Cambridge International Catalogue 2024 - Final - Flipbook - Page 49
CAMBRIDGE IGCSETM
Workbook Fifth Edition
PRINT
ENDORSED
Author
An ideal course companion to use in class or at home ⸀
• Additional exercises that perfectly supplement the Student’s Book ⸀
• Keep track of students’ work with ready-to-go, write-in exercises ⸀
• Ensure students know what to expect for their assessment with a wide
breadth of practice questions ⸀
£9 ⸀50
Core and Extended 9781398373921
Teacher’s Guide with Boost Subscription
PRINT
DIGITAL
ENDORSED
Guide includes:
• Schemes of Work
• Numerical answers
• Teacher’s notes
• Worked solutions for assessment
exercises
• CPD videos
• Problem-solving videos
• ESL support
• Past paper questions
• Assign Knowledge Tests and access
results reports
• Mark schemes
£145 excl ⸀ VAT
9781398373624
Multiples
1 NUMBER AND LANGUAGE
Exercise 1.4
Prime factors
The factors of 12 are 1, 2, 3, 4, 6 and 12.
Of these, 2 and 3 are prime numbers, so 2 and 3 are the prime factors
of 12.
Exercise 1.3
1 List the prime factors of the following numbers:
a 15
b 18
c 24
d 16
f 13
g 33
h 35
i 70
Highest common factor
The factors of 12 can be listed as 1, 2, 3, 4, 6, 12.
e 20
j 56
The factors of 18 can be listed as 1, 2, 3, 6, 9, 18.
As can be seen, the factors 1, 2, 3 and 6 are common to both numbers.
They are known as common factors. As 6 is the largest of the common
factors, it is called the highest common factor (HCF) of 12 and 18.
An easy way to find prime factors is to divide by the prime numbers in
order, smallest first.
a
Worked examples
The prime factors of 12 are 2 × 2 × 3.
Find the prime factors of 18 and express it as a product of prime
numbers:
So the highest common factor can be seen by inspection to be 2 × 3, i.e. 6.
The prime factors of 18 are 2 × 3 × 3.
18
2
Multiples
9
3
3
Multiples of 2 are 2, 4, 6, 8, 10, etc.
3
1
Multiples of 3 are 3, 6, 9, 12, 15 etc.
The numbers 6, 12, 18, 24 etc., are common multiples as these appear
in both lists.
18 = 2 × 3 × 3 or 2 × 32
b
Find the prime factors of 24 and express it as a product of prime numbers:
The lowest common multiple (LCM) of 2 and 3 is 6, since 6 is the
smallest number divisible by 2 and 3.
24
Look inside
2
12
2
6
2
3
3
1
The LCM of 3 and 5 is 15.
The LCM of 6 and 10 is 30.
Exercise 1.5
24 = 2 × 2 × 2 × 3 or 2 3 × 3
c
Find the prime factors of 75 and express it as a product of prime numbers:
75
3
25
1 NUMBER AND LANGUAGE
View sample material
from our Student’s
Books
1 Find the prime factors of the following numbers and express them as
a product of prime numbers:
a 12
b 32
c 36
d 40
e 44
f 56
g 45
h 39
i 231
j 63
5
5
5
1
Exercise
75 =1.8
3 ×(cont)
5 × 5 or 3 ×252 Check your answers to question 1 above by using the
1 Find the HCF of the following numbers:
a 8, 12
b 10, 25
d 15, 21, 27
e 36, 63, 108
g 32, 56, 72
h 39, 52
j 60, 144
2 Find the LCM of the following:
a 6, 14
b 4, 15
d 3, 9, 10
e 6, 8, 20
g 4, 5, 10
h 3, 7, 11
j 25, 40, 100
Exercise 1.10
The cube shown has sides of 2 units and occupies 8 cubic units of space.
(That is, 2 × 2 × 2.)
So the cube root of 8 is 2.
6
This can be written as 3 8 = 2.
3
3
12, 18, 24
22, 110
34, 51, 68
c
f
i
2, 7, 10
3, 5, 7
6, 10, 16
Directed numbers
You will find a button on your calculator to help you to calculate with
roots too. On most calculators, it will look like x y .
key on a
calculator.
Cube roots
c
f
i
is read as ‘the cube root of … ’.
1 Work out the following:
a 64
b 35 + 2 4
d 0.16 ÷ 0.014
e 4 2401
g
( 5 243 )
j
6
3
1
× 27
64
h
( 9 36 )
k
4
c
f
9
(34)2
8
256
i
27 × 1
l
(10 59049 )2
4
7
54
Directed numbers
64 is 4, since 4 × 4 × 4 = 64.
Note that 3 64 is not −4
since −4 × −4 × −4 = −64
20
15
10
5
0
5
10
15
20
but 3 −64 is −4.
Exercise 1.9
1
Find the following cube roots:
a 38
b 3 125
Worked example
3
27
d
3
0.001
e
3
0.027
f
3
216
g
3
1000
h
3
1000 000
i
3
−8
j
3
−27
k
3
−1000
l
3
−1
c
Further powers and roots
We have seen that the square of a number is the same as raising that
number to the power of 2, for example, the square of 5 is written as 52
and means 5 × 5. Similarly, the cube of a number is the same as raising
that number to the power of 3, for example, the cube of 5 is written as
53 and means 5 × 5 × 5.
Numbers can be raised by other powers too. Therefore, 5 raised to the
power of 6 can be written as 56 and means 5 × 5 × 5 × 5 × 5 × 5.
You will find a button on your calculator to help you to do this. On
most calculators, it will look like yx.
We have also seen that the square root of a number can be written
symbol. Therefore, the square root of 16 is ± 16 and is ±4,
using the
because both 4 × 4 = 16 and −4 × −4 = 16.
The cube root of a number can be written using the 3 symbol.
Therefore, the cube root of 27 is written as 3 27 and is 3, because
3 × 3 × 3 = 27.
Other roots of numbers can also be found. The fourth root of a number
can be written using the symbol 4 . Therefore the fourth root of 625
can be expressed as ± 4 625 and is ±5, because both 5 × 5 × 5 × 5 = 625
and (−5) × (−5) × (−5) × (−5) = 625.
10
The diagram above shows the scale of a thermometer. The temperature at
04 00 was −3 °C. By 09 00, the temperature had risen by 8 °C. What was the
temperature at 09 00?
(−3)° + (8)° = (5)°
Exercise 1.11
1 The highest temperature ever recorded was in Libya. It was 58 °C.
The lowest temperature ever recorded was −88 °C in Antarctica.
What is the temperature difference?
2 My bank account shows a credit balance of $105. Describe my
balance as a positive or negative number after each of these
transactions is made in sequence:
a rent $140
b car insurance $283
c 1 week’s salary $230
d food bill $72
e credit transfer $250
3 The roof of an apartment block is 130 m above ground level. The car
park beneath the apartment is 35 m below ground level. How high is
the roof above the floor of the car park?
4 A submarine is at a depth of 165 m. If the ocean floor is 860 m from
the surface, how far is the submarine from the ocean floor?
Student assessment 1
1 State whether the following numbers are rational or irrational:
.
a 1.5. .
b
c 0. 7
7
d 0. 7 3
e
f π
121
2 Show, by expressing them as fractions or whole numbers, that the
following numbers are rational:
a 0.625
b 3 27
c 0.44
11
Endorsed for the Cambridge Pathway to support the syllabus for examination
from 2025. The Study and Revision Guides have not been through the Cambridge
International Education endorsement process.
Return to the contents page
ANY QUESTIONS?
Talk to your local consultant:
hoddereducation ⸀com/here-to-help
47
