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CBSE Class 12 Maths Syllabus 2020-21: Download PDF

Check the latest CBSE Class 12 Maths Syllabus 2020-21 and download it in PDF format. This syllabus has been recently released by the Central Board of Secondary Education (CBSE).

Apr 21, 2020 10:55 IST
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CBSE Syllabus 2020-21 for Class 12 Maths
CBSE Syllabus 2020-21 for Class 12 Maths

Download CBSE 12th Maths Syllabus 2020-21 in PDF format. Link to download CBSE Syllabus for Class 12 Maths 2020-21 is given at the end of this article. Links to download NCERT Textbook, Exemplar and Lab Manual is also available at the end of this article.

CBSE Class 12 Maths Syllabus 2020-21:

Unit Name

Number of Periods

Marks

I. Relations and Functions

30

8

II. Algebra

50

10

III. Calculus

80

35

IV. Vectors & 3 - Dimensional Geometry

30

14

V. Linear Programming

20

05

VI. Probability

30

08

Total

240

80

Internal Assessment

 

20

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, inverse of a function.

Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functionsElementary properties of inverse trigonometric functions.

Unit-II: Algebra

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 (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Determinants

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, 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

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. Rolle’s and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.

Applications of Derivatives

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, 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).

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.

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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, circles/ parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).

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 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:

(dy/dx) + py = q, where p and q are functions of x or constants.

(dx/dy) + px = q, where p and q are functions of y or constants.

Unit-IV: Vectors and Three-Dimensional Geometry

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.

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 (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

Unit-V: Linear Programming

Linear Programming

Introduction, 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 (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit-VI: Probability

Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Binomial probability distribution.

Prescribed Books:

- Mathematics Part I - Textbook for Class XII, NCERT Publication

- Mathematics Part II - Textbook for Class XII, NCERT Publication

- Mathematics Exemplar Problem for Class XII, Published by NCERT

- Mathematics Lab Manual class XII, published by NCERT

For details about question paper design and internal assessment, download CBSE Class 12 Maths Syllabus 2020-21.

Download CBSE Class 12 Maths Syllabus 2020-21

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