PSEB 11th Class Syllabus 2023 Maths

CLASS - XI ( MATHEMATICS)

Time: 3:00 hrs Theory : 80 Marks
INA : 20 Marks
Total : 100 Marks
Unit-1:Sets and Functions
1. Sets: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 .

2. Relations & Functions:Ordered pairs, Cartesian product of sets. Number of
elements in the Cartesian product of two finite sets. Cartesian product of the reals
with itself (upto R  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
function, 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: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 2x + cos2x
= 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric
function 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 cot cot ∓ 1
tan ( ± ) = , cot ( ± ) =
1 ∓ tan tan cot ± cot

sin ± = 2 sin ( ± ) cos ( ∓ )

cos + cos = 2 cos ( + ) cos ( − )

1 1
cos − cos = −2 sin ( + ) sin ( − )
2 2

Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. General
solutionof trigonometric equations of the type siny = sina, cosy = cosa and tany = tana

Unit-II Algebra

4. 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.

5. Complex Numbers and Quadratic Equations:Need for complex numbers,
especially √−1 , to be motivated by inability to solve some of the quadratic equation.
Algebraic properties of complex number. 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.

6. 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 system of linear inequalities in two variables .

7. Permutations & Combinations : Fundamental principle of counting, Factorial
n(n!) Permutations and combinations, derivation of formulae for and and their
connections, simple applications.

8. Binomial Theorem :History, statement and proof of the binomial theorem for
positive integral indices. Pascal’s triangle. General and middle term in binomial
expansion, simple applications.

9. Sequence and series: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

10. Straight Lines :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, slop–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.

11. 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 equations of a circle.

12. Introduction to Three-dimensional Geometry:Coordinate axes and
coordinate planes in three dimensions.Coordinates of a point. Distance between two
points and section formula.

Unit-IV: Calculus

13. 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 logarithimic functions. Definition of
derivative, relate it to slope of tangent of the curve, derivative of sum, difference,
product and quotient of functions. Derivatives of polynomial and trigonometric
functions.

Unit-V: Mathematical Reasoning

14. Mathematical Reasoning: 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

Mathematics. Validating the statements involving the connecting words- difference
among contradiction, converse and contrapositive.

Unit-VI: Statistics and Probability

15. Statistics: Measure of Dispersion: Range, mean deviation, variance and
standard deviation of ungrouped/grouped data. Analysis of frequency distributions
with equal means but different variances.

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

INTERNAL ASSESSMENT 20 Marks
Mathematics Activities 10 Marks
Periodic Tests (Best 2 out of 3 tests coducted) 08 Marks
Book Bank 02 Marks
Note : For activities NCERT Lab Manual may be referred.

Conduct of Periodic Tests
1. Periodic Test is a Pen and Paper assessment which is to be conducted by the
subject teacher.
2. In the entire Academic year, three periodic Tests in each subject may be
conducted.
3. Once schools complete the conduct of all 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.

4. The school will ensure simple documentation to keep a record of performance.

Assessment of Activity work:

Time : 2hrs 10 Marks

Throughtout the year any 10 activities shall be performed be 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. An year end test on the activity may be
conducted at the School Level. The weightage are as under:

 The activities and one of the projects performed by the student through
out the year and recordkeeping : 5marks
 Assessment of the activity performed during the year end test: 3 marks
 Viva-voce: 2 marks
ACTIVITIES
1. To find the number of subsets of a given set and verify that if a set has n
number of elements, then the total number of subsets is 2 .
2. To verify that for two sets A and B, ( × )= and the total number of
relations from A to B is 2 , where ( )= and n (B) = q
3. To represent set theoretic operations using Venn diagrams.
4. To verify distributive law for three given non-empty sets A,B and C, that is,
∪( ∩ )=( ∪ )∩( ∪ )
5. To identify a relation and a function.
6. To distinguish between a Relation and a Function.
7. To verify the relation between the degree measure and the radian measure of an
angle.
8. To find the values of sine and cosine functions in second, third and fourth
quadrants using their given values in first quadrant.
9. To prepare a model to illustrate the values of sine functions and cosine
functions for different angles which are multiples of and

10. To plot the graphs of sin , sin 2 , 2 sin , using same coordinate axes.

11. To interpret geometrically the meaning of = √− 1 and its integral powers.
12. To obtain a quadratic function with the help of linear functions graphically.
13. To verify that the graph of a given inequality, say 5 + 4 − 40 < 0, of the form
+ + < 0, , > 0, < 0 represents only one of the two half planes.
14. To find the number of ways in which three cards can be selected from given five
cards.

15. To construct a Pasal's Triangle and to write binomial expansion for a given
positive integral exponent.
16. To obtain formula for the sum of squares of first n-natural numbers.
17. An alternative approach to obtain formula for the sum of squares of first n
natural numbers.
18. To demonstrate that the Arithmetic mean of two different positive numbers is
always greater than the Geometric mean.
19. To establish the formula for the sum of the cubes of the first n natural
numbers.
20. To verify that the equation of a line passing through the point of intersection of
two lines + + = 0 and + + = 0 is of the form
( + + )+ ( + + )=0
21. To construct different types of conic section.
22. To construct a parabola.
23. An alternative method of constructing a parabola.
24. To construct an ellipse using a rectangle.
25. To construct am ellipse with given major and minor axes.
26. To construct an ellips when two fixed points are given.
27. To explain the concept of octants by three mutually perpendicular planes in
space.

28. To find analytically ( )=

29. Verification of the geometrical significance of derivative.
30. To obtain truth values of compound statement of the type ⋎ by using switch
connections in parallel.
31. To obtain truth values of compound statement of the types ⋏ by using switch
connections in series.
32. To write the sample space, when a die is rolled once, twice...........
33. To write the sample space,when a coin is tossed once, two times, three times,
four times.