| Additional Questions for each Class with Solution | ||||||
|---|---|---|---|---|---|---|
| 6th | 7th | 8th | 9th | 10th | 11th | 12th |
Class 12th Mathematics Additional Questions
Chapter 1 Relations and Functions
This chapter introduces relations, functions, domain, range, and the types of functions including injective, surjective, and bijective.
Chapter 2 Inverse Trigonometric Functions
Students learn about the inverse of trigonometric functions and how to solve problems involving them.
Chapter 3 Matrices
This chapter covers the basic operations on matrices (addition, subtraction, multiplication), types of matrices, and the concept of matrix determinants.
Chapter 4 Determinants
The chapter focuses on calculating the determinant of a matrix and applying it to solve systems of linear equations.
Chapter 5 Continuity and Differentiability
This chapter introduces the concepts of continuity and differentiability, the properties of continuous and differentiable functions, and their application in calculus.
Chapter 6 Application of Derivatives
Students explore the use of derivatives to solve problems involving rates of change, tangents, normals, and motion.
Chapter 7 Integrals
This chapter introduces the integral concept, including methods of integration and the Fundamental Theorem of Calculus.
Chapter 8 Application of Integrals
Students apply integration to find areas under curves, volumes of solids of revolution, and solve real-world problems.
Chapter 9 Differential Equations
This chapter deals with the formation and solution of differential equations, both ordinary and partial differential equations, and their applications.
Chapter 10 Vector Algebra
Students learn about vector addition, scalar and vector products, and the application of vectors in geometry and physics.
Chapter 11 Three Dimensional Geometry
This chapter extends 2D geometry concepts into three dimensions, covering the distance formula, section formula, and the equations of lines and planes in 3D.
Chapter 12 Linear Programming
The chapter covers the optimization of linear functions subject to linear constraints and introduces graphical methods of solving linear programming problems.
Chapter 13 Probability
This chapter revises probability theory and extends it to advanced topics such as conditional probability, Bayes' theorem, and random variables.