# CBSE Maths Syllabus Class 12 | CBSE Maths Syllabus for Class 12 2020-21 PDF

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## CBSE Maths Syllabus Class 12

COURSE STRUCTURE CLASS-XII (2020-21)

 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 andonto
functions, composite functions, inverse of a function.

2. Inverse Trigonometric Functions 15 Periods

Definition, range, domain, principal value branch. Graphs of inversetrigonometric
functionsElementary properties of inverse trigonometricfunctions.

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.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).

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. 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.

Prescribed Books:

• Mathematics Part I – Textbook for Class XII, NCERT Publication
• Mathematics Part II – Textbook for Class XII, NCERT Publication

MATHEMATICS (Code No. – 041) QUESTION PAPER DESIGN CLASS – XII (2020 – 21)

Time : 3 Hours Max. Marks: 80

 S. No. Typology of Questions Total Marks % Weightage (approx.) 1 Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas 44 55 2 Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way 20 25 3 Analysing: Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions 16 20 Total 80 100

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 form of questions and typology of questions same.

Choice(s):

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 Mathematics Activities 10

Note: For activities NCERT Lab Manual may be referred

### CBSE Mathematics Syllabus for Class 12 2020-21 PDF

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 test must have questions items with a balance mix,
assess the knowledge, understanding, application, skills, analysis, evaluation and
synthesis. Depending on the nature of 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-papertest.

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 pertheir
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

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 levelof
learning that has taken place during different periods. Feedback will help parents
formulate interventions (conducive ambience, support materials, motivation and moraleboosting) to further enhance learning. A teacher, while sharing the feedback with
student or parent, should be empathetic, non- judgmental and motivating. It is
recommended that the teacher share best examples/performances of IA with the class to motivate all learners.

Assessment of Activity Work:

Through out 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.html a record
of the same may be kept by the student.Anyear end test on the activity may be
conducted

The weightage are as under:

• The activities performed by the student through out the year and record keeping: 5 marks
• Assessment of the activity performed during the year end test: 3 marks
• Viva-voce : 2 marks

Conclusion

So, these were the CBSE Maths Syllabus Class 12 | CBSE Maths Syllabus for Class 12 2020-21 PDF. If I forgot any book please mention it in the comment section, I will add it.