
Introduction to Functions

Function: A Special Relation

Terms Related to Functions

Domain and Range of a Function

Even Functions and Odd Functions

Identity Function and Constant Function

Understanding Polynomial Functions

Quadratic Polynomial Function

Problems Related to Quadratic Functions

Rational Functions

Understanding the Modulus Function

Properties of Modulus Function

Problems on the Modulus Function

Understanding the Signum Function

The Greatest Integer Function

Problems on the Step Function

Fractional Part Function

e: A Special Number

The Exponential Function

The Logarithm Function

Properties of Logarithms – 1

Properties of Logarithms – 2

Problems on the Domain and Range of Logarithms

Graph of Logarithmic Functions

Problems Related to Logarithmic Functions

What Is an Angle?

Introduction to Trigonometric Functions

Definitions of Trigonometric Functions

Observations on the Definition

Domain, Range and Graph of the Sine Function

Domain, Range and Graph of the Cosine Function

Comparing Sine and Cosine Functions

Domain, Range and Graph of the Cosecant and Secant Functions

Domain, Range and Graph of the Tangent and Cotangent Functions

Problems on Trigonometric Functions – 1

Problems on Trigonometric Functions – 2

Finding the Trigonometric Values of Some Specific Angles

Problems on Finding the Values of Trigonometric Functions

Introduction to OnetoOne and Onto Functions

Properties of OnetoOne Functions

Methods to Find OnetoOne Functions

Problems on OnetoOne and Onto Functions

Understanding Composition of Functions

Properties of Composite Functions

Defining the Inverse of a Function

Properties of Inverse Functions

Problems on Composite and Inverse Functions

Introduction to Inverse Trigonometric Functions

Sine and Cosine Inverse Functions

Tangent and Cotangent Inverse Functions

Cosecant and Secant Inverse Functions

Problems on Inverse Trigonometric Functions

Transformations of Graphs – 1

Transformations of Graphs – 2

Problems on Transformations of Graphs – 1

Problems on Transformations of Graphs

Periodic Functions

Properties of Periodic Functions

Functional Equations

Solving Nonstandard Functional Equations

Finding the Number of Functions

Problems on Finding the Number of Functions

Practice Questions (Set 1)

Practice Questions (Set 2)

Practice Questions (Set 3)

Practice Questions (Set 4)

Introduction to Permutations and Combinations

The Fundamental Principle of Counting

Examples on the Fundamental Principle of Counting

The Meaning of n!

Number of Arrangements – Permutations

Properties of ^{n}P_{r} and Examples

Number of Selections – Combinations

Properties of ^{n}C_{r} and Examples

Examples of Permutations and Combinations

Permutations of Alike Objects

The Classical Problem of Seating Arrangements

Game of Words: Lexicography and Dictionary

Game of Digits and Divisibility Concept

Permutations and Combinations of Playing Cards

Circular Permutation

Distribution of Identical Objects Into Groups – Part 1

Distribution of Identical Objects Into Groups – Part 2

Distribution of Distinct Objects Into Groups

Practice Questions (Set 1)

Practice Questions (Set 2)

Practice Questions (Set 3)

Practice Questions (Set 4)

Introduction to Binomial Theorem

Factorial and ⁿCᵣ

Derivation of Binomial Expansion

Problems on Binomial Expansion

General Term and Middle Term

Problems on the General Term

Finding the Term From the End in a Binomial Expansion

Problems on the Middle Term

Problems on the Term Independent of ‘x’

Numerically Greatest Term and Numerically Greatest Coefficient

Problems on the Numerically Greatest Term

Counting Rational and Irrational Terms

Divisibility Problems – Type I

Divisibility Problems – Type II

Divisibility Problems – Type III

Use of Differentiation in Binomial Theorem

Binomial Expansion for Negative Index

Problems on Binomial Expansion for Negative Index

Practice Questions (Set 1)

Practice Questions (Set 2)

Practice Questions (Set 3)

Practice Questions (Set 4)