Class 12th Maths

The CBSE Class 12th Mathematics syllabus for the academic year 2024-25 covers a wide range of topics organized into six units. Here's a breakdown:
Unit 1: Relations and Functions
* Types of relations: reflexive, symmetric, transitive and equivalence relations.
* Functions: One to one and onto functions, composite functions, inverse of a function.
* Binary operations.
Unit 2: Algebra
* Matrices: Concepts of matrices, types of matrices, equality of matrices, transpose of a matrix, symmetric and skew symmetric matrices, elementary row and column operations, invertible matrices.
* Determinants: Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors, and applications of determinants in finding the area of a triangle, Adjoint and inverse of a square matrix, Solving system of linear equations (two or three variables) using inverse of a matrix.
Unit 3: Calculus
* Continuity and Differentiability: Continuity, differentiability, derivative of composite functions, chain rule, Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.
* Applications of Derivatives: Increasing/decreasing functions, tangents and normals, maxima/minima.
* Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the type -
* Applications of the Integrals: Finding areas under simple curves, especially lines, circles, parabolas and ellipses (standard forms only).
* Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables.
Unit 4: Vectors and Three-Dimensional Geometry
* Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio.
* Three - dimensional Geometry: Cartesian equation of a line, vector equation of a line, angle between (i) two lines, (ii) two planes. Distance of a point from a plane.
Unit 5: Linear Programming
* Introduction to Linear Programming, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible solutions.
Unit 6: Probability
* Conditional probability, multiplication theorem on probability.
* Independent events, total probability, Bayes' theorem, Binomial distribution.
Internal Assessment (20 Marks)
* Mathematics activities and projects.
Note: This is a general overview. For the most accurate and detailed information, please refer to the official CBSE website or the latest NCERT textbooks.