 # Class 12 Syllabus

CBSE Class 12 Maths syllabus for the academic year 2022 – 2023 is given here for reference. Students can go through the following topic wise marking scheme and prepare for the final board examination.

## Course Structure for CBSE Class 12 Maths 2022 – 2023

Time Duration: Three Hours                                                               Max. Marks: 100

 Unit Topics Marks I. Relations and Functions 08 II. Algebra 10 III. Calculus 35 IV. Vectors and 3D Geometry 14 V. Linear Programming 05 VI. Probability 08 Internal Assessment 20 Total 100

## CBSE Class 12 Maths 2022 – 23 Syllabus

The following are the topics and sub topics covered for the class 12 Maths syllabus 2022 – 2023:

#### 1. Relations and Functions

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

#### 1. Matrices

• 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.
• Non Commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix.
• Invertible matrices and proof of the uniqueness of inverse.

#### 2. Determinants

• Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors 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 using inverse of a matrix.

#### 2. Applications of Derivatives

• Applications of derivatives: rate of change of bodies, increasing/decreasing functions.
• Use of derivatives in maxima and minima.

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

#### 4. Applications of the Integrals

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

#### 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 given type.

#### 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, scalar triple 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, coplanar and skew lines, shortest distance between two lines, Cartesian and vector equation of a plane.
• Angle between two lines.

#### Linear Programming

• Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming problems.
• Mathematical formulation of L.P. Problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

#### Probability

• Conditional probability, multiplication theorem on probability
• Independent events, total probability, Baye’s theorem, Random variable and its probability distribution, mean and variance of random variable.

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