Algebra, Vector Algebra, Trigonometry

This chapter deals with functions. Ordered pairs, the definition of the Cartesian product, and relation are explained here. We will understand the types of functions and inverse function, and theorems. Real valued functions are described here.

This chapter talks about mathematical induction. Principles of mathematical induction and theorems are explained in detail here. We will also understand applications of mathematical induction and learn how to solve problems on divisibility.

This chapter provides knowledge of matrices. Types of matrices are described here. We will learn scalar multiple of matrix and multiplication of matrices, transpose of a matrix. It explains determinants, adjoint, and inverse and rank of a matrix.

This chapter describes the addition of vectors. A vector is a triad of real numbers. Some basic concepts and classification of vectors are discussed. We learn the sum and scalar multiplication of vectors and vector equations of line and plane.

This chapter describes the product of vectors. The scalar of two vectors, the dot product properties, and geometrical vector methods are explained here. The vector product of two vectors and the scalar triple product is learnt with solved problems.

This chapter highlights the sum and product transformations. It explains trigonometric ratios, variations, graphs, and periodicity. Trigonometric ratios of compound angles, multiple and submultiple angles are learnt here with some example problems.

This chapter provides knowledge of trigonometric equations. General solutions of trigonometric equations are described here in detail. Solved examples and illustrations are also provided for reference.

This chapter talks about inverse trigonometric functions. We will learn to reduce a trigonometric function into a bijective function. Graphs of these are explained here. We will also understand the properties of inverse trigonometric functions.

This chapter discusses the hyperbolic functions. Definitions of hyperbolic and inverse hyperbolic functions are given, and their respective graphs are illustrated. We will understand the addition formulas of hyperbolic functions.

This chapter discusses the properties of triangles. We will learn the relation between the sides and angles of a triangle. Projection rules such as sine, cosine, and tangent rules are given. We will also study the half-angle formula of a triangle.