# CBSE Maths Syllabus Class 11 | CBSE Maths Syllabus for Class 11 2020-21 PDF

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## CBSE Maths Syllabus Class 11

COURSE STRUCTURE CLASS XI (2020-21)

Three Hours. Max Marks: 80

 No Units No. of Periods Marks I Sets and Functions 60 23 II Algebra 70 30 III Coordinate Geometry 40 10 IV Calculus 30 05 V Mathematical Reasoning 10 02 VI Statistics and Probability 30 10 Total 240 80 Internal Assessment 20

Unit-I: Sets and Functions

1. Sets (20) Periods

Sets and their representations.Empty set.Finite and Infinite sets.Equal sets.Subsets.Subsets of a
set of real numbers especially intervals (with notations). Power set. Universal set. Venn
diagrams. Union and Intersection of sets.Difference of sets. Complement of a set. Properties of
Complement.

2. Relations & Functions (20) Periods

Ordered pairs.Cartesian product of sets.Number of elements in the Cartesian product of two finite
sets.Cartesian product of the set of reals with itself (upto R x R x R).Definition of relation, pictorial
diagrams, domain, co-domain and range of a relation. Function as a special type of relation.
Pictorial representation of a function, domain, co-domain and range of a function. Real valued
functions, domain and range of these functions, constant, identity, polynomial, rational, modulus,
signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum,
difference, product and quotients of functions.

3. Trigonometric Functions (20) Periods

Positive and negative angles.Measuring angles in radians and in degrees and conversion from
one measure to another.Definition of trigonometric functions with the help of unit circle. Truth of
the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of
trigonometric functions and their graphs.Expressing sin (x±y) and cos (x±y) in terms of sinx, siny,
cosx&cosy and their simple applications. Deducing identities like the following:
tan(x ± y) = tan x ± tan y/1 ∓ tan x tan y , cot(x ± y) =cot x cot y ∓ 1/cot y ± cot x
sinα ± sinβ = 2sin1/2(α ± β)cos1/2(α ∓ β)
cosα + cosβ = 2cos1/2(α + β)cos1/2(α − β)
𝑐𝑜𝑠𝛼 − 𝑐𝑜𝑠𝛽 = −2𝑠𝑖𝑛1/2(𝛼 + 𝛽)𝑠𝑖𝑛1/2(𝛼 − 𝛽)

Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and tan3x. General solution of trigonometric
equations of the type siny = sina, cosy = cosa and tany = tana.

Unit-II: Algebra

1. Principle of Mathematical Induction (10) Periods

Process of the proof by induction, motivating the application of the method by looking at natural
numbers as the least inductive subset of real numbers.The principle of mathematical induction
and simple applications.

2. Complex Numbers and Quadratic Equations (15) Periods

Need for complex numbers, especially√−1, to be motivated by inability to solve some of the
quardratic equations. Algebraic properties of complex numbers.Argand plane and polar
representation of complex numbers.Statement of Fundamental Theorem of Algebra, solution of
quadratic equations (with real coefficients) in the complex number system.Square root of a
complex number.

3. Linear Inequalities (15) Periods

Linear inequalities.Algebraic solutions of linear inequalities in one variable and their
representation on the number line.Graphical solution of linear inequalities in two
variables.Graphical method of finding a solution of system of linear inequalities in two variables.

4. Permutations and Combinations (10) Periods

Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation
ofFormulae forn୮౨and nୡ౨and their connections, simple applications.

5. Binomial Theorem (10) Periods

Historical perspective, statement and proof of the binomial theorem for positive integral
indices.Pascal’s triangle, General and middle term in binomial expansion, simple applications.

6. Sequence and Series (10) Periods

Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric
Progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum,
geometric mean (G.M.), relation between A.M. and G.M. Formulae for the following special
sums.

Unit-III: Coordinate Geometry

1. Straight Lines (10) Periods

Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line
and angle between two lines. Various forms of equations of a line: parallel to axis, point -slope
form, slope-intercept form, two-point form, intercept form and normal form. General equation of a
line.Equation of family of lines passing through the point of intersection of two lines.Distance of a
point from a line.

2. Conic Sections (20) Periods

Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of
intersecting lines as a degenerated case of a conic section. Standard equations and simple
properties of parabola, ellipse and hyperbola.Standard equation of a circle.

3. Introduction to Three-dimensional Geometry (10) Periods

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance
between two points and section formula.

Unit-IV: Calculus

1. Limits and Derivatives (30) Periods

Derivative introduced as rate of change both as that of distance function and
geometrically.Intuitive idea of limit.Limits of polynomials and rational functions trigonometric,
exponential and logarithmic functions.Definition of derivative relate it to scope of tangent of the
curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial
and trigonometric functions.

Unit-V: Mathematical Reasoning

1. Mathematical Reasoning (10) Periods

Mathematically acceptable statements. Connecting words/ phrases – consolidating the
understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied
by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and
Mathema tics. Validating the statements involving the connecting words, difference among

Unit-VI: Statistics and Probability

1. Statistics (15) Periods

Measures of Dispersion: Range, Mean deviation, variance and standard deviation of
ungrouped/grouped data. Analysis of frequency distributions with equal means but different
variances.

2. Probability (15) Periods

Random experiments; outcomes, sample spaces (set representation). Events; occurrence of
events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set
theoretic) probability, connections with other theories of earlier classes. Probability of an event,
probability of ‘not’, ‘and’ and ‘or’ events.

MATHEMATICS QUESTION PAPER DESIGN CLASS – XI (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

Prescribed Books:

• Mathematics Textbook for Class XI, NCERT Publications
• CBSE Maths Syllabus Class 10

### CBSE Mathematics Syllabus for Class 11 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

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