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 4: Linear Equations in Two Variables

Exercise 4.2 - Solutions

❓Question 1

$y = 3x + 5$ has how many solutions?

(iii) Infinitely many solutions ✓

❓Question 2

Write 4 solutions of $2x + y = 7$ :

$(0, 7)$
$(1, 5)$
$(2, 3)$
$(3, 1)$

❓Question 3

Check if solutions of $x - 2y = 4$ :

(iii) $(4, 0)$ : $4 - 0 = 4$ ✓ → Yes

❓Question 4

Find $k$ if $(2, 1)$ is solution of $2x + 3y = k$ :

$2(2) + 3(1) = k$ $k = 7$