# West Bengal Board Class 12 Mathematics Syllabus 2022-23

#### We​st Bengal Board (WBBSE & WBCHSE)

Mathematics is named as universal language. An equation or an expression written using notation are often read and understood by anyone across the world. West Bengal Council of upper education announced the Syllabus 2022-23 for sophistication 12th. Candidates can check their Syllabus through wbchse.nic.in. WBCHSE conducting HS Board Exam for state and personal schools.

West Bengal Board Class 12 Maths Syllabus is prescribed by the West Bengal Council of upper education, commonly called as WBCHSE. The board was formed during the year 1975 and focuses on establishing quality higher education within the state of West Bengal.

## Download WBCHSE Class 12 Mathematics Syllabus

Students can get the detailed syllabus of West Bengal Board Class 12 Mathematics provided in the table below:

Unit wise Mark​s Distribution

 Unit Name Marks Unit I: Relations and Functions 08 Unit II: Algebra 11 Unit III: Calculus 36 Unit IV: Three-Dimensional Geometry 13 Unit V: Linear Programming 04 Unit VI: Probability 08 Total 80

### West Bengal Board Class 12 Mathematics Syllabus 2022-23 #### UNIT-I: RELATIONS AND FUNCTIONS

• Relations and Functions: Types of relations: reflexive, symmetric, transitive, and equivalence relations. One to one and onto functions, composite functions, the inverse of a function. Binary operations.
• Inverse Trigonometric Functions: Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

#### UNIT-II: ALGEBRA

• Matrices: Concept, notation, order, equality, types of matrices, zero matrices, transpose of a matrix, symmetric and skew-symmetric matrices. Addition, multiplication, and scalar multiplication of matrices, simple properties of addition, multiplication, and scalar multiplication
• Determinants: Determinants 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 several solutions of the system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using the inverse of a matrix. Cramer’s Rule and its applications.

#### UNIT-III: CALCULUS

• Continuity and Differentiability: Continuity and differentiability, a derivative of composite functions, chain rule, derivates of inverse trigonometric functions, a derivate of implicit functions, the concept of exponential and logarithmic functions to the base e. Logarithmic functions as inverse of exponential functions.
• Applications of derivatives: rate of change, increasing/decreasing functions, tangents, normals, approximation, maxima and minima, and Simple problems.
• Integrals: Integration is the inverse process of differentiation. Integration of various functions by substitution, partial fractions, and parts, only simple integrals of the type to be evaluated.Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
• Applications of the Integrals: Applications in finding the area under simple curves, especially lines, areas of circles/parabolas/ ellipses (in standard form only), Area under the curve y=sin x, y=cos x, and Area between the two above said curves (the region should be identifiable).
• Differential Equations: Definition, order, and degree, general and particular differential equation solutions. Formation of differential equation whose general solution is given. Solution of differential equations by separating variables, homogeneous, differential equations of the first order and first degree.

#### UNIT-IV: THREE-DIMENSIONAL GEOMETRY

• Vectors: Types of vectors (equal, unit, zero, parallel and collinear vectors), Position vector of a point, negative of a vector, 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. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors.
• Three-dimensional Geometry: Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between (i) two lines, (ii) two planes, and (iii) a line and a plane. Distance of a point from a plane.

#### UNIT-V: LINEAR PROGRAMMING

• Linear Programming: Introduction, the definition of related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions.

#### UNIT-VI: PROBABILITY

Multiplication theorem on probability Conditional probability, independent events, total probability, Baye’s theorem, mean and variance of a random variable. Repeated independent (Bernoulli) trials.