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Secondary 1 Maths - 2nd Pass
11/08/2013
Preface
This book aims to help students get a firm grasp of
the concepts involved in this level of Mathematics
curriculum. The chapters are in accordance with
the latest (2013) GCE O-Level Mathematics. Each
chapter starts with brief notes and examples,
where necessary. Questions in each chapter take
students on a trip from easy sums to tough ones,
developing their confidence along the way.
A Specimen paper at the end of this book is
designed to let students self-test themselves within
the allotted time.
The Answers section provides worked solutions
for practically all the questions. We sincerely hope
that students will benefit greatly from this book.
Secondary 1 Maths - 2nd Pass
11/08/2013
Contents
Chapter 1
Factors and Multiples
Chapter 2
Real Numbers
12
Chapter 3
Approximation and Estimation
30
Chapter 4
Introduction to Algebra
41
1
Chapter 5Simplifying Algebraic Expressions
(Number Sequence Also Included)
50
Chapter 6
Solving Equations and Inequalities
68
Mid Year Exam
Specimen Paper - 1
82
Mid Year Exam
Specimen Paper - 2
94
Chapter 7
Angles and Parallel Lines
108
Chapter 8
Triangles and Polygons
119
Chapter 9
Ratio, Rate and Percentage
135
Chapter 10
Perimeter and Areas of Plane Figures
158
Chapter 11
Volume and Surface Area
167
Chapter 12
Co-ordinates and Linear Graphs
180
Chapter 13
Data Handling
196
End Year Exam
Specimen Paper - 1
209
End Year Exam
Specimen Paper - 2
221
Answers
239
Secondary 1 Maths - 2nd Pass
Chapter
1
11/08/2013
FACTORS AND
MULTIPLES
1. A factor of a number divides the number exactly.
2. A multiple of a number is exactly divisible by the number.
3. Highest Common Factor (HCF) of two or more numbers is a unique
number which
(i) is a factor of each of the numbers:
(ii) which is the greatest among the common factors of these numbers
Example
Consider numbers 12 and 16
Factors of 12 are 1,2,3,4,6,12
Factors of 16 are 1,2,4,8,16
Here the common factors are 1,2, and 4. Out of these, 4 is the
greatest
HCF of 12 and 16 is 4
HCF is also known as the greatest common divisor (GCD)
4. Lowest common Multiple (LCM) of two or more numbers is a number
which is a common multiple of the numbers and is the smallest among
all the multiples
Example
Consider the numbers 8 and 12
Multiples of 8 are 8, 16, 24,.........
Multiples of 12 are 24, 48,.........
Here 24 is the smallest of the multiples.
So LCM is 24.
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Chapter 1: Factors and multiples
Secondary 1 Maths - 2nd Pass
11/08/2013
5. The product of HCF and LCM of two numbers a and b is equal to the product of the
numbers a × b.
6. The HCF of two numbers a and b is a factor of the LCM of a and b, likewise LCM
of a and b is a multiple of HCF of a and b.
7. A natural number which has only two different factors 1 and the number itself, is
a Prime number.
8. A natural number which has more than two different factors is a composite
number.
9. The process of expressing a composite number as a product of prime factors is
called Prime factorization.
10. Number 1 is neither prime or composite, 2 is the only even prime number.
Secondary
1 Maths
2
Secondary 1 Maths - 2nd Pass
11/08/2013
QUESTIONS
1. List all prime numbers between 80 and 100.
2. List all prime numbers between 101 and 179.
3. Find the sum of all prime numbers between 160 and 200.
4. Use the sieve of Eratosthenes to find all the prime numbers between 1 and 30.
Which are the even prime numbers in the list?
5. Write the prime factors of the following:−
(a)
253
(b) 231
3
Chapter 1: Factors and multiples
Secondary 1 Maths - 2nd Pass
11/08/2013
(c)
3795
(d) 8008
(e)
15625
(f) 1911
(g)
2145
(h) 51051
(i)
41503
6. Write the largest 4 digit number and express it as a product of its primes.
Secondary
1 Maths
4