**1. Relations and Functions**

1.1 Introduction

1.2 Types of Relations

1.3 Types of Functions

1.4 Composition of Functions and Invertible Function

1.5 Binary Operations

**2. Inverse Trigonometric Functions **

2.1 Introduction

2.2 Basic Concepts

2.3 Properties of Inverse Trigonometric Functions

**3. Matrices **

3.1 Introduction

3.2 Matrix

3.3 Types of Matrices

3.4 Operations on Matrices

3.5 Transpose of a Matrix

3.6 Symmetric and Skew Symmetric Matrices

3.7 Elementary Operation (Transformation) of a Matrix

3.8 Invertible Matrices

**4. Determinants**

4.1 Introduction

4.2 Determinant

4.3 Properties of Determinants

4.4 Area of a Triangle

4.5 Minors and Cofactors

4.6 Adjoint and Inverse of a Matrix

4.7 Applications of Determinants and Matrices

**5. Continuity and Differentiability**

5.1 Introduction

5.2 Continuity

5.3 Differentiability

5.4 Exponential and Logarithmic Functions

5.5 Logarithmic Differentiation

5.6 Derivatives of Functions in Parametric Forms

5.7 Second Order Derivative

5.8 Mean Value Theorem

**6. Application of Derivatives**

6.1 Introduction

6.2 Rate of Change of Quantities

6.3 Increasing and Decreasing Functions

6.4 Tangents and Normals

6.5 Approximations

6.6 Maxima and Minima

**Appendix 1: Proofs in Mathematics**

A.1.1 Introduction

A.1.2 What is a Proof?

**Appendix 2: Mathematical Modelling**

A.2.1 Introduction

A.2.2 Why Mathematical Modelling?

A.2.3 Principles of Mathematical Modelling