CBSE Class 12 Syllabus Maths

CLASS-XII 

 MATHEMATICS (2021-22) 

 TERM – I 

One Paper :90 minutes                                                             Max Marks: 40 

 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.

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).

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).

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

Total 50  

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.

2. 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).

3. 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.

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-VI: Probability 

1. Probability 

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

  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
4. Mathematics Exemplar Problem for Class XI, Published by NCERT
5. Mathematics Exemplar Problem for Class XII, Published by NCERT
6. Mathematics Lab Manual class XI, published by NCERT
7. Mathematics Lab Manual class XII, published by NCERT