# 8: Exercise solutions - Mathematics

8: Exercise solutions - Mathematics

## NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4

Get Free NCERT Solutions for Class 10 Maths Chapter 8 Ex 8.4 Introduction to Trigonometry Class 10 Maths NCERT Solutions are extremely helpful while doing homework. Exercise 8.4 Class 10 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 8 Maths Class 10 Introduction to Trigonometry Exercise 8.4 Provided in NCERT Textbook.

Topics and Sub Topics in Class 10 Maths Chapter 8 Introduction to Trigonometry:

You can also download the free PDF of Chapter 8 Ex 8.4 Coordinate Geometry NCERT Solutions or save the solution images and take the print out to keep it handy for your exam preparation.

 Board CBSE Textbook NCERT Class Class 10 Subject Maths Chapter Chapter 8 Chapter Name Introduction to Trigonometry Exercise Ex 8.4 Number of Questions Solved 5 Category NCERT Solutions

## NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4

NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Exercise 6.4

Ex 6.4 Class 8 Maths Question 1.
Find the square root of each of the following numbers by Long Division method.
(i) 2304
(ii) 4489
(iii) 3481
(iv) 529
(v) 3249
(vi) 1369
(vii) 5776
(viii) 7921
(ix) 576
(x) 1024
(xi) 3136
(xii) 900
Solution:

Ex 6.4 Class 8 Maths Question 2.
Find the number of digits in the square root of each of the following numbers (without any calculation)
(i) 64
(ii) 144
(iii) 4489
(iv) 27225
(v) 390625
Solution:
We know that if n is number of digits in a square number then
Number of digits in the square root = (frac < n >< 2 >) if n is even and (frac < n+1 >< 2 >) if n is odd.
(i) 64
Here n = 2 (even)
Number of digits in √64 = (frac < 2 >< 2 >) = 1
(ii) 144
Here n = 3 (odd)
Number of digits in square root = (frac < 3+1 >< 2 >) = 2
(iii) 4489
Here n = 4 (even)
Number of digits in square root = (frac < 4 >< 2 >) = 2
(iv) 27225
Here n = 5 (odd)
Number of digits in square root = (frac < 5+1 >< 2 >) = 3
(iv) 390625
Here n = 6 (even)
Number of digits in square root = (frac < 6 >< 2 >) = 3

Ex 6.4 Class 8 Maths Question 3.
Find the square root of the following decimal numbers.
(i) 2.56
(ii) 7.29
(iii) 51.84
(iv) 42.25
(v) 31.36
Solution:

Ex 6.4 Class 8 Maths Question 4.
Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.
(i) 402
(ii) 1989
(iii) 3250
(iv) 825
(v) 4000
Solution:
(i)

Here remainder is 2
2 is the least required number to be subtracted from 402 to get a perfect square
New number = 402 – 2 = 400
Thus, √400 = 20

(ii)

Here remainder is 53
53 is the least required number to be subtracted from 1989.
New number = 1989 – 53 = 1936
Thus, √1936 = 44

(iii)

Here remainder is 1
1 is the least required number to be subtracted from 3250 to get a perfect square.
New number = 3250 – 1 = 3249
Thus, √3249 = 57

(iv)

Here, the remainder is 41
41 is the least required number which can be subtracted from 825 to get a perfect square.
New number = 825 – 41 = 784
Thus, √784 = 28

(v)

Here, the remainder is 31
31 is the least required number which should be subtracted from 4000 to get a perfect square.
New number = 4000 – 31 = 3969
Thus, √3969 = 63

Ex 6.4 Class 8 Maths Question 5.
Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained.
(i) 525
(ii) 1750
(iii) 252
(iv) 1825
(v) 6412
Solution:
(i)

Here remainder is 41
It represents that square of 22 is less than 525.
Next number is 23 an 23 2 = 529
Hence, the number to be added = 529 – 525 = 4
New number = 529
Thus, √529 = 23

(ii)

Here the remainder is 69
It represents that square of 41 is less than in 1750.
The next number is 42 and 42 2 = 1764
Hence, number to be added to 1750 = 1764 – 1750 = 14
Require perfect square = 1764
√1764 = 42

(iii)

Here the remainder is 27.
It represents that a square of 15 is less than 252.
The next number is 16 and 16 2 = 256
Hence, number to be added to 252 = 256 – 252 = 4
New number = 252 + 4 = 256
Required perfect square = 256
and √256 = 16

(iv)

The remainder is 61.
It represents that square of 42 is less than in 1825.
Next number is 43 and 43 2 = 1849
Hence, number to be added to 1825 = 1849 – 1825 = 24
The required perfect square is 1848 and √1849 =43

(v)

Here, the remainder is 12.
It represents that a square of 80 is less than in 6412.
The next number is 81 and 81 2 = 6561
Hence the number to be added = 6561 – 6412 = 149
The require perfect square is 6561 and √6561 = 81

Ex 6.4 Class 8 Maths Question 6.
Find the length of the side of a square whose area = 441 m 2
Solution:
Let the length of the side of the square be x m.
Area of the square = (side) 2 = x 2 m 2
x 2 = 441 ⇒ x = √441 = 21

Thus, x = 21 m.
Hence the length of the side of square = 21 m.

Ex 6.4 Class 8 Maths Question 7.
In a right triangle ABC, ∠B = 90°.
(a) If AB = 6 cm, BC = 8 cm, find AC
(b) If AC = 13 cm, BC = 5 cm, find AB
Solution:
(a) In right triangle ABC

AC 2 = AB 2 + BC 2 [By Pythagoras Theorem]
⇒ AC 2 = (6) 2 + (8) 2 = 36 + 64 = 100
⇒ AC = √100 = 10
Thus, AC = 10 cm.
(b) In right triangle ABC

AC 2 = AB 2 + BC 2 [By Pythagoras Theorem]
⇒ (13) 2 = AB 2 + (5) 2
⇒ 169 = AB 2 + 25
⇒ 169 – 25 = AB 2
⇒ 144 = AB 2
AB = √144 = 12 cm
Thus, AB = 12 cm.

Ex 6.4 Class 8 Maths Question 8.
A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain the same. Find the minimum number of plants he needs more for this.
Solution:
Let the number of rows be x.
And the number of columns also be x.
Total number of plants = x × x = x 2
x 2 = 1000 ⇒ x = √1000

Here the remainder is 39
So the square of 31 is less than 1000.
Next number is 32 and 32 2 = 1024
Hence the number to be added = 1024 – 1000 = 24
Thus the minimum number of plants required by him = 24.
Alternative method:

The minimum number of plants required by him = 24.

Ex 6.4 Class 8 Maths Question 9.
There are 500 children in a school. For a P.T. drill, they have to stand in such a manner that the number of rows is equal to the number of columns. How many children would be left out in this arrangement?
Solution:
Let the number of children in a row be x. And also that of in a column be x.
Total number of students = x × x = x 2
x 2 = 500 ⇒ x = √500

Here the remainder is 16
New Number 500 – 16 = 484
and, √484 = 22
Thus, 16 students will be left out in this arrangement.

## RS Aggarwal Class 8 Solutions

Mathematics is a challenging subject to study for. Those who are fundamental concepts are strong enjoy the subject and score high marks. However, it might be the other way around for students who do not have a good grip on the subject. Learning RS Aggarwal solutions class 8 by practising from the RS Aggarwal text-book can be a game changer for those who want to do well in this subject. The RS Aggarwal text-book for class 8 is considered to be one of the most comprehensive materials for Maths. Solving the problems in this book will give a good grip over each chapter.

On our website, we have made CBSE RS Aggarwal Class 8 Maths solutions in free pdf available to download for all our students. This document can be accessed by anyone who wants to go through the solutions for problems from RS Aggarwal class 8 text-book. Vedantu is a platform that provides free NCERT Solution and other study materials for students. Science Students who are looking for NCERT Solutions for Class 8 Science will also find the Solutions curated by our Master Teachers really Helpful.

## NCERT Solutions For Class 10 Maths Chapter 8: Introduction To Trigonometry

Before getting into the details of CBSE NCERT Solutions For Class 10 Maths Chapter 8 – Introduction to Trigonometry, let’s have an overview of the topics and subtopics under this chapter. So, let’s glance through the exercises included in the NCERT Solutions for Class 10 Chapter 8. The exercises included in Class 10 Maths Chapter 8 are Exercise 8.1, Exercise 8.2, Exercise 8.3, Exercise 8.4, Exercise 8.5, and Exercise 8.6.

 Ex 8.1 Introduction Ex 8.2 Trigonometric Ratios Ex 8.3 Trigonometric Ratios of Some Specific Angles Ex 8.4 Trigonometric Ratios of Complementary Angles Ex 8.5 Trigonometric Identities Ex 8.6 Summary

### NCERT Solutions For Class 10 Maths Chapter 8: Introduction to Trigonometry (PDF)

Students can download the CBSE Solutions for Class 10 Maths Chapter 8 from the link given below in this article or bookmark this page to view the NCERT Solutions when necessary. Moreover, Students can also download NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.1, Exercise 8.2, Exercise 8.3, Exercise 8.4, Exercise 8.5, and Exercise 8.6. This will help the students to have a sound knowledge about every topic covered in Chapter 8.

### NCERT Class 10 Maths Chapter 8 PDF: Introduction To Trigonometry

Chapter Description: The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides), and ‘metron’ (meaning measure). Trigonometry is the study of relationships between the sides and angles of a triangle. Long ago, ancient Greek and Indian astronomers used these handy techniques to measure the distances of stars and planets from the Earth very precisely. Even today, most of the technologically advanced methods used in Engineering and Physical Sciences are based on trigonometrical concepts. This branch of Mathematics, called Trigonometry is extremely helpful in dealing with height and distances which are not easy to measure.

In this chapter, you will first study the ratios of sides of a right triangle concerning its acute angles and see how these ratios only depend on the measure of the angles involved. You will then go through the names and definitions of these six trigonometric ratios of an angle. You will also define the value of these trigonometric ratios for standard angles including 0° and 90°. At last, you will also establish some relationships among these trigonometric ratios which are termed as trigonometric identities.

Apart from the theoretical and application part, this chapter is very important and will always serve as fundamentals and pre-requisites for nearly all streams of higher studies including reputed national and international competitions. From the exam point of view, this chapter remains one of the interesting and scoring one with a good number of questions being asked frequently in board exams every year.

### Trigonometry Questions For Class 10 PDF Download: Benefits Of Embibe’s NCERT Solutions For Class 10 Maths Chapter 8

The NCERT Solutions provided by Embibe are prepared by the top teachers with decades of teaching experience. Given below are the benefits of using the NCERT solutions by Embibe:

1. With the help of these solutions, you will not only find answers but also the correct methods to solve problems.
2. NCERT solutions by Embibe include all the exercise questions of the NCERT 10th Maths textbook. By following these solutions, you can easily solve and revise the syllabus of CBSE Class 10 Maths.
3. All the exercises of the NCERT 10th Maths textbook have been solved in a detailed and step-wise manner.
4. Embibe’s NCERT solutions have been compiled in accordance with the latest NCERT guidelines and revised CBSE syllabus.
5. You are not required to pay or sign-up to download the NCERT solutions by Embibe.

Trigonometry is a very important unit in Maths. It finds immense application in real life. The concepts taught in Class 10 Trigonometry are covered in details in Class 11 and 12. Students can find NCERT Solutions for Class 10 Maths Chapter 8 including Exercise 8.1, Exercise 8.2, Exercise 8.3, Exercise 8.4, Exercise 8.5, and Exercise 8.6. So, if you are planning to opt for PCM subjects in your higher secondary, make sure you finish this chapter diligently, understand the concepts and trigonometry formulas, and solve the questions.

### FAQs On NCERT Solutions For Class 10 Maths Chapter 8

Some of the frequently asked questions are given below:

Q1. Find the value of sin 35°/cos 54°.
A. 1

Q2. Find the value of A + B given that sin A = 1/2 and cos B = 1/2.
A. 90 0

Q3. Find the value of cos A and tan A if sin A is given as 3/4.
A. cos A is √7/4 and tan A is 3/√7.

Q4. Given a right-angled triangle ABC with tan A = 1/√3. Calculate cos A cos C – sin A sin C.
A. 0

Q5. There is a pole of height 6m that makes a shadow of length 2√3 m. Find the sun’s angle of elevation.
A.60°

### Practice Class 10 Maths Questions With Embibe

Now that you are provided with CBSE NCERT Solutions For Class 10 Maths Chapter 8 – Introduction to Trigonometry, you can start practicing the questions from this chapter. You can also take a free Class 10 Trigonometry Mock Test on Embibe’s digital learning platform. Taking mock tests on the chapter will give you a better understanding of trigonometric concepts and where you stand in terms of your preparation.

You can also solve free CBSE Class 10 Practice Questions or take Class 10 Mock Tests on Embibe. The best part is that you can access all the solutions, sample questions, and mock tests on Embibe’s learning platform for free. So, now you do not have to worry about scoring well in the exams as Embibe is here to help you with your concepts.

We hope this detailed article on CBSE NCERT Solutions For Class 10 Maths Chapter 8 (Introduction to Trigonometry) is helpful.

If you have any queries regarding this article, drop your questions in the comment section below and we will get back to you as soon as possible.

## 8: Exercise solutions - Mathematics

NCERT Solutions for Class 8 Maths consists of the chapter-wise solutions of all the problems provided in the NCERT textbook for Class 8 Mathematics. GeeksforGeeks has created a detailed chapter-wise solution for the NCERT book of class 8 that contains problems on various topics like Rational Numbers, Linear Equations, Quadrilaterals, Data Handling, and many more. Each chapter in this solution thoroughly covers every exercise along with a detailed step-by-step explanation of the solutions.

### Chapter 1: Rational Numbers

The chapter Rational numbers mainly discuss the characteristics of all the real numbers, integers, whole numbers, rational numbers, and natural numbers. This chapter consists of two exercises only in which the problems in Exercise 1.1 are related to the properties of the rational numbers (closure, commutativity, associativity, etc). However, in Exercise 1.2 the problems are related to the advanced concepts of the rational number like the representation of rational numbers on a number line and to determine any numbers of rational number between any two rational numbers.

### Chapter 2: Linear Equations in One Variable

The linear equations in one variable deal with the expression defined in one variable only and its algebraic operations. This chapter contains six different exercises that have problems based on the linear equations in one variable and its application. Exercises 2.1, 2.2, 2.3, and 2.4 are designed to determine the solution of the linear equation. However, Exercises 2.5 and 2.6 are based on the topic e quations reducible to the linear form.

This chapter covers all types of quadrilaterals such as polygonal shapes like square, rectangle, triangle, pentagon, hexagon, etc. In total, this chapter contains four exercises in which Exercise 3.1 covers the problems on the definition of various polygons and their properties, Exercise 3.2 is based on the concept of the Angle sum property of a polygon. However, Exercise 3.3 covers the elements and the properties of quadrilaterals like trapezium, kite, and parallelogram, and Exercise 3.4 is designed to learn some special types of parallelogram like square, rectangle, and rhombus.

### Chapter 4: Practical Geometry

The chapter practical geometry helps to learn the construction of quadrilateral when different parameters of it are known. This chapter contains a total of five exercises only in which Exercise 4.1 covers the problem for the case when the lengths of four sides and a diagonal are given. Similarly, E xercises 4.2, 4.3 , and 4.4 are based on the topics when two diagonals and three sides are known, two adjacent sides and three angles are given and three sides and two included angles are provided. However, Exercise 4.5 contains problems based on some special cases.

### Chapter 5: Data Handling

Data handling is a method of organizing data or information systematically using diagrams like bar graphs, pictographs, pie charts, and histograms. This chapter consists of only three exercises. Exercise 5.1 is based on the basic concept of representing, organizing, and grouping the data provided while Exercise 5.2 helps to make a pie chart for the given data. Moreover, Exercise 5.3 coves the topic that helps to understand the basic concept of probability.

### Chapter 6: Squares and Square Roots

As the name of the chapter says, Squares and square roots this chapter gives the knowledge of the concept to determine the squares and square root of a number. The different properties and the pattern followed to find a square number are discussed in four exercises. Exercises 6.1 and 6.2 are based on the basic idea of the square numbers and different ways to determine them. Though Exercises 6.4 and 6.5 are focused on the concept of the determination of the square root of a number.

### Chapter 7: Cubes and Cube roots

Again, as the title of the chapter suggest that Cubes and Cube roots this chapter helps to understand the concept to determine the cubes and cube root of a number. The different patterns followed to find a cube and cube root of a number are discussed in only two exercises. Exercises 7.1 contains the problem to determine whether the given number is a perfect cube or not. And Exercises 7.2 focused on the idea of the cube root and the determination of the cube root of a number.

### Chapter 8: Comparing Quantities

This chapter gives a basic understanding of the topics such as increased and decreased percentage, market price, selling price, cost price, discount, and discount price, profit or loss, interest, etc. Total there are three exercises in this chapter, Exercise 8.1 based on the topics ratios and percentage, and Exercises 8.2 and 8.3 covers a wide range of concepts such as percentage, profit or loss, tax, and compound interest.

### Chapter 10: Visualising Solid Shapes

This chapter provides the understanding of different solids shapes when visualized in different dimensions and various terms used to describe their properties. The chapter explains this in three different exercises. Here exercises 10.1 and 10.2 are based on the concept of the visualisation of different solid shapes at different positions and the mapping spaces around the observer. Though, Exercise 10.3 discussed the terms like faces, edges, vertices, and relation between them, related to a solid shape.

### Chapter 11: Mensuration

Mensuration is the chapter that deals with the measurement or the calculations related to determine the area, perimeter, volume of various geometrical figures like square, cube, rectangle, cuboid, cylinder, and triangle, etc. This chapter consists of only four exercises in which Exercises 11.1 and 11.2 deal with problems related to the areas of different geometrical shapes, combination of shapes, and every-day life examples. However, Exercises 11.3 and 11.4 discussed the terminology related to 3-Dimensional shapes.

### Chapter 12: Exponents and Powers

The chapter Exponents and powers cover the primary concepts such as laws of exponents and their applications. This chapter consists of only two exercises, Exercise 12.1 is specifically based on the laws of exponents, and Exercise 12.2 deals with the problems using the applications of power to write large numbers in exponents and vice-versa.

### Chapter 13: Direct and Inverse Proportions

This chapter gives a detailed explanation of inverse and direct proportions through problems discussed in two exercises. In which Exercise 13.1 contains problems to determine the direct proportions between any quantity and Exercise 13.2 deals with the questions from the indirect inverse.

### Chapter 14: Factorisation

This chapter comprises the problems on the factors of natural numbers and algebraic expressions, factorisation by regrouping terms, factorisation using identities, division of algebraic expressions. The chapter includes four exercises out of which exercises 14.1 and 14.2 are based on the topic factorisations and their application while exercises 14.3 and 14.4 emphasize the division of algebraic expressions.

### Chapter 15: Introduction to Graphs

This chapter is all about the basic understanding of the graphs, kinds of graphs, etc. It is mainly explained using three exercises, Exercise 15.1 deals with problems from introduction to graphs and terminology related to it while, problems in Exercises 15.2 and 15.3 provided emphasis on the construction of different types of graphs and their applications.

### Chapter 16: Playing with Numbers

All the above-mentioned chapters basically helped to learn about various kinds of numbers and their different properties likewise in this chapter the concept of numbers is discussed in a more general way. This chapter includes two exercises only, Exercise 16.1 and 16.2 which contains fun activities, puzzles, etc. such as divisibility tests to determine any missing number in a series of numbers.

Maharashtra Board Class 8 Maths Chapter 1 Rational and Irrational Numbers

Maharashtra Board Class 8 Maths Chapter 2 Parallel Lines and Transversals

Maharashtra Board Class 8 Maths Chapter 3 Indices and Cube Root

Maharashtra Board Class 8 Maths Chapter 4 Altitudes and Medians of a Triangle

Maharashtra Board Class 8 Maths Chapter 5 Expansion Formulae

Maharashtra Board Class 8 Maths Chapter 6 Factorisation of Algebraic Expressions

Maharashtra Board Class 8 Maths Chapter 7 Variation

Maharashtra Board Class 8 Maths Chapter 8 Quadrilateral: Constructions and Types

## NCERT Solutions for Class 8 Maths

NCERT Solutions for Class 8 Maths comprises of 16 Chapters for Class 8, which contains 52 Exercises. These Solutions are provided where each of these exercises, have been answered in detail by our team of experts which includes teachers at professionals. These solutions have been compiled in an easy to understand manner, keeping in mind, the perspective of strong, and weak students.

Download chapter wise detailed NCERT Solutions for Class 8 Maths/ CBSE Class 8 Maths NCERT Solutions .

### Chapter 1 – Rational Numbers Class 8 Maths

Class VIII Mathematics opens up with revision of Rational Numbers in chapter 1. It covers important topics like properties of rational numbers like closure, commutativity, and associativity.

It discusses the role of zero and one. Further, it investigates additive inverse, reciprocal, distributivity, rational numbers on a number line and between two rational numbers.

### Chapter 2 – Linear Equation in one Variable

Chapter 2 of class VIII teaches the methods of solving different types of linear equations. It familiarises us with some applications of linear equations. We also come across equations reducible to the linear form.

### Chapter 3 – Understanding Quadrilaterals Class 8 Maths

Classification of polygons, angle sum property of quadrilaterals, sum of exterior angles of a polygon, kite, parallelograms, elements of a parallelogram, angles and diagonals of parallelogram, rhombus, rectangle, and square are discussed in chapter 3 of class VIII.

### Chapter 4 – Practical Geometry Class 8 Maths

We further deepen our understanding of Practical Geometry in chapter 4 of class VIII. We lean the construction of quadrilaterals when certain measurements like sides and angles are given, we also learn about some special cases in construction of quadrilaterals.

### Chapter 5 – Data Handling

Chapter 5 for class VIII is a lesson on Data handling. We determine the ways of collecting, organising, and grouping data. We study about bar graphs, pie-charts or circles graphs, histograms, and chance and probability.

### Chapter 6 – Square and Square roots Class 8 Maths

In chapter 6 of class VIII, we come across the concepts of squares and square roots. We analyse the properties of square numbers, study patterns, and we learn to find the square of a number.

We are then introduced to square roots. We discover various ways to find square roots like repeated subtraction, prime factorisation, and division method. We learn square roots of decimals and estimating square roots.

### Chapter 7 – Cube and Cube roots

Chapter 7 of class VIII explores the concepts of cubes and cube roots. We learn about interesting patterns that cubes follow. We also learn to find cube root of a cube number.

### Chapter 8 – Comparing Quantities Class 8 Maths

This chapter further digs the concepts involved in comparing quantities like ratios and percentages. It unriddles the methods of finding increase or decrease per cent, finding discounts, estimation in percentages, profit and loss, calculating taxes, compound interest and its applications.

### Chapter 9 – Algebraic Expressions and Identities Class 8 Maths

Definition of expressions, terms, factors and coefficients, monomials, binomials, polynomials, like and unlike terms, addition, subtraction, and multiplication of algebraic expressions are discussed in chapter 9 of class 8.

We also explore the concepts of identity, standard identities, and we applying identities.

### Chapter 10 – Visualising Solid Shapes

We exemplify our knowledge of solid shapes in the chapter Visualising Solid Shapes. We learn about the various views of 3D-shapes, we learn about mapping space around us. We then discuss faces, edges and vertices, and Euler’s formula by the end of chapter 10 of class 8.

### Chapter 11 – Mensuration Class 8 Maths

Chapter 11 of class 8 begins with recalling the previous concepts of mensuration. The area of trapezium, area of a general quadrilateral, area of special quadrilaterals, and area of a polygon are determined.

We are introduced to surface areas and volumes of solid shapes like cube, cuboid, and cylinders.

### Chapter 12 – Exponents and Powers

The concepts surrounding exponents and powers are further elucidated in chapter 12 of class 8. Powers with negative exponents, laws of exponents, and use of exponents to express small numbers in standard form are are practised.

### Chapter 13 – Direct and Inverse Proportions Class 8 Maths

We are introduced to direct and inverse proportions in chapter 13 of class 8. This chapter explores direct proportions, inverse proportions, and helps us understand their application through solving problems.

### Chapter 14 – Factorisation Class 8 Maths

Factors of natural numbers, factors of algebraic expressions, factorisation, common factors, regrouping, factorisation using identities, factors of the form (x+a)(x+b), division of algebraic expressions, etc are explained in chapter 14 of class 8.

### Chapter 15 – Introduction to Graphs

An essential part of mathematics, graphs are discussed in chapter 15 of class 8. We are demystify bar graphs, pie graphs, line graphs, histograms, linear graphs, location of a point, coordinates, and some applications of the explained topics like time and distance, and simple interest.

### Chapter 16 – Playing with Numbers Class 8 Maths

Last chapter of class 8 helps us in playing with numbers. We study about numbers in general form, games with numbers, letters for digits, tests of divisibility by numbers like 10 and 2.

You can also download Maths Class 8 NCERT Book Pdf from official website.

## 8: Exercise solutions - Mathematics

Hey, are you a class 12 Student and Looking for Ways to Download Class 12 Maths Chapter 8 Exercise 8.2 Solutions? If Yes then you are at the right place.

All the solutions of Class 12 Math Chapter 8 exercise 8.2 is prepared by Kota’s top IITian’s Faculties by keeping Simplicity in mind.

If you want to score high in your class 12 Maths Exam then it is very important for you to have a good knowledge of all the important topics, so to learn and practice those topics you can use eSaral NCERT Solutions.

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