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# NCERT Solutions For Class 8 Maths

Last updated date: 20th Sep 2024
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## NCERT Solutions for Class 8 Maths 2024-25 - Free PDF Download

NCERT Solutions of Class 8 cover extensive chapters like Rational Numbers, Practical Geometry, Cubes and Cube Roots, Data Handling, Mensuration, and Factorization. To tackle this, Vedantu offers expertly crafted Maths class 8 NCERT solutions, aligned with CBSE guidelines. These NCERT 8th maths solutions are available in a PDF for the 2024-25 academic year, are ideal for both preparation and revision. They simplify concepts, boosting students understanding and confidence, ultimately helping them score well in exams.

Table of Content
1. NCERT Solutions for Class 8 Maths 2024-25 - Free PDF Download
2. Chapter-Specific NCERT Solutions for Class 10 Maths
3. Glance on NCERT Solutions Class 8 Maths
4. NCERT Solutions for Class 8 Maths Chapter Details, Formulas and Exercises PDF
4.1Chapter 1 - Rational Numbers
4.2Chapter 2 - Linear Equations in One Variable
4.4Chapter 4 - Practical Geometry
4.5Chapter 5 - Data Handling
4.6Chapter 6 - Squares and Square Roots
4.7Chapter 7 - Cubes and Cube Roots
4.8Chapter 8 - Comparing Quantities
4.9Chapter 9 - Algebraic Expressions and Identities
4.10Chapter 10 - Visualising Solid Shapes
4.11Chapter 11 - Mensuration
4.12Chapter 12 - Exponents and Powers
4.13Chapter 13 - Direct and Inverse Proportions
4.14Chapter 14 - Factorisation
4.15Chapter 15 - Introduction to Graphs
4.16Chapter 16 - Playing with Numbers
5. What are the Key Features of Vedantu’s Class 8 Maths NCERT Solutions?
6. CBSE Class 8 Maths NCERT Solutions 2024-25 - Benefits of the NCERT Solutions for Students
8. NCERT Solution Class 8 Maths Related Links
FAQs

## Chapter-Specific NCERT Solutions for Class 10 Maths

Given below are the chapter-wise NCERT Solutions for Class 8 Maths. You can use it as your 8th maths guide. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

## Glance on NCERT Solutions Class 8 Maths

• NCERT Solutions for Class 8 Maths for all the chapters and exercises from Chapters 1 to 14 are available.

• Using these solutions to practice textbook questions can help students assess their level of preparation and understanding of concepts.

• The provided link also offers details about the exam pattern, marks weightage, and question paper design for CBSE Class 8 Maths.

• The chapters cover topics such as Whole Numbers, Fractions and Decimals, Rational Numbers, Linear Equations in One Variable, Understanding Quadrilaterals, Visualizing Solid Shapes, Exponents and Powers, Introduction to Graphs, Playing with Numbers, and more.

• In addition to solutions, the link provides resources like class notes, important questions and formulas, exemplar solutions, and recommended books for further reference.

## NCERT Solutions for Class 8 Maths Chapter Details, Formulas and Exercises PDF

### Chapter 1 - Rational Numbers

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

1. Exercise 1.1 contains 11 questions focusing on properties of numbers. Solve each question and review using the solutions provided. you will learn about commutative, distributive, and other properties, as well as inverses and multiplicative inverses. Keep separate notes for practice and revision.

2. Exercise 1.2 teaches representing numbers on the number line with 7 questions. Thoroughly practice and revise this exercise. Cover all methods, solve related questions, and learn from examples to understand crucial points.

### Topics That are Covered in the Rational Numbers are as follows:

• Properties Of Rational Numbers

• Representation Of Rational Numbers On The Number Line

• Rational Numbers Between Two Rational Numbers

 Chapter 1 - Rational Numbers Exercises in PDF Format Class 8 Maths Chapter 1 Exercise 1.1 - 11 Questions & Solutions (11 Short Answers) Class 8 Maths Chapter 1 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

### Chapter 2 - Linear Equations in One Variable

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 6 exercises, and you have to learn and solve them all.

1. Exercise 2.1: Understanding fractions and decimals, operations with fractions and decimals, simplification.

2. Exercise 2.2: Comparing and ordering fractions and decimals, addition, subtraction, multiplication, and division of fractions and decimals.

3. Exercise 2.3: Fraction and decimal operations, real-life applications.

4. Exercise 2.4: Word problems involving fractions and decimals, simplification and conversion.

5. Exercise 2.5: Percentage conversion, expressing fractions and decimals as percentages.

6. Exercise 2.6: Application of percentages in different scenarios, solving percentage-based problems.

### Topics That are Covered in the Linear Equation in One Variable are as Follows:

• Solving Equations Which Have Linear Expressions On One Side And Numbers On The Other Side

• Some Applications

• Solving Equations Having The Variable On Both Sides

• Some More Applications

• Reducing Equations To Simpler Form

• Equations Reducible To The Linear Form

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

### Chapter 3 - Understanding Quadrilaterals

In Chapter 3 of your Class 8 Maths NCERT Solutions, there are 5 exercises covering understanding quadrilaterals and polygons. Polygon, the second topic, is crucial.

1. Exercise 3.1 focuses on identifying and classifying quadrilaterals based on their properties like sides, angles, diagonals, and whether they are convex or concave.

2. Exercise 3.2 tests your knowledge on the number of diagonals present in different quadrilaterals.

3. Exercise 3.3 dives deeper into specific quadrilaterals like squares, rectangles, parallelograms, and rhombuses. It explores how these shapes fit into the broader category of quadrilaterals and their unique characteristics.

4. Exercise 3.4 is a mix of true/false statements and open-ended questions that require applying your understanding of quadrilateral relationships. you will be classifying quadrilaterals based on properties, explaining how certain shapes fit into multiple categories, and recognizing special properties of diagonals in specific quadrilaterals.

### Topics Covered in Understanding Quadrilaterals are as Follows:

• Polygons

• Sum Of The Measures Of The Exterior Angles Of A Polygon

• Some Special Parallelograms

 Chapter 3 - Understanding Quadrilaterals Exercises in PDF Format Class 8 Maths Chapter 3 Exercise 3.1 - 7 Questions & Solutions (1 Long Answer, 6 Short Answers) Class 8 Maths Chapter 3 Exercise 3.2 - 6 Questions & Solutions (6 Short Answers) Class 8 Maths Chapter 3 Exercise 3.3 - 12 Questions & Solutions (6 Long Answers, 6 Short Answers) Class 8 Maths Chapter 3 Exercise 3.4 - 6 Questions & Solutions (1 Long Answer, 5 Short Answers)

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

### Chapter 4 - Practical Geometry

Chapter four, practical geometry, is important for scoring well. It contains 3 exercises.

The first key topic is constructing quadrilaterals, where you will learn to construct them with given sides, diagonals, and angles.

1. Exercise 4.1 instructs you on how to construct quadrilaterals with specific side lengths and given information about angles or radii. you will be drawing arcs and using a compass to meet these requirements.

2. Exercise 4.2 focuses on constructing triangles with given side lengths and angle measures. Similar to exercise 4.1, you will be using a compass and ruler to create these constructions.

3. Exercise 4.3 dives into constructing circles with a given radius. you will learn how to use a compass to achieve this.

4. Exercise 4.4 deals with constructing tangents to a circle from an external point. This exercise will require you to carefully place the compass to draw these tangents accurately.

5. Exercise 4.5 presents a challenge where you will combine your learnings from the previous exercises. you will be asked to construct more complex shapes that involve multiple circles, tangents, or quadrilaterals.

### Topics in Practical Geometry are as Follows:

• Some Special Cases

 Chapter 4 - Practical Geometry Exercises in PDF Format Class 8 Maths Chapter 4 Exercise 4.1 - 1 Questions & Solutions (1 Long Answer) Class 8 Maths Chapter 4 Exercise 4.2 - 1 Questions & Solutions (1 Long Answer) Class 8 Maths Chapter 4 Exercise 4.3 - 1 Questions & Solutions (1 Long Answer) Class 8 Maths Chapter 4 Exercise 4.4 - 1 Questions & Solutions (1 Long Answer) Class 8 Maths Chapter 4 Exercise 4.5 - 4 Questions & Solutions (4 Long Answers)

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

### Chapter 5 - Data Handling

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.

1. Exercise 5.1 deals with how to represent data visually using histograms and bar graphs. It might ask you to decide which type of graph is suitable for a particular set of data and why.

2. Exercise 5.2 is about interpreting data presented in tables or graphs. It might ask you questions about the data, such as finding the most frequent value or calculating the total.

3. Exercise 5.3 involve analysing data to draw conclusions. It could ask you to compare different sets of data or identify trends.

### Topics that are Covered in Data Handling are as Follows:

• Looking for Information

• Organising Data

• Grouping Data

• Circle Graph or Pie Chart

• Chance and Probability

 Chapter 5 - Data Handling Exercises in PDF Format Class 8 Maths Chapter 5 Exercise 5.1 - 5 Questions & Solutions (5 Short Answers) Class 8 Maths Chapter 5 Exercise 5.2 - 5 Questions & Solutions (3 Long Answers, 2 Short Answers) Class 8 Maths Chapter 5 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

### Chapter 6 - Squares and Square Roots

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.

1. Exercise 6.1 focuses on patterns involving perfect squares. You might be asked to identify perfect squares or complete a pattern by finding the missing perfect squares.

2. Exercise 6.2 relates to expressing perfect squares as the sum of consecutive odd numbers.

3. Exercise 6.3 involves finding the least number that needs to be subtracted from a given number to get a perfect square.

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

• Properties Of Square Numbers

• Some More Interesting Patterns

• Finding The Square Of A Number

• Square Roots

 Chapter 6 - Squares and Square Roots Exercises in PDF Format Class 8 Maths Chapter 6 Exercise 6.1 - 9 Questions & Solutions (9 Short Answers) Class 8 Maths Chapter 6 Exercise 6.2 - 2 Questions & Solutions (2 Short Answers) Class 8 Maths Chapter 6 Exercise 6.3 - 10 Questions & Solutions (3 Long Answers, 7 Short Answers) Class 8 Maths Chapter 6 Exercise 6.4 - 9 Questions & Solutions (3 Long Answers, 6 Short Answers)

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

### Chapter 7 - Cubes and Cube Roots

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.

1. Exercises 7.1 covers a topic from cubes and cube roots, which is the focus of exercise 7.2 in NCERT Class 8 Maths Chapter 7.

2. Exercise 7.2 deals with finding the cube root of perfect cubes. Perfect cubes are integers which can be obtained by cubing an integer. For example, 27 is a perfect cube because 3 x 3 x 3 = 27.

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

• Cubes

• Cube Roots

 Chapter 7 - Cubes and Cube Roots Exercises in PDF Format Class 8 Maths Chapter 7 Exercise 7.1 - 4 Questions & Solutions (4 Short Answers) Class 8 Maths Chapter 7 Exercise 7.2 - 3 Questions & Solutions (2 Long Answers, 1 Short Answer)

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 7 of CBSE Class 8 Maths Solutions

### Chapter 8 - Comparing Quantities

Comparing different quantities helps in analysing 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.

1. Exercise 8.1: This exercise deals with percentages. you will likely practice converting between percentages, fractions, and decimals. You might also solve problems involving calculating a part (percentage) of a whole.

2. Exercise 8.2: This exercise explores ratios and proportions. you will probably work on finding ratios between quantities, writing proportions, and solving problems based on proportional relationships.

3. Exercise 8.3: This exercise introduces compound interest. you will likely learn the formula for compound interest and solve problems to find the future value of an investment considering interest earned on interest.

### Topics Covered in Comparing Quantities are as Follows:

• Recalling Ratios And Percentages

• Finding The Increase Or Decrease percent

• Finding Discounts

• Prices Related To Buying And Selling (profit And Loss)

• Compound Interest

• Deducing A Formula For Compound Interest

• Rate Compounded Annually Or Half Yearly (semi Annually)

• Applications Of Compound Interest Formula

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

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

### Chapter 9 - Algebraic Expressions and Identities

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.

1. Excercise 9.1 & 9.2: Identify terms, coefficients, and classify polynomials (monomials, binomials, trinomials)

2. Excercise 9.3 & 9.4: Not directly related to identities, covers using exponents or performing basic operations on polynomials

3. Excercise 9.5: Here, you will use standard identities like the one for squaring a binomial [(x + a)(x + b) = x^2 + (a + b)x + ab] to multiply polynomials, find squares of expressions, and simplify them.

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

• What Are Expressions?

• Terms, Factors And Coefficients

• Monomials, Binomials And Polynomials

• Like And Unlike Terms

• Addition And Subtraction Of Algebraic Expressions

• Multiplication Of Algebraic Expressions: Introduction

• Multiplying A Monomial By A Monomial

• Multiplying A Monomial By A Polynomial

• Multiplying A Polynomial By A Polynomial

• What Is An Identity?

• Standard Identities

• Applying Identities

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

### Chapter 10 - Visualising Solid Shapes

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 get to learn about the concept of 3D geometry and visualise solid shapes in different dimensions.

1. Exercise 10.1 This exercise asks you to practice drawing different 3D shapes like cuboids, cones, and cylinders. You can draw these shapes on your notebook to improve your spatial visualization skills.

2. Exercise 10.2 In this exercise, you will be looking at everyday objects like bricks, pencils, and erasers. Imagine them as 3D shapes and identify their faces, edges, and vertices.

3. Exercise 10.3 This exercise challenges you to think in the opposite direction. Here, you will be given a specific number of faces and asked to name 3D shapes that have that many faces. For example, if the question asks for shapes with 4 faces, you might identify a pyramid as an answer.

### Topics Covered in Visualizing Solid Shapes are as Follows:

• Views Of 3d-Shapes

• Mapping Space Around Us

• Faces, Edges And Vertices

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

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 8 Maths Solutions

### Chapter 11 - Mensuration

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.

1. Exercise 11.1 compares the areas of a square and a rectangle with the same perimeter. It helps solidify the understanding that a square often encloses a larger area compared to a rectangle with the same boundary length.

2. Exercise 11.2 This exercise might involve finding the area of a square plot or solving for the side length of a square given its area. It reinforces the formula for area of a square (side x side).

3. Exercise 11.3 covers topics related to two-dimensional shapes. It deals with finding the area of a triangle, which requires the formula (1/2 * base * height).

4. Exercise 11.4 While similar to Exercise 11.3, this exercise likely focuses on finding the area of a parallelogram, another 2D shape. The area formula for a parallelogram is (base x height).

### Topics Covered in Mensuration are as Follows:

• Let Us Recall

• Area Of Trapezium

• Area Of A General Quadrilateral

• Area Of A Polygon

• Solid Shapes

• Surface Area Of Cube, Cuboid, and Cylinder

• Volume Of Cube, Cuboid, and Cylinder

• Volume And Capacity

 Chapter 11 - Mensuration Exercises in PDF Format Class 8 Maths Chapter 11 Exercise 11.1 - 5 Questions & Solutions (5 Long Answers) Class 8 Maths Chapter 11 Exercise 11.2 - 11 Questions & Solutions (11 Long Answers) Class 8 Maths Chapter 11 Exercise 11.3 - 10 Questions & Solutions (2 Short Answers, 8 Long Answers) Class 8 Maths Chapter 11 Exercise 11.4 - 8 Questions & Solutions (2 Short Answers, 6 Long Answers)

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 11 of CBSE Class 8 Maths Solutions

### Chapter 12 - Exponents and Powers

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).

1. Exercise 12.1 This exercise focuses on evaluating expressions that involve exponents with positive whole numbers as powers. you will likely be asked to simplify these expressions and find the final answer.

2. Exercise 12.2 Here, you will get some practice comparing expressions that include exponents. Remember that comparing exponents sometimes requires simplifying the expressions first. This exercise will help you solidify your understanding of how exponents affect the value of an expression.

3. Exercise 12.3 This exercise introduces you to the concept of exponents with zero as the base. You will learn that any non-zero number raised to the power of 0 results in 1. This is an important foundation for future maths concepts.

### Topics Covered in Exponents and Powers are as Follows:

• Powers With Negative Exponents

• Laws Of Exponents

• Use Of Exponents To Express Small Numbers In Standard Form

 Chapter 12 - Exponents and Powers Exercises in PDF Format Class 8 Maths Chapter 12 Exercise 12.1 - 7 Questions & Solutions (7 Long Answers) Class 8 Maths Chapter 12 Exercise 12.2 - 4 Questions & Solutions (4 Short Answers)

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 12 of CBSE Class 8 Maths Solutions

### Chapter 13 - Direct and Inverse Proportions

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.

1. Exercise 13.1 This exercise likely covers the introduction to direct proportion. Direct proportion means that as the value of one quantity increases, the value of the other quantity also increases proportionally. In other words, the product of the two quantities remains constant.

2. Exercise 13.2 This exercise likely deals with inverse proportion. Inverse proportion means that as the value of one quantity increases, the value of the other quantity decreases proportionally, and vice versa. The product of the two quantities, however, remains constant.

### Topics Covered in Direct and Inverse Proportions:

• Introduction

• Direct Proportion

• Inverse Proportion

 Chapter 13 - Direct and Inverse Proportions Exercises in PDF Format Class 8 Maths Chapter 13 Exercise 13.1 - 10 Questions & Solutions (10 Short Answers) Class 8 Maths Chapter 13 Exercise 13.2 - 11 Questions & Solutions (11 Long Answers)

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 13 of CBSE Class 8 Maths Solutions

### Chapter 14 - Factorisation

The factorisation is a very important tool in solving quadratic equations. It helps in simplifying complex problems and equations. The factorisation of algebraic expressions and natural numbers are dealt with in this chapter. Students  learn how to factorize using factorisation 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.

1. Exercise 14.1 deals with finding factors of a given number. you will need to identify all the numbers that divide the given number exactly.

2. Exercise 14.2 focuses on representing a number as a product of its prime factors. Prime factors are numbers divisible only by 1 and itself.

3. Exercise 14.3 introduces the concept of Highest Common Factor (HCF). HCF is the largest number that is a factor of two or more numbers.

4. Exercise 14.4 introduces the concept of Least Common Multiple (LCM). LCM is the smallest number that is a multiple of two or more numbers.

### Topics Covered in Factorisation:

• What Is Factorisation?

• Division Of Algebraic Expressions

• Division Of Algebraic Expressions Continued (polynomial ÷ Polynomial)

• Can You Find The Error?

 Chapter 14 - Factorisation Exercises in PDF Format Class 8 Maths Chapter 14 Exercise 14.1 - 3 Questions & Solutions (3 Short Answers) Class 8 Maths Chapter 14 Exercise 14.2 - 5 Questions & Solutions (5 Short Answers) Class 8 Maths Chapter 14 Exercise 14.3 - 5 Questions & Solutions (5 Short Answers) Class 8 Maths Chapter 14 Exercise 14.4 - 21 Questions & Solutions (21 Short Answers)

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 14 of CBSE Class 8 Maths Solutions

### Chapter 15 - Introduction to Graphs

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.

1. Exercise 15.1 likely involves interpreting a graph that represents real-world data. You might be asked to read temperatures recorded every hour or analyse distances travelled during a trip based on the graph.

2. Exercise 15.2 is probably based on the same graph from Exercise 15.1. It will ask you questions about the graph itself, such as the number of data points or intervals shown.

3. Exercise 15.3 most likely asks you to create graphs based on given data tables. You will need to choose appropriate scales for the axes and plot the data points to visually represent the information.

### Topics Covered in the Introduction to Graphs:

• Linear Graphs

• Some Applications

 Chapter 15 - Introduction to Graphs Exercises in PDF Format Class 8 Maths Chapter 15 Exercise 15.1 - 7 Questions & Solutions (7 Short Answers) Class 8 Maths Chapter 15 Exercise 15.2 - 4 Questions & Solutions (4 Short Answers) Class 8 Maths Chapter 15 Exercise 15.3 - 2 Questions & Solutions (2 Short Answers)

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 15 of CBSE Class 8 Maths Solutions

### Chapter 16 - Playing with Numbers

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.

1. Exercise 16.1: This exercise involves solving maths problems where letters represent unknown digits in numbers. You will need to use your understanding of place value and basic arithmetic operations to figure out the values of these letters.

2. Exercise 16.2: Here, you will use divisibility rules to find the missing digits represented by letters in numbers. The problems ask you to determine the value of the letter that makes the entire number divisible by a specific number (like 3 or 9).

### Topics Covered in Playing with Numbers:

• Introduction

• Numbers In General Form

• Games With Numbers

• Letters For Digits

• Tests Of Divisibility

 Chapter 16 - Playing with Numbers Exercises in PDF Format Class 8 Maths Chapter 16 Exercise 16.1 - 10 Questions & Solutions (10 Short Answers) Class 8 Maths Chapter 16 Exercise 16.2 - 4 Questions & Solutions (4 Short Answers)

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 12 of CBSE Class 8 Maths Solutions

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.

## 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.

## CBSE Class 8 Maths NCERT Solutions 2024-25 - Benefits of the NCERT Solutions for Students

Following are the benefits of the NCERT Class 8 Maths Solutions:

• The NCERT Solutions are considered to be helpful study materials for students as these can help in completing their syllabus properly. Students can get access to quality information through these solutions and improve their study sessions a lot more. Following are the benefits of NCERT Maths Book Class 8 Solutions PDF Free Download.

• The concepts are explained in much detail and in easy language. So, students will have no trouble understanding the concepts. This is how they can score good marks in their examinations.

• The NCERT Solutions for Class 9 Mathematics have been created by some of the best subject matter experts in Vedantu. These teachers and professionals and well-versed in the concepts of mathematics. Also, the solutions are reviewed for accuracy and hence students can definitely rely on the solutions and study materials.

• In case there are any topics where you might be a bit confused, the NCERT solutions can be your guide. These solutions have been explained in an easy-to-understand manner by Vedantu experts. Thus, students can use the resources to clear any doubts that they might have about the chapter.

• The NCERT Solutions incorporate a Chapter Wise List Of Class 8 Maths which helps the students in finding out the important chapters in the syllabus. They will be able to identify the chapters that have significant weightage in the CBSE examinations and prepare a strategy to score more marks.

• While revising the chapters, students don’t have to go through the entire book. The NCERT solutions have explained all the topics and concepts in a very easy manner. While solving the problems, students will learn about the theorems, formulas, and descriptions that are used. Thus, they will easily be able to complete the chapter without any interruptions.

This is your only chance to get your hands on the chapter-wise NCERT Solutions for Class 8 Maths and boost your preparation. These solutions will help you get a proper understanding of the Maths chapters and topics. Practice with the NCERT solutions and clarify your doubts to improve your hold on the mathematics subject.

## NCERT Solution Class 8 Maths Related Links

Check on the additional study materials provided for Class 8 Maths

## 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

12. Can I use NCERT Solutions for Class 8 Maths as a reference for other competitive exams?

While NCERT Solutions for Class 8 Maths are primarily designed for CBSE students, they can also serve as a valuable reference for other competitive exams, as they cover fundamental mathematical concepts applicable across various syllabi and exam patterns.

13. Are NCERT Solutions for Class 8 Maths suitable for self-study?

Yes, NCERT Solutions for Class 8 Maths are ideal for self-study, as they provide comprehensive explanations and solutions to all exercises. Whether you are studying independently or seeking additional support outside the classroom, these solutions can be immensely helpful.

14. How can NCERT Solutions for Class 8 Maths help improve my grades?

By regularly practicing with NCERT Solutions for Class 8 Maths, you can strengthen your understanding of mathematical concepts and develop problem-solving skills. This, in turn, can lead to improved performance in exams and better grades.

15. Which is the toughest lesson in maths class 8?

The perception of the toughest lesson in Class 8 Maths can vary from student to student. However, concepts like algebraic expressions and equations, as well as mensuration, are often considered challenging by many students.

16. What is important in maths in class 8?

Understanding fundamental concepts and building a strong foundation is crucial in Class 8 Maths. Topics like integers, fractions and decimals, geometry, and understanding basic algebraic concepts are important for further studies in mathematics.

17. Is maths easy in class 8?

Whether maths is easy or difficult depends on individual aptitude, interest, and the effort put into learning. Some students find maths easy, while others may find it challenging. Consistent practice and understanding concepts thoroughly can make it easier.

18. Which is the most easiest chapter in class 8 maths?

The perception of the easiest chapter in Class 8 Maths may vary among students. However, chapters like "Understanding Quadrilaterals" or "Playing with Numbers" are often considered relatively easier compared to others.

19. Who is the father of mathematics?

The ancient Greek mathematician Euclid is often referred to as the "father of geometry," and his work "Elements" laid down the foundations of geometry as a mathematical discipline. While he's not necessarily the father of all mathematics, his contributions are significant in the development of mathematical principles.