GCSE & IGCSE maths practice

Frequency trees questions and answers

A frequency tree splits a group in stages. The first branches split the total (e.g. men and women); the next split each of those (e.g. passed and failed). The numbers on the branches from any point add up to the number at that point. Frequency trees show numbers of people, while tree diagrams show probabilities.

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

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Where frequency trees comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees.

The method

Start with the total at the left.
Split it on the first branches, then split each of those.
Branches from one point add to the number at that point.
Probability: the number you want over the total.

Frequency trees questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

100 people took a driving test: 60 men and 40 women. 45 of the men passed. How many men failed?

Question 2Warm-upFoundation

In the same test, 22 of the 40 women passed. How many women failed?

Exam-style

Question 3Exam-styleFoundation

How many of the 100 people passed?

Question 4Exam-styleFoundation

One of the 100 people is chosen at random. What is the probability they failed?

Question 5Exam-styleFoundation

What fraction of the women passed? Give it in its simplest form.

Question 6Exam-styleFoundation

200 students: $\tfrac{3}{5}$ are in Year 10 and the rest in Year 11. 40% of Year 10 and 30% of Year 11 walk to school. How many students walk?

Challenge

Question 7ChallengeFoundation

In the same school, how many Year 11 students don't walk?

Question 8ChallengeFoundation

A student who walks is chosen at random. What is the probability they are in Year 11?

Common mistakes

Adding across the wrong branches.
Using the grand total when the question is about one group.
Mixing up frequencies and probabilities.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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