The CBSE Board has prepared a uniform syllabus for 12th Class Mathematics subject which is followed throughout the country in all the schools affiliated with CBSE. The Board has designed the syllabus in a structured format so that students can enhance their mathematics aptitude. There are various chapters or parts in 12th class Mathematics like Algebra, Linear Programming, Relation and Functions, Vectors & Three Dimensional Geometry, Probability, and Calculus. The Mathematics paper is a 100 Marks paper where 20 Marks for internal assessment and the remaining 80 marks are assigned for the exam syllabus. Students must go through the prescribed CBSE Class 12 Mathematics Syllabus 2022-23 to prepare for the 12th board exams.
Table of Contents
CBSE Class 12 Mathematics Syllabus 2022
The examination pattern and syllabus details with regard to CBSE 12th Class Mathematics Subjects for the academic session 2022-23 have been provided below:
| Unit No. | Name of Units | No. Of 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 | 240 | 80 | |
| Internal Assessment | 20 |
Note: There will be only one paper on mathematics. Maximum marks of the paper will be 80 while 20 marks have been assigned to internal assessment.
CBSE 12th Class Maths Syllabus: Chapter Wise Details
Here students can check the detailed syllabus of the 12th class mathematics paper below:
Unit I: Relations and Functions
1. Relations and Functions (15 Periods)
Types of relations: transitive, equivalence, reflexive, and symmetric relations. One to one and onto functions, composite functions, the inverse of a function.
2. Inverse Trigonometric Functions (15 Periods)
Range, Definition, principal value branch and domain. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
Unit-II: Algebra
1. Matrices (25 Periods)
Order, concept, equality, notation, types of matrices, transpose of a matrix, zero and identity 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). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
2. Determinants (25 Periods)
Properties of determinants, determinants 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 the number of solutions of the system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using an inverse of a matrix.
Unit-III: Calculus
1. Continuity and Differentiability (20 Periods)
Continuity and differentiability, a derivative of inverse trigonometric functions, derivative of composite functions, derivative of implicit functions, chain rule. Concept of exponential and logarithmic functions.
Logarithmic differentiation, derivatives of logarithmic and exponential functions. Second-order derivatives. Derivative of functions expressed in parametric forms. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.
2. Applications of Derivatives (10 Periods)
Applications of derivatives: rate of change of bodies, increasing/decreasing functions, use of derivatives in approximation, tangents and normals, 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 an 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.
Basic properties of definite integrals and evaluation of definite integrals. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).
4. Applications of the Integrals (15 Periods)
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).
5. Differential Equations (15 Periods)
Definition, order, and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by the method of separation of variables, solutions of homogeneous differential equations of the first order and first degree.
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), negative of a vector, position vector of a point, components of a vector, the 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, the scalar triple product of vectors.
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, shortest distance between two lines, coplanar and skew lines. Cartesian and vector equation of a plane. The angle between (i) two planes, (ii) two lines, (iii) a line and a plane. Distance of a point from a plane.
Unit-V: Linear Programming
1. Linear Programming (20 Periods)
Introduction, objective function, optimization, related terminology such as constraints, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, feasible and infeasible regions (bounded or unbounded), graphical method of solution for problems in two variables, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
Unit-VI: Probability
1. Probability (30 Periods)
Conditional probability, total probability, independent events, multiplication theorem on probability, Bayes’ theorem, mean and variance of a random variable, Random variable, and its probability distribution. Binomial probability distribution.
CBSE 12th Mathematics Syllabus: Question Paper Design
Time: 3 Hours
Maximum Marks: 80
| S.No. | Typology of Questions | Total Marks | Weightage (%) |
| 1 |
Remembering: Exhibit memory of previously learned material by recalling facts, answers, terms, and basic concepts. Understanding: Demonstrate understanding of facts and ideas by organizing, translating, comparing, giving descriptions, interpreting, 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 |
Analyzing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations
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 |
Note: Cover all the chapters as there is no chapter-wise weightage. Suitable internal variations may be made for generating various templates keeping the overall weightage to various forms of questions and typology of questions same.
Choice (s):
There will be no overall choice in the question paper.
However, 33% of internal choices will be given in all the sections.
| Internal Assessment | 20 Marks |
| Periodic Tests (Best 2 out of 3 tests conducted) | 10 Marks |
| Mathematics Activities | 10 Marks |
CBSE 12th Class Syllabus 2022-23
CBSE 12th Mathematics: Prescribed Books
- Mathematics Textbook for Class XI, NCERT Publications
- Mathematics Part I – Textbook for Class XII, NCERT Publication
- Mathematics Part II – Textbook for Class XII, NCERT Publication
- Mathematics Exemplar Problem for Class XII, Published by NCERT
- Mathematics Lab Manual class XII, published by NCERT
CBSE 12th Class Mathematics Syllabus 2022: Download PDF Here
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