NCERT Solutions for Class 8 Maths - Free Latest PDF (2024-25)

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.

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

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.

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

• Kinds Of Quadrilaterals

• Some Special Parallelograms

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

Chapter 4 - Data Handling

The fifth chapter is data handling, this chapter is important and it holds 11 marks. There are 4 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 4.1 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 4.2 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.

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

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

Chapter 5 - 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 5.1 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 5.2 relates to expressing perfect squares as the sum of consecutive odd numbers.

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

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

Chapter 6 - 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 6.1 covers a topic from cubes and cube roots, which is the focus of exercise 6.1 in NCERT Class 8 Maths Chapter 6.

2. Exercise 6.2 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

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

Chapter 7 - 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 7.1: 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 7.2: 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 7.3: 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)

• Sales Tax/Value Added Tax

• Compound Interest

• Deducing A Formula For Compound Interest

• Rate Compounded Annually Or Half Yearly (semi Annually)

• Applications Of Compound Interest Formula
  
  

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

Chapter 8 - 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 8.1 & 8.2: Identify terms, coefficients, and classify polynomials (monomials, binomials, trinomials)

2. Excercise 8.3 & 8.4: Not directly related to identities, covers using exponents or performing basic operations on polynomials

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

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

Chapter 9 - 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 9.1 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 9.2 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 9.3

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

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 9 of CBSE Class 8 Maths Solutions–

Chapter 10 - 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 10.1 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 10.2 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.

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

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

Chapter 11 - 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 11.1 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 11.2 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

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

Chapter 12 - 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 12.1 deals with finding factors of a given number. you will need to identify all the numbers that divide the given number exactly.

2. Exercise 12.2 focuses on representing a number as a product of its prime factors. Prime factors are numbers divisible only by 1 and itself.

3. Exercise 12.3 introduces the concept of Highest Common Factor (HCF). HCF is the largest number that is a factor 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?

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

Chapter 13 - 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 13.1 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 13.2 is probably based on the same graph from Exercise 13.1. It will ask you questions about the graph itself, such as the number of data points or intervals shown.

Topics Covered in the Introduction to Graphs:

• Linear Graphs

• Some Applications

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

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.

Download 8th Maths Book Answers to Complete Your Syllabus

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.

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