CBSE Class 12 Maths Syllabus 2026-27 with Marks Distribution Free PDF Download (Sign-in Required)

S.No.

Unit Name

Periods

Marks

I

Relations and Functions

30

08

II

Algebra

50

10

III

Calculus

80

35

IV

Vectors and Three-Dimensional Geometry

30

14

V

Linear Programming

20

05

VI

Probability

30

08

TOTAL

80

Internal Assessment

-

20

Units

Topics / Subtopics

Unit-I: Relations and Functions

1. Relations and Functions

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

2. Inverse Trigonometric Functions

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

Unit-II: Algebra

1. 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 non-zero matrices whose product is the zero matrix (restricted to square matrices of order 2). Invertible matrices and proof of the uniqueness of the inverse, if it exists (Here all matrices will have real entries).

2. Determinants

Determinants of a square matrix (up to 3 × 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 a system of linear equations by examples, solving a system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.

Unit-III: Calculus

1. Continuity and Differentiability

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, like sin⁻¹x, cos⁻¹x, tan⁻¹x, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation and derivative of functions expressed in parametric forms. Second-order derivatives.

2. Applications of Derivatives

Applications of Derivatives: rate of change of quantities, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

3. Integrals

Integration is the inverse process of differentiation. Integration of a variety of functions by substitution, partial fractions, and parts. Evaluation of simple integrals of the following types and problems based on them. 

∫ dx / (x² ± a²), ∫ dx / √(x² ± a²), ∫ dx / √(a² − x²), ∫ dx / (ax² + bx + c), ∫ dx / √(ax² + bx + c), ∫ (px + q) / (ax² + bx + c) dx, ∫ (px + q) / √(ax² + bx + c) dx, ∫ √(a² ± x²) dx, ∫ √(x² − a²) dx, ∫ √(ax² + bx + c) dx

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

4. Applications of the Integrals

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

5. 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. Solutions of linear differential equations of the type:

• 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

1. 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.

2. 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. The angle between two lines.

Unit-V: Linear Programming

1. 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-VI: Probability

1. Probability

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

S. No

Typology of Questions

Total Marks

% Weightage

1

Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organising, comparing, translating, interpreting, giving descriptions, and stating main ideas.

44

55%

2

Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques, and rules in a different way.

20

25%

3

Analysing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalisations. Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions.

16

20%

Total

80

100%

Component

Marks

Periodic Tests (Best 2 out of 3 tests conducted)

10 Marks

Mathematics Activities

10 Marks

Total

20 Marks

S.No.

Related Topic Pages for Class 12 Maths

1.

Class 12 Maths Trigonometric Formula

2.

Class 12 Maths Relations and Functions Formula

3.

Class 12 Maths Differentiation

S.No.

Related Study Materials Links for Class 12 Maths

1

CBSE Class 12 Maths NCERT Solutions

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CBSE Class 12 Maths Important Questions

3

CBSE Class 12 Maths Formulas

4

CBSE Class 12 Maths RD Sharma Solutions

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CBSE Class 12 Maths RS Aggarwal Solutions

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CBSE Class 12 Maths Sample Papers

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CBSE Class 12 Maths NCERT Exemplar Solutions

8

CBSE Class 12 Maths Previous Year Question Papers