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XI-XII
MATHEMATICS
(Code No. 041)
Session-2018-19
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 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 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 gender
biases.
to develop reverence and respect towards great Mathematicians for their
contributions to the field of Mathematics.
COURSE STRUCTURE
CLASS XI (2018-19)
One Paper Total Period–240 [35 Minutes Each]
Three Hours Max Marks: 100
No. Units No. of Periods Marks
I. Sets and Functions 60 29
II. Algebra 70 37
III. Coordinate Geometry 40 13
IV. Calculus 30 06
V. Mathematical Reasoning 10 03
VI. Statistics and Probability 30 12
Total 240 100
*No chapter/unit-wise weightage. Care to be taken to cover all the chapters.
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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). Power set. 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:
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Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of
trigonometric equations of the type siny = sina, cosy = cosa and tany = tana.
Unit-II: Algebra
1. Principle of Mathematical Induction (10) 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 (15) 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 (with real coefficients) in the complex number system. Square root of a complex
number.
3. Linear Inequalities (15) 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 method of
finding a solution of system of linear inequalities in two variables.