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. 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.

2 O. Box 27750 - 00506,Nairobi, PROBLEMS ON SETS ..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 .. 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.

3 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 .. 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.

4 Simultaneous linear inequalities with one unknown .. Linear inequalities in two unknowns .. 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 .. Solving Quadratic equations by synthetic division method .. Problems involving quadratic equations ..81 Unit 5 Test.

5 846. 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.. 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.

6 The compound interest formula .. Compound proportional change ..112 Unit Test 7 ..1148. RIGHT-ANGLED TRIANGLES ..116 Key unit competence ..116 Unit outline ..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 .. Circle theorem .. Angles at the centre and circumference of a circle.

7 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 .. Applications of collinearlity in proportional division of lines .. Orthogonal vectors ..180 Unit 10 Test ..18311. ENLARGEMENT AND SIMILARITY IN 2D ..185 Key unit competence ..185 Unit outline ..185 Introduction .. Similarity .. Similar Similar polygons .. Calculating lengths of sides of similar shapes using similarity and Thales theorem.

8 Definition and properties of similar solids .. Enlargement .. Definition of enlargement .. Constructing objects and images under enlargement .. Locating the centre of enlargement and finding the scale factor .. Properties of enlargement .. Enlargement in the Cartesian plane .. Area scale factor .. Volume scale factor ..212 Unit Summary ..214 Unit 11 test ..215viii12. INVERSE AND COMPOSITE TRANSFORMATIONS ..217 Key unit competence ..217 Unit outline ..217 Introduction .. Composite translations in two dimensions .. Composite reflections in two dimensions .. Composite rotations in two Mixed composite transformations in two dimensions .. Inverse transformations in two dimensions ..229 Unit 12 Test ..23213. STATISTICS (BIVARIATE DATA).

9 233 Key unit competence ..233 Unit outline ..233 Introduction .. Definition and example of Bivariate data .. Frequency distribution table for bivariate data .. Review of data presentation using graphs .. Representing bivariate using scatter diagrams .. Definition of scatter diagrams .. The line of best fit in a scatter diagram .. Correlation ..242 Unit 13 Test ..247 Glossary ..249 References ..2511 Problems on SetsPROBLEMS ON SETS1 Key unit competence: By the end of this unit, the learner should be able to solve problems involving outline Analysis and interpretation of problems using sets. Representation of a problem using a Venn focus ActivityUse your knowledge on sets to solve the following problem."For planning purposes, a Physical Education ( ) teacher asked a Senior 3 class of 24 students to vote by raising of hands for the ball games they liked playing from among football, volleyball and basketball.

10 After the voting, he observed that each of the 24 students liked at least one game. 1 student liked all the three games. 2 students liked volleyball and basketball but not football. 2 students liked volleyball and football but not basketball. In summary, he noted that 6 students liked volleyball, 12 liked basketball and 15 liked football .The teacher went back to the staffroom and realised that he had not established the number of students who liked football and basketball but not volleyball. He has called you to help him determine that number using your knowledge, to avoid calling the whole class to vote again. Kindly, determine the number and give to the teacher. The knowledge of operations on set is very useful in solving some complex real life problems that are not easy to solve through other analytical methods.