1. Relations and Functions

    Content: This chapter covers types of relations and functions, inverse of functions, and composite functions. It also includes a detailed study of binary operations and equivalence relations.

    Objective: To help students understand and apply different types of relations and functions, their properties, and their importance in mathematics. Students learn how to work with functions analytically and algebraically.

 2. Algebra

    Content: This section focuses on various algebraic structures, including matrices, determinants, and their applications in solving systems of linear equations using Cramer’s Rule. It also covers complex numbers, quadratic equations, and sequences and series.

    Objective: To develop a strong foundation in advanced algebraic techniques and tools, such as matrices and determinants, and to enhance problem solving skills in algebraic equations.

 3. Calculus

    Content: This chapter is an introduction to calculus, covering limits, continuity, differentiation, and their applications. Topics like maxima and minima, tangent and normal to curves, and the Mean Value Theorem are also included.

    Objective: To equip students with the fundamental concepts of differentiation and its applications. It aims to develop a conceptual understanding of change and motion, which are central to physics and engineering.

 4. Probability

    Content: It covers the basic concepts of probability theory, including conditional probability, independent events, Bayes' Theorem, and random variables. It also delves into probability distributions such as binomial, Poisson, and normal distributions.

    Objective: To teach students how to calculate probabilities in various situations and apply probability theory to real life situations, particularly in statistics, economics, and sciences.

 5. Vectors

    Content: This chapter introduces vector quantities and operations on vectors, such as addition, scalar and vector products, and applications of vectors in geometry and physics.

    Objective: To help students understand vector algebra and its applications in three dimensional spaces, focusing on solving problems in physics and engineering contexts.

 6. Three Dimensional Geometry

    Content: It covers the geometry of three dimensional space, including the equation of lines and planes, the angle between two lines, and the shortest distance between skew lines. Topics like the intersection of lines and planes are also included.

    Objective: To enable students to visualize and solve geometrical problems in three dimensions, important for fields such as architecture, computer graphics, and physics.

 7. Application of Integral

    Content: This chapter deals with definite integrals and their applications in finding areas under curves, areas between curves, and volumes of solids of revolution. It also covers integration techniques.

    Objective: To teach students how to apply integration to solve practical problems related to geometry, engineering, and physics. Understanding these concepts is key to advanced mathematical modeling.

 8. Application of Calculus

    Content: It explores advanced applications of calculus in various fields, such as economics (cost functions, revenue functions), biology (growth rates), and physics (motion and forces).

    Objective: To extend the understanding of calculus to real world problems, fostering an appreciation of its utility across various domains of study.

 9. Linear Regression

    Content: This chapter focuses on statistical methods, including the concept of regression, fitting a linear regression model, and interpreting the slope and intercept of regression equations.

    Objective: To develop the ability to use regression techniques for data analysis and prediction, this is essential in fields like economics, biology, and machine learning.

 10. Linear Programming

    Content: It introduces linear programming concepts, including graphical and algebraic methods to solve linear optimization problems. It focuses on maximization and minimization of Objective functions subject to constraints.

    Objective: To enable students to model and solve optimization problems using linear programming techniques, useful in resource management, logistics, and operations research.