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## 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 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 3

## 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