# igcse maths 3ed core practice book answers

```CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
The questions and example answers that appear in this resource were written by the author. In examination, the way marks would
be awarded to answers like these may be different.
Chapter 1
Exercise 1.1
Exercise 1.3
1
Student’s own tables.
1
2
Various answers are possible; these are examples:
a 12 . 11
b x&lt;5
c 4x = 12 ∴ x = 3
___
d​​√25 ​​ = 5
e 32 ≠ 3 &times; 2
f k&gt;2
g 4,5
a
b
c
2, 3, 5, 7
53, 59
97, 101, 103
2
a
b
c
d
e
f
g
h
2&times;2&times;3&times;3
5 &times; 13
2&times;2&times;2&times;2&times;2&times;2
2&times;2&times;3&times;7
2&times;2&times;2&times;2&times;5
2&times;2&times;2&times;5&times;5&times;5
2 &times; 5 &times; 127
13 &times; 151
3
a
b
c
d
e
f
g
h
LCM = 378, HCF = 1
LCM = 255, HCF = 5
LCM = 864, HCF = 3
LCM = 848, HCF = 1
LCM = 24 264, HCF = 2
LCM = 2574, HCF = 6
LCM = 35 200, HCF = 2
LCM = 17 325, HCF = 5
3
4
−2, 0, −7, −32, __
​​ 1 ​​
2
1 ​​
b​​ __
2
c 3, 5, 23, 29
d 1, 9, 4, 25
a
a
121, 144, 169, 196, …
1 ​​, __
b​​ __
​​  1 ​​, __
​​  2 ​​, __
​​  2 ​​, etc.
4 6 7 9
c 83, 89, 97, 101, …
d 2, 3, 5, 7
5
a
b
365 289
1 703 473 212
Exercise 1.4
Exercise 1.2
1
1
a
d
g
18
24
72
b
e
h
36
36
96
c
f
90
24
2
a
d
g
6
3
12
b
e
h
18
10
50
c
f
9
1
3
18 metres
4
120 shoppers
5
20 students
6
14 cm, 165 squares
1
−3 &deg;C
2
a
−2 &deg;C
b
−9 &deg;C
c
−12 &deg;C
3
a
d
4
−2
b
e
7
−3
c
−1
4
a
d
−3
0
b
−26
c
−14
5
a
d
−5
−9
b
e
41
16
c
−78
6
a
b
80.34 to the euro
−5.5
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Exercise 1.5
1
2
a
d
g
9
625
5832
b
e
h
324
216
42 875
c
f
441
3375
a
d
g
11
11
56
b
e
h
8
36
27
c
f
i
21
51
6
3
square: 121, 144, 169, 196, 225, 256, 289
cube: 125, 216
4
square: 1, 49, 64, 256, 676, 625
cube: 1, 64
5
a
d
6
7
8
9
7
10
3
__
g​​   ​​
4
j
5
b
e
5
3
c
f
14
25
h
5
i
2
k
l
12
c
65 536
a
64
b
3
​1 __
​   ​​
4
2401
d
1728
e
8000
f
100 000
g
1954
h
155
i
1028
j
4096
1 ​​
a​​ __
4
1  ​​
d​​ ___
​5​​ 2​
1  ​​
g​​ ___
​3​​ 4​
1  ​​
j​​ ____
​12​​ 4​
1 ​​
b​​ __
5
1  ​​
e​​ ___
​3​​ 3​
1  ​​
h​​ ___
​8​​ 6​
1 ​​
c​​ __
8
1  ​​
f​​ ___
​2​​ 5​
1  ​​
i​​ ____
​23​​ 3​
a
d
g
j
2−1
2−3
11−2
3−1
b
e
h
6−1
3−3
4−3
c
f
i
3−2
2−4
5−1
a
d
g
j
m
p
38
32
4−1
412
109
46
b
e
h
k
n
102
2−7
103
36
10−4
c
f
i
l
o
33
31
1
42
21
Exercise 1.6
1
2
a
d
g
26
15.66
3.83
b
e
h
66
3.39
2.15
c
f
i
25
2.44
1.76
j
m
p
s
v
k
n
q
2.79
8.04
304.82
4.03
3.90
l
o
r
u
x
7.82
1.09
94.78
6.87
−19.10
t
w
0.21
8.78
0.63
6.61
20.19
Exercise 1.7
1
a
b
c
d
e
f
g
h
i
i
i
i
i
i
i
i
ii
ii
ii
ii
ii
ii
ii
ii
2
a
c
53 200
17.4
b
d
713 000
0.00728
3
a
c
e
g
36
12 000
430 000
0.0046
b
d
f
h
5.2
0.0088
120
10
4
a
c
4 &times; 5 = 20
1000 &times; 7 = 7000
b
d
70 &times; 5 = 350
42 &divide; 6 = 7
5
a
20
b
c
12
5.65
9.88
12.87
0.01
10.10
45.44
14.00
26.00
3
iii
iii
iii
iii
iii
iii
iii
iii
5.7
9.9
12.9
0.0
10.1
45.4
14.0
26.0
d
6
10
13
0
10
45
14
26
243
Review exercise
1
24, −12, 0, −15, −17
2
15, 30, 45, 60, 75
3
60
4
a
b
c
5
14
6
a
d
g
5
145
5
b
e
h
5
138
10
c
f
64
−168
7
a
d
16.07
11.01
b
e
9.79
0.12
c
f
13.51
−7.74
8
a
d
g
30
3−1
38
b
e
h
33
32
3−4
c
f
3−2
30
2&times;2&times;7&times;7
3 &times; 3 &times; 5 &times; 41
2&times;2&times;3&times;3&times;5&times;7&times;7
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
9
a
d
10 a
d
37
40
b
26
c
2−1
1240
31.5
b
0.765
c
0.0238
11 Yes (80 &times; 80)
3
___
12 Yes, table sides are ​​√1.4 ​​= 1.18 metres
or 118 cm long. Alternatively, area of
cloth = 1.44 m2 and this is greater than the
table area.
13 1.5 metres
14 a
40
b
6
c
22
d
72
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 2
Exercise 2.4
Exercise 2.1
1
a
7x
c
5x − 2
2
a
p+5
3
x
a​
\$ __
​   ​​
3
6x
x
2x
2x
​   ​​ ​​(\$ = ​ ___ ​)​​
b​
\$ __
​   ​​, ​\$ ___
​   ​​ and ​\$ ___
3
9
9
9
1
b
b
x + 12
x
d ​2x − __
​   ​​
3
p−4
c
4p
2
Exercise 2.2
1
2
3
a
d
g
j
m
p
20
25
75
15
15
7.5
b
e
h
k
n
60
−50
100
2
3
c
f
i
l
o
11
9
9
16
15
a
d
g
−10
−23
−1000
b
e
h
−10
−26
8000
c
f
12
28
a
c
54 cm2
110.25 cm2
b
d
1.875 m2
8 cm2
3
2
4
a
b
c
d
e
f
g
h
b
e
h
8ab
−30mn
−4x3y
c
f
i
k
3b
l
20y
m​​ ____ ​​
3x
n
3​x​​ ​
____
​
​​   ​
​y​​ 2​
p​​ ___ ​​
2
x
s​​ ___ ​​
6y
15​a​​ 2​
​
​
q​​ _____
4
27​x​​ 2​
t​​ _____
​
​
10
12xy
−6x
6xy3
1  ​​
j​​ ___
4y
2
y
x2
6x2y
4b
9m
___
​​   ​​
4
2​y​​ 2​
o​​ ____
​​
​x​​ 2​
− 14y
r​​ _____
​
​
5
b
d
f
h
j
l
b
d
f
h
2x − 8
−9 + 6x
2x − x2
3x2 − 9x
−x + 2
4x −2x2
xy − 3x
−3x + 2
3x + 1
x2 + x + 2
b
x2 + xy
x 3y
​​ __ ​ + ___
​   ​​
2
2
2
−5x − 6x
d
f
3x2 − 6x
Exercise 2.5
1
a
d
g
2
2​x​​ 2​
​
​
a​​ ____
3
2y
c​​ ___ ​​
3
3​x​​ −2​​y​​ −5​ ______
3
​
​ or ​​  2 5 ​​
e​​ ________
2
2​x​​ ​​y​​ ​
7
​​  x ​​
g 7x−1 or __
2m + 6n
6x + 2
a2 + 6a − 5
y2 − 5y − 2
3x2 − 2x + 3
4x2y − 2xy
5ab − 4ac
4x2 + 5x − y − 5
a
d
g
3x + 6
−2x − 6
x2 + 3x
−2x − 2x2
−4x + 10x2
4x2 − 4xy
2x2 − 4x
−2x − 2
−2x2 + 6x
x3 − 2x2 − x
x
a​
​x​​ 2​ + __
​   ​​
2
c −8x3 + 4x2 + 2x
e
Exercise 2.3
1
a
c
e
g
i
k
a
c
e
g
3
x11
6x8
2x3y2
b
e
h
c
f
y13
x5y4
−27x12
b
3x2
d
​x​​ −1​
1  ​​
​​ ____ ​​ or ​​ ___
2
2x
f
2 ​x​​ 2​z
​​  3 ​
2x2y−3z or _____
​
​y​​ ​
4x
4xy−1 or ___
​​  y ​​
h
x ​y​​ −1​ ___
x
i​​ _____
​
​ or ​​   ​​
3
3y
j
− 3x ​z​​ 3​
​
​
k​​ _______
2
l
1  ​​ or __
a​​ ___
​​  1 ​​
​3​​ 2​ 9
x
c​​ ___ ​​
2y
1  ​​ or ________
e​​ ______
​​  1  ​​
(​​ 8xy)​​​ 2​ 64 ​x​​ 2​​y​​ 2​
3
b​​ ___3 ​​
​x​​ ​
1
d​​ ___
xy ​​
g
y
​x​​ 2​
i​​ ___2 ​​
​y​​ ​
8​x​​ 7​
k​​ ____3 ​​
9​y​​ ​
6x3
48x4
f
​x​​ 3​
x3y−2 or ___
​​  2 ​​
​y​​ ​
5y−6
5
x
​x​​ ​
​​ ____6 ​​ or _____
​​   ​​
2
2 ​y​​ ​
16x2y2
​x​​ 3​
h​​ ___4 ​​
​y​​ ​
​___
y​​ 2​
j​​  6 ​​
​x​​ ​
4​x​​ 3​
l
​​ ____2 ​​
7​y​​ ​
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
4
5
a
d
g
j
​x​​ 6​
a​​ ___2 ​​
​y​​ ​
7
b −8x9
e −x9y18
h 16x5
k​
​3​​ y​​x​​ ​y​​ 2​​​
c
f
i
l
b
2 ​x​​ 2​
c​​ ____ ​​
3y
f
x7y 3
i
x7y
3x4y
50​x​​ 3​
g​​ _____ ​​
27y
8​x​​ 10​​y​​ 3​
​
​
j​​ _______
3
​x​​ 8​
a​​ ___2 ​​
​y​​ ​
1  ​​
d​​ ___
​x​​ 9​
​x​​ 16​
k​​ ____
​​
​y​​ 16​
​x​​ 5​
b ​​ ___4 ​​
​y​​ ​
​y​​ 16​
e​​ ____
​​
​x​​ 22​
16
8
​​
c​​ _____
​x​​ 5​​y​​ 7​
​y​​ 22​
f ​​ ____4 ​​
2​x​​ ​
a
d
b
e
c
f
xy10
x=3
x=4
x=5
x = −5
Review exercise
1
5
16x4
x12y8
1
−8x6
5​x​​ 9​
e​​ ____3 ​​
2​y​​ ​
49
h ​​ _______
​​
25​x​​ 3​y
d
6
x6
x27
−2x3y3
x16y4
a
x + 12
b
c
5x
d
e
4x
f
g
12 − x
h
x−4
x
__
​​   ​​
3
x
​​ __ ​​
4
x3 − x
l
2
a
−6
b
24
c
3
a
−2
b
c
d
7
e
2 ​​
​​ __
3
−4
− 14
​​ ____
​
​
9
5
4
a
d
630
12
b
44
c
150
5
a
c
e
g
i
2y + 10
12x − 8y
20x − 14y + 6z
2x + 7
15x − 6y
b
d
f
h
4y − 4
xy + 2x
6x2 + 2x
4x + 18
6
a
9a + b
b
x2 + 3x − 2
c
−4a4b + 6a2b3
d
−7x + 4
5y
10x2 − ___
​​   ​​
2
2
6x + 15x − 8
−x3 + 3x2 − x + 5
3125​x​​ ​​y​​ ​
__________
​
​
​​
4 2
x=4
x = −3
4x
e​​ ___
y ​​
f
7
a
c
b
d
8
5​x​​ 5​
​
​
a​​ ____
6
b
d
64​x​​ 9​
e​​ _____
​​
​y​​ 15​
11x − 3
−2x2 + 5x + 12
16x4y8
9​x​​ 4​
g​​ ____3 ​​
4​y​​ ​
h
15
1  ​​
c​​ ___
​x​​ 4​
f
x9y8
x​y​​ 6​
​
​
​​ ____
2
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 3
Exercise 3.1
1
a
c
e
obtuse, 112&deg;
right, 90&deg;
obtuse, 125&deg;
b
d
f
2
a
b
d
i
90&deg;
ii 180&deg;
30&deg;
c 360&deg;
quarter to one or 12:45
acute, 32&deg;
reflex, 279&deg;
reflex, 193&deg;
3
No. If the acute angle is &lt;45&deg; it will produce
an acute or right angle.
4
Yes. The smallest obtuse angle is .90&deg; and
the largest is ,180&deg;. Halving will give angles
between (but not equal to) 45&deg; and 90&deg;, all of
which are acute.
a 45&deg;
b 28&deg;
c (90 − x)&deg;
d x&deg;
5
6
a
c
e
g
7
z = 65&deg; (angles on line); y = 65&deg; (VO);
x = 25&deg; (comp angle to z)
8
angle QON = 48&deg; (85&deg; − 37&deg;), so a = 48&deg; (VO)
9
a
b
135&deg;
76&deg;
x&deg;
(90 − x)&deg;
b
d
f
h
b
c
d
e
f
6
f
1
x = 47&deg; (alt angles); y = 81&deg; (angles in
triangle BEF or on st line); z = 52&deg;
(alt angles)
x = 72&deg; (angle BFE = 72&deg;, then alt angles);
y = 43&deg; (angles in triangle BCJ )
x = 45&deg; (angles round a point);
y = 90&deg; (co-int angles)
a
b
c
d
e
f
g
h
i
j
k
angle EOD = 41&deg; (angles on line),
so x = 41&deg; (VO)
x = 20&deg; (angles round point)
x = 68&deg; (angle BFG = 68&deg;, angles on line,
then alt angles)
x = 85&deg; (co-int angles); y = 72&deg; (alt angles)
x = 99&deg; (co-int angles); y = 123&deg;
(angle ABF = 123&deg;, co-int angles then VO)
x = 15&deg; (co-int angles)
x = 60&deg; (co-int angles)
x = 45&deg; (angle STQ corr angles then VO)
x = 77.5&deg; and y = 75&deg; (co-int angles)
x = 90&deg; (angle ECD and angle ACD co-int
angles then angles round as point)
x = 18&deg; (angle DFE co-int with angle CDF
then angle BFE co-int with angle ABF,
then subtract DFE from BFE )
Exercise 3.2
90&deg;
(180 − x)&deg;
(90 + x)&deg;
(220 − 2x)&deg;
10 angle HGB = 143&deg; (angles on line);
angle AGF = 143&deg; (VO); angle BGF = 37&deg; (VO);
angle DFG = 143&deg; (corr angles);
angle CFG = 37&deg; (corr angles);
angle CFE = 143&deg; (VO);
angle EFD = 37&deg; (VO)
11 a
12 a
b
c
d
e
l
2
a
b
c
d
e
f
74&deg; (angles in triangle)
103&deg; (angles in triangle)
58&deg; (ext angle equals sum int opps)
51&deg; (ext angle equals sum int opps)
21&deg; (ext angle equals sum int opps)
68&deg; (ext angle equals sum int opps)
53&deg; (base angles isosceles)
60&deg; (equilateral triangle)
x = 58&deg; (base angles isosceles and angles
in triangle); y = 26&deg; (ext angle equals sum
int opps)
x = 33&deg; (base angles isosceles then ext
angles equals sum int opps)
x = 45&deg; (co-int angles then angles in
triangle)
x = 45&deg; (base angles isosceles);
y = 75&deg; (base angles isosceles)
x = 36; so A = 36&deg; and B = 72&deg;
x = 40; so A = 80&deg;; B = 40&deg; and angle
ACD = 120&deg;
x = 60&deg;
x = 72&deg;
x = 60; so R = 60&deg; and angle RTS = 120&deg;
x = 110&deg;
Exercise 3.3
1
a
b
c
d
e
f
g
square, rhombus
rectangle, square
square, rectangle
square, rectangle, rhombus, parallelogram
square, rectangle
square, rectangle, parallelogram, rhombus
square, rhombus, kite
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
2
3
Review exercise
h
i
rhombus, square, kite
rhombus, square, kite
a
c
e
f
x = 69&deg;
b x = 64&deg;
x = 52&deg;
d x = 115&deg;
x = 30&deg;; 2x = 60&deg;; 3x = 90&deg;
a = 44&deg;; b = 68&deg;; c = 44&deg;; d = e = 68&deg;
1
b
c
A − Kite
B − Trapezium
C − Rhombus
D − Parallelogram
E − Square
F − Rectangle
d
e
f
g
Exercise 3.4
1
a
60&deg;
b
720&deg;
c
120&deg;
2
a
1080&deg;
b
1440&deg;
c
2340&deg;
3
900
____
​​   ​= 128.57&deg;​
4
20 sides
5
a
h
2
7
165.6&deg;
360
​​ _____ ​ = 25​sides
14.4
b
Exercise 3.5
a
c
e
g
i
b
d
f
h
j
circumference
chord
segment
sector
diameter
arc
semicircle
segment
tangent
Exercise 3.6
1
a
b
3
Student’s own diagram
3
Student’s own diagram
4
Scalene
5
a
5
He’s drawn the arcs using the length of
AC instead of the lengths of the other two
given sides.
B
7 cm
a
x = 113&deg;
b
x = 41&deg;
c
x = 89&deg;
d
x = 66&deg;
e
x = 74&deg;; y = 106&deg;; z = 46&deg;
f
x = 38&deg;; y = 104&deg;
g
x = 110&deg;; y = 124&deg;
h
x = 40&deg;; y = 70&deg;; z = 70&deg;
a
x = 60 + 60 + 120 = 240&deg;
b
x = 90 + 90 + 135 = 315&deg;
7
8 cm
chord
diameter
b
OA, OB, OC, OD
c
24.8 cm
d
Student’s own diagram
AB, AC and BC are radii of the circles, so
they must measure half the diameter, in other
words, 4.5 cm long. Use that measurement to
construct the equilateral triangle.
C
4.5 cm
4.5 cm
3 cm
A
A
When two parallel lines are cut by a
transversal, the alternate angles are
formed inside the parallel lines, on
opposite sides of the transversal
A triangle with two equal sides
sides equal in length
A quadrilateral with four equal sides and
opposite sides parallel to each other
A many-sided shape with all sides equal
and all interior angles equal
An eight-sided shape
The distance around the perimeter of a
circle
A straight line that crosses a pair of
parallel lines
4 a i
ii
iii
Either B A D E C or B D A E C
draw the arcs in different order.
2
b
a
4.5 cm
B
C
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 4
Exercise 4.1
f
Stem
1
eye colour, hair colour
2
6
2
grade, height, shoe size, mass, number of
brothers/sisters
3
8
4
0245689
3
shoe size, number of brothers/sisters
5
1234444555566777899
6
013335577799
7
013688
8
028
9
1
4
height, mass
5
hair colour – observation; height, mass –
measured; grade, shoe size, number of siblings
– survey, questionnaire
Key: ​​2 |​ 6 = 26 per cent​
Exercise 4.2
1
2
Mark
a
b
3
a
Tally
Frequency
|
1
2
||
2
3
||
2
4
​​| | | |​​
5
Hair colour
5
​| | | |​​ | | | |
9
6
​| | | |​​ | |
7
7
​| | | |​​ |
6
8
|||
3
9
|||
3
10
||
2
4
a
Eye colour
Brown
Blue
Green
Blonde
0
0
1
Brown
3
0
0
Black
3
1
2
b
Score
1
2
3
4
5
6
Frequency
5
8
7
7
7
6
c
5
a
The scores are fairly similar for even a low
number of throws, so the dice is probably
fair.
Score
Score
Frequency
b
e
The actual data values are given, so you
can calculate exact mode, median and
range. You can also see the shape of the
distribution of the data quite clearly.
1
Frequency
8
Leaf
0–29 30–39 40–49 50–59
1
1
7
19
60–69 70–79 80–100
12
6
Stem
Leaf
0
1257
1
22689
2
0349
3
1113579
4
138
5
1
Key: ​​0 |​ 1 = 1 car​, ​​1 |​ 2 = 12 cars​
4
10
c 2
d 26
There are very few marks at the low and
high end of the scale.
Answers may vary. For example: All the
students with brown hair have brown eyes.
There are no blonde students with brown
eyes. Most students have black hair. And
so on, based on the data.
Student’s own answer with a reason.
b
51 cars
Exercise 4.3
1
a
b
pictogram
number of students in each year group in
a school
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
c
d
e
f
g
2
30 students
half a stick figure
225
Year 11; 285
rounded; unlikely the year groups will all
be multiples of 15
6
7
Student’s own chart, for example:
Time spent on social media
Key
Alain
=1hr
Li
Zayn
David
3
a
b
d
e
f
g
4
The number of students in Grade 10 whose
home language is Bahasa and Chinese.
18
c 30
The favourite sports of students in Grade
10, separated by class.
athletics
athletics
9
a
Pie chart with sector sizes:
A – 18&deg;; B – 43&deg;; C – 148&deg;; D – 90&deg;;
E or lower – 61&deg;
b
6
a
b
c
d
e
f
g
29.6&deg; C
April–November
northern hemisphere
no
10 mm
February
There is little or no rain.
c
1
a
b
c
survey or questionnaire
discrete; you cannot have half a child
quantitative; it can be counted
d
No. of
children in
family
Tally
Frequency
0
​​| | | |​ |​ | ​
Charts can be drawn vertically or horizontally.
1
​​| | | |​ ​| | | |​​
10
a
2
​​| | | |​ ​| | | |​ | ​
11
3
​​| | | |​ ​| | | |​ | | ​
12
4
​​| | | |​ ​
5
5
​​| | | |​ ​
2
Hot porridge
6
|
1
Breakfast food chosen
e
0
4
8
f
12 16 20 24 28 32
Frequency
b
Breakfast food chosen
2
a
10A
Leaf
Key
Hot porridge
0
4
8
57
9
15
479
7665
16
1223446
886554
17
11
7543
18
0
12 16 20 24 28 32
Key: ​​9 |​ 15 = 159 cm​ and ​​14 |​ 5 = 145 cm​
Frequency
a
d
cars
b 17%
handcarts and bicycles
10B
Leaf
Stem
14
Cereal
7
Pie chart with sector sizes:
0 − 53&deg;; 1 − 75&deg;; 2 − 83&deg;; 3 − 90&deg;; 4 − 37&deg;;
5 − 15&deg;; 6 − 7&deg;
The number of families that have three or
fewer children is five times greater than
the number of families with four or more
children.
9
C
Review exercise
Cereal
5
d
50
c
20
b
13
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
c
3
Student’s own pictogram
4
a
b
c
d
e
f
g
10
The heights in 10A are clustered more
towards the higher end, suggesting they are
taller (as a group) than the students in 10B.
Compound bar chart
It shows how many people, out of every
100, have a mobile phone and how many
have a land line phone.
No. The figures are percentages.
Germany, UK, Sweden and Italy
Denmark
Student’s opinion with reason
5
a
b
c
d
e
Downtown
\$4750
\$2500
\$3750
15%
6
a
The value drops very quickly in the first
year. After that the value drops more
b
\$3600
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 5
35
j​​ ___ ​​
6
18
m​​ ___ ​​
65
−5
p​​ ___ ​​
6
Exercise 5.1
1
2
1 ​​
a​​ __
2
__
d​​  1 ​​
4
__
g​​  1 ​​
5
3
__
j​​   ​​
8
b
a
d
g
j
b
e
h
33
65
117
63
e
h
__
​​  1 ​​
3
__
​​  1 ​​
4
__
​​  2 ​​
3
300
168
48
c
__
​​  1 ​​
f
__
​​  1 ​​
i
3
__
​​   ​​
c
f
i
25
55
104
3
8
4
13 ​​
​ ___
s​
21
5
a
6
10
d​​ ___ ​​
27
38
a​​ ___ ​​
9
19
d​​ ___ ​​
4
Exercise 5.2
1
2
3
4
11
25
​​ ___ ​​
8
59
e​​ ___ ​​
5
25
h​​ ___ ​​
9
13
a​​ ___ ​​
6
93
d​​ ___ ​​
10
59
g​​ ___ ​​
4
− 25
j​​ ____
​
​
9
1  ​​
a​​ ___
25
9
d​​ ___ ​​
20
30
g​​ ___ ​​
91
9
j​​ ___ ​​
44
72
m​​ ___ ​​
5
108
​
​
a​​ ____
5
28
d​​ ___ ​​
5
b
e
g
120
h
j
3
k
11 ​​
a​​ ___
20
13
d​​ ___ ​​
24
19
g​​ ___ ​​
21
c
f
i
17
​​ ___ ​​
11
15
___
​​   ​​
4
28
___
​​   ​​
3
24
183
​​ ____ ​​
56
41 ​​
n ​​ ___
40
−
10
q​​ ____
​​
3
43
___
t​​   ​​
12
96
b ​​ ___ ​​
7
10
e ​​ ___ ​​
9
4
b ​​ __ ​​
5
5
e ​​ ___ ​​
12
11  ​​
h ​​ ____
170
k
l
o
161
​​ ____ ​​
20
29
​​ ___ ​​
21
r
− 26 ​
____
​​   ​
c
7
​​ ___ ​​
96
9
​​ ___ ​​
14
39
___
​​   ​​
7
215
​​ ____ ​​
72
187
​​ ____
​
​
9
f
c
f
g
0
7
a
\$525
8
a
b
300
450 per day &times; 5 days = 2250 tiles per week
b
i
9
\$375
2  ​​
9​​ ___
25
b
___
​​  1  ​​
10
16
e ​​ ___ ​​
99
6
h ___
​​   ​​
25
1 ​​
k​​ __
2
21 ​​
n​​ ___
4
63
b ​​ ___ ​​
13
b
e
h
c
__
​​  2 ​​
5
f ___
​​  4  ​​
11
15
___
i
​​   ​​
28
3
l​​ ___ ​​
25
1 ​​
o​​ __
6
c
14
3
f
6
___
​​   ​​
3
​​ ___ ​​
14
233
____
​​   ​​
50
11
___
​​   ​​
30
___
​​  4  ​​
15
16
___
​​   ​​
15
i
72
19
7
l​​ __ ​​
4
c ___
​​  4  ​​
45
19
f ___
​​   ​​
60
13
___
i
​​   ​​
24
Exercise 5.3
1
a
d
g
j
b
e
h
67%
29.8%
47%
c
f
i
16.7%
30%
112%
2
1 ​​
a​​ __
4
1 ​​
d​​ __
8
3
__
g​​   ​​
5
b
__
​​  4 ​​
c
9
___
​​   ​​
f
49
___
​​   ​​
a
60 kg
b
\$24
c
d
g
j
55 ml
258 km
475 m3
e
h
k
\$64
0.2 grams
\$2
f
i
l
150 litres
\$19.50
\$2.08
4.2 kg
4
a
d
40%
40%
b
e
2%
31.25%
c
54%
5
a
d
g
+20%
+3.3%
+2566.7%
b
e
−10%
−28.3%
c
f
+53.3%
+33.3%
3
50%
62.5%
4%
207%
e
h
5
__
​​  1 ​​
2
___
​​  11 ​​
50
10
50
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
6
a
d
\$54.72
\$40 236
b
e
\$945
\$98.55
c
f
\$32.28
\$99.68
7
a
d
\$58.48
\$19 882
b
e
\$520
\$76.93
c
f
\$83.16
\$45.24
8
28 595 tickets
9
1800 shares
10 \$129 375
4
a
c
e
g
i
1.2 &times; 1031
3.375 &times; 1036
2 &times; 1026
1.2 &times; 102
3 &times; 10−8
b
d
f
h
4.5 &times; 1011
1.32 &times; 10−11
2.67 &times; 105
2 &times; 10−3
5
a
the Sun
b
6.051 &times; 106
6
a
b
500 seconds = 5 &times; 102 seconds
19 166.67 seconds = 1.92 &times; 104 seconds
11 21.95%
12 \$15 696
Review exercise
13 \$6228
1
14 2.5 g
7
15 ___
​​   ​ = 28%​increase, so \$7 more is better
2
25
16 a
b
76 droplets
380 000 virus particles
3
Exercise 5.4
1
2
3
12
a
c
e
g
i
k
4.5&times; 104
8 &times; 10
4.19 &times; 106
6.5 &times; 10−3
4.5 &times; 10−4
6.75 &times; 10−3
b
d
f
h
j
l
8 &times; 105
2.345 &times; 106
3.2 &times; 1010
9 &times; 10−3
8 &times; 10−7
4.5 &times; 10−10
4
a
c
e
g
i
2500
426 500
0.00000915
0.000028
0.00245
b
d
f
h
39 000
0.00001045
0.000000001
94 000 000
a
c
e
g
i
5.62 &times; 1021
1.28 &times; 10−14
1.58 &times; 10−20
1.98 &times; 1012
2.29 &times; 108
b
d
f
h
6.56 &times; 10−17
1.44 &times; 1013
5.04 &times; 1018
1.52 &times; 1017
5
4 ​​
a​​ __
5
__
a​​  1 ​​
6
13
___
d​​   ​​
15
71
g​​ ___ ​​
6
1 ​​
​​ __
4
b
63
e
3
​​ ___ ​​
h
44
361
____
​​   ​​
16
a
b
8%
b
__
​​  2 ​​
c
__
​​  2 ​​
c
5
__
​​   ​​
f
31
​​ ___ ​​
i
334
​​ ____ ​​
5%
c
63.33%
3
3
3
48
45
2.67%
6
a
24.6 kg
b
0.5 litres
c
\$70
7
a
12.5%
b
33.33%
c
34%
8
\$103.50
9
\$37.40
b
0.625%
10 67.7%
11 a
97.5%
12 2940 metres
13 a
b
5.9 &times; 109 km
5.753 &times; 109 km
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 6
Exercise 6.1
1
2
a
c
e
g
i
k
x = 16
x=8
x=7
x = −16
x = −9
x = 13
b
d
f
h
j
l
x = 24
x = 54
x = −2
x = −60
x = −15
x = 15
a
x=8
b
x = 15
c
5
x ​= − __
​   ​ = −2 __
​  1 ​​
2
2
x = −4
d
x = −10
f
x = −12
e
3
4
Exercise 6.2
a
x=3
b
9
1
__
__
c x​= ​   ​ = 4 ​   ​​
d
2
2
3
36 18
​   ​​ f
e​
x = ___
​   ​ = ​ ___ ​= 3 __
5
5
10
g
x=2
h
i
x=4
j
5
x=5
a
b
x = −2
d
4 ​ = 1​ __
1 ​​
​x = ​ __
1 ​​
​ = ​ __
x
3
2
a
c
e
g
i
k
m
o
12(x + 4)
4(a − 4)
4(x − 5)
x(3 − y)
3(x − 5y)
6(2x − 3)
3b(3a − 4c)
2x(7 − 13y)
b
d
f
h
j
l
n
p
2(1 + 4y)
2(x − 6)
8(2a − 1)
a(b + 5)
8(a + 3)
8xz(3y − 1)
2y(3x − 2z)
−7x2(2 + x3)
3
a
x(x + 8)
b
a(12 − a)
c
x(9x + 4)
d
2x(11 − 8x)
e
2b(3ab + 4)
f
18xy(1 − 2x)
g
3x(2 − 3x)
h
2xy2(7x − 3)
i
3abc2(3c −ab)
j
x(4x − 7y)
k
b2(3a − 4c)
l
7ab(2a − 3b)
a
c
e
g
i
k
(3 + y)(x + 4)
(a + 2b)(3 − 2a)
(2 − y)(x + 1)
(2 − y)(9 + x)
(x − 6)(3x − 5)
(2x + 3)(3x + y)
b
d
f
h
j
l
(y − 3)(x + 5)
(2a − b)(4a − 3)
(x − 3)(x + 4)
(2b − c)(4a + 1)
(x − y)(x − 2)
(x − y)(4 − 3x)
b
a = 2c + 3b
x = −5
3
1 ​​
​x = − ​ __ ​ = −1​ __
2
2
x=3
3
3
a
4xy
xy2z
x=4
l
8
c​
x = − __
​   ​ = −2 __
​  2 ​​
a
d
g
j
x=4
1 ​​
11 ​= 5 ​ __
k​
x = ​ ___
2
2
x = 10
1
3
4
3
e
x=8
f
g
x = −4
h
4
x = −9
i
x = −10
j
x = −13
k
x = −34
l
7
20
​x = ___
​   ​ = 1​ ___ ​​
13
13
Exercise 6.3
a
x = 18
b
x = 27
1
c
x = 24
d
x = −44
e
x = 17
f
x = 29
g
x = 16
h
i
x = −1
2
​m = __
​  D ​​
k
c = y − mx
x = 23
3
P+c
​b = ______
​  a ​
​
j
1 ​
x = ​ __
2
4
a−c
​
​b = ​ ___
x ​
k​
x = − __
​  1 ​​
3
3
16
___
m​
x = ​   ​ = 1​ ___ ​​
13
13
l
x=9
5
a
n
x = 10
o
p
1 ​​
−11
​​ = −5​​ __
x = ​​ ____
2
2
x = 42
a=c−b
8
3y
pq
ab3
c
f
i
l
5
5ab
7ab
3xy
c+d
d−c
c​
a = ​ ____
​
​
d ​a = ​ ____
​
​
b
b
e a = bc − d (or a = −d + bc)
f
a = d + bc
de − c
h​
a = ​ ____
​
​
b
13
b
e
h
k
g
i
cd − b
​a = ​ _____
​
​
2
e+d
​a = ​ ____
​
​
bc
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
ef − d
​
​
j​
a = ​  ____
bc
6
7
8
k
c (​ f − de)​
​a = ​ ________
​
​
b
d​(e − c)​
d
l​
a = ​ ________
​
​
m a​ = ​ __
c ​ + b​
b
c
n​
a = __
​   ​ − 2b​
d
a​
w = __
​  P ​ − l​
b w = 35.5 cm
2
C
b 9 cm
c 46 cm
a​
r = ___
​   ​​
2π
2A ​​ − a; b = 3.8 cm
​b = ​ ___
h
2
m+r
​
a​
x = _____
​  np ​
b
mq − p
​x = ​ ______
​
n ​
3
a
c
e
g
4(x − 2)
−2(x + 2)
7xy(2xy + 1)
(4 + 3x)(x − 3)
b
d
f
h
3(4x − y)
3x( y − 8)
(x − y)(2 + x)
4x(x + y)(x − 2)
4
a
b
4(x − 7) = 4x − 28
2x(x + 9) = 2x2 + 18x
c
d
4x(4x + 3y) = 16x2 + 12xy
19x(x + 2y) = 19x2 + 38xy
Review exercise
1
14
a
c
e
g
x = −3
x=9
x=2
x = 1.5
b
d
f
h
x = −6
x = −6
x = −13
x=5
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Exercise 7.2
Chapter 7
Exercise 7.1
1
2
a
c
e
120 mm
128 mm
36.2 cm
b
d
f
45 cm
98 mm
233 mm
a
c
e
g
15.71 metres
53.99 mm
18.85 metres
24.38 cm
b
d
f
h
43.98 cm
21.57 metres
150.80 mm
23.00 cm
3
90 metres
4
164 &times; 45.50 = \$7462
5
9 cm each
6
7
a
63π cm
b
70π cm
8
a
c
e
g
i
k
m
841 mm2
332.5 cm2
186 cm2
150 cm2
71 cm2
5.76 m2
243 cm2
b
d
f
h
j
l
406 m2
1.53 m2
399 cm2
59.5 cm2
2296 mm2
7261.92 cm2
a
c
e
7853.98 mm2
7696.90 mm2
17.45 cm2
b
d
2290.22 cm2
18.10 m2
10 a
c
e
g
i
288 cm2
373.5 cm2
366 cm2
272.97 cm2
5640.43 cm2
b
d
f
h
82 cm2
581.5 cm2
39 cm2
4000 cm2
11 a
c
e
30 cm2
36.4 cm2
720 cm2
b
d
f
90 cm2
61.2 cm2
600 + 625π cm2
b
47.12 cm
b
266.67π cm2
9
1
a
b
c
d
cube
cuboid
square-based pyramid
octahedron
2
a
b
c
cuboid
triangular prism
cylinder
3
The following are examples; there are other
possible nets.
a
b
12 11.1 m2
13 70 mm = 7 cm
14 a
c
43.98 mm
8.38 mm
15 6671.70 km
16 a
c
24π cm2
(81π − 162) mm2
17 61.4 cm2
15
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CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
c
7 a Volume = 480 cm3
Surface area = 376 cm2
b Volume = 66 m3
Surface area = 110 m2
c Volume = 4904.78 mm3
Surface area = 1901.59 mm3
8
332.5 cm3
9
a
b
224 m3
44
10 67.5π m3
d
11 Various answers – for example:
Volume (mm3) 64 000 64 000 64 000 64 000
Length (mm)
80
Height (mm)
50
100
50
40
64
80
80
20
20
8
16
Review exercise
Exercise 7.3
a
2
4.55 cm
3
a
c
e
g
346.4 cm2
2000 mm2
40 cm2
106 cm2
175.93 cm2
1
a
c
2.56 mm2
13.5 cm2
b
d
523.2 m2
402.12 mm2
2
a
384 cm2
b
8 cm
4
15 metres
3
a
c
340 cm2
4 tins
b
153 000 cm2
5
243 cm2
6
4
a
c
e
g
90 000 mm3
20 420.35 mm3
960 cm3
1800 cm3
b
d
f
h
60 cm3
1120 cm3
5.76 m3
1.95 m3
a
b
c
d
7
64
5
a
c
5.28 cm3
b
33 510.32 m3
8
a
b
c
9
37.7 cm3
6
16
1
25.2 cm3
56 cm3
b
66.0 cm
b
d
f
33 000 mm2
80 cm2
35 cm2
cuboid B
14 265.48 mm3
student’s own diagram
cylinder 7539.82 mm2, cuboid 9000 mm2
180π cm3
565.49 cm3
Radius of base = 3 cm, so C = 6π cm
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 8
Exercise 8.1
Exercise 8.2
9
17
3
​​   ​​, green = ___
​​   ​​
red = ___
​​   ​​, white = ___
25
50
10
1 ​​
b 30%
c 1
d​​ __
3
2 a A: 0.61, B: 0.22, C: 0.11, D: 0.05, E: 0.01
b i
highly likely
ii unlikely
iii highly unlikely
1
3
a
a
b
c
53.89%
77.22%
Yes, 53.89 rounds down to 50%
4
a
red, blue
5
a
6
1 ​​
1 ​​
c​​ __
b​​ __
2
2
a 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10
1 ​​
b​​ __
2
1, 2, 3, 4, 5 or 6
1  ​​
i​​ ___
10
3
iv​​ ___ ​​
10
3
vii​​ ___ ​​
10
2 ​​
7 a​​ __
5
1 ​​
8 a​​ __
4
7
___
9 a​​   ​​
20
3
d​​ ___ ​​
10
13
10​​ ___ ​​
40
0.73
11
ii
b
yes
d
0
ix
17
0.12
2000
HH
HT
T
TH
TT
2
0.88
1 ​​
c​​ __
2
2
__
c​​   ​​
5
c
1 ​​
b​​ __
4
Yellow
a
b
3
0.24
1
2
3
1
1, 1
1, 2
1, 3
2
2, 1
2, 2
2, 3
3
3, 1
3, 2
3, 3
1 ​​
d​​ __
3
1 ​​
c​​ __
3
1  ​​
b​​ ___
18
d __
​​  1 ​​
9
9
1  ​​
a​​ ___
36
1 ​​
c​​ __
6
Exercise 8.3
1
a
0
5
1 ​​
b​​ __
2
__
b​​  1 ​​
2
__
e​​  1 ​​
5
b
H
3
no sugar; probability = __
​​   ​​
5
12​​ __ ​​
8
13 a 0.16
b 0.84
c 0.6
d strawberry 63, lime 66, lemon 54,
blackberry 69, apple 48
14 a
d
T
3
a​​ __ ​​
4
3
iii​​ ___ ​​
10
1 ​​
vi​​ __
2
1
H
Green
c
2 ​​
v​​ __
5
9
___
viii​​   ​​
10
b
1
4
b​​ ___
​​
15
1 ​​
2​​ __
6
16
3 a​​ ___ ​​
81
A
E
A
C
CA
CE
CA
N
NA
NE
NA
B
BA
BE
BA
R
RA
RE
RA
R
RA
RE
RA
c
1 ​​
​​ __
5
d
b
25
​​ ___ ​​
81
40
c​​ ___ ​​
81
___
​​  4  ​​
15
Review exercise
1
a
b
10 000
Heads = 0.4083, Tails = 0.5917
1 ​​
c​​ __
2
d could be – probability of the tails
outcome is higher than the heads outcome
for a great many tosses
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CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
2
3
18
1 ​​
a​​ __
2
9
e​​ ___ ​​
10
1  ​​
a​​ ___
36
1 ​​
c​​ __
2
2 ​​
b​​ __
5
9
f ___
​​   ​​
10
b
d
c
___
​​  1  ​​
10
1 ​​
g​​ __
2
d
7, probability is __
​​ 1 ​​
6
__
​​  1 ​​
6
0
4
5
1  ​​
a​​ ___
10
1 ​​
a​​ __
6
c
0
1 ​​
b​​ __
2
1 ​​
b​​ __
3
d __
​​  1 ​​
2
c
__
​​  1 ​​
5
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 9
Exercise 9.1
1
a
b
c
d
e
f
g
h
8, 4, 2 (divide by 2)
−10, −12, −14 (subtract 2)
2, 4, 8 (multiply by 2)
11, 16, 22 (add one more each time than
a
7, 9, 11, 13
c
e
1, __
​​  1 ​​, __
​​  1 ​​, __
​​  1 ​​
d
2 4 8
100, 47, 20.5, 7.25
a
b
c
d
e
f
5, 7, 9
1, 4, 9
5, 11, 17
0, 7, 26
0, 2, 6
1, −1, −3
4
a
c
d
8n − 6
b 1594
th
30 : 234 + 6 = 240, 240 &divide; 8 = 30
18th term = 138 and 19th term = 146,
so 139 is not a term
5
a
b
c
d
e
f
2n + 5
3 − 8n
6n − 4
(n + 1)2
1.2n + 1.1
n3 + 1
2
3
b
3
_
_
_ 3
_
a
b
{−2, −1, 0, 1, 2}
{1, 2, 3, 4, 5}
4
a
b
A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A ∩ B = {}
5
a
{−2, −1, 0, 1, 2}
6
a
b
{x: x is even, x &lt; 10}
{x: x is square numbers, x &lt; 25}
50th = 105
50th = −397
50th = 296
50th = 2601
50th = 61.1
50th = 125 001
{1, 2, 3, 4, 5}
C
P
h
i
s
c
y
p
5, 11, 23, 47
35th term = 73
35th term = 1225
35th term = 209
35th term = 42 874
35th term = 1190
35th term = −67
b
a, b, d, f, g, j, k
7
37, 32, 27, 22
8
a
c
9
a
t, e, m, r
l, n, o, q, u, v, w, x, z
b
d
9
{c, h, i, s, y}
20
{c, e, h, i, m, p, r, s, t, y}
B
A
2 4 6 8
10
5
1, 3, 7, 9
b i
ii
iii
10
Exercise 9.2
1
3
A ∩ B = {10}
4
A ∪ B = {2, 4, 5, 6, 8, 10}
18 − 4 = 14
a​
​√16 ​, ​√12 ​​, 0.090090009
B
A
4
12 − 4 = 8
_
b​
​√45 ​, ​√90 ​, π, √​ 8 ​​
Exercise 9.3
19
4
1
a
d
false
true
b
e
2
a
b
{}
{1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 18}
true
false
c
false
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
T-shirts tested(100)
11
logo flaw
stitching flaw
4
12 − 4 = 8
15 − 4 = 11
_
4
0.213231234 …, ​√2, ​ 4π​
5
−3
2 ​​, ___
a​​ __
​​   ​​, −4, 0, 25, 3.21, −2.5, 85, 0.75
3 5
b −4, 0, 25, 85
6
a
A
77
a
23
b
B
2, 4, 8, 10
6
3, 9
77
Review exercise
1
a
b
c
d
5n − 4
26 − 6n
3n − 1
−n2
2
a
b
2, −1, −6, −13, −22 …
5, 11, 21, 35, 53 …
3
a
120th term = 596
120th term = −694
120th term = 359
120th term = −14 400
1, 5, 7
b
c
A ∩ B = {6}
n(A ∪ B) = 7
cracked
7
wrong size
3
8−3=5
11 − 3 = 8
= 120
b
c
20
n2 + 3
327
a
13
104
b
104
c
16
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 10
Exercise 10.1
1
a
b
c
d
e
6
g
h
j
0
1
2
3
b
y
4
5
6
7
8
c
x
−1
0
1
2
3
y
1
−1
−3
−5
−7
x
−1
0
1
2
3
y
9
7
5
3
1
x
−1
0
1
2
3
y
−1
−2
−3
−4
x
4
4
4
y
−1
0
1
d
g
m = __
​​  1 ​​, c = __
​​  1 ​​
2
4
4
m = ​​ __ ​​, c = −2
5
m is undefined, c = 7
h
m = −3, c = 0
a
y = −x
b
−5
c
d
4
4
e
f
y =2x + 1
2
3
g
y = 2.5
1 ​​x −1
y = ​​ __
2
x=2
1 ​​x
y = ​​ __
2
y = −2x −1
h
i
y = −2x
j
y = ​− __
​  1 ​​x + 2
3
y=x+4
k
y = 3x − 2
l
y=x−3
a
x = 2, y = −6
b
x = 6, y = 3
c
x = −4, y = 6
d
x = 10, y = 10
e
−5
x = ​​ ___ ​​, y = −5
2
b
d
f
h
j
x2 − x − 6
x2 + 2x − 35
2x2 + x − 1
6x2 − 7xy + 2y2
x2 + x − 132
1 − __
​​  1 ​​x2
4
m −12x2 + 14x − 4
l
−3x2 + 11x − 6
2
a
c
e
x2 + 8x + 16
x2 + 10x + 25
x2 + 2xy + y2
b
d
f
x2 − 6x + 9
y2 − 4y + 4
4x2 − 4xy + y2
3
a
b
c
Length x + 40; width x − 40
A = x2 − 1600
1600 cm2
x
−1
0
1
2
3
y
−2
−2
−2
−2
−2
x
−1
0
1
2
3
y
1.5
e
f
7
x
−1
1
−1.2 −0.8 −0.4
2
3
0
0.4
x
−1
0
1
2
3
y
−1
−0.5
0
0.5
1
x
−1
0
1
2
3
y
0.5
Exercise 10.2
1
y=x−2
4
a
d
g
h
no
b yes
no
e no
yes (horizontal lines)
yes (vertical lines)
a
m=1
6
m = __
​​   ​​
7
undefined
c
f
yes
no
b
m = −1
c
m = −1
e
m=2
f
m=0
h
m = ___
​​  1  ​​
16
a
c
e
g
i
x2 + 5x + 6
x2 + 12x + 35
x2 − 4x + 3
y2 − 9y + 14
2x4 − x2 − 3
k
−0.5 −1.5 −2.5 −3.5
3
g
21
0
student’s graphs of values above
d
8
−0.5 −2.5 −4.5 −6.5
2
5
m = −1, c = −1
m=−
​ __
​  1 ​​, c = 5
2
m = 1, c = 0
−1
y
i
m = 3, c = −4
x
(in fact, any five values of y are correct)
f
a
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Review exercise
a
b
c
d
y = __
​​  1 ​​x
2
x
−1
0
1
2
3
y
−0.5
0
0.5
1
1.5
a
b
3
x
−1
0
1
2
3
y
2.5
3
3.5
4
4.5
22
4
6
D
0
14
28
42
b
y=2
x
−1
0
1
2
3
y
2
2
2
2
2
Caroline’s distance at 7 km/h
y
45
25
20
15
5
x
−1
0
1
2
3
y
2
4
6
8
10
y=x−3
b
c
y = −x − 2
d
e
y = 2x −3
f
2 ​​ x + ​​ __
1 ​​
y = ​− ​ __
3
2
4
y = ​− __
​   ​​ x − 3
5
y = −x + 2
g
y=2
h
x = −4
b
y=7
d
x = −10
f
y = −3
4
A 0, B 1, C 2, D 1, E 4
5
a
y = −2x − 6
4 ​​ x + 4
y = ​​ __
3
y = −x
30
10
y − 2x − 4 = 0
a
e
2
35
d
c
0
40
m = −2, c = −1
m = 1, c = −6
m = 0, c = ​− __
​  1 ​​
2
m = −1, c = 0
c
t
y = __
​​  1 ​​x + 3
2
Student’s graphs of four lines using values
above.
2
a
Distance (kilometres)
1
6
0
c
x
0
2
4
6
Time (hours)
y = 7x
e i
ii
iii
f i
ii
iii
d
7
b
d
x2 − 3x − 40
4x2 + 12x + 9
3 hours
1 h 26 min
43 min
21 km
17.5 km
5.25 km
7
a
c
x2 + 10x −24
4x2 + 18x + 20
8
a
14, 48 i.e.
(x + 6)(x + 8) = x2 + 14x + 48
4, 24 i.e.
(x + 4)(x + 6) = x2 + 10x + 24
2, 2, 14 i.e.
(2x + 2)(2x + 7) = 4x2 + 18x + 14
b
c
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 11
Exercise 11.1
1
Exercise 11.4
a
c
e
g
5 cm
12 mm
1.09 cm
8.49 cm
b
d
f
h
17 cm
10 cm
0.45 cm
6.11 cm
2
a
c
e
55.68 mm
5.29 cm
9.85 cm
b
d
f
14.36 cm
10.91 mm
9.33 cm
3
a
no
c
no
4
20 mm
5
44 cm
6
height = 86.60 mm, area = 4330.13 mm2
7
13 metres and 15 metres
8
1562 metres
b
yes
d
A, C, F and G are congruent.
2
Only 4 are possible.
3
a
Yes, angle sum of a triangle is 180&deg;, so
third angle of each must be 60&deg;.
No. the 3 cm side is the hypotenuse of one
triangle and the side adjacent to the right
angle of the other.
For example:
b
c
yes
3cm
30&deg;
3cm
4
a
67.4&deg;
b
7 cm
Exercise 11.2
5
a
Yes
b
76.2 cm
1
A and C, B and D, E and F
2
a
c
e
f
g
h
Review exercise
2.24 cm
b 6 mm
7.5 mm
d 6.4 cm
y = 6.67 cm, z = 4.8 cm
x = 5.59 cm, y = 13.6 cm
x = 9 cm, y = 24 cm
x = 50 cm, y = 20 cm
3
angle ABC = angle ADE (corr angle are equal)
angle ACB = angle AED (corr angle are equal)
angle A = angle A (common)
∴ triangle ABC is similar to triangle ADE
4
25.5 metres
Exercise 11.3
1
23
1
a
b
Measurement 200 mm on D is incorrect, it
should be 160 mm.
100 mm
2
a
b
x = 18 cm
x = 27 cm, y = 16 cm
3
scale factor = 27 &divide; 15 = 1.8
perimeter of A = 83 cm, perimeter of B = 83 &times;
1.8 = 149.4 cm
1
a
b
Sketch of rectangle with width labelled 50
metres and length 120 metres.
130 metres
2
102 = 62 + 82 ∴ triangle ABC is right-angled
(converse Pythagoras)
3
P = 2250 mm
4
a
b
c
5
a, b and d
6
Reasons will vary, but here are some
suggestions.
a True, sides will be exactly the same length
in both rectangles.
b True, the base and height will be equal in
congruent triangles, so their area will be
equal too.
c False, they may be congruent but you
cannot say they will be congruent as they
could be differently shaped triangles with
the same area.
x = 3.5 cm
x = 63&deg;, y = 87&deg;
x = 12 cm
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
d
False, they could be the same type of
quadrilateral and be congruent, but they
could also be different shaped rectangles
(for example) or a square a rectangle.
7
5.63 metres
8
a
140 mm
]
68 mm
560 mm
420 mm
140 mm
b
24
156 mm
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 12
Exercise 12.1
1
a
b
c
d
e
f
2
mean
6.14
27.44
13.08
5
4.89
5.22
median
6
27
13
5
5
5
mode
6
27 and 38
12
no mode
4
6
b
3
a iii and vi
b For example:
Different sets can still add up to the same
total as another set. If divided by the same
number they will have the same mean.
3
255
4
15
5
a
c
6
Need to know how many cows there are to
work out mean litres of milk produced per
cow.
4
b
d
14 metres
10 metres
40
8
a
d
e
\$20.40
b \$6
c \$10
2 (only the category B workers)
The mean is between \$20 and \$40 so the
statement is true.
a
32
b
b
111
38
c
2.78
c
d
c
25
Score
Frequency
0
6
1
6
2
10
3
11
4
5
5
1
6
1
Total
40
1
38.5
a
2
2.25
Data set
mean
Exercise 12.2
b
Runner B has the faster mean time; they
also achieved the faster time, so would
technically be beating Runner A.
A is more consistent with a range of only
2 seconds (B has a range of 3.8 seconds).
Median. The mean will be affected by the
very high value of 112 minutes and the
mode has only two values, so unlikely to be
statistically valid. The median is 21 minutes
which seems reasonable given the data.
1
8.6 metres
10 metres
a
a
mean = 12.8, median = 15, mode = 17,
range = 19
mode too high, mean not reliable as range
is large
Exercise 12.3
7
1
a
b
2
9
a
mean = 4.3, median = 5, mode = 2 and 5.
The data is bimodal and the lower mode
(2) is not representative of the data.
mean = 3.15, median = 2, mode = 2.
The mean is not representative of the data
because it is too high. This is because
there are some values in the data set
that are much higher than the others.
(This gives a big range, and when the
range is big, the mean is generally not
representative.)
mean = 17.67, median = 17, no mode.
There is no mode, so this cannot be
representative of the data. The mean
and median are similar, so they are both
representative of the data.
median
mode
3
a
b
c
2
d
3
A
B
C
3.5
46.14
4.12
3
40
4.5
3 and 5
40
6.5
8 years
288
c​​ ____ ​​= 5.3 years
54
b
4 years
d
5 years
6
Review exercise
1
a
b
c
mean 6.4, median 6, mode 6, range 6
mean 2.6, median 2, mode 2, range 5
mean 13.8, median 12.8, no mode,
range 11.9
2
a
19
b
9 and 10
c
5.66
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
3
a
b
c
4
26
a
c
mode 154, median 154, mean 145,
range 96
One value is very low and that lowers the
mean height. You can see from the range
that the data is spread out.
The mode or the median as they are both
unaffected by very high or very low values.
You could also work out the mean of ten
values, leaving out the outlier of 60 cm
and you would get a mean of 153.5, which
is more representative of the sample data.
28 kg
61 kg
b
d
61 kilograms
20
e
Given that these are rounded masses and
the mean of the given data is 61, it could
be argued that a mean of approximately
60 kg is accurate enough, but given that
both the mode and the median are 61 it
would be more accurate to round 60.5
to 61 and to use that as the approximate
mean.
5
C – although B’s mean is bigger it has a larger
range. C’s smaller range suggests that its mean
is probably more representative.
6
a
4.82 cm3
b
5 cm3
c
5 cm3
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 13
Exercise 13.1
1
Student’s own diagrams
2
a
c
e
2600 metres
820 cm
20 mm
b
d
f
230 mm
2450.809 km
0.157 metres
3
a
c
e
9080 g
500 g
0.0152 kg
b
d
f
49 340 g
0.068 kg
2.3 tonnes
4
a
b
c
d
e
f
19 km
9015 cm
435 mm
492 cm
635 metres
580 500 cm
5
a
c
e
1200 mm2
16 420 mm2
0.009441 km2
b
d
f
900 mm2
370 000 m2
423 000 mm2
6
a
c
e
g
69 000 mm3
30 040 mm3
0.103 cm3
0.455 litres
b
d
f
h
19 000 mm3
4 815 000 cm3
0.0000469 m3
42 250 cm3
7
220 metres
8
110 cm
9
42 cm
100 metres
15 cm
2 mm
63 cm
35 metres
500 cm
10 88 (round down as you cannot have part of
a box)
Exercise 13.2
1
27
Name
Time in
Time out
Lunch
a
Hours worked
b
Daily earnings
Dawoot
__
​​  1 ​​ past 9
Half past five
3
​​ __ ​​ hour
4
​7__
​  1 ​​ hours
2
\$100.88
8.17 a.m.
5.30 p.m.
__
​​  1 ​​ hour
8 h 43 min
\$117.24
John
Robyn
Mari
08 23
7.22 a.m.
08 08
17 50
4.30 p.m.
18 30
8 h 42 min
8 h 8 min
9 h 37 min
\$117.02
\$109.39
\$129.34
2
6 h 25 min
3
20 min
4
2
45 min
1 hour
45 min
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
4
5
a
c
5 h : 47 min
12 h : 12 min
b
d
a
d
e
09 00
b 1 hour
c 10 05
30 minutes
It would arrive late at East Place at 10 54
and at West Lane at 11 19.
10 h : 26 min
14 h : 30 min
Exercise 13.3
1
2
The upper bound is ‘inexact’ so 42.5 in table
means ,42.5
Upper
bound
Lower
bound
a
42.5
41.5
b
13 325.5
13 324.5
c
450
350
d
12.245
12.235
e
11.495
11.485
f
2.55
2.45
g
395
385
h
1.1325
1.1315
a
b
71.5 &lt; h , 72.5
Yes, it is less than 72.5 (although it
would be impossible to measure to that
accuracy).
Exercise 13.4
1
a
1 cm per 100 000 rupiah
b i
ii
iii
2
c
i
a
Temperature in degrees C against
temperature in degrees F
i 32 &deg;F
ii 50 &deg;F
iii 210 &deg;F
Oven could be marked in Fahrenheit, but
of course she could also have experienced
a power failure or other practical problem.
b
c
d
28
525 000 rupiah
1 050 000 rupiah
5 250 000 rupiah
Aus\$38
ii
Aus\$304
3
a
c
9 kg
i
20 kg
b
45 kg
ii 35 kg
iii
145 lb
Exercise 13.5
1
a
c
e
US\$1 = &yen;115.76
€1 = IR84.25
&yen;1 = &pound;0.01
b
d
f
2
a
3800
b
50 550
c
9650.10
3
a
13 891.20
b
64 160
c
185 652
&pound;1 = NZ\$1.97
Can\$1 = €0.71
R1 = US\$0.07
Review exercise
1
a
c
e
g
i
k
2
23 min 45 s
3
2 h 19 min 55 s
4
1.615 metres &lt; h , 1.625 metres
5
a
b
2700 m
6000 kg
263 000 mg
0.24 litres
0.006428 km2
29 000 000 m3
b
d
f
h
j
l
690 mm
0.0235 kg
29 250 ml
1000 mm2
7 900 000 cm3
0.168 cm3
No, that is lower than the lower bound
of 45.
Yes, that is within the bounds.
6
a
7
€590.67
8
a
b
c
9
&pound;4046.25
conversion graph showing litres against
gallons (conversion factor)
b i
45 litres
ii 112.5 litres
c i
≈3.3 gallons
ii ≈26.7 gallons
d i
48.3 km/g and 67.62 km/g
ii
10.62 kilometres per litre and
14.87 kilometres per litre
US\$1 = IR76
152 000 rupees
US\$163.82
Fahrenheit scale as 50 &deg;C is hot, not cold
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 14
Exercise 14.1
1
a
c
x = 3, y = 2
x = 3, y = −1
b
d
x = 1, y = 2
x = 3, y = 5
2
a
c
x = 2, y = 1
x = 5, y = 2
b
d
x = 3, y = −1
x = 3, y = 2
3 a A: y = −2
B: y = x
C: y = 3x − 6
D: y = −7x − 1
E: y = −2x + 4
b i
ii
iii
iv
v
4
5
6
x = −2, y = −2
x = 3, y = 3
x = 3, y = −2
x = −1, y = 6
x = 2, y = 0
2
Answers may vary within the given range.
a 9, 8 …
b 10, 11 …
c 2, 1, 0 …
d 3…6
e 300, 301 …
f 0, −1, −2 …
g −3, −2, −1, … 0
h 2, 3
i
6, 7 … or 3, 2, 1 …
3
a
c
e
g
x , −4
x &gt; −2
−5 &lt; x , 0
−5 , x &lt; 17
i
1 ​​ j
x , −2 or x &gt; 2​​ __
2
4
x &gt; −4
x . 10
−3 , x , 4
x &lt; −2 or x &gt; 3
2.7 &lt; x &lt; 6.3
a
x
6
a
c
e
x = 1, y = 3
x = 3, y = 1
x = −1, y = −6
b
d
f
x = −3, y = 10
x = 1, y = 2
x = 2, y = 3
a
x = 2, y = −1
b
x = 4, y = 1
c
d
x = 4, y = −3
e
x = __
​​  2 ​​, y = 2
3
x = 2, y = 1
f
x = −1, y = 4
a
c
x = 1, y = −2
x = 3, y = 1
b
d
x = 2, y = 1
x = 5, y = 2
e
x = 7, y = −4
f
g
i
x = 3, y = 2
x = 2, y = −1
h
j
1 ​​, y = −2
x = ​​ __
3
x = 3, y = 3
x = 5, y = 1
7
x = 70 and y = 50
8
A pack of markers is 150 grams, a notebook is
80 grams.
9
x + y = 23; 8x − 15y = 92, x = 19
19 people took a class
b
x
−3
c
x
−5
d
x
−3
e
x
1.2
4.8
f
x
a
x.9
b
y , −5
c
x&lt;1
d
−2 , y , 6
e
−10 &lt; x , −4
f
(y + 3) &gt; (x − 4)
−3.5
2.8
−8
−3
g
x
Exercise 14.2
1
b
d
f
h
h
x
15
17
i
x
3
29
9
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Review exercise
1
a
x = 2, y = 5
b
x = 4, y = 2
c
x = 0.5, y = 1.5
d
x = 1, y​ = − __
​  1 ​​
2
2
x = 2 and y = −6
3
x = 1, y = −1
4
x = 31 and y = 7
5
Melon costs \$2.60 and peach costs \$0.35
6
a
b
c
7
b
15
b L &lt; 15
L
11
A: y = −2x + 6; B: y = −x + 5
x = 1 and y = 4
4 = −2(1) + 6 = −2 + 6 = 4 and 1 + 4 = 5
10 cm
8 a b , 15
c p , 500
p
500
d 1200 &lt; p &lt; 1500
p
1200
1500
e 180 &lt; u , 250
u
180
250
f 60 &lt; m , 75
m
60
30
75
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 15
Exercise 15.1
1
1 cm
0.5 cm
0.5 cm
0.5 cm
0.5 cm
0.4 cm
2
3.3 cm
2.1 cm
5.4 cm
5.4 cm
5.4 cm
3.3 cm
3
a
ii
iv
200 mm
125 mm
b
i
100 mm
iii 250 mm
1 : 200
4
a
c
16 metres
12.4 metres
b
d
10 metres
2 metres
5
13 mm or 1.3 cm
6
0.32 mm
ii
333&deg; &plusmn; 1&deg;
b
037&deg; &plusmn; 1&deg;
Exercise 15.2
1
a
b
c
B
i
115&deg; &plusmn; 1&deg;
022&deg; &plusmn; 1&deg;
2
329&deg; &plusmn; 1&deg;
3
a
4
6 km
200 metres
Exercise 15.3
1
Triangle
Hypotenuse
Opposite u
ABC
AB
BC
AC
DEF
DF
EF
DE
XYZ
XZ
XY
YZ
a
b
c
d
e
f
i
sin u
0.6
0.385
0.814
0.96
0.471
0.6
ii
cos u
0.8
0.923
0.581
0.28
0.882
0.8
iii
tan u
0.75
0.417
1.400
3.429
0.533
0.75
2
31
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
3
a
d
g
0.743
0.416
0.185
4
a
c
e
5.75 cm
7.27 metres
61.44 cm
a
d
32&deg;
39&deg;
b
e
12&deg;
73&deg;
c
f
44&deg;
50&deg;
a
d
36.9&deg;
66.0&deg;
b
e
23.2&deg;
68.0&deg;
c
f
45.6&deg;
9.6&deg;
5
6
b
e
h
0.978
0.839
0.993
b
d
f
c
f
2.605
0.839
2
(v)
26.26 mm
7.56 cm
7.47 metres
(i)
N
control tower
(iv)
(ii)
Exercise 15.4
1
a
2
6.06 metres
3
16.62 cm
4
52.43 km
5
a
15.08 metres
1689 metres
b
30.16 cm
200 km
b
975 metres
Review exercise
1
32
(iii)
Lines drawn accurately to the following
lengths:
a 1 cm
b 2 cm
c 3.4 cm
d 1.4 cm
e 3.6 cm
f 1.8 cm
3
a
150&deg;
b
160&deg;
4
a
0.8
b
0.6
c
d
0.8
e
0.8
f
5
a
c
e
g
x = 14.43 cm
x = 14.41 cm
x = 12.49 cm
x = 36.03&deg;
6
185.41 metres
7
a
8
4.71 metres
64.2&deg;
__
​​  4 ​​or 1.33
3
0.75
b
d
f
h
x = 13.44 cm
x = 51.82 cm
x = 43.34&deg;
x = 58.67&deg;
b
4.36 metres
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 16
Exercise 16.1
Review exercise
1
1
a
2
a
a
A strong negative correlation. The more
hours of watching TV, the lower the test
score.
b A strong positive correlation. The longer
the length of arm, the higher the bowling
speed.
c Zero correlation. The month of birth has
no effect on mass.
d A strong negative correlation. The more
someone sits during the day (eg the less
active they are), the less the length of life.
e A moderate positive correlation. Usually
the taller one is, the bigger the shoe size.
2 a Student’s own line (line should go close to
(160, 4.5) and (175, 5.5))
Answers (b) and (c) depend on student’s
best fit line
b​
≈​4.80 metres
c i
Between 175 cm and 185 cm
ii
This is not a reliable prediction
because 6.07 metres is beyond the
range of the given data.
d Moderately positive
e Taller athletes can jump further
3
The number of accidents at different
speeds
b average speed
answers to (c) depend on student’s best fit line
c i
​≈​35 accidents
ii ,45 km/h
d strong positive
e There are more accidents when vehicles
are travelling at a higher average speed.
b
c
d
e
There is a strong negative correlation at
first, but this becomes weaker as the cars
get older.
0−2 years
it stabilises around the \$6000 level
≈3 years
\$5000 – \$9000. This is not very reliable
as there is limited data from only one
dealership.
a
y
10
9
8
7
6
Rating 5
4
3
2
1
0
0
1
2
3x
Price (\$)
b
c
33
Weak positive
Answers will vary. Reasons should include
that for prices above \$2 dollars, all of the
taste ratings are six or higher, but also
that two of the cheaper ones are also rated
highly.
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Unit 5
Chapter 17
Exercise 17.1
Review exercise
1
\$19.26
1
a
12 h
b
40 h
c
2
\$25 560
2
a
\$1190
b
\$1386
c
3
a
c
3
a
\$62 808
b
\$4149.02
4
\$1203.40
4
a
Student’s own graph showing values:
5
\$542.75
6
a
b
d
\$930.75
\$765
\$625
\$1083.75
\$1179.38
Years
b
c
\$25
\$506.50
Exercise 17.2
5
1500
1592.74
10
3000
3439.16
A comment such as, the amount of
compound interest increases faster than
the simple interest
5 years
5
\$862.50
3
2.8%
6
\$3360
4
\$2800 more
7
a
\$1335, \$2225
5
\$2281 more
6
a
d
b
c
\$1950, \$3250
\$18 000, \$30 000
8
a
\$4818
9
\$425
7
\$562.75
8
a
\$2000
b
e
\$187.73
\$346.08
b
\$9000
c
\$210
\$225.75
1
a
c
2
\$1080
3
\$387.20
4
\$64.41
5
a
120%
11 \$43.36 (each)
b
d
\$144
\$245.65
\$179.10
b
10 \$211.20
Exercise 17.3
34
300
2
\$160
\$343.75
c
300
a
d
\$7.50
\$574.55
b
e
Simple interest Compound interest
1
1
\$7.50
\$448
​25 __
​  1 ​​ h
2
\$1232
b
\$40.04
12 \$204
\$264.50
\$400
c
\$963.90
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 18
Exercise 18.1
1
a
b
c
x
−6
−4
−3
−2
−1
0
1
2
3
y
−33 −22 −13
−6
−1
2
3
2
−1
−6
x
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
y
50
37
26
17
10
5
2
1
2
5
10
17
26
x
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
y
4
1
0
1
4
9
16
25
36
49
64
81
100
−5
y
100
b
4
5
6
−13 −22 −33
y
8
90
(0, 8)
y = 3x2 + 6x + 3
80
70
60
(b)
50
40
(−2, 0)
30
−2
20
x
y = −2x2 + 8
10
(c)
(0, 2)
0 2
c
0
−6 −5 −4 −3 −2 −1
−10
1
2
3
4
5
y
6x
−20
−30
(a)
−40
2
a
3
a
D
b
B
c
A
1.5
d
y
1.0
0.5
x
−3.0 −2.5 −2.0 −1.5 −1.0 −0.5 0
−0.5
−1.0
0.5
C
2
0
​
y = __
​  1 ​​x​​ 2​ + 2​
2
4 a 8 metres
b
c 6 metres
d
e 3 seconds
x
2 seconds
just short of 4 seconds
−1.5
−2.0
y = x2 + 3x
35
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
5
a
y = 2x2 + 3
b
x
−10
−5
0
5
10
y
203
53
3
53
203
c
y
250
200
150
100
50
−10
d
e
0
−5
10 x
5
As the temperature increases from 0 &deg;C,
so does the price and as the temperature
decreases from 0 &deg;C, so does the price.
7 &deg;C or −7 &deg;C
Exercise 18.2
1
a
x
−5
y​ = __
​ 2
x ​​
−0.4
−4
−3
−0.5 −0.67
−2
−1
1
2
3
4
5
−1
−2
2
1
0.67
0.5
0.4
3
4
5
y
x
0
b
x
−5
−4
−3
−2
−1
1
−1 ​​
y = ​​ ___
x
0.2
0.25
0.33
0.5
1
−1
2
−0.5 −0.33 −0.25 −0.2
y
1.0
0.8
0.6
0.4
0.2
−5
−4
−3
−2
−1 0
−0.2
1
2
3
4
5x
−0.4
−0.6
−0.8
−1.0
36
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
c
x
−5
y=1
−4
−3
−2
−0.2 −0.25 −0.33 −0.5
−1
1
2
3
4
5
−1
1
0.5
0.33
0.25
0.2
3
4
5
y
1.0
0.8
0.6
0.4
0.2
−5
−4
−3
−2
−1 0
−0.2
1
2
3
4
5x
−0.4
−0.6
−0.8
−1.0
d
x
−5
−4
−3
−2
−1
1
2
y=1
0.4
0.5
0.67
1
2
−2
−1
−0.67 −0.5
−0.4
y
2.0
1.5
1.0
0.5
−5
−4
−3
−2
−1 0
−0.5
1
2
3
4
5x
−1.0
−1.5
−2.0
37
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
2
a
length
1
2
3
4
6
8
12
24
width
24
12
8
6
4
3
2
1
Width (m)
b
c
d
24
22
20
18
16
14
12
10
8
6
4
2
0
0 2 4 6 8 10 12 14 16 18 20 22 24
Length (m)
The curve represents all the possible
measurements for the rectangle with an
area of 24 m2
≈3.4 metres
Exercise 18.3
1
a
b
c
2
a
x = 1, x = 3
x = 0, x = 4
x = 4.2, x = −0.2
y
8
y = x2 − 4x − 5
7
6
5
4
3
2
1
−7 −6 −5 −4 −3 −2 −1 0
−1
1
2
3
4
5
6
7
8
9x
−2
−3
−4
−5
−6
−7
−8
−9
−10
b i
ii
iii
38
x = −1 or x = 5
x = 1 or x = 3
x = −0.5 or x = 4.5
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
3
a
b
y
14
y = x2 − x − 6
13
12
11
10
9
8
7 (iii) y = 6
6
5
4
3
2
(ii) y = 0
1
x
−4
b i
ii
iii
4
3
2
1
−3
a
4 ​​
c​
y = − __
​  x
2
a
−1
0
1
2
3 x
1
2
3
−2
c
y
40
20
x = 0 or x = 1
x = −2 or x = 3
x = −3 or x = 4
y = x2 − 4
−2
−1
0
−2 −1 1 2 3 4 5
−2
−3
−4
−5
(i) y = −6
−6
−7
−8
−3
−2
−1
0
4x
−20
−40
3
Review exercise
1
y
5
b
9
y = ​​ __
x ​​
d
y = −x2 + 9
y
5
a
A is y = x2 + 2x − 8 because the
coefficient of x2 is positive and so the
graph is ∪-shaped.
B is y = −x2 + 2x + 8 because the
coefficient of x2 is negative and so the
graph is ∩-shaped.
b i
ii
iii
iv
v
4
3
2
x = −4 or x = 2
x = −2 or x = 4
x = −3 or x = 1
x=1
x = −1.5 or x = 3.5
1
−1.5 −1.0 −0.5 0
0.5
1.0
1.5 x
−1
−2
39
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 19
Exercise 19.1
Exercise 19.2
1
1
a
b
2
a
C = 1, A = 1, M = 1, B = 1, R = 0, I = 2,
D = 1, G = 0, E = 1
I = 2, all other letters have no rotational
symmetry.
A
B
C
D
E
Working and reasoning may vary but size of
angle should be as given below. Students must
show their working and valid reasoning using
statements that demonstrate knowledge of
angle properties and relationships.
a
d
b
e
40&deg;
40&deg;
22&deg;
122&deg;
2
100&deg;
3
54&deg;
4
w = 90&deg;, tangent meets radius
x = 53&deg;, angles on a straight line
y = 90&deg;, angle in a semi-circle
z = 53&deg;, angles in a triangle
F
c
f
45&deg;
64&deg;
Review exercise
1
a
b
c
d
e
2
a = b = 28&deg;, c = 56&deg;, d = e = 34&deg;
G
H has no line symmetry
40
b
A = 0, B = 3, C = 4, D = 4, E = 5,
F = 2, G = 2, H = 2
3
a
b
2, student’s diagram
2
4
Student’s own diagram but as an example:
i
i
i
i
i
1
1
4
8
1
ii
ii
ii
ii
ii
none
none
4
8
none
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 20
Exercise 20.1
1
2
a
d
g
j
4:5
5 : 14
1:5
6:5
b
e
h
k
a
c
e
g
i
k
x=9
x = 16
x=4
x = 1.875
x=7
x = 2.4
c
f
i
3:4
9 : 40
1 : 20
1 : 15
b
d
f
h
j
l
3
\$7200 and \$4800
4
100 and 250
5
60 cm and 100 cm
6
a
b
c
6:1
7:8
1:4
x=4
x=3
x = 1.14
x = 2.67
x = 13.33
x = 0.16
60&deg;, 30&deg; and 90&deg;
8
810 mg
8
a
c
4:1
b 14.8 cm
120 mm or 12 cm
Exercise 20.3
20 ml oil and 30 ml vinegar
240 ml oil and 360 ml vinegar
300 ml oil and 450 ml vinegar
7
b A is 6 metres (6000 mm acceptable)
B is 12 metres (12 000 mm acceptable)
C is 15.75 metres (15 750 mm acceptable)
1
25.6 litres
2
11.5 kilometre per litre
3
a
b
c
78.4 km/h
520 km/h
240 km/h (or 4 km/minute)
4
a
c
5h
40 h
b
d
9 h 28 min
4.29 min
5
a
c
150 km
3.75 km
b
d
300 km
18 km
6
167 seconds or 2.78 minutes
7
14500
______
​
​= 20 g/cm3
​​
725
Exercise 20.4
Exercise 20.2
1
a
1 : 2.25
b
1 : 3.25
c
1 : 1.8
2
a
1.5 : 1
b
5:1
c
5:1
3
240 km
4
30 metres
5
a
b
5 cm
3.5 cm
6
a
It means one unit on the map is equivalent
to 700 000 of the same units in reality.
1 a i
ii
iii
b
d
100 km
200 km
300 km
100 km/h
250 km
c
e
vehicle stopped
125 km/h
2
b
Map
distance
(mm)
10
71
50
80
1714 2143
Actual
distance
(km)
7
50
35
56
1200 1500
a 2 hours
b 190 min = 3 h 10 min
c 120 km/h
d i
120 km
ii 80 km
e 48 km/h
f 40 min
g 50 min
h 53.3 − 48 = 5.3 km/h
i
Pam 12 noon, Dabilo 11.30 a.m.
7 a A is 8 mm
B is 16 mm
C is 21 mm
41
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
a
Distance (m)
3
Ani’s distance from the classroom
y
35
30
1
a
14 : 19
25
2
a
c
420 and 180
210 and 390
3
a
c
b 0.5 bags
0.375 wheelbarrows full
4
a
b
90 mm, 150 mm and 120 mm
Yes, (150)2 = (90)2 + (120)2
5
5 cm
6
1 : 50
7
a
20
15
10
5
0
b
c
d
0
5
10 15 20 25 30 35 40 45 50 55 x
Time (s)
2.5 m/s
64 metres
1.28 m/s
a
b
c
Yes, __
​​  A ​ = ____
​  1  ​​
B 150
8
No, ​​ ___ ​​is not = __
​​ 1 ​​
2
15
10
A
Yes, ​​ __ ​ = ___
​   ​​
B
1
2
a
3
\$12.50
4
60 metres
5
a
c
75 km
3 h 20 min
b
375 km
6
a
15 litres
b
540 km
7
a
inversely proportional
b
i
\$175
b
9
a
9
5 h 30 min
1 : 500
c
b
d
350 and 250
300 and 300
b
1:8
36.36 km/h
85 km
382.5 km
21.25 km
0.35 h
4.7 h
1.18 h
150 km
100 km/h
500 km
b
d
after 2 hours for 1 hour
100 km/h
10 4.5 min
1 ​​ days
​2 ​ __
2
12 days
b
8
\$250
a
c
e
b
10.10 m/s
8 a i
ii
iii
b i
ii
iii
Exercise 20.5
1
Review exercise
ii
11 187.5 g
__
​​  1 ​​ day
2
5 days
10 1200 km/h
42
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 21
Exercise 21.1
1
a
d
g
9
8
7 and 2
2
9 cm
3
a
c
x−4
A = x2 − 4x
4
a
S = 5x + 2
Review exercise
b
e
h
26
6
40 and 60
b
c
f
134
2
P = 4x − 8
5x + 2
​
​
b​
M = ​ ______
3
a P = 3x + 12
b i
11 cm, 15 cm and 19 cm
ii 3.75 cm, 7.75 cm and 11.75 cm
1
10
2
4
3
4
4
Nathi has \$67 and Faisal has \$83
5
55
6
\$40 and \$20
7
a
b
8
144 km
9
Pam = 11, Amira = 22
5
6
a
x + 1, x + 2
b
S = 3x + 3
7
a
c
x+2
S = 3x − 1
b
x−3
8
14
9
width = 13 cm, length = 39 cm
10 a
b
2x + 5 = 2 − x
P = 4x + 2
length = 27 mm, width = 22 mm
10 4.00 p.m.
11 80 km
x = −1
11 80 silver cars, 8 red cars
12 father = 35, mother = 33 and Nadira = 10
43
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 22
Exercise 22.1
1
5
A9
B
10
8
B9
D
C
C9
C0
2
I0
6
(c) (ii)
2
H
x
10
A''
(c) (i)
4
6K9 8
I
x
7
A: centre (0, 2), scale factor 2
B: centre (2, 0), scale factor 2
C: centre (−4, −7), scale factor 2
D: centre (9, −5), scale factor __
​​ 1 ​​
4
a i
A'
J
F −8
A
3
y
8
A
P9
B
(b i)
C
S9
X
4
Q9 Q
2
−8
A: y = 5
B: x = 0
C: y = −1.5
D: x = −6
P
6
P99 R9
−8 −6 −4 −2 0
−2
(b ii)
Q99
−4
S99
R99
−6
4
J9
K
−6
G
K0
I9
E −4
D
6
J0
C94 H0
2
B
C F9
G9
(b)
−10 −8 −6 −4 −2 0
E9 −2
D9
8
−10
8
B9
B
6
−8
y
(a)
A
D''
4
2
−6
B0
A9
2
−10 −8 −6 −4 −2 0
−2
C
−4
(b)
A0
B''
4
C''
D9
D D0
A
6
(a)
A
y
S
R
2
4
6
A9
(a)
8
x
b
i
B'
B9
B
C9
X
c
C'
C
X
44
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
d
i
8
a
y
A'
D'
D
A
7
6
5
4
3
C'
2
1
B'
C
−5 −4 −3 −2 −1 0
−4
−5
−6
A'' −7
ii
A
b
A''
9
a
y
X
b
10
8
ii
C
6
C
B
4
C''
A
2
c
x
1 2 3 4 5
−2
C'' −3
B''
a
B
−4
ii
−2
0
x
2
4
6
8
−2
B
−4
B''
b
X
d
enlargement scale factor 2, using (8, −1)
as centre
Review exercise
ii
D
D''
1 a i
ii
iii
b i
reflect in the line x = −1
rotate 90&deg; clockwise about the origin
reflect in the line y = −1
rotate 90&deg; anti-clockwise about (0, 0)
​ 2)
then translate (
​−
​ ​
−1
ii reflect in the line y = −1 then
translate ​(−
​ 8 ​)
​​
0
iii rotate 180&deg; about origin then
translate ​(6​ ​)​
0
iv reflect in the line x = 0 ( y-axis) then
translate ​(​  0​ )
​ ​
−2
45
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
2
4
y
D99
7
6
5
4 D'
G'
3
2
1 E'
F'
−5 −4 −3 −2 −10 1 2 3 4 5
F
−2 G
−3
−4 D
−5
−6
−7
G''
B' A'''
(c) A'''' 6
4
F''
D
C
A A9
B
B9
A99
−4
B99
0
−2
2
4
6
8x
−2
(d)
c
B''''
B
1:2
d
4:1
4
C'''
C''''
C
2
A''
D''' D''''
C'
−10 −8 −6 D'−4 −2D''
2 4 6 8
(b)
B''
−2
A'
C9
6
E''
B'''8
D9
8
x
E
y
C99
10
2
10
(a)
y
14
12
D''
3
a&amp;b
−4
x
10
C''
−6
−8
−10
a
c
46
B9 (−6, 6)
B9 (−1, 8)
b
d
B9 (6, −2)
B9 (3, 9)
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Chapter 23
Exercise 23.1
1
3
Card
Traffic light
G
B
Green
3
4
2
3
4
1
6
Exercise 23.3
1
Even
2
Yellow
Black
1
2
H
1
2
1
2
T
H
1
2
1
2
T
H
1
2
T
12
H
1
2
H
1
2
1
2
T
H
1
2
T
1
2
1 ​​
b​​ __
e
47
6
12
T
__
​​  1 ​​
1
2
1
2
1
2
H
1
2
T
3, 9
1, 5, 7, 11
T
H
1 ​​
a​​ __
2
2
a
2 ​​
b​​ __
3
c
1 ​​
​​ __
d
6
B
1 ​​
​​ __
3
S
5
d​​ ___ ​​
12
___
​​  1  ​​
a
1
2
M3
2, 4, 8, 10
c
Not stop
7
c​​ ___ ​​
12
1  ​​
b​​ ___
18
Blue
1 ​​
b​​ __
4
Stop
2
9
7
9
a
1
3
Not stop
Not green
Exercise 23.2
1
2
7
9
1
4
G
H
A
B
C
D
E
F
1
Stop
2
9
H
T
H
T
H
T
H
T
Y
1
Pedestrian crossing
Coin
R
2
a
9
1
2
H
1
2
1
2
T
1
2
1
2
T
1
2
1
2
T
H
ii
1
2
T
iii
24
23
H
H
1 ​​
d​​ __
c
2
2
8
0, not possible on three coin tosses
19
b
i
8
​   ​​
P(both) = ___
​​  24 ​ = ___
75 25
19
P(neither) = ___
​​   ​​
75
56
P(at least one) = ​​ ___ ​​
75
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: CORE PRACTICE BOOK
Review exercise
1
a &amp;b
1
6
1
1
6
2
1
6
3
1
6
4
1
6
1
6
5
6
1 ​​
c​​ __
8
2
3
1
2
H
1
2
1
2
T
H
1
2
1
2
T
H
1
2
1
2
T
H
1
2
1
2
T
H
1
2
1
2
T
H
1
2
T
H
1
2
T
1
2
1
2
1
2
H
1
2
T
D
H
T
H
3
3
2
T
H
b
1
2
1
2
1
2
H
1
2
T
c
3
i​​ ___ ​​
3
ii​​ ___ ​​
10
10
20% chance of getting neither.
2
4 ​​
iii​​ __
5
T
H
___
​​  1  ​​
d
a
1
2
1
2
1
2
a
12
W
G
1
5
3
11
b
48
i
__
​​  4 ​​ 5
ii
1 ​​
​​ __
4
iii
11 ​​
​​ ___
20
Cambridge IGCSE™ Mathematics – Morrison &copy; Cambridge University Press &amp; Assessment 2023
```