TABLE OF CONTENTS – GENERAL MATHEMATICS-1 (INTRODUCTION TO ALGEBRA)

ENTER TO STUDYAugust 18, 2023

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TABLE OF CONTENTS

GENERAL MATHEMATICS-1 (INTRODUCTION TO ALGEBRA)

Unit #	CONTENTS	Page #
1	1. INTRODUCTION TO MATHEMATICS	1
2	2. REAL NUMBER SYSTEMS
	2.1 Real Numbers	7
	2.2 Properties of Real Numbers	11
	2.3 Rational and Irrational Numbers	16
	2.4 Decimal Presentation of Rational and Irrational Numbers	18
	PRACTICE EXERCISE – 2.1	21
	2.5 HCF & LCM	29
	PRACTICE EXERCISE – 2.2	32
3	3. COMPLEX NUMBERS
	3.1 Definition of Complex Numbers	35
	3.2 Operations on Complex Numbers	37
	3.3 Properties of the Complex Numbers	39
	3.4 Geometrical Representation of Complex Numbers	42
	3.5 Graphical Addition and Subtraction of Complex Numbers	44
	PRACTICE EXERCISE – 3	45
4	4. INTRODUCTION TO SETS
	4.1 Basic Definitions of Sets	54
	4.2 Representation of Sets in Set Theory	56
	4.3 Types of Sets	57
	4.4 Subsets and its Types with Examples	58
	4.5 Operations on Sets	60
	4.6 Properties of Sets	62
	PRACTICE EXERCISE – 4	63
5	5. FUNCTIONS
	5.1 Definition of Function	75
	5.2 How to Evaluate the Function	76
	5.3 Function, Domain and Range	78
	5.4 SET- Builder Notation for a Function	79
	5.5 Types of Function	80
	5.6 Linear and Quadratic Function	86
	5.7 Inverse of Function	88
	PRACTICE EXERCISE – 5	89
6	6. INTRODUCTION TO MATRIX
	6.1 Basic Introduction	99
	6.2 Important Formulas for Matrices	100
	6.3 Types of Matrices	101
	6.4 Operations on Matrices	103
	6.5 Properties of Matrix	105
	6.6 Transpose of Matrix with Examples	106
	6.7 Special Types of Matrices	108
	6.8 Echelon and Reduced Echelon Forms of Matrices	110
	6.9 Invertible Matrix	112
	PRACTICE EXERCISE – 6	114
7	7. DETERMINANTS
	7.1 Determinants of Square Matrix	126
	7.2 Types of Determinants	127
	7.3 Properties of Determinants	130
	7.4 Adjoint of a Matrix	136
	7.5 Application of Determinants and Matrices	138
	PRACTICE EXERCISE – 7	140
8	8. SYSTEMS OF LINEAR EQUATIONS
	8.1 Basic Introduction	149
	8.2 Methods to Solve Systems of Linear Equation	150
	8.3 Systems of Linear Equations in Two Variables	153
	8.4 Cramer’s Rule	161
	8.5 Application of Systems of Linear Equations	163
	PRACTICE EXERCISE – 8	164
9	9. SOLUTION OF QUADRATIC EQUATIONS
	9.1 Basic Introduction	174
	9.2 Solution of Quadratic Equations with Examples	174
	9.3 Derivation of the Quadratic Formula	180
	PRACTICE EXERCISE – 9.1	184
	9.4 Qualitative Analysis of Roots of Quadratic Equations	189
	PRACTICE EXERCISE – 9.2	192
	9.6 Solution of Equations Reducible to the Quadratic Equation with Examples	194
	PRACTICE EXERCISE – 9.3	203
	9.7 Cube Root of Unity	204
	9.8 Properties of Cube Root of Unity	209
	9.9 Four Fourth Roots of Unity	212
	PRACTICE EXERCISE – 9.4	213
	9.10 Relations Between the Roots and the Coefficients of a Quadratic Equation	216
	PRACTICE EXERCISE – 9.5	219
10	10. SEQUENCES & SERIES
	10.1 Introduction to Sequence and Series	226
	10.2 Types of Sequence & Series	228
	10.3 Sequence and Series Formulas	228
	PRACTICE EXERCISE – 10.1	232
	10.4 Arithmetic Progression / Sequence	236
	PRACTICE EXERCISE – 10.2	240
	10.5 Arithmetic Mean (A.M)	242
	PRACTICE EXERCISE – 10.3	243
	10.6 Arithmetic Series	244
	PRACTICE EXERCISE – 10.4	247
	10.8 Geometric Progression / Sequence	251
	PRACTICE EXERCISE – 10.5	254
	10.9 Geometric Means (G.M)	256
	PRACTICE EXERCISE – 10.6	258
	10.10 Geometric Series	260
	PRACTICE EXERCISE – 10.7	264
	10.11 Application of Geometric Sequence & Series	266
	10.12 Harmonic Progression / Sequence	268
	10.13 Harmonic Mean	270
	10.14 Application of Harmonic Sequence	272
	PRACTICE EXERCISE – 10.8	273
11	11. MATHEMATICAL INDUCTION
	11.1 Principles of Mathematical Induction	282
	11.2 Principles of Extended Mathematical Induction	284
	PRACTICE EXERCISE – 11	286
12	12. BINOMIAL THEOREM
	12.1 Introduction to Binomial Theorem	291
	PRACTICE EXERCISE – 12.1	296
	12.2 Application of Binomial Theorem	303
	PRACTICE EXERCISE – 12.2	308
13	13. TRIGONOMETRY
	13.1 Fundamentals of Trigonometry	313
	Practice Exercise 13.1	320
	13.2 Trigonometric Functions	323
	Practice Exercise 13.2	327
	13.3 The Values of Trigonometric Functions	331
	Practice Exercise 13.3	334
	13.4 Fundamental Law of Trigonometry	344
	13.5 Trigonometric Ratios of Allied Angles	344
	13.6 Applications of Basic Identities	346
	Practice Exercise 13.4	349
	13.7 Half, Double and Triple Angle Identities	352
	Practice Exercise 13.5	354
14	Important Definitions	361
15	Paper Pattern and Guideline for Mid and Final Exam	373
16	Question Papers	374
17	References	382