# CBSE Syllabus 2021-22 for Class 12 Maths (New): CBSE Academic Session 2021-22

Mayank Uttam

- units & topics to be studied,

- unit-wise weightage in CBSE 12th Maths board exam 2022

- paper pattern

- internal assessment

Students should thoroughly study the new CBSE Class 12 Maths Syllabus 2021-22 and plan their studies accordingly.

New CBSE Class 12 Maths Syllabus 2021-22:

One Paper, Max Marks: 80

 No. Units No. of Periods Marks I. Relations and Functions 30 08 II. Algebra 50 10 III. Calculus 80 35 IV. Vectors and Three - Dimensional Geometry 30 14 V. Linear Programming 20 05 VI. Probability 30 08 Total 240 80 Internal Assessment 20

Unit-I: Relations and Functions

1. Relations and Functions (15 Periods)

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 (15 Periods)

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

Elementary properties of inverse trigonometric functions.

Unit-II: Algebra

1. Matrices (25 Periods)

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. On- 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).

2. Determinants  (25 Periods)

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

1. Continuity and Differentiability (20 Periods)

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.

2. Applications of Derivatives (10 Periods)

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).

3. Integrals (20 Periods)

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.

4. Applications of the Integrals (15 Periods)

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).

5. Differential Equations (15 Periods)

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

1. Vectors (15 Periods)

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.

2. Three - dimensional Geometry (15 Periods)

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

1. Linear Programming (20 Periods)

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

1. Probability (30 Periods)

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.

CBSE Class 12 Maths Paper Pattern 2021-22:

https://img.jagranjosh.com/images/2021/April/942021/cbse-12th-maths-paper-pattern-2021-22.jpg

1. No chapter wise weightage. Care to be taken to cover all the chapters.

2. Suitable internal variations may be made for generating various templates keeping the overall weightage to different forms of questions and typology of questions the same.

Choice(s):

There will be no overall choice in the question paper.

However, 33% internal choices will be given in all the sections.

There will be no overall choice in the question paper.

However, 33% internal choices will be given in all the sections

INTERNAL ASSESSMENT: 20 MARKS

⇒ Periodic Tests ( Best 2 out of 3 tests conducted): 10 Marks

⇒ Mathematics Activities: 10 Mark

Note: For activities NCERT Lab Manual may be referred.

Conduct of Periodic Tests:

Periodic Test is a Pen and Paper assessment which is to be conducted by the respective subject teacher. The format of periodic tests must have questions items with a balance mix, such as, very short answer (VSA), short answer (SA) and long answer (LA) to effectively assess  the  knowledge,  understanding,  application,  skills,  analysis,  evaluation  and synthesis. Depending on the nature of the subject, the subject teacher will have the liberty of incorporating any other types of questions too. The modalities of the PT are as follows:

a) Mode: The periodic test is to be taken in the form of pen-paper test.

b) Schedule: In the entire Academic Year, three Periodic Tests in each subject may be conducted as follows:

 Test Pre Mid-term (PT-I) Mid-Term (PT-II) Post Mid-Term (PT-III) Tentative Month July-August November December-January

This is only a suggestive schedule and schools may conduct periodic tests as per their convenience. The winter bound schools would develop their own schedule with similar time gaps between two consecutive tests.

c) Average of Marks: Once schools complete the conduct of all the three periodic tests, they will convert the weightage of each of the three tests into ten marks each for identifying best two tests. The best two will be taken into consideration and the average of the two shall be taken as the final marks for PT.

d) The  school will ensure simple documentation to keep  a  record of performance as suggested in detail circular no.Acad-05/2017.

e) Sharing of Feedback/Performance: The students’ achievement in each test must be shared with the students and their parents to give them an overview of the  level of learning that has taken place during different periods. Feedback will help parents formulate interventions (conducive ambience, support materials, motivation and morale - boosting)  to  further  enhance  learning.  A  teacher,  while  sharing  the  feedback  with a student or parent, should be empathetic, non- judgmental and motivating. It is recommended that the teacher share the best examples/performances of IA with the class to motivate all learners.

Assessment of Activity Work:

Throughout  the  year any 10 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. An year end test on the activity may be conducted

The weightage are as under:

· The activities performed by the student throughout the year and record keeping : 5 marks

· Assessment of the activity performed during the year end test: 3 marks

· Viva-voce : 2 marks

Prescribed Books:

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

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