Class 12 Maths 2022-23 Syllabus

DEEPR@$ September 25, 2022

Syllabus

CBSE Revised Syllabus for Clas...

A syllabus is basically a tool to plan a course within a stipulated time. It not only gives an idea about the goal and objective of the course but also helps to prepare oneself beforehand and develop concepts and confidence thereby. You might be looking for a platform where you can get the Syllabus for CBSE Class 12 Maths 2022-23. The Central Board of Secondary Education (CBSE) has announced a subject-by-subject new CBSE Syllabus 2022-2023 for 9th, 10th, 11th, and 12th grades, which will be used for the CBSE Academic Session 2022-2023.

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. Oncommutativity 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).

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.

CBSE Class 12 Maths Syllabus - Free PDF Download

Is this page helpful?

A syllabus is basically a tool to plan a course within a stipulated time. It not only gives an idea about the goal and objective of the course but also helps to prepare oneself beforehand and develop concepts and confidence thereby. You might be looking for a platform where you can get the Syllabus for CBSE Class 12 Maths 2022-23. The Central Board of Secondary Education (CBSE) has announced a subject-by-subject new CBSE Syllabus 2022-2023 for 9th, 10th, 11th, and 12th grades, which will be used for the CBSE Academic Session 2022-2023.

CBSE Class 12 Maths Revised Syllabus 2022-23

Si. No.	Unit Name	Marks
I	Relations and Functions	08
II	Algebra	10
III	Calculus	35
IV	Vectors and Three - Dimensional Geometry	14
V	Linear Programming	05
VI	Probability	08
	Internal Assessment	20
	TOTAL	100

Unit-I: Relations & Functions

1. Relations & 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

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 inverse trigonometric functions, like sin−1 𝑥 , cos−1 𝑥 and tan−1 𝑥, 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 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 reallife 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.

$\begin{aligned} \int \frac{d x}{x^{2} \pm a^{2}}, \int \frac{d x}{\sqrt{x^{2} \pm a^{2}}}, \int \frac{d x}{\sqrt{a^{2} - x^{2}}}, \int \frac{d x}{a x^{2} + b x + c}, \int \frac{d x}{\sqrt{a x^{2} + b x + c}} \\ \int \frac{p x + q}{a x^{2} + b x + c} d x, \int \frac{p x + q}{\sqrt{a x^{2} + b x + c}} d x, \int \sqrt{a^{2} \pm x^{2}} d x, \int \sqrt{x^{2} - a^{2}} d x \\ \int \sqrt{a x^{2} + b x + c} d x \end{aligned}$

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

4. Applications of 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:

$\frac{d y}{d x} + p y = q$ , where p and q are functions of x or constants.

$\frac{d y}{d x} + p x = q$ , where p and q are functions of x or constants.

Unit-IV: Vectors and Three-Dimensional Geometry

1. 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.

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 random variable.

Conclusion

Research has been done by the Vedantu’s ‘syllabus setters’ inboard to facilitate students to learn and prepare themselves for the future world of science and technology. Students can study the math syllabus in detail where they can know their weak and strong areas and devote the time accordingly.

Class 12 Maths 2022-23 Syllabus

CBSE Class 12 Maths Syllabus - Free PDF Download