CBSE Class XI 11th Syllabus - Mathematics Class 11 Syllabus
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Course Structure
| Unit | Topic | Marks |
| I. | Sets and Functions | 29 |
| II. | Algebra | 37 |
| III. | Co-ordinate Geometry | 13 |
| IV. | Calculus | 6 |
| V. | Mathematical Reasoning | 3 |
| VI. | Statistics and Probability | 12 |
| Total | 100 |
Unit-I: Sets and Functions
1. Sets
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 Sets. Practical Problems
based on sets.
2. Relations & Functions
Ordered pairs, Cartesian product of
sets. Number of elements in the cartesian product of two finite sets.
Cartesian product of the sets of real (upto R x 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 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
Positive and negative angles. Measuring
angles in radians and in degrees and conversion of one into other.
Definition of trigonometric functions with the help of unit circle.
Truth of the 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 and their simple application. Deducing identities like
the following:
Identities related to sin 2x, cos2x, tan
2x, sin3x, cos3x and tan3x. General solution of trigonometric equations
of the type sin y = sin a, cos y = cos a and tan y = tan a.
Unit-II: Algebra
1. 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.
2. Complex Numbers and Quadratic Equations
Need for complex numbers, especially √1,
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
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 and Combinations
4. Permutations and Combinations
Fundamental principle of counting.
Factorial n. (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 (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. Formula for the following special sum:
Unit-III: Coordinate Geometry
1. 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, slope-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.
2. 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 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.
Intutive idea of limit. Limits of
polynomials and rational functions, trignometric, exponential and
logarithmic functions. Definition of derivative, relate it to slope of
tangent of a curve, derivative of sum, difference, product and quotient
of functions. The derivative of polynomial and trignometric functions.
Unit-V: Mathematical Reasoning
1. 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 contrapositive.
Unit-VI: Statistics and Probability
1. Statistics
Measures of dispersion; Range, 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' and 'or'
events.
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