1. Relations and Functions

 Content: This chapter covers the concept of relations and functions, types of relations (reflexive, symmetric, transitive, and equivalence), types of functions (one one, onto, etc.), and their composition and inverses.

 Objective: Understand the definitions, types, and properties of relations and functions. Learn how to compose functions and find the inverse of a function.

 2. Inverse Trigonometric Functions

 Content: Focuses on inverse trigonometric functions, their properties, and the principal values of inverse trigonometric functions.

 Objective: Gain knowledge about the domain, range, and principal values of inverse trigonometric functions. Use these functions to solve equations.

 3. Matrices

 Content: Introduction to matrices, their types, operations on matrices (addition, multiplication, and transpose), and the properties of these operations. Special types of matrices like the identity matrix are also discussed.

 Objective: Understand the types, properties, and operations of matrices. Learn how to solve matrix equations and use matrices in various mathematical applications.

 4. Determinants

 Content: This chapter covers the definition and properties of determinants, their evaluation, and the application of determinants to solve systems of linear equations using Cramer’s rule.

 Objective: Develop a thorough understanding of determinants and their properties, and learn to apply them in solving systems of equations.

 5. Continuity and Differentiability

 Content: Discusses the concepts of continuity, differentiability, the derivatives of various functions, and their applications. The chapter also introduces higher order derivatives and the chain rule.

 Objective: Learn how to check the continuity and differentiability of functions. Master the application of derivatives in solving various problems, including rate of change.

 6. Application of Derivatives

 Content: Focuses on the application of derivatives in finding the rate of change of quantities, tangents and normal to curves, increasing and decreasing functions, maxima and minima, and approximation.

 Objective: Understand the realworld applications of derivatives in determining the behavior of functions and solving optimization problems.

 7. Integrals

 Content: Covers the concept of integration as the inverse of differentiation, methods of integration, definite and indefinite integrals, and properties of definite integrals.

 Objective: Master techniques of integration and apply integrals in solving problems involving areas and volumes.

 8. Application of Integrals

 Content: Discusses the applications of integrals in finding areas under curves, areas between curves, and calculating volumes of solids of revolution.

 Objective: Learn how to use integrals to compute areas and volumes in different geometric contexts.

 9. Differential Equations

 Content: Introduces differential equations, their formation, order, and degree, along with methods for solving them. It covers general and particular solutions of differential equations.

 Objective: Understand how to form and solve differential equations, and apply them to model realworld phenomena.

 10. Vector Algebra

 Content: This chapter deals with vectors in three dimensional space, their addition, subtraction, and multiplication (scalar and vector products), and their properties.

 Objective: Develop a solid understanding of vector operations and their applications in physics and engineering.

 11. Three Dimensional Geometry

 Content: Focuses on the geometry of three dimensional space, including the equation of a line, plane, and the shortest distance between two lines and a point.

 Objective: Learn to solve geometrical problems involving lines, planes, and distances in three dimensional space.

 12. Linear Programming

 Content: Introduces the concept of linear programming, formulation of linear programming problems, and methods for solving them graphically.

 Objective: Learn how to formulate and solve optimization problems using linear programming techniques.

 13. Probability

 Content: This chapter explores the concept of conditional probability, the multiplication theorem, independent events, and Bayes' theorem. It also covers random variables and probability distributions, including the binomial distribution.

 Objective: Gain a deep understanding of probability theory and apply it in solving real world problems involving randomness and uncertainty.