The CBSE designs the syllabus for class 12^{th} Mathematics in a well-structured manner so as to cover all the important topics not just for board exams but for competitive exams as well. It is therefore crucial to check for the syllabus carefully and then prepare accordingly for the exam. The board exam will be conducted in single term, there will be no term 1 and term 2 exam in 2024. Candidates can check the in-depth CBSE Class 12 Maths Syllabus 2024-25 from this article below.

**Number of paper: One paper****Total period: 240 period****Marks: 80 marks**

**CBSE Class 12 Maths Paper Format 2024-25**

- Relations and Functions: 30 period (8 marks)
- Algebra: 50 period (10 marks)
- Calculus: 80 period (35 marks)
- Vectors and Three – Dimensional Geometry: 30 period (14 marks)
- Linear Programming: 20 period (5 marks)
- Probability: 30 period (8 marks)

**CBSE Class 12 Mathematics Syllabus 2024-25 **

The details of unit, periods given to finish them and the marks they will carry in the board examinations have been provided in the table below.

Unit-I: Relations and Functions

1. Relations and Functions 15 Periods

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

2. Inverse Trigonometric Functions 15 Periods

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

Unit-II: Algebra

1. Matrices 25 Periods

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. On-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 25 Periods

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 20 Periods

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, ππππ sinβ1 π₯ , cosβ1 π₯ and tanβ1 π₯, 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 10 Periods

Applications of derivatives: rate of change of bodies, 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 20 Periods

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.

4. Applications of the Integrals 15 Periods

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

5. Differential Equations 15 Periods

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:

Unit-IV: Vectors and Three-Dimensional Geometry

1. Vectors 15 Periods

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.

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2. Three – dimensional Geometry 15 Periods

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-V: Linear Programming

1. Linear Programming 20 Periods

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 30 Periods

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

**INTERNAL ASSESSMENT **

- Periodic Tests ( Best 2 out of 3 tests conducted): 10 marks
- Mathematics Activities: 10 marks

**List of Recommended Books**

Here is the list of prescribed books for Mathematics:

1) Mathematics Textbook for Class XI, NCERT Publications

2) Mathematics Part I – Textbook for Class XII, NCERT Publication

3) Mathematics Part II – Textbook for Class XII, NCERT Publication

4) Mathematics Exemplar Problem for Class XI, Published by NCERT

5) Mathematics Exemplar Problem for Class XII, Published by NCERT

6) Mathematics Lab Manual class XI, published by NCERT

7) Mathematics Lab Manual class XII, published by NCERT

**Check Maths syllabus class 12 CBSE 2024**: Download

**Also Check**

**CBSE Class 12th Syllabus (All Subjects)**

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