PrefaceThis 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

ContentsChapter 1 Factors and Multiples 1

Chapter 2 Real Numbers 12

Chapter 3 Approximation and Estimation 30

Chapter 4 Introduction to Algebra 41

Chapter 5 Simplifying 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 11/08/2013

Chapter

Chapter 1: Factors and multiples1

Chapter 1 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 16Factors of 12 are 1,2,3,4,6,12Factors of 16 are 1,2,4,8,16Here the common factors are 1,2, and 4. Out of these, 4 is the greatestHCF of 12 and 16 is 4HCF 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 12Multiples 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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Secondary 1 Maths 2

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 - 2nd Pass 11/08/2013

Chapter 1: Factors and multiples3

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

Secondary 1 Maths - 2nd Pass 11/08/2013

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(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 - 2nd Pass 11/08/2013