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Catalogue

Additional Mathematics Form 2


About the book

Additional Mathematics 2 contains demonstrations by way of worked out examples, carefully selected illustrations and graphics that makes reading and learning process enjoyable. To encourage inquisitiveness and love of mathematics, the coverage and questions address community ’ s cross cutting issues in health, gender , culture, environment among others. This book covers algebra and for that matter word problems involving simultaneous equations, variations, logic - where among others the Student shall be able to determine the validity of an argument, locus and sets.

Author: Innocent K Mitala

Table of contents

CONTENTS ACKNOWLEDGEMENT....................................................................................................iii INTRODUCTION...............................................................................................................viii

 

CHAPTER 1: ALGEBRA………………………………………..........................................................1

 

1.1 Simultaneous Equations; one Linear and one Quadratic................................1

1.1.1 Quadratic Equations ..............................................................................................2

1.1.2. Solving Simultaneous Equations; one Linear and another Quadratic by Substitution Method.......................................................................................................13

1.2 Solving Simultaneous Equations Using Graphs...............................................19

1.2.1 Drawing a graph of a linear and a quadratic equations..........................20

1.3 Word Problems leading to Simultaneous Equations ...................................26

Revision Exercise 1.........................................................................................................32

 

CHAPTER 2: VARIATIONS………………................................................……………....….......35

2.1 Direct Variations.......................................................................................................35

2.1.1 Linear Direct Variations…………………...........................................…….................36

2.1.2 Non Linear Direct Variations…………......................................………..............…..39

2.2 Inverse Variations…..................................................................................................44

2.3 Joint Variations…………………………….............................................………………..........51

Revision Exercise 2………………………………................................................................…...58

 

CHAPTER 3: LOGIC…………............................................……………........………….....…….....63

3.1 Statements..................................................................................................................64

3.1.1 Connective words used in Logic...........................................................….........65

3.1.2 Negation of a statement...........................................................................….......66

3.2 Truth Tables……..........................................................................................................70

3.2.1 Construction of Truth Tables.............................................................................71

3.2.2 Tautology and Contradiction.............................................................................77

3.2.3 Electrical Network…………......................................................................................81

3.3 Arguments………….......................................................................................................87

3.4.1 Logical Argument …………..........................………...............................................…87

3.4.2 Identifying basic Proposition in an Arguments ................…......…......………89

3.3.3 Determining Validity of an Argument with Truth Tables...............…..…….90

3.3.4 Determining Validity of an Argument with Venn Diagrams.......……..……90

Revision Exercise 3..........................................................................................................97

 

CHAPTER 4: LOCUS…………………………..............................................…………..........…..104

4.1 Locus on a Fixed Point……....................................................................................106

4.2 Locus on Two Fixed Points..................................................................................109

4.3 Locus on a Line…….................................................................................................113

4.4 Locus on Intersecting lines..................................................................................117

Revision Exercise 4.......................................................................................................123

 

CHAPTER 5: SETS…………………………...........................……………………………….............126

5.1 Operations on Sets...............................................................................................126

5.1.1 Venn diagrams………………………................................……………..........................126

5.2 The Universal Set………………………….....................................................................135

5.2.1 Complement of a Set……………………….................................……..........…......…136

5.2.2 Number of Elements in a Set………………...............................……..............….138

5.3 Use of Venn Diagrams to Solve Set Problems………….........................….....140

Revision Exercise 5…………………….....................................................……………….....…149

 

ANSWERS.......................................................................................................................154

Exercise 1.1 ………………………………………………......................................…….........…….154

Exercise 1.2 ……………………………………………………...............................................…….154

Exercise 1.3 ………………………………………………………...............................................….154

Exercise 1.4 …………………………………………………………................................................155

Exercise 1.5 …………………………………………………...............................................……….155

Exercise 1.6 …………………………………………………...............................................……….156

Revision Exercise 1…………………………………………………........................…..........…….156

 

Exercise 2.1 ………………………………………………......................................….........……….157

Exercise 2.2 …………………………………………......................................……….........……….158

Exercise 2.3 ……………………………………………......................................…….........……….158

Revision Exercise 2………………………………………........................…………..........……….159

 

Exercise 3.1 ……………………………………......................................………….........………….160

Exercise 3.2 ……………………………………………......................................…….........……….162

Exercise 3.3 …………………………………...................................……………...……..........……167

Exercise 3.4 ……………………………...................................…………………………............….168

Revision Exercise 3…………………………….............................…………............….……...…172

 

Exercise 4.1 ………………………………………….................................................……………….182

Exercise 4.2 …………………………………………...............................................………………….182

Exercise 4.3 ……………………………………......................................….........…………………….182

Exercise 4.4 …………………………………......................................……….........………………….183

Revision Exercise 4………………………………………........................…….........………….…….183

 

Exercise 5.1 ……………………………………......................................…….........………………….184

Exercise 5.2 ………………………………...............................................…………………………….185

Exercise 5.3 ………………………………………...............................................…………………….187

Revision Exercise 5 …………………………………….................................……………………….188

 

INDEX…………………………………….......................................................……………………………189