CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Answers
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
2
3 ____
1 51 √512 = 8
3 ____
−57 0 1 51 10 270 √512 = 8
11
1 __
2 (−0.2, 3.142 and 0 .3̇ can also be
d
− __
7 expressed as fractions)
4
1
a
b
c
2
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
b
3
3
a
6.35
c
4
a
b
$2 847 379 794 and $2 797 501 328
$49 878 466 or forty-nine million, eight
hundred and seventy-eight thousand, four
hundred and sixty-six dollars
2.6
d
2
Exercise 1.2
1
39.55
a
b
c
d
e
f
g
2×2×3×3
5 × 13
2×2×2×2×2×2
2×2×3×7
2×2×2×2×5
2×2×2×5×5×5
2 × 5 × 127
h
13 × 151
a
b
c
d
e
f
LCM = 378, HCF = 1
LCM = 255, HCF = 5
LCM = 864, HCF = 3
LCM = 848, HCF = 1
LCM = 24 264, HCF = 2
LCM = 2970, HCF = 6
Exercise 1.4
1
−3 °C
2
a
−2 °C
b
−9 °C
c
−12 °C
1
a
d
18
24
b
e
36
36
c
f
90
24
3
a
d
4
−2
b
e
7
−3
c
−1
2
a
d
6
3
b
e
18
10
c
f
9
1
4
a
d
−3
0
b
−26
c
−14
3
18 metres
5
−5
−9
b
e
41
16
−78
120 shoppers
a
d
c
4
5
20 students
6
6
a
a
b
80.34 rupees : 1 euro
−5.5
1024 cm2
b
210 tiles
Exercise 1.3
Exercise 1.5
1
1
a
b
c
2, 3, 5, 7
53, 59
97, 101, 103
square: 121, 144, 169, 196, 225, 256, 289
cube: 125, 216
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
2
a
d
7
10
3
g __
4
j
5
b
e
5
3
c
f
14
25
h
5
i
2
k
l
12
m −5
n
3
1 __
4
5
__
6
o
6
3
a
d
g
1954
4096
3130
b
e
155
1250
c
f
1028
1875
4
a
23 cm
b
529 cm2
5
1
a __
4
___
d 12
5
___
g 14
3
____
j 1 4
12
5
___
e 13
3
___
h 16
8
8
___
f 15
2
____
i 1 3
23
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
7
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
_
b√ 4
d
(√ 4 )
e(√ 6 )
8
9
_
3
a √
3
_ 3
_ 4
9
_1
b6 3
_3
e5 6
a7 2
d9 4
_1
_5
c8 3
b
d
65
−163
a
d
g
j
m
p
s
v
26
15.66
3.83
2.79
8.04
304.82
4.03
3.90
b
e
h
k
n
q
66
3.39
2.15
7.82
1.09
94.78
6.87
−19.10
t
w
c
f
i
l
o
r
u
x
23.2
2.44
1.76
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 × 5 = 20
1000 × 7 = 7000
b
d
70 × 5 = 350
42 ÷ 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
_5
10 a
d
g
j
0.04
0.273
27
0.111
b
e
h
9
0.16
0.8
11 a
1296
b
−1
d
2
1
e __
4
g
32
h
3
j __
2
1
_
9
c√ 5
17
15
Exercise 1.6
1
c __
6
8
2
1
b __
12 a
c
4
c
f
i
1.5
2
18
8
c __
3
1
f ____
625
3
i __
2
Review exercise
1
natural: 24, 17
3
1 , 0, 0.66, 17
rational: − __
, 24, 0.65, −12, 3 __
4
2
integer: 24, −12, 0, 17
prime: 17
2
a
b
c
d
e
1, 2, 3, 4, 6, 9, 12, 18, 36
two are prime: 2 and 3
2×2×3×3
Any two from: 1, 2, 3, 4, 6, 9, 12, 18, 36
36
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
3
9
2×2×7×7
3 × 3 × 5 × 41
2×2×3×3×5×7×7
4
14th and 26th March
5
a
c
true
false
b
d
true
false
a
d
g
5
145
5
b
e
h
5
48
10
c
f
64
112
7
a
d
16.07
11.01
b
e
9.79
0.12
c
f
13.51
−7.74
8
a
30
6
3
a
b
c
b
33
c
3−2
d
3−1
e3 2
_3
f
32
g
30
h
3−2
i
38
j
3−4
a
37
b
26
c
2−1
10 a
c
x = −3
x = −2
b
d
x = −3
x=6
11 a
c
1240
0.0238
b
d
0.765
31.5
12 a
b
92.16 cm2
19.78 cm2
d
40
_
13 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.
14 1.5 metres
15 a
40
b
6
c
22
d
72
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 2
Exercise 2.1
1
a
3(x + 2)
b
6(x − 1) or 6(1 − x)
c
2(11 + x)
d
18x
f
x2 + 8
x + __
1
3
12 − 5x or 5x − 12
e
3x2 + 4
1 − x
g __
5
i
4 + 3x
h
j
p−4
c
b
2x
x 2x
$ __ , $ ___
, and $ ___
3
9
9
3
c
d
3
x
a
$ __
3
4
a
b
3(x + 7) = 3x + 21
2x(4 + x) = 2x2 + 8x
c
3x(6x) = 18x2
Exercise 2.4
d
2(x + __
1 ) = 2x + 1
2
1
4p
4
x
___
s
6y
Rectangle, P = 20x − 4
Right angled isosceles triangle,
P = 13x − 1
Square, P = 8x − 16
Kite, P = 6x − 14
a
Working shown to give the answers:
a −3x3 + x2 + 9x
b −7x2 − 3x + 11
c
2x2 − 3x + 5
d
3xy − 4xy2 + 2
a
2x2 − 4x
b
xy − 3x
c
−2x − 2
d
−3x + 2
Exercise 2.2
e
−2x2 + 6x
f
3x + 1
1
g
x3
h
x2 + x + 2
x
a
x 2 + __
2
3
c −8x + 4x2 + 2x
b
e
3x2 − 6x
f
x2 + xy
x 3y
__ + ___
2
2
2
−5x − 6x
g
−5x2 − 6x
a
2(5x + 4) − 3(x − 7) = 10x + 8 − 3x + 21
= 7x + 29
x3(x + 2y) − 2(x4 − y) = x4 + 2x3y − 2x4 + 2y
= −x4 + 2x3y + 2y
a
c
b
d
54 cm2
110.25 cm2
2
−104
3
17
4
17.75
5
a
6
b
1.875 m2
8 cm2
91
2
3
Exercise 2.3
1
a
b
c
2
C is correct
A cannot be simplified as there are no like
terms
B can be simplified, the correct answer is
4xy
a
c
e
3x2 − 2x + 3
5ab − 4ac
−30mn
f
h
−4x3y
k
3b
3 x 2
n ____
y
4
a
b
2
p+5
b
− 14y
r _____
5
15 a
2
_____
q
4
27 x 2
t _____
10
b
d
6x2y
4x2y − 2xy
4x2 + 5x − y − 5
g 6xy 3
1
i
4b
j
___
4y
20y
9m
l
___
m ____
4
3x
2
2
y
y
2
___
o ____
p
2
2
x
b
−
2x 2
−x
d
Exercise 2.5
1
x 6
a ___2
y
2
x 2
c ____
3y
5x 9
e ____3
2y
50x 3
g _____
27y
i
x7y
x 16
k ____
y 16
b
3x4y
d
xy10
f
x7y3
h
49
_______
25x 3y
j
8x 10y 3
_______
3
l
3125x y
__________
4 2
16
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2
x 8
a ___2
y
8
c _____
x 5y 7
b
d
y 16
e ____
x 22
3
f
4
y 22
____4
2x
bx 15
cx 6
_1
dx 9
e
f
2x 3y 3
i
_1
x 3
h
x 3y −1 or ___
y
_
1
2
y 4
_2
b
x2
_7
d
x2
ax 3
_1
e
a
9a + b
b
c
−4a4b + 6a2b3
d
6
5x 5
a ____
6
b
d
64x 9
e _____
y 15
11x − 3
−2x2 + 5x + 12
16x4y8
a
2
b
2
c
e
−4
f
2
3
g __
2
1
d __
4
3
h __
4
4
a
x + 12
b
c
5x
d
e
4x
f
g
12 − x
h
x−4
x
__
3
x
__
4
x3 − x or x − x3
a
−6
b
24
c
a
_1
5xy 3
y
9
c
x −9yor ___
x
h
5
x2 + 3x − 2
b
d
29
__
Review exercise
5
7
c
a
c
7
fx − 4 y − 16 or _____
_11 __29
x 4 y 16
_3
ex 4 y 2
2
d
27x 4
g ____
4y 3
cy 3
1
b
5
j
x −2y −4 or _____
21 4
x y
x3
−2
4x
e ___
y
_1
8x3
2
__
3
−2
a
−7x + 4
5y
f5x − ___
2
8
__
12
k
y −2 or ___
y
5
3
_1
ax 2
gx
4
x 5
___4
y
___
19
x
6x2 + 15x − 8
−x3 + 3x2 − x + 5
1
c ___
x 4
15
f
x9y8
xy 6
____
2
_1
bx 2
_5
2y 3
_1 _5
_1
d
2x − 3 y 3 or ____
x 3
8
Since n is even, we can replace n with 2x where
x is some unknown number. Since m is even,
we can replace it with 2y. Therefore,
nm = 2x × 2y = 4xy. 4xy is a multiple of 4 and
must be divisible by 4.
9
a
b
1.86 mg
3.79 mg (Note that you have to work out
four-hour dose then add that to next dose
before applying formula for one hour to
get the amount after five hours.)
10 44%
____
− 14
9
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 3
Exercise 3.1
Exercise 3.2
1
a
b
c
d
i
150°
ii 180°
45°
i
810°
ii 72°
quarter to one or 12 45
2
No. If the acute angle is < 45° it will produce
an acute or right angle.
a
b
c
d
e
f
3
Yes. The smallest obtuse angle is 91° and the
largest is 179°. Half of those will range from
45.5° to 89.5°, all of which are acute.
g
4
a
b
c
45°
(90 − x)°
x°
5
a
c
e
135°
(180 − x)°
(90 + x)°
iii
i
b
d
f
90°
x°
(90 − x)°
angle QON = 48°, so a = 48° (vertically
opposite)
7
a
8
a
b
c
d
9
a
b
c
d
e
f
1
h
6
b
135°
angle EOD = 41 ° (angles on line), so x =
41° (vertically opposite)
x = 20° (angles round point)
x = 85° (co-int angles); y = 72° (alt angles)
x = 99° (co-int angles); y = 123° (angle
ABF = 123°, co-int angles then vertically
opposite)
x = 72° (angle BFE = 72°, then alt angles);
y = 43° (angles in triangle BCJ )
x = 45° (angles round a point); y = 90°
(co-int angles )
x = 112° (angle AFG = 112°, vertically
opposite, then co-int angles)
x = 45° (angle STQ corr angles then
vertically opposite)
x = 90° (angle ECD and angle ACD co-int
angles then angles round a point)
x = 18° (angle DFE co-int with angle CDF
then angle BFE co-int with angle ABF )
x = 85° (angles ADC and EDF vertically
opposite, then co-int with angles BAD)
BCF = 98° (alt angles),
so DCF = 98° − 43° = 55°; x = 125°
(co-int angles)
2
a
b
c
d
3
103° (angles in triangle)
51° (ext angle equals sum int opps)
68° (ext angle equals sum int opps)
53° (base angles isosceles)
60° (equilateral triangle)
x = 58° (base angles isosceles and angles
in triangle); y = 26° (ext angles equals
sum int opps)
x = 33° (base angles isosceles then ext
angles equals sum int opps)
x = 45° (co-int angles, angles on aline,
then angles in triangle)
x = 45° (base angles isosceles); y = 75°
(base angles isosceles)
x = 36°; so angle BAC = 36° and angle
ABC = 72°
x = 40°; so angle BAC = 80°;
angle ABC = 40° and angle ACD = 120°
x = 60°
x = 72°
angle ABC = 34°; angle ACB = 68°
Exercise 3.3
1
a
b
c
d
e
f
g
h
i
2
square, rhombus
rectangle, square
square, rectangle
square, rectangle, rhombus, parallelogram
square, rectangle
square, rectangle, parallelogram, rhombus
square, rhombus, kite
rhombus, square, (kite: one diagonal
bisects one pair of angles)
rhombus, square, kite
a
a
f
b
e
d
g
f
a=b=c=d=e=f
= 45°
c
a = d = e = 63°
b = c = f = 27°
63° a
e
6
b
d
b
c
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
3
a
c
e
f
x = 69°
b x = 64°
x = 52°
d x = 115°
x = 30°; 2x = 60°; 3x = 90°
a = 44°; b = 68°; c = 44°; d = e = 68°
a
b
c
angle Q + angle R = 210°
angle R = 140°
angle Q = 70°
5
a
b
c
angle MNP = 42°
angle MNO = 104°
angle PON = 56°
6
A − Kite
B − Trapezium
C − Rhombus
D − Parallelogram
E − Square
F − Rectangle
4
Exercise 3.5
1
2
(b) chord
i
i
i
1080°
1440°
2340°
sector
50° (a)
O
diameter
(e) major
arc
E
N
(c)
P
Exercise 3.6
1, 2 student’s own diagrams
ii
ii
ii
3
student’s own diagram; scalene
4
If you only have the length of two sides, you
need to know the size of the angle at A or B or
the length of the third side to make sure you
draw the given triangle. This diagram shows
that AC could be any 5 cm length and that
would mean that BC could be a number of
different lengths, so Jay’s reasoning is faulty.
135°
144°
156°
5 cm arc
C
C
AC = 5 cm, so point
C can be anywhere
on the arc:
C
900
____
= 128.57°
3
7
20 sides
4
a
165.6°
5
a
b
c
x = 156°
x = 85°; x − 50° = 35°, x − 10° = 75°
x = 113°; y = 104°
6
Divide 360 by the number of angles to find the
size of one exterior angle. Then use the fact
that the exterior and interior angles form a
straight line (180°) to work out the size of the
interior angle.
7
7
a
b
c
(d) tangent
D
Exercise 3.4
1
M
C
b
360
_____ = 25sides
14.4
Yes. If internal angle is 170°, then external
angle = 10°. Sum of external angles is 360°,
and 360° ÷ 10° = 36, so this would be a
36-sided regular polygon.
A
5
7 cm
B
For example:
Start by marking vertex A. Draw two 5 cm
long lines from A to vertices B and C.
Use compasses to mark 5 cm arcs from B
and C. The arcs will intersect at vertex D.
Join the vertices to form a rhombus.
Review exercise
1
a
b
c
d
e
f
g
h
x = 113°
x = 41°
x = 66°
x = 74°; y = 106°; z = 37°
x = 46°; y = 104°
x = 110°; y = 124°
x = 40°; y = 70°; z = 70°
x = 35°; y = 55°
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
2
a
b
c
x = 60 + 60 + 120 = 240°
x = 90 + 90 + 135 = 315°
x = 80°
3 a i
radius
ii chord
iii diameter
b OA, OB, OC, OD
c 24.8 cm
d Student’s own diagram
8
4
Student’s own diagram
5
Students should construct a triangle with sides
3 cm, 12 cm and 13 cm.
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED 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
4
height, mass
6
013335577799
5
possible answers include: eye colour, hair
colour – collected by observation; height,
mass – collected by measuring; grade, shoe
size, number of siblings – collected by survey,
questionnaire
7
013688
8
028
9
1
Key: 2 | 6 represents 26 per cent
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.
Exercise 4.2
1
2
Text
messages
a
b
3
a
Tally
|
1
2
||
2
3
||
2
4
| | | |
5
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
Hair colour
b
c
5
a
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.
Stem
Leaf
No. of
0
mosquitoes
1
2
3
4
5
6
0
1257
Frequency
6
9
7
8
7
6
1
22689
2
0349
3
1113579
4
138
5
1
7
It is impossible to say; frequency is very
similar for all numbers of mosquitoes.
Score
Score
Frequency
b
e
Frequency
1
Frequency
9
Leaf
0–29 30–39 40–49 50–59
1
1
7
19
Key: 0 | 1 represents 1 car,
1 | 2 represents 12 cars
60–69 70–79 80–100
12
6
4
10
c 2
d 26
There are very few marks at the low and
high end of the scale.
6
b
51 cars
a
b
74
34
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
c
d
e
It does not show the games against each
other, it simply shows the points scored
in 12 games by the home team and their
opponents. There is no link between the
scores as there would be in a table or
double bar graph showing points per
game.
Their lowest score of 34 is higher than the
lowest opponent team score, so the home
team could not have lost the game where
the opponents scored 28 points.
8 games. Four of the opponents scores
(74, 63, 64, 64) are higher than the highest
home team score of 59. This means they
could not win these four games. This does
not mean that they won eight games, just
that this is the most games they could
have won.
4
Charts can be drawn vertically or horizontally.
a
Breakfast food chosen
Bread
Hot porridge
Cereal
0
4
8
12 16 20 24 28 32
Frequency
b
Breakfast food chosen
Bread
Key
Grade 10
Exercise 4.3
1
a
b
c
d
e
f
g
pictogram
number of students in each year group in
a school
30 students
half a stick figure
225
Year 11; 285
rounded; unlikely the year groups will all
be multiples of 15
2
student’s own pictogram
3
a
e
The number of students in Grade 10
whose home language is Bahasa and
Chinese.
18
30
The favourite sports of students in Grade
10, separated by class
athletics
f
g
athletics
9
b
c
d
10
Hot porridge
Grade 11
Cereal
0
4
8
12 16 20 24 28 32
Frequency
5
a
d
cars
b 17%
handcarts and bicycles
6
a
b
Pie chart with sector sizes:
A − 18°; B − 43°; C − 148°; D − 90°;
E or lower − 61°
6
c 50
d C
a
b
c
d
e
f
g
29.7 ± 0.1° C
April–November
northern hemisphere
no
10 mm
February
There is little or no rain.
7
c
20
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Review exercise
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
0
Tally
| | | | | |
Frequency
2
1
7
Pie chart with sector sizes:
0 − 53°; 1 − 75°; 2 − 83°; 3 − 90°; 4 − 37°;
5 − 15°; 6 − 7°
f
The number of families that have three or
fewer children is five times greater than
the number of families with four or more
children.
Pulse rate
before
exercise
Pulse
rate after
exercise
Stem
5 5 0
5
9 9 7 4
6
4 3
7
0
8
4
9
5 7 8
10
3
11
3 5 5
12
0 1
3
| | | | | | | | | | | | | | | | | | | | | | | | | | |
e
a
2
10
11
5
a
c
e
6
a
12
4
5
6
| | | |
| | | |
|
5
2
1
b
d
Downtown
$2500
15%
$4750
$3750
Rice
Not rice
Pasta
13
24
Not pasta
32
6
b
49%
7
a
b
Student’s own chart
Student’s own chart
8
a
49.6%
b
$3 600
Key:
Before exercise0 | 5 represents 50 beats
per minute
After exercise8 | 4 represents 84 beats
per minute
b
3
Student’s own pictogram
4
a
b
c
d
e
f
g
11
In every person, the pulse rate increased
after exercise.
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.
Canada, USA and Denmark
Germany, UK, Sweden and Italy
Denmark
Student’s own opinion with reason.
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 5
Exercise 5.1
5
1
a
d
2
5 5 __
3 3 __
a __ , 1 __
, , __
, 1
3 8 4 8 8
5 13 7 ___
11 , __
, ___ , ___
, 4
b
___
9 9 24 18 15
13 2 __
5 3 ___
17
c ___ , 2 __
, , __
,
3 3 6 4 24
x = 65
x = 117
b
e
x = 168
x = 48
c
f
x = 55
x = 104
2
3
4
12
25
a ___
8
15
d ___
4
33
g ___
10
b
17
___
11
59
e ___
4
29
h ___
4
c
f
59
___
63
___
13
c
14
e
3
f
6
___
g
120
h
i
72
j
3
k
3
___
14
233
____
50
7
l __
4
19
___
c
b
e
h
k
24
b
10
d ___
27
e
g
h
2
f
0
6
a
$525
b
$375
7
a
300
b
6 hours 56 min
8
28 000 litres
60
183
____
56
41
___
40
− 10
____
3
96
___
7
32
___
45
3
__
5
1
2
b
a
c
g
5
25
___
9
108
a ____
5
28
d ___
5
13
a ___
24
35
d ___
6
18
g ___
65
−5
j ___
6
4
__
5
25
e ____
576
11
h ____
170
b
i
39
___
7
215
____
72
187
____
9
Exercise 5.3
Exercise 5.2
1
38
a ___
9
19
d ___
4
f
i
l
19
3
4
7
c ___
96
9
f ___
14
152
i ____
39
16.7%
b
62.5%
c
29.8%
d
30%
e
4%
f
47%
g
112%
h
207%
i
125%
j
250%
k
1750%
l
103.8%
b
__
1
c
49
___
c
9.05%
1
a __
8
3
d __
5
a 53.33%
a
c
e
g
i
k
60 kg
150 litres
$64
18 km
0.2 g
475 m3
5
a
c
e
g
6
7
19
___
21
161
____
20
29
___
21
− 26
____
9
a
e
b
2
___
11
50
37.62%
b
d
f
h
j
$24
55 ml
$19.50
$108
$2.08
l
99 km
+20%
+53.3%
−28.3%
+2 566.7%
b
d
f
−10%
+3.3%
+33.3%
a
c
e
$54.72
$32.28
$98.55
b
d
f
$945
$40 236
$99.68
a
c
e
$58.48
$83.16
$76.93
b
d
f
$520
$19 882
$45.24
50
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
8
28 595 tickets
9
1800 shares
4
a
c
e
g
i
1.2 × 1031
3.375 × 1036
2 × 1026
1.2 × 102
3 × 10−8
b
d
f
h
4.5 × 1011
1.32 × 10−11
2.67 × 105
2 × 10−3
5
a
the Sun
b
6.051 × 106
6
a
b
500 seconds = 5 × 102 seconds
19 166.67 seconds = 1.92 × 104 seconds
10 $129 375
11 21.95%
12 $15 696
13 $6228
14 2.5 g
7
15 ___ = 28% increase, so $7 more is better
25
16 $50
17 a
1 200
b
960
18 $150
19 a
b
2 hrs 54 mins (174 mins)
4 hrs 46 mins (286 mins)
Review exercise
1
a
b
2
1
a __
6
3
d ___
44
361
g ____
16
14
j ___
9
20 26.59 grams (two decimal places)
21 a
$12
b
27 750
c
$114 885
Exercise 5.4
1
13
a
c
e
g
i
k
4.5× 104
8 × 10
4.19 × 106
6.5 × 10−3
4.5 × 10−4
6.75 × 10−3
b
d
f
h
j
l
8 × 105
2.345 × 106
3.2 × 1010
9 × 10−3
8 × 10−7
4.5 × 10−10
2
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
3
a
c
e
g
i
6.56 × 10−17
1.44 × 1013
5.04 × 1018
1.52 × 1017
4.50 × 10−3
b
d
f
h
1.28 × 10−14
1.58 × 10−20
1.98 × 1012
2.29 × 108
Any multiple of 8 (8, 16, 24 etc.)
Two trays
b
63
c
e
31
___
48
334
____
45
f
h
3
$10 000
4
a
5
67.7%
6
8.15%
7
a
5.9 × 109 km
b
5.753 × 109 km
a
b
c
9.4637 × 1012 km
1.6 × 10−5 light years
3.975 × 1013 km
8
719
b
i
5
__
3
71
___
6
68
___
15
11 779
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 6
Exercise 6.1
1
a
3
b
x=4
d
x=4
f
x=5
h
x = −5
j
3
= − __ = −1 __
x
1
1
k
x = ___
11 = 5 __
l
x=3
a
b
x = −2
8
c
x = − __ = −2 __
2
3
3
d
e
x=8
f
g
x = −4
h
1
x = __
4 = 1 __
3
3
1
__
x =
4
x = −9
i
x = −10
j
x = −13
x=3
9
c
x = __
= 4 __
1
2
2
18
3
36 ___
___
e
x = = = 3 __
5
5
10
g
i
x=2
x=4
2
2
3
2
x = 10
2
a
x(x + 8)
b
a(12 − a)
c
e
g
i
k
x(9x + 4)
2b(3ab + 4)
3x(2 − 3x)
3abc2(3c − ab)
b2(3a − 4c)
d
f
h
j
l
2x(11 − 8x)
18xy(1 − 2x)
2xy 2(7x − 3)
x(4x − 7y)
7ab(2a − 3b)
4
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)
5
a
c
e
(2 + a)(2x + 3)
(b + 4)(2c + 3a)
(2y + 3x)(x2 + y2)
b
d
f
(x − 3)(x + 2y)
(3x2 + 4)(2x + 1)
(a + 9)(2 − b)
2
Exercise 6.3
k
x = −34
l
7
20
x = ___ = 1 ___
a
x = 18
b
x = 27
2
m = __
D
k
c = y − mx
c
x = 24
d
x = −44
e
f
P+c
b = ____
a
x = 17
g
x = −1
h
23
5
x = ___
= 3 __
6
6
x=9
3
4
a−c
b = ___
x
3
16
i
x = ___ = 1 ___
13
13
5
a
j
x = 10
k
l
x = ____
− 11
2
1
x = __
5
x = −1
x = 42
m x=2
n
o
p
x=1
13
13
1
14
a
d
g
j
3
a
4xy
xy2z
2
a
c
e
g
i
12(x + 4)
4(a − 4)
a(b + 5)
8xz(3y − 1)
2y(3x − 2z)
b
e
h
k
c
f
i
l
8
3y
pq
ab3
b
d
f
h
j
f
5
5ab
7ab
3xy
2(1 + 4y)
x(3 − y)
3(x − 5y)
3b(3a − 4c)
2x(7 − 13y)
b
a = 2c + 3b
c+d
d−c
c
a = ____
d a = ____
b
b
e a = bc − d (or a = −d + bc)
Exercise 6.2
1
a=c−b
6
7
8
a = d + bc
g
de − c
h
a = ____
b
i
ef − d
j
a = ____
bc
k
cd − b
a = _____
2
e+d
a = ____
bc
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
use b = ___
2A − a; b = 3.8 cm
h
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
9
a
i
b
11 656 kg
70 kg
ii
12 kg
b
6 seconds
3
a
c
e
g
i
4(x − 2)
−2(x + 2)
7xy(2xy + 1)
(4 + 3x)(x − 3)
(a2 + 10)(a − 6)
4
a
b
c
d
4(x − 7) = 4x − 28
2x(x + 9) = 2x2 + 18x
4x(4x + 3y) = 16x2 + 12xy
19x(x + 2y) = 19x2 + 38xy
5
a
b
x = 15°, so ∠DEG = ∠FEH = 135°
x = 26°, so ∠ABC = 26°, ∠ACB = 94°,
∠BAC = 60°
x = 30°, so ∠ADB = ∠ADC = 135°
T − 70P
= B
c ________
12
d 960 kg
10 a
√
__
h
t = __
5
Review exercise
1
2
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
m+r
a
x = _____
np
b
mq − p
x = ______
n
c
3(4x − y)
3x( y − 8)
(x − y)(2 + x)
4x(x + y)(x − 2)
y
× a;
Young’s Rule: d = ______
y + 12
y
Dilling’s Rule: d = ___
× a
20
6
a
b
c
15
b
d
f
h
Young’s Rule: 6.77 mg/6–8 hours;
Dilling’s Rule: 5.25 mg / 6–8 hours.
Clark’s rule: 6.75 mg/6–8 hours.
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 7
Exercise 7.1
Exercise 7.2
1
a
c
e
120 mm
128 mm
36.2 cm
b
d
f
45 cm
98 mm
233 mm
2
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 m
4
164 × 45.50 = $7462
5
9 cm each
6
about 88 cm
7
8
a
a
c
e
g
63π cm
332.5 cm2
399 cm2
59.5 cm2
2 296 mm2
b
b
d
f
h
70π cm
1.53 m2
150 cm2
71.5 cm2
243 cm2
9
a
c
e
7853.98 mm2
7696.90 mm2
167.55 cm2
b
d
153.94 mm2
17.45 cm2
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
33.6 cm2
720 cm2
b
d
f
90 cm2
61.2 cm2
(625π + 600) cm2
b
15π cm
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
14π mm
8
c __ π mm (or 2.6π mm)
3
15 6671.70 km
16 a
c
24π cm2
(81π − 162) mm2
b
233.33π cm2
17 61.4 cm2
16
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
9
c
a
5.28 cm3
c
e
25.2 cm3
65 144.07 mm3
b
d
33 510.32 m3
169.65 cm3
b
1868.36 cm2
b
21π cm
b
d
f
h
33 000 mm2
80 cm2
35 cm2
159.27 cm2
10 a i
1.08 × 1012 km3
ii 5.10 × 108 km2
b 1.48 × 108 km2
11 a
0.498 m2
Review exercise
1
d
3
65
π cm
√ ___
a
2000 mm2
c
e
g
40 cm2
106 cm2
175.93 cm2
4
15 metres
5
243 cm2
6
a
b
c
d
Exercise 7.3
Cuboid B is smaller
14 265.48 mm3
student’s own diagram
cylinder 7539.82 mm2, cuboid 9000 mm2
a
c
2.56 mm2
13.5 cm2
b
d
523.2 m2
128π mm2
7
42
2
a
384 cm2
b
8 cm
8
3
a
c
340 cm2
4 tins
b
153 000 cm2
volume pyramid = 30 cm3
15
volume cone = ___
π cm3
2
difference = 6.44 cm3
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
9
5
332.5 cm3
729
π cm3
volume 3 balls = ____
2
14812
π cm3
volume tube = ______
25
space = 716.22 cm3
6
a
b
44 people
7
67.5π m3
8
Various answers – for example:
224 m3
10 a
b
Volume (mm3) 64 000 64 000 64 000 64 000
17
110.25π cm2
___
2
1
a
Length (mm)
80
50
100
50
Breadth (mm)
40
64
80
80
Height (mm)
20
20
8
16
13 014.57 mm3
For example: the cylinder may be hollow,
or, part of the sphere will be removed
where it joins the cylinder.
11 37.7 cm3
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 8
Exercise 8.1
1
a
b
Exercise 8.2
9
17
3
, green = ___
red = ___
, white = ___
25
50
10
1
30%
c 1
d __
3
1
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
3
4
4 or equivalent
a ___
18
4 or equivalent
b __
9
7
c __ or equivalent
9
a 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10
9
i
H
HH
HT
T
TH
TT
3
a __
4
2
Yellow
3
c
0.6
b
0.97
c
11
2
3
1
1, 1
1, 2
1, 3
2
2, 1
2, 2
2, 3
3
3, 1
3, 2
3, 3
vi
10
__
1
2
ix
0
a
cola, biscuit
Drink
fruit juice,
biscuit
water,
biscuit
2
__
2
5
d
Snack
cola,
cake
fruit juice,
cake
water, cake
cola, muffin
fruit juice,
muffin
water,
muffin
2
c __
3
1
b __
9
__
1
1
d __
3
1
c __
3
3
___
iii
c
1
9
Exercise 8.3
1
a
0.73
12 a
1
b __
4
a
b
5
10 __
8
11 a 0.16
b 0.84
c 0.6
d strawberry 63, lime 66, lemon 54,
blackberry 69, apple 48
114
2
3
4
18
T
Green
___
1
ii 1
10
3
2
iv ___
v __
5
10
9
3
___
___
viii
vii
10
10
2
5 a __
5
3
b no sugar; probability = __
5
1
6 a __
b __
1
4
2
7
b __
1
7 a ___
20
2
3
___
__
e 1
d
5
10
13
8 ___
40
b
H
4
b ___
15
7
a ___
13
1
a __
8
A
E
A
C
CA
CE
CA
N
NA
NE
NA
B
BA
BE
BA
R
RA
RE
RA
R
RA
RE
RA
1
__
5
6
b ___
13
1
b __
8
c
d
___
4
15
9
c ___
13
3
c __
8
Removing a flavour has an effect on the
second choice (there are fewer left to choose
from) so the events are not independent.
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Review exercise
a
10 000
b
heads 0.4083; tails 0.5917
1
c __
2
d The coin could be biased – probability of
the tails outcome is higher than the heads
outcome for a great many tosses
2
3
1
a __
2
9
e ___
10
1
a ___
36
2
b __
5
9
f ___
10
b 7, __
1
6
c
___
1
10
1
g __
2
1
c __
2
d
d
a Josh
Carlos
1
4
0
__
1
6
5
$1
$1
$1 50c 50c $5 20c 20c
$5
6
6
6
5.5 5.5 10 5.2 5.2
$5
6
6
6
5.5 5.5 10 5.2 5.2
$5
6
6
6
5.5 5.5 10 5.2 5.2
$5
6
6
6
5.5 5.5 10 5.2 5.2
$2
3
3
3
2.5 2.5
2.2 2.2
50c 1.5 1.5 1.5
1
1
5.5 0.7 0.7
50c 1.5 1.5 1.5
1
1
5.5 0.7 0.7
3
b ___
14
1
c __
4
a
b
0.4
1
6 __
8
7 a 40
b i
0.025
c i
1
19
7
35
d ___
56
0.85
ii
ii
0.3
0.625
iii
0.925
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 9
Exercise 9.1
1
2
3
4
5
6
7
a
b
c
d
e
f
g
a
c
n = 24
h
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 T35 = 73
1, 4, 9
T35 = 1225
5, 11, 17
T35 = 209
0, 7, 26
T35 = 42 874
0, 2, 6
T35 = 1190
1, −1, −3
T35 = −67
2
1
They are all prime numbers. They have no
square number factors.
a
d
8n − 6
b 1594
c 30th
T18 = 138 and T19 = 146, so 139 is not a
term.
2
a
3√
3
b
4 √
3
4 √
7
d
15 √
2
e
9√
2
f
− 8 √ 6
h
24 √
6
√
a
27
b
√ 216
√ 20
d
− √ 175
a
b
c
d
e
2n + 5
3 − 8n
6n − 4
(n + 1)2
1.2n + 1.1
a
n
Tn
b
5, 11, 23, 47
1
T50 = 105
T50 = −397
T50 = 296
T50 = 2601
T50 = 61.1
_
_
3
_
4
a __
9
103
____
d
900
_
b
e
_
c
g
3
c
5
6
6
11
16
21
26
31
3, 4, 7, 12, 19
_
a
√ 16 , √
12 , 0.090090009…
74
___
c
99
943
____
999
f
79
___
90
928
_____
4995
Exercise 9.3
4
5, 10, 15
9, 6, 3
2, 1, __
1
2
3
Tn = 3n2 + 1
√
b
45 , √ 90 , π, √
8
3
a
c
b
Tn = n2
Exercise 9.2
2
Tn = 5n + 1
496
11 a
37, 32, 27, 22
1
b
c
10 a First difference: 7, 9, 11, 13
Second difference is 2, which is constant,
so sequence is quadratic.
b 65
c Tn = n2 + 4n + 5
d 2705
d
55th
b
d
7, 10, 13
−20, −16, −12
f
1, 2, 4
_
_
_
− 10 √ 3
_
_
_
_
_
_
_
_
_
_
_
_
_
4
3 , 6 √
5 , 3 √
8 , 3 √
3 , √
12
9 √
5
a
6√
7 + 3 √
5
_
c
_
_
3 √ 6
_
_
√
10 − 2 √
7
_
a
4√
2
_
c 7 √ 2
_
√
a
21
_
c √ 10
_
e
4 √ 2
b
d
e
6
7
g
20
b
un = 8 − 3n
u30 = −82
17, 19, 21 (add 2)
121, 132, 143 (add 11)
8, 4, 2 (divide by 2)
40, 48, 56 (add 8)
−10, −12, −14 (subtract 2)
2, 4, 8 (multiply by 2)
11, 16, 22 (add one more each time than
added to previous term)
21, 26, 31 (add 5)
e
8
9
78
_
_
_
√
3 − √
7
b
_
√
5
_
− √
2
_
√ 22
d
4
f
6 √
35
h
15 √
15
b
d
_
3 √ 6 + 3 √
2
_
_
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
8
_
b
_
√
3
1_
___
√
3
d
1
__
2
e
3
f
6 √
3
g
8
h
4 √
3
a
2√
2
c
_
2
e
f
{2}
{10, 12}
3
a
b
c
d
e
f
{}
{1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 18}
{1, 3, 5, 7, 9, 11, 13, 15}
{2, 4, 8, 10, 14, 16, 17, 19, 20}
{2, 4, 6, 8, 10, 12}
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18}
4
a
b
{−2, −1, 0, 1, 2}
{1, 2, 3, 4, 5}
5
a
b
{x: x is even, x < 10}
{x: x is square numbers, x < 25}
6
a
It is the set of ordered coordinate pairs on
the straight line y = 5x − 2.
There are an infinite number of points on
the line so it is not possible to list them
all.
_
_
2√
3
____
b
5
3
_
_
√
√
−
7
6
____
___
c
d
7
3
_
_
− 4 √ 3
2√
21
e _____
f ______
3
9
_
_
2√
3 + 3
2 √ 3 + 3
h ________
g ________
3
6
10 a Incorrect multiplication when expanding
brackets.
9
b
c
d
The set of even numbers from two to
twelve.
6
{2}
{2, 4, 6, 8}
_
6√
5
a ____
b
Student B would get full marks.
Student C did not multiply by ___
− 1 to fully
−1
simplify the fraction.
_
1+√
5
11 a ______
4
_
_
12 a
√ 15 + 7 √
3
c
_
18 √ 5
_
_
_
b
− 6 − 3 √ 5
b
8 √
3 − 2 √
6
d
12 √
3 − 6
_
_
a
b
_
13 √
54 = 3 √
6 cm
7
_
a
14 2π √
5 cm
b
d
f
15 5 √
3 cm
p
_
16 100 √
3 metres
√
2
200 10 √
____
_
= _____
cm
_
l
√ π
18 40 √
5 cm
_
8
a
b
c
d
e
f
9
a
_
_
19 a
P = ( 2 √
2 + √
5 + √
3 )cm
_
√
15
cm2
b
A = ____
2
_
_
20 a
V = ( √
110 + 3 √
55 ) m3
b
_
_
_
( 2 √
Surface
55 + 2 √
10 + 6 √
5
_area = _
+ 2√
22 + 6 √
11 )m2
n
o
a
d
g
false
true
false
q
u
v
w
x
z
M
b
e
h
true
false
true
c
f
false
true
S
78 − x
x
c
0.57
36 − x
7
b
21
C
9
20
{c, h, i, s, y}
{c, e, h, i, m, p, r, s, t, y}
{a, b, d, f, g, j, k, l, n, o, q, u, v, w, x, z}
{c, h, i, s, y}
Exercise 9.4
1
k
_
____
π
j
t e
m
r
h
i
s
c
y
_
17
g
P
21
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
_
11 a
3√
3
10 a
x=4
b i
iv
ii
v
12
3
23
7
iii
11
Review exercise
1
2
a
b
c
5n − 4
26 − 6n
3n − 1
a
b
c
−4, −2, 0, 2, 4, 8
174
T46
54 = 3 √
6
PR = √
_
_
27
1
__
c Area = (3 √3 )(3 √3 ) = __
1 (9 × 3) = ___
2
2
2
= 13.5 cm2
12 a
B
b
21
4
u51 = 44
d
i
5
a
b
u4 = 105 ml
The volume of medication in the blood
after 24 hours (four six−hour periods).
6
a
b
c
44, 60
Tn = n2 + 5n − 6
12th
7
a
Student A multiplies each term by 3 to get
the next term in the sequence.
Student B adds 4, then 12, then 20 and
has a constant second difference of 8.
A: Tn = 2 × 3n − 1 B: Tn = 4n2 − 8n + 6
146
T10
b
286
____
999
c
17
___
40
59
___
iv
80
13 a
b
c
18
14
16
41
___
80
___
v 21
80
ii
iii
1
__
5
(A ∩ C) ∩ B9
B∪C
A ∪ (B ∩ C)
Sequence
1st
term
2nd
term
3rd
term
A
1
8
27
B
2
16
54
C
−1
10
45
Sequence
4th
term
nth
term
A
64
n3
B
128
2n3
C
116
2n3 − 3n
_
0.213231234…, √
2 , 4π
23
a ___
99
10 n = 4
9
16
21
2, 0, −2
8
C
25
3
b
c
d
22
T120 = 596
T120 = −694
T120 = 359
_
_
b
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED 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
−5
x
4
4
4
4
y
−1
0
1
2
d
g
m = __
1 , c = __
1
2
4
4
__
m = , c = −2
5
m = 0, c = 7
h
m = −3, c = 0
i
j
m = − __
1 , c = ___
14
3
3
m = −1, c = −4
4
k
m = 1, c = −4
3
l
m = −2, c = 5
x
−1
0
1
2
3
y
−2
−2
−2
−2
−2
x
−1
0
1
2
3
y
1.5
e
f
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
−0.5 −1.5 −2.5 −3.5
3
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
g
23
0
student’s graphs of values above
d
m m = −2, c = −20
7
a
y = −x
b
c
d
f
y = 2x + 1
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
1
b 1
e
−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
8
9
a
d
10 a
b
c
f
yes
no
b
m = −1
c
m = −1
e
m=2
f
m=0
h
m = ___
1
16
11 a
b
c
12 a
c
−1
1
2
e 0
f __
2
a: (0, 0), b: (−1.5, 0.5), c: (−2, 3)
d: 13.42 units, e: 3 units, f: 6.71 units
AD: y = x + 3, AB: y = −x + 3,
BC: y = x − 3, DC: y = −x − 3
(−1.5, 1.5)
ABCD is a _
square; side lengths are all
equal to √
18 and gradient of adjacent
sides has a product of −1, so sides are
perpendicular.
y = 3x − 10
_
13 a
2 √ 26 cm
b
y = 2x − 6
b
10.20 cm
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
k (x + 5)(x − 2)
m (x − 3)(x − 4)
o (x + 9)(x − 6)
l
n
p
(x + 4)(x − 8)
(x + 4)(x − 3)
(4x + 1)2
q
s
(x + 6)2
(5x − y)2
r
t
2(3x − 1)2
(2x + 3y)2
6
a
c
e
g
i
5(x + 2)(x + 1)
3x(x − 3)(x − 1)
x(x + 10)(x + 2)
x(x + 7)(x − 2)
−2(x + 4)(x − 6)
b
d
f
h
j
3(x − 4)(x − 2)
5(x − 2)(x − 1)
x2y(x + 2)(x − 1)
3(x − 3)(x − 2)
2(x + 7)(x − 8)
7
a
b
c
d
e
f
g
h
i
j
k
l
m
n
(x + 3)(x − 3)
(4 + x)(4 − x)
(x + 5)(x − 5)
(7 + x)(7 − x)
(3x + 2y)(3x − 2y)
(9 − 2x)(9 + 2x)
(x + 3y)(x − 3y)
(11y + 12x)(11y − 12x)
(4x + 7y)(4x − 7y)
2(x + 3)(x − 3)
2(10 + x)(10 − x)
(x2 + y)(x2 − y)
(5 + x8)(5 − x8)
(xy + 10)(xy − 10)
14 Write the formula with (4, 6) as one of the
points and (x, 0) as the other point and solve
for x. The two points are (12, 0) and (−4, 0).
_
15 2 √
(x 2 + y 2)
Exercise 10.2
1
a
c
e
g
i
x2 + 5x + 6
x2 + 12x + 35
x2 − 4x + 3
y2 − 9y + 14
2x4 − x2 − 3
b
d
f
h
j
x2 − x − 6
x2 + 2x − 35
2x2 + x − 1
6x2 − 7xy + 2y2
x2 + x − 132
k
1 − __
1 x2
l
−3x2
n
x2 + 8x + 16
4
m −12x2 + 14x − 4
2
a
c
e
g
i
k
m
x2 + 8x + 16
x2 + 10x + 25
x2 + 2xy + y2
9x2 − 12x + 4
4x2 + 20x + 25
9 − 6x + x2
36 − 36y + 9y2
b
d
f
h
j
l
x2 − 6x + 9
y2 − 4y + 4
4x2 − 4xy + y2
4x2 − 12xy + 9y2
16x2 − 48x + 36
16 − 16x + 4x2
3
a
c
e
g
i
x2 − 25
49y2 − 9
9x2 − 16
16x4y4 − 4z4
16x2y4 − 25y2
b
d
f
h
j
4x2 − 25
x4 − y4
x6 − 4y4
4x8 − 4y2
64x6y4 − 49z4
a
b
c
d
e
f
g
h
i
j
k
l
x3 + 5x2 + 11x + 15
x3 + 3x2 + x − 5
x3 − 3x2 − 6x + 8
x3 − 14x2 + 64x − 96
x3 + 2x2 − 5x − 6
x3 − 4x2 + 3x
x3 − 5x2 + 8x − 4
x3 − 3x2 + 3x − 1
2x3 − 11x2 + 12x + 9
3x3 − 36x2 + 144x − 192
−2x3 − 6x2 − 6x − 2
8x3 − 27
a
c
e
g
i
(x + 2)(x + 2)
(x + 3)(x + 3)
(x + 3)(x + 5)
(x − 5)(x − 3)
(x − 26)(x − 1)
4
5
24
+ 11x − 6
b
d
f
h
j
(x + 4)(x + 3)
(x + 1)(x + 4)
(x − 1)(x − 8)
(x − 1)(x − 3)
(x − 8)(x + 1)
5x 8w
5x 8w
o ___
+ ___
− ___
z ___
z
( y 2
)( y 2
)
p (5x5 + 1)(5x5 − 1)
q (1 + 9x2y3)(1 − 9x2y3)
_
_
r
(x + √
2 )( x − √
2 )
8
9
a
x=2
b
c
x=1
d
e
x=1
f
a
x = 0 or x = 3
b
c
x = 0 or x = 2
d
e
x = −1 or x = 1
f
g
h
x = −4 or x = −2
i
1 or x = __
x = − __
1
2
2
x = −4 or x = −1
j
x = 5 or x = −1
k
x = 5 or x = −4
l
x = −10 or x = 2
m x = 5 or x = 3
n
x = 20 or x = −3
o
x = 7 or x = 8
p
x = 10
q
x=2
r
x = −7 or x = 2
x = −10 or x = 1
3
x = __
2
x = −12
x = −2 or x = 2
x = 0 or x = − __
2
3
7
7
__
x = − or x = __
2
2
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Review exercise
a
b
c
d
y = __
1 x
2
40
x
−1
0
1
2
3
y
−0.5
0
0.5
1
1.5
3
25
30
2
x
−1
0
1
2
3
y
2.5
3
3.5
4
4.5
x
−1
0
1
2
3
20
15
y
2
2
2
2
2
y − 2x − 4 = 0
x
−1
0
1
2
3
y
2
4
6
8
10
5
x
0
m = −2, c = −1
b
c
m = 1, c = 8
d
e
2 , c = 2
m = − __
3
f
m = −1, c = 0
a
y=x−3
b
c
y = −x − 2
d
e
y = 2x − 3
f
y = − __
2 x + __
1
3
2
4
y = − __
x − 3
5
y = −x + 2
g
y=2
h
x = −4
j
y = −4x + 34
b
y=7
d
x = −10
8
f
y = −3
9
4
A 0, B 1, C 2, D 1, E 4
5
a
y = −2x − 6
c
y = __
4 x + 4
3
e y = −x
m = 1, c = −6
m = 0, c = − __
1
2
t
0
2
4
6
D
0
14
28
42
2
4
6
Time, hours
c y = 7x
d 7
e i
3 hours
ii 1 h 26 min
iii 43 min
f i
28 km
ii 17.5 km
iii 5.25 km
a
a
25
10
y=2
i
y = − __
1 x + 1
2
6
35
y = __
1 x + 3
All four plotted on the same graph.
2
Caroline’s distance at 7 km/h
y
45
Distance, km
1
b
7
a
b
c
i
1
(0.5, 6.5)
4.243
ii
2
(0, 5)
4.472
iii
−1
(1, 3)
2.828
iv
4
− __
3
(−0.5, 3)
5
v
undefined
(−1.5, 0.25)
3.5
1
a(0, __
2)
b
_
√ 89
a
b
c
d
e
f
g
x2 − 16x + 64
2x2 − 2
9x2 − 12xy + 4y2
1 − 12y + 36y2
9x2 − 4
4x2 + 20x + 25
9x4y2 + 6x2y + 1
h
x 2 + xy + __
1 y 2
4
1
__
2
i
x −
4
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1 − 4
j ___
x 2
k
l
m
n
o
p
10 a
b
c
d
e
f
g
26
h
i
j
k
l
10x − 45
−2x3 + 16x2 − 8x
2x3 + 8x2 + 16x
x3 − 6x2 + 12x − 8
3x3 − 6x2 − 3x + 6
−x3 + 12x + 16
a(a + 2)(a − 2)
(x2 + 1)(x + 1)(x − 1)
(x − 2)(x + 1)
(x − 1)(x − 1)
(2x − 3y + 2z)(2x − 3y − 2z)
(x + 12)(x + 4)
x
x
x
2 + __
x 2 − __
(
2 )(
2)
11 a
b
c
d
e
f
g
h
i
(x + 1)(x − 6)
4(x + 3)(x − 4)
2(x − 3)(x − 4)
5(1 + 2x8)(1 − 2x8)
3(x + 3)(x + 2)
x = −5 or x = −1
x = −2 or x = 2
x = 2 or x = 1
x = −1
x = 5 or x = −1
x=2
x = 6 or x = −4
1 or x = 6
x = __
2
x=7
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 11
Exercise 11.1
1
2
9:4
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
3
a
254.48 cm2
b
529 mm2
4
a
x = 2 cm
b
x = 15 m
5
28 000 cm3
a
c
e
55.7 mm
5.29 cm
9.85 cm
b
d
f
14.4 cm
10.9 mm
9.33 cm
6
a
Exercise 11.4
3
a
no
c
no
4
a
√ 32 = 5.66
b
√ 18 = 4.24
c
√ 32 = 5.66
d
√ 180 = 13.4
e
f
√ 45 = 6.71
2
_
b
yes
_
3
_
d
yes
_
20 mm
6
44 cm
7
height = 86.6 mm, area = 4330 mm2
8
13 metres and 15 metres
9
310 cm
b
c
25 : 1
125 : 1
1
x = 2.9 cm
2
x = 3 cm
3
BCA = EFD (corresponding angles in
congruent triangles)
So 2x + 15 = 3x − 2 and x = 17°
So, ABC = DEF = 29°, BCA = EFD = 49° and
CAB = FDE = 102°
4
a
_
5
5:1
Yes
b
76.2 cm
5
Exercise 11.2
1
a
c
e
f
g
h
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
2
angle ABC = angle ADE (corr angle are equal)
angle ACB = angle AED (corr angle are equal)
angle BAC = angle DAE (common)
∴ triangle ABC is similar to triangle ADE
3
25.5 metres
4
Angle ACB = angle ECD (vertically opposite
angles)
Angle ABC = angle EDC (alternate angles)
Angle BAC = angle DEC (alternate angles)
Three equal angles so triangles are congruent.
Length AE = 28 cm
Review exercise
1
a
2
102 = 62 + 82 ∴ triangle ABC is right angled
(converse Pythagoras)
3
a
√ 18 = 4.24
b
√ 20 = 4.47
c
√ 8 = 2.83
d
5
27
a
b
x = 18 cm
x = 27 cm, y = 16 cm
b
1:9
_
_
e
b
130 metres
_
3.5
4
P = 2250 mm
5
a
b
c
x = 3.5 cm
x = 63°, y = 87°
x = 12 cm
6
a
4:1
Exercise 11.3
1
sketch
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7
18 cm2
8
23 750 mm2
9
a
b
10 a
b
c
d
11 a
b
13 a
3 cm
height = 12 cm, area of base = 256 cm2
68 mm
triangle ABC is congruent to triangle HGI
triangle ABC is congruent to triangle
DEF
triangle ACB is congruent to triangle EDF
triangle CAB is congruent to triangle GIH
The lines are perpendicular.
It is a rectangle or a square.
140 mm
560 mm
420 mm
140 mm
b
156 mm
12 5.63 metres
28
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 12
Exercise 12.1
1
2
2
a
b
c
d
e
f
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
a
iii and vi
b
Sensible answer from student, e.g.
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.
a
b
3
a
b
mean = 12.8, median = 15, mode = 17,
range = 19
mode too high, mean not reliable as range
is large
Runner B has the faster mean time; he or
she 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).
4 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
3
255
Exercise 12.3
4
15
1
5
a
c
6
Need to know how many cows there are to
work out mean litres of milk produced per
cow.
b
d
14 metres
10 metres
b
8.6 metres
10 metres
7
a
2.78
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.
1
Exercise 12.2
1 a
b
c
a
2
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.
Score
Frequency
Score ×
frequency (fx)
0
6
0
1
6
6
2
10
20
3
11
33
4
5
20
5
1
5
6
1
6
Total
40
90
2.25
Data set
mean
b
3
a
B
C
3.5
46.14
4.12
3
40
4.5
3 and 5
40
6.5
Stem
Leaf
1
679
2
125599
3
0458
4
19
6
Key: 1 | 6 represents 16 years
4
b
33 years
b
29 years
a
8 years
b
4 years
d
5 years
288
c ____ = 5.3 years
54
29
d
2
A
median
mode
c
3
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5
a
Group A
Leaf
Group B
Leaf
Stem
4
077899
98776
5
123446778999
986666542110
6
2344566678
76544322100
7
12
10
8
Key: (Group A) 6 | 5 represents 65 kgand (Group B) 4 | 0 represents 40 kg
b Range for group A is 81 − 56 = 25; for group B 72 − 40 = 32.
Median for group A is 67 kg, for group B is 58.5 kg.
In general, group A are h eavier than group B. The distribution for group A is more clustered
around the higher values and only five competitors in group A weigh less than 60 kg.
18 competitors in group B have a mass of less than 60 kg and only two have a mass of 70 or more
kilograms while 13 group A competitors weigh 70 or more kilograms.
Exercise 12.4
1
a
Marks (m)
Mid-point
Frequency ( f )
0 , m < 10
5
2
10
10 , m < 20
15
5
75
20 , m < 30
25
13
325
30 , m < 40
35
16
560
40 , m < 50
45
14
630
50 , m < 60
55
13
715
63
2315
Total
b
c
2
36.75 (2 d.p.)
30 , m , 40
Words per
minute (w)
Mid-point
Frequency
31 , w < 36
33.5
40
1340
36 , w < 41
38.5
70
2695
41 , w < 46
43.5
80
3480
46 , w < 51
48.5
90
4365
51 , w < 55
53.5
60
3210
55 , w < 60
58.5
20
1170
360
16 260
Total
a
b
30
Frequency ×
mid-point
f × mid-point
45.17 (2 d.p.)
46 , w , 51
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Exercise 12.5
1
a
b
c
d
Q1 = 47, Q2 = 55.5, Q3 = 63, IQR = 16
Q1 = 8, Q2 = 15, Q3 = 17, IQR = 9
Q1 = 0.7, Q2 = 1.05, Q3 = 1.4, IQR = 0.7
Q1 = 1, Q2 = 2.5, Q3 = 4, IQR = 3
3
C – although B’s mean is bigger it has a larger
range. C’s smaller range suggests that its mean
is probably more representative.
4
a
c
4.82 cm3
5 cm3
5
a
b
36.47 years
40 < a , 50
c
don’t know the actual ages
a
b
c
d
19
5
Q1 = 18, Q3 = 23, IQR = 5
fairly consistent, so data not spread out
Review exercise
1
2
31
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
a
19
b
9 and 10
c
6
5.66
b
5 cm3
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED 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 tonne
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
0.000 046 9 cm3
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
32
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
Nadira
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
4
2
45 min
1 hour
45 min
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2
6 h 25 min
Exercise 13.4
3
20 min
1
4
a
c
5 h 47 min
12 h 12 min
5
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.
6
b
d
10 h 26 min
14 h 30 min
a
b i
ii
iii
2
2 hours, 1 minute and 39 seconds
(or 02:01:39)
i
a
d
Temperature in degrees F against
temperature in degrees C
i 32 °F
ii 50 °F
iii 210 °F
Oven could be marked in Fahrenheit, but
of course she could also have experienced
a power failure or other practical
problem.
Fahrenheit scale as 50 °C is hot, not cold
a
c
9 kg
i
20 kg
b
c
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
g
h
a
b
ii
Aus$38
b
Aus$304
45 kg
ii 35 kg
iii
145 lb
Exercise 13.5
1
a
c
e
US$1 = ¥115.76
€1 = IR84.25
¥1 = £0.01
2.45
2
a
3800
b
50 550
c
9650.10
395
385
3
a
13 891.20
b
64 160
c
185 652
1.1325
1.1315
4
US$294.50
5
$0.70 or 70c
6
C$676
71.5 < h , 72.5
Yes, it is less than 72.5 (although it
would be impossible to measure to that
accuracy).
3
upper bound: 28.0575 m2
lower bound: 26.9875 m2
4
a
a
b
d
f
£1 = NZ$1.97
Can$1 = €0.71
R1 = US$0.07
Review exercise
1
195.5 cm < h , 196.5 cm
93.5 kg < m , 94.5 kg
b maximum speed
greatest distance _____
405
=
= _______________
33.5
shortest time
= 12.09 m/s
a
c
e
g
i
k
2
23 min 45 s
5
3
2 h 19 min 55 s
4
1.615 metres < h , 1.625 metres
5
a
No, that is lower than the lower bound of
45.
b
Yes, that is within the bounds.
b
6
33
3
525 000 rupiah
1 050 000 rupiah
5 250 000 rupiah
c
Exercise 13.3
1
1 cm per 100 000 rupiah
upper bound of area: 15.5563 cm2
lower bound of area: 14.9963 cm2
upper bound of hypotenuse: 8.0910 cm
lower bound of hypotenuse: 7.9514 cm
0.4425 cm2
2700 metres
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
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
6
a
c
3.605 cm to 3.615 cm
2.565 cm to 2.575 cm
lower bound of area: 9.246825 cm2
upper bound of area: 9.308625 cm2
lower: 9.25 cm2, upper: 9.31 cm2
7
a
b
21 600 m3/hr
31.46 m3/m2
8
a
b
c
d
Brigid Kosgei
3 minutes 53 seconds
3 minutes 41 seconds faster
3 minutes 11 seconds per kilometre
b
9
a
conversion graph showing litres against
imperial gallons (conversion factor)
b i
45 litres
ii 112.5 litres
c i
approximately equal to 3.5 gallons
ii approximately equal to 26.5 gallons
d i
48.3 km/gal and 67.62 km/gal
ii
10.62 kilometres per litre and
14.87 kilometres per litre
10 €590.67
11 a
b
c
US$1 = IR76
152 000 rupees
US$163.82
12 £4046.25
34
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 14
Exercise 14.1
b
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
4
5
x = 2, y = 1
x = 5, y = 2
e
x = 7, y = −4
f
g
i
k
m
o
q
x = 3, y = 2
x = 2, y = −1
x = 2, y = 1
x = 3, y = 2
x = 4, y = 2
x = 0.5, y = −0.5
h
j
l
n
p
r
x = __
1 , y = −2
3
x = 3, y = 3
x = 5, y = 1
x = 2, y = 2
x = 3, y = 2.5
x = 5, y = 3
x = −9, y = −2
a
c
x = 15, y = 30
x = 2, y = 1
b
x = 4, y = 2
x = 70 and y = 50
7
Pack of markers is 150 grams, notebook is
80 grams.
8
a
b
9
x + y = 23; 8x − 15y = 92, x = 19 people took
a class
c + d = 15, 50c + 120d = 960
3 desks and 12 chairs
7
−8
4
6
5
−6
−5
6
7
x
x
x
5
x
x < −15
−17
2
13
x,6
f
b
d
12
x > −7
x = 1, y = −2
x = 3, y = 1
Exercise 14.2
a
−16 −15 −14
x
x>4
x
b
3
4
5
x<6
c
3
4
5
6
7
x
x>6
d
4
5
6
7
8
9
10
x
x,8
e
7
8
9
−6
−5
x
x > −6
−7
x
f
x < 18 __
1
3
18
18 1
3
18 2
3
x
x,6
35
8
e
x = −2, y = −2
x = 3, y = 3
x = 3, y = −2
x = −1, y = 6
x = 2, y = 0
11
x<7
−7
a
c
a
c
d
6
1
10
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
x > 11
7
6
5
4
x
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
5
g
x . − __
8
−
h
c
6
8
−
5
8
−
4
8
y
6
x
4
x < −1
i
−3
2
−2
−1
0
x
−6
−2 , x < 1
−4
−2
0
2
4
6x
2
4
6x
4
6x
−2
j
−3 −2 −1 0 1 2
x
y = 2x + 2
1
2
3
4
5
−6
x
d
3
x > 39
4
1 , x , 11 __
1
1 __
2
2
1 but she cannot buy __
x > 3 __
1 cookie, so she
4
4
has to buy at least four.
5
6
−4
2,x,4
y
6
2y + x = 6
4
2
p < 6.2 As she can only buy whole pizzas,
the most she can buy is six to still have enough
money for a cake.
−6
−4
−2
0
−2
Exercise 14.3
1
a
−4
y
2
1
y=x−3
−6
y>x−3
−2 −1 0
−1
1
2
3
4
x
e
y
6
−2
−3
4
−4
−5
b
2
y
5
y = 2x
4
(2, 4)
3
2
0
−3 −2 −1
−1
−4
−4
−2
0
2
−4
1
2
3x
−6
−2
−3
−6
−2
(1, 2)
1
36
2x + y = 4
y < 2x
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f
y
6
4
1
y = –x + 2
2
2
−6
−4
0
−2
2
6x
4
−2
−4
−6
2
a
y > 2x + 1
y , − __
1 x + 2
3
2x
x > 3 and y , ___
− 1
3
c
3
4
b
y . 2x − 1
d
3x
y > ___ + 3
2
y
8
7
6
5
4
This is solution region
3
2
y>1
1
−7 −6 −5 −4 −3 −2 −1 0
−1
1
2
3
4
5
6
7
8
9
10 x
−2
−3
−4
y<−x+5
−5
−6
−7
−8
37
x
1
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
5
y
8
7
x > −4
6
5
4
3
2
x−y<7
1
−8 −7 −6 −5 −4 −3 −2 −1 0
−1
1
2
3
4
5
6
8x
7
−2
−3
−4
−5
−6
−7
2x + y < 4
−8
Exercise 14.4
1
a
x = 4, x = −1
b
x=√
6 − 1, x = − √
6 − 1
c
3
3
− ___
x = __ + ___
11 , x = __
11
2
2
12
12
_
_
√
√
2
+
2
−
10
10
x = _______
, x = _______
3
3
d
2
a
b
c
d
e
f
_
√
2
_
___
√
x = 2, x = −0.5
x = 3, x = 1
x = 2.53, x = −0.53
x = 3, x = −0.5
x = 7.47, x = −1.47
x = −2.27, x = 1.77
Exercise 14.5
1
38
a
b
c
d
e
f
g
h
x = 1.85 or x = −0.180
x = 1.18 or x = − 0.847
x = 0.922 or x = −3.25
x = 1.70 or x = − 4.70
x = 1.45 or x = −3.45
x = 4.44 or x = 0.564
x=1
x = −0.618 or x = 1.62
___
_
_
a
x = −2 − √
7 or x = √
7 − 2
b
x = −4 − √
10 or x = √
10 − 4
c
1 + √ 13
1−√
13
or x = _______
x = _______
d
√
−1 − √ 7
7 − 1
x = ________
or x = ______
_
_
_
3
_
_3
_
2
2
_
_
√
b 2 −
−b +
b 2 − 4ac
4ac − b − √
3 _______________
− _______________
2a _
2a
_
− b + √ b 2 − 4ac + b + √
b 2 − 4ac
= _____________________________
2a
_
2 − 4ac
√
2
b
= ___________
2a
_
√ b 2 − 4ac
= __________
a
Exercise 14.6
1
a
c
e
(2x + 1)(x + 1)
( y + 2)(5y − 1)
(3x + 5)(2x − 1)
b
d
f
(x + 2)(3x − 1)
( y − 1)(5y − 3)
(3x + 2)(4x − 3)
2
a
c
e
g
i
2(x + 2)(2x + 1)
(x − 3) (2x − 3)
(3x + 2) (4x + 5)
(x + 3)(x + 2)
(2y − 7)(2y − 1)
b
d
f
h
4(x + 6)(x − 3)
2(x + 1) (5x − 7)
6(x + 2) (x − 1)
(3x + 8)(x − 4)
3
(3x + 1) cm
4
(3x − 1) cm
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Exercise 14.7
1
2
3
e
8x
b ___
28
a
− ___
x
d
36xy 2
3y
x 4
_____
e 3 3
y z
a
d
g
b
e
h
xy
2x2 + 3x
x−1
c
7x y
− _____
2 2
z
f
5z
f ___3
x
c
f
y
x+3
2x − 1
x − 2xy
x+1
45
30
46
30
47
30
48
30
x
x
4
3x − y > −6
2x + y , 4
−2
6
x
2
y
11
10
y + x < 10
9
8
7
x.0
6
x + 2y < 16
5
3
2
1
3
$5000 at 5% and $10 000 at 8%
3
a x < − __ 4
−
4
5
6
x , 9 7
−2 −1 0
−1
1
2
3
4
−
−
−
4
4
4
4
x , 5 3
d
−6
4
x = −2, y = 5
c
−7
y
x = 2, y = −5
b
−8
6
(2x − 1)
a ________
( x + 1)
x(2x + 1)
b _______________
6(x + 1)( 4x − 5)
x+2
c _____
2
7x − 11
d _____________
( x + 3)( x − 5)
2x + 7
e ________2
(x + 4)
(x 2 + 4)
2
f _________
( x 2 − 4)
2x 3 − 18x 2 − 13x + 117
g _______________________
x 4 − 13x 2 + 36
4x 2 − 3x + 3
h ____________
x − x 3
2
i ___________________
( x − 4)( x − 2)( x + 1)
2
4
47
x < ___
30
−9
5
Review exercise
1
x , −7 8
9
10
4
−
x
7
8
x
9
x
7
x > − __
8
7
6
5
−
−
−
4
4
4
4
−2
1
2
3
4
5
6
7
8
9
10 11 x
y>0
_
_
−5 − √
17
−5 + √
17
or x = _________
= _________
x
2
2
_
_
√
√
14
____
14
____
or x = −1 −
x = − 1 +
2
2
2(x + 5)
3x + 19
a ________2
b ________
x+4
(x + 4)
10 Pencil = $1.20 and ruler = $2.00
x
11 a i (1 + 3)(1 + 7) = 4 × 8 = 32
ii (−4 + 3)(−4 + 7) = −1 × 3 = −3
iii (−8 + 3)(−8 + 7) = −5 × −1 = 5
b when x = −7 answer is zero
c −3 > x > −7
12
x = __
2 , y = __
1
3
4
39
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED 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 i
100 mm
iii 250 mm
b 1 : 200
ii
iv
200 mm
125 mm
4
a
c
b
d
10 metres
2 metres
5
13 mm or 1.3 cm
6
0.32 mm
ii
333° ± 1°
b
036° ± 1°
16 metres
12.4 metres
Exercise 15.2
1
a
b
c
B
i
115° ± 1°
022° ± 1°
2
329° ± 1°
3
a
4
6 km
200 metres
Exercise 15.3
1
Triangle
Hypotenuse
Opposite u
Adjacent u
ABC
AB
BC
AC
DEF
DF
EF
DE
XYZ
XZ
XY
YZ
2
40
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
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
3
a
d
g
0.743
0.416
0.185
a
c
e
5.75 cm
7.27 metres
61.44 cm
5
a
d
32°
39°
b
e
12°
73°
c
f
44°
50°
6
a
d
36.9°
66.0°
b
e
23.2°
68.0°
c
f
45.6°
9.6°
4
b
e
h
c
f
0.978
0.839
0.993
b
d
f
2.605
0.839
26.26 mm
7.56 cm
7.47 metres
Exercise 15.4
1
2
3
√ 2 + 2 √
4 √ 3
3
d _________
e ____
f
2
3
1
b __
1
c
a __
4
3
d
0
√ 3
a
√ 3
3
1 __
__
LHS = __
1 + (
___
) = +
1
_
b
_
e
(2)
2
√ 3
_
c
f
1
_ 2
2
1
a
c
e
cos 88°
sin 121°
−cos 45°
2
a
d
135°
630°
3
a
b
c
d
e
f
g
h
i
j
k
l
x = 108° or 288°
x = 60° or 120°
x = 135° or 225°
x = 120° or 300°
x = 180°
x = 90° or 270°
x = 98° or 278°
x = 40°, 80°, 160°, 200°, 280° or 320°
x = 120° or 240°
x = 60° or 300°
x = 49° or 131° (nearest degree)
x = 60° or 300°
4
a
b
10°, 50°, 130°, 170°, 250° or 290°
90°, 210° or 330°
_
_
√ 2
+ 1
___
2
1
1 __
2
__
1
2
a
Exercise 15.6
4
_
4
= 1 = RHS
b
d
f
b
e
240°
300°
−cos 140°
sin 99°
−cos 150°
c
f
235°
350°
Exercise 15.7
_
√ 3
_
___
_
√
3 __
2 = ___
× 2 = √ 3 ;
b LHS = ___
2
1
__
1
2
__
RHS = √3 , so LHS = RHS.
1
sin Q _____
sin R
sin P _____
_____
=
=
2
a
x = 10.46 cm
b
x = 8.915 cm
3
a
c
e
g
i
k
m
o
x = 9.899 cm
x = 5.477 cm
x = 328.3 mm
x = 14.51 cm
x = 10.95 cm
x = 108.1°
x = 22.19°
x = 7.756 cm
b
d
f
h
j
l
n
p
x = 11.20 cm
x = 106.6°
x = 134.5°
x = 136.1 mm
x = 61.50°
x = 4.396 metres
x = 17.28 cm
x = 23.45°
4
a
b
x = 74.6° or x = 105.4°
x = 47.0° or x = 133.0°
5
a
b
QP = 8.401 metres
QS = 7.928 metres
6
x = 1081 cm
10 1.14 metres
7
AB = DC = 19.8 m, AD = BC = 7.7m
11 4.86 metres
8
139 metres
9
22 cm
Exercise 15.5
1
a
2
6.06 metres
3
16.62 cm
4
9 + 4√
3 metres
5
52.43 km
6
a
7
185 metres
8
a
9
50.3°
15.08 metres
b
30.16 cm
_
1689 metres
64.2°
b
b
975 metres
4.36 metres
p
q
r
10 0° − 20°
41
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Exercise 15.8
1
a
c
5.85 cm2
25.82 cm2
b
d
18.21 cm2
41.93 cm2
2
a
106.5 cm2
b
2226.43 cm2
3
65.0 cm2
3
a
150°
4
a
b
c
d
e
f
g
h
i
j
x = 30° or x = 150°
x = 120° or x = 240°
x = 44.4° or x = 135.6°
x = 60° or x = 240°
x = 210° or x = 330°
x = 30° or x = 60° or x = 210° or x = 240°
x = 30° or x = 210°
x = 135° or x = 225°
x = 45° or x = 225°
x = 40° or x = 80° or x = 160° or x = 200°
or x = 280° or x = 320°
5
a
b
c
x = 190° or x = 310°
x = 56.3° or x = 236.3°
x = 72.2° or x = 117.8° or x = 297.8°
or x = 252.2°
6
approximately equal to 16 metres
Exercise 15.9
1
24.22 cm
2
DB = 37.30 metres tall
3
a
b
4
a
CD = 74.69 metres
Area ACD = 1941.52 m2
In triangle AFB: FB 2 = h2 + w2
(Pythagoras’ theorem)
FB = DB (diagonals of congruent
rectangles)
FD2 = FE 2 + ED2 = w2 + w2 = 2w2
So using the Cosine rule
lookout
(L)
2(w 2 + h 2) − 2w 2
cos u = ________________
2(w 2 + h 2)
h 2
= ________
2
w + h 2
b
50°
u = 50.21°
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
2
(v)
(i)
N
(iv)
160°
25 m
Review exercise
1
b
control tower
(ii)
base of lookout
(B)
7
5m
swimmer
(W)
shark
(S)
RS = 591 metres
cos 60° + sin 30° = __
1 + __
1 = 1
2 2
_
_
√
√
3 √_
3 ___
___
= 3
b cos 30° + sin 60° = +
2
2
_
2
2
3
1 + √___
c (sin 30°)2 + (cos 30°)2 = (
__
( 2)
2)
3
1 + __
= __
= 1
4 4
9 a 2 metres
b Greatest depth: noon and midnight
Empty: 6.00 p.m.
c Between noon and 2.00 p.m. and from
10.00 p.m. onwards (to 2.00 a.m. the next
day).
8
a
10 AB = 9.90 cm, AC = 5.43 cm
11 E = 22.2°, F = 34.8°, DE = 89.2 mm
(iii)
200 km
42
12 31.37 km
13 a
869 mm2
b
585 mm2
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
14 54 metres
15 10.2 cm
43
16 a
c
5.19 metres
5.52 metres
b
d
17 a
b
9.28 km (three significant figures)
268.0° (one decimal place)
18 a
b
A = 150°
B = 190°
A = 134.730 km, B = 153.209 km
62.0°
6.38 metres
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 16
Exercise 16.1
Review exercise
1
1
a
2
a
a
b
c
d
e
2
a
d
e
student’s own line (line should go close to
(160, 4.2) and (175, 5.55));
answers (b) and (c) depend on student’s
best fit line
approximately equal to 4.7 metres
Between 175 cm and 185 cm.
This is not a reliable prediction because
6.07 metres is beyond the range of the
given data.
fairly weak positive
taller athletes can generally jump further
a
distance (metres)
b
c
3
A strong negative correlation. The more
hours of watching TV, the less the test
score.
A strong positive correlation. The longer
the length of arm, the higher the bowling
speed.
Zero correlation. The month of birth has
no effect on mass.
A strong negative correlation. The more
cigarettes smoked daily, the less the length
of life.
A fairly strong positive correlation.
Usually the taller one is, the bigger the
shoe size.
b
600
b
c
d
e
3
a
b
There a strong negative correlation at
first, but this becomes weaker as the cars
get older.
approximately equal to 3 years
It stabilises around the $6000 level.
2−3 years
$5000−$9000 This is not very reliable
as there is limited data from only one
dealership.
There is no correlation. As one variable
increases (x), there is no increase or
decrease in the other variable.
There is no correlation. As one variable
increases ( y), there is no increase or
decrease in the other variable.
d
500
Distance (m)
the number of accidents at different
speeds
b average speed
c answers to (c) depend on student’s best fit
line
i
approximately equal to 35 accidents
ii , 45 km/h
d strong positive
e There are more accidents when vehicles
are travelling at a higher average speed.
400
300
200
100
0
c
e
f
g
44
0
6
8 10 12 14 16
Age (years)
weak positive
12 years old
Not very reliable because correlation is
very weak and beyond the range of the
data
600 metres
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
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
$930.75
$765
b
d
$1083.75
$1179.38
3
a
$62 808
b
$4149.02
4
a
$1203.40
b
$830.72
4
Student’s own graph showing values:
5
$542.75
6
a
$625
b
c
$25
Years
$506.50
Exercise 17.2
300
300
5
1500
1592.74
10
3000
3439.16
A comment such as, the amount of compound
interest increases faster than the simple
interest
2
5 years
5
$862.50
3
2.8%
6
$2678.57
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
b
$160
$343.75
$187.73
$346.08
c
1
a
d
$7.50
$574.55
b
e
Simple interest Compound interest
1
$7.50
$448
c
$210
$225.75
$9000
b
120%
10 $272.73
1 %, year 3: 50%
9 Year 1: 25%, year 2: 33 __
3
10 a $184 000
b $117 760
11 $43.36 (each)
11 a
b
160 mg (50% of original amount)
35.4% of original amount
13 161
12 a
c
$2.04x
$200 000
b
25 __
1 h
2
$1232
12 $204
14 326.84 hPa (using power 8.849 in formula)
$3.1216x
Exercise 17.3
45
1
$64.41
2
a
$179.10
b
$40.04
c
$963.90
3
a
d
$100
$900
b
$200
c
$340
4
$300
5
$500
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED 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
50
iii
b i
ii
iii
(−1, 8)
x = −4 and x = 0
x = −2
(−2, 4)
40
4
80
70
60
30
20
10
0
−6 −5 −4 −3 −2 −1
−10
1
2
3
4
5
6x
a
b
c
d
e
y = 3(x + 1)2 + 0
(0, 3)
x = −1, vertex (−1, 0)
(−1, 0)
axis of symmetry
x = −1 y
−20
y = 3x2 + 6x + 3
−30
(a)
(0, 3)
y-intercept
−40
2
a
6
−13 −22 −33
x = −3 or x = 1
x = −1
90
(c)
5
3 a i
ii
y
100
(b)
4
y
x-intercept −1
turning point, (−1, 0)
minimum
y = x2 − 4x + 3
3
5
a
y
y=
0
1
3
−1
46
1 2 1
x −
2
2
x
−1
b
y = −1 [when x = 2]
c
x=2
x
0
0
1
x
−1
2
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
b
e
y
y =−2x2 + 8
y
5
8
4
3
0
−2
x
2
2
1
y = x2 − x + 1
−2
c
y
y=
f
1 2
x +2
2
−1
0
1
2
3x
y
5
4
3
2
2
x
0
1
0
d
y
−1
6
−2
4
6
2
−4
−2 0
−2
2
4
6
8
x
a
b
c
d
e
5x
y = x2 − x + 1
8 metres
2 seconds
6 metres
just short of 4 seconds
3 seconds
−4
−6
−8
y = −x + 4x + 1
2
−10
−12
47
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Exercise 18.2
1
a
x
2
y = __
x
−5
−4
−0.4
−3
−0.5 −0.67
−2
−1
1
2
3
4
5
−1
−2
2
1
0.67
0.5
0.4
y
2.0
1.5
1.0
y=
0.5
−5 −4 −3 −2 −1 0
−0.5
1
2
3
2
x
4
5x
−1.0
−1.5
b
−2.0
x
−5
−4
−3
−2
−1
1
xy = −1
0.2
0.25
0.33
0.5
1
−1
2
3
4
5
−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
xy = −1
−1.0
c
x
−5
−4
−3
−2
−1
1
2
3
4
5
4
y = __
x + 2
1.2
1
0.67
0
−2
6
4
3.33
3
2.8
y
7
6
5
4
y= x+2
4
3
y=2
2
1
−5 −4 −3 −2 −1 0
−1
48
1
2
3
4
5x
−2
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d
x
−5
9
y = − __
x − 3
−4
−3
−2
−1
1
2
3
0
1.5
6
−12
−7.5
−6
−1.2 −0.75
4
5
−5.25 −4.8
y
6
y =−
9
−3 5
x
4
3
2
1
−8 −7 −6 −5 −4 −3 −2 −1 0
−1
1
−2
2
3
4
5
6
7
8x
y = −3
−3
−4
−5
−6
−7
−8
−9
−10
−11
−12
2
a
y
3
y=1
−4
−2
b
1
y= x+1
2
1
0
−1
y
3
2
1
c
−2
y
4
2
−3 −2 −1 0
−2
1
+1
x
y=1
y =−
2
−4
4x
0
−1
2
4x
2
y= x−1
1
2
3x
−4 y = −3
−6
−8
−10
49
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3
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
b i
ii
iii
y
x
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
approximately equal to 3.4 metres
Exercise 18.3
1
2
a
b
c
a
a&c
y
y = x2 − x − 6
(iii) y = 6
(ii) y = 0
x
1 2 3 4 5
(i) y = –6
y
12
10
y
14
y = x2 − x − 6
13
12
11
10
9
8
7
6
5
4
3
2
1
x
0
−5−4−3−2−1
−2
−3
−4
−5
−6
−7
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
−4 −2−1
−2
−3
−4
−5
−6
−7
−8
3
x = 1, x = 3
x = 0, x = 4
x = 4.2, x = −0.2
x = 1, x = 0
x = 3, x = −2
x = 4, x = −3
8
y = 2x2 + x − 3
6
4 y = 2x + 1
2
−3
−2
−1
0
1
2x
1 2 3 4 5
2
4
b
x = 1 and x = −1.5 (answers within the
range of −1.5 to − 1.6 are acceptable)
d (1.7, 4.4) and (−1.2, −1.4) (1 dp)
e At the points of intersection, the two
equations are equal, so:
2x2 + x − 3 = 2x + 1
If you rearrange this equation, you get
2x2 − x − 4 = 0.
50
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
4
a&b
6
y
12
y = 3x − 5 and x2 + y2 = 5
Substituting x = 2 and y = 1 shows point of
intersection at (2, 1)
Substituting x = 1 and y = −2 shows point of
intersection at (1, −2)
10
y = x2 = 2x + 3
8
Exercise 18.5
1
6
a
y
8
y = x3
6
4
4
2
2
−2 −1 0
−2
−3
−2
−1
0
1
2
3
1
2x
−6
−8
b
4
2x
−4
y = −2x + 5
2
c
4x
1
y
8
6
±1.41
4
Exercise 18.4
2
1
a
b
2
x = 1, y = 0 or x = 3.5, y = 1.25
(1, −4) and (2, −5)
x = 1, y = −4 and x = 2, y = −5
3
−6
c
2
y=x+2
6
4
−2
−1
−0.4
−0.6
1x
x = −0.4, y = 1.6 and x = −2.6, y = −0.6
51
12
8
1
5
y = 2x3
10
−1.6
−2.6
a
b
c
d
y
16
14
1
4
y = −x3
−8
3
−3
−4
y
4
y = x2 + 4x + 3
−4
−2 −1 0
−2
(−0.5, 3.25) and (6, 0)
(−3, −8) and (2, −3)
(−5, 4) and (−2, −2)
(3, 4) and (4, 3)
x = −2 or x = 1; y = −4 or y = 5, points of
intersection are (−2, −4) and (1, 5)
2
−2 −1 0
−2
1
2x
−4
−6
−8
−10
−12
−14
−16
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2
a
x
y
−2.5
−2
−1.5
−1
−36.875 −18 −4.625
b
50
4
−0.5
0
0.5
8.625 10 8.875
y
1
6
5
1.5
a&b i
x
1
2
3
4
5
300
Number of organisms
20
−4 −3 −2 −1 0
−10
6
−20
−30
−40
y = x3 − 5x2 + 10
c i
ii
iii
3
−50
b ii
c i
ii
y
y = 2−x
3
4
5
6
−6
10
46
y
y = 3x
250
200
150
100
50
y = 12x + 1
−1 0
x = −1.3, 1.8 or 4.5
x = 0 or 5
x = −1.6, 2.1 or 4.5
a–d
2.5
2.125 −2 −5.62 −8
40
30
10
2
1
2
3
4
Time (hours)
5
x
6
12 per hour
approximately equal to 3.4 hours
approximately equal to 42
Exercise 18.6
y = 2x + 1
1
y = 2x
a
b
approximately equal to −4
approximately equal to 12
2
y
6
2
y = x2 − 2x − 5
4
1
2
x
−4
−1
−2
0
2
4
6x
−2
y = −2x
−4
−6
a i
4
ii −6
b x = 3.8, x = −1.8 (one decimal place)
4
y
3
y = 4x − 5
y = −2x3 + 2
2
0
52
1
x
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Exercise 18.7
1
a
c
e
g
i
Review exercise
3x2
6
6x
6x2 + 4
4x3 − 6x2
b
d
f
h
j
−4x
−2
−x
15 − 12x
6x2 − 12x
k
6x − 10
l
2
a
x = 1, x = −1
b
9
_____1 + 2
4x 4
x=2
3
a
(−1, 1)
b
y = −8x − 7
4
y
2
1.5
1
1
a
x
−1
−0.5
0
0.5
x3
−1
−0.125
0
0.125
2x
−2
−1
0
1
y = x3 − 2x
1
0.875
0
−0.875
x
1
1.5
2
2.5
x3
1
3.375
8
15.625
2x
2
3
4
5
y = x3 − 2x
−1
0.375
4
10.625
y
11
0.5
0
−1 −0.5
−0.5
0.5
10
1
9
8
−1
a(__
1 , −1)(− __
1 , 1) b
2
2
7
y = 9x − 8
6
Local max. = 1 at x = − __
1
2
1
__
Local min. = −1 at x =
2
5
5
1
c
a
y
4
4
3
2
y = x3 − 3x3
0
−2 −1
−1
3
2
1
(0, 0)
−3 −2 −1 0
−1
1
(3, 0)
2
3
4
5x
−2
−3
−4
b
(2, −4)
y
4
3
y = x(x − 1)(x + 1)
2
(−0.58, 0.38) 1
(−1, 0)
(0, 0) (1, 0)
−3 −2 −1 0
1 2 3 4x
−1 (0.58, −0.38)
−2
−3
−4
53
1
2
3x
−2
b
x
−1
−0.5
0
0.5
x2
1
0.25
0
0.25
1
__
x
−1
−2
−
2
1
y = 2 + x2 − __
x
4
4.25
−
0.25
x
1
1.5
2
2.5
x2
1
2.25
4
6.25
__
1
x
1
0.67
0.5
0.4
1
y = 2 + x2 − __
x
2
3.58
5.5
7.85
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
4
y
10
a
y
y=x+2
9
6
8
4
7
2
6
5
−4
4
−2
4
2
x
−2
3
2
1
−1
2
a
b
0
y=
−x2
c
y = __
4
x
3
1
2
+1
y
4
y =−
x
3x
b
y=
d
xy = −6
2−x
−4
−6
−2
A: y = x + 2
B: y = −2x + 10
8
C: y = __
x or xy = 8.
b i
x = 2, y = 4 and x = −4, y = −2
ii x = 1, y = 8 and x = 4, y = 2
c
x
6
y
8
Substitute x and y coordinates of each
point of intersection into the original
equations:
y = −2x + 10
(4, 2):
2 = −2(4) + 10
2 = −8 + 10 = 2
LHS = RHS
(1, 8):
8 = −2(1) + 10
8 = −2 + 10 = 8
LHS = RHS
8
y = __
x , so xy = 8
y = 3x
6
4
(1, 3)
2
(0, 1)
−2
−1
2
1
d
x
y
y = −x2 + 3
3
2
1
−2 –√3
−1
√3
1
2
x
−1
(4, 2):
5
a&b
y=x
2
1 × 8 = 8, so RHS = LHS
d
4
−5
c
4 × 2 = 8, so RHS = LHS
2
(2, −2)
a
(1, 8):
5
(−2, 2)
y
4
2
y=0
−3
−2
−1
y = 2x = 1
0
1
2x
−2
−4
54
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c
d
6
e
x=1
It is the tangent to the curve at the
point (1,1).
2
a
(0, 1)
Many possibilities, for example (
1, __
1 )
2
1
__
and (
2, )
4
c Decreasing because for larger x-values
the y-values are decreasing and the graph
slopes down to the right.
d y = 2x
b
7
a
y
3
2
y = 2x − 1
1
−4 −3 −2 −1 0
−1
2
y= x−1
−2
−3
−4
b
c
55
x = 1 and x = −1
1.5 units
1
2
3
4x
8
2x + 6
9
−3
10 a
b
y = 1 and gradient = 2
y = −5 and gradient = 4
11 a
local maxima – the maximum height of
the rocket
b (1.4, 12.8), maximum height reached is
12.8 m after 1.4 s
c minimum height, h is 0,
maximum h is 12.8
minimum time, t is 0,
maximum t is 2.8
dy
12 a ___ = −6x 2 + 6x + 12
dx
b (−1, −7) and (2, 20)
c (−1, −7) is a minimum, (2, 20) is a
maximum
13 Differentiate and set equal to 0 to get
t2 − 5t + 4 = 0, so t = 1 and t = 4 are the
turning points.
t = 1 is a local maximum, t = 4 is a local
minimum, so substitute t = 1 into equation to
get max level is 51.83 metres
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 19
Exercise 19.1
1
a
A
B
2
C
D
E
F
G
3
A = 0, B = 3, C = 4, D = 4, E = 5, F = 2,
G = 2, H = 2
2
a
b
2, student’s diagram
2
3
Student’s own diagrams but as an example:
2
Infinite number corresponding to the
number of diameters of the sphere
a
4
b
3
c
1
d
infinite
e
4
f
8
a
Shape A has a limited order of rotational
symmetry (order 4) about a vertical and
horizontal axis (order 2) because it has
vertices, it also has only five planes of
symmetry. Shapes B and C have an infinite
order of rotational symmetry about a
vertical axis and none about a horizontal
axis. This means they also have an infinite
number of vertical planes of symmetry
and no horizontal ones.
Answers will vary, but can only involve
shapes based on circles. For example:
b
H has no lines of
symmetry
b
g
h
Exercise 19.3
a
b
c
d
e
f
56
a
7.75 cm
b
13.9 cm
2
a
x = 25°
b
x = 160°, y = 20°
3
6.5 cm
4
a
b
177.72 cm
49.07 cm
c
25.4 mm
Exercise 19.4
Exercise 19.2
1
1
3
4
Infinite number corresponding to the
number of diameters of the circle face
(+1 parallel to the circular face)
Infinite number correponding to the
number of diameters of the circle face
2
3 (all dimensions different), 5 (two
dimensions equal) or 9 (3 dimensions
equal)
1
144°
2
a
b
c
d
15° (isosceles triangle)
150° (angles in a triangle)
35° (angle MON = 80°, and triangle
MNO in isosceles, so angle NMO =
angle MNO = 50°, so angle MNP = 35°)
105° (angle PON = 210° so angle
PMN = 105° − half the angle at the
centre)
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
3
a
b
c
55° (angles in same segment)
110° (angle at centre twice angle at
circumference)
25° (angle ABD = angle ACD, opposite
angles of intersecting lines AC and BD,
so third angle same)
3
a
c
true
false
4
a
x = (w + z) = 90° (angle in semicircle) so
AB // DC, z = 28° (alt) and and w = 62°
(base angle isosceles triangle, alt), y = 62°
(angles in a triangle)
x = 100° (reflex angle ADB = 200°, angle
at circumference = half angle at centre)
x = 29° (angle ADB is angle in a
semicircle so angle BDC = 90°,
then angles in a triangle)
x = 120° (angle at centre), y = 30°
(base angle isosceles triangle)
angle QPR = 39° (alternate segment
theorem), therefore x = 180 − (39 + 66)
= 75° (angle sum of triangle)
angle OTB = 90° (tangent and radius),
angle CTO = 60° (90° − 30°),
angle OCT = 60° (isosceles triangle),
angle BCT = 120° (angles on straight
line), so x = 30° (angles in triangle)
angle at circumference = 180° − 108°
= 78°, so x = 156° (angle at centre)
angle QLN = 78° (alternate angles),
so x = 78° (alternate segment)
4
angle DAB = 65°, angle ADC = 115°,
angle DCB = 115°, angle CBA = 65°
b
5
35°
c
6
59.5°
7
a
22°
b
116°
c
42°
8
a
56°
b
68°
c
52°
9
a
angle NDF = 40° (alternate segment
theorem)
angle NEF = 40° (alternate segment
theorem)
angle DNF = 90° (angle in a semicircle),
so angle DFN = 180° − (90° + 40°) = 50°
(angle sum of triangle)
b
c
d
e
f
g
Review exercise
1
2
57
a
b
c
d
e
i
i
i
i
i
a
b
c
d
a hexagonal prism
the axis of rotational symmetry
6
7
1
1
4
8
1
ii
ii
ii
ii
ii
none
none
four
eight
none
h
5
a
b
b
d
true
true
x = 7.5 cm, y = 19.5 cm
x = 277.3 mm, y = 250 mm
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 20
Exercise 20.1
Frequency density
1
2
y
1.0
a
b
c
d
166 cm
Q1 = 156.5, Q3 = 176
19.5
12.5%
0.5
Review exercise
0
0
10 20 30 40 50 60 70 80 90 100 x
1
a
Time (t) in minutes
Frequency
125 < t < 140
6
140 , t < 160
16
160 , t < 170
28
170 , t < 195
35
195 , t < 235
8
235 , t < 285
5
Mass (in grams)
a
b
c
3
Eight students
4
P(,5 km) = 0.70
Frequency density
2.5
a
b
2.0
1.5
c
1.0
2
0.5
0
4
Ages of internet cafe users
y
3.0
b
300
Number of students
a
b
c
d
e
58
a
15 20 25 30 35 40 45 50 55 x
Age (years)
240
c
100
Exercise 20.2
1
Slowest is 285 minutes and fastest is 125
minutes.
Approximately 50 runners
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
b
y
Seconds
Frequency
1 < t < 21
8
21 , t < 31
10
31 , t < 41
9
41 , t < 46
3
21 < t , 31
c
Seconds
Frequency
Frequency
density
1 < t , 21
8
0.4
21 , t < 31
10
P60
31 , t < 41
9
0.9
Q2
41 , t < 46
3
0.6
P80
Q3
Q1
x
0 10 20 30 40 50 60 70 80 90 100
Percentage
Median = 57%, Q1 = 49% and Q3 = 65%
IQR = 16
91%
60% of students scored 59 or less;
80% of the students scored 67 or less.
Frequency density
2
1
Histogram to show how long Sandra’s
classmates can hold their breath
y
1.0
0.8
0.6
0.4
0.2
0
0
5
10 15 20 25 30 35 40 45 50 x
Time (seconds)
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
3
a
Mass
0,m,3
Cumulative
frequency
b
3 < m , 3.5 3.5 < m , 4 4 < m , 4.5 4.5 < m , 6
8
57
92
99
100
y
100
90
Cumulative frequency
80
70
60
50
40
30
20
10
0
c i
iii
v
4
a
0
1
2
3
4
Mass of baby (kg)
ii
iv
3.4 kg
0.5 kg
3.8 kg
6x
5
3.7 kg
43
6.5 cm
b
Cumulative frequency of plant heights
Cumulative
frequency
y
30
20
Q3
10
Q2
Q1
0
0
1
2
3
4
5
6
7
8
9
10
11
12 x
Height (cm)
median height = 6.8 cm
c
d
59
IQR = 8.3 − 4.7 = 3.6
13.33%
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
5
Frequency
density
0 , x < 10
3
10 , x < 15
9
15 , x < 25
4.1
25 , x < 30
6.6
30 , x < 40
2.5
Histogram to show the distribution of swimming times
y
10
Frequency density
Swimming time
(x minutes)
5
0
0
5
10
15
20
25
30
35
40 x
Time (minutes)
60
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 21
Exercise 21.1
1
2
10 a
a
c
e
3:4
7:8
1:4
b
d
f
6:1
1:5
31 : 50 : 45
a
c
e
g
i
k
x=9
x = 16
x=4
x = 1.875
x=7
x = 6, y = 30
b
d
f
h
j
l
x=4
x=3
x = 1.14
x = 2.67
x = 13.33
x = 3, y = 24
3
60 cm and 100 cm
4
a
b
c
20 ml oil and 30 ml vinegar
240 ml oil and 360 ml vinegar
300 ml oil and 450 ml vinegar
5
60°, 30° and 90°
6
810 mg
Exercise 21.2
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
6
1 cm : 90 km
7 a
5 cm
b
3.5 cm
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)
61
8
a
b
c
4:1
14.8 cm
120 mm or 12 cm
9
a
b
3.5 : 1 = 7 : 2
2.14 cm
b
1120 cm2
c
4:1
Exercise 21.3
1
25.64 litres (2 d.p.)
2
11.5 kilometres 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
15.658 g/cm3 (three d.p.)
8
60 000 N/m2
Exercise 21.4
1
i
100 km
ii
200 km
a
iii 300 km
b 100 km/h
d 250 km
2
A is 8 mm
B is 16 mm
C is 21 mm
280 cm2
a
b
c
c
e
vehicle stopped
125 km/h
2 hours
190 min = 3 h 10 min
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.
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Exercise 21.6
3 a i
40 km/h
ii 120 km/h
b 3.5 min
c 1200 km/h2
d 6 km
a
i
y ∝ x 2
ii
y = kx2
b
i
y ∝ ___
12
x
ii
k
y = ___2
x
c
i
m ∝ T
ii
m = kT
d
i
ii
e
i
1
A ∝ ___
M
1
y ∝ ___
x 3
k
A = ___
M
k
y = ___3
x
2
a
k=7
3
m
Ratio of m to T is constant, __ = 0.4587,
T
so m varies directly with T
4
4
a
3
5
4
a = 2, b = 8, c = __
3
a y=2
1
4
a
c
0−30 s, 0.83 m/s2
90 km/h
5
a
Speed changes from 0 m/s to 3.5 m/s over
a period of 10 seconds.
17.5 metres
0.35 m/s2
b
c
a
after 70 s, 0.5 m/s2
2 km
y
5
Velocity (m/s)
6
b
d
2
a
b
c
b
m = 4.5
b
x = 0.5
b
y = 1250
7
a = 17 __
9
x=2
0
7
a
c
y=
x=9
8
a
b
c
y√ x = 80
y=8
x = 15.49
9
a
b = 40
b
10 a
y = 2.5
b
11 a
xy = 18 for all cases, so relationship is
inversely proportional
18
xy = 18 or y = ___
x
y = 36
0
10
20
30
40
0.33 m/s
approximately equal to 17 metres
Yes, __
A = ____
1
B 150
8
No, ___ is not = __
1
2
15
10
A = ___
Yes, __
B
1
$175
b
50 x
b
c
2x2
__
2
a
3
$12.50
4
60 metres
5
a
c
75 km
3 h 20 min
b
375 km
1
a
b
6
a
15 litres
b
540 km
2
1 : 50
7
a
inversely proportional
3
x = 6 or x = −6
b
2 __
1 days
2
1
__
ii day
2
12 days
4
a
b
i 85 km
i 0.35 h
5
a
b
c
d
e
150 km
after two hours; stopped for one hour
100 km/h
100 km/h
500 km
$250
8
a
9
5 h 30 min
12 8192
Review exercise
i
10 1200 km/h
62
F = 40
a = 84
6
Exercise 21.5
1
b
1
Time (s)
b
c
ii
b
5 days
90 mm, 150 mm and 120 mm
Yes, (150)2 = (90)2 + (120)2
ii 382.5 km
ii 4.7 h
iii
iii
21.25 km
1.18 h
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
6
a
c
7
4.5 min
8
187.5 g
20 seconds
200 metres
b
d
2 m/s2
100 metres
k
k
y ∝ ___
13 , so y = ___
3 and 1728 = ___
3 , so k = 1728
x
x
1
1728
Substitute x = 4 into y = _____
3
to give
x
1728 1728
= 27
y = _____
3 = _____
64
4
k
10 a
P = __
v or PV = k
b P = 80
11 a F = 0.02125 v2
b 200 m/s
9
63
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 22
_
Exercise 22.1
3
b
y − 2
a
3
V
a
I = __
R
b
l = g(___
T )
2π
b
20 amps
2
1
a
c
x−4
A = x2 − 4x
2
a
S = 5x + 2
3
a
c
x+2
S = 3x − 1
4
80 silver cars, 8 red cars
5
father = 35, mother = 33 and Nadira = 10
6
X cost 90c, Y cost $1.80 and Z cost 30c
Exercise 22.3
7
9 years
1
8
97 tickets
a
c
11
5
9
x + y = 112 and x − y = 22
2
a
b
i 17
ii 53
iii 113
f(2) + f(4) = 17 + 53 = 70 ≠ f(6) which
is = 113
P = 4x − 8
5x + 2
b
M = ______
3
b x−3
4
10 x + (x − 5) = 30, so 2x = 35
Length = 17.5 metres and width = 12.5 metres
11 x = 13 and y = 2
12 6 and 8
13 −9, −8 or 8, 9
√
__
5
a
r = __
A
π (note, radius cannot be negative)
b r = 5.64 mm
6
9
a
F = __ C + 32
5
c 323 K
x = 67 and y = 45
b
d
b
80.6 °F
−1
2m + 5
c i
3a2 + 5
ii 3b2 + 5
iii 3(a + b)2 + 5
d a = ±3
3
a
h(1) = ±2
b
h(−4) = ±3
4
a
4(x − 5)
b
4x − 5
15 0.98 metres
5
18
16 b2 + 25b = 2000. Using the quadratic formula,
b = 339 or −589, but as this is a length,
−589 is an impossible answer, so the width is
339 mm.
6
a
f−1(x) = x − 4
b
f−1(x) = x + 9
x
f−1(x) = __
5
f−1(x) = −2x
14 17 cm (x = 8, x cannot be 0 as it’s the length of
a side)
1
2ab − P
a
h = ________
2a
2y
c
h = _____
1−y
2
a
a
b = ______
1 − 2a
3p
c
q = _____
p−1
6n + 1
e
m = ______
5
c
d
Exercise 22.2
64
√
x = ______
S − πr 2
b
h = _______
πr
E − __
1 mv 2
2
dh = __________
mg
2m
bn = ______
1−m
d
a = 2x − 3y
x
a __ − 3
2
d 2x + 3
e
8
a
b
9
a
3√
x +1 +1
7
b
x
_
x−3
____
2
2x + 3
c
2(x + 3)
f
2(x + 3)
x+1
_____
x−1
c
9
__
7
_
b
1 ± √ 5
x = ______
2
a 2
fy = _____
a−b
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
c
5 a (2x + 1)(x − 3) = 60
2x2 − 6x + x − 3 = 60
g−1(x) = x2−1
y
2x2 − 5x − 63 = 0
b Sides are 4 metres and 15 metres.
c y = x2 −1
d y = x + 1 for x > −1
1
0
−1
x
1
−1
d
Note that the curves are symmetrical
about y = x when
x > 0 for y = x2 − 1
_____
and x > − 1 for y = √ x + 1 .
Solve simultaneously: 3a + 2 = 2b − a and
2b − a = b + 3. Side length are 8 cm (a = 2
and b = 5), so perimeter = 24 cm.
7
4.00 p.m.
8
80 km
9
a
b = ±√
a 2 + 2ac
_
9a − 26
b
b = ______
8
a 2 − 4
c
b = _____
17
10 a 2.07
b 2.43
11 15
12 96 km
10 a
b
c
d
e
f
x = −2 and x = −6
x . 1 and x , −1
−3 < x < 3
−2 , x , 3
−4 , x , 1.5
all values can be included
13 a
11 a
a = 35, b = 80, c = 75 and d = 160
5
x
f −1(x) = __
8
5x + 3
14 f−1(x) = _____
2
x−4
15 a f−1(x) = ____
3
c a=6
e 37
b
Review exercise
65
6
1
Four years
2
Sindi puts in $40, Jonas $20 and Mo $70
3
44 children
4
kiwi fruit = 40c and plum = 15c
b
c
16 a
b
Domain: {x: x is a real number}
Range: { y: y is a real number}
Domain: {x: x . 0 and x is a real number}
Range: { y , 4 and y is a real number}
Domain: {x: x is a real number}
Range: { y: y is a real number and y ≠ 0}
5
i __
3
x = −3
ii −5
b
3
d
9x + 16
iii
1
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 23
Exercise 23.1
1
5
A'
B
10
B'
8
D
C
C'
C''
A''
10
A'
6
I''
6
c ii
2
H
c i
4
6K' 8
I
x
K
J
A
y
B
b i
C
–8
S'
–6
S''
X
P
6
4
Q' Q
2
P'' R'
–4 –2 0
–2
b ii
Q''
–4
R''
–6
–8
66
7
J'
8
A
P'
A''
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
F −8
3
x
10
A'
−6
G
K''
I'
E −4
D
4
J''
C'4 H''
2
B
C F'
G'
b
−10 −8 −6 −4 −2 0
D'
E' −2
8
−10
8
B'
B
6
−8
y
9
a
A
D''
4
2
−6
B''
2
2
−10 −8 −6 −4 −2 0
−2
C
−4
(b)
B''
4
C''
D'
D D''
A
6
(a)
A
y
ii
S
R
2
4
6
A'
a
A
8
x
A''
X
B'
C'
A: y = 5
B: x = 0
C: y = −1.5
D: x = −6
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
b
Exercise 23.2
i
1
B'
a
y
A'
B
X
B'
ii
B
B
x
1 2 3 4 5
–2
C'' –3
B''
–4
–5
–6
A'' –7
X
i
C'
b
C
2
rotation 180° about (0, 0) or enlargement
scale factor −1, using (0, 0) as centre
a
y
10
X
8
ii
C
6
C
C''
A
2
−4
i
b
3
D'
B
4
X
d
C
–5 –4 –3 –2 –1 0
B''
c
A
7
6
5
4
3
C'
2
1
D
a
x
0
−2
2
4
6
8
enlargement scale factor 2, using (8, −1)
as centre
y
10
X
8
F'
6
B
A
4
ii
2
X
D'' D
0
b
67
D
0
C
2
x
4
6
8
10
rotation 180° about (4, 5)
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
4
a
b
2
Scale factor 3, centre of enlargement
(−4, 1).
Scale factor − __
1 , centre of enlargement
2
(−1, 1).
5
B
A
1 , centre of enlargement
Scale factor − __
2
(1, 2).
c
a
b
D
y
6
C
4
C'
c
F
2
−8
−6
−4
A'
−2 0
A' −2
−4
2
4
B
6
10 12 x
B'
8
E
C
d
6
G
y
5
4
H
3
S'
R'
2
P
3
Q
1
Q'
−4
P'
−3
−2
−1 0
−1
1
−2
2
3
4
5
R
S
−3
⟶
i AB = (
5 )
0
⟶
iii AE = (
0 )
−6
⟶
1 )
v DB = (
6
⟶
vii CD = (
−5
)
−6
b they are equal
a
4
B (2 )
3
D (−3
)
−3
E (9 )
3
C ( 4 )
−3
a
(−8
)
16
b
(2 )
6
c
( 0)
12
d
(−1
)
7
e
(−2
)
1
f
(−1
)
4
g
(−4
)
18
h
(−8
)
22
i
( 0 )
−20
j
( 10 )
−16
Exercise 23.3
1
6 x
A (8 )
1
⟶
BC = (
4 )
0
⟶
iv BD = (
−1
)
−6
⟶
vi EC = (
9 )
6
⟶
viii BE = (
−5
)
−6
ii
c
(9 )
0
d
(−5
)
−6
e Yes
68
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
5
6
a
d
g
−a
b 2b
2c
e 2b
b
h −c
b
__
j + 3c
2
a–e student’s own diagrams
7
a
c
6.40 cm
15 cm
b
d
7.28 cm
17.69 cm
8
a
c
5.10
8.06
b
d
5
9.22
9
a
c
f
i
−a + c
2c
−7a + 7c
A(−6, 2), B (−2, −4), C (5, 1)
⟶
b AB= (
4 )
−6
⟶
BC= (
7 )
5
⟶
CA= (
−11
1 )
⟶
10 XZ = x + y
⟶
ZX= −x − y
⟶ __
MZ
= x + y
2
11 a i
x = (2 )
7
−3
ii y = ( )
−3
iii z = ( 10)
−4
b i
ii
iii
7.28
4.24
21.5
⟶
12 a i XY = b − a
⟶ 1
ii AD = __
(a + b)
2
⟶
iii BC = 2(b − a)
⟶
⟶
b XY = b − a and, BC
= 2(b − a) so they
are both multiples of (b − a), and hence
⟶
⟶
parallel, and XY is half BC
⟶
13 a
MN = 4a + 6b
⟶
b
MP = (2a + 3b) × 7 = 14a + 21b
⟶
3
3 ⟶ __
3
14 a
AD = − __
a + __
b; OD
= 1 a + __
b
2
4
2
4
⟶
b
OB = 2a + 3b
⟶ 1
⟶
⟶
OD = __
( 2a + 3b)= __
1 OB , so OD
is
4
4
⟶
parallel to OB
, point O is common and
the points must be on a line.
Review exercise
1 a i
ii
iii
reflect in the line x = −1
rotate 90° clockwise about the origin
reflect in the line y = −1
b
irotate 90° anti-clockwise about (0, 0)
then translate (
−2
)
−1
ii reflect in the line y = −1 then
translate (−8
)
0
iii rotate 180° about origin then
translate (6 )
0
iv reflect in the line x = 0 ( y−axis) then
translate ( 0 )
−2
2
y
5
4 D'
G'
3
2
1 E'
F'
−5 −4 −3 −2 −10 1 2 3 4 5
F
−2 G
a&b
−3
−4 D
−5
−6
−7
G''
F''
E
D''
3
10
E''
y
d
B''' 8
B' A'''
a
4
A'
D'''
C'
−10 −8
B
−6 D'−4
B9(−6, 6)
B09(−1, 8)
C'''
D''''
−2 D''
−2
C''''
C
A''
2
−4
a
c
B'''
A'''' 6
c
x
x
2
b
4
6
8
10
B''
C''
b
d
B0(6, −2)
B00(3, 9)
15 28.3 (1 d.p.)
69
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
4
iii
y
5
F'
4
G'
E'
a
b
a
b
a−b
3
D'
2
D
1
−4
−3
−2
G
−1 0
−1
1
2
3
4
5
x
6
iv
E
−2
−3
F
−4
5
a
b
c
(11, 5) (8, 4) (9, 8)
(3, −2) (2, 1) (6, 0)
(−3, −6) (−2, −3) (−6, −4)
( 0 )
−8
iv
(12
)
0
( 6)
12
iii
( 1)
10
6
a
b
ii
i
i
2a + 3b
⟶
i ED = y
⟶
ii DE = −y
⟶
iii FB = x + y
⟶
iv EF = x − y
⟶
v FD = 2y − x
7
a
2a
8
b
c
b+c
70
b
4. 47
a
c
26.4
14.9
b
d
3.0
11.1
⟶
i
= −a + b
AF
⟶
ii
OE = −a + b
⟶
⟶ ⟶ ⟶
+ OD
= −2a, BC
= −a,
b
AD = AO
⟶
⟶
so AD = 2 BC
⟶
10 a
OQ = 2a − 6b
⟶
b
AB = 2b + a − 3b = a − b
⟶
BR = a − 3b + 2a = 3a − 3b
⟶
⟶
⟶
⟶
So, BR = 3 AB , so BR
and AB
are
parallel and they have a common point B,
so ABR is a straight line and the points
are collinear.
9
ii
a
a
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Chapter 24
Exercise 24.1
1
2
Card
G
B
1
2
2
3
4
1
2
3
0.4
0.6
7
11
1
6
1
b __
4
71
1
2
T
H
0.054
Green
4
11
Yellow
0.7
0.35
C
0.245
8
11
Green
D
0.455
3
11
Yellow
B
0.65
4
a
First fruit
Second fruit
4
15
Bus
4
15
0.9
Walk
1
3
0.1
Bus
5
16
7
16
1
2
H
1
2
1
2
T
H
1
2
1
2
T
H
1
2
T
1
c ___
12
Plum
Mango
P
7
15
1
3
Banana
1
5
1
2
1
2
1
2
H
1
2
T
T
H
M
B
P
6
15
4
15
1
4
Black
T
D
0.95
Yellow
1
2
1
2
H
0.18
Not Rain
1
3
T
A
Walk
Blue
1
2
1
2
H
0.3
Rain
1
2
T
0.246
0.05
a
1
2
1
2
C
Exercise 24.2
1
T
H
0.82
Yellow
4
H
1
2
1
1
1
b __
c __
d __
2
2
8
e 0, not possible on three coin tosses
Green
1
3
1
2
T
T
a&b
2
3
1
2
1
2
G
H
A
B
C
D
E
F
1
H
H
H
T
H
T
H
T
H
T
Y
3
1
2
Coin
R
2
a
M
B
P
7
15
M
B
1
b ___
12
5
d ___
12
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CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Exercise 24.3
1
2
Even
3
M3
6
12
2, 4, 8, 10
3, 9
4
1, 5, 7, 11
1
a __
2
2
2
b __
3
a
c
__
1
d
6
W
__
1
3
1
3
a __
7
6
G
5
5
5
2
2
b __
c __
d __
1
a __
5
3
9
9
1
2
1
1
d ___
b ___
c ___
a ___
45
30
15
15
8
7
3
e ___
f ___
g ___
15
15
10
28
5
40
40
a ___
b ____
c ____
d ____
17
153
153
153
e The four situations represent all the
possible outcomes, so they must add up to
one.
b
0.1
Fail
0.8
0.9
Don’t fail
0.2
0.15 Fail
A
B
3
a
i __
4 5
1
ii __
4
iii
Science Museum
5
3
11
b
3
__
11
___
20
London Eye
0.85 Don’t fail
3
P(B given it failed test) = ___
11
5
__
7
8
8 a
Train
Bus
130
20
10
10%
45%
30
20
30
b
30%
Madame Tussauds
130
c
0
15%
d
160
30 __
= 1 However, this is a small
Yes, ____
240 8
sample for a busy city like London and
the answer can only apply to this group
and not to tourists as a whole.
9
2
b ___
11
c
a
0.2
b
0.56
b
e
10 a
2
__
5
__
2
7
0.35
Exercise 24.4
1
72
66
a ____ = 0.413
160
19
b ___ = 0.288
66
51
___
c = 0.543
94
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK
Review exercise
1
a&b
1
6
1
6
1
6
1
6
1
2
3
4
1
6
1
6
5
2
1
2
H
1
2
T
1
2
H
1
2
T
1
2
H
1
2
T
1
2
H
1
2
T
1
2
H
1
2
6
1
c __
8
3
T
1
2
H
1
2
T
1
2
1
2
1
2
H
4
T
H
5
1
2
T
1
2
1
2
1
2
H
1
2
T
H
1
2
T
5
7
10c
5
5 =1
c
9
___
13
F
1
3
6
0
4
M
b
i
___
2
15
___
iii 2
15
1
6 a __
6
10c
5
6
P
1
T
H
a&b
2
7
a
11
1
d ___
12
5c
b
T
H
1
2
1
2
1
2
1
6
4
___
13
1
b ___
12
1
a ___
52
5
a __
8
4
8
___
15
3
__
iv
8
b __
1
4
ii
__
1
7
3
5c
10c
5
1
c __
d ___
7
21
e 1 (there are no 5c coins left)
73
Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023
