Class 12 Math

This chapter revisits the concepts of relations and functions, introducing types of relations (reflexive, symmetric, transitive), types of functions (one-one, onto), the composition of functions, and the concept of an invertible function.

This chapter covers the definitions, domains, principal value branches, graphs, and properties of the inverse trigonometric functions. It also includes the summation of series and simplification of complex expressions involving these functions.

This chapter introduces matrices, their types, and various operations such as addition, multiplication, and transpose. It also covers the concepts of symmetric and skew-symmetric matrices, elementary row/column operations, and invertible matrices.

This chapter explores the concept of determinants for square matrices. It covers the evaluation of determinants up to order 3, calculating the area of a triangle, finding minors and cofactors, determining the adjoint and inverse of a matrix, and applying these concepts to solve systems of linear equations.

This chapter builds upon the concepts of limits and derivatives from Class 11. It provides a detailed study of continuity, differentiability, derivatives of various types of functions (implicit, inverse trigonometric, exponential, logarithmic), and introduces second-order derivatives and important mean value theorems.

This chapter explores the practical applications of derivatives in various fields. It covers calculating the rate of change of quantities, determining intervals where functions are strictly increasing or decreasing, and finding the local and absolute maxima and minima of functions to solve optimization problems.

This chapter introduces integration as the inverse process of differentiation. It covers various techniques for finding indefinite integrals, including substitution, partial fractions, and integration by parts. It then transitions to definite integrals, introducing the Fundamental Theorem of Calculus and the powerful properties of definite integrals used to evaluate complex areas and functions.

This chapter explores the practical geometric application of definite integrals. It focuses on finding the area of regions bounded by simple curves, lines, and the coordinate axes, extending the concepts learned in the previous chapter to visualize and calculate two-dimensional spaces.

This chapter introduces differential equations, their order and degree, and the difference between general and particular solutions. It covers various techniques for solving first-order, first-degree differential equations, including variable separable, homogeneous, and linear differential equations, which are essential for modeling real-world dynamic systems.

This chapter introduces the fundamental concepts of vectors and scalars. It covers vector representation, types of vectors, basic algebra (addition, scalar multiplication), and the products of vectors (dot/scalar product and cross/vector product) along with their geometric interpretations.

This chapter extends the concepts of vector algebra to three-dimensional space. It covers the direction cosines and ratios of lines, various forms of equations for lines and planes in space, and the geometric relationships between them, including angles, intersections, and shortest distances.

This chapter introduces the concept of Linear Programming Problems (LPP). It covers the mathematical formulation of LPPs, graphical methods for solving two-variable problems, and applications in real-life scenarios like diet, manufacturing, and transportation.

This chapter builds upon the basic concepts of probability to explore advanced topics like conditional probability, Bayes' Theorem, and probability distributions. It covers the mathematical framework for analyzing random experiments and making predictions under uncertainty, essential for both Board exams and competitive entrance tests like JEE.