# NCERT Solutions for Class 8 Maths

Vedantu brings you comprehensive NCERT Solutions for Class 8 Maths. This PDF is the best study material for Class 8 Maths you can find. You can use these solutions during your preparation as well as for revision for your examination.

These NCERT Solutions are based on the updated CBSE syllabus, and guidelines. The NCERT Solutions for Class 8 Maths are solved in such a way that it will help students to understand with ease and further learn the topic with confidence. Following these solutions will help students to develop and score well in the Class 8 Maths Exam.

Moreover, the solutions for each exercise are arranged in separate PDF files. These Maths NCERT Solutions Class 8 PDF files can be downloaded for free from the official website of Vedantu.

You can also download and refer to the Class 8 Maths book PDF by signing up on Vedantu. For better assistance, you can register for the online live classes conducted by our mentors. Our mentors will help you with your doubts so you can prepare better for your examination. Besides Maths, you can also get reliable NCERT Solutions for Class 8 Science on Vedantu.

## NCERT Solutions for Class 8 Maths Chapter-wise PDFs

The NCERT Class 8 Maths Solutions are made available in a systematic manner. The methodical chapter-wise arrangement of the solutions ensures that students make judicious use of their time. The explanations provided are in accordance with the NCERT Book of Class 8 Maths and will allow students to understand the concept behind each topic. Even the most complex problems have been deconstructed in a logical manner to ensure smooth understanding. Students can find complete details of the chapters and exercises included in Maths Class 8 NCERT Solutions below:

### NCERT Class 8 Maths Solutions Chapter 1 Rational Numbers Exercise PDF

The importance of rational numbers is that they help describe certain quantities or measures that simply integers cannot. Rational numbers are used to measure quantities like length, mass, time, or other quantities.

The first chapter in the NCERT Class 8 textbook is based on the topic of rational numbers. Students will learn about the properties of integers, natural and whole numbers. Representation of rational numbers on the number line, the role of zero and one in addition and multiplication have been discussed as well. Students need to have a good grasp of this chapter to understand more complex concepts. Details of exercises and questions included in the chapter are

 Chapter 1 - Rational Numbers Exercises in PDF Format Exercise 1.1 11 Questions & Solutions (11 Short Answers) Exercise 1.2 7 Questions & Solutions (7 Short Answers)

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 1 of CBSE Class 8 Maths Solutions –

There are 2 exercises in the rational numbers chapter of your Class 8 Maths Solutions and maths textbook.

The first topic in rational numbers is the introduction. You will learn the basics and revise some of the previous topics. You should not skip the introduction; instead, go through it once as it will help you to understand the basic concepts. Use the NCERT maths book solutions for class 8.

In the first exercise, there are 11 questions. In this exercise, you will learn about the properties and how to use them properly. Solve all the questions and revise them using the solutions. You will get to know about the commutative, distributive, etc. properties and how to solve questions using them. You will also learn inverse and multiplicative inverse. Maintain separate notes for practicing and revising.

In the next exercise, you will learn how to represent numbers on the number line. This exercise is very important. Practice thoroughly and revise. In this exercise, there are 7 questions. Practice all the properties and methods, solve related questions, learn the method, cover all the crucial points, and solve examples.

The last topic in this chapter is about the rational number between two rational numbers, in this topic you have to learn how to find a rational number between two rational numbers. Practice the method and solve examples. Use the solutions to solve the exercise questions. Rational numbers is an important chapter and it holds 8 marks. Prepare properly and you can easily score well in this chapter and the exam.

### NCERT Class 8 Maths Solutions Chapter 2 Linear Equations in One Variable Exercise PDF

The most important use of linear equations in one variable is to calculate an integer’s value in cases where two or more integers are given, where one integer is unknown.

Students in this chapter are introduced to the concept of linear equations in one variable. Several methods to solve these linear equations have also been provided. The exercises provided in this chapter test the ability of the students to solve these problems by employing different methods. The 65 questions in this chapter are divided into 6 exercises in the following manner.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 2 of CBSE Class 8 Maths Solutions –

Topics that are Covered in the Linear Equation in one Variable are as follows:

This chapter introduces you to the linear equation and its forms. Learn how to solve an equation in one and two variables. The chapter linear equation in one variable comprises 7 exercises and you have to learn and solve them all.

The second topic in this chapter is solving equations, learn all the methods by which you can solve an equation. The following are the methods by which you can solve an equation: graphical method, elimination method, substitution method, matrix, and determinants method. Practice all the methods and solve at least a few questions using each method.

The next topic is the application of linear equations, in this, you have to learn about the applications of linear equations. To understand you can go through the examples. The 6th topic in this chapter is reducing equations to a simpler form, learning how you can reduce equations, and solving as many examples as possible.

You also have to learn how to reduce it to linear form. Solve all the exercise questions and be thorough with the examples while learning. Use the NCERT solutions to practice additional questions. Linear equations in two variables is an important chapter and you have to prepare it properly only then can you score well in it. This chapter holds 10 marks.

### NCERT Class 8 Maths Solutions Chapter 3 Understanding Quadrilaterals Exercise PDF

Understanding quadrilaterals can help greatly in architecture and engineering. It helps in creating floor plans for buildings or similar structures.

This chapter provides the students with a general understanding of the topic of quadrilaterals along with the study of their properties. Students get to explore the dynamic world of quadrilaterals and also polygons (pentagon, hexagon, etc.). The four exercises included in this chapter have the questions distributed as

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 3 of CBSE Class 8 Maths Solutions –

Topics Covered in Understanding Quadrilaterals are as Follows:

The third chapter in your Class 8 Maths NCERT Solutions and NCERT textbook is understanding quadrilaterals. In this chapter, there are 5 exercises. The topic polygon is the second topic and it is very important.

Learn about polygons and their shapes. Learn about the types of polygons and check a few examples for each. The next subtopic in this topic is angles of polygons and it is very important and you should solve examples for all the formulas and properties. Learn the formulas for interior angles and formulas for area and perimeter. Learn about the quadrilaterals when they have 3 sides and 4 sides. Solve all the questions and examples present in this topic.

The next topic in this chapter is exterior angles of a polygon, learn about exterior angles, the sum of the exterior angles, and solve questions related to them. Go through a few examples to understand the concept well. In the next topic in this chapter, you will learn about parallelogram, trapezium, and kite. Learn all the properties of each shape and be thorough with it.

The last topic in this chapter talks about some special parallelograms. They are rhombus, square, and rectangle. Learn about two and three-dimensional shapes. Learn and practice all the properties and formulas of each special parallelogram. Solve exercise questions and use the NCERT solutions to your advantage. This chapter holds 13 marks and you have to study it properly. Practice solving additional questions for each chapter.

### NCERT Class 8 Maths Solutions Chapter 4 Practical Geometry Exercise PDF

Practical geometry helps in the visualization and realization of geometry in the real world. This can be used in areas of construction, sculpture, computation of dimensions, and so on.

Now that the students are equipped with the knowledge of quadrilaterals, the chapter on Practical Geometry teaches them to construct quadrilaterals on the basis of the given parameters such as lengths of certain sides, enclosing angle, and length of the diagonal, etc. By practicing the exercise questions given in this chapter, students are likely to become well-versed with the concept of quadrilaterals and utilize their understanding for solving more complex problems. The five exercises included in this chapter are:

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 4 of CBSE Class 8 Maths Solutions –

Topics in Practical Geometry are as Follows:

The fourth chapter is practical geometry and with preparation, you can score well in this chapter. There are 3 exercises in this chapter. The first important topic in this chapter is constructing a quadrilateral, you have to learn how to construct quadrilaterals when 4 sides and 1 diagonal are given, 3 sides with 2 angles are given, and 2 sides with 3 angles are given.

Solve examples and questions for better understanding. Practice the steps and try to memorize them by understanding the concept. The last topic in this chapter is some special cases, in this topic, you will learn how to construct a rhombus.

Learn the steps to construct a rhombus and practice it. You will be asked to construct different shapes from this chapter thus, you have to practice and memorize them all. This chapter holds 8 marks and it's easy thus, you can score well with preparations. You will get long answers to questions from this chapter. Solve all the exercise questions and use the NCERT solutions to get help.

### NCERT Class 8 Maths Solutions Chapter 5 Data Handling Exercise PDF

Storage of data and its security banks on the art and skill of data handling. Students need to have an idea of data handling to be able to manage their own and others’ important information safely and accurately.

Storage of data and its security banks on the art and skill of data handling. Students need to have an idea of data handling to be able to manage their own and others’ important information safely and accurately.

Data is a set of information that can be subjected to analysis. In this chapter, students learn to organize the given data in a systematic way which is the basis of data handling. Students also learn to represent the organized data in the form of bar graphs, pie charts, histograms, etc. The details of the exercises included in this chapter are given below.

 Chapter 5 - Data Handling Exercises in PDF Format Exercise 5.1 5 Questions & Solutions (5 Short Answers) Exercise 5.2 5 Questions & Solutions (3 Long Answers, 2 Short Answers) Exercise 5.3 6 Questions & Solutions (2 Long Answers, 4 Short Answers)

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 5 of CBSE Class 8 Maths Solutions –

Topics that are Covered in Data Handling are as Follows:

The fifth chapter is data handling, this chapter is important and it holds 11 marks. There are 5 exercises in this chapter and you have to be thorough with them all. The chapter talks about how you can handle data and make use of them. The first topic is organizing data, in this topic you have to learn how to organize and group data.

Learn the method and check a few examples to understand the topic properly. Learn why we need to organize and group data, their advantages, and their disadvantages. Solve the exercise questions and sample papers. Learn about grouping of data, lower-class limit, upper-class limit, etc. The next topic in this chapter is the pie chart. Learn what a pie chart is and its formulas. Learn how to work with percentages for a pie chart, and learn and practice all the steps and formulas. Learn how to create a pie chart with given values and solve a few examples to learn it properly.

Last but not least you have to learn the uses of the pie chart and also study the advantages and disadvantages of the pie chart. You can easily score good marks if you prepare the chapter properly. Practice the exercise questions and examples. learn about the types of graphs such as bar, linear graph, and histogram. Learn how to make them and their uses. Know their advantages and disadvantages.

The last topic in this chapter is chance and probability, this topic is small and you can learn it quickly. Learn about chance and probability of events and probability formulas. Practice a few examples and exercise questions related to this topic. Practice all the exercise questions from the NCERT solutions to understand the topics and concepts better.

### NCERT Class 8 Maths Solutions Chapter 6 Squares and Square Roots Exercise PDF

Squares and square roots are primarily used in calculating the constructional area of spaces, calculating financial gains and losses, interest rates, and so on.

A very important chapter in Class 8 from an examination point of view. If you are familiar with all the concepts in this chapter, it can also be very interesting to solve. Students are taught about the concept of squares and square roots and the interesting patterns that are associated with the same. The concept and properties of Pythagorean triplets have also been included in this chapter. Students should solve all the exercise questions of this chapter, which includes:

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 6 of CBSE Class 8 Maths Solutions –

Topics that are Covered in Squares and Square Roots are as Follows:

The sixth chapter is squares and square roots. There are 7 exercises in this chapter and you have to practice them all. First, you have to learn about square numbers and the properties of square roots. Learn about one’s digit in the square of a number and solve examples to understand it. learn the interesting patterns of square roots and solve a few examples before solving the exercise questions.

The next topic in this chapter will teach you how to find the square of a number. Learn about odd and even square numbers, learn their properties and square roots. Practice as many questions as possible, and use the NCERT solutions to speed up your preparation.

The next topic in this chapter talks about how you can find the square root of a number by repeated subtraction. Learn the method and practice examples and questions related to this topic. The 6th topic in this chapter is finding the square root of a decimal, in this, you will learn how to find the square root of a decimal. Learn the steps and understand them properly. Practice a few examples related to this topic. The last topic in this chapter is estimating square roots. Learn how to estimate a square root, and practice examples and questions related to it. This chapter is important and you have to prepare it properly. Square and square roots hold 12 marks and both short and long questions will be asked in this chapter. Solve additional questions from the NCERT solutions.

### NCERT Class 8 Maths Solutions Chapter 7 Cubes and Cube Roots Exercise PDF

Cubes and cube roots are also used in calculating the volumes of objects, exponents, interest rates, and so on.

This chapter is an advancement over the previous chapter as it introduces students to cubes and cube roots. Students get to learn the properties and patterns associated with the same as they go through the chapter. To become thorough with the chapter, students are urged to solve all the exercises which include:

 Chapter 7 - Cubes and Cube Roots Exercises in PDF Format Exercise 7.1 4 Questions & Solutions (4 Short Answers) Exercise 7.2 3 Questions & Solutions (2 Long Answers, 1 Short Answer)

Topics that are Covered in Cubes and Cube Roots are as Follows:

The next chapter is cubes and cube roots. The first topic in this chapter is the cube and it is on how to find perfect cube numbers. Learn the application of perfect cubes and solve questions related to them. Solve the exercise questions and examples to understand the topic better. Practice questions on perfect cubes also.

The last topic in this chapter is the cube root of a number, first, learn the definition of a cube root, then practice how to find a cube root of a number. Practice all the exercise questions and use the NCERT solutions to understand and chapter better.

Go through the cubes and cube roots table. This chapter is comparatively smaller than the rest and it holds 6 marks. This does not mean that you can skip it. Practice and cover all the topics only then you can score well in the exam. Another important topic in this chapter is the cube root by prime factorization method, as you can already understand that this topic is going to be about how you can find the cube root of a number by prime factorization. Practice examples and solve similar questions. Some examples of numbers are cube roots of 512, 759, 216, etc.

### NCERT Class 8 Maths Solutions Chapter 8 Comparing Quantities Exercise PDF

Comparing different quantities helps in analyzing and studying two or more quantities and their properties to be able to understand the relation between them or to differentiate them.

This chapter on Comparing Quantities can prove to be very interesting for the students as they are made familiar with the concepts of percentages, discounts, sales, etc., some terms that we come across in our day-to-day life. Students also get to learn how to calculate simple, compound interests, concepts that have profound uses in our lives. So make sure to practice all the 28 questions included in the exercises.

 Chapter 8 - Comparing Quantities Exercises in PDF Format Exercise 8.1 6 Questions & Solutions (1 Long Answers, 5 Short Answers) Exercise 8.2 10 Questions & Solutions (4 Long Answers, 6 Short Answers) Exercise 8.3 12 Questions & Solutions (6 Long Answers, 6 Short Answers)

Topics Covered in Comparing Quantities are as Follows:

This chapter is fairly bigger but do not be discouraged as you can easily learn it. There are 9 exercises in this chapter and you have to be thorough with each. You must also know that this chapter holds 16 marks thus, you have to prepare this chapter very thoroughly.

The first topic in this chapter is percentages and ratios. Learn about percentage difference, percentage increase, decrease, etc. Practice and memorize the formulas and practice solving examples and questions. Learn how to convert fractions to a percentage, percentages vs percent, etc. All the topics are covered in the NCERT solutions and use them to practice the exercise questions.

Practice the percentage tricks and try to solve questions by using them. Practice questions related to ratios and revise the topic. Learn the formulas for profit and loss and their percentage, discount percentage, increase and decrease percentage. The next topic is compound interest. Learn all the formulas and solve questions related to them.  The topic of simple interest is another important topic and you must learn the related formulas and practice questions and examples. The 8th topic in this chapter is on rate compounded annually or half-yearly, this is an important topic and you must practice and solve questions related to it. The last topic in this chapter is the applications of compound interest formulas, so, learn the advantages and disadvantages. Solve as many questions and examples as possible and be very thorough with this chapter.

### NCERT Class 8 Maths Solutions Chapter 9 Algebraic Expressions and Identities Exercise PDF

Learning about algebraic expressions and identities helps students find unknown values and retrieve mathematical information. These can also help in manipulating information to solve mathematical problems.

Students in this chapter are brief about the various terms associated with Algebraic Expressions and Identities. The concept of factors, coefficients, monomials, binomials, and polynomials have been explained and students are also taught how to perform various operations on them. Students need a thorough practice of all the exercise questions to solidify their grasp of this chapter in CBSE class 8 maths. Details of the questions included in this exercise are:

 Chapter 9 - Algebraic Expressions and Identities Exercises in PDF Format Exercise 9.1 4 Questions & Solutions (4 Short Answers) Exercise 9.2 5 Questions & Solutions (5 Short Answers) Exercise 9.3 5 Questions & Solutions (5 Short Answers) Exercise 9.4 3 Questions & Solutions (3 Short Answers) Exercise 9.5 8 Questions & Solutions (8 Short Answers)

Topics that are Covered in Algebraic Expressions and Identities are as Follows:

The ninth chapter and one of the most important chapters in the class 8 maths is algebraic expression and identities. In this chapter, there are 12 exercises and this chapter holds 12 marks. The first topic in this chapter is about expressions, you have to learn about the types of algebraic expressions and learn their formulas.

Solve a few examples for each expression and use the NCERT solutions for the exercise questions. Some of the important expressions that you must be attentive to are monomial, binomial, polynomial, and variable expressions. Go through all the examples before solving the exercise questions.

In the next topic, you have to learn about factors, coefficients, and terms. Another important topic in this chapter is the addition and subtraction of algebraic expressions. In this chapter, you will learn how to add and subtract algebraic expressions. Learn the methods properly and solve examples to get better clarity of the topic. Solve all the exercise questions, you can use the NCERT solutions for help. Following the 5th topic, the 6th topic is about the multiplication of algebraic expressions. You have to learn how to multiply algebraic expressions, their formulas, and the terms used.

Next, you have to learn how to multiply monomial by a monomial and monomial by a polynomial, and practice questions related to it. Exercise 11 is about standard identities, in this learn the conditions for the standard equation. Learn all the types of standard identities and practice questions related to each identity. The last topic in this chapter is how to apply identities. Learn the method and practice exercise questions and examples. You have to put more emphasis on this chapter because it is a little lengthy.

### NCERT Class 8 Maths Solutions Chapter 10 Visualising Solid Shapes Exercise PDF

Most of our lives depend on solid shapes and their dimensions. Therefore, learning about solid shapes is important and rewarding in many ways, starting from calculating volumes to constructing monuments and buildings.

Students of Class 8 often find this Maths chapter very intriguing as it expires one’s imagination. Students get to learn about the concept of 3D geometry and visualize solid shapes in different dimensions. The concepts of edges, faces, and vertices are explained in this chapter, and students are taught how to map a solid shape in the three dimensions. One of the prominent topics which students get to learn in this chapter is Euler’s formula. This chapter requires rigorous practice and students should, thus, solve all the questions given in the exercise.

 Chapter 10 - Visualizing Solid Shapes Exercises in PDF Format Exercise 10.1 4 Questions & Solutions (4 Short Answers) Exercise 10.2 4 Questions & Solutions (3 Short Answer, 1 Long Answers) Exercise 10.3 8 Questions & Solutions (8 Short Answers)

Topics Covered in Visualizing Solid Shapes are as Follows:

In this chapter, there are 4 exercises. Visualizing solid shapes carries 6 marks and the chapter can be learned easily. The first important topic in this chapter is mapping space around us, in which you will learn how to space maps and their uses. Another important topic in this chapter is the faces, edges, and vertices of 3D shapes. Learn about the faces, edges, and vertices of 3D shapes, learn their properties, and solve questions related to them. You also have to learn about the types of polyhedrons. This chapter is small and you can finish preparing it quickly.

### NCERT Class 8 Maths Solutions Chapter 11 Mensuration Exercise PDF

Mensuration is a mathematical tool to find the area, perimeter, volume, etc. of spaces or objects.

This chapter is designed to build upon the students’ concept of quadrilaterals and triangles as it deals with measuring the area of these figures. In addition to this, students will also learn how to calculate the area and volume of cubes and cuboidal structures using various formulae. Students must ensure that they solve all the questions included in the exercises of this chapter.

Topics Covered in Mensuration are as Follows:

This chapter is very important and you must learn it thoroughly. There are 9 exercises in this chapter and this chapter carries 15 marks. The first important topic in this chapter is the area of a trapezium. In this chapter, you have to learn about the concept of trapezium and its properties.

Learn the formula for the area and perimeter of the trapezium and solve questions related to it. The last sub-topic is the derivation of the area of a trapezium and applications of a trapezium. Practice the derivation properly as it may come in a long answer question. Solve all the exercise questions and go through the examples also.

The next topic in this chapter is the area of quadrilateral, learn the properties of quadrilaterals and try to memorize them, also learn the formula for the area of quadrilateral and solve questions. The 5th exercise of this chapter is the area of a polygon, so,  learn about the area of the polygon and its formula. Practice exercise examples and questions.

The next topic is the surface area of a cube, you have to learn how to find the surface area of a cube, cuboid, and cylinder. You also have to learn how to find the length of the edge of the cube. Practice and learn the formulas and solve all the exercise questions and examples. The topic volume of cube, cuboid, and the cylinder is very important and questions will be asked about this topic. Learn the formulas of the cube, cuboid, and cylinder. Solve the exercise questions and practice additional questions from the NCERT solutions.

The last topic in this chapter is volume and capacity, learn the definition of volume and capacity, their difference, and their formulas. Practice the exercise questions. All the exercise questions must be at least solved once and you can maintain a separate note for revision. Use the NCERT solutions to learn the examples and textbook exercise questions properly.

### NCERT Class 8 Maths Solutions Chapter 12 Exponents and Powers Exercise PDF

Exponents and powers help us shorten or abbreviate values that would otherwise be difficult or too cumbersome to write and make easily readable.

Students in this chapter get to be familiar with the concepts of powers and exponents (positive as well as negative). Expressing numbers in standard form by making use of exponents and comparisons of very large with very small numbers is also an integral part of this chapter. To understand this chapter, practice the exercises which include:

 Chapter 12 - Exponents and Powers Exercises in PDF Format Exercise 12.1 7 Questions & Solutions (7 Long Answers) Exercise 12.2 4 Questions & Solutions (4 Short Answers)

Topics Covered in Exponents and Powers are as Follows:

The next chapter in the maths syllabus is exponents and powers. This chapter has 4 exercises and it carries 6 marks. In this chapter, you have to learn about exponents vs powers, integers with positive and negative exponents. Solve examples related to each topic and practice solving all the exercise questions.

You also have to learn all the integer exponent rules. This chapter is easy and small and with little dedication, you can easily learn and prepare it. The next topic in this chapter is the laws of exponents. You have to learn about the rules of exponents and practice every example. You also have to learn about the product, and quotient with the same bases, and solve questions related to each. Product to power and quotient to power are also important topics and you must learn and solve questions related to them.

The last sub-topic in this topic is negative and fractional exponent rules. Solve all the exercise questions and practice examples also. Another important topic is zero power. The last topic in this chapter discusses the use of exponents to express small numbers in standard form. Learn all the methods and tricks. Solve the exercise questions and use the solutions for help.

### NCERT Class 8 Maths Solutions Chapter 13 Direct and Inverse Proportions Exercise PDF

Direct and inverse proportions are used mainly to understand how quantities and amounts are related to each other.

In direct proportion, the two quantities involved increase/decrease in a manner that their corresponding values remain the same while the opposite happens in inverse proportion. The exercises provided contains questions involving both the scenarios and students must attempt to solve them all.

 Chapter 13 - Direct and Inverse Proportions Exercises in PDF Format Exercise 13.1 10 Questions & Solutions (10 Short Answers) Exercise 13.2 11 Questions & Solutions (11 Long Answers)

Topics Covered in Direct and Inverse Proportions:

This chapter has only two exercises and it carries 8 marks. The first topic is direct proportions. In this topic you have to learn about direct proportions and their symbol, formula, and constant of proportionality. Solve the exercise questions and examples. The next topic in this chapter is inverse variation. In this topic learn about inverse variation, its equation, and its formula. Practice the examples and solve the exercise questions. Use the NCERT solutions for help.

### NCERT Class 8 Maths Solutions Chapter 14 Factorisation Exercise PDF

The factorization is a very important tool in solving quadratic equations. It helps in simplifying complex problems and equations.

The factorization of algebraic expressions and natural numbers are dealt with in this chapter. Students  learn how to factorize using factorization identities, regrouping terms, etc. Moreover, students also learn how to divide a polynomial or a monomial by a monomial and more. Make sure you practice all the 34 questions distributed among the various exercises of this chapter.

Topics Covered in Factorization:

The 14th chapter is factorization. This chapter is important and carries 12 marks. You must prepare this chapter thoroughly. There are 5 exercises in this chapter. You have to learn how to factorize using common factors and solve questions related to them. Next, you have to learn factorization by regrouping and using standard identities. solve all the examples and exercise questions. The next topic in this chapter is polynomial division and the algorithm of long division. This topic is important so practice examples and solve exercise questions.

Learn the types of polynomial division and practice a few questions for each. Also, learn the division of a polynomial by a polynomial. The last topic is on finding the error, practicing the examples, and solving questions.

### NCERT Class 8 Maths Solutions Chapter 15 Introduction to Graphs Exercise PDF

Graphs can prove to be effective visual tools by presenting data and information in an easily consumable manner.

Since students have already been introduced to the concept of data handling earlier, this chapter primarily focuses on representing data in different types of graphs such as pie charts, histograms, linear graphs, etc. This chapter takes the challenge up a notch as students learn how to locate points and coordinate them on a graph. To gain confidence in this chapter practice is key which you can achieve by solving all the questions of the exercises.

 Chapter 15 - Introduction to Graphs Exercises in PDF Format Exercise 15.1 7 Questions & Solutions (7 Short Answers) Exercise 15.2 4 Questions & Solutions (4 Short Answers) Exercise 15.3 2 Questions & Solutions (2 Short Answers)

Topics Covered in the Introduction to Graphs:

This is the 15th chapter and there are 3 exercises in this chapter. In this chapter, you have to learn line graphs, type of line graphs, vertical line graphs, straight-line graphs, etc. You also have to learn about double line graphs and the uses of a line graph. Solve the examples and exercise questions. The next topic in this chapter is line graphs, learning the linear graph equation, and solving its exercise questions. Go through some of the examples to understand the topic better. The last topic in this chapter is on applications of linear graphs, learning the applications and solving questions related to them. This chapter is also important and it holds 12 marks.

### NCERT Class 8 Maths Solutions Chapter 16 Playing with Numbers Exercise PDF

The importance of number sense cannot be overlooked. It helps children to think in a flexible manner.

The chapter acts as a culmination of the concepts that students learn with respect to numbers. The broad genre of numbers has been discussed in detail in this chapter and students can use the concepts to justify the test of divisibility. The two exercises of this chapter include a total of 14 questions.

 Chapter 16 - Playing with Numbers Exercises in PDF Format Exercise 16.1 10 Questions & Solutions (10 Short Answers) Exercise 16.2 4 Questions & Solutions (4 Short Answers)

Topics Covered in Playing with Numbers:

This is the last chapter and it has 5 exercises in it. The first topic that you have to learn in this chapter is about numbers in a general form. In this, you will learn how to represent numbers in their general form and solve the exercise questions.

The next topic is games with numbers. In this, you have to learn the rules for solving puzzles. solve the examples to understand the topic properly. The last topic in this chapter is the test of divisibility. In this, you have to learn all the 13 divisibility rules and solve questions related to them. Solve the exercise questions and be thorough with all the topics. Use the NCERT solutions if you need help.

Above are all the important topics that you have to prepare for the class 8 maths. Try to maintain separate notes for solving questions, you can also use the same notes during revision.

The Class Maths marks weightage has been provided below according to the chapters and the corresponding marks they carry in the exam. The knowledge of uni-wise marks distribution is very important as it allows students to formulate their preparation strategy accordingly.

### CBSE Class 8 Maths Unit-Wise Marks Weightage

 Chapter No Weightage Chapter 1 08 Chapter 2 10 Chapter 3 13 Chapter 4 08 Chapter 5 11 Chapter 6 12 Chapter 7 06 Chapter 8 16 Chapter 9 12 Chapter 10 07 Chapter 11 15 Chapter 12 06 Chapter 13 08 Chapter 14 12 Chapter 15 12 Chapter 16 10

### Benefits of Vedantu’s NCERT Solutions for Class 8 Maths

NCERT Solutions are touted as resourceful study material among the students. Vedantu provides the NCERT Solutions for Class 8 Maths compiled in a PDF format. What is even better is that this PDF can be downloaded for free. Expert academicians have provided the solutions here in a stepwise manner and this allows students to get familiar with all the concepts included in the syllabus of Class 8 Maths. Practicing using these solutions can prove to be very beneficial for the students as these are error-free which ensures that students can use them while studying for exams. So make sure you explore the full benefits of downloading these solutions.

You can download these solutions on your smartphone or your PC and you can access them any time anywhere. You will be provided with the best teachers and materials for proper guidance. Students can also adjust the class hours accordingly and there is no need to be afraid of deadlines. You can always learn the NCERT chapters using these solutions as it will help you practice and understand the topic better. The NCERT Maths book Class 8 Solutions pdf free download is available.

### What are the Key Features of Vedantu’s Class 8 Maths NCERT Solutions?

One of the key features of the solutions is how well-structured and explained it is. You can study and prepare separate topics, download particular sections and prepare them along with their important questions, etc. You can also use the solutions for revision purposes. The most important thing is that you can download these for free at any time. The solutions are properly prepared by the experts for your advantage and hence, you will be able to learn better.

### Conclusion

For students appearing in the Class 8 Maths exam, the NCERT solutions can prove to be of great help. Improving your scores in Mathematics is something very achievable with these NCERT Solutions. To sum it all up, it serves as an excellent resource for any student aspiring to do well in their Math examination for class 8.

## FAQs on NCERT Solutions for Class 8 Maths

1. What Chapters are Important in the NCERT Class 8 Maths Textbook?

The chapters in Class 8 Maths NCERT Solutions which are important from an examination point of view are:

• Linear Equations in One Variable

• Rational Numbers

• Data Handling

• Comparing Quantities

• Squares and Square Roots

• Algebraic Expressions and Identities

• Mensuration

• Introduction to Graphs

• Factorization

• Playing with Numbers

2. Where can I get for NCERT Class 8 Maths Chapter-wise Solutions in PDF Format?

You can refer to Vedantu to download the NCERT Class 8 Maths Solution Chapter-wise. These solutions are compiled in the form of PDFs corresponding to each chapter and can be easily downloaded just by clicking on the link(s) provided.

Yes, with Veantu you can avail the PDFs of the various chapters of NCERT Maths Class 8 Solutions for absolutely free of cost. You are not required to pay in exchange for downloading the PDF. NCERT Solutions are referred source of study material and you can keep the same handy by downloading from the official website.

4. Can I Score Good Marks if I Study From NCERT Solutions for Class 8 Maths?

All the exercises of the Class 8 Maths NCERT textbook have been extensively covered in these solutions. If you make a habit of regular practice with the aid of these solutions, you can definitely aim to score higher in your exams. Additionally, these solutions are also beneficial in preparing for various competitive examinations.

5. How can I Download Chapter-wise NCERT Solutions for Class 8 Maths?

6. Is Studying From NCERT Solutions Enough for CBSE Class 8 Maths to Score Better?

The NCERT Solutions of Class 8 Maths will provide you with an in-depth understanding of the concepts crucial to each of the chapters. While studying using these solutions can definitely help you score better, you can also benefit from solving previous year questions papers and sample papers for the same.

7. Can you provide me with the syllabus of Class 8 Maths?

The syllabus for Class 8 Maths is given below:

• 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 – Visualising Solid Shapes

• Chapter 11 – Mensuration

• Chapter 12 – Exponents and Powers

• Chapter 13 – Direct and Inverse Proportions

• Chapter 14 – Factorisation

• Chapter 15 – Introduction to Graphs

• Chapter 16 – Playing With Numbers

8. Why do most of the students prefer Vedantu to study for Class 8 Maths?

Due to the listed reasons, most of the students choose Vedantu to study for Class 8 Maths:

• The NCERT Solutions for all the chapters of Class 8 Maths are available for both English and Hindi medium students on Vedantu.

• The PDF files of these solutions are accessible to students.

• The creators of the content are subject matter experts.

• The language used to write the content is very easy to understand.

• Students can clarify their doubts with the help of the teachers.

9. How can I make a stepwise study plan for Class 8 Maths?

Beneath are the points which will assist you in making a detailed study plan for Class 8 Maths:

• The most vital thing is managing your time. For time management, construct a timetable.

• Concentrate on each chapter by using the NCERT book.

• Practice each example and exercise are given in the book.

• Resist studying for longer periods and do not pressurise yourself.

• Also, play for some time to refresh your mind.

• Make use of sample papers to clear your concepts.

10. How should students study class 8 Maths?

Maths requires lots of calculations. Therefore, you need good calculative skills to solve questions. Students can make Class 8 Maths easy if they focus on this subject. They can refer to the NCERT book to read the theory of the chapters. By solving the examples and the exercises, students can clear the concepts. Attend your classes and centralize on what the teacher is teaching. Make notes for the chapters so that you can learn all the formulas easily.

11. Give the chapter-wise marks weightage for CBSE Class 8 Maths.

The marks or weightage allotted to each chapter of CBSE Class 8 Maths is discussed here:

• Chapter 1 – 8 marks

• Chapter 2 – 10 marks

• Chapter 3 – 13 marks

• Chapter 4 – 8 marks

• Chapter 5 – 11 marks

• Chapter 6 – 12 marks

• Chapter 7 – 6 marks

• Chapter 8 – 16 marks

• Chapter 9 – 12 marks

• Chapter 10–7 marks

• Chapter 11 – 15 marks

• Chapter 12 – 6 marks

• Chapter 13 – 8 marks

• Chapter 14 – 12 marks

• Chapter 15 – 12 marks

• Chapter 16 – 10 marks SHARE TWEET SHARE SUBSCRIBE