### CBSE Class 12th Syllabus Maths # CBSE Class 12 Syllabus Maths

CLASS-XII

MATHEMATICS (2021-22)

TERM – I

One Paper :90 minutes                                                             Max Marks: 40

 No. Units Marks I. Relations and Functions 08 II. Algebra 10 III. Calculus 17 V. Linear Programming 05 Total 40 Internal Assessment 10

Total : 50

## Unit-I: Relations and Functions

1. ### Relations and Functions

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

1. ### 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).

1. ### 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.

1. ### 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).

## 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).

 INTERNAL ASSESSMENT 10 MARKS Periodic Test 5 Marks Mathematics Activities: Activity file record +Term end assessment of one activity & Viva 5 Marks

TERM – II
Note: For activities NCERT Lab Manual may be referredOne Paper
Max Marks: 40

 No. Units Marks III. Calculus 18 IV. Vectors and Three-Dimensional Geometry 14 VI. Probability 8 Total 40 Internal Assessment 10

## Unit-III: Calculus

1. ### 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.
\$int frac{d x}{x^{2} pm a^{2}} int frac{d x}{sqrt{x^{2} pm a^{2}}}, intfrac{d x}{sqrt{a^{2}-x^{2}}}, int frac{d x}{a x^{2}+b x+c}, int frac{dx}{sqrt{a x^{2+b x+c}}}\$
\$int frac{p x+q}{a x^{2}+b x+c} d x, int frac{p x+q}{sqrt{a x^{2+} bx+c}} d x, int sqrt{a^{2} pm x^{2}} d x, quad int sqrt{x^{2}-a^{2}} d x\$
Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation  of definite integrals.

1. ### 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).

1. ### 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:\$frac{d y}{d x}=f(mathrm{y} / mathrm{x})\$ Solutions of linear differential equation of the type: \$frac{d y}{d x}+p y=q\$ where p and q are functions of x or constant.

## 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.

1. ### 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-VI: Probability

1. ### Probability

Conditional probability, multiplication theorem on probability, independent events, total probability,  Bayes’ theorem, Random variable and its probability distribution.

 INTERNAL ASSESSMENT 10 MARKS Periodic Test 5 Marks Mathematics Activities: Activity file record +Term end assessment of one activity & Viva 5 Marks

Note: For activities NCERT Lab Manual may be referred

Assessment of Activity Work:

In first term any 4 activities and in second term any 4 activities shall be performed by the student from the activities given in the NCERT Laboratory Manual for the respective class
(XI or XII) which is available on the link : http://www.ncert.nic.in/exemplar/labmanuals.htmla record of the same may be kept by the student. A term end test on the activity is to be conducted.
The weightage are as under:

1. The activities performed by the student in each term and record keeping : 3 marks
2. Assessment of the activity performed during the term end test and Viva-voce: 2 marks

Prescribed Books:

1. Mathematics Textbook for Class XI, NCERT Publications
2. Mathematics Part I – Textbook for Class XII, NCERT Publication
3. Mathematics Part II – Textbook for Class XII, NCERT Publication