Cambridge IGCSE™ Mathematics Core and Extended
Student Book answers
All answers were written by the authors. In examination, the way marks would be awarded to answers like these may be
different.
10
Set notation and Venn diagrams
Exercise 10.1 page 86
1
a
i
ii
Continents of the world
Student’s own answers
b
i
Even numbers
ii
Student’s own answers
i
Days of the week
ii
Student’s own answers
i
Months with 31 days
ii
Student’s own answers
i
Triangle numbers
ii
Student’s own answers
i
Boy’s names beginning with the letter M
ii
Student’s own answers
i
Prime numbers greater than 7
ii
Student’s own answers
i
Vowels
ii
o, u
i
Planets of the solar system
ii
Student’s own answers
i
Numbers between 3 and 12 inclusive
ii
Student’s own answers
i
Numbers between –5 and 5 inclusive
ii
Student’s own answers
c
d
e
f
g
h
i
j
k
2
a
c
7
7
d
7
f
Unquantifiably finite, though theoretically infinite
h
5
i
8
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
1
Cambridge IGCSE Mathematics Core and Extended 10 Student Book answers
Exercise 10.2 page 87
a
b
Q = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}
R = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
c
S = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
d
T = {1, 4, 9, 16, 25}
e
U = {1, 3, 6, 10, 15, 21, 28}
a
b
B = {55, 60, 65}
C = {51, 54, 57, 60, 63, 66, 69}
c
D = {64}
3
a
b
{p, q, r}, {p, q}, {p, r}, {q, r}, {p}, {q}, {r}, { }
{p, q}, {p, r}, {q, r}, {p}, {q}, {r}
4
a
b
True
True
c
True
d
False
e
False
f
True
g
True
h
False
1
2
Exercise 10.3 page 89
1
2
3
4
a
b
True
True
c
False
d
False
e
False
f
True
a
b
A ∩ B = {4, 6}
A ∩ B = {4, 9}
c
A ∩ B = {yellow, green}
a
b
A ⋃ B = {2, 3, 4, 6, 8, 9, 10, 13, 18}
A ⋃ B = {1, 4, 5, 6, 7, 8, 9, 16}
c
A ⋃ B = {red, orange, blue, indigo, violet, yellow, green, purple, pink}
a
E = {a, b, p, q, r, s, t}
b
A' = {a, b}
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
2
Cambridge IGCSE Mathematics Core and Extended 10 Student Book answers
5
6
a
E = {1, 2, 3, 4, 5, 6, 7, 8}
b
A' = {1, 4, 6, 8}
c
A ∩ B = {2, 3}
d
A ⋃ B = {1, 2, 3, 4, 5, 7, 8}
e
(A ∩ B)' = {1, 4, 5, 6, 7, 8}
f
A ∩ B' = {5, 7}
a
i
ii
A = {even numbers from 2 to 14}
B = {multiples of 3 from 3 to 15}
iii C = {multiples of 4 from 4 to 20}
b
i
A ∩ B = {6, 12}
ii
A ∩ C = {4, 8, 12}
iii B ∩ C = {12}
iv A ∩ B ∩ C = {12}
v
A ⋃ B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15}
vi C ⋃ B = {3, 4, 6, 8, 9, 12, 15, 16, 20}
7
a
i
ii
A = {1, 2, 4, 5, 6, 7}
B = {3, 4, 5, 8, 9}
iii C' = {1, 2, 3, 4, 5, 8, 9}
iv A ∩ B = {4, 5}
v
A ⋃ B = {1, 2, 3, 4, 5, 6, 7, 8, 9}
vi (A ∩ B)' = {1, 2, 3, 6, 7, 8, 9}
8
b
C⊂A
a
i
ii
W = {1, 2, 4, 5, 6, 7, 9, 10}
X = {2, 3, 6, 7, 8, 9}
iii Z' = {1, 4, 5, 6, 7, 8, 10}
iv W ∩ Z = {2, 9}
v
W ∩ X = {2, 6, 7, 9}
vi Y ∩ Z = { } or \
b
Z
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
3
Cambridge IGCSE Mathematics Core and Extended 10 Student Book answers
Exercise 10.4 page 91
1
a
b
2
i
A ∩ B = {Egypt}
ii
A ⋃ B = {Libya, Morocco, Chad, Egypt, Iran, Iraq, Turkey}
i
P ∩ Q = {11, 13, 17}
ii
P ⋃ Q = {2, 3, 5, 7, 11, 13, 15, 17, 19}
a
b
3
4
5
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
4
Cambridge IGCSE Mathematics Core and Extended 10 Student Book answers
Exercise 10.5 page 93
1
a
b
5
14
c
13
2
3
45
a 10
b 50
4
a
b
100
Student assessment 1 page 93
1
2
a
b
{even numbers from 2 to 8}
{even numbers}
c
{square numbers}
d
{oceans}
a
b
7
2
c
6
d
366
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
5
Cambridge IGCSE Mathematics Core and Extended 10 Student Book answers
3
a
b
4
5
{a, b}, {a}, {b}, {
A' = {m, t, h}
}
Student assessment 2 page 94
1
2
3
{2, 4}, {2, 6}, {2, 8}, {4, 6}, {4, 8}, {6, 8}, {2, 4, 6}, {2, 4, 8}, {2, 6, 8}, {4, 6, 8}
a
b
{Ankara, Cairo}
c
{Nairobi, Pretoria}
a
b
{2, 3, 5, 7, 11, 13, 17, 19}
c
{4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 23, 29}
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
6
Cambridge IGCSE Mathematics Core and Extended 10 Student Book answers
4
a
b
5
X = {multiples of 10}
a
b
6
Student assessment 3 page 94
1
a
b
2
a
32
{a, e, i, o, u}, {a, e, i, o}, {a, e, i, u}, {a, e, o, u}, {a, i, o, u}, {e, i, o, u}
b
{lion, cheetah}
c
\
d
\
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
7
Cambridge IGCSE Mathematics Core and Extended 10 Student Book answers
3
4
a
Let the number liking only cricket be x
b
15
c
5
d
16
a
b
5
35
c
40
d
50
e
15
f
12
g
10
h
78
i
78
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
8