# CBSE Class 11 Maths Syllabus

## CBSE Syllabus for Class 11 Maths 2023-2024 PDF

Mathematics is undoubtedly one of the most important subjects in any class, especially in the higher grades. For good preparation for the Class 11 Mathematics exam, the students should be aware of the CBSE Syllabus to be able to understand all the important Mathematics topics. It will provide the details on the structure of the course, exam pattern as well as the weightage of each unit in the Mathematics syllabus.  The CBSE Class 11 Maths Syllabus will be a good checklist for students.

## CBSE Class 11 Maths Syllabus

Unit-I: Sets and Functions

1. Sets

Sets and their representations, empty sets, 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.

1. 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 (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.

1. 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 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.

Unit-II: Algebra

1. Complex Numbers and Quadratic Equations

Need for complex numbers, especially -1 to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane.

1. Linear Inequalities

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 a system of linear inequalities in two variables.

1. Permutations and Combinations

Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of Formula for nPr and nCr and their connections, simple applications.

1. 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.

1. 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.

1. 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. Derivatives 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.

1. 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.

### Types of Questions from the CBSE Syllabus for Class 11 Maths 2023-2024

Some adjustments were made to the CBSE Class 11 Maths Syllabus 2023-24. This was done because of the Covid 19 pandemic situation.

• Usually, there will be a range of questions according to the CBSE Class 11 Maths Syllabus
• There will also be a set of memory questions. These questions will examine the students’ understanding of fundamental concepts, their ability to recall things that were taught previously, as well as their memory.
• There will be questions that will be based on the knowledge of the subject. There will be 55% of the questions.
• Some questions are given on the basis of the application of a specific notion or theorem. A quarter of the questions may be application-based.
• 20% of the questions will be based on the ability to analyse a situation.

### CBSE Syllabus for Class 11 Maths 2023-2024 and Marks Distribution

 S.NO Unit Name Marks 1 Sets and Functions 19 2 Algebra 25 3 Coordinate Geometry 15 4 Calculus 10 5 Statistics and Probability 12 Internal Assessment 20 Total 100

### Conclusion

You can get access to the CBSE Class 11 Maths syllabus 2023-24 from our website. We have provided the latest syllabus for the benefit of the students.

## MATHEMATICS (XI-XII)

(Code No. 041)

### Session – 2022-23

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
• to apply the knowledge and skills acquired to solve problems and wherever possible, by more than one
• to develop positive attitude to think, analyze and articulate
• to develop interest in the subject by participating in related
• to acquaint students with different aspects of Mathematics used in daily
• to develop an interest in students to study Mathematics as a
• to develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of gender
• to develop reverence and respect towards great Mathematicians for their contributions to the field of

### COURSE STRUCTURE CLASS XI (2022-23)

One Paper Total Period–240 [35 Minutes each]

### Three Hours Max Marks: 80

 No. Units No. of Periods Marks I. Sets and Functions 60 23 II. Algebra 50 25 III. Coordinate Geometry 50 12 IV. Calculus 40 08 V. Statistics and Probability 40 12 Total 240 80 Internal Assessment 20

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

### 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). 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

1

, cot(x ± y) =

1

cot x cot y ∓ 1

cot y ± cot x

sinα ± sinβ = 2sin

2

(α ± β)cos

2

(α ∓ β)

1

cosα + cosβ = 2cos

2

1

(α + β)cos

2

1

(α − β) 1

𝑐𝑜𝑠𝛼 − 𝑐𝑜𝑠𝛽 = −2𝑠𝑖𝑛

(𝛼 + 𝛽)𝑠𝑖𝑛

2

(𝛼 − 𝛽)

2

Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and tan3x.

### Unit-II: Algebra

1. Complex Numbers and Quadratic Equations (10) Periods

Need for complex numbers, especially√−1, to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane

### 2. Linear Inequalities (10) Periods

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

### 3. Permutations and Combinations (10) Periods

Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of Formulae for nPr and nCr and their connections, simple applications.

### 4. Binomial Theorem (10) Periods

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

### 5. Sequence and Series (10) Periods

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 (15) Periods

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 (25) 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.

### Unit-IV: Calculus

1. Limits and Derivatives (40) 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 Statistics and Probability

1. Statistics (20) Periods

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

### 2. Probability (20) Periods

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

### Time: 3 Hours Max. Marks: 80

 S. No. Typology of Questions Total Marks % Weight age 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 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

### 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

Note: Please refer the guidelines given under XII Mathematics Syllabus:

### CLASS-XII

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.

1. Inverse Trigonometric Functions 15 Periods Definition, range, domain, principal value branch. Graphs 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). 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), 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, chain rule, derivative of inverse trigonometric functions,

𝑙𝑖𝑘𝑒 sin−1 𝑥 , cos−1 𝑥 and tan−1 𝑥, 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.

1. Applications of Derivatives 10 Periods Applications of derivatives: rate of change of bodies, increasing/decreasing functions, 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.

dx dx dx dx dx

 ax

∫ x2 ± a2, ∫ √x2 ± a2 , ∫ √a2 − x2 , ∫ ax2 + bx + c , ∫ √ 2+bx+c

px + q

∫ ax2 + bx + c

px + q

dx, ∫ dx, ∫ √a2 ± x2 dx, ∫ √x2 − a2 dx

√ax2+bx + c

∫ √𝑎𝑥2 + 𝑏𝑥 + 𝑐 𝑑𝑥,

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)

### 5. Differential Equations 15 Periods

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. Solutions of linear differential equation of the type:

dy dx d𝑥 d𝑦

+ py = q, where p and q are functions of x or constants.

+ 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.

1. Three – dimensional Geometry 15 Periods Direction cosines and direction ratios of a line joining two Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.

### Unit-V: Linear Programming

1. Linear Programming 20 Periods

Introduction, related terminology such as constraints, objective function, optimization, 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 of random variable.

### MATHEMATICS (Code No. – 041)

QUESTION PAPER DESIGN CLASS – XII

### (2022-23)

Time: 3 hours Max. Marks: 80

 S. No. Typology of Questions Total Marks % Weightage 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 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

### 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

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 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:

1. Mode: The periodic test is to be taken in the form of pen-paper
1. 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.

1. 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
2. The school will ensure simple documentation to keep a record of performance as suggested in detail circular Acad-05/2017.
3. 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 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 Part I – Textbook for Class XII, NCERT Publication
• Mathematics Part II – Textbook for Class XII, NCERT Publication

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### 1. Is CBSE Class 11 Maths Syllabus really hard?

Yes, the CBSE Class 11 and 12 Mathematics is quite hard. Students have to put in a lot of hard work and effort to score well. They have to be thorough with the Mathematics topics in the NCERT Books according to the CBSE Syllabus. Go through the CBSE Revision Notes to revise concepts and be able to solve problems easily.

### 2. What is the total number of chapters in CBSE Class 11 Mathematics?

There are a total of 16 chapters in CBSE Class 11 Mathematics starting from Sets and ending with Probability.

### 3. What are the benefits of the CBSE Class 11 Maths Syllabus?

The CBSE Class 11 Maths Syllabus will help the students to get a proper understanding of the subject. Discussing the syllabus will help students understand the course easily. It specifies the grading and time limit for each section as well. It gives the details of how many marks are decided for each unit. So, students can plan accordingly to study the subject areas that are more important. It will also help the students in the following ways:

• It acts as a checklist for the students.
• Includes information on all the projects, practicals, and assignments that have to be done.

### 4. Are NCERT Books enough for Class 11 Mathematics?

Class 11 Mathematics NCERT Books are the best for the students. Mathematics is one of the difficult subjects in Class 11. However, with regular practice of the problems given in the Mathematics books, they can score well.

### 5. What are some of the tips for preparation for Class 11 Mathematics?

• Make sure to solve the CBSE PastYears’ Question Papers for scoring well in the exam.
• We have provided CBSE Sample Papers on our website which consist of CBSE Important Questions which will give you good practice.
• Solve CBSE extra questions to work on speed and accuracy.
• Be thorough with the formulas and revise them regularly.
• Make sure to take out time for revising all subjects.