GCSE · Venn diagrams & set notation

Venn diagramsExam-style questions

Building a Venn diagram from worded information — why you fill the overlap first and work outwards, what the number in a region actually counts, the universal set and the "neither" region outside the circles, and how the grand total pins down whichever region is missing.

Start practising Read the lesson

13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
$85$ $85$ students were asked whether they study Spanish and whether they study German.
- $47$ study Spanish,
- $33$ study German,
- $15$ study both Spanish and German.
(a) Draw a Venn diagram to show this information.

(b) Work out how many of the $85$ $85$ students study exactly one of the two languages.
Level 3 · 5 marksTry it
2
A sports club has $50$ members.

$26$ of the members play badminton, $19$ play squash and $8$ play both badminton and squash.

(a) Work out how many members play neither badminton nor squash.

(b) Sam says: " $26 + 19 = 45$ , and $50 - 45 = 5$ , so $5$ members play neither."

Explain why Sam's method is wrong.
Level 3 · 4 marksTry it
3
$50$ people were asked whether they had visited France ( $F$ ) or Spain ( $S$ ).

$28$ had visited France, $24$ had visited Spain, and $6$ had visited neither.

(a) Work out how many people had visited both France and Spain. (2 marks)

(b) One of the $50$ people is chosen at random. Work out the probability that they had visited France but not Spain. (1 mark)
Level 3 · 3 marksTry it