Syllabus: Mathematics for Class 11 | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


COURSE STRUCTURE 
CLASS XI (2023-24) 
 
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 
Page 2


COURSE STRUCTURE 
CLASS XI (2023-24) 
 
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
 , cot(x ± y) =
cot x cot y ± 1
cot y ± cot x
 
sina ± sinß = 2sin
1
2
(a ± ß)cos
1
2
(a ± ß) 
cosa + cosß = 2cos
1
2
(a + ß)cos
1
2
(a - ß) 
???????? - ???????? = -2?????? 1
2
(?? + ?? )?????? 1
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, especiallyv-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 
n
P r  and 
n
C r 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.  
 
Page 3


COURSE STRUCTURE 
CLASS XI (2023-24) 
 
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
 , cot(x ± y) =
cot x cot y ± 1
cot y ± cot x
 
sina ± sinß = 2sin
1
2
(a ± ß)cos
1
2
(a ± ß) 
cosa + cosß = 2cos
1
2
(a + ß)cos
1
2
(a - ß) 
???????? - ???????? = -2?????? 1
2
(?? + ?? )?????? 1
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, especiallyv-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 
n
P r  and 
n
C r 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. 
Page 4


COURSE STRUCTURE 
CLASS XI (2023-24) 
 
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
 , cot(x ± y) =
cot x cot y ± 1
cot y ± cot x
 
sina ± sinß = 2sin
1
2
(a ± ß)cos
1
2
(a ± ß) 
cosa + cosß = 2cos
1
2
(a + ß)cos
1
2
(a - ß) 
???????? - ???????? = -2?????? 1
2
(?? + ?? )?????? 1
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, especiallyv-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 
n
P r  and 
n
C r 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 
CLASS – XI (2023-24) 
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 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 
 
Note: Please refer the guidelines given under XII Mathematics Syllabus: 
INTERNAL ASSESSMENT        20 MARKS 
Periodic Tests ( Best 2 out of 3 tests conducted)            10 Marks 
Mathematics Activities                                                                                          10 Marks