# CBSE 11th Class Mathematics Syllabus

## Course Structure

Units Topics 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

## Course Syllabus

### Unit-I: Sets and Functions

Chapter 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

Chapter 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 (up to R × R)

• Definition of −

• Relation

• Pictorial diagrams

• Domain

• Co-domain

• 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

• Greatest integer functions (with their graphs)

• Sum, difference, product and quotients of functions.

Chapter 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 trigonometric functions and their graphs

• Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application

• 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

Chapter 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

Chapter 2: Complex Numbers and Quadratic Equations

• Need for complex numbers, especially √1, to be motivated by inability to solve some of the quadratic 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

Chapter 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

Chapter 4: Permutations and Combinations

• Fundamental principle of counting
• Factorial n
• (n!) Permutations and combinations
• Derivation of formulae and their connections
• Simple applications.

Chapter 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

Chapter 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.

### Unit-III: Coordinate Geometry

Chapter 1: Straight Lines

• Brief recall of two dimensional geometries 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

• 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

Chapter 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

• Hyperbola

• Standard equation of a circle

Chapter 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

Chapter 1: 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 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 trigonometric functions

### Unit-V: Mathematical Reasoning

Chapter 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

Chapter 1: Statistics

• Measures of dispersion −

• Range

• Mean deviation

• Variance

• Standard deviation of ungrouped/grouped data

• Analysis of frequency distributions with equal means but different variances.

Chapter 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