math assignment 3 class 8

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NCERT Solutions for Class 8 Maths

Ncert solutions for class 8 maths cbse 2023-24 edition – free pdf download.

NCERT Solutions for Class 8 Maths includes all the questions provided in the textbook that is prescribed in accordance with the CBSE Board. The syllabus given for all the classes is completely based on the NCERT curriculum. Hence, preparing for exams using NCERT Solutions will definitely provide students with an advantage.

BYJU’S NCERT Class 8 Solutions for Maths has been designed to help students solve problems with ease. The CBSE 8th Class Solutions for Maths provided here come with well-prepared exercises along with detailed explanations given by our expert teachers that further make learning and understanding concepts an easy task. So, if students have been looking for the most detailed and accurate Class 8 NCERT Solutions for Maths,  which is also free, this is the right place.

Chapter-Wise NCERT Solutions for Class 8 Maths

NCERT Solutions for Class 8th Maths provided here are very beneficial for students. They can use these  NCERT Solutions for Class 8 as a reference while practising the problems and developing better skills along with preparing efficiently for the exams. The exercises are given at the end of every chapter to practise the concepts learned in the chapter.

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

In this chapter, students will be learning properties related to real numbers, integers, whole numbers, rational numbers and natural numbers – independent, associative and closure. The chapter deals with the role of zero and one, multiplication over addition, representation of rational Numbers on the number line , and searching for rational numbers between two rational numbers. The topics of additive identity (0) and multiplicative identity (1) are also covered in this chapter. There are 2 exercises in this chapter, which contain questions from all the topics present in the chapter.

Also, access the following resources for Class 8 Chapter 1 Rational Numbers  at BYJU’S:

• Rational Numbers Class 8 Notes – Chapter 1
• NCERT Exemplar Class 8 Maths Solutions for Chapter 1 – Rational Numbers
• RD Sharma Solutions for Class 8 Maths Chapter 1 – Rational Numbers

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable

The chapter, Linear Equations in One Variable, deals with linear expression in one variable alone. Such equations are known as linear equations in one variable . There are six exercises in this chapter with a total of 65 questions in them. The chapter includes different concepts, including solving linear equations in one variable, some of its applications, reducing equations to a simpler form and word problems related to linear equations in one variable.

Also, access the following resources for Class 8 Chapter 2 Linear Equations in One Variable  at BYJU’S:

• Linear Equations In One Variable Class 8 Notes- Chapter 2
• NCERT Exemplar Class 8 Maths Solutions for Chapter 4 – Linear Equations In One Variable
• RD Sharma Solutions for Class 8 Maths Chapter 9 Linear Equation in One Variable

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

The chapter Understanding Quadrilaterals of Class 8 Maths provides the students with a proper understanding of the quadrilaterals . The chapter also covers different kinds of polygons, including triangles, quadrilaterals, pentagons, hexagons, etc. The chapter contains 4 exercises which aid the students in understanding these shapes properly.

Also, access the following resources for Class 8 Chapter 3 Understanding Quadrilaterals  at BYJU’S:

• Understanding Quadrilaterals Class 8 Notes – Chapter 3
• Important Questions for Maths Class 8 Chapter 3 Understanding Quadrilaterals
• NCERT Exemplar Class 8 Maths Solutions for Chapter 5 – Understanding Quadrilaterals Practical Geometry
• RD Sharma Solutions for Class 8 Maths Chapter 16 Understanding Shapes- II (Quadrilaterals)

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

The chapter, Practical Geometry, includes the method of constructing a quadrilateral with various parameters given. The chapter consists of 5 exercises, each dealing with different methods of constructing the quadrilateral. For instance, the first exercise deals with the construction of quadrilaterals when the length of four sides and a diagonal are given; similarly, the second exercise involves the method of construction of quadrilaterals when two diagonals and three sides are given, and so on. Hence, we can conclude that learning this chapter will make the students well-versed in all the concepts of quadrilateral for further classes.

Also, access the following resources for Class 8 Chapter 4 Practical Geometry  at BYJU’S:

• Practical Geometry Class 8 Notes – Chapter 4
• Important Questions Maths Class 8 Chapter 4: Practical Geometry
• RD Sharma Solutions for Class 8 Maths Chapter 18 Practical Geometry (Constructions)

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

The collection of information that can be used for analysis is known as data. In this chapter, students learn about the organisation and representation of data. Organising the data in a systematic method is referred to as data handling . In this chapter, students learn to represent these data diagrammatically as a pictograph, a bar graph, a double bar graph, a pie chart and a histogram. During the course of this chapter, students will be briefed about the concept of probability or likelihood. There are 3 exercises in this chapter that deal with all the concepts covered in the chapter.

Also, access the following resources for Class 8 Chapter 5 Data Handling  at BYJU’S:

• Data Handling Class 8 Notes- Chapter 5
• Important Questions Class 8 Maths Chapter 5 Data Handling
• NCERT Exemplar Class 8 Maths Solutions for Chapter 2 – Data Handling
• RD Sharma Solutions for Class 8 Maths Chapter 23 Data Handling – I (Classification and Tabulation of Data)

NCERT Solutions for Class 8 Maths Chapter 6 Square and Square Roots

This chapter, Squares and Square Roots, helps the students learn about the concept of square numbers and the square root of a number. The chapter deals with properties of square numbers, interesting patterns that could be learnt using square numbers, finding the square of a number, Pythagorean triplets , finding square roots through various methods, square roots of decimals and much more.

Also, access the following resources for Class 8 Chapter 6 Square and Square Roots  at BYJU’S:

• Squares and Square Roots Class 8 Notes: Chapter 6
• RD Sharma Solutions for Class 8 Maths Chapter 3 – Squares and Square Roots
• NCERT Exemplar Class 8 Maths Solutions for Chapter 3 – Squares And Square Roots Cubes And Cube Roots
• Important Questions Class 8 Maths Chapter 6- Squares and Square Roots

NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots

In the chapter, Cubes and Cube Roots, students learn about numerous strategies to find out the cubes and cube roots of a number. The chapter discusses finding the cubes of different numbers, some interesting patterns that could be learnt using cubes and finding the cube roots . There are 2 exercises in the chapter that will help the students understand the basics of cubes and cube roots in depth.

Also, access the following resources for Class 8 Chapter 7 Cube and Cube Roots  at BYJU’S:

• Cubes and Cube Roots Class 8 Notes: Chapter 7
• Important Questions Class 8 Maths Chapter 7: Cubes and Cube Roots
• RD Sharma Solutions for Class 8 Maths Chapter 4 – Cubes and Cube Roots

NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities

The chapter, Comparing Quantities, helps the students in learning the comparison between the rise and decrease of percentages, market value, sales value, discount, etc. The chapter deals with an important concept that can be used in day-to-day life, Interest. Students learn about simple interest , compound interest calculated half-yearly, quarterly, monthly or yearly, and much more. There are 3 exercises in this chapter which help the students in learning the concept of comparing quantities.

Also, access the following resources for Class 8 Chapter 8 Comparing Quantities  at BYJU’S:

• Important Question Class 8 Maths Chapter 8: Comparing Quantities
• NCERT Exemplar Class 8 Maths Solutions for Chapter 9 – Comparing Quantities
• Comparing Quantities Class 8 Notes: Chapter 8

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

This chapter, Algebraic Expressions and Identities, helps the students understand the concepts like terms, factors and coefficients related to algebraic expressions. A brief on the basics of monomials , binomials and polynomials is also given in the chapter. Students learn the addition, subtraction and multiplication of algebraic expressions. The concept of identity is also covered in the chapter. The 5 exercises in the chapter cover all the concepts present in algebraic expressions and identities.

Also access the following resources for  Class 8 Chapter 9 Algebraic Expressions and Identities  at BYJU’S:

• Algebraic Expressions and Identities Class 8 Notes: Chapter 9
• RD Sharma Solutions for Class 8 Maths Chapter 6 – Algebraic Expressions and Identities
• NCERT Exemplar Class 8 Maths Solutions for Chapter 7 – Algebraic Expressions And Identities Factorisation
• Important Questions Class 8 Maths Chapter 9 Algebraic Expressions and Identities

NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes

In this chapter, with the help of 3 exercises present, students learn to visualize solid shapes in different dimensions. The chapter is very interesting since it deals with viewing 3D shapes, mapping the space around us, and learning about faces, edges and vertices. The chapter also discusses Euler’s formula , which states that F + V – E = 2, where F is Faces, V is Vertices, and E is Edges, along with its application.

Also, access the following resources for Class 8 Chapter 10 Visualizing Solid Shapes  at BYJU’S:

• Visualising Solid Shapes Class 8 Notes: Chapter 10
• Important Questions Class 8 Maths Chapter 10 Visualising Solid Shapes
• RD Sharma Solutions for Class 8 Maths Chapter 19 Visualising Shapes
• NCERT Exemplar Class 8 Maths Solutions for Chapter 6 – Visualising Solid Shapes

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration

Students in lower classes must have learnt about the area and perimeter of various closed plane figures such as triangles, rectangles, circles, etc. In this chapter, Mensuration , students will learn to solve problems related to the perimeter and area of other plane closed figures like quadrilaterals. Eventually, the students will learn about the surface area and volume of different solid shapes such as a cube, cuboids and cylinders. A total of 4 exercises are present in this chapter.

Also, access the following resources for Class 8 Chapter 11 Mensuration  at BYJU’S:

• Mensuration Class 8 Notes- Chapter 11
• Important Questions Class 8 Maths Chapter 11 Mensuration
• RD Sharma Solutions for Class 8 Maths Chapter 20 Mensuration – I (Area of a Trapezium and a Polygon)
• NCERT Exemplar Class 8 Maths Solutions for Chapter 11 – Mensuration

NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

In the chapter, Exponents and Powers, students learn different concepts, including powers with negative exponents, laws of exponents , use of exponents to express the numbers in standard form and comparison of extremely large numbers with small numbers. The chapter consists of 2 exercises to help the students learn about the topics of exponents and powers.

Also, access the following resources for Class 8 Chapter 12 Exponents and Powers  at BYJU’S:

• NCERT Exemplar Class 8 Maths Solutions for Chapter 8 – Exponents And Powers
• Important Questions Class 8 Maths Chapter 12 Exponents And Powers
• RD Sharma Solutions for Class 8 Maths Chapter 2 – Powers

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions

This chapter contains 2 exercises with questions based on the concepts of direct proportion and inverse proportion. Two quantities, x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant. On the other hand, two quantities, x and y, are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant.

Also, access the following resources for Class 8 Chapter 13 Direct and Inverse Proportions  at BYJU’S:

• Direct and Inverse Proportions Class 8 Maths Notes – Chapter 13
• NCERT Exemplar Class 8 Maths Solutions for Chapter 10 – Direct And Inverse Proportions
• Important Questions Class 8 Maths Chapter 13 Direct and Inverse Proportions
• RD Sharma Solutions for Class 8 Maths Chapter 10 Direct and Inverse Variations

NCERT Solutions for Class 8 Maths Chapter 14 Factorization

In this chapter, students learn to perform Factorization. The topics covered in this chapter include factors of natural numbers and algebraic expressions , factorisation by regrouping terms and factorisation using identities. The chapter also deals with the division of algebraic expressions that, includes division of a monomial by another monomial, division of a polynomial by a monomial, etc. There are 4 exercises in this chapter that contain questions covering all the topics present in the chapter.

Also, access the following resources for Class 8 Chapter 14 Factorization  at BYJU’S:

• RD Sharma Solutions for Class 8 Maths Chapter – 7 Factorization
• Factorisation Class 8 Notes- Chapter 14
• Important Questions Class 8 Maths Chapter 14 Factorization

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

In the chapter, Introduction to Graphs, students learn to represent different types of data with various kinds of graphs. The different types of graphs include bar graphs , pie graphs, line graphs and linear graphs. The chapter will help the students in learning how to locate a point and coordinate in a graph. A total of 3 exercises are present in the chapter that will help the students understand the concepts of Graphs.

Also, access the following resources for Class 8 Chapter 15 Introduction to Graphs  at BYJU’S:

• Introduction To Graphs Class 8 Notes- Chapter 15
• Important Questions Class 8 Maths Chapter 15: Introduction to Graphs
• NCERT Exemplar Class 8 Maths Solutions for Chapter 12 – Introduction To Graphs
• RD Sharma Solutions for Class 8 Maths Chapter 27 Introduction to Graphs

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers

Students, so far, have studied various types of numbers, such as natural numbers, whole numbers, integers and rational numbers . They might have also studied a number of interesting properties of these numbers, finding factors, multiples and the relationships among them. Likewise, in this chapter, students can explore the vast genres of numbers in detail. These ideas can help the students in justifying tests of divisibility. There are 2 exercises in this chapter that covers the topic of playing with numbers.

Also, access the following resources for Class 8 Chapter 16 Playing with Numbers  at BYJU’S:

• Playing With Numbers Class 8 Notes- Chapter 16
• Important Questions Class 8 Maths Chapter 16: Playing with Numbers
• NCERT Exemplar Class 8 Maths Solutions for Chapter 13 – Playing with Numbers
• RD Sharma Solutions for Class 8 Maths Chapter 5 – Playing with Numbers

CBSE Class 8 Maths Solutions of NCERT Book

We are providing chapter-wise NCERT Maths Solutions for Class 8. The solutions provided on this page will help students understand and solve all the NCERT Class 8 mathematics book questions. These solutions are free, and students can view them online on the website or download the PDF.

Solving NCERT Maths question papers and sample papers will also help the students to understand different types of questions as well as the marking scheme. Also, students can learn from NCERT Exemplar Class 8 to practise exemplar problems.

Key Features of BYJU’S NCERT Class 8 Maths Solutions

• These solutions cover all the chapters that are included in the Class 8 Maths book.
• The solutions are given in easy steps to help students understand the concepts better.
• These solutions can be downloaded and referred to at any time and at any place.
• These CBSE 8th Class Maths solutions are available for free, and any student can access them.

These are just a few benefits of using the Solutions of Maths NCERT 8th Class . Students can register with BYJU’S and get the opportunity to learn topics of CBSE or NCERT syllabus for Class 8 Maths or any other Class more effectively. They can learn different topics right from their homes using the internet, where they can browse content on their PCs. Moving on, students can customize their learning experience, and they can do it all at their own pace without worrying about deadlines or any stress. Further, we are providing the best subject experts or mentors who will guide students to learn the subject and its concepts in a more simple and fun manner.

Another benefit that students can experience with BYJU’S is that they can opt to learn NCERT subjects by accessing our solutions anywhere and at any time of the day. In addition, BYJU’S is keen on tracking the progress that students make. Feedback and counselling are provided via periodic assessments. In case students face any doubts while going through the CBSE Class 8 Maths NCERT Solutions , they can always approach our BYJU’S support team to clear all their doubts. Besides, students can bring in all their queries regarding Maths as well as other subjects, including Physics, Chemistry, and Biology. Our responsive team is always ready to answer all types of questions.

Students can also download the BYJU’S app and get complete assistance for Class 8 with a new method of learning through educational videos.

Frequently Asked Questions on NCERT Solutions for Class 8 Maths

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NCERT Solutions For Class 8 Maths

• NCERT Solutions

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.

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 Class 8 Maths Chapter wise Solutions in Hindi

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 .

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.

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

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

Rational Numbers Important Questions

Rational Numbers Important Formulas

Rational Numbers Revision Notes

Rational Numbers NCERT Exemplar Solutions

Rational Numbers RD Sharma Solutions

Rational Numbers RS Aggarwal 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.

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

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

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

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

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

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 –

Linear Equations in One Variable Important Questions

Linear Equations in One Variable Important Formulas

Linear Equations in One Variable Revision Notes

Linear Equations in One Variable NCERT Exemplar Solutions

Linear Equations in One Variable RD Sharma 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.

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

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

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.

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:

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 –

Understanding Quadrilaterals Important Questions

Understanding Quadrilaterals Revision Notes

Understanding Quadrilaterals & Practical Geometry NCERT Exemplar Solutions

Understanding Shapes II (Quadrilaterals) RD Sharma 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.

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.

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.

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

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.

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:

Constructing A Quadrilateral

Some Special Cases

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

Practical Geometry Practical Geometry Important Questions

Practical Geometry Important Formulas

Practical Geometry Revision Notes

Practical Geometry RD Sharma 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.

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.

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.

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

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

Data Handling Important Questions

Data Handling Revision Notes

Data Handling NCERT Exemplar Solutions

Data Handling 1 (Classification and Tabulation of Data) RD Sharma Solutions

Data Handling RS Aggarwal 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.

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.

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

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

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

Squares and Square Roots Important Questions

Squares and Square Roots Important Formulas

Squares and Square Roots Revision Notes

Square-Square Root & Cube-Cube Root NCERT Exemplar Solutions

Squares and Square Roots RD Sharma Solutions

Squares-Square Root RS Aggarwal 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.

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.

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:

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

Cubes and Cube Roots Important Questions

Cubes and Cube Roots Important Formulas

Cubes and Cube Roots Revision Notes

Cubes-Cube Roots NCERT Exemplar Solutions

Cubes-Cube Roots RD Sharma Solutions

Cubes-Cube Roots RS Aggarwal 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.

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.

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.

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)

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 8 of CBSE Class 8 Maths Solutions –

Comparing Quantities Important Questions

Comparing Quantities Important Formulas

Comparing Quantities Revision Notes

Comparing Quantities NCERT Exemplar 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.

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

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

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 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.

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.

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.

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

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

Visualising Solid Shapes Important Questions

Visualising Solid Shapes Important Formulas

Visualising Solid Shapes Revision Notes

Visualising The Solid Shapes NCERT Exemplar Solutions

Visualising Solid Shapes RD Sharma 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.

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.

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).

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).

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

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

Mensuration Important Questions

Mensuration Important Formulas

Mensuration Revision Notes

Mensuration NCERT Exemplar Solutions

Mensuration I (Area of a Trapezium and a Polygon) RD Sharma 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).

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.

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.

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

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

Exponents and Powers Important Questions

Exponents and Powers Important Formulas

Exponents and Powers Revision Notes

Exponents and Powers NCERT Exemplar 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.

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.

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

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

Direct and Inverse Proportions Important Questions

Direct and Inverse Proportions Important Formulas

Direct and Inverse Proportions Revision Notes

Direct and Inverse Proportions NCERT Exemplar Solutions

Direct and Inverse Proportions RD Sharma Solutions

Direct and Inverse Proportions RS Aggarwal 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.

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.

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.

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.

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?

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

Factorisation Important Questions

Factorisation Important Formulas

Factorisation Revision Notes

Factorisation RD Sharma Solutions

Factorisation RS Aggarwal 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.

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.

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.

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

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

Introduction to Graphs Important Questions

Introduction to Graphs Important Formulas

Introduction to Graphs Revision Notes

Introduction to Graphs RD Sharma 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.

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.

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:

Numbers In General Form

Games With Numbers

Letters For Digits

Tests Of Divisibility

Playing with Numbers Important Questions

Playing with Numbers Important Formulas

Playing with Numbers Revision Notes

Playing with Numbers RD Sharma Solutions

Playing with Numbers RS Aggarwal 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.

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.

NCERT Solution Class 8 Maths Related Links

Check on the additional study materials provided for Class 8 Maths

Important Questions for CBSE Class 8 Maths

Maths Class 8 Formula List

Revision Notes for CBSE Class 8 Maths

RD Sharma Solutions for CBSE Class 8 Maths

RS Aggarwal Class 8 Solutions for Maths book

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

Understanding Quadrilaterals

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.

3. Can NCERT Solutions for Class 8 Maths PDFs be Downloaded for Free?

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?

To download the NCERT Solutions for Class 8 Maths, students can simply click on the links provided on this page. The links will allow them to download the solutions of the corresponding chapters. Additionally, students can also download the Vedantu app to download the solutions from there.

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.

NCERT SOLUTIONS FOR CLASS 8

Cbse class 8 study materials.

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3

Class 8 Maths Exercise 3.3 Solutions Class 8 Maths Exercise 3.3 in Hindi Class 8 Maths Book Download in PDF Class 8 Maths Chapter 3 Solutions Class 8 Maths NCERT Solutions Class 8 All Subjects Solutions

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3 in Hindi and English Medium revised and updated for new session 2024-25. The solutions of ex. 3.3 class VIII mathematics are modified on the basis of new NCERT textbooks issued for 2024-25 examination.

Class VIII Mathematics NCERT Ex. 3.3 of chapter 3 Understanding Quadrilaterals in Hindi and English Medium updated for academic session 2024-25. Here we have to learn about the properties of quadrilateral and their internal angles along with angle sum property of quadrilateral based question. All the questions are solved with easy method, according to standard 8 NCERT Book. Videos related to 8th mathematics ex. 3.3 also helps a lot during the practice.

8th Maths Exercise 3.3 Solution in Hindi and English Medium

• Class 8 Maths Exercise 3.3 in English
• Class 8 Maths Exercise 3.3 in Hindi
• Class 8 Maths Chapter 3 in PDF
• Class 8 Maths Chapter 3 Solutions
• Class 8 Maths NCERT Solutions
• Class 8 All Subjects Solutions

Download App for Class 8

A quadrilateral is called a parallelogram if both pairs of its opposite sides are parallel. ABCD is a quadrilateral in which AB || DC and AD || BC. So, ABCD is parallelogram.

A parallelogram having all sides equal is called a rhombus. ABCD is a rhombus in which AB || DC, AD || BC and AB = BC = CD = DA

A parallelogram in which each angle is a right angle is called a rectangle. ABCD is a quadrilateral in which AB || DC, AD || BC and ∠A = ∠B = ∠C = ∠D = 90°. So, ABCD is a rectangle.

parallelogram in which all the sides are equal each angle measures 90° is called a square. ABCD is a quadrilateral in which AB || DC, AD || BC, AB = BC = CD = DA and ∠A = ∠B = ∠C = ∠D = 90°. So, ABCD is a square.

A quadrilateral is called a kite if it has two pairs of equal adjacent sides but unequal opposite sides. In the adjoining figure, ABCD is a quadrilateral in which AB = AD, BC = DC, AD ≠ BC and AB = DC. So, ABCD is a kite.

Class 8 Maths Exercise 3.3 Important Questions

Prove that any two adjacent angles of a parallelogram are supplementary..

Let ABCD be a parallelogram. Then, AD || BC and AB is a transversal. So, ∠A + ∠B = 180°, [ sum of interior angles on the same side if the transversal is 180°] Similarly, ∠B + ∠C = 1800, ∠C + ∠D = 1800 and ∠D + ∠A = 180°. Thus, the sum of any two adjacent angles of a parallelogram is 180°. Hence, any two adjacent angles of a parallelogram are supplementary.

The ratio of two sides of a parallelogram is 4 :3 If its perimeter is 56 cm, find the lengths of its sides.

Let the lengths of two sides of the parallelogram be 4x cm and 3x cm respectively. The, its perimeter = 2 (4x + 3x) cm = 14x cm. 14x = 56 x = 4 one side = (4 x 4) cm = 16 cm and other side = (3 x 4) cm = 12 cm.

• (i) The opposite sides are equal;
• (ii) The opposite angles are equal;
• (iii) Diagonals bisect each other.

Class 8 Maths Exercise 3.3 Extra Questions for Practice

What makes a parallelogram special.

Properties of a Parallelogram Parallelograms are quadrilaterals that have two sets of parallel sides and two sets of congruent sides. A parallelogram’s opposite angles are congruent; its consecutive angles are supplementary; its diagonals bisect each other and its diagonals form two congruent triangles.

Is diagonal of parallelogram equal?

The diagonals of a parallelogram are equal. The opposite sides and opposite angles of a parallelogram are equal. And these opposite sides and angles make up for two congruent triangles, with the two diagonals being the sides of these two congruent triangles. Hence the diagonals of the parallelogram are equal.

A square is a parallelogram. This i

Is a parallelogram a square?s always true. Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides.

Let ABCD be a parallelogram. Draw its diagonals AC. In DABC and DCDA, we have: ∠1 = ∠4 (alternate angles) ∠3 = ∠2 (alternate angles) and AC = CA (common) DABC congruent DCDA (by ASA congruence) AB = CD, BC = DA and ∠B = ∠D. Similarly, by drawing the diagonal BD, we can prove that triangle ABD congruent triangle CDB. ∠A = ∠C Thus, AB = CD, BC = DA, B = D and A = C. This proves (i) and (ii).

In order to prove (iii) consider parallelogram ABCD and draw its diagonals AC and BD, intersecting each other at O. In triangle OAB and triangle OCD, we have AB = CD (opposite sides of a parallelogram) ∠AOB = ∠COD (vertically opposite angles) ∠OAB = ∠OCD (alternate angles) triangle OAB = triangle OCD (by ASA property) OA = OC and OB = OD. This shows that the diagonals of a parallelogram bisect each other.

This converse of the above result is also true, i.e.,

• A quadrilateral is a parallelogram if its opposite sides are equal.
• A quadrilateral is a parallelogram if its opposite angles are equal.
• A quadrilateral is a parallelogram if its diagonals bisect each other.

Remark: A rectangle, a square and a rhombus are special types of parallelogram. So, all the properties of a parallelogram are satisfied by each one of them.

(i) opposite sides are equal (ii) opposite angles are equal (iii) diagonals bisect each other.

(i) If the opposite sides of a quadrilateral are equal then it is a parallelogram (ii) If the opposite angles of a quadrilateral are equal then it is a parallelogram (iii) If the diagonals of a quadrilateral bisect each other then it is a parallelogram

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NCERT Solutions for Class 8 Maths Free PDF Download

Ncert solutio ns for class 8 maths.

NCERT Solutions for Class 8 Maths will help you to ace the unsolved problems in the maths book prescribed by the CBSE. NCERT Solutions for Class 8 breaks down the solutions into detailed steps to increase your score in exams.

NCERT Solutions are prepared by our team of highly professional, qualified and experienced faculties. These NCERT Solutions for Class 8 Maths helps you to quickly grasp all the concepts and formulas of maths. In case you have a doubt while you are studying NCERT Solutions for Class 8 Maths which we are providing, for this, we have a team of teachers who are just a click away to solve your doubt any time.

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Download NCERT Solutions for other subjects here .

Download NCERT Solutions for Class 8 here.

NCERT Solutions for Class 8 Maths Chapter-wise

• 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

CBSE Class 8 Maths Chapter-wise NCERT Solutions

Ncert solutions for class 8 maths chapter 1 – rational numbers.

In this chapter will learn the properties of real numbers, rational numbers, representation of a rational number on number line, additive and multiplicative identity.

NCERT Solutions for Class 8 Maths Chapter 2 – Linear Equations in One Variable

In this chapter you will learn the concept of linear equation and methods to solve them, reducing equations to a simpler form and their applications.

NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals

In this chapter, you will learn the basics of a quadrilateral, polygon, kinds of quadrilateral and polygon, the measure of external angle of polygons.

NCERT Solutions for Class 8 Maths Chapter 4 – Practical Geometry

This chapter includes drawing 4 sides in a quadrilateral with 2 adjacent sides, 3 angles, and 1 diagonal area given.

NCERT Solutions for Class 8 Maths Chapter 5 – Data Handling

In this chapter you will learn to organize the data in a systematic method, represent the data in a pictograph, a bar graph, double bar graph, pie chart, and histogram.

NCERT Solutions for Class 8 Maths Chapter 6 – Square and Square Roots

In this chapter, you will learn about the squares of numbers and their properties, various patterns of squares, and square roots of numbers.

NCERT Solutions for Class 8 Maths Chapter 7 – Cube and Cube Roots

In this you will study about cubes of different numbers, cubes of numbers by adding consecutive odd numbers pattern, cube roots of a number, solving cube roots by prime factorization method.

NCERT Solutions for Class 8 Maths Chapter 8 – Comparing Quantities

In this chapter you will compare quantities, increase or decrease of percentage, discount, profit and loss, vat tax, sales tax, computing interest.

NCERT Solutions for Class 8 Maths Chapter 9 – Algebraic Expressions and Identities

In this chapter, you will learn about the algebraic expressions and their types, like and unlike terms, addition and subtraction, multiplication of algebraic expressions, standard identities and their implementation.

NCERT Solutions for Class 8 Maths Chapter 10 – Visualizing Solid Shapes

In this chapter, you will study the cubes, cuboids, cones, cylinders, spheres, hemispheres and their area, triangular pyramids, triangular and square base prisms, application of Euler’s formula.

NCERT Solutions for Class 8 Maths Chapter 11 – Mensuration

In this chapter, you will learn about the perimeter and areas of plane closed figure and surface area, the volume of a solid figure, transform the quantity into other units.

NCERT Solutions for Class 8 Maths Chapter 12 – Exponents and Powers

In this chapter you will study powers with negative exponents, laws of exponents, express the numbers in standard form and comparison of extremely large numbers.

NCERT Solutions for Class 8 Maths Chapter 13 – Direct and Inverse Proportions

In this chapter, you will solve the problems related to direct and inverse proportion and their identification based on relative increase or decrease of a quantity with respect to the first one.

NCERT Solutions for Class 8 Maths Chapter 14 – Factorization

In this chapter, you will learn methods of factorization, division of algebraic expression, error finding in algebraic equations.

NCERT Solutions for Class 8 Maths Chapter 15 – Introduction to Graphs

In this, you will study the representations of data by a bar graph, histogram, pie chart, line graph, and linear graph, application based on the graph using the dependent & independent variable.

NCERT Solutions for Class 8 Maths Chapter 16: Playing with Numbers

In this chapter, you will deal with numbers in a general form, puzzles related to numbers, divisibility tests.

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Solved Questions For You:

Question 1. For which of these would you use a histogram to show the data? (a) The number of letters for different areas in a postman’s bag. (b) The height of competitors in an athletics meet. (c) The number of cassettes produced by  5  companies. (d) The number of passengers boarding trains from  7 : 0 0  a.m. to  7 : 0 0  p.m. at a station. Give reasons for each.

(a) We can’t use the histogram in this case because we cannot define the class intervals for this data.

(b) We can use histogram here because it will be easy to divide the data into class intervals.

(c) We do not have approximate data we won’t use a histogram. We do not know about the number of cassettes produced by companies.

Question 2. List the outcomes you can see in these experiments.

(a) Possible outcomes would be:  A , B , C , D

Question 3. When a die is thrown, list the outcomes of an event of getting

(i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than  5

Possible outcomes:  1 , 2 , 3 , 4 , 5 , 6 (i) (a) Prime numbers:  2 , 3 , 5 It represents the outcomes of Prime numbers (b) Not a prime number:  1 , 4 , 6 It represents the outcomes of not prime numbers. (ii) (a) A number greater than  5 : Only when  6  comes (b) Number not greater than  5 : Only when outcomes:  1 , 2 , 3 , 4  and  5

Question 4. A survey was made to find the type of music that a certain group of young people liked in a city. The adjoining pie chart shows the findings of this survey.

From this pie chart answer the following: (i) If  2 0  people liked classical music, how many young people were surveyed? (ii) Which type of music is liked by the maximum number of people? (iii) If a cassette company were to make  1 0 0 0  CDs, how many of each type would they make?

The light chart represents the maximum number as it is  4 0 % of the total.  ∴  Light music is liked by max. people.

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NCERT Solutions for Class 8

• NCERT Solutions for Class 8 Chemistry Chapter 3 Free PDF Download
• NCERT Solutions for Class 8 Chemistry Chapter 4 Free PDF Download
• NCERT Solutions for Class 8 Chemistry Chapter 5 Free PDF Download
• NCERT Solutions for Class 8 Physics Chapter 11 Free PDF Download
• NCERT Solutions for Class 8 Physics Chapter 16 Free PDF Download
• NCERT Solutions for Class 8 Physics Chapter 13 Free PDF Download
• NCERT Solutions for Class 8 History Chapter 3 Free PDF Download
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Worksheets For class 8

• CBSE Worksheet for Class 8 Math’s

CBSE Worksheet for Chapter - 3 Percentage Class 8

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In this CBSE Worksheet for chapter 3, we shall discuss more word problems based on percentage. Students who struggle to solve problems have arrived at the right platform. The solutions here are solved and prepared by our expert tutors at Physics Wallah in a step-by-step format to help students understand the concepts.

When preparing for the exam, students can refer to RS Aggarwal Solutions Class 8 , the best study material prepared by our experts by the latest CBSE patterns. For other CBSE Worksheet for Class 8 Mathematics check out main page of Physics Wallah.

Q1. Two fifth of one third of three seventh of a number is 15. What is 40 percent of that number?

Q2. If A is 20% more than B, by what percent is B less than A?

Q3. In order to compute 0.15% of a number, it must be multiplied by:

Q4. If 25% of a number is subtracted from a second number, the second number reduces to its five-sixth. What is the ratio of the first number to the second number?

• Data inadequate

Q5. A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are:

Q6. Peter earns 40% more money than Albert. Albert earned 20% less than Michael. Peter earned more than Michael by:

Q7. Milk contains 5% water. What quantity of pure milk should be added to 10 litres of milk to reduce this to 2%.

• Cannot be determined
• None of these

Q8. In an examination A gets 10% marks less than B and B gets 10% marks less than C. If A gets 810 marks, what marks does C get?

Q9. If the cost of the book worth Rs. 50 is increased by Rs. 25, the rate of increase is:

Q10. A man spends Rs, 3500 and saves 12 % of his income. His monthly salary is:

Q11. In an examination 52% candidates failed in English, 42% in Maths and 17% in both. The percentage of those passed in both the subjects is:

Q12. The numerator of a fraction is increased by 20% and its denominator be diminished by 10%. The value of new fraction is , then the fraction is:

Q13. If A is 25% of B then what % is B of A?

Q14. Let x and y be two numbers such that x = 6y. Then y is less than x by:

Q15. The price of sugar rises by 50%. By what factor a family reduces the consumption of sugar, so that the expenditure does not increase?

Word Problems

Q1. A coolie deposits Rs 150 monthly in his post office Savings Bank account. If this is 15% of his monthly income, find his monthly income.

Ans. Let the monthly income of a coolie be ‘x.’

Here, coolie deposits Rs 150 per month, which is 15% of his monthly income

From the above, we can derive that,

x × (15/100) =150

Which implies, x = (150 × 100) / 15

x = 15000/15

The monthly income is Rs 1000

Q2. Isha got 86.875% marks in the annual examination. If she got 695 marks, find the total number of student Isha marks for the examination.

Ans. Given, Marks scored by Isha are 695

And Percentage of marks Isha got was 86.875%

Let the total marks be ‘x.’

x × (86.875/100) =695

Here, 86.875 can be expressed as 86875/1000

Which implies, x = (695 × 100 × 1000) / 86875

x = 6950000/86875 = 800

Total no: of Marks, x = 800

The total number of marks is 800marks

Q3. Aysha went to school for 216 days in a full year. If her attendance is 90%, find the days on which the school was opened.

Ans. Given the number of days Aysha went to school = 216 days

Aysha's Attendance percentage is = 90%

So, let the number of days when school remained open be x days

(x × 90)/100 = 216

By using cross multiplication, we get,

x = (216×100)/90

Number of days the school remained open for 240 days

Q4. A garden has 2000 trees. 12% are mango trees, 18% are lemon, and the rest are orange trees. Find the number of orange trees.

Ans. Given details are,

Total number of trees = 2000

Number of mango trees = 12% of 2000

= (12/100) × 2000

= 240 trees

Number of lemon trees = 18% of 2000

= (18/100) × 2000

= 360 trees

Number of orange trees = 2000 – (Number of mango trees+ Number of lemon trees)

= 2000 – (240+360)

= 2000 – 600

= 1400 trees

The number of orange trees is 1400 trees

Q5. A balanced diet should contain 12% proteins, 25% fats, and 63% carbohydrates. If a child needs 2600 calories in this food daily, calculate the calories and the amount of each of these in his daily food intake.

Ans. The given details are,

Amount of calorie daily needed = 2600 calorie

Amount of protein needed = 12% of 2600

= (12/100) × 2600

= 312 calorie

Amount of fats needed = 25% of 2600

= (25/100) × 2600

= 650 calorie

Amount of carbohydrate needed = 63% of 2600

= (63/100) × 2600

= 1638 calorie

The amount of calories required in protein is 312 calories, fat is 650 calories, and carbohydrates is 1638 calories.

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Understanding Quadrilaterals Assignment 3 Worksheet Class 8 PDF with Answers

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DAV Class 8 Maths Chapter 8 Worksheet 3 Solutions

The DAV Class 8 Maths Solutions  and DAV Class 8 Maths Chapter 8 Worksheet 3 Solutions of Polynomials offer comprehensive answers to textbook questions.

DAV Class 8 Maths Ch 8 Worksheet 3 Solutions

Question 1. Using factor method, divide the following polynomials by a binomial:

(i) x 2 + 3x + 2 by x + 1 Solution: x 2 + 3x + 2 ÷ x + 1 \(\frac{x^2+3 x+2}{x+1}\) = \(\frac{x^2+2 x+x+2}{x+1}\) = \(\frac{x(x+2)+1(x+2)}{x+1}\) = \(\frac{(x+1)(x+2)}{x+1}\) = x + 2 Hence the quotient is (x + 2)

(ii) x 2 – 7x – 18 by x – 9 Solution: x 2 – 7x – 18 ÷ x – 9 \(\frac{x^2-7 x-18}{x-9}\) = \(\frac{x^2-9 x+2 x-18}{x-9}\) = \(\frac{x(x-9)+2(x-9)}{x-9}\) = \(\frac{(x+2)(x-9)}{x-9}\) = x + 2 Hence the quotient is (x + 2)

(iii) p 2 + 6p + 8 by p + 2 Solution: p 2 + 6p + 8 ÷ p + 2 \(\frac{p^2+6 p+8}{p+2}\) = \(\frac{p^2+4 p+2 p+8}{p+2}\) = \(\frac{p(p+4)+2(p+4)}{p+2}\) = \(\frac{(p+2)(p+4)}{(p+2)}\) = (p + 4) Hence the quotient is (p + 4)

(iv) p 2 – p – 42 by p + 6 Solution: p 2 – p – 42 ÷ p + 6 \(\frac{p^2-p-42}{p+6}\) = \(\frac{p^2-7 p+6 p-42}{p+6}\) = \(\frac{p(p-7)+6(p-7)}{p+6}\) = \(\frac{(p+6)(p-7)}{p+6}\) = (p – 7) Hence the quotient is (p – 7).

(v) y 2 + 12y + 35 by y + 7 Solution: y 2 + 12y + 35 ÷ y + 7 \(\frac{y^2+12 y+35}{y+7}\) = \(\frac{y^2+7 y+5 y+35}{y+7}\) = \(\frac{y(y+7)+5(y+7)}{y+7}\) = \(\frac{(y+7)(y+5)}{(y+7)}\) = y + 5 Hence the quotient is (y + 5).

(vi) z 2 – 10z + 16 by z – 2 Solution: z 2 – 10z + 16 ÷ z – 2 \(\frac{z^2-10 z+16}{z-2}\) = \(\frac{z^2-8 z-2 z+16}{z-2}\) = \(\frac{z(z-8)-2(z-8)}{z-2}\) = \(\frac{(z-8)(z-2)}{(z-2)}\) = z – 8 Hence the quotient is (z – 8).

(vii) x 4 + 3x 2 – 10 by x 2 + 5 (Hint: put x 2 = y) Solution: x 4 + 3x 2 – 10 ÷ x 2 + 5 \(\frac{x^4+3 x^2-10}{x^2+5}\) = \(\frac{y^2+3 y-10}{y+5}\) = \(\frac{y^2+5 y-2 y-10}{y+5}\) = \(\frac{y(y+5)-2(y+5)}{(y+5)}\) = \(\frac{(y+5)(y-2)}{(y+5)}\) = y – 2 = x 2 – 2 Hence the quotient is (x 2 – 2).

(viii) x 2 – 7x + 12 by x – 4 Solution: x 2 – 7x + 12 ÷ x – 4 \(\frac{x^2-7 x+12}{x-4}\) = \(\frac{x^2-4 x-3 x+12}{x-4}\) = \(\frac{x(x-4)-3(x-4)}{x-4}\) = \(\frac{(x-4)(x-3)}{x-4}\) = (x – 3) Hence the quotient is (x – 3).

Question 2. Using long division method, divide the following polynomials by a binomial and check your answer.

(i) 4p 3 – 4p 2 + 6p – \(\frac{5}{2}\) by 2p – 1 (ii) x – 6 + 15x 2 by 2 + 3x (iii) 4x 3 – 37x 2 + 52x – 15 by 4x – 5 (iv) y 3 – 8 by y – 2 (v) 29z – 6z 2 – 28 by 3z – 4 (vi) p 4 + p 3 – p 2 + 1 by p – 1 (vii) 12z 3 + 4z + 3z 2 + 1 by 4z + 1 (viii) 8x 2 – 2 – 3x + 12x 3 by 4x 2 – 1 Solution: (i) 4p 3 – 4p 2 + 6p – \(\frac{5}{2}\) ÷ 2p – 1

Check: Dividend = Divisor × Quotient + Remainder 4p 3 – 4p 2 + 6p – \(\frac{5}{2}\) = (2p – 1) × (2P 2 – p + \(\frac{5}{2}\)) + o = 2p (2p 2 – p + \(\frac{5}{2}\)) – 1 (2P 2 – p + \(\frac{5}{2}\)) = 4p 3 – 2p 2 + 5p – 2p 2 + p – \(\frac{5}{2}\) = 4p 3 – 4p 2 + 6p – \(\frac{5}{2}\) ⇒ L.H.S. = R.H.S. Hence verified.

(ii) Let us write dividend and divisor in standard form. Dividend = 15x 2 + x – 6 and Divisor = 3x + 2

Check: Dividend = Divisor × Quotient + Remainder 15x 2 + x – 6 = (3x + 2) × (5x – 3) + 0 = 3x (5x – 3) + 2 (5x – 3) = 15x 2 – 9x + 10x – 6 = 15x 2 + x – 6 ⇒ L.H.S. = R.H.S. Hence verified.

(iii) 4x 3 – 37x 2 + 52x – 15 ÷ 4x – 5

Check: Dividend = Divisor × Quotient + Remainder 4x 3 – 37x 2 + 52x – 15 = (4x – 5) x (x 2 – 8x + 3) + 0 = 4x (x 2 – 8x + 3) – 5 (x 2 – 8x + 3) = 4x 3 – 32x 2 + 12x – 5x 2 + 40x – 15 = 4x 3 – 37x 2 + 52x – 15 ⇒ L.H.S. = R.H.S. Hence Verified.

(iv) y 3 – 8 ÷ y – 2

Check: Dividend = Divisor × Quotient + Remainder L.H.S. = y 3 – 8 R.H.S. = (y – 2) (y 2 + 2y + 4) + 0 = y (y 2 + 2y + 4) – 2 (y 2 + 2y + 4) = 9 + 2y 2 + 4y – 2y 2 – 4y – 8 = y 3 – 8 ⇒ L.H.S. = R.H.S. Hence Verified.

(v) Let us write the dividend in standard form. We have 29 – 6z 2 – 28 = – 6z 2 + 29z – 28

Check: Dividend = Divisor × Quotient + Remainder – 6z 2 + 29z – 28 = (3z – 4) × (- 2z + 7) + 0 = 3z (- 2z + 7) – 4(- 2z + 7) = – 6z 2 + 21z + 8z – 28 = – 6z 2 + 29z – 28 ⇒ L.H.S. = R.H.S. Hence verified.

(vi) p 4 + p 3 – p 2 + 1 ÷ p – 1

Quotient = p 3 + 2p 2 + p + 1 Remainder = 2

Check: Dividend = Divisor × Quotient + Remainder p 4 + p 3 – p 2 + 1 = (p – 1) (p3 + 2p2 +p + 1) = p (p 3 + 2p 2 + p + 1) – 1 (p 3 + 2p 2 + p + 1) = p 4 + 2p 3 + p 2 + p – p 3 – 2p 2 – p – 1 = p 4 + p 3 – p 2 – 1 ∴ L.H.S. = R.H.S. Hence verified.

(vii) Let us write the dividend in standard form: Dividend = 12z 3 + 3z 2 + 4z + 1

Check: Dividend = Divisor × Quotient + Remainder 12z 3 + 3z 2 + 4z + 1 = (4z + 1) (3z 2 + 1) + 0 = 4z (3z 2 + 1) + 1(3z 2 + 1) = 12z 3 + 4z + 3z 2 + 1 = 12z 3 + 3z 2 + 4z + 1 L.H.S. = R.H.S. Hence verified.

(viii) Let us write the dividend in standard form: Dividend = 12x 3 + 8x 2 – 3x – 2

Check: Dividend = Divisor × Quotient + Remainder 12x 3 + 8x 2 – 3x – 2 = (4x 2 – 1) × (3x + 2) + 0 = 4x 2 (3x + 2) – 1 (3x + 2) = 12x 3 + 8x 2 – 3x – 2.

Here, remainder = 0 Hence (x + 2) is a factor of x 4 – 16.

(ii) z 4 – z 3 + 3z 2 – 2z + 2 ; z 2 + 2

Here, the remainder = 0 Hence z 2 + 2 is a factor of z 4 – z 3 + 3z 2 – 2z + 2.

(iii) x 3 – 4x 2 – 3x + 5 ; x – 3

As remainder = – 13 which is not equal to 0. So, x – 3 is not a factor of x 3 – 4x 2 – 3x + 5.

(iv) 4p 3 – 12p 2 – 37p – 15 ; 2p + 1

Here, remainder = 0 Thus, (2p + 1) is a factor of 4p 3 – 12p 2 – 37p – 15.

(v) 4q 3 – 6q 2 – 4q + 3 ; 2q – 1

Here, remainder = 0 Thus, (2q – 1) is a factor of 4q 3 – 6q 2 – 4q + 3.

(vi) 20x 2 – 32x – 16 ; 5x + 2

Here, remainder = 0 Thus, (5x + 2) is a factor of 20x 2 – 32x – 16.

(vii) 12a 2 – 7a – 2 ; 4a – 1

As remainder = – 3 which is not equal to 0. So 4a – 1 is not a factor of 12a 2 – 7a – 2.

(viii) 6x 3 + 19x 2 + 13x + (- 3) ; 2x + 3

Here, remainder = 0 Thus, (2x + 3) is a factor of 6x 3 + 19x 2 + 13x – 8.

DAV Class 8 Maths Chapter 8 Value Based Questions

Question 1. Mr. Lalit donated (x 2 + 12x + 35) for the education of (x + 7) children. (i) Find the amount received by each child, if each child got the equal amount. (ii) Why it is necessary to educate children? Give one reason. Solution: (i) Total donation = (x 2 + 12x + 35) = [x 2 + (7 + 5) x + 7 × 5] = [x 2 + 7x + 5x + 7 × 5] = [x (x + 7) + 5 (x + 7)] = (x + 7) (x + 5) Number of children = (x + 7) Amount received by each child = \(\frac{(x+7)(x+5)}{(x+7)}\) = (x + 5)

(ii) Children is the future asset of the nation as they have to represent the nation. So, it is necessary to educate children.

Question 2. Every morning Abhay goes for Jogging in a park. (i) Find the time taken by him to cover a distance of (2t 4 + 3t 3 – 2t 2 – 9t – 12) km at the speed of (t 2 – 3) km/hr. (ii) Write the importance of physical exercises like jogging, walking, etc. Solution: (i) Distance = (2t 4 + 3t 3 – 2t 2 – 9t – 12) km Speed = (t 2 – 3) km/hr Time = \(\frac{\text { Distance }}{\text { Speed }}\) = \(\frac{\left(2 t^4+3 t^3-2 t^2-9 t-12\right) \mathrm{km}}{\left(t^2-3\right) \mathrm{km} / \mathrm{hr}}\)

= (2t 2 + 3t + 4) hr

(ii) Physical exercises keeps the body fit and sound.