SYLLABUS

**1. Set**

1.1 Introduction

1.2 Sets and their Representation

1.3 The Empty Se

1.4 Finite and Infinite Set

1.5 Equal Set

1.6 Subset

1.7 Power Set

1.8 Universal Set

1.9 Venn Diagrams

1.10 Operations on Sets

1.11 Complement of a Set

1.12 Practical Problems on Union and Intersection of Two Sets

**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

3.5 Trigonometric Equations

**4. Principle of Mathematical Induction**

4.1 Introduction

4.2 Motivation

4.3 The Principle of Mathematical Induction

**5. Complex Numbers and Quadratic Equations**

5.1 Introduction

5.2 Complex Numbers

5.3 Algebra of Complex Numbers

5.4 The Modulus and the Conjugate of a Complex Number

5.5 Argand Plane and Polar Representation

5.6 Quadratic Equations

**6. Linear Inequalities**

6.1 Introduction

6.2 Inequalities

6.3 Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation

6.4 Graphical Solution of Linear Inequalities in Two Variables

6.5 Solution of System of Linear Inequalities in Two Variables

**7. Permutations and Combinations**

7.1 Introduction

7.2 Fundamental Principle of Counting

7.3 Permutations

7.4 Combinations

**8. Binomial Theorem**

8.1 Introduction

8.2 Binomial Theorem for Positive Integral Indices

8.3 General and Middle Terms

**9. Sequences and Series**

9.1 Introduction

9.2 Sequences

9.3 Series

9.4 Arithmetic Progression (A.P.)

9.5 Geometric Progression (G.P.)

9.6 Relationship Between A.M. and G.M.

9.7 Sum to n terms of Special Series

**10. Straight Lines**

10.1 Introduction

10.2 Slope of a Line

10.3 Various Forms of the Equation of a Line

10.4 General Equation of a Line

10.5 Distance of a Point From a Line

**11. Conic Sections**

11.1 Introduction

11.2 Sections of a Cone

11.3 Circle

11.4 Parabola

11.5 Ellipse

11.6 Hyperbola

**12. Introduction to Three Dimensional Geometry**

12.1 Introduction

12.2 Coordinate Axes and Coordinate Planes in Three Dimensional Space

12.3 Coordinates of a Point in Space

12.4 Distance between Two Points

12.5 Section Formula

**13. Limits and Derivatives**

13.1 Introduction

13.2 Intuitive Idea of Derivatives

13.3 Limits

13.4 Limits of Trigonometric Functions

13.5 Derivatives

**14. Mathematical Reasoning**

14.1 Introduction

14.2 Statements

14.3 New Statements from Old

14.4 Special Words/Phrases

14.5 Implications

14.6 Validating Statements

**15. Statistics**

15.1 Introduction

15.2 Measures of Dispersion

15.3 Range

15.4 Mean Deviation

15.5 Variance and Standard Deviation

15.6 Analysis of Frequency Distributions

**16. Probability**

16.1 Introduction

16.2 Random Experiments

16.3 Event

16.4 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