| Classwise Concept with Examples | ||||||
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| 6th | 7th | 8th | 9th | 10th | 11th | 12th |
Class 12 Mathematics: Concepts and Examples
Chapter 1 Relations and Functions
This chapter explores different types of relations (reflexive, symmetric, transitive) and functions (one-to-one, onto, bijective). Students also study the composition of functions, the inverse of functions, and operations with functions.
Chapter 2 Inverse Trigonometric Functions
Students are introduced to the inverse of trigonometric functions. The chapter covers how to define and work with inverse trigonometric functions, along with their graphs and properties.
Chapter 3 Matrices
The chapter introduces matrices and their operations, including addition, subtraction, and multiplication. Students also study the concept of the determinant of a matrix and its applications in solving systems of linear equations.
Chapter 4 Determinants
This chapter explores the concept of determinants, their properties, and their applications in solving linear systems using Cramer's Rule. Students also learn about the calculation of the determinant for matrices of various orders.
Chapter 5 Continuity and Differentiability
Students learn about the concepts of continuity and differentiability of functions. The chapter covers theorems such as Rolle's Theorem and Mean Value Theorem, and their applications in solving problems related to rates of change and slopes of curves.
Chapter 6 Application of Derivatives
This chapter applies derivatives in real-world contexts. Students study concepts such as maxima and minima, tangents and normals, and the use of derivatives to solve optimization problems.
Chapter 7 Integrals
This chapter covers the basics of integration, including indefinite and definite integrals, integration techniques, and the fundamental theorem of calculus. Students learn to integrate functions and use integrals to find areas and volumes.
Chapter 8 Application of Integrals
Students apply integration to calculate the area between curves, volumes of solids of revolution, and other real-world problems. The chapter emphasizes the use of integrals in geometry and physics.
Chapter 9 Differential Equations
The chapter introduces differential equations, including first-order and second-order differential equations. Students learn methods to solve them and apply them in modeling physical situations such as motion and growth.
Chapter 10 Vector Algebra
This chapter introduces vectors and their properties, including addition, subtraction, scalar multiplication, and the dot and cross products. Students also learn how to apply vector algebra in geometry and physics.
Chapter 11 Three Dimensional Geometry
Students study three-dimensional space, focusing on the geometry of lines, planes, and distances in 3D. This chapter covers the equation of a plane, distance from a point to a plane, and the angle between lines and planes.
Chapter 12 Linear Programming
This chapter covers linear programming problems, including formulation, graphical solutions, and finding the optimal solution for problems involving constraints and objective functions.
Chapter 13 Probability
This chapter delves deeper into probability theory. Students study the probability of events, conditional probability, Bayes’ Theorem, and the application of probability in real-world situations like games of chance and statistics.