CBSE Syllabus for Class 12 Maths Academic year 2024-2025

Mathematics is the most scoring subject if you get an understanding of the CBSE Class 12 Maths Syllabus. Before we proceed with starting to learn a new chapter, we must thoroughly check and get to know the syllabus. This helps students to have clear insights on the topics and chapters present under several units of the subject. CBSE has suggested the NCERT textbooks should be the ideal one students must stick to score good in mathematics.

Students preparing for the approaching board examination must go through the Maths cbse class 12 syllabus provided below. Scroll down to look at the complete syllabus.

CBSE Class 12 Maths Syllabus

Unit-I: Relations and Functions

Relations and Functions

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.

Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Unit-II: Algebra

Matrices

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operations on matrices such as addition and multiplication, and multiplication with a scalar. Non Commutativity of multiplications, and non-zero matrix existence whose product is the zero matrix. Invertible matrices followed by proving the uniqueness of the inverse, in case it exists.

Determinants

Determinant of a square matrix: till 3*3, performing minors, cofactors and applications of determinants in calculating the triangle’s area. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of systems related to the linear equations with provided illustrations, solving the number of systems of linear equations with two or three variables carrying unique solutions using the inverse of a matrix.

Unit-III: Calculus

Continuity and Differentiability

Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions like sin-1 x, cos-1 x and tan-1 x, derivative of implicit functions. Concept of exponential and logarithmic functions.

Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

Applications of Derivatives

Applications of Derivatives consist of rate of change of quantities, their increasing/decreasing functions, followed by maxima and minima that is the first derivative test motivated geometrically followed by the second derivative test given as a provable tool. Simple problems showcasing the basic principles and application of the same in accordance with the real-life situations as well.

Integrals

Integration as an inverse process of differentiation. Integration of a variety of functions by substitution, including both by partial fractions and by parts, evaluating the simple form of integrals of the following types and questions based on them.

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

Applications of the Integrals

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

Differential Equations

The basic definition of the concept, its order and degree, followed by general and particular solutions of a differential equation. Solving the differential equations by using the method of separation of variables, also, solving the homogeneous differential equations of first order and first degree. The solutions of linear differential equation of the following types:

dy/dx + py = q, where p and q are functions of x or constants.

dx/dy + px = q, where p and q are functions of y or constants.

Unit-IV: Vectors and Three-Dimensional Geometry

Vectors

Definition of vectors and scalars, followed by magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Discussing various types of vectors such as equal, unit, zero, parallel and collinear vectors, addition of the vector, negative of a vector, position vector of a point, components of a vector, multiplication of a vector by a scalar, position vector of a point dividing a line segment with provided ratios. Introduction of topic of geometrical interpretation, its properties and application of scalar product of vectors, and product of vectors.

Three – dimensional Geometry

Introducing the direction cosines and direction ratios through detailed definition, followed by the ratios of a line joining two points. Cartesian equation, skew lines, shortest distance between two lines and angle between two lines.

Unit-V: Linear Programming

Linear Programming

Introducing the topic with basic definition, its related terminology including the constraints, objective function, optimization, graphical method approach for solving questions in two variables, feasible and infeasible regions: bounded or unbounded, the solutions of feasible and infeasible, and optimal feasible solutions up to three non-trivial constraints.

Unit-VI: Probability

Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.

CBSE Class 12 Maths Syllabus 2024-25 Chapter-Wise Topics & Weightage