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.
13
Equations and inequalities
Exercise 13.1 page 126
1
2
3
4
5
a
b
x = –4
y=5
c
y = –5
d
p = –4
e
y=8
f
x = –5.5
a
x4
b
x=5
c
x=6
d
y = –8
e
y=4
f
m = 10
a
b
m=1
p=3
c
k = –1
d
x = –21
e
x=2
f
y=3
a
b
x=6
y = 14
c
x=4
d
m = 12
e
x = 35
f
p = 20
a
b
x = 15
x = –5
c
x = 7.5
d
x=8
e
x = 2.5
f
x = 10
1
3
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
1
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
6
7
a
b
x=5
x = 14
c
x = 22
d
x=5
e
x=8
f
x=2
a
b
y = 10
x = 17
c
x = 13
d
y = –5
e
x=4
f
x = 6.5
Exercise 13.2 page 128
1
a
i
ii
3x + 60 = 180
x = 40
iii 40°, 60°, 80°
b
i
3x = 180
ii
x = 60
iii 20°, 80°, 80°
c
i
18x = 180
ii
x = 10
iii 20°, 50°, 110°
d
i
6x = 180
ii
x = 30
iii 30°, 60°, 90°
e
i
7x – 30 = 180
ii
x = 30
iii 10°, 40°, 130°
f
i
9x – 45 = 180
ii
x = 25
iii 25°, 55°, 100°
2
a
i
ii
12x = 360
x = 30
iii 90°, 120°, 150°
b
i
11x + 30 = 360
ii
x = 30
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
2
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
iii 90°, 135°, 135°
c
i
12x + 60 = 360
ii
x = 25
iii 35°, 80°, 90°, 155°
d
i
10x + 30 = 360
ii
x = 33
iii 33°, 94°, 114°, 119°
3
a
i
ii
11x – 80 = 360
x = 40
iii 40°, 80°, 80°, 160°
b
i
10x + 60 = 360
ii
x = 30
iii 45°, 90°, 95°, 130°
c
i
16x + 8 = 360
ii
x = 22
iii 44°, 96°, 100°, 120°
d
i
9x + 25 = 360
ii
x = 37.2 (to 1 d.p.)
iii 37°, 57°, 127°, 139° (to the nearest whole number)
e
i
6x + 18 = 180
ii
x = 27
iii 50°, 50°, 130°, 130°
4
5
6
a
b
20
25
c
14
d
25
e
31
f
40
a
b
50
13
c
40
d
40
a
b
5
2
c
7
d
1.1
e
25
f
15
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
3
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
Exercise 13.3 page 132
1
2
3
4
5
6
a
b
x=4
x=6
y=2
y=5
c
x=6
y = –1
d
x=5
y=2
e
x=5
y=2
f
x=4
y=9
a
b
x=3
x=7
y=2
y=4
c
x=1
y=1
d
x=1
y=5
e
x=1
y = 10
f
x=8
y=2
a
b
x=5
x=4
y=4
y=3
c
x = 10 y = 5
d
x=6
y=4
e
x=4
y=4
f
x = 10 y = –2
a
b
x=5
x=4
y=4
y=2
c
x=5
y=3
d
x=5
y = –2
e
x=1
y=5
f
x = –3 y = –3
a
b
x = –5 y = –2
x = –3 y = –4
c
x=4
y 3
d
x=2
y=7
e
x=1
y=1
f
x=2
y=9
a
b
x=2
x=5
y=3
y = 10
c
x=4
y=6
d
x=4
y=4
e
x=5
y=1
f
x = –3 y = –3
2
3
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
4
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
7
a
x=1
y = –1
b
x  11
2
y=8
3
c
x=4
y=0
d
x=3
y=4
e
x=2
y=8
f
x=1
y=1
Exercise 13.4 page 134
1
2
3
4
a
b
x=2
x=1
y=3
y=4
c
x=5
y=2
d
x=3
y=3
e
x=4
y=2
f
x=6
y=1
a
b
x=1
x=5
y=4
y=2
c
x=3
y=3
d
x=6
y=1
e
x=2
y=3
f
x=2
y=3
a
b
x=0
x=5
y=3
y=2
c
x=1
y=7
d
x=6
y=4
e
x=2
y=5
f
x=3
y=0
a
b
x = 1 y = 0.5
x = 2.5 y = 4
c
x
1
5
y=4
d
x
3
4
y
1
2
e
x=5
y
1
3
f
x
1
2
y=1
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
5
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
Exercise 13.5 page 134
1
2
3
4
5
6
10 and 7
16 and 9
x=1 y=4
x=5 y=2
Question should read: A man’s age is three times his son’s age. Ten years ago he was two and a
half times his son’s age. To give the answers: 60 and 20 years old.
60 and 6 years old
Exercise 13.6 page 136
1
2
3
4
a
b
7
3
c
6
d
7
e
10
f
15
a
b
7
6
c
6
d
10
e
3
a
b
8
5
c
8
d
6
e
6
a
b
6, 18, 26
160, 214, 246, 246
c
50°, 80°, 100°, 140°, 170°
d
80°, 80°, 80°, 160°, 160°, 160°
e
150°, 150°, 150°, 150°, 120°, 120°, 120°, 120°
Exercise 13.7 page 138
1
a
b
–4 and –3
–2 and –6
c
1 and –12
d
2 and 5
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
6
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
2
3
4
e
2 and 3
f
2 and 4
a
b
–5 and 2
–2 and 5
c
–7 and 2
d
–2 and 7
e
–5 and 3
f
–3 and 5
a
b
–3 and –2
–3
c
–8 and –3
d
4 and 6
e
–4 and 3
f
–2 and 6
a
b
–2 and 4
–4 and 5
c
–6 and 5
d
–6 and 7
e
–7 and 9
f
–9 and 6
Exercise 13.8 page 138
1
2
–3 and 3
a
b
–4 and 4
c
–5 and 5
d
–11 and 11
e
–12 and 12
f
–15 and 15
a
b
–2.5 and 2.5
–2 and 2
c
–1.6 and 1.6
d

1
1
and
2
2
e

1
1
and
3
3
f

1
1
and
20
20
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
7
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
3
4
5
6
7
8
–4 and –1
a
b
–5 and –2
c
–4 and –2
d
2 and 4
e
2 and 5
f
–4 and 2
a
b
–2 and 5
–5 and 2
c
–3 and 6
d
–6 and 3
e
–4 and 6
f
–6 and 8
a
b
–4 and 3
–6 and –2
c
–9 and 4
d
–1
e
–2
f
–9 and –8
a
b
0 and 8
0 and 7
c
–3 and 0
d
–4 and 0
e
0 and 9
f
0 and 4
a
b
–1.5 and –1
–1 and 2.5
c
–1 and
1
3
d
–5 and
1
2
e
1.5 and 5
f
1
a
b
–12 and 0
–9 and –3
c
–8 and 4
d
–7 and 2
e
–6 and 6
f
–10 and 10
1
1
and
3
2
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
8
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
Exercise 13.9 page 139
1
2
3
4
5
6
7
8
–4 and 3
–6 and 7
2
4
Height = 3 cm, base length = 12 cm
Height = 20 cm, base length = 2 cm
Base length = 6 cm, height = 5 cm
a 9x + 14 = 50
b x=4
c
11 m × 6 m
Exercise 13.10 page 141
1
2
3
4
a
b
–3.14 and 4.14
–5.87 and 1.87
c
–6.14 and 1.14
d
–4.73 and –1.27
e
–6.89 and 1.89
f
3.38 and 5.62
a
b
–5.30 and –1.70
–5.92 and 5.92
c
–3.79 and 0.79
d
–1.14 and 6.14
e
–4.77 and 3.77
f
–2.83 and 2.83
a
b
–0.73 and 2.73
–1.87 and 5.87
c
–1.79 and 2.79
d
–3.83 and 1.83
e
0.38 and 2.62
f
0.39 and 7.61
a
b
–0.85 and 2.35
–1.40 and 0.90
c
0.14 and 1.46
d
–2 and –0.5
e
–0.39 and 1.72
f
–1.54 and 1.39
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
9
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
Exercise 13.11 page 142
x = 3 and y = 4
x = –6 and y = 9
x = –1 and y = –1
3 x = –2.5 and y = 3.5
x = 2 and y = 17
1
1
4 x = – and y = 4
3
3
x = 2 and y = 16
5 x = 0 and y = 2
x = 5 and y = –8
6 x = –3 and y = –20
4
4
x=
and y = 2
5
5
7 x = 5 and y = 6
x = 6 and y = 5
8 x = –0.6 and y = –3.3
x = 4.1 and y = 0.5
1
9 x=1
3
10 p = 1.17
1
2
Exercise 13.12 page 144
1
a
x<4
b
x>1
c
x⩽3
d
x⩾7
e
x<2
f
x>2
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
10
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
2
3
a
x<7
b
x ⩾ –2
c
x > –3
d
x ⩾ –12
e
x > –24
f
x ⩾ –3
a
x<2
b
x ⩽ 12
c
x⩾2
d
x ⩾ –2
e
x > –0.5
f
x⩾2
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
11
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
Exercise 13.13 page 144
1
2
a
2<x⩽4
b
1⩽x<5
c
3.5 ⩽ x < 5
d
2 ⩽ x < 4.2
a
1<x⩽5
b
–1 ⩽ x < 1
c
2<x<3
d
No solution
Student assessment 1 page 144
1
2
3
a
b
–6
6
c
4
d
2.4
a
b
0.5
4
c
9.5
d
5
a
b
6
15
c
22
d
6
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
12
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
4
5
6
a
8.5
b
4
c
8.5
d
12
a
b
x=7
p=1
y=4
q=2
c
x=7
y=1
d
m=3
n=5
x=
1
1
and y = 4
4
4
1
3
x = –3 and y = 14
Student assessment 2 page 145
1
a
b
9x – 90 = 360
x = 50
c
50°, 60°, 100°, 150°
2
3
4
5
6
7
2
85°, 95°, 95°, 130°, 135°
–4 and 5
2.77 and –1.27 (3 s.f.)
x = 1.24 and y = 2.61 (3 s.f.) x = –3.24 and y = 0.38 (3 s.f.)
3<x⩽5
8
x>5
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
13
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
Student assessment 3 page 146
1
a
b
2
a
x – y = 30 x + y + 40 = 180
x = 85 y = 55
b
5x + 100
c
92°
d
e
3
4
92° + 82° + 72° + 62° + 52° = 360°
a
b
120 – 4x2
c
4x2 = 64
b
0.44 and 4.56 (2 d.p.)
x=4
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
14
Cambridge IGCSE Mathematics Core and Extended 13 Student Book answers
5
a
c
10 cm, 8 cm, 6 cm
Cambridge IGCSE Mathematics Core and Extended Teacher’s Guide
© Hodder & Stoughton Ltd 2018
15