Math Uce Book 4 Caltec S.4

UCE M a t h e m a t i c s 4 ( For S.4) BY Chepa Y. M Department of Mathematics, Kibuli Secondary School. Telephone: +256 772 481628 Email: y mussy @yahoo.co m 3 Second edition 2008 © Chepa Y. M. March 2008 All Rights Reserved. No p art 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. 4 Contents Chapter Page 1 Gradients and rates of change ................................ ............. 6 The gradient of a straight line ................................ ...................... 6 The equation of a straight line ................................ ...................... 7 The graph of a straight line ................................ ....................... 14 The gradients of parallel lines ................................ .................... 15 The gradients of perpendicular lines ................................ ............ 17 Rates of change ................................ ................................ ..... 19 2 Equations ................................ ................................ ........... 32 Simultaneous equations ................................ ........................... 32 Problem solving involving simul taneous equations ......................... 36 Quadratic equations ................................ ................................ 38 Solving quadratic equations by factors method .............................. 39 Solutions of quadratic equations by formula ................................ .. 42 Solutions of quadratic equations by formula ................................ .. 42 Problems solved by quadratic equations ................................ ...... 44 Graphs of quadratic functions ................................ .................... 47 Graphical solution of equations ................................ .................. 51 Simultaneous equations – one linear and one quadratic ................... 58 3. Circles ................................ ................................ ................ 60 Area o f a sector ................................ ................................ ...... 60 Chord of a circle ................................ ................................ ..... 62 Angle properties of a circle ................................ ........................ 63 4. Linear programming ................................ ............................ 79 5 Forming linear inequalities ................................ ........................ 79 Forming and solving inequalities ................................ ................ 81 Optimization ................................ ................................ .......... 84 The objective function ................................ .............................. 86 5. Constructions and Loci ................................ .................. 95 Perpendicular bisector …