# NCERT Solutions for Class 8 Maths

NCERT Solutions for Class 8 Maths in PDF file format Hindi Medium as well as English Medium free to download or view online. All the solutions are updated for academic session 2021-2022 based on latest NCERT Books 2021-2022.

NCERT Solutions and Exemplar problems both are important for class 8 Mathematics practice. NCERT Solutions 2021-22 of all questions are described completely showing all steps with formulae. If someone is still facing problem to understand the solution any question, please specify through “Discussion Forum” section. Download 8 Maths Solutions App or 8 Ganit App, which work offline without internet also.## NCERT Solutions for Class 8 Maths 2021-2022

##### Chapter 1 Rational Numbers

To download class 8 Maths, just follow the links given below. There are solutions in Hindi as well as English Medium free to use.

##### Chapter 2 Linear Equations in one Variable

There are seven main points given in chapter 2 of 8th Mathematics. All the topics are given separately in six exercises.

##### Chapter 3: Understanding Quadrilaterals

There are total four exercises in class 8 Maths chapter 3. Students can get there solutions from the links given below.

##### Chapter 4: Practical Geometry

Just picked up the geometrical instruments and start doing each constructions. This is the only way to learn chapter 4 of class viii mathematics.

##### Chapter 5: Data Handling

There are only three exercises in chapter 5 of class 8th Maths. Solutions links of these exercises are given below.

##### Chapter 6: Square and Square Roots

Square and square roots is one of the most important chapters of class 8th Math. This chapter is useful not only in class 8 but in next classes also. Practice well to learn it better using the solutions given below.

##### Chapter 7: Cube and Cube Roots

There are only two exercises in class 8th Maths chapter 7, which are given below with the complete solutions.

##### Chapter 8: Comparing Quantities

Find the links given below to practice all the questions of class 8 Maths chapter 8. Solutions of all three exercises are given here with chapter 8 main link.

##### Chapter 9: Algebraic Expressions and Identities

There are total five exercises in class 8 Maths chapter 9 as per NCERT Textbooks. All the exercises need more practice to be confident. This chapter is one of the most important chapters of 8th Mathematics.

##### Chapter 10: Visualizing Solid Shapes

All the topics of 8th Maths chapter 10 are divided into three exercises. The links of the solutions of these exercises are given below.

##### Chapter 11: Mensuration

If someone practice these exercises, learning the formulae, find it as an easier chapter otherwise it is considered as a difficult chapter. Get here the solutions, and start practicing.

##### Chapter 12: Exponents and Powers

None of the two exercises are difficult in class 8 Maths chapter 12. But the exercise 12.1 takes little bit more time as compare to exercise 12.2, get the solutions in link given below to practice.

##### Chapter 13: Direct and Inverse Proportions

Once read the concepts given in textbook of 8th Mathematics and now start practicing. To know whether the direction of practice is write or not, follow the solutions given below.

##### Chapter 14: Factorization

If someone have done chapter 9 of 8th Maths confidently, he would have not any difficult term in chapter 14. Otherwise there may be difficulties in forming the factors of polynomials. Just get the solutions and try yourself to check whether it difficult or not.

##### Chapter 15: Introduction to Graphs

Making graphs based on statistical data is always seems easier to most of the students. Here also the exercises are based on formation as well as observation of the graphs.

##### Chapter 16: Playing with Numbers

In first exercise of chapter 16 of 8th math, we have to learn and prepare to play with the questions given in exercise 16.2 of 8th Mathematics.

### Get here NCERT Solutions for Class 8 Maths All Chapters

- Chapter 1: Rational Numbers
- Chapter 2: Linear Equations in one Variable
- Chapter 3: Understanding Quadrilaterals
- Chapter 4: Practical Geometry
- Chapter 5: Data Handling
- Chapter 6: Square and Square Roots
- Chapter 7: Cube and Cube Roots
- Chapter 8: Comparing Quantities
- Chapter 9: Algebraic Expressions and Identities
- Chapter 10: Visualizing Solid Shapes
- Chapter 11: Mensuration
- Chapter 12: Exponents and Powers
- Chapter 13: Direct and Inverse Proportions
- Chapter 14: Factorization
- Chapter 15: Introduction to Graphs
- Chapter 16: Playing with Numbers

Class: 8 | Mathematics |

Contents: | NCERT Solutions 2021-2022 |

### 8th Mathematics NCERT Solutions

NCERT Solutions for class 8 Maths are given on this webpage. Please give feedback and suggestions to improve the contents and quality of 8th Maths if possible. Use Vedic Maths to make your calculations faster and better. We have started Holiday Homework section to help the students in solving holiday home work in summer vacation. Assignments, Notes, Sample Papers, Chapter test and other study material related to class 8 Maths will be uploaded for the session 2021-22.

### Class 8 Maths NCERT Solutions & Main Points of All Chapters

#### Chapter 1: Rational Numbers

Class 8 Maths Chapter 1 is based on Rations Numbers, which is the collection of Integers, Natural Numbers, Whole Numbers, Decimal and Fractions. We will check here the closure property under Addition, Multiplication, Division and Subtraction for Rational Numbers. **Exercise 1.1** of Class 8 Maths is covering the questions on Multiplicative Inverse and other properties of Rational Numbers. In **Exercise 1.2** Class 8 Maths, we will draw the Rational Numbers on Number Line.

#### Chapter 2: Linear Equations in one Variable

Class 8 Maths Chapter 2 describes how to solve a linear equation in one variable. In **Exercise 2.1**, the simple linear equations in the variable are given to simplify and solve them, whereas **Exercise 2.2** contains the questions based on the application of linear equations. Class 8 Maths **Exercise 2.3** contains some tricky linear equations to solve them by simplification. **Exercise 2.4** of 8th Maths contains some application on a day to day life based on linear equations in one variable concept. In **Exercise 2.5**, we have to reduce the given equation into linear before solution and **Exercise 2.6** has the miscellaneous questions on Chapter 2 of Class 8 Maths.

#### Chapter 3: Understanding Quadrilaterals

Class 8 Maths Chapter 3 deals with the plane curves like various type of polygons as a triangle, quadrilateral, pentagon, hexagon, heptagon, etc. **Exercise 3.1** briefs about the interior and exterior parts of a closed figure, diagonals of a polygon, convex and concave polygons and angle sum property of a polygon. All the questions in **Exercise 3.2** are following the property of the Measures of the Exterior Angles of a Polygon. **Exercise 3.3** is based on types of quadrilaterals like Trapezium, Kite, Parallelogram with its angles and diagonals. We will discuss some particular type of quadrilateral in **Exercise 3.4**. These quadrilaterals are Rhombus, Rectangle and Square.

#### Chapter 4: Practical Geometry

In Class 8 Maths Chapter 4, we will discuss how to construct a unique quadrilateral under the given measurements. All the questions of **Exercise 4.1** are on the condition when four sides and one diagonal are given, whereas in **Exercise 4.2**, and we have to construct a quadrilateral when two diagonals and three sides are given. Similarly, in **Exercise 4.3**, the given conditions are two adjacent sides and three angles, and in **Exercise 4.4**, it is three sides, and two included angles of a quadrilateral are given. The last exercise that is **Exercise 4.5** contains the constructions of quadrilateral when other special properties are known.

#### Chapter 5: Data Handling

Class 8 Maths Chapter 5 starts with the concepts of Class Intervals, Lower and Upper Limits, Range, Class Width and Class Size. This is an introduction to Histogram. So, we have to deal with Histogram in **Exercise 5.1** of Class 8th Maths. The second exercise that is **Exercise 5.2** represents another way of graphical representation, which is Pie Chart or Circle Graph. The third and last topic in **Exercise 5.3** is Probability. It describes the concepts of events, outcomes, total favourable events and the total number of events. The Probability is an important topic, even in higher classes.

#### Chapter 6: Square and Square Roots

In Class 8 Maths Chapter 6, we will learn how to find square or square roots of a number. In **Exercise 6.1**, most of the questions are based on hit and trial method or successive addition method. **Exercise 6.2** is related to find the square of a number by just multiplying the number to itself or using the Binomial Formula of expansion. A brief intro about Pythagoras Triplet is also given in the second exercise. In **Exercise 6.3**, we have to find square roots of a number by successive subtraction or using Prime Factorisation method. **Exercise 6.4** is designed to find the square roots using division methods as well as by estimation. Here we can find the square roots of decimal numbers also.

#### Chapter 7: Cube and Cube Roots

In Class 8 Maths Chapter 7, we will discuss with the cubes of a number and its cube root also. **Exercise 7.1** explain the method of finding cube by adding a consecutive odd number or by using prime factors. Questions related to cube roots are given in **Exercise 7.2** of Class 8 Maths. We can also find the cube root of a number using its Prime Factorisation.

#### Chapter 8: Comparing Quantities

Class 8 Maths Chapter 8 includes the questions related to ratio and proportion. In **Exercise 8.1**, questions are on ratios and percentage with some practical application. Increase and decrease the percentage, profit and loss percentage, discount, sell tax and VAT related questions are there in **Exercise 8.2** of Class 8 Maths. **Exercise 8.3** covers the questions based on Simple and Compound Interest when the interest is compounded yearly, half-yearly or quarterly. It also includes the sums of compound interest based on daily life.

#### Chapter 9: Algebraic Expressions and Identities

In Class 8 Maths Chapter 9, the concepts of algebraic expression with terms, factors and coefficient of Monomial, Binomial and Trinomials are given. Questions of **Exercise 9.1** are based on like and unlike terms and addition or subtraction of algebraic expression. Introduction of multiplication of algebraic expression is given in **Exercise 9.2** of 8th Maths. Most of the questions carry the product of monomials. **Exercise 9.3** includes the questions in which we multiply a polynomial by a monomial, whereas in **Exercise 9.4**, we learn how to multiply a polynomial by another one. The questions based on identities are given in **Exercise 9.5** of Class 8 Maths.

#### Chapter 10: Visualizing Solid Shapes

In Class 8 Maths Chapter 10 states that the 3-dimensional object looks different when seen from different positions. In **Exercise 10.1**, we will learn to plot a 3-D object using its Side view, Front view, Top view or some other factors. The description of mapping places and spaces are given in **Exercise 10.2** of Class 8 Maths. In **Exercise 10.3**, we will learn to find out the Edges, Faces and Corners or Vertices of a 3 – D object. Euler’s Formula (F + V – E = 2) is important in this exercise. Most of the time, a question based on Euler’s Formula is asked in school exams.

#### Chapter 11: Mensuration

Class 8 Maths Chapter 11 Mensuration is not only the main topic for class 8, but it is important for further classes also. **Exercise 11.1** contains only five questions, in which the 5th question is tricky. In **Exercise 11.2**, we will deal with the areas related to Trapezium and another quadrilateral, when the perpendicular to the side or diagonal is given. Next step is to find the surface area of solid figures in **Exercise 11.3** of Class 8 Maths. Here, we will learn to find out the areas of Cube, Cuboid, Cylinder, Sphere, Hemi-sphere or Cone. The volume of these 3 – D figures can be obtained using the formulae used for **Exercise 11.4** in 8th Maths.

#### Chapter 12: Exponents and Powers

In Class 8 Maths Chapter 12, we will study the numbers having negative or positive powers. **Exercise 12.1** is based on the Laws of Exponents. Questions 5, 6 and 7 are important for exams. The second exercise explains about the Scientific Form or Standard Form. In **Exercise 12.2**, we convert the numbers in the standard form with the help of exponents.

#### Chapter 13: Direct and Inverse Proportions

Class 8 Maths Chapter 13, we have to check whether the value of both the quantities are increasing or one is increasing and other is decreasing. **Exercise 13.1** has the questions of Direct Proportion, where the two quantities increase or decrease together. Similarly, **Exercise 13.2** also deals with Inverse Proportion, where one value is increasing, but other is decreasing. The second exercise also contains the questions where Direct and Inverse are implemented in the same question.

#### Chapter 14: Factorization

In Class 8 Maths Chapter 14, we will study about factors of natural numbers as well as algebraic expressions. In **Exercise 14.1**, we will make factors by regrouping the terms, whereas, in **Exercise 14.2**, identities are the main tool for Factorisation. Division of algebraic expression by monomial or polynomial is important for class 8th students. **Exercise 14.3** contains questions based on the division of polynomials by another polynomial. At last, in **Exercise 14.4**, there some errors given in equations. Students have to remove these errors to make the equations or identities true.

#### Chapter 15: Introduction to Graphs

Class 8 Maths Chapter 15 describes the methods to plot a Bar Graph, a Pie Chart or Circle Graph, Histograms and a Line Graph. Most of the questions in **Exercise 15.1** are based on Line Graphs. Concepts of the coordinate system, x-axis and y-axis are given in **Exercise 15.2** of Class 8 Maths. Here, we learn how to take points of x – coordinates and y – coordinates on a plain sheet of paper. Graphs related to two variables are present in **Exercise 15.3** of 8th Maths. These are the questions based on the application of linear equations in two variables.

#### Chapter 16: Playing with Numbers

In Class 8 Maths Chapter 16, we have to represent numbers in a general form. **Exercise 16.1** is just based on addition, subtraction and multiplication of numbers in the form of a puzzle. This the most exciting exercise to solve the questions with fun. In **Exercise 16.2** of Class 8 Maths, we will discuss the test of divisibility by 2, 3, 5, 9 and 10. This exercise is also enjoyable. No one bore doing these exercises of Class 8 Maths Chapter 16 Playing with Numbers.

##### How many chapters are ther in Class 8 Maths?

There are total 16 Chapters in Class 8 Maths NCERT Book. All chapters are compulsory for the exams.

##### Which is the most interesting chapter in Class 8 Maths?

The most interesting chapter of class 8 is Chapter 16 Playing with Numbers. It is really a play with Maths. There are puzzles of missing numbers.

##### How can I manage to score good marks in 8th Maths being an average student?

There are some easy as well as difficult chapters in all the subjects. Its all varies from student to student. Some student enjoy doing all the time Maths but some get tired and bored in the same calculations. If a student who is somehow weak in Maths, he should start that chapter of Maths, which is most easier for him. Gradually practicing will increase the level of confidence and the interest towards Maths will be generated automatically.

##### What is better for class 8 Mathematics – Studying online on website or offline through books?

Studying offline through books is always better than any website or other online portals. Offline study using latest NCERT Books for class 8 Maths generates interest to do hard work whereas online portals are good only if you have any doubt in questions. Studying through Phone, laptops, computers, tablets make us mentally tired where studying offline compel us to think more and more about the fact we are studying.

##### How to score 90% or more marks in class 8 Maths exams?

Mathematics, as we all know, is a practice oriented subject. The more you practice, the more you will understand that will help you score good in the examinations. In Class 8 Maths, everyone should carefully read the examples given in each chapter of mathematics and then solve each question given in the exercises on its own. If the question is not solved or answered, then you should try and try again. Solving the questions by various methods help us to learn many different ways of doing each question. If you have no idea about a question in the exam or do not have complete confidence in any question, then this practice of solving help you here to find proper solutions. We see that even the toughest question gets solved by trying once or twice. In this way. Students will feel that their performance in day to day examinations gets better and easily get 90% or even more marks in the annual examination of Class 8 Maths.

##### How can I easily pass the Class 8 Maths exam?

There are a total of 16 chapters in the class 8 Maths NCERT Textbook. According to the interest of the students, they find that some chapters are simple but few are difficult one. By solving all the questions of the easy chapters we can easily manage passable marks in 8th Maths. For example, linear equations with one variable, rational numbers, Data Handling, introduction to graphs and playing with numbers all seem easy.

##### Which is the easiest chapter of class 8 Maths NCERT?

The easiest chapter in Class 8 Mathematics is chapter 2 Linear Equations in One Variable. It has a total of 6 exercises. Chapter 2 of 8th Maths is easy as well as very useful for examinations. By practicing this chapter, we can score better marks even in less practice. Class 8 Chapter 2 is one of the very important chapters in next classes also.

##### Which lesson is considered the most difficult chapter of Class 8 Maths?

Which chapter is difficult and which is simple, generally it can vary from student to student. But most of the students find difficulty in Chapter 9 algebraic expressions and identities of Class 8 Maths. Most of the students face difficulties during implementation of identities in questions. Even after solving each question repeatedly, one is not able to get the confidence which is easily found in the rest of the chapters.

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