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preface
Chapter 1 Prime Numbers, Factors and Multiples
Secondary 1 Mathematics Tutorial 1A and 1B are designed to prepare Secondary 1 students
in their understanding and application of mathematical concepts, skills and processes.
What’s covered in this book?
Written in accordance with the latest syllabus, each chapter includes Objectives, Key Concepts
and Formulae and Worked Examples to supplement and complement the lessons taught in
school. Practice questions are structured as core, consolidation and challenging to ensure
steady improvement and quick mastery of concepts. Books 1A and 1B cover all the topics for
the entire school year.
Additional feature
Teacher’s Desk that provides important notes, tips, examples and common student errors.
Important concepts are highlighted to enhance understanding and retention.
Tests and Assessments
There are 4 assessment papers: Mid Year Examination Paper 1 and 2 (found in Book 1A) and
End of Year Examination Paper 1 and 2 (found in Book 1B).
Answer Key
Fully worked solutions are provided for students to understand better how each problem is
solved. These also serve as a tool for self study and assessment.
It is hoped that this book will help students to gain confidence in the subject and be better
equipped to face the examinations.
The Editorial Team
Contents
Chapter
Objectives
Page
1
Prime Numbers, Factors and Multiples
Recognise prime numbers
Perform prime factorisation on a composite number
Find the HCF and LCM of a group of numbers using prime
factorisation
Find the square root and cube root of a number using prime
factorisation
1
2
Real Numbers and Approximation
Identify rational and irrational numbers
Perform the four operations on real numbers
Approximate using decimal places and significant figures
Estimate the results of computations
23
3
Introduction to Algebra
Evaluate algebraic expressions and formulae
Express real-world problems in algebraic terms
44
4
Algebraic Manipulation
Evaluate and simplify algebraic expressions
Factorise algebraic expressions by extracting common factors
Express real world problems in algebraic terms
61
5
Solving Linear Equations and Inequalities
Solve linear equations
Formulate linear equations to solve word problems
84
6
Number Patterns
Recognise number patterns and find the terms of a sequence
Find the general term of a sequence
Solve problems involving number patterns and sequences
112
7
Ratio, Rate and Speed
Find ratios involving two or more quantities
Calculate average speed
Convert speed from one unit to another
Solve problems involving ratio, rate and speed
130
Mid Year Examination Paper 1
156
Mid Year Examination Paper 2
162
Fully worked solutions
 Complete the course with Secondary 1 Mathematics Tutorial 1B (Chapters 8 – 14)
S1 – S38
Chapter 1
Prime Numbers, Factors and Multiples
Objectives




Recognise prime numbers
Perform prime factorisation on a composite number
Find the HCF and LCM of a group of numbers using prime factorisation
Find the square root and cube root of a number using prime factorisation
Key Concepts and Formulae
1
Whole numbers
E.g. 0, 1, 2, 3, 4, 5, ...
Neither Prime nor Composite
(0 and 1 only)
Prime Numbers
has only 2 factors, 1 and itself
E.g. 2, 3, 5, 7, 11, ...
Composite Prime Numbers
has more than 2 factors
E.g. 4, 6, 8, 9, 10
2
3 × 3 × 3 × 5 × 5 when expressed in index notation is 33 × 52.
3
Prime Factorisation is the process of expressing a composite number as a product of its
prime factors.
E.g.504 = 23 × 32 × 7
4
Square and Square roots: Square of 6 = 62 = 36 ⇒ ​√36 ​ = 6
A perfect square is a number whose square root is a whole number.
E.g. 1, 4, 9, 16, 25, 36 are perfect squares.
5
Cube and Cube roots: Cube of 5 = 53 = 125 ⇒ ​√ 125 ​ = 5
A perfect cube is a number whose cube root is a whole number.
E.g. 1, 8, 27, 64, 125 are perfect cubes.
6
Highest Common Factor (HCF) and Lowest Common Multiple (LCM) can be found
using Prime Factorisation.
___
3
© Singapore Asia Publishers Pte Ltd
____
Chapter 1 Prime Numbers, Factors and Multiples
WORKeD eXAMPLe
1
Findtheprimefactorisationof150inindexnotation.
Solution:
Method 1:
Usingthefactortree:
150
2
2
×
75
2
×
3
×
25
×
3
×
5
×
Hence,theprimefactorisationof150is2×3×52.
Method 2:
Usingsuccessivedivision:
2 150
Teacher’s Desk
3 75
Onlyuseprimenumbers
when finding the factors.
5 25
5 5
1
Hence,theprimefactorisationof150is2×3×52.
©SingaporeAsiaPublishersPteLtd
2
Chapter 1 Prime Numbers, Factors and Multiples
5
2
WORKeD eXAMPLe
FindtheHCFandLCMofthenumbers40,60and100.
Solution:
Method 1:
Teacher’s Desk
InMethod1,youwill
need to find the prime
factorisationofeach
number first.
Usingprimefactorisation:
40 =23×5
60 =22×3×5
100 =22×52
HCF =22×5 →Extractcommonfactorswithlowest
index.
LCM =23×3×52 → Extractcommonfactorswithhighest
indexandallremainingfactors.
∴HCF=22×5=20
LCM=23×3×52=600
Method 2:
Usingsuccessivedivision:
2 40,60,100
Commonprime
factors
Teacher’s Desk
2 20,30,50
Stopdividingwhen
therearenocommon
factorsbetweenany
twonumbers
5 10, 15,25
2, 3,5
∴HCF=2×2×5=20
LCM=2×2×5×2×3×5=600
©SingaporeAsiaPublishersPteLtd
3
Chapter 1 Prime Numbers, Factors and Multiples
Useonlyprimenumbers
whenperformingprime
factorisation.
WORKeD eXAMPLe
3
Buses on 3 different routes start their journey from the interchange at
regularintervals.
BusesforrouteAleavetheinterchangeevery18minutes,busesforroute
Bleaveevery20minutesandbusesforrouteCleaveevery24minutes.
Given that all the first buses for all 3 routes leave at 7 a.m., what time will
theynextleavetogether?
Solution:
FindtheLCMof18,20and24.
2 18,20,24
Teacher’s Desk
Successivedivisionis
a more efficient way to
find LCM/HCF.
2 9,10,12
2 9,5,6
3 9,5,3
3 3,5,1
5 1,5,1
1,1,1
LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360
360 minutes=3hours
Thebuseswillnextleavetogetherat10a.m.
WORKeD eXAMPLe
4
Using prime factorisation, find the
(a) squarerootof784,
(b) cuberootof216.
Solution:
Teacher’s Desk
_____
=a
√a × a ________
3
=b
√ b × b × b (a) Usingprimefactorisation,784=24×72
(b) Usingprimefactorisation,216=23×33
©SingaporeAsiaPublishersPteLtd
_______________
____
784=√(22×7)×(2
2×7)
√
2
=2 ×7
=28
3
____
3
_____________________
√ 216=√ (2×3)×(2×3)×(2×3)
=2×3
=6
4
Chapter 1 Prime Numbers, Factors and Multiples
core Practice
Prime Factorisation
1
Expressthefollowingnumbersinindexnotation.
Teacher’s Desk
index
53=5×5×5
Base
To find the prime factorisation of a number:
Method 1:Factortree
Method 2:Successivedivision
(a) 2×2×3×3×7
(b) 2×5×5×5×5×5×11×11
(c) 7×7×11×23×23×23
(d) 3×3×3×3×3×37
(e) 3×3×7×7×7×13
(f) 2×11×11×11×19×19
(g) 5×7×17×17×17×17
(h) 3×3×3×23×23×29×29×29
(i) 11×13×19×19×13×13
(j) 5×19×3×5×3×3×19
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5
Chapter 1 Prime Numbers, Factors and Multiples
2
Findtheprimefactorisationofthefollowingnumbers.
Teacher’s Desk
Anumberisdivisibleby3ifthesumof
itsdigitsisdivisibleby3.Anumberis
divisibleby5ifitslastdigitis0or5.
(a) 200
(b) 945
(c) 735
(d) 1000
(e) 1350
(f) 1372
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Chapter 1 Prime Numbers, Factors and Multiples