}{\text{second sample size}}$.
• Rearrange to $N=\frac{Mn}{R}$, where $M$ is tagged, $n$ is the second sample size and $R$ is how many of those were already tagged.
• State the modelling assumptions when asked (mixing, tags stay on, population unchanged).
• Give the estimate as a whole number.

Worked examples

Questions and answers

GCSE Maths capture recapture questions and answers. Try each one, then open the answer. Easy questions come first.

Common mistakes

Most lost marks on this topic are one slip.

1. Dividing the sample by the tagged count and stopping

   Multiply by the number tagged first

2. Expecting every first-catch animal to appear in the second sample

   Use the sample as a fraction of the population

3. Giving the second sample size as the first catch when working backwards

   First catch = estimate × tagged in the sample ÷ sample size

Exam tips

• This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
• If the question says “show that”, the result is given. The marks are for the steps that reach it.
• The method is the same on AQA-style and Edexcel-style papers.
• Write the two fractions equal before you rearrange — that is the method mark even if the arithmetic slips.
• If $R$ does not divide $Mn$ exactly, round to the nearest whole number and say so.

Printable worksheet

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Questions students ask

Related topics

• Box plots
  Grade 6 · Higher
• Cumulative frequency
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• Histograms
  Grade 7 · Higher
• Averages from frequency tables
  Grade 4 · Foundation and Higher
• Sampling & bias
  Grade 4 · Foundation and Higher

More on Capture recapture

• Capture recapture worked examples and method
  The method in order, key facts and the full lesson explanation
• Capture recapture practice questions
  A second set of questions with answers, plus quick checks

AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Last updated 9 November 2026.