1. Relations and Functions

• Introduction
• Types of Relations
• Types of Functions
• Composition of Functions and Invertible Function
• Binary Operations

2. Inverse Trigonometric Functions

• Introduction
•  Basic Concepts
•  Properties of Inverse Trigonometric Functions

3. Matrices

• Introduction
• Matrix
• Types of Matrices
• Operations on Matrices
• Transpose of a Matrix
• Symmetric and Skew Symmetric Matrices
• Elementary Operation (Transformation) of a Matrix
• Invertible Matrices

4. Determinants

• Introduction
• Determinant
• Properties of Determinants
• Area of a Triangle
• Minors and Cofactors
• Adjoint and Inverse of a Matrix
• Applications of Determinants and Matrices

5. Continuity and Differentiability

• Introduction
• Continuity
• Differentiability
• Exponential and Logarithmic Functions
• Logarithmic Differentiation
• Derivatives of Functions in Parametric Forms
• Second-Order Derivative
• Mean Value Theorem

6. Application of Derivatives

• Introduction
• Rate of Change of Quantities
• Increasing and Decreasing Functions
• Tangents and Normals
• Approximations
• Maxima and Minima

7. Integrals

• Introduction
• Integration as an Inverse Process of Differentiation
• Methods of Integration
• Integrals of some Particular Functions
• Integration by Partial Fractions
• Integration by Parts
• Definite Integral
• Fundamental Theorem of Calculus
• Evaluation of Definite Integrals by Substitution
• Some Properties of Definite Integrals

8. Application of Integrals

• Introduction
• Area under Simple Curves
• Area between Two Curves

9. Differential Equations

• Introduction
• Basic Concepts
• General and Particular Solutions of a Differential Equation
• Formation of a Differential Equation whose General Solution is given
• Methods of Solving First Order, First Degree Differential Equations

10. Vector Algebra

• Introduction
• Some Basic Concepts
• Types of Vectors
• Addition of Vectors
• Multiplication of a Vector by a Scalar
• Product of Two Vectors

11. Three Dimensional Geometry

• Introduction
• Direction Cosines and Direction Ratios of a Line
• Equation of a Line in Space
• Angle between Two Lines
• Shortest Distance between Two Lines
• Plane
• Coplanarity of Two Lines
• Angle between Two Planes
• Distance of a Point from a Plane
• Angle between a Line and a Plane

12. Linear Programming

• Introduction
• Linear Programming Problem and its Mathematical Formulation
• Different Types of Linear Programming Problems

13. Probability

• Introduction
• Conditional Probability
• Multiplication Theorem on Probability
• Independent Events
• Bayes' Theorem
• Random Variables and its Probability Distributions
• Bernoulli Trials and Binomial Distribution