# WBCHSE Class 12 Maths Syllabus

Mathematics is called as an interesting subject and students can refer to the West Bengal Board Class 12 Maths Syllabus to understand the concepts.Â An equation or an expression written using Mathematical notation can be read and understood by anyone across the globe. Thus, having and firm foundation in Mathematics will benefit the student to a greater extent in developing problem-solving skills, Mathematical modelling and also in understanding allied subjects. Students can refer to the WBCHSE Class 12 Maths Syllabus to get an overview of the topics and concepts taught in Class for the current academic year.

West Bengal board class 12 mathematics syllabus is prescribed by the West Bengal Council of Higher Secondary Education, commonly called as WBCHSE. The board was formed during the year 1975 and focuses on establishing quality higher secondary education in the state of West Bengal.

WBCHSE Class 12 Mathematics Syllabus enfolds diverse topics from Algebra, coordinate geometry, differential calculus, integral calculus, differential equations, application of calculus. The prime concepts studied here includes – Probability, principle mathematical induction, Binomial theorem for a positive integral index, infinite series, matrices and determinants, cones, parabola, elipse, hyperbola, differential calculus, indefinite integral, integration by parts, definite integral, differential equations, Tangent and normal, maxima and minima, determination of areas in simple cases, expression for velocity and acceleration etc.

### Unitwise Marks Distribution From 2021-22 Syllabus

 Unit Name Marks Unit I: Relations and Functions* 08 Unit II: Algebra* 11 Unit III: Calculus* 35 Unit IV: Three-Dimensional Geometry* 13 Unit V: Linear Programming 05 Unit VI: Probability* 08 Total 80

Students can get the detailed syllabus of WBCHSE Class 12 Mathematics provided in the table below:

Unit-1 : Relations and Function
1 . Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function
2. Inverse Trigonometric Functions
Definition.range , domain , principal value branches

Unit-II: Algebra
1 . Matrices:
Concept, notation order equality, types of matrices, zero matrix, transpose of a matrix and symmetric and skew symmetric matrices, Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. NonÂ­commutativity 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(Here all matrices will have real entries)
2. Determinants:
Determinants of a square matrix(upto 3×3 matrices), properties of determinants, minors and Cofactors 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 system of linear equations by examples, solving system of linear equations in two or three variables(having unique solutions) using inverse of a matrix.

Unit-Ill : Calculus
1.Continuity and Differentability:
Continuity and differentiability, derivative of composite functions ,chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions, concept of exponential and logarithmic functions to the base e . Logarithmic functions as inverse of exponential functions.
Derivatives of logarithmic and exponential functions . logarithmic, differentiation, derivative of function expressed in parametric forms. Second order derivatives.
2. Applications of derivatives:
Applications of derivatives, increasing/ decreasing functions, 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 a real time situation)
3. Integrals:
Integration as inverse process of differentiation. Integration of a variety of functions by substitution by partial fractions and by parts, only simple integrals of the type to be evaluated.
dx,dx
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 ,areas of circles/ parabola/ ellipse (in standard form only)
5 Differential Equations :
Definition , order and degree, general and particular solutions of a differential equation Formation of differential equation whose general solution is given.
Solution of differential equation by method of separation of variables, homogenius differential equation of first order and first degree.

UNIT-IV: Vectors and Three-Dimensional Geometry
1. Vectors:
Vectors and Scalars, magnitude and direction of a vector, Direction cosines/ ratios of vectors , 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 vectors by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar(dot) product of the vectors, projection of a vector on a line . Vector(cross) product of vectors.
. Thre-Dimensional Geometry :
Direction Cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines ,shortest distance between two lines. Cartesian and vector equation of a plane .Distance of a point from a plane.
UNIT-V: Linear Programming :
1. Linear Programming
Introduction, Definition of related terminology such as constraints,objective function, optimization, different types of linear programming(L.P.) problems, graphical method of solution for problems in two variables feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions( up to three non-trivial constraints).

UNIT-VI: Probability:
1. Probability :
Multiplication theorem on probability, Conditional probability, independent events, total probability, Bayes’ Theorem, Random variable and its probability distribution.

Some details of the syllabus were deleted for previous year syllabus, details are given below:

## WBCHSE Class 12 Deleted Portion of Mathematics Syllabus 2020-21

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