NCERT Solutions Class 8 Mathematics

NCERT syllabus introduces Class 8 students to several new topics and chapters. The students learn new Mathematical formulas and concepts at this level. And for this, they need the right learning aids and guidance to understand the chapters thoroughly. According to academic experts, the NCERT solutions are the best study materials to help the students. The solutions present detailed explanations of the Mathematics problems followed by examples. 

The subject-matter experts draft the Mathematics chapter-wise solutions in separate files to ease the study process for the students. Students can download the NCERT solutions for class 8 Mathematics from the official website of Extramarks for free.

 

Download NCERT Class 8 Mathematics Solutions 

Extramarks brings NCERT solutions to the class 8 students to impart a comprehensive knowledge about the subsequent chapters and topics. The study materials help the students in their examination preparation and during the daily revision process. Class 8 Mathematics NCERT solutions encourage the students to learn the subject further with more confidence and zeal. Students can take the help of the Mathematics solutions to develop their subject base and get high grades in the examination. The solutions cover answers to all the questions provided in the textbooks. The syllabus follows the NCERT curriculum, and the questions have been arranged as per the CBSE board guidelines. The students learn about the marks’ weightage, frequently asked questions, and significant chapters from the solutions. Advanced knowledge of the mark division helps the students to answer the questions to the point. The answers provided in the solutions teach the students how to answer the questions based on marks’ weightage. 

The NCERT solutions aid the students’ learning process and enable them to solve complex Mathematics problems with ease. Mathematics faculties all over the country recommend the 8th standard CBSE board students to study Mathematics with reference to NCERT solutions for class 8 Mathematics to develop a solid grasp of the subject. The students can avail these accurate and reliable Mathematics solutions for free from Extramarks. For this, they need to sign in to the website and access the materials. The class 8 students can enjoy the convenience to download the solutions online and study them later.

 

NCERT Solutions for Class 8 Mathematics Chapter Wise Download

NCERT Mathematics book class 8 solutions are available on Extramarks website. Students can easily find the chapter-wise solutions they need to study. The systematic arrangement of the chapters in the solution book saves time. The solutions provided are based on the NCERT books syllabus. The explanations accompanied by examples guide the students to understand the core concept of each chapter. Students find even the difficult and complex topics elaborated and decoded in a simpler manner. The use of easy-to-understand language enables the students to learn the crux of every chapter. The direct and logical approach of the solutions encourages the students to solve more Mathematical problems and practice consistently. Understanding one chapter eases the learning process of others as almost all the chapters are interlinked with each other. 

 

NCERT Solutions for Class 8 Mathematics – Chapter-wise Solutions

 

Chapter 1: Rational Numbers

1.1 – Introduction 

1.2 – Properties of Rational Numbers 

1.3 – Representation of Rational Numbers on the Number Line

1.4 – Rational Number between Two Rational Numbers 

 

Chapter 2: Linear Equations in One Variable 

2.1 – Introduction

2.2 – Solving Equations Which have Linear Expressions on One Side and Numbers on the Other Side

2.3 – Some Applications 

2.4 – Solving Equations Having the Variables on Both Sides

2.5 – Some More Application Names

2.6 – Reducing Equations to Simpler Form

2.7 – Equations Reducible to the Linear Form

 

Chapter 3: Understanding Quadrilaterals 

3.1 – Introduction 

3.2 – Polygons

3.3 – Some of the Measures of the Exterior Angles of a Polygon

3.4 – Kinds of Quadrilaterals 

3.5 – Some Special Parallelograms 

 

Chapter 4: Practical Geometry

4.1 – Introduction 

4.2- Constructing a Quadrilateral

4.3 – Some Special Cases

 

Chapter 5: Data Handling

5.1 – Looking for Information 

5.2 – Organizing Data

5.3 – Grouping Data

5.4 – Circle Graph or Pie Chart

5.5 – Chance and Probability 

 

Chapter 6: Squares and Square Roots

6.1 – Introduction

6.2 – Properties of Square Numbers 

6.3 – Some More Interesting Numbers 

6.4 – Finding the Square of a Number

6.5 – Square Roots

6.6 – Square Roots of Decimals

6.7 – Estimating Square Root

 

Chapter 7: Cubes and Cube Roots

7.1 – Introduction

7.2 – Cubes 

7.3 – Cubes Roots

 

Chapter 8: Comparing Quantities

8.1 – Recalling Ratios and Percentages 

8.2 – Finding the Increase and Decrease Percentage

8.3 – Finding Discounts 

8.4 – Prices Related to Buying and Selling (Profit and Loss)

8.5 – Sales Tax/Value Added Tax/Goods and Services Tax

8.6 – Compound Interest

8.7 – Deducing a Formula for Compound Interest

8.8 – Rate Compounded Annually or Half Yearly (Semi-Annually)

8.9 – Applications of Compound Interest Formula

 

Chapter 9: Algebraic Expressions and Identities 

9.1 – What are Expressions?

9.2 – Terms, Factors, and Coefficients 

9.3 – Monomials, Binomials, and Polynomials 

9.4 – Like and Unlike Terms

9.5 – Addition and Subtraction of Algebraic Expressions 

9.6 – Multiplication of Algebraic Expressions: Colon

9.7 – Multiplying a Monomial by a Monomial 

9.8 – Multiplying a Monomial by a Polynomial

9.9 – Multiplying a Polynomial by a Polynomial

9.10 – What is an Identity

9.11 – Standard Identities 

9.12 – Applying Identities 

 

Chapter 10: Visualising Solid Shapes

10.1 – Introduction

10.2 – View of 3D-Shapes

10.3 – Mapping Space Around Us

10.4 – Faces, Edges, and Vertices 

 

Chapter 11: Mensuration 

11.1 – Introduction

11.2 – Let Us Recall

11.3 – Area of Trapezium

11.4 – Area of General Quadrilateral

11.5 – Area of Polygons

11.6 – Solid Shapes

11.7 – Surface Area of Cube, Cuboid, and Cylinder

11.8 – The volume of Cube, Cuboid, and Cylinder

11.9 – Volume and Capacity 

 

Chapter 12: Exponents and Powers

12.1 – Introduction 

12.2 – Powers with Negative Exponents

12.3 – Laws of Exponents

12.4 – Use of Exponents to Express Small Numbers in Standard Forms

 

Chapter 13: Direct and Inverse Proportions 

13.1 – Introduction

13.2 – Direct Proportion 

13.3 – Inverse Proportion 

 

Chapter 14: Factorization 

14.1 – Introduction 

14.2 – What is Factorization?

14.3 – Division of Algebraic Expressions 

14.4 – Division of Algebraic Expressions Continued (Polynomial/Polynomial)

14.5 – Can You Find the Error?

 

Chapter 15: Introduction to Graphs 

15.1 – Introduction 

15.2 – Linear Graphs

15.3 – Some Applications 

 

Chapter 16: Playing with Numbers 

16.1 – Introduction 

16.2 – Numbers in General Form

16.3 – Game with Numbers 

16.4 – Letters for Digits 

16.5 – Test of Divisibility 

 

NCERT Class 8  Chapter-wise Solutions in Hindi

 

अध्याय 1 – परिमेय संख्याएं

1.1 – परिमेय संख्याओं के गुणों पर प्रश्न।

1.2 – एक संख्या रेखा पर परिमेय संख्याओं को निरूपित करने वाले प्रश्न।

अध्याय 2 – एक चर में रैखिक समीकरण

2.1 – एक चर में रैखिक समीकरणों को सरल और हल करने पर प्रश्न।

2.2 – रैखिक समीकरणों के अनुप्रयोग पर प्रश्न।

2.3 – कुछ जटिल रैखिक समीकरणों को सरल बनाने से संबंधित प्रश्न।

2.4 – दैनिक जीवन में एक चर में रैखिक समीकरणों के अनुप्रयोग पर प्रश्न।

2.5 – एक समीकरण को रैखिक में कैसे परिवर्तित करें और उन्हें कैसे हल करें, इस पर प्रश्न।

2.6 – विविध प्रश्न।   

 

अध्याय 3 – चतुर्भुज को समझना

3.1 – एक बंद आकृति के आंतरिक और बाहरी भागों, बहुभुज के विकर्ण, बहुभुज के कोण योग गुण, और अवतल और उत्तल बहुभुज पर आधारित प्रश्न।

3.2 – बहुभुज के बहिष्कोणों के मापों के गुणधर्म पर प्रश्न।

3.3 – समांतर चतुर्भुज, पतंग, समलम्ब चतुर्भुज जैसे विभिन्न प्रकार के चतुर्भुजों पर प्रश्न।

3.4 – आयत, वर्ग और समचतुर्भुज जैसे विशिष्ट प्रकार के चतुर्भुजों पर प्रश्न। 

अध्याय 4 – व्यावहारिक ज्यामिति

4.1 – एक चतुर्भुज की रचना पर प्रश्न जब चार भुजाएँ और एक विकर्ण दिया गया हो।

4.2 – त्रिभुज की रचना पर प्रश्न जब तीन भुजाएँ और एक विकर्ण दिया गया हो।

4.3 – एक चतुर्भुज की रचना पर प्रश्न जब तीन कोण और दो आसन्न भुजाएँ दी गई हों।

4.4 – एक चतुर्भुज की रचना पर प्रश्न जब तीन भुजाएँ और दो कोण दिए गए हों।

4.5 – अन्य गुण ज्ञात होने पर एक चतुर्भुज की रचना पर प्रश्न। 

अध्याय 5 – डेटा हैंडलिंग

5.1 – हिस्टोग्राम पर प्रश्न।

5.2 – पाई चार्ट या वृत्त ग्राफ पर प्रश्न।

5.3 – परिणामों, घटनाओं, घटनाओं की कुल संख्या और कुल अनुकूल घटनाओं सहित संभाव्यता पर प्रश्न। 

अध्याय 6 – वर्ग और वर्गमूल

6.1 – क्रमागत योग विधि की हिट और परीक्षण विधि का उपयोग करके किसी संख्या के वर्ग की गणना करने पर प्रश्न।

6.2 – द्विपद प्रसार सूत्र द्वारा किसी संख्या के वर्ग की गणना करने या संख्या को स्वयं से गुणा करने और पाइथागोरस त्रिक से संबंधित प्रश्न।

6.3 – क्रमागत घटाव या अभाज्य गुणनखंड विधि द्वारा किसी संख्या के वर्गमूल की गणना पर प्रश्न।

6.4 – एक दशमलव संख्या के वर्गमूल की गणना के साथ-साथ अनुमान या भाग विधि द्वारा वर्गमूल की गणना पर प्रश्न।

अध्याय 7 – घन और घनमूल

7.1 – अभाज्य गुणनखंडों द्वारा किसी संख्या का घन ज्ञात करने या क्रमागत विषम संख्याओं के योग से संबंधित प्रश्न।

7.2 – अभाज्य गुणनखंड विधि द्वारा घनमूलों पर आधारित प्रश्न।

अध्याय 8 – मात्राओं की तुलना

8.1 – अनुपात और प्रतिशत पर आधारित प्रश्न और उनके व्यावहारिक अनुप्रयोग।

8.2 – प्रतिशत में वृद्धि और कमी, लाभ और हानि, छूट, वैट और बिक्री कर में प्रश्न।

8.3 – साधारण और चक्रवृद्धि ब्याज पर प्रश्न।

अध्याय 9 – बीजीय व्यंजक और सर्वसमिकाएँ

9.1 – बीजीय व्यंजकों और समान और विषम पदों को जोड़ने और घटाने पर आधारित प्रश्न।

9.2 – बीजीय व्यंजकों के गुणन पर आधारित प्रश्न।

9.3 – एक एकपदी से एक बहुपद के गुणन से संबंधित प्रश्न।

9.4 – एक बहुपद को दूसरे बहुपद से गुणा करने वाले प्रश्न।

9.5 – सर्वसमिकाओं पर आधारित प्रश्न।

अध्याय 10 – ठोस आकृतियों की कल्पना करना

10.1 – एक 3-डी वस्तु को विभिन्न दृष्टिकोणों से आलेखित करने पर प्रश्न।

10.2 – मानचित्रण रिक्त स्थान पर प्रश्न।

10.3 – किसी 3D वस्तु के कोनों, फलकों, शीर्षों और किनारों को ढूँढना।

अध्याय 11 – क्षेत्रमिति

11.1 – बुनियादी क्षेत्रमिति प्रश्न।

11.2 – चतुर्भुज जैसे चतुर्भुज के क्षेत्रों पर आधारित प्रश्न।

11.3 – एक ठोस आकृति के पृष्ठीय क्षेत्रफल की गणना करना।

11.4 – आकृतियों के आयतन की गणना पर प्रश्न।

अध्याय 12 – घातांक और शक्तियाँ

12.1 – घातांक के नियमों पर आधारित प्रश्न।

12.2 – मानक रूप या वैज्ञानिक रूप पर आधारित प्रश्न और घातांक का उपयोग करके किसी संख्या को उनमें कैसे परिवर्तित किया जाए।

अध्याय 13 – प्रत्यक्ष और व्युत्क्रमानुपाती

13.1 – प्रत्यक्ष अनुपात पर आधारित प्रश्न।

13.2 – प्रतिलोम अनुपात पर आधारित प्रश्न और ऐसे प्रश्न जिनमें प्रत्यक्ष और अप्रत्यक्ष अनुपात शामिल हों।

अध्याय 14 – गुणनखंड

14.1 – कारक बनाने के लिए पुनर्समूहीकरण शर्तों पर आधारित प्रश्न।

14.2 – एक बीजीय व्यंजक को बहुपद या एकपदी से विभाजित करने में आने वाली समस्याएँ।

14.3 – एक बहुपद को दूसरे बहुपद से भाग देने में आने वाली समस्याएँ।

14.4 – प्रश्न समीकरणों में त्रुटियों को कवर कर रहे हैं और समीकरणों और पहचानों को सही साबित करने के लिए उन्हें हटा रहे हैं।

अध्याय 15 – रेखांकन का परिचय

15.1 – रेखा आलेखों पर प्रश्न।

15.2 – x और y-अक्ष से संबंधित समस्याएं, और समन्वय प्रणाली और उन्हें एक ग्राफ पेपर पर प्लॉट करना।

15.3 – दो चरों का उपयोग करते हुए आलेख और दो चरों में रैखिक समीकरणों के अनुप्रयोग पर प्रश्न।

 

अध्याय 16 – संख्याओं के साथ खेलना

16.1 – जोड़, घटाव, गुणा और भाग पर प्रश्न और पहेलियाँ।

16.2 – किसी संख्या की 2, 3, 5, 9 और 10 से विभाज्यता का परीक्षण करना।

 

NCERT Class 8 Mathematics Solutions Chapter 1: Rational Numbers Exercise 

NCERT Class 8 Mathematics Solutions on Chapter 1: Students learn about natural and whole numbers and the properties of integers. NCERT solutions for class 8 Mathematics explain the representation of rational numbers on the number line and the role of zero and one in multiplication and addition. 

The first topic of the chapter is an introduction to rational numbers. The introduction is one constitutive section to obtain the fundamentals of the respective chapter. The first exercise deals with properties and how to use them the right way. The students learn how to represent numbers on the number line in the next topic. The third and last topic of the chapter teaches how to find a rational number between two rational numbers. 

 

NCERT Class 8 Mathematics Solutions Chapter 2: Linear Numbers in One Variable Exercise

Chapter 2 introduces the class 8 students the concept of linear equations in one variable. The solution guides the students with several methods and examples to ease the Mathematics solving process. The exercises at the end of the chapter help students assess their understanding and ability to solve more complex sums. 

In the beginning, the topic introduces the students to the linear equation and its forms. The students learn to solve equations with one and two variables. The second topic deals with methods of solving equations. The third topic explains the application of linear equations. The students learn about the application methods. The examples preferred in the solutions benefit the students. The next concept teaches to reduce equations to simpler forms, how to reduce equations, and solve the exercise questions. The students also learn how to reduce the equations to linear forms. NCERT solutions are the best material to practise the additional questions. The students can boost their overall score by securing good marks in this section. 

 

NCERT Class 8 Mathematics Solutions Chapter 3: Understanding Quadrilaterals Exercise 

NCERT Class 8 Mathematics Solution chapter 3 provide the students with a comprehensive understanding of quadrilaterals and the study of their properties. Students learn about different polygons such as hexagons, pentagons, octagons,  and so on.

The students learn about the formulas of interior angles, areas, and perimeter. The students are suggested to solve the in text and end text questions in the exercises , to develop a profound grasp of the concept.

The next topic includes the exterior angles of a polygon. The students learn about exterior angles and the sums and solve the questions. The examples help them to understand the concept clearly. Class 8 students also learn about the properties of various shapes like  parallelogram, trapezium, and also that of a kite. 

The last topic describes the special parallelograms, including squares, rectangles, and rhombus. Students learn about two and three-dimensional (3D) shapes. Practising the additional questions of every topic helps the students clear all doubts regarding each subtopic.

 

NCERT Class 8 Mathematics Solutions Chapter 4: Practical Geometry Exercise 

As the class 8 students have learned about quadrilaterals in detail, chapter 4 teaches the students: how to form quadrilaterals based on the given parameters like lengths of the sides, angles, length of diagonals, etc. The students can excel in solving complex problems with regular practice of the topics. 

The chapter ‘Practical Geometry’ comprises three exercises. The students learn about constructing quadrilaterals. Solving examples and additional questions from NCERT Solution books help the students acquire a good grasp of the chapter. The students can practice and revise the steps regularly to strengthen their ability to construct required shapes with the exact measurements given.

The last topic teaches the students how to construct different special shapes? The class 8 students learn how to draw a rhombus. Geometry is a scoring topic, and students can improve their overall results with regular practice. 

 

NCERT Class 8 Mathematics Solutions Chapter 5: Data Handling Exercise

In this Chapter, the students learn how to organize the data systematically. Class 8 students learn how to represent information or data through bar graphs, pie charts, or histograms. The chapter carries vital importance in the Mathematics syllabus of CBSE Class 8 students. 

The chapter includes five chapters, and the students need to learn all. The chapter explains how to handle and use data. They learn the methods and check the elaborate examples to understand the topic to the core. . The chapter includes concepts like why to organise group data and their advantages and disadvantages. The students must solve the exercise questions and sample papers to learn about lower-class limits, upper-class limits, and how to make a pie chart?

The students learn the uses of pie charts with the advantages and disadvantages. They can improve their score by practicing the exercise questions and examples. The last topic describes chance and probability. Students learn about probability formulas and chance and probability of events, besides learning how to represent through various graphs. Examples in NCERT Mathematics book class 8 solutions enable the students to create a strong base in data handling. 

 

NCERT Class 8 Mathematics Solutions Chapter 6: Squares and Square Roots Exercise

‘Square and Square Roots’ is one of the most crucial chapters in the class 8 Mathematics syllabus. The chapter teaches the students the concept of square and square roots and the pattern which resembles the same. When the students become familiar with the concepts they find it more exciting to solve the exercises. The chapter includes the concept and properties of Pythagorean triples. 

The chapter covers seven exercises. The students must practise them all to attain a solid grasp of the concept. It is essential to learn about square numbers and the square root properties. 

The second chapter is about how to find the square of a number. The students learn about even and odd square numbers, their properties, and square roots. NCERT Mathematics Class 8 solutions guide the students to speed up their preparation for the examination.

The next topic in Chapter 6 is how to find the square root of a number by repetitive subtraction. The students learn how to solve the Mathematics problems and practice more examples and questions associated with the topic. The chapter also teaches the students how to find the square root of a decimal. 

The last topic is about estimating a square root. The references and solutions help the students learn how to measure a square root. The topic is an important one from the examination perspective. 

The students can easily get a high score in this chapter with guided practice.  All long and short questions come from this chapter. The class 8 students need to practice the solutions to delve deep into the concept.

 

NCERT Class 8 Mathematics Solutions Chapter 7: Cubes and Cubes Roots Exercise

Chapter 7 in the CBSE Class 8 Mathematics syllabus is one continuation of the previous topic of ‘Square and Square Roots’. It introduces the students to the concepts of cubes and cube roots for the first time. Class 8 students learn about patterns and properties associated with the same as they proceed with the chapter. The students are suggested to solve and practise the exercises to get complete knowledge of the chapter.

The first topic of the chapter covers the definition of a cube and how to find perfect cube numbers. The students learn about the application of perfect cubes and practice questions associated with the concept. It is necessary to solve the questions to understand the topic in detail. 

Another significant topic is the cube root of a number. In this subtopic, the students learn about cube roots and how to find the cube root of a number. The NCERT solutions by the subject experts are of great benefit to the students to understand the topic in-depth.

Mathematics faculties recommend the students of class 8 study the cube and cube roots table. The chapter is not a big one. Six marks are allotted for the chapter in the examination, but it does not mean that the students can skip this chapter. 

Another topic includes the cube root by prime factorization method. The students learn how to find the cube root of a number. Only the formulas change. A few examples include the cube roots of 759, 512, 216, and so on. The students must practice the samples to acquire detailed knowledge about the chapter.

 

NCERT Class 8 Mathematics Solutions Chapter 8: Comparing Quantities Exercise

The chapter ‘Comparing Quantities’ is an absorbing topic for the class 8 students because they learn about percentages (%), sales, discounts, and other real-life commercial terms. We come across these words often in our everyday life. Students learn to calculate simple and compound interests, which are of daily use in our lives. The students need to practise the solutions and exercises to gain a solid grasp of the topics. Knowledge regarding these topics helps the students. to get an experiential learning of the concept.

The students find the concept to be easy to learn. It comprises nine exercises, and each one is equally significant to understanding the chapter in its entirety. The chapter holds 16 marks in the examination, and therefore the students must prepare the topics comprehensively for the exams. 

The first topic is percentages and ratios. The students learn about differences in percentages and increase and decrease in percentage. It is essential to memorise the formulas to solve the questions at ease. The topic includes how to convert the fraction into percentages, the difference between percentages and percent, etc. NCERT Mathematics book class 8 solutions explain all the topics to the students with a direct approach. 

Class 8 students study and learn the formulas on profit and loss, their percentages, discounted percentages, with rise and fall in it. The students need to practise the percentage formulas and solve the questions; using the formulae.

Another topic explains simple interest and compound interest. The students get to know about the formulas associated with the topics. Then, another topic covers the rate compounded half-yearly and annually. It is a crucial one. Practice is the only way to have a grasp over it. 

The last topic is about applications of compound interest formulas. The students learn about the advantages and disadvantages of compound interest. The students should solve questions and exercise as many as they can to be at ease with the concept and solve the Mathematics problems effortlessly. 

 

NCERT Class 8 Mathematics Solutions Chapter 9: Algebraic Expressions and Identities Exercise 

Class 8 is one of the initial academic years when the students are introduced to the basics of Algebra. Students become familiar with the terms related to Algebraic Expressions and Identities. The chapter explains the topics such as factors, monomials, binomials, polynomials, coefficients, and so on. Students learn how to solve Mathematics  problems based on these formulas. The students can acquire a solid grasp of the chapter through  regular practice of the exercises and solutions.

The chapter comprises twelve exercises. The first topic of the chapter is Algebraic expressions. In this chapter, the students learn about different kinds of Algebraic expressions and their formulas. The students must solve the NCERT solutions to understand the topic extensively. Some of the most significant expressions include monomial, binomial, polynomial, and variable expressions. CBSE Class 8 students have to read all the expressions and the examples before solving the exercise questions.

The next topic is about factors, coefficients, and terms. The formulas and solved examples play a crucial role in the students’ learning process. The chapter includes the addition and subtraction of algebraic expressions. The 6th topic is about the multiplication of algebraic expressions. The students learn how to multiply algebraic expressions, the formulas, and the terms used in the chapter.

The chapter continues to teach the students how to multiply monomial with a monomial and monomial by a polynomial. Exercise 11 explains the standard identities, which are about the conditions for the standard equation. The students learn about every kind of standard identity in this chapter. 

The last topic describes how to apply identities. The students learn the formulas and methods to solve the exercises and practice the questions.  The chapter needs some more attention, as it is a lengthy one.

 

NCERT Class 8 Mathematics Solutions Chapter 10: Visualizing Solid Shapes Exercise 

Chapter 10 intrigues the class 8 students with its concept. The students are introduced to 3D Geometry. They learn how to visualize solid shapes in different dimensions. The chapter includes the topics like edges, faces, and vertices and teaches the students to create a solid 3D shape. The students learn Euler’s formula. The chapter needs the undivided attention of the students. The students can gather a comprehensive understanding of the topic, by solving the exercise questions.

The topic comprises four exercises. The concept is a new one, but the concept is easy to learn. The first topic is about mapping the space around us. The students learn how to space maps and their uses. Another crucial topic is about faces, edges, and vertices of 3-Dimensional shapes. The students also get to learn about types of polyhedrons. The chapter is not too long and easy to score from the examination point of view.

 

NCERT Class 8 Mathematics Solutions Chapter 11: Mensuration Exercise 

The chapter intends to develop the students’ ideas of quadrilaterals and triangles. It is about measuring the area of these figures. The students also get to learn to calculate the area and volumes of cubes and cuboidal structures with the use of various formulas. The students need to solve the in-text and end text questions to have a clear understanding of the topic.

The chapter has nine exercises, and 15 marks in the examination. The students learn about the area of a trapezium and its properties.

Class 8 students learn the formulas of the area and perimeter of the trapezium and practise the questions associated with it. Another vital topic is the derivation of the area of a trapezium and its applications of a trapezium. The students must practise the derivation exercises in detail as the topic is most likely to come in long answer questions. NCERT Mathematics book class 8 solutions help the students by offering them explanations and elaborate examples.

The next topic covers the area of a quadrilateral and the properties of quadrilaterals. The students need to learn and memorise the formulas to solve the questions at ease. Topic 5 is about the area of a polygon which teaches about the area of a polygon and its formula. 

Another topic includes the surface area of a cube, cuboid, and cylinder and how to find them. The students learn how to find the length of the edge of a cube. Regular practice is the most effective tool to remember formulas and apply them rightly while solving problems. . The chapter presents the formulas of the cube, cuboid, and cylinder to the students. NCERT Mathematics book class 8 solutions are of great help to the students to understand the topics in-depth.

The last topic of Chapter 11 talks about volume and capacity. The students learn the definition of volume,  capacity,  their differences, and formulas. The subtopics need profound attention from the students to understand the answers. 

 

NCERT Class 8 Mathematics Solutions Chapter 12: Exponents and Powers Exercise 

The chapter introduces the students to the concepts of power and exponents. Representation of numbers in standard form using exponents and comparisons is one intricate section of the chapter. The students need to solve the exercises to understand the concept with clarity. The chapter consists of four exercises. It teaches the students about exponents VS power and integers with positive and negative exponents. The students solve the examples associated with every topic and practise the questions.

The class 8 students also get to learn the integer exponent rules. The chapter is easy to learn. The students can understand the topics easily with little attention and dedication. Another topic is the laws of exponents. The students learn about the rules of the exponents and practise the examples to be familiar with the topic. It is essential to learn about the product and quotient with a similar base and solve the questions associated with each. Two other significant topics are the product to power and quotient to power.

The last and the final topic of the chapter is negative and fractional exponent rules. The students are advised to solve the exercise questions and practise the examples. The students learn about zero power. Another topic in the chapter discusses the use of exponents to express the small number in standard form. The students need to remember all the formulas and methods to solve the questions at ease.

 

NCERT Class 8 Mathematics Solutions Chapter 13: Direct and Inverse Proportions Exercise

Chapter 13 explains that two involved quantities can decrease or increase in a way that the corresponding values remain the same, and the opposite happens in inverse proportion. The students need to solve the exercise questions regularly for vivid memorization.

The chapter covers two exercises. The first exercise teaches about direct proportions. The students know what direct proportions are and the symbols, formulas and, constants of proportionality. The second topic is inverse variation. It teaches the students about the inverse variation, its equations and formulas. The students must solve the exercise questions to acquire a good grasp of the concept. NCERT solutions help the students with detailed explanations of the topics and exercise questions. 

 

NCERT Class 8 Mathematics Solutions Chapter 14: Factorization Exercise 

The chapter deals with the factorization of natural numbers and algebraic expressions. Class 8 students learn how to factorize using factorization identities, regrouping terms, etc. The chapter also teaches how to divide a polynomial or a monomial by a monomial. The students must practise the exercise questions from the factorization.

Chapter 14 carries a significant role in the class 8 Mathematics syllabus. It carries 12 marks. The students need to read and study the chapter thoroughly to understand the basics. The chapter consists of five exercises. The students learn how to factorize using common factors and practise the questions associated with the topic. 

The next topic deals with polynomial division and the algorithm of long division. It is a crucial one. For this reason, the students need to practise the examples and study the solved examples minutely. The students learn about the types of a polynomial division and the division of a polynomial by a polynomial. The last topic teaches how to find the error. The students can take the assistance of Class 8 Mathematics NCERT Solutions to understand the concepts better.

 

NCERT Class 8 Mathematics Solutions Chapter 15: Introduction to Graphs Exercise 

Class 8 syllabus has already introduced the concept of data handling to the students. In ‘Introduction to Graphs’, the students learn how to represent data in different types of graphs like histograms, pie charts, linear graphs, etc. The chapter teaches the students: how to locate points and sync them on the graph? 

The students can practise exercise questions and exercise to have a clear idea about the concept. Chapter 15 comprises three exercises. The chapter teaches the students about line graphs, types of line graphs, straight-line graphs, vertical line graphs, and double line graphs. The students learn the concepts through the intext and end text exercise for a better understanding. 

Another topic is line graphs, where the students learn about linear graph equations and solve the exercise questions. NCERT Mathematics book class 8 solutions enable the students to understand and absorb the topic better.

The last topic is the application of linear graphs. The students learn about the applications of linear graphs and solve the questions associated with it.

 

NCERT Class 8 Mathematics Solutions Chapter 16: Playing with Numbers Exercise 

The last chapter is the gist of all the topics allotted in the CBSE Class 8 Mathematics syllabus. The most crucial concepts have been discussed in the chapter in minute detail. It includes five exercises. The students need to use the methods and formulas to justify the tests of divisibility. 

The first topic teaches the students about numbers in a general form. The students learn how to represent numbers in general form and solve the exercise questions.

The second topic is numbers. The students learn the rules to solve puzzles and the exercise and understand the topic better. The last topic is the test of divisibility. The students learn all the divisibility rules. Solving questions is the best way to have a good grasp of the concept. The students can bank on the NCERT Solutions for thorough and complete preparation. 

 

CBSE Class 8 Mathematics Unit-Wise Marks Weightage 

Unit No Chapter Name Marks Weightage
Unit 1 Rational Number 8
Unit 2 Linear Equations in One Variable 10
Unit 3 Understanding Quadrilaterals 13
Unit 4 Practical Geometry 08
Unit 5 Data Handling 11
Unit 6 Squares and Square Roots 12
Unit 7 Cubes and Cube Roots 06
Unit 8 Comparing Quantities 16
Unit 9 Algebraic Expressions and Identities 12
Unit 10 Visualizing Solid Shapes 07
Unit 11 Mensuration 15
Unit 12 Exponents and Powers 06
Unit 13 Direct and Inverse Proportions 08
           

Unit 14

     

Factorisation

12
Unit 15 Introduction to Graphs 12
Unit 16 Playing with Numbers 10

 

Benefits of NCERT Solutions for Class 8 Mathematics by Extramarks

NCERT solutions are the most effective study materials for class 8 students. Subject-matter experts have compiled and drafted the materials to impart detailed knowledge about Mathematics to the students. They are provided with step-wise solutions for each chapter to make the students familiar with all the concepts  given  in the syllabus. The students are encouraged to solve more Mathematical questions with great confidence and ease. The solutions provided in the NCERT books are reliable and accurate.  The students are guided the right way, and are able to score good marks in the examination. 

The Class 8 students can enjoy several benefits of the NCERT Mathematics book class 8 Solutions in their learning process. The materials are accessible through any smart device that can connect to the internet. Extramarks believes in an open education system where the students can download the Solutions online and study them later, at their convenience. The answers are available on the website for free. 

In a nutshell  , the benefits include,

  • Expert Mathematics faculty with years of experience and knowledge have created the Solutions.
  • Solutions are both descriptive yet concise. .
  • The NCERT solutions strictly follow the CBSE guidelines.
  • The Solutions help the students practise the exercises and solve the questions.
  • It guides the students to make a solid preparation for the examination.
  • The solutions help the students learn about the mark weightage of every chapter and how to write on-point answers for each question.
  • The solutions allow the students to study the subject within the time frame.
  • The students can complete the syllabus on time with NCERT Solutions.

 

What are the Key Features of Extramarks Class 8 Mathematics NCERT Solutions?

The key features of Extramarks’ Class 8 Mathematics NCERT Solutions are:

  • Subject-matter experts have prepared the solutions.
  • The solutions are well-structured and self-explanatory.
  • Students can study  at their convenience, download specific chapter wise  topics  and prepare the important questions for the examination.
  • Students can revise  regularly before the exam.
  • The solutions are available on the site for free.
  • It helps the students get  a clear idea about the topics and concepts.
  • The students can  check improvement in their performance with constant revision and practice.
  • They can  devote more time on  difficult  and complex topics.

Conclusion:  One Solution for all problems

For the class 8 students who appear for the Mathematics examination, the NCERT solutions are very helpful. The solutions help the students to attain a solid grasp of Mathematics and perform well in the examination; irrespective of whether it is a class test or a final exam. NCERT Mathematics solutions are the best resources the students can avail. 

FAQs (Frequently Asked Questions)
1. Where can I find the NCERT Mathematics solutions for class 8 students?

You will find the NCERT Mathematics Solutions for class 8 students at Extramarks.

2. Does NCERT Solutions cover the entire syllabus of Class 8 mathematics?

Certainly! It has all the chapters from 1 to 16 along with intext and end text solutions.

3. How much does it cost to download the NCERT Solutions?

It doesn’t cost a penny. Most of the  NCERT solutions are absolutely free.

4. Do the NCERT Mathematics solutions provide the students with the distribution of marks?

Definitely! The marks distribution of each unit provided in the Solutions help you to prioritise important topics and  also gives you an idea about the time  you need to devote in each section.

5. How to prepare well before the Mathematics exam?

The best way to begin your preparation is at the time when you start the new academic session. You must do your homework, attend your online or offline classes, take tests and make sure your mentor is good. However, self-study with guided practise provided by NCERT Solutions will save the day.