GCSE & IGCSE maths practice

Venn diagrams questions and answers

A Venn diagram sorts things into sets. $A \cap B$ (A intersection B) is the overlap: in both. $A \cup B$ (A union B) is everything in A or B or both. $A'$ is everything not in A. $\xi$ is the universal set. Fill a Venn diagram from the middle (the overlap) outwards.

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

Start the questions Venn diagrams guide

Where venn diagrams comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: enumerate sets and combinations of sets using Venn diagrams. Higher only: conditional probability from Venn diagrams.
Cambridge IGCSE (0580)	Core: Venn diagrams with two sets and set notation. Extended: up to three sets and conditional probability from Venn diagrams.

The method

Put the overlap in first.
Then the rest of each set (set total − overlap).
Then the outside: total − everything in the circles.
Probability: the region's number ÷ the total (or ÷ the given set for conditional).

Venn diagrams questions

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Warm-up

Question 1Warm-upFoundation

$\xi = \{1, 2, \ldots, 10\}$ , $A$ = even numbers, $B$ = multiples of 3. List $A \cap B$ .

Question 2Warm-upFoundation

Using the same sets, find $n(A \cup B)$ , the number of elements in $A \cup B$ .

Exam-style

Question 3Exam-styleFoundation

Using the same sets, find $n(A')$ .

Question 4Exam-styleFoundation

30 students: 18 play football, 12 play tennis and 5 play both. How many play neither?

Question 5Exam-styleFoundation

One of the same 30 students is picked at random. Find the probability they play football only.

Question 6Exam-styleHigher

A student who plays tennis is picked at random. Find the probability they also play football.

Challenge

Question 7ChallengeFoundation

$n(A) = 20$ , $n(B) = 15$ and $n(A \cup B) = 28$ . Find $n(A \cap B)$ .

Question 8ChallengeFoundation

Which region is $A \cap B'$ ?

Common mistakes

Counting the overlap twice.
Forgetting the region outside the circles.
Using the wrong total for a "given that" probability.

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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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