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Class 9 Maths (NCERT)

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Module 1: Chapter 1: Number Systems

Introduction to Number Systems

ch1-introduction

Rational Numbers

ch1-rational-numbers

Exercise 1.1 - Detailed Solutions

ch1-exercise-1-1

Irrational Numbers

ch1-irrational-numbers

Exercise 1.2 - Detailed Solutions

ch1-exercise-1-2

Real Numbers & Decimal Expansions

ch1-real-decimals

Exercise 1.3 - Detailed Solutions

ch1-exercise-1-3

Operations on Real Numbers

ch1-operations

Rationalizing the Denominator

ch1-rationalization

Exercise 1.4 & 1.5 - Solutions

ch1-exercise-1-4-5

Laws of Exponents for Real Numbers

ch1-laws-exponents

Chapter 1 Summary

ch1-summary

Module 2: Chapter 2: Polynomials

What is a Polynomial?

ch2-introduction

Types of Polynomials

ch2-types

Zeroes of a Polynomial

ch2-zeroes

Exercise 2.1 - Detailed Solutions

ch2-exercise-2-1

Remainder Theorem

ch2-remainder-theorem

Factor Theorem

ch2-factor-theorem

Algebraic Identities

ch2-identities

Exercise 2.4 - Identity Applications

ch2-exercise-2-4

Chapter 2 Summary

ch2-summary

Module 3: Chapter 3: Coordinate Geometry

The Cartesian Plane

ch3-introduction

Understanding Coordinates

ch3-coordinates

Exercise 3.1 & 3.2 - Solutions

ch3-exercise-1-2

Exercise 3.3 - Plotting Points

ch3-exercise-3

Chapter 3 Summary

ch3-summary

Module 4: Chapter 4: Linear Equations in Two Variables

Linear Equations Introduction

ch4-introduction

Solutions of Linear Equations

ch4-solutions

Exercise 4.1 - Solutions

ch4-exercise-4-1

Exercise 4.2 - Solutions

ch4-exercise-4-2

Chapter 4 Summary

ch4-summary

Module 5: Chapter 5: Introduction to Euclid's Geometry

Euclid's Definitions & Axioms

ch5-definitions

Exercise 5.1 - Solutions

ch5-exercise

Module 6: Chapter 6: Lines and Angles

Types of Angles

ch6-types-angles

Parallel Lines & Transversal

ch6-parallel

Module 7: Chapter 7: Triangles

Congruence of Triangles

ch7-congruence

Properties of Triangles

ch7-properties

Module 8: Chapter 8: Quadrilaterals

Types of Quadrilaterals

ch8-types

Module 9: Chapter 9: Circles

Circle Properties

ch9-properties

Module 10: Chapter 10: Heron's Formula

Heron's Formula

ch10-herons-formula

Module 11: Chapter 11: Surface Areas and Volumes

Surface Areas

ch11-surface-areas

Volumes

ch11-volumes

Module 12: Chapter 12: Statistics

Data Presentation

data-presentation

Measures of Central Tendency

central-tendency

Module 13: Chapter 13: Constructions

Basic Constructions

basic-constructions

Triangle Constructions

triangle-constructions

Module 14: Chapter 14: Probability

Introduction to Probability

intro-probability

Experimental Probability

experimental-probability

Chapter 2: Polynomials

Types of Polynomials

By Number of Terms

Type	Terms	Examples
Monomial	1 term	$5x^2$ , $-3y$ , $7$
Binomial	2 terms	$x + 5$ , $3y^2 - 2$
Trinomial	3 terms	$x^2 + 2x + 1$

By Degree

Degree	Name	Standard Form	Example
0	Constant	$a$	$7$ , $-3$
1	Linear	$ax + b$	$2x + 1$
2	Quadratic	$ax^2 + bx + c$	$x^2 + 3x + 2$
3	Cubic	$ax^3 + bx^2 + cx + d$	$x^3 - 2x^2 + x - 1$
4	Quartic	$ax^4 + ...$	$x^4 - 1$

How to Find the Degree

Step 1: Write polynomial in standard form (descending powers) Step 2: The highest power is the degree

Examples:

Polynomial	Standard Form	Degree
$5 + 3x^2 + x$	$3x^2 + x + 5$	2
$7x - 2x^3 + x^2$	$-2x^3 + x^2 + 7x$	3
$8$	$8$	0

Practice: Classify These

$x^2 + x$ → Quadratic (degree 2), Binomial (2 terms)
$x^3$ → Cubic (degree 3), Monomial (1 term)
$5$ → Constant (degree 0), Monomial (1 term)