Uce Book 1 Caltec S.1

U.C.E Mathematics 1 (For S.1 ) BY Chepa Y. M Department of Mathematics, Kibuli Secondary School. Telephone: +256 772 481628 Email: ymussy @yahoo.co m UUCCEE MMaatthheemmaattiiccss 11 2 Second edition 2008 © Chepa Y. M. March 2008 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 author. UUCCEE MMaatthheemmaattiiccss 11 3 CONTENTS 1. NUMBER SYSTEMS -------------------------------- --------------------- 4 2. SETS AND OPERATIONS -------------------------------- ------------ 24 3 COORDINATES -------------------------------- -------------------------- 32 4 FRACTIONS -------------------------------- ------------------------------ 49 5 ANGLES AND BEARINGS -------------------------------- ------------ 66 6. POLYGONS -------------------------------- ------------------------------ 83 7. AREA AND VOLUME -------------------------------- ------------------ 93 8 LINEAR RELATIONS -------------------------------- ------------------ 119 9 REFLECTION -------------------------------- ---------------------------- 131 10 BRACKETS -------------------------------- ------------------------------- 137 11 EQUATIONS AND INEQUALITIES -------------------------------- 139 12 APPROXIMATIONS -------------------------------- -------------------- 157 ANSWERS -------------------------------- -------------------------------- ----- 160 UUCCEE MMaatthheemmaattiiccss 11 4 1. NUMBER SYSTEMS 1.1 NUMBER BASES Definiti on: Number bases are different ways of using the same number. We use a system called base 10, or decimal , for our arithmetic, but there are as many number bases as there are numbers . These common bases also have proper names, shown in parentheses:  base 2 (binary)  base 8 (octal)  base 10 (decimal)  base 12 (duodecimal)  base 16 (hexadecimal) We are accustomed to writing numbers in base ten, using the symbols for 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For example, 75 means 7 tens and five ones . However numbers can b e written in any number base. If we use base 8 instead of base ten, then 75 is written as 113 which denotes one sixty four (82 ), one eight (81 …