Transcription of Student’s Book
1 MathematicsFor Rwanda SchoolsSenior 3 Student s BookEastone NdyabasaFred AngoliStephen KirangiLucy MainaPublished by Longhorn Publishers (Rwanda) LtdRemera opposite COGE Box 5910 Kigali, RwandaLonghorn Publishers (Kenya) LtdFunzi Road, Industrial Box 18033-00500 Nairobi, KenyaLonghorn Publishers (Uganda) LtdPlot 4 Vubyabirenge, NtindaP. O. Box 24745 Kampala, UgandaLonghorn Publishers (T) LtdNew Bagamoyo Road/Garden RoadMikocheni B, Plot No. MKC/ Box 1237 Dar es Salaam, Tanzania E.
2 Ndyabas, F. Angoli, S. Kirangi, L. Maina 2017 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 written permission of the Copyright published 2017 ISBN 978 9997 77 118 6 Printed by Ramco Printing Works Ltd,Unit 2, Ramco Industrial Complex,Before Imara Daima Turn off, Mombasa Road, P. O. Box 27750 - 00506,Nairobi, PROBLEMS ON SETS.
3 1 Key unit competence ..1 Unit outline ..1 Introduction .. Review of union, intersection and complement of sets .. Representation of problems using a Venn diagram.. Venn diagrams involving two sets .. Venn diagrams involving three sets..6 Unit 1 Test ..112. NUMBER BASES ..13 Key unit competence ..13 Unit outline ..13 Introduction .. Numbers and numerals .. Number bases .. Definition of number bases .. Change of base .. Operations using bases .. Addition and subtraction .. Division.
4 Special bases .. The binary system (base two) .. Base twelve (Duodecimal system) .. Solving equations involving numbers in other bases ..28 Unit Summary ..30 Unit 2 Test ..30 Contentsiv3. ALGEBRAIC FRACTIONS ..31 Key unit competence ..31 Unit outline ..31 Introduction .. Definition of algebraic fraction .. Simplification of Fractions .. Addition and subtraction of algebraic fractions with linear denominators, .. Multiplication of algebraic fractions .. Division of algebraic fractions.
5 Solving rational equations ..41 Unit Summary ..43 Unit 3 Test ..434. SIMULTANEOUS LINEAR EQUATIONS AND INEQUALITIES ..45 Key unit competence ..45 Unit outline ..45 Introduction .. Simultaneaous linear equations ..46 Solving simultaneous equations graphically .. Solving problems involving simultaneous equations .. Inequalities .. Graphical representation of linear inequalities .. Forming inequalities from given regions .. Simultaneous linear inequalities with one unknown .. Linear inequalities in two unknowns.
6 Graphical solution of simultaneous linear inequalities with two unknowns .. Linear inequalities from inequality graphs ..58 Unit 4 Test ..625. QUADRATIC EQUATIONS ..64 Key unit competence ..64 Unit outline ..64 Introduction .. Definition and examples of quadratic equations .. Solving quadratic equations.. Quadratic equations by factorisation method .. Solving quadratic equations by graphical method.. Solving quadratic equations by completing square method .. Solving quadratic equations by using formula method.
7 Solving Quadratic equations by synthetic division method .. Problems involving quadratic equations ..81 Unit 5 Test ..846. LINEAR AND QUADRATIC FUNCTIONS ..85 Key unit competence ..85 Unit outline ..85 Introduction .. Linear functions .. Definition of linear functions .. Slope/Gradient of a linear function .. Cartesian Equation of a line .. Parallel and Perpendicular lines .. Quadratic functions .. Table of values .. Determining the Vertex of a quadratic function and axis of symmetry from the graph.
8 Determining intercepts, vertices and sketching quadratic graphs ..101 Unit 6 Test ..1047. COMPOUND INTEREST, REVERSE PERCENTAGE AND COMPOUND PROPORTIONAL CHANGE ..106 Key unit competence ..106 Unit outline ..106 Introduction .. Reverse Percentage .. Compound interest .. Definition of compound interest .. Step by Step Method .. The compound interest formula .. Compound proportional change ..112 Unit Test 7 ..1148. RIGHT-ANGLED TRIANGLES ..116 Key unit competence ..116 Unit outline.
9 116 Introduction .. Review of Pythagoras theorem .. Median theorem a right-angled triangle .. Altitude theorems of a right-angled triangle .. Leg theorem of a right-angled triangle .. Introduction to trigonometry .. Trigonometric Ratios .. Sine and cosine of an acute angle .. Tangent of an acute angle .. Application of trigonometric ratios (sine, cosine, and tangents) ..138 Unit 8 Test ..1429. CIRCLE THEOREM ..144 Key unit competence ..144 Unit outline ..144 Introduction .. Elements of a circle and disk.
10 Circle theorem .. Angles at the centre and circumference of a circle .. Angle in a semicircle .. Angles in the same segment .. Angles in a cyclic quadrilateral .. Tangent to a circle .. Angles in alternate segment .. Properties of chords ..168 Unit 9 Test ..173vii10. COLLINEAR POINTS AND ORTHOGONAL VECTORS ..175 Key unit competence ..175 Unit outline ..175 Introduction .. Collinear points .. Definition of colinearity .. Verifying collinearlity of points using vector laws.
