Student’s Book

1 MathematicsSenior 1 Student s BookEastone NdyabasaFred AngoliDaniel GituLucy MainaFor Rwandan SchoolsiiPublished by Longhorn Publishers (Rwanda) Ltd166 Kg 13 Off Kg 11 Box 5910 Kigali, RwandaLonghorn Publishers (Kenya) LtdFunzi Road, Industrial Box 18033-00500 Nairobi, KenyaLonghorn Publishers (Uganda) LtdKanjokya Street, Plot Box 24745 Kampala, UgandaLonghorn Publishers (Tanzania) LtdNew Bagamoyo Road/Garden RoadMikocheni B, Plot No. MKC/ Box 1237 Dar es Salaam, Tanzania E. Ndyabasa, F. Angoli, D. Gitu, L. Maina 2016 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 2016 Reprinted 2016 ISBN 978 9997 74 483 8 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, 1: Sets ..1 Key unit competence ..1 Unit outline ..1 Introduction to set concept ..1 Describing sets ..1 Set Notation ..2 Membership of a Set ..2 Number of members in a set..2 Subsets of a set ..5 The numbers of subsets in a set ..5 Subsets of natural numbers ..6 Venn diagrams ..7 Set operations ..8 Intersection of sets ..8 Union of sets ..10 Universal set ..12 Complement of a set ..13 Simple and symmetric differences of sets 15 Special sets (empty and disjoint sets) ..16 Comparison of sets ..17 General problems in sets using Venn diagram ..18 Relations and functions ..20 Introduction to relations ..20 Properties of relations ..21 Papygram ..22 Terms used to express a relation .. 24 Ordered pair ..24 Cartesian product ..24 Mapping ..25 Graphs of relations ..28 Functions ..30 Inverse of a function ..31 Composite functions.

3 33 Summary ..34 Unit Test 1 ..35 Unit 2: Sets of numbers ..37 Key unit competence ..37 Unit outline ..37 Sets of numbers, its subsets and notation 37 Set of natural numbers ..38 Subsets of natural numbers ..39 Operations on natural numbers ..41 The Set of integers (Z) ..44 Subsets of integers ..44 Relationship between integers and natural numbers ..45 Operation on integers ..46 Fractional Numbers (rational numbers) .49 Types of fractions ..50 Operations on fractional numbers ..50 Decimals ..53 Types of decimals ..54 Operations on decimals ..54 Conversion between decimals and fractions ..58 Changing Fractions to decimals ..58 Changing decimals to fractions ..59 Changing recurring decimals to fractions ..59 Sets of real numbers ..60 Summary of properties of operations on the sets of real numbers ..62 Summary ..62 Unit Test 2 ..63ivUnit 3: Linear functions, equations and inequalities.

4 64 Key unit competence ..64 Unit outline ..64 Linear functions ..64 The number of a point on a line ..64 Position of a point on a plane surface ..65 Drawing and labelling axes ..65 Drawing vertical and horizontal lines ..66 Cartesian plane ..67 Plotting points ..70 Linear graphs ..72 Graphs of linear equations ..73 The y and x intercepts ..75 The gradient of a straight line ..77 Gradient of x and y intercepts ..81 Linear equations ..83 Meaning of letters in Algebra ..84 Solving linear equations ..84 Solving equations by the balancing method ..86 Linear equations involving fractions ..88 Equations involving brackets ..89 Forming and solving linear equations ..91 Inequalities ..94 Inequalities symbols ..94 Compound statements ..96 Solution of linear inequalities in one unknown ..96 Manipulating algebraic inequalities ..97 Solving simultaneous inequalities.

5 98 Forming inequalities from word statements ..100 Application of inequalities in life ..101 Summary ..102 Unit Test 3 ..103 Unit 4: Percentage, discount, profit and loss ..105 Key unit competence ..105 Unit outline ..105 Percentages ..105 Discount ..107 Commission ..109 Profit and Loss ..110 Percentage loss and percentage profit ..111 Loans and savings ..113 Simple interest ..113Ta x ..116 Indirect taxes ..116 Withholding tax ..117 VAT (Value Added Tax) ..117 Insurance ..119 Summary ..121 Unit Test 4 ..121 Unit 5: Ratio and proportion ..123 Key unit competence ..123 Unit outline ..123 Ratios ..123 Simplifying ratios ..124 Sharing quantities using ratios ..126 Application of ratios in scale drawing ..127 Proportion ..128 Properties of proportion ..129 Direct proportion ..131 Inverse proportion ..134 Summary ..137 Unit Test 5 ..138vUnit 6: Points, lines and angles.

6 139 Key unit Competence ..139 Unit outline ..139 Points and lines .. of angles ..140 Angles on a straight line ..144 Angles at a point ..146 Angles on a parallel line ..148 Summary ..152 Unit Test 6 ..152 Unit 7: Solids ..154 Key unit competence ..154 Unit outline ..154 Properties of solids ..154 Surface area of solids ..158 Surface area of a cuboid ..158 Surface area of a cube ..160 Surface area of a cylinder ..161 Surface area of a prism ..162 Surface area of a pyramid ..165 Surface area of a cone ..168 Surface area of a sphere ..171 Surface area of composite solids ..173 Volume of cubes and cuboids ..175 Volume of a prism ..176 Volume of a cylinder ..179 Volume of a cone ..181 Volume of a pyramid ..183 Volume of a sphere ..185 Problem solving: areas and volumes ..187 Summary ..191 Unit Test 7 ..191 Unit 8: Statistics ..193 Key Unit Competence.

7 193 Unit outline ..193 Introduction ..193 Types of data ..193 Collecting and organising data ..195 Frequency distribution table ..196 Measures of central tendency ..199 The arithmetic mean ..199 Mode ..201 The median ..202 Quartiles ..204 Presentation and reading of statistical graphs ..206 Rank order list ..206 Pictogram (or pictograph) ..207 Pie-chart ..210 Bar chart/ bar graph ..212 Line graph ..216 Histogram and frequency polygon ..221 Cumulative frequency diagram ..225 Summary ..227 Unit Test 8 ..228 Unit 9: Probability ..231 Key unit competence ..231 Unit outline ..231 Introduction ..231 Definition of terms used to describe probability ..232 Types of events ..233 Probability expression ..233 Experimental probability ..233 Basic rules in probability ..234 Theoretical probability ..238 Summary ..242 Unit Test 9 ..242vi1 AlgebraSETS1 Key unit competenceBy the end of the unit, I should be able to use sets, venn diagrams and relations to represent situations and solve outline Set concept.

8 Relations. Inverse and composite relations. Introduction to set conceptActivity groups of four:1. Identify and list any ten items in your home that can be grouped Name the groups you have identified in step 1 Let the group members select one member to present their findings in part 1 and 2 on the chalk Activity above, you may have obtained groups that consist of utensils, domestic animals, furniture and so on. Most things in life have common features. Such features are used to group the things together. A group of items with a common feature is called a set. Examples of sets are: a set of animals, a set of houses, set of cars and so on. An object or item in a set is called a member or an element of the set. This unit will introduce us to the knowledge of sets and a number of terms concerning sets.

9 We will define the terms as we meet them in their respective sections. Describing setsActivity groups of three:1. Find out from the internet, reference books or any other relevant materials how sets are By use of examples, show other students how sets are described on the are three methods commonly used to describe or represent a set(i) Statement form method(ii) Roster or tabular form method(iii) Set builder form methodAll these methods are used together with a pair of curly brackets within which the description is enclosed.(a) Statement form methodConsider: (i) the alphabets a, b, c, d and e. These letters can be described using a statement as follows: {the first six letters of the alphabets}(ii) the set of the numbers 2, 4, 6, 8, 10. This can be described as: {the first five even numbers} or {the first five natural numbers divisible by 2}Individually, identify another five sets and describe them in a similar method.

10 (b) Roster or tabular methodUsing this method, we describe a set by listing all the elements in it. 2 Algebrabiology, history, religious }. Capital letters are used to represent sets set S. Members of a set are separated by commas and the set is enclosed with a curly bracket{ }.For example, a set of odd numbers (O) less than 10 can be written as O = {1, 3, 5, 7, 9}.A set of the first six letters of an alphabet (A) can be written as A = {a, b, c, d, e, f}. Membership of a setActivity individual basis. 1. Write down the set of four legged domestic animals you Is a cow a member of that set? If so how can you represent this in set notation?3. Is a lion a member of the above set? If so how can you represent this in set notation?We use symbol to mean is a member of and to mean "is not a member of ".