1. Sets
1.1 Introduction
1.2 Sets and their Representations
1.3 The Empty Set
1.4 Finite and Infinite Sets
1.5 Equal Sets
1.6 Subsets
1.7 Universal Set
1.8 Venn Diagrams
1.9 Operations on Sets
1.10 Complement of a Set
2. Relations and Functions
2.1 Introduction
2.2 Cartesian Product of Sets
2.3 Relations
2.4 Functions
3. Trigonometric Functions
3.1 Introduction
3.2 Angles
3.3 Trigonometric Functions
3.4 Trigonometric Functions of Sum and Difference of Two Angles
4. Complex Numbers and Quadratic Equations
4.1 Introduction
4.2 Complex Numbers
4.3 Algebra of Complex Numbers
4.4 The Modulus and the Conjugate of a Complex Number
4.5 Argand Plane and Polar Representation
5. Linear Inequalities
5.1 Introduction
5.2 Inequalities
5.3 Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
6. Permutations and Combinations
6.1 Introduction
6.2 Fundamental Principle of Counting
6.3 Permutations
6.4 Combinations
7. Binomial Theorem
7.1 Introduction
7.2 Binomial Theorem for Positive Integral Indices
8. Sequences and Series
8.1 Introduction
8.2 Sequences
8.3 Series
8.4 Geometric Progression (G.P.)
8.5 Relationship Between A.M. and G.M
9. Straight Lines
9.1 Introduction
9.2 Slope of a Line
9.3 Various Forms of the Equation of a Line
9.4 Distance of a Point From a Line
10. Conic Sections
10.1 Introduction
10.2 Sections of a Cone
10.3 Circle
10.4 Parabola
10.5 Ellipse
10.6 Hyperbola
11. Introduction to Three Dimensional Geometry
11.1 Introduction
11.2 Coordinate Axes and Coordinate Planes in Three Dimensional Space
11.3 Coordinates of a Point in Space
11.4 Distance between Two Points
12. Limits and Derivatives
12.1 Introduction
12.2 Intuitive Idea of Derivatives
12.3 Limits
12.4 Limits of Trigonometric Functions
12.5 Derivatives
13. Statistics
13.1 Introduction
13.2 Measures of Dispersion
13.3 Range
13.4 Mean Deviation
13.5 Variance and Standard Deviation
14. Probability
14.1 Event
14.2 Axiomatic Approach to Probability
Appendix 1: Infinite Series
A.1.1 Introduction
A.1.2 Binomial Theorem for any Index
A.1.3 Infinite Geometric Series
A.1.4 Exponential Series
A.1.5 Logarithmic Series
Appendix 2: Mathematical Modelling
A.2.1 Introduction
A.2.2 Preliminaries
A.2.3 What is Mathematical Modelling