CBSE Class 12 Maths Syllabus 2026-27, Download PDF

Unit-Wise Marks Distribution

Unit No.

Unit Name

Marks

I

Relations and Functions

08

II

Algebra

10

III

Calculus

35

IV

Vectors & Three-Dimensional Geometry

14

V

Linear Programming

05

VI

Probability

08

Total (Theory)

80

Internal Assessment

20

Maths Class 12 Syllabus Chapter Wise (Detailed Topics)

Unit No.

Unit Name

Key Topics Covered

Unit 1

Relations & Functions

Types of relations (reflexive, symmetric, transitive, equivalence), one-one and onto functions, inverse trigonometric functions (domain, range, principal values, graphs)

Unit 2

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: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non- commutativity of multiplication of matrices and existence of nonzero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Determinants: Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Unit 3 

Calculus

• Continuity & Differentiability: Continuity and differentiability, chain rule, derivative of composite functions, derivatives 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: rate of change of quantities, increasing/decreasing functions, maxima and minima, simple problems

• 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 following types and problems based on them, Fundamental Theorem of Calculus

• Applications of Integrals: area under curves

• Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree

Unit 4

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. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

Three-Dimensional Geometry

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines

Unit 5

Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit 6

Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem