SAMPLE. stinction. Secondary. Ivan Lau Kim Soon. ~ Marshall Cavendish ~Education

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1 stinction Ivan Lau Kim Soon Secondary ~ Marshall Cavendish ~Education

2 0 Marshall Cavendish International (Singapore) Private Limited Published by Marshall Cavendish Education An imprint of Marshall Cavendish International (Singapore) Private Limited Times Centre, New Industrial Road, Singapore 5696 Customer Service Hotline: (65) tmesales@sg.marshallcavendish.com Website: First published 0 Reprinted 04 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. Any requests for permission should be addressed to the Publisher. Marshall Cavendish is a trademark of Times Publishing limited. ISBN Editor: Nurul Huda Bin\ ~ Nur Affandy Printed in Malaysia \ ' ~

3 reface Distinction in Mathematics-Revision Guide is written for students preparing for tests and examinations as well as the crucial GCE '0' Level Examinations. Ea_ch chapter begins with a set of 'Keynotes'. This is where concepts and various formulae are compiled for pupils' easy reference during revision. It also includes essential formulae from the GCE '0' Level Mathematical Formulae List. Every chapter has a variety of questions for practice and exposure. Emphasis is given to commonly asked questions in examinations to better equip pupils with the skills to answer effectively and efficiently. I sincerely hope that pupils will benefit greatly from this book by maximizing their potential and scoring better grades for tests and examinations. Ivan Lau Kim Soon

4 o tents Factors and Multiples... Real Numbers... 6 Approximation and Estimation Introduction to Algebra and Manipulation... ~... 5 Linear Equations Angles, Parallel Lines and Triangles Polygons Ratio, Rate and Speed...: _,., "' 9 Percentage...:. ~.:... ~ Number Patterns Coordinates and Linear Graphs Simple Inequalities... ', Area and Perimeter... 4 Volumes and Surface Areas of Solids Data Analysis Answer Key

5 Factors and Multiples_ eynotes: 0 Prime factorization 8 Definition: A method to express number as a product of prime factors. Example: Find the product of the prime factors for 7. Solution: :.7 = X Lowest Common Multiple (LCM) and Highest Common Factor (HCF) Definition: (} The smallest common multiple of a two or more numbers is called Lowest Common Multiple (LCM). () The largest common factor of two or more numbers is Highest Common Factors (HCF). Student must know how to find LCM and HCF of a number in the form of ordinary notation and index notation. (a) Ordinary notation Example: Find the HCF and LCM for 7 and 84. Solution: HCF 7,84 6,4 8, 6, 7 HCF = x x = LCM 7, 84 6,4 8, 6 6, 7 7, 7, LCM = X X X 6 X 7 = Marshall Cavendish International (Singapore) Private limited. Factors and Multiples

6 (b) Index notation HCF Consider the smaller power for each of the base LCM Consider the bigger power for each of the base Example: Find the HCF and LCM for 4 x 7 5 x 4 and 8 x x?9. Express your answer in index notation. Solution: HCF 8 Square and square root LCM Definition: Since 4 = 6 and (- 4) = 6, then 6 is known as the square of 4 and - 4. Alternatively, 4 and - 4 are known as the square root of 6. (a) Square Number.. Square Number X 7 X 4 X 7 X 6 X X 6 Topic 0 Marshall Cavendish International (Singapore) Private Limited.

7 (b) Square root Use the function &., ' on a calculator to find the square of a number.. All the numbers in the "ct column are called perfect square numbers. Number Positive Square Root Negative Square Root Use the function E..t of a number on a calculator to find the square root. If the given number is in index notation, divide the power by two in order to find the square root. 0 Marshall Cavendish International (Singapore) Private Limited. Factors and Multiples

8 Cube and cube root Definition: Since 4 = 64, then 64 is called as the cube of 4. Alternatively, 4 is known as the cube root of 6. (a) Cube.T, (b) Cube root Number Cube Number x7x P 6 X 7 X 9 X X 9 Use the function Fx;. on a calculator to -find the cube of a number.. All the numbers in the nd column are called perfect cube numbers. Number Cube Root X 7 X 9 x7 x P X 9 X J 4 Topic 0 Marshall Cavendish International (Singapore) Private Limited.

9 0 Prime number Use the function Be, on a calculator to find the cube root of a number.. If the given number is in index notation, divide the power by three in order to find the cube root. Definition: A number is called a prime number if it is divisible only by or itself. Example:,, 5, 7,,, 7,... All prime numbers are positive numbers. The smallest prime number is. 0 Marshall Cavendish International (Singapore) Private Limited. Factors and Multiples

10 Quiz: 0 Find the product of the prime factors for the following: (a) 75 (b) 70 (c) 585 (d) 540 (e) 486 (f) 50 (a) (d) (b) (e) ' ' ~ (c) (f),.. 6 Topic 0 Marshall Cavendish International (Singapore) Private Limited.

11 Find the (i) HCF and (ii) LCM for (a) 50 and 60, (b) 5, 6 and 66, (c) 80 and 50. (a) (i) (a) (ii) (b) (i) (b) (ii) Consider the numbers 98 and 456. Find (a) the product of the prime factors for each number, (c) (i) (c) (ii) (b) the HCF of both numbers, leaving your answers in ordinary notation, (c) the LCM of both numbers, leaving your answers in index notation. (a) (b) (c) 0 Marshall Cavendish International (Singapore) Private Limited. Factors and Multiples

12 Answer. (a) (i) 5 50,60 Factors and Multiples. (a) 5~ :. 75 = X 5 (b) 70 5 :. 70 = x x (c) :. 585 = X 5 X (d) ' I :. 540 = X 5 X 7 X (e) :. 486 = X X X 7 (f) :. 50 = x x 7 0, 7 0, 4 5, :. HCF = x X 5 = 0 (ii) 5 50,60 0, 7 0, 4 5 5,,, 6,, :. LCM = x X 5 = 800 (b) (i) 5, 6, 66 5,, :. HCF = < (ii).- ~ 5,6,66 5,, 5 5, 6,, 6,,,,,,, :. LCM = X X 5 X = 980 (c) (i) 80, , 75 8, 5 :. HCF = x 5 = 0 (ii) 5 80, 50 40, 75 8, 5 4, 5, 5, 5 5, 5, :. LCM = 4 X X 5 = 00,., 0 Marshall Cavendish International (Singapore) Private Limited.

13 . (a) :.98=x x 9 :.456= xxl9 (b) (c) 4. (a) 98,456 66, 5, 76 :. HCF = x = 6 98,456 66, 5, 76, 76 ' 76, 8 9, 9, LCM = X X X :. 089 = X! :.4= x7 x (b) j089, 4 (c) 99, 9 :. HCF = ,4 99, 9 9, 9 9, 56 9, 8, 8, 8, 4,, :. LCM = X x7 X! (a) :. 564 = X 9 X :. 76 = X X X 7 0 Marshall Cavendish International (Singapore) Private limited. Answer d.9