Mathematics – Eduxir

CBSE Class 11 Mathematics Syllabus for academic session 2026-27

This page contains the CBSE Class 11 Mathematics syllabus for the academic session 2026-27, as prescribed by CBSE curriculum.

Buy CBSE Class 11 Mathematics Books

The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. Senior Secondary stage is a launching stage from where the students go either for higher academic education in Mathematics or for professional courses like Engineering, Physical and Biological science, Commerce or Computer Applications. The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students. Motivating the topics from real life situations and other subject areas, greater emphasis has been laid on application of various concepts.

Objectives

The broad objectives of teaching Mathematics at senior school stage intend to help the students:

•

to acquire knowledge and critical understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles, symbols and mastery of underlying processes and skills.

•

to feel the flow of reasons while proving a result or solving a problem.

•

to apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method.

•

to develop positive attitude to think, analyze and articulate logically.

•

to develop interest in the subject by participating in related competitions.

•

to acquaint students with different aspects of Mathematics used in daily life.

•

to develop an interest in students to study Mathematics as a discipline.

•

to develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of gender biases.

•

to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics.

COURSE STRUCTURE

Three Hours

Max Marks: 80

No.

Units

Marks

Sets and Functions

II.

Algebra

III.

Coordinate Geometry

IV.

Calculus

Statistics and Probability

Total

Internal Assessment

*No chapter/unit-wise weightage. Care to be taken to cover all the chapters.

Unit-I: Sets and Functions

1. Sets

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

2. Relations & Functions

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 (up toR × R × 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

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

{\sin^2 x + \cos^2 x = 1}

, for all

x

. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing

{\sin (x \pm y)}

and

{\cos (x \pm y)}

in terms of

{\sin x}

{\sin y}

{\cos x}

{\cos y}

and their simple applications. Deducing identities like the following:

{tan (x \pm y) = \dfrac{\tan x \pm \tan y}{1 \mp \tan x \tan y}}

{cot (x \pm y) = \dfrac{\cot x \cot y \mp 1}{\cot y \pm \cot x}}

{\sin α \pm \sin β = 2 \sin \dfrac{1}{2} (α \pm β) \cos \dfrac{1}{2} (α \mp β)}

{\cos α + \cos β = 2 \cos \dfrac{1}{2} (α + β) \cos \dfrac{1}{2} (α - β)}

{\cos α - \cos β = -2 \sin \dfrac{1}{2} (α + β) \sin \dfrac{1}{2} (α - β)}

Identities related to

{\sin 2x}

{\cos 2x}

{\tan 2x}

{\sin 3x}

{\cos 3x}

and

{\tan 3x}

Unit-II: Algebra

1. Complex Numbers and Quadratic Equations

Need for complex numbers, especially

\sqrt{-1}

, to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane.

2. Linear Inequalities

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line.

3. Permutations and Combinations

Fundamental principle of counting. Factorial

n

(n!)

Permutations and combinations, derivation of Formulae for

^nP_r

^nC_r

and their connections, simple applications. r

4. Binomial Theorem

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

5. Sequence and Series

Sequence and Series. 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

Unit-III: Coordinate Geometry

1. Straight Lines

Brief recall of two-dimensional geometry from earlier classes. 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. Distance of a point from a line.

2. Conic Sections

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

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

Unit-IV: Calculus

1. Limits and Derivatives

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 of polynomial and trigonometric functions.

Unit-V Statistics and Probability

1. Statistics

Measures of Dispersion: Range, Mean deviation, variance and standard deviation of ungrouped/grouped data.

2. Probability

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.

Additional Topics

The following topics are included in the syllabus but will be assessed only formatively to reinforce understanding without adding to summative assessments. This reduces academic stress while ensuring meaningful learning. Schools can integrate these with existing chapters as they align well. Relevant NCERT textual material is enclosed for reference.

Unit-I: Sets and Functions

1. Sets

Practical problems on Union and Intersection of two sets.

2. Relations and Functions

Composition of Functions

3. Trigonometric Functions

General solution of trigonometric equations of the type

{\sin 𝑦 = \sin 𝑎}

{\cos 𝑦 = \cos 𝑎}

and

{\tan 𝑦 = \tan 𝑎}

Unit-II: Algebra

1. Principle of Mathematical Induction

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

Polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system.

3. Linear Inequalities

Graphical solution of linear inequalities in two variables. Graphical method of finding a solution of system of linear inequalities in two variables.

4. Binomial Theorem

General and middle term in binomial expansion.

5. Sequence and Series

Formulae for the following special sums

{\LARGE \displaystyle \sum_{k=1}^{n} k}

{\LARGE \displaystyle \sum_{k=1}^{n} k^2}

{\LARGE \displaystyle \sum_{k=1}^{n} k^3}

Unit-III: Coordinate Geometry

1. Straight Lines

Normal form. General equation of a line.

2. Introduction to Three-dimensional Geometry

Section formula.

Unit-IV: Calculus

1. Limits and Derivatives

Derivatives of composite functions (Chain rule).

Unit-V Statistics and Probability

1. Probability

Random experiments; outcomes, sample space (set representation).

QUESTION PAPER DESIGN

Time: 3 hours

Max. Marks: 80

S.
No.

Typology of Questions

Total
Marks

%
Weightage

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

Applying:Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.

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

Total

100

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

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 Marks

Mathematics Activities

10 Marks

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, 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 subject, the subject teacher will have the liberty of incorporating any other types of questions too. The modalities of the PT are as follows:

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

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.

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.

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

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 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:

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 Textbook for Class XI, NCERT Publications

Mathematics Exemplar Problem for Class XI, Published by NCERT

Mathematics Lab Manual class XI, published by NCERT