CONTENTS

This page gives the contents of class 11. For contents of class 12, click here.

1. Chapter 1 - Sets
• Definition of set
• Natural numbers, integers, rational numbers etc.,
• Elements of a set
Chapter 1.1
• Roster or tabular form
• Set-builder form
Chapter 1.2
• Empty Set
• Finite Set
• Equal sets
Chapter 1.3
• Subsets
• Super sets
• Singleton Set
Chapter 1.4
• Intervals as subsets of R
• Closed intervals and Open intervals
• Power set
• Universal set
Chapter 1.5
• Venn diagrams
• Union of sets
Chapter 1.6
• Intersection of sets
• Disjoint sets
Chapter 1.7
• Difference of two sets
Chapter 1.8
• Complement of a set
• De Morgan's Law
Chapter 1.9
• Practical problems involving two sets
Chapter 1.10
• Some interesting relations between two sets
Chapter 1.11
• Some interesting relations between three sets
Chapter 1.12
• Practical problems involving three sets
2. Chapter 2 - Relations and Functions
• Definition of Cartesian product of sets
• Ordered pairs and Ordered triplets
• Number of elements in a Cartesian product
Chapter 2.1
• Relations
• Arrow diagram
• Domain, Codomain and Range
Chapter 2.2
• Functions
• Identity function
Chapter 2.3
• Constant function
• Polynomial function
Chapter 2.4
• Rational function
Chapter 2.5
• Modulus function
• Signum function
Chapter 2.6
• Greatest integer function
Chapter 2.7
• Algebra of real functions
Chapter 2.8
• Solved examples on functions
3. Chapter 3 - Trigonometric Functions
• Derivation of some simple trigonometric identities
• Solved examples
Chapter 3.1
• Definition of angle
• Measurement of angles using degrees
Chapter 3.2
• Measurement of angles using radians
Chapter 3.3
• Conversion from degree to radian and vice versa
Chapter 3.4
• Trigonometric ratios of acute angles using unit circle
Chapter 3.5
• Trigonometric ratios of obtuse angles using unit circle
Chapter 3.6
• Trigonometric ratios of negative angles using unit circle
Chapter 3.7
• Input values for trigonometric functions
• Values at which sine and cosine functions become zero
Chapter 3.8
• Signs of trigonometric functions in the four quadrants
• Domain and range of sine and cosecant functions
• Graphs of sine and cosecant functions
Chapter 3.9
• Domain and range of cosine and secant functions
• Graphs of cosine and secant functions
Chapter 3.10
• Domain and range of tangent and cotangent functions
• Graphs of tangent and cotangent functions
Chapter 3.11
• Sum and difference of two angles
• Derivation of Trigonometric identities
Chapter 3.12
• Derivation of more Trigonometric identities
Chapter 3.13
• Solved examples related to Trigonometric identities
Chapter 3.14
• Period of Trigonometric functions
Chapter 3.15
• Trigonometric equations
• Theorem 1
Chapter 3.16
• Trigonometric equations
• Theorems 2 and 3
Chapter 3.17
• Solved examples on Trigonometric equations
Chapter 3.18
• More Solved examples on Trigonometric equations
Chapter 3.19
• Miscellaneous examples
Chapter 3.20
• Details about sine formula
Chapter 3.21
• Details about cosine formula
Chapter 3.22
• Napier's Analogies
• Solved examples
4. Chapter 4 - Principles of Mathematical Induction
• Basic details about mathematical induction
• Examples
Chapter 4.1
• Mathematical induction involving inequalities
Chapter 4.2
• Solved examples related to mathematical induction
5. Chapter 5 - Complex Numbers and Quadratic Equations
• Square root of -ve real numbers
• Significance of i
Chapter 5.1
• Complex numbers
• Addition, subtraction and multiplication of Complex numbers
Chapter 5.2
• Division of complex numbers
• Powers of i
• Identities related to Complex numbers
• Expressing a given number in the form a+bi
Chapter 5.3
• Modulus and conjugate of a complex number
• Method to remove i from denominator 
Chapter 5.4
• Argand Plane
• Representing a complex number on the Argand plane
• Representing modulus on the Argand plane
• Representing conjugate on the Argand plane
Chapter 5.5
• Polar representation
• Polar coordinates
• Argument of a complex number
Chapter 5.6
• Quadratic Equations when discriminant is less than zero
• Miscellaneous examples
Chapter 5.7
• More Miscellaneous examples
6. Chapter 6 - Linear Inequalities
• Different types of inequalities
• Linear inequalities in one variable
• Disadvantages of trial and error method
Chapter 6.1
• Rules for solving linear inequalities in one variable
• Solved examples
Chapter 6.2
• Solved examples on linear inequalities in one variable
Chapter 6.3
• Graphical method for solving linear inequalities in two variables
• Shading of appropriate half plane
• Solved examples
Chapter 6.4
• Solved examples demonstrating the graphical method for solving linear inequalities in two variables
Chapter 6.5
• System of linear inequalities
• Overlapping of shaded areas
Chapter 6.6
• Miscellaneous examples
7. Chapter 7 - Permutations and Combinations
• Maximum number of possible arrangements
• Fundamental principle of counting
Chapter 7.1
• Application of multiplication principle
• Solved examples
Chapter 7.2
• Permutations
• Expression for permutations
• The factorial notation
• Solved examples
Chapter 7.3
• Expression for permutations using the factorial notation
• Solved examples
Chapter 7.4
• Permutations when all objects are not different
Chapter 7.5
• Combinations
• Relation between number of permutations and number of combinations
Chapter 7.6
• Formula for number of combinations
Chapter 7.7
• Miscellaneous examples
8. Chapter 8 - Binomial Theorem
• Basic details of Pascal's triangle
Chapter 8.1
• Pascal's triangle as the basis of binomial theorem
• Binomial theorem for any positive integer n
Chapter 8.2
• Solved examples
Chapter 8.3
• General and middle terms
Chapter 8.4
• Solved examples related to General and middle terms
Chapter 8.5
• Miscellaneous examples
9. Chapter 9 - Sequences and Series
• Basics about sequences
• The nth term of a sequence
• Basics about series
Chapter 9.1
• Solved examples related to the nth term of sequences and series
Chapter 9.2
• Solved examples related to Arithmetic progression and Arithmetic mean
• Inserting n terms in between two numbers so that the resulting sequence is an A.P
Chapter 9.3
• Details about geometric progression (G.P)
• nth term of a G.P
• Sum of n terms of a G.P
Chapter 9.4
• Details about geometric mean (G.M)
• Relation between AM and G.M
• Inserting n terms in between two numbers so that the resulting sequence is an G.P
Chapter 9.5
• Special series: Sum of the squares of the first n natural numbers
Chapter 9.6
• Special series: Sum of the cubes of the first n natural numbers
Chapter 9.7
• Miscellaneous examples on chapter 9
10. Chapter 10 - Straight Lines
• Basics about coordinate geometry
• The Distance formula
• The section formula
• Area of a triangle using coordinates of vertices
Chapter 10.1
• Inclination and Slope of lines
• Condition for two lines to be parallel
• Condition for two lines to be perpendicular
Chapter 10.2
• Angle between two non-parallel lines in terms of slopes
Chapter 10.3
• Condition for collinearity of three points
Chapter 10.4
• Various forms of equations of a line
• Point-slope form
• Two point form
• Slope-intercept form
Chapter 10.5
• Intercept form
Chapter 10.6
• Normal form
Chapter 10.7
• General equation of a line
• Reducing general form into slope-intercept form, intercept form and normal form
Chapter 10.8
• Appropriate signs for sine and cosine terms in the normal form of a line
• Solved examples demonstrating the reducing of general form into slope-intercept form, intercept form and normal form
Chapter 10.9
• Distance of a point from a line
• Distance between two parallel lines
Chapter 10.10
• Miscellaneous examples
11. Chapter 11 - Conic Sections
• Double napped right circular cone
• Circle, Ellipse, Parabola and Hyperbola
• Degenerated cases
Chapter 11.1
• General equation of a Circle
• Method of finding center and radius from the general equation
Chapter 11.2
• Definition of a parabola
• Simplest equation of a parabola
Chapter 11.3
• Latus rectum of a parabola
Chapter 11.4
• Basic properties of Ellipse
Chapter 11.5
• Simplest equation of an Ellipse
Chapter 11.6
• Another simplest equation of Ellipse
• Symmetry of Ellipse
• Comparison between the two forms
Chapter 11.7
• Latus rectum of Ellipse
Chapter 11.8
• Solved examples on Ellipse
Chapter 11.9
• Basic properties of Hyperbola
Chapter 11.10
• Simplest equation of Hyperbola
Chapter 11.11
• Another simplest equation of Hyperbola
Chapter 11.12
• Latus rectum of Hyperbola
Chapter 11.13
• Solved examples on Hyperbola
Chapter 11.14
• Miscellaneous examples
12. Chapter 12 - Three Dimensional geometry
• Rectangular coordinate system
• Names and numbers of the eight octants
Chapter 12.1
• Coordinates of a point in space
• Position of a point whose coordinates are given
Chapter 12.2
• Finding the coordinates of a point in space using planes
• Finding the Position of a point whose coordinates are given, using planes
Chapter 12.3
• Distance formula
• Collinearity of three points in space
Chapter 12.4
• Section formula
Chapter 12.5
• More solved examples on Section formula
Chapter 12.6
• Miscellaneous examples
13. Chapter 13 - Limits and Derivatives
• Basic details about limits
• Examples demonstrating the limiting process
Chapter 13.1
• Examples demonstrating the limiting process
• Right side and left side limits
• Cases when limit at a point does not exist
Chapter 13.2
• More examples demonstrating the limiting process
Chapter 13.3
• Algebra of limits
• Theorem related to addition, subtraction, multiplication and division
• Examples for addition and subtraction
Chapter 13.4
• Algebra of limits
• Examples for multiplication and division
Chapter 13.5
• Limits of polynomial and rational functions
Chapter 13.6
• Examples on Limits of polynomial and rational functions
Chapter 13.7
• Theorem 2 and examples
Chapter 13.8
• Theorem 3
• Theorem 4 - The sandwich theorem
Chapter 13.9
• Theorem 5
• Solved examples related to limits of trigonometric functions
Chapter 13.10
• Basics about derivatives
• Derivatives as a rate of change
Chapter 13.11
• Derivatives as slope of tangent
Chapter 13.12
• Method to find Derivative at a given point
Chapter 13.13
• Derivative of a function f(x) is a new function f'(x)
Chapter 13.14
• Solved examples
• Plotting f(x) and f'(x) on the same graph
Chapter 13.15
• Algebra of derivatives
• Proof for the sum rule
• Leibnitz rule for the product of differentiation
Chapter 13.16
• Derivatives of Polynomial functions
Chapter 13.17
• Derivatives of Trigonometric functions
Chapter 13.18
• Miscellaneous examples
14. Chapter 14 - Mathematical Reasoning
• Basic details about Statement
• Checking whether a given sentence is a statement or not
Chapter 14.1
• Negation of a statement
• Compound statement
• Component statements
Chapter 14.2
• Connectives
• Exclusive and Inclusive "or"
• Quantifiers
Chapter 14.3
• Implications
• Contrapositive statements
• Converse statements
• If and only if statements
Chapter 14.4
• Validating statements
• Counter example for proving a statement to be false
Chapter 14.5
• Miscellaneous examples
15. Chapter 15 - Statistics
• Range of a data
Chapter 15.1
• Calculation of mean deviation
Chapter 15.2
• Calculation of mean deviation for continuous frequency distribution
Chapter 15.3
• Variance and Standard deviation
Chapter 15.4
• Solved examples on Variance and Standard deviation
• Another formula for Variance and Standard deviation
Chapter 15.5
• Variance and Standard deviation for continuous frequency distribution
Chapter 15.6
• Coefficient of Variance
Chapter 15.7
• Miscellaneous examples
16. Chapter 16 - Probability
• Random experiment
• Outcome
• Sample space
• Sample point
Chapter 16.1
• Events
• Occurrence of events
• Types of events
Chapter 16.2
• Algebra of Events
• Union, Intersection, Difference, Complement
• Mutually exclusive Events
Chapter 16.3
• Exhaustive Events
• Mutually exclusive and Exhaustive Events
Chapter 16.4
• Axiomatic approach to probability
• Conditions that the assigned probabilities must satisfy for them to be valid
Chapter 16.5
• Probability of an event
• Probabilities of equally likely outcomes
Chapter 16.6
• Probability of the event "A or B"
Chapter 16.7
• Probability of the event "not A"
Chapter 16.8
• Solved examples
Chapter 16.9
• Miscellaneous examples
A. Appendix A - Infinite Series
• Binomial expansion as an infinite series
A.1
• Infinite geometric series
A.2
• Exponential series
Appendix B - Mathematical Modeling
• Steps in mathematical modeling
• Finding the height of a tower
B.1
• Mathematical modeling of the motion of a simple pendulum
B.2
• Mathematical modeling involving linear inequalities
B.3
• Mathematical modeling for predicting population
• Mathematical modeling involving exponential functions
B.4
• Applications of Mathematical modeling
• The case of bridge in Konigsberg town

The above given are the contents of class 11. For contents of class 12, click here.