CBSE Class 12 Maths Revised Syllabus for the academic session 2022-2023 is provided here in PDF for the students to download. Students must go through this rationalized syllabus to know the prescribed course material for the current session and understand the exam plan. CBSE Class 12 Maths Syllabus 2022-2023 is as per the Annual Assessment Scheme which mentions the syllabus structure to prepare the students for the annual board exams.

Check below CBSE Class 12 Maths Syllabus 2022-23:

Course Structure:

a paper

Maximum Marks: 80

 No. units number of periods scar I relationships and tasks 30 08 Second algebra 50 10 third Calculation 80 35 IV vector and three-dimensional geometry 30 14 V linear programming 20 05 Sixth Possibility 30 08 gross 240 80 internal assessment 20

## Unit-I: Relationships and Functions

1. Relationships and Actions (15 Periods)

Types of relations: reflex, symmetric, transitive and equivalence relations. on one to one more tasks.

2. Inverse Trigonometric Functions (15 Periods)

Definition, category, domain, key value branch. Graphs of inverse trigonometric functions.

## Unit-II: Algebra

1. Matrix (25 Periods)

Concept, notation, order, similarity, types of matrices, zero and identity matrices, transpose of a matrix, symmetric and diagonally symmetric matrices. Operations on Matrices: Addition and Multiplication and Multiplication with a Scalar. Simple properties of addition, multiplication and scalar multiplication. Permutation of multiplication of matrices and existence of non-zero matrices whose product is a zero matrix (limited to square matrices of order 2). Inverse matrix and proof of uniqueness of the inverse, if it exists; (Here all matrices will have actual entries).

2. Determinant 25 Periods

Determinants of a square matrix (up to 3 x 3 matrix), minor, co-factors and application of determinants in finding the area of ​​a triangle. Addition and inverse of a square matrix. Solving systems of linear equations in two or three variables (having unique solutions) using the inverse of a matrix, for example, consistency, inconsistency, and number of solutions of a system of linear equations.

## Unit-III: Calculus

1. Continuity and Variation (20 Periods)

Continuity and Differentiation, Series Rule, Derivation of Inverse Trigonometric Functions, sin-1 cursing-1 and body-1 , the derivative of the 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. Application of Derivatives (10 Periods)

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and minima (first derivative test is geometrically motivated and second derivative test given as a proven tool). Simple problems (which reflect basic principles and understanding of the subject as well as real life situations).

3. Integral (20 periods)

Integration as an inverse process of differentiation. Substitution of functions of different types, integration by partial fractions and parts, evaluation of simple integrals of the following types and problems based on them.

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

4. Applications of Integrals (15 Periods)

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

5. Differential Equations (15 Periods)

Definition, order and degree, general and special solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of first order and first order homogeneous differential equations. Solutions of Linear Differential Equations of Type: ## Unit-IV: Vector and Three Dimensional Geometry

1. Vectors (15 periods)

Vector and scalar, magnitude and direction of a vector. Direction cosine and direction ratio of a vector. Types of vectors (equal, unit, zero, parallel and collinear vector), Position vector of a point, Negative of a vector, Components of a vector, Sum of vectors, Multiplication of a vector by a scalar, Position vector of a point division A line segment in a given ratio. Definition, geometric interpretation, properties and applications of scalar (dot) product of vectors, vector (cross) product of vectors.

2. Three-dimensional Geometry (15 Periods)

Direction cosine and direction ratio of the line joining two points. Cartesian equation and vector equation of a line, diagonal lines, shortest distance between two lines. The angle between two lines.

## Unit-V: Linear Programming

1. Linear Programming (20 Periods)

Introduction, related terminology such as constraints, objective functions, optimizations, graphical method of solving problems in two variables, feasible and inexact fields (bounded or infinite), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

## Unit-VI: Probability

1. Probability 30 (period)

Conditional Probability, Multiplication Theorem on Probability, Independent Events, Total Probability, Bayes Theorem, Random Variables and its Probability Distribution, Mean of Random Variables.

## CBSE Class 12 Maths Question Paper Design (Code No. 041) 2022-2023: 1. No chapter wise weightage. Care should be taken to cover all the chapters

2. Appropriate internal changes may be made to prepare different templates keeping in mind the overall importance of different types of questions and typology of questions.

Choice (Options): There will be no composite option in the question paper. However, 33% internal choices will be given in all sections.

Note: NCERT Lab Manual can be referred for activities.

## Internal Assessment – 20 Marks

• Periodic Tests (Best 2 out of 3 tests taken) 10 Marks
• Maths Activities 10 Marks

Conducting periodic tests:

Periodic test is a pen and paper evaluation which is to be conducted by the concerned subject teacher. To effectively assess knowledge, understanding, application, skills, analysis, assessment, the format of periodic test should contain question items with a balance mix, such as Very Short Answer (VSA), Short Answer (SA) and Long Answer (LA) and synthesis. The subject teacher will be at liberty to include other types of questions depending on the nature of the subject. The modalities of PT are as follows:

a) Mode: Periodic Examination is to be taken in the form of Pen-Paper Test.

b) Schedule: Throughout the academic year, three periodic tests in each subject may be conducted as follows: This is a suggestive program only and schools may conduct tests from time to time as per their convenience. Winter bound schools will develop their own schedule with equal time intervals between two consecutive tests.

c) Average of marks: Once schools have completed conducting all three periodic tests, they will convert the weightage of each of the three tests to ten marks to identify the best two tests. The best two will be taken into account and the average of both will be taken as the final score for PT.

d) The school shall ensure simple documentation for record keeping of performance as suggested in the detailed circular no. Acad-05/2017.

e) Sharing of Feedback/Performance: Students’ achievement in each test should be shared with the students and their parents to give them an overview of the level of learning achieved during different periods. Feedback will help parents to design interventions (conducive environment, support material, motivation and morale boosting) to further enhance learning. When sharing feedback with a teacher, student or parent, one should be empathetic, non-judgmental and persuasive. It is recommended that teachers share the best examples/demonstration of IA with the class to inspire all learning.

During the year any 10 activities will be performed by the student for the respective class (XI or XII) from the activities given in the NCERT Laboratory Manual which is available at the link: http://www.ncert.nic.in/exemplar /labmanuals.html A record of the same can be kept by the student. Testing may be conducted at the end of a year on the activity.

The weightage is as follows:

• Student activities and record keeping throughout the year : 5 marks
• Activity Assessment During Year End Examination: 3 Marks
• Viva-Voice: 2 Digits

## Prescribed Books:

• Mathematics Part I – Textbook for Class XII, NCERT Publications
• Mathematics Part II – Textbook for Class XII, NCERT Publications

ncert book for class 12 maths

NCERT Solutions for Class 12 Maths

NCERT Example Solutions for Class 12 Maths