CBSE Board Math Syllabus for Class 11
CBSE Board Syllabus for Class 11 Math
6. MATHEMATICS (Code No 041)
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 Bioscience, commerce or computer applications.
The present revised syllabus has been designed in accordance with National Curriculum Frame work
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 pupil:
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 sex biases.
to develop reverence and respect towards great Mathematicians for their contributions to
the field of Mathematics.
COURSE STRUCTURE
Class XI
One Paper Three Hours Max Marks. 100
Units Marks
I. SETS AND FUNCTIONS 29
II. ALGEBRA 37
III. COORDINATE GEOMETRY 13
IV. CALCULUS 06
V. MATHEMATICAL REASONING 03
VI. STATISTICS AND PROBABILITY 12
100
UNITI: SETS AND FUNCTIONS
1. Sets : (12) Periods
Sets and their representations. Empty set. Finite & Infinite sets. Equal sets.Subsets. Subsets
of the 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 Sets.
2. Relations & Functions: (14) 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, codomain and range of a relation. Function as a
special kind of relation from one set to another. Pictorial representation of a
function, domain, codomain & range of a function. Real valued functions, domain and
range of these functions, constant, identity, polynomial, rational, modulus, signum and
greatest integer functions, with their graphs. Sum, difference, product and quotients of
functions.
3. Trigonometric Functions: (18) Periods
Positive and negative angles. Measuring angles in radians & 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 trignometric functions and their graphs. Expressing sin
(x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy. Deducing the identities like
the following:
Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x. General solution of trigonometric
equations of the type sinθ = sin α, cosθ = cos α and tanθ = tan α. Proof and simple applications of sine
and cosine formulae.
UNITII: ALGEBRA
1. Principle of Mathematical Induction: (06) 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: (10) Periods
Need for complex numbers, especially , 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 in the complex number system. Square root of a complex
number.
3. Linear Inequalities: (10) 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 solution of system of linear inequalities in two variables.
4. Permutations & Combinations: (12) Periods
Fundamental principle of counting. Factorial n. (n!)Permutations and combinations,
derivation of formulae and their connections, simple applications.
5. Binomial Theorem: (08) Periods
History, 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., Arithmetic and
Geometric series infinite G.P. and its sum, geometric mean (G.M.), relation between A.M.
and G.M. Sum to n terms of the special series .
UNITIII: COORDINATE GEOMETRY
1. Straight Lines: (09) 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 axes,
pointslope form, slopeintercept form, twopoint 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: (12) 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 of equation of a circle.
3. Introduction to Three dimensional Geometry (08) Periods
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point.
Distance between two points and section formula
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 Bioscience, commerce or computer applications.
The present revised syllabus has been designed in accordance with National Curriculum Frame work
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 pupil:
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 sex biases.
to develop reverence and respect towards great Mathematicians for their contributions to
the field of Mathematics.
COURSE STRUCTURE
Class XI
One Paper Three Hours Max Marks. 100
Units Marks
I. SETS AND FUNCTIONS 29
II. ALGEBRA 37
III. COORDINATE GEOMETRY 13
IV. CALCULUS 06
V. MATHEMATICAL REASONING 03
VI. STATISTICS AND PROBABILITY 12
100
UNITI: SETS AND FUNCTIONS
1. Sets : (12) Periods
Sets and their representations. Empty set. Finite & Infinite sets. Equal sets.Subsets. Subsets
of the 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 Sets.
2. Relations & Functions: (14) 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, codomain and range of a relation. Function as a
special kind of relation from one set to another. Pictorial representation of a
function, domain, codomain & range of a function. Real valued functions, domain and
range of these functions, constant, identity, polynomial, rational, modulus, signum and
greatest integer functions, with their graphs. Sum, difference, product and quotients of
functions.
3. Trigonometric Functions: (18) Periods
Positive and negative angles. Measuring angles in radians & 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 trignometric functions and their graphs. Expressing sin
(x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy. Deducing the identities like
the following:
Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x. General solution of trigonometric
equations of the type sinθ = sin α, cosθ = cos α and tanθ = tan α. Proof and simple applications of sine
and cosine formulae.
UNITII: ALGEBRA
1. Principle of Mathematical Induction: (06) 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: (10) Periods
Need for complex numbers, especially , 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 in the complex number system. Square root of a complex
number.
3. Linear Inequalities: (10) 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 solution of system of linear inequalities in two variables.
4. Permutations & Combinations: (12) Periods
Fundamental principle of counting. Factorial n. (n!)Permutations and combinations,
derivation of formulae and their connections, simple applications.
5. Binomial Theorem: (08) Periods
History, 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., Arithmetic and
Geometric series infinite G.P. and its sum, geometric mean (G.M.), relation between A.M.
and G.M. Sum to n terms of the special series .
UNITIII: COORDINATE GEOMETRY
1. Straight Lines: (09) 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 axes,
pointslope form, slopeintercept form, twopoint 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: (12) 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 of equation of a circle.
3. Introduction to Three dimensional Geometry (08) Periods
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point.
Distance between two points and section formula