HP Board Class 11 Syllabus 2024 Math

Himachal Pradesh Board of School Education, Dharamshala
MATHEMATICS
10 +1

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 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 of
visualization of basic facts, concepts, terms, principles and
 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 awareness of the 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 contribution
to the field of Mathematics

Unit-I : Sets and Functions

1: Sets

Sets and their representations. Empty set Finite and 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.

2: Relations and 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 Rx Rx R)
Definition of relation, pictorial diagrams, domain, co domain and range of a relation
Function as a special kind of relation from one set to another. Pictorial representation
of a function domain, co-domain & range of a function. Real valued function of the
real variable domain and range of these functions, constant, identity, polynomial,
rational, modulus, signup 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 & in degrees and
conversion from one measure 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 and sketch of their graphs Expressing sin (x + y) and
cos (x + y) in terms of sin x, sin y, cos x & cos y. Deducing the identities like following
± ±
tan (x ± y) = ±
, cot (x ± y) = ±

sin x + sin y = 2 sin cos , cos x +cos y = 2 cos cos

sin x - sin y = 2 cos sin , cos x - cos y = -2 sin sin
Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x General
solution of trigonometric equations of the type sin =sin , cos = cos and tan =
tan . Proofs and simple applications of sine and cosine formulae

Unit -II : Algebra

1. Principle of Mathematical Induction :

Processes 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:

Need for complex numbers, expecially √−1 to be motivated by inability to solve
every quadratic equation Brief description of 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.

3. 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 Solution of system of linear inequalities in two variables-graphically

4. Permutations & Combinations :

Fundamental principle of counting. Factorial n Permutations and combinations,
derivation of formulae and their connections simple applications

5. 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,

6. Sequence and Series:

Sequence and Series. Arithmetic progression (A.P). arithmetic mean (AM)
Geometric progression (GP) general term of a GP., sum of n terms of a GP
geometric mean (GM) relation between A.M. and G.M. Sum to n terms of the special
series∑ ∑ 2 and ∑ 3.

UNIT-III : COORDINATE GEOMETRY

1. Straight Lines :

Brief recall of 2D from earlier classes Slope of a line and angle between two lines.
Various forms of equations of a line parallel to axes, point slope form, slope-intercept
form, two-point form, intercepts form and normal form General equation of a line.
Distance of a point from a line

2. Conic Sections :

Sections of cone circles ellipse, parabola, hyperbola, a point, a straight. line and 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 and section formula

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. 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

2. 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 between contradiction, converse and contapositive

UNIT-V: STATISTICS & PROBABILITY

1. Statistics :

Measure of dispersion Mean deviation, variance and standard deviation of
ungrouped/grouped data Analysis of frequency distributions with equal means but
different variances

2. Probability :

Random experiments outcomes, sample spaces (set representation) Events
occurrence of events, 'not, 'and' and 'or' events, exhaustive events, mutually
exclusive events, Axiomatic (set theoretic) probability, connections with the theories
of earlier classes. Probability of an event probability of 'not', 'and' & 'or events

HIMACHAL PRADESH BOARD OF SCHOOL EDUCATION, DHARAMSHALA
Mathematics

XI Class

Syllabus and Distribution of Marks

Session - 2022-23

Time : 3 hrs Max. Marks : 80

Unit Wise Distribution of Marks

Unit No. Particulars Marks Assigned
Unit-01 (i) Sets
Sets and Functions (ii) Relations and Functions 23
(iii) Trigonometric Functions
Unit-02 (i) Principal of Mathematical Induction
Algebra (ii) Complex Numbers and Quadratic Equations
(iii) Linear Inequalities 25
(iv) Permutations and Combinations
(v) Binomial Theorem
(vi) Sequence and Series
Unit-03 (i) Straight Lines
Coordinate Geometry (ii) Conic Sections 12
(iii) Introduction to Three-Dimensional Geometry
Unit-04 (i) Limits and Derivatives
08
Calculus (ii) Mathematical Reasoning
Unit-05 (i) Statistics
12
Statistics and Probability (ii) Probability
Total 80

Design of Question Paper ( Blue Print )
Name of the Unit 1mark 2marks 3marks 4marks 5marks Total
MCQ Questions Questions Questions Questions
Questions
Unit-01 05 01 01 02 01 23
Sets and Functions
Unit-02 04 02 01 01 02 25
Algebra
Unit-03 03 - 03 - - 12
Coordinate Geometry
Unit-04 04 02 - - - 08
Calculus and
Mathematical Reasoning
Unit-05 - - 01 01 01 12
Statistics and Probability
Total 1x16 =16 2x5 =10 3x6 =18 4x4 =16 5x4 =20 80

Chapter Wise Distribution of Marks

Name of the Chapter 1mark 2marks 3marks 4marks 5marks Total
Questions Questions Questions Questions Questions
(MCQ)
01- Sets 02 - - 01 - 06
02- Relations and 01 - - 01 - 05
Functions
03- Trigonometric and 02 01 01 - 01 12
functions
04- Principle of - - - 01 - 04
Mathematical Induction
05- Complex Numbers 02 01 - - - 04
and Quadratic Equations
06- Linear Inequalities - - 01 - - 03
07- Permutations and 01 01 - - - 03
Combinations
08- Binomial Theorem - - - - 01 05
09- Sequence and Series 01 - - - 01 06
10- Straight Lines 01 - 01 - - 04
11- Conic Sections 02 - 01 - - 05
12- Introduction to Three- - - 01 - - 03
Dimensional Geometry
13- Limits and 04 01 - - - 06
Derivatives
14- Mathematical - 01 - - - 02
Reasoning
15- Statistics - - - - 01 05
16- Probability - - 01 01 - 07
Total 80

PRESCRIBED BOOKS

Mathematics Published by HPBOSE Dharamshala