Venn diagrams test questions - WJEC - GCSE Maths Revision

1

A Venn diagram with two overlapping circles. One circle is marked 'Set A' and the other 'Set B'. It also has numbers 8 and 9 in the universal set.

Which elements are contained within set A?

Set A = {2, 5, 11, 12}

Set A = {2, 3, 4, 5, 6, 7, 11, 12}

Set A = {1, 3, 4, 6, 7, 10, 13, 14, 15}

2

Which elements are contained within set B?

Set B = {1, 3, 4, 6, 7, 10, 13, 14, 15}

Set B = {2, 3, 4, 5, 6, 7, 11, 12}

Set B = {1, 10, 13, 14, 15}

3

Which items are not in either set A or set B?

{1, 10, 13, 14, 15}

{2, 5, 11,12}

{8, 9}

4

12 pupils were asked whether they had any pets. The four options were dog, cat, rabbit and none.

A table with one column labelled 'Pet' and another column labelled 'Name'. There are four rows: dog, cat, rabbit and none.

Which Venn diagram shows this information correctly?

A Venn diagram with 3 overlaping circles marked as Dog, Cat and Rabbit.

A Venn diagram with three overlapping circles. One marked 'Dog', another 'Cat' and the other 'Rabbit'.

A Venn diagram with three overlapping circles. One marked 'Dog', another 'Cat' and the other 'Rabbit'. It also has the name Sophie in the universal set.

5

A survey was carried out on 150 tourists to Wales asking which of the following museums, if any, they had visited:

St Fagans National History Museum
National Museum Cardiff
Big Pit National Coal Museum

27 of the visitors had visited St Fagans National History Museum and National Museum Cardiff and, of these, 8 had visited all the museums.

72 of the people had visited Big Pit National Coal Museum.

70 of the people had visited St Fagans National History Museum.

Some further information is given on the Venn diagram below. How many visitors had visited National Museum Cardiff?

A Venn diagram with three overlapping circles. One marked 'St Fagans National History Museum', another 'Big Pit National Coal Museum' and the other 'National Museum Cardiff'.

6

A survey was carried out on 150 tourists to Wales asking which of the following attractions, if any, they had visited:

National Slate Museum
National Wool Museum
National Library of Wales

27 of the visitors had visited National Slate Museum and National Wool Museum and, of these, 8 had visited all three attractions.

72 of the people had visited National Library of Wales.

70 of the people had visited National Slate Museum.

Some further information is given on the Venn diagram below. How many visitors had visited the National Library of Wales only?

A Venn diagram with three overlapping circles. One marked 'National Slate Museum', another 'National Library of Wales' and the other 'National Wool Museum'.

34 visitors

38 visitors

30 visitors

7

A survey was carried out on 200 tourists to the UK asking which of the following mountains, if any, they had visited:

Snowdon
Scafell Pike
Ben Nevis

6 of the visitors had visited all three mountains.

56 of the people had visited Ben Nevis.

70 of the people had visited Snowdon.

53 people had not visited any of the mountains.

Some further information is given on the Venn diagram below. How many visited Scafell Pike only?

A Venn diagram with three overlapping circles. One marked 'Snowdon', another 'Ben Nevis' and the other 'Scafell Pike'.

41 visitors

36 visitors

94 visitors

8

400 tourists were surveyed and asked which of the following mountains, if any, they had visited.

Snowdon
Scafell Pike
Ben Nevis

67 of the visitors had visited Snowdon and Scafell Pike and, of these, 8 had visited all three mountains.

23 people had visited Ben Nevis and Scafell Pike but not Snowdon.

125 of the people had visited Ben Nevis.

137 of the people had visited Snowdon.

Some further information is given on the Venn diagram below. How many visitors did not visit any of the three mountains?

400 visitors

47 visitors

353 visitors

9

Questions 9 - 10 are for Intermediate and Higher tier

A Venn diagram with two overlapping circles. One circle is marked 'Set A' and the other 'Set B'.

Find \({A}\cap{B}\)

\({A}\cap{B}\) = {1, 2, 3, 4, 5, 6, 7, 10,11 ,12, 13, 14 ,15}

\({A}\cap{B}\) = { 3, 4, 6, 7}

\({A}\cap{B}\) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11,12, 13, 14,15}

10

Find \({A}\cup{B}\)

\({A}\cup{B}\) = {1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 20, 22, 24}

\({A}\cup{B}\) = {1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 20, 22, 24, 28, 30}

\({A}\cup{B}\) = {3, 4, 6, 7}