Syllabus

In 2020-2021 CBSE declared new syllabus that is:-

                                                                   

                                       CLASS-XII                           

                                                                                         

No.	Units	No. of Periods	Marks
I.	Relations and Functions	17	08
II.	Algebra	35	10
III.	Calculus	57	35
IV.	Vectors and Three - Dimensional Geometry	26	14
V.	Linear Programming	13	05
VI.	Probability	20	08
	Total	168	80
	Internal Assessment		20

Unit-I: Relations and Functions

1. Relations and 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.

Unit-II: Algebra

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, Invertible matrices; (Here all matrices will have real entries).

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. 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, derivative of composite functions,

 chain rule, derivative of inverse trigonometric functions, 

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: 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 real-life 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.

 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, parabolas; area of circles /ellipses (in standard form only) (the region should be clearly identifiable)

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 of the type: dy/dx = 𝑓(y/x). Solutions of linear differential equation of the type: 

     

Unit-IV: Vectors and Three-Dimensional Geometry

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.

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. Distance of a point from a plane.

                      

Unit-V: Linear Programming

1.Linear Programming            

Introduction, 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 (bounded), 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.      

  
  You can also download Pdf of the syllabus from this link:-
  http://cbseacademic.nic.in/web_material/CurriculumMain21/revisedsyllabi/SrSecondary/REVISEDMathematics_Sr.Sec_2020-21.pdf


According to the latest update, CBSE reduced 30% syllabus deleted syllabus is 

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