Cambridge IGCSE®
Set notation and Venn diagrams – Past paper
questions
The questions in this document have been compiled from a number of past papers, as indicated in the table
below.
Use these questions to formatively assess your learners’ understanding of this topic. Some questions have
additional ‘Challenge questions’ included. These do not form part of the original questions, but have been
added as part of the lesson plans included in Resource Plus.
Question
17
23
10
15
23
20
23
18
Year
2017
2017
2017
2017
2017
2020
2020
2020
Series
June
June
June
November
November
Specimen
Specimen
Specimen
Paper number
21
22
43
21
23
P1
P1
P2
The mark scheme for each question is provided at the end of the document.
You can find the complete question papers and the complete mark schemes (with additional notes where
available) on the School Support Hub www.cambridgeinternational.org/support.
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
1
17
(a) In this Venn diagram, shade the region F , G l .
F
G
[1]
(b)  = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {x: x is an odd number}
B = {x: x is a square number}
C = {x: x is a multiple of 3}
(i)
Write all the elements of  in the Venn diagram below.
B
A
C
[2]
(ii)
Another number is included in the set .
This number is in the region Al + B + C .
Write down a possible value for this number.
.............................................. [1]
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
2
23
(a)  = {students in a class}
P = {students who study physics}
C = {students who study chemistry}
The Venn diagram shows numbers of students.
P
C
5
11
8
7
(i)
Find the number of students who study physics or chemistry.
................................................. [1]
(ii)
Find n ^P k C lh .
................................................. [1]
(iii)
A student who does not study chemistry is chosen at random.
Find the probability that this student does not study physics.
................................................. [1]
(b) On the Venn diagram below, shade the region D j E l .
D
E
[1]
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
3
10
 = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
A = { x : x is a multiple of 3}
B = { x : x is prime}
C = { x : x G 25}
(a) Complete the Venn diagram.
B
A
C
[4]
(b) Use set notation to complete the statements.
(i)
26 ..................... B
[1]
(ii)
A + B = .....................
[1]
(c) List the elements of B , (C + A).
................................................... [2]
(d) Find
(i)
n(C),
................................................... [1]
(ii)
n ^Bl , ^B + Chh .
................................................... [1]
(e) ^A + Ch is a subset of ^A , Ch .
Complete this statement using set notation.
^A + Ch ..................... ^A , Ch [1]
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
4
15
(a) Q = {1, 2, 3, 4, 5, 6}
Write down a set P where P 1 Q.
P = .................................................. [1]
(b) Shade these regions in the Venn diagrams.
(A B) C'
M N'
M
N
A
B
C
[2]
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
5
23
(a) Shade the required regions on the Venn diagrams.
A
B
A
B
A ∪ B'
A' ∩ B
[2]
(b)  = { x : x is an integer and 60 1 x 1 70}
E = {x : x is an odd number}
F = {x : x is a prime number}
G = {x : x is a square number}
(i)
Complete the Venn diagram below to show this information.
E
F
61
G
[3]
(ii)
Find n ^E , F , Ghl .
................................................. [1]
(iii)
Use set notation to complete the statement.
E + F + G = ..................................
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
[1]
6
20 Use set notation to describe the shaded regions in each Venn diagram.
(a)
A
B
............................................... [1]
(b)
A
B
............................................... [1]
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
7
23
= {children who go to the park}
T = {children who play tennis}
G = {children who play golf}
120 children go to the park.
50 play tennis.
75 play golf.
25 do not play tennis or golf.
(a) Complete the Venn diagram.
T
G
...... ...... ......
......
[2]
(b) Find n(T ∩ G).
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
............................................... [1]
8
18 Shade the region in each of the Venn diagrams below.
(a)
A
B
A′ ∪ B
[1]
(b)
D
E
F
(D ∩ E)′ ∩ F.
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
[1]
9
Mark schemes
Question
Answer
Marks
17(a)
1
17(b)(i)
2
17(b)(ii)
Any even square number that is also a
multiple of 3
Question
Answer
23(a)(i)
23(a)(ii)
23(a)(iii)
24
5
7
12
23(b)
Question
Part marks
B1 for four out of the eight regions
correct
1
Marks
Part marks
1
1
1
1
Answer
10(a)
Marks
4
10(b)(i)
10(b)(ii)
10(c)
∉
∅
21, 23, 24, 29
1
1
2FT
10(d)(i)
10(d)(ii)
10(e)
5
9
⊂ or ⊆
1FT
1FT
1
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
Part marks
All 8 regions correct
M3 for 6 or 7 regions correct
M2 for 4 or 5 regions correct
M1 for 3 regions correct
Correct or FT
SC1 for 1 omission or 4 correct and
1 extra
Correct or FT if less than 10
Correct or FT if less than 10
10
Question
Answer
Marks
15(a)
Fewer than 6 elements from
{1, 2, 3, 4, 5, 6} or ∅
15(b)
Part marks
1
1
1
Question
Answer
23(a)
Marks
Part marks
2
B1 for each
3
B2 for 6 or 7 correct
B1 for 4 or 5 correct
A ∪ B′
A′ ∩ B
23(b)(i)
23(b)(ii)
23(b)(iii)
3
∅ or { }
1FT
1FT
FT their n(E ∪ F ∪ G)
FT their E ∩ F ∩ G
Question
Answer
Marks
Part marks
20(a)
20(b)
A oe
B′ ∩ A oe
1
1
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
11
Question
Answer
23(a)
23(b)
30
Question
Answer
Marks
Part marks
2
B1 for any 2 correct
1
FT from their diagram
Marks
18(a)
1
18(b)
1
Set notation and Venn diagrams – Past paper questions Copyright © UCLES 2018
Part marks
12