CBSE Class 12 Maths Syllabus 2026-27

Mathematics Subject Code – 041 Class XII (2026 – 27)

The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. Senior Secondary stage is a launching stage from where the students go either for higher academic education in Mathematics or for professional courses like Engineering, Physical and Biological science, Commerce or Computer Applications. The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students. Motivating the topics from real life situations and other subject areas, greater emphasis has been laid on application of various concepts.

Objectives

The broad objectives of teaching Mathematics at senior school stage intend to help the students:

<math>\bullet</math> to acquire knowledge and critical understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles, symbols and mastery of underlying processes and skills.

<math>\bullet</math> to feel the flow of reasons while proving a result or solving a problem.

<math>\bullet</math> to apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method.

<math>\bullet</math> to develop positive attitude to think, analyze and articulate logically.

<math>\bullet</math> to develop interest in the subject by participating in related competitions.

• to acquaint students with different aspects of Mathematics used in daily life.

<math>\bullet</math> to develop an interest in students to study Mathematics as a discipline.

<math>\blacktriangle</math> to develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of gender biases.

<math>\bullet</math> to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics.

COURSE STRUCTURE

CLASS - XII

<math>(2025-26)</math>

Max. Marks: 80

One Paper

No. Units Marks

• ١. Relations and Functions 80

1. Algebra 10
2. Calculus 35
3. ٧. Linear Programming 05
4. Probability 80 Total 80 Internal Assessment 20

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 (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).

2. 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-III: Calculus

1. Continuity and Differentiability

Continuity and differentiability, chain rule, derivative of composite functions, derivatives of inverse trigonometric functions like <math>\sin^{-1} x</math>, <math>\cos^{-1} x</math> and <math>\tan^{-1} x</math>, 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.

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 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.

<math>\int \frac{dx}{x^2 \pm a^2}</math>, <math>\int \frac{dx}{\sqrt{x^2 + a^2}}</math>, <math>\int \frac{dx}{\sqrt{a^2 - x^2}}</math>, <math>\int \frac{dx}{ax^2 + bx + c}</math>, <math>\int \frac{dx}{\sqrt{ax^2 + bx + c}}</math>, <math>\int \frac{px + q}{ax^2 + bx + c} dx</math>, <math display="block">\int \frac{px+q}{\sqrt{ax^2+bx+c}} dx, \int \sqrt{a^2\pm x^2} dx, \int \sqrt{x^2-a^2} dx, \int \sqrt{ax^2+bx+c} dx</math>

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

4. Application 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 equation of the type:

<math>\frac{dy}{dx} + py = q</math>, where p and q are functions of x or constants.

<math>\frac{dx}{dy} + px = q</math>, where <math>p</math> and <math>q</math> are functions of <math>y</math> or constants.

<u>Unit-IV: Vectors and Three-dimensional Geometry</u>

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. Angle between two lines.

<u>Unit-V: Linear Programming Problem</u>

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.