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1. Sets 1
1.1 Introduction 1
1.2 Sets and their Representations 1
1.3 The Empty Set 5
1.4 Finite and Infinite Sets 6
1.5 Equal Sets 7
1.6 Subsets 9
1.7 Power Set 12
1.8 Universal Set 12
1.9 Venn Diagrams 13
1.10 Operations on Sets 14
1.11 Complement of a Set 18
1.12 Practical Problems on Union and Intersection of Two Sets 21

2. Relations and Functions 30
2.1 Introduction 30
2.2 Cartesian Product of Sets 30
2.3 Relations 34
2.4 Functions 36

3. Trigonometric Functions 49
3.1 Introduction 49
3.2 Angles 49
3.3 Trigonometric Functions 55
3.4 Trigonometric Functions of Sum and Difference of Two Angles 63
3.5 Trigonometric Equations 74

4. Principle of Mathematical Induction 86
4.1 Introduction 86
4.2 Motivation 87
4.3 The Principle of Mathematical Induction 88

5. Complex Numbers and Quadratic Equations 97
5.1 Introduction 97
5.2 Complex Numbers 97
5.3 Algebra of Complex Numbers 98
5.4 The Modulus and the Conjugate of a Complex Number 102
5.5 Argand Plane and Polar Representation 104
5.6 Quadratic Equations 108


6. Linear Inequalities 116
6.1 Introduction 116
6.2 Inequalities 116
6.3 Algebraic Solutions of Linear Inequalities in One Variable
and their Graphical Representation 118
6.4 Graphical Solution of Linear Inequalities in Two Variables 123
6.5 Solution of System of Linear Inequalities in Two Variables 127


7. Permutations and Combinations 134
7.1 Introduction 134
7.2 Fundamental Principle of Counting 134
7.3 Permutations 138
7.4 Combinations 148


8. Binomial Theorem 160
8.1 Introduction 160
8.2 Binomial Theorem for Positive Integral Indices 160
8.3 General and Middle Terms 167


9. Sequences and Series 177
9.1 Introduction 177
9.2 Sequences 177
9.3 Series 179
9.4 Arithmetic Progression (A.P.) 181
9.5 Geometric Progression (G.P.) 186
9.6 Relationship Between A.M. and G.M. 191
9.7 Sum to n terms of Special Series 194


10. Straight Lines 203
10.1 Introduction 203
10.2 Slope of a Line 204
10.3 Various Forms of the Equation of a Line 212
10.4 General Equation of a Line 220
10.5 Distance of a Point From a Line 225


11. Conic Sections 236
11.1 Introduction 236
11.2 Sections of a Cone 236
11.3 Circle 239
11.4 Parabola 242
11.5 Ellipse 247
11.6 Hyperbola 255


12. Introduction to Three Dimensional Geometry 268
12.1 Introduction 268
12.2 Coordinate Axes and Coordinate Planes in
Three Dimensional Space 269
12.3 Coordinates of a Point in Space 269
12.4 Distance between Two Points 271
12.5 Section Formula 273


13. Limits and Derivatives 281
13.1 Introduction 281
13.2 Intuitive Idea of Derivatives 281
13.3 Limits 284
13.4 Limits of Trigonometric Functions 298
13.5 Derivatives 303


14. Mathematical Reasoning 321
14.1 Introduction 321
14.2 Statements 321
14.3 New Statements from Old 324
14.4 Special Words/Phrases 329
14.5 Implications 335
14.6 Validating Statements 339


15. Statistics 347
15.1 Introduction 347
15.2 Measures of Dispersion 349
15.3 Range 349
15.4 Mean Deviation 349
15.5 Variance and Standard Deviation 361
15.6 Analysis of Frequency Distributions 372



16. Probability 383
16.1 Introduction 383
16.2 Random Experiments 384
16.3 Event 387
16.4 Axiomatic Approach to Probability 394


Appendix 1: Infinite Series 412
A.1.1 Introduction 412
A.1.2 Binomial Theorem for any Index 412
A.1.3 Infinite Geometric Series 414
A.1.4 Exponential Series 416
A.1.5 Logarithmic Series 419


Appendix 2: Mathematical Modelling 421
A.2.1 Introduction 421
A.2.2 Preliminaries 421
A.2.3 What is Mathematical Modelling 425


Answers 433\


Supplementary Material 466