NCERT Solutions for Class 8 Maths

The knowledge of basic math is crucial for everyone. Therefore, it is being taught to the students from the early academic days. So that their base becomes strong in this subject. However, while learning maths students face many challenges to solve some problems given in their textbooks. That is why NCERT Solutions for Class 8 Maths are being prepared by the subject matter experts. In class 8 Mathematics Textbooks there are a total of 16 chapters, and a thorough understanding of all those chapters is important. 

It is up to the candidates to choose their  NCERT Solutions For Class 8 Maths in Hindi Medium or English medium. The end goal of NCERT Solutions for class 8 maths PDF is to enable students to understand the topics and their questions properly.

Therefore, we are providing the NCERT Solutions For Class 8 Maths PDF 2021-2022 that is based on the latest syllabus of CBSE. It is prepared by subject matter experts by following the guidelines of CBSE Board.

NCERT Solutions for Class 8 Maths Chapter Wise

Class 8 Maths Solutions consists of a total of 16 chapters and each chapter has its own individual exercises. So, NCERT Solutions for Class 8 Maths Chapter Wise can be used as a reference while solving the problems from the NCERT Mathematics Textbooks. These Maths Textbook solutions are very beneficial for the students. They can use it to clear their doubts in the subjects and solve all the chapter’s exercises for free of cost. 

Download NCERT Solutions Class 8 Maths PDF from the links given here on this website for free. The  NCERT Solutions for Class 8 Maths in Hindi Medium PDF isn't available here at this moment. However, we will try to provide them on this site very soon.

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 Squares and Square Roots
Chapter 7 Cubes 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

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

In Class 8 Maths Solutions Chapter 1 Rational Numbers, students will be learning properties related to real numbers, integers, whole numbers, rational numbers and natural numbers, etc. This chapter explains to the learners how rational numbers can be identified and expressed in simple form and on the line. There are a total of 2 exercises in this chapter that assist the students to learn the basics of various types of numbers along with how to represent them. In addition to the topics of additive identity and multiplicative identity are also covered in this chapter. 

NCERT Solutions Class 8 Maths Chapter 1 Rational Numbers Exercises

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

Class 8 Maths Solutions Chapter 2 Linear Equations in One Variable contains a total of 6 exercises and 65 questions. With this many questions, this chapter helps students to get a deep understanding of the given chapter. This chapter includes questions based on the application of linear equations, some tricky linear equations, application on a day-to-day life based on linear equations in one variable concept, etc. Using the NCERT Solutions For Class 8 Maths for chapter 2 enables you to boost your knowledge in these topics.

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

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals includes topics on various types of polygons such as a triangle, quadrilateral, pentagon, hexagon, heptagon, etc. Also, briefs about the interior and exterior parts of a closed figure, diagonals of a polygon, convex and concave polygons, and angle sum property of a polygon. The given 4 exercises helps students to understand this chapter precisely. To understand the quadrilaterals properly students are required to practice all the given exercises.

NCERT Solutions For Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercises

NCERT Solutions For Class 8 Maths Chapter 4 Practical Geometry

How to construct a unique quadrilateral under the given measurements, It has been explained In Chapter 4 Practical Geometry. It has a total of 5 exercises in which students are given different measurements of different sides. Along with that, a few questions are given that can be solved by having knowledge of special properties. To get an in-depth understanding of this chapter and its questions students are required to solve all the given examples and practice all questions with the help of solutions.

NCERT Solutions Class 8 Maths Chapter 4 Practical Geometry Exercises

NCERT Solutions For Class 8 Maths Chapter 5 Data Handling

Organizing the data in a systematic method is known as Data Handling and class 5 maths chapter 5 is all about the data and their representation. In this chapter, students learn to represent these data with the help of a pictograph, a bar graph, a double bar graph, a pie chart and a histogram. In this chapter, students are also briefed about the concept of probability. With the help of 3 exercises, students can understand the given chapter easily.

NCERT Solutions Class 8 Maths Chapter 5 Data Handling Exercises

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

Chapter 6 Squares and Square Roots, helps students to learn about the concept of square numbers and the square root of a number. The chapter explains the properties of square numbers, interesting patterns Wise 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, etc. All these topics have been distributed between 4 exercises and by practising the given exercises students can get a deep understanding of this chapter.

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

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

NCERT Solutions Class 8 Maths Chapter 7 Cube and Cube Roots assist students to learn about various methods to find out the cubes and cube roots of a number. With a total number of 2 exercises, this chapter gives students a brief summary of this chapter and helps them to at least get a good grasp over the basics of Cube and Cube roots.

NCERT Solutions For Class 8 Maths Chapter 7 Cube and Cube Roots Exercises

NCERT Class 8 Maths Chapter 8 Comparing Quantities

This chapter aids students to learn How to find discounts, Estimation in percentages, Profit and Loss, Finding cost price and selling price, Compound Interest, etc. There are questions based on Ratio and proportion too. This chapter mostly covers topics that have real-life applications. Students also get to learn about the simple interest, compound interest calculated half-yearly, quarterly, monthly or yearly, etc. With the availability of 3 exercises, it helps the learners to learn the topics and concepts of Comparing Quantities very easily.

NCERT Solutions Class 8 Maths Chapter 8 Comparing Quantities Exercises

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

Chapter 9 Algebraic Expressions and Identities of class 8 maths help students to learn how to add or subtract the algebraic expression. Along with that it guides students to learn concepts of algebraic expression with terms, factors and coefficients of Monomial, Binomial and Trinomials. All the topics given in this chapter have been concluded in a total of 5 exercises. A rigorous practice of all those exercises and questions is imperative.

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

NCERT Class 8 Maths Chapter 10 Visualizing Solid Shapes

The Class 8 Maths Chapter 10 Visualizing Solid Shapes is one of the most interesting chapters that help students to learn about viewing 3-D shapes, Mapping the space around us along with faces, edges, and vertices. This chapter also assists the learners to learn about Euler’s Formula. There are a total of 3 exercises that give students a brief on these given topics. With the help of NCERT Solutions For Class 8 Maths, all these 3 exercises can be solved with ease.

NCERT Solutions Class 8 Maths Chapter 10 Visualizing Solid Shapes Exercises

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration

The topics of Mensurations are being taught to the students from early classes. However, in this class, the concepts of mensuration are taken a little forward where a bunch of topics are given to the students to practice and get a good grasp on. There are a total of 4 exercises in Chapter 11 Mensuration where students learn about the surface area and volume of different solid shapes such as a cube, cuboid and cylinder, etc. 

NCERT Solutions Class 8 Maths Chapter 11 Mensuration Exercises

NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

NCERT Class 8 Maths Chapter 12 Exponents and Powers Solutions assist students to learn about the negative and positive powers, laws of exponents, use of exponents to express the numbers in standard form, etc. These topics have been explained in this chapter throughout the 2 exercises.

NCERT Solutions Class 8 Maths Chapter 12 Exponents and Powers Exercises

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

Direct and Inverse Proportions chapter 13 enable the learners to practice the questions based on quantities that may have several conditions. Students are required to identify those conditions and then solve the questions. For instance in order to solve the questions on the given topics students need to check whether quantities are increasing or one is increasing and other is decreasing, if both are increasing, etc. Chapter 13 Direct and Inverse Proportions contains a total of 2 exercises.

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

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation

A total of 4 exercises of Class 8 Maths Chapter 14 Factorisation help students to learn to perform Factorization. It includes the factors of natural numbers and algebraic expressions, factorization by regrouping terms, factorization using identities, etc. Practising the questions given in these 4 exercises gives students the ability to divide the algebraic expression by monomial or polynomial too. It is a very important chapter for the higher classes. 

NCERT Solutions Class 8 Maths Chapter 14 Factorisation Exercises

NCERT Solutions For Class 8 Maths Chapter 15 Introduction to Graphs

Introduction to graphs help students to learn how to represent numerical data in visual form so that data can be easily understood by the viewers. Data can be shown in different ways so this chapter helps students to know different types of graphs including bar graphs, pie graphs, line graphs and linear graphs. This chapter consists of a total of 3 exercises, the questions given in these exercises guide them to be conscious and practice the questions hassle-free.

NCERT Solutions Class 8 Maths Chapter 15 Introduction to Graphs Exercises

NCERT Solutions For Class 8 Maths Chapter 16 Playing with Numbers

Playing with Numbers is an enjoyable chapter, it contains questions in the form of puzzles. In order to solve the given exercises of this chapter students are required to have a deep understanding of various types of numbers such as natural numbers, whole numbers, integers and rational numbers and the properties of numbers. Although students have already learnt these things in previous chapters and classes, it will be fun to solve the given exercises of Class 8 Maths Chapter 16 Playing with Numbers.

NCERT Solutions Class 8 Maths Chapter 16 Playing with Numbers Exercises

Chapter Wise Study Tips For Class 8 Maths

There are 16 chapters in NCERT Class 8 Maths and all of them are extremely important to cover as it builds the basics of mathematics. 

However, there are variations in difficulty levels so, here are some of the study tips for each chapter as well as the lessons and its topics are explained here.

Rational Numbers (Chapter 1)

The very first lesson of NCERT Class 8 Mathematics is Rational Numbers. There are 2 exercises and some extra questions that help the learners to practice an ample number of questions. 

This lesson is broken down in 4 different sections:

1.1 Introduction:-The section 1.1 is dedicated to give students a brief of this topic and what they are going to study further in this lesson. By recalling the simple equations, the natural numbers, Whole numbers, integers, (positive and negative), and rational numbers have been defined in this section.

1.2 Properties Of Rational Numbers:- After the introduction of rational numbers and relevant terms, the section 1.2 is focused on helping students to understand the Properties Of Rational Numbers. The properties has been distributed into 8 subsections: (1.2.1) Closure, (1.2.2) Commutativity, (1.2.3) Associativity, (1.2.4) The role of zero (0), (1.2.5 ) The role of 1, (1.2.6) Negative of a number, (1.2.7) Reciprocal, (1.2.8) Distributivity of multiplication over addition for rational numbers.

1.3 Representation Of Rational Numbers On The Number Line:- In the previous standard, students are already taught how to represent natural numbers, whole numbers, integers and rational numbers. Here, this topic has been extended further. Based on the examples and topics explanations the NCERT Class Maths Books have asked some questions to try: 

 

1.4 Rational Numbers Between Two Rational Numbers:- This section is trying to explain how many Rational Numbers we can write Between Two Rational Numbers. By giving some examples of writing between numbers of integers and natural numbers, this section has explained: we can write definite numbers between Natural numbers or integers. However, this doesn’t apply to rational numbers as we can’t find definite numbers Between Two Rational Numbers.

Rational Numbers Chapter 1 Exercises 

➤ Exercise 1.1 – 11 Questions (11 Short Answers)

➤ Exercise 1.2 – 7 Questions (7 Short Answers)

Important Formula of Class 8 Rational Numbers

1. The additive inverse of the rational number and Vice-versa.

2. The reciprocal or multiplicative inverse of the rational number 

Study Tips for Class 8 Rational Numbers

Before studying this chapter, first of all recall the definitions of Simple equations, Whole Numbers, Rational Numbers, Integers, and some arithmetic properties.

After doing the above things, you are ready to study this lesson to score high marks. As you have recalled the topics before giving this lesson a start, you will enjoy studying rational numbers and its related topics.

Linear Equations in One Variable (Chapter 2)

With a total of 65 questions, the chapter 2 Linear Equations in One Variable has explained various conditions for the algebraic expression having only one variable.

The lesson 2 has been distributed among 7 sections: 

2.1 Introduction:- The introduction part of this chapter helps students to recall the basic knowledge of Linear Equations they have studied in earlier classes. Also, some sneak peak of what they are going to learn in this lesson.

2.2 Solving Equations Which Have Linear Expressions On One Side And Numbers On The Other Side:- With the help of some suitable examples, the section 2.2 helps students to learn how to solve an equation which has linear expressions On One Side And Numbers On The Other Side.

2.3 Some Applications:- After elaborating the techniques to solve Linear Equations when One Variable Linear Expressions On One Side And Numbers On The Other Side the section 2.2 allow students to solve some word problems based on the method described.

2.4 Solving Equations Having The Variable On Both Sides:- What if the Variable is on Both Sides? For such cases, section 2.4 has elaborated the methods to solve questions based on this condition.

2.5 Some More Applications:- Furthermore, some more questions are given in section 2.5 to ensure students have grasped the techniques properly.

2.6 Reducing Equations To Simpler Form:- Generally, the majority of quotations are in complex form so, the 2.6 section has explained how to reduce an equation into simpler form.

2.7 Equations Reducible To The Linear Form:- With the help of two solid examples, section 2.7 has explained to students how to reduce an equation into linear form.

Linear Equations in One Variable Chapter 2 Exercises

➤ Exercise 2.1 – 12 Questions (12 Short Answers)

➤ Exercise 2.2 – 16 Questions (6 Long Answers, 10 Short Answers)

➤ Exercise 2.3 – 10 Questions (3 Long Answers, 7 Short Answers)

➤ Exercise 2.4 – 10 Questions (4 Long Answers, 6 Short Answers)

➤ Exercise 2.5 – 10 Questions (1 Long Answer, 9 Short Answers)

➤ Exercise 2.6 – 7 Questions (1 Long Answer, 6 Short Answers)

Study Tips for Class 8 Linear Equations in One Variable

To comprehend this topic, stick to the basics of equations. Go through each section given in NCERT Class 8 Maths Book chapter 2 and try to solve their examples to clear the confusion.

Also, you can use the NCERT Solutions for Class 8 Maths Chapter 2 to practice several questions while clearing all the doubts.

Understanding Quadrilaterals (Chapter 3)

Quadrilateral is a four sided figure where the figure will have four sides and four edges. Chapter 3 of Class 8 Maths contains 5 sections to help students to understand quadrilaterals and its types. Mainly polygons and their types have been covered in this lesson. A total of 4 exercises and 31 questions are asked to ensure a learner has gained the complete knowledge of this topic.

3.1 Introduction:- In this section, the plane surface, plane curve and about its type has been explained along with the images. 

3.2 Polygons:- The section 3.2 begins with the definition of Polygons: A closed figure made up with only line segments. Further in this section, Classification of Polygons, about Diagonals, Convex and concave polygons, Regular and irregular polygons, Angle sum property have been covered.

3.3 Sum Of The Measures Of The Exterior Angles Of A Polygon:- The centre focus of this section is Sum Of The Measures Of The Exterior Angles Of A Polygon since, the knowledge of exterior angles may impact the nature of interior angles and sides.

3.4 Kinds Of Quadrilaterals:- There are a variety of Quadrilaterals based on their sides or angles. So, the various kinds of Quadrilaterals have been covered in this part. A few of the names of its kinds are - Trapezium, Kite, Parallelogram. Also, Elements of a parallelogram, Angles of a parallelogram, Diagonals of a parallelogram have been covered.

3.5 Some Special Parallelograms:- Rhombus, A rectangle, A square has been considered special Parallelograms. So, in section 3.5, this has been elaborated with the proper example and images. Their properties have been also covered to assist students to understand the special cases of Parallelograms.

Understanding Quadrilaterals Chapter 3 Exercises

➤ Exercise 3.1 – 7 Questions (1 Long Answer, 6 Short Answers)

➤ Exercise 3.2 – 6 Questions (6 Short Answers)

➤ Exercise 3.3 – 12 Questions (6 Long Answers, 6 Short Answers)

➤ Exercise 3.4 – 6 Questions (1 Long Answer, 5 Short Answers)

Study Tips for Class 8 Understanding Quadrilaterals

It is advised to focus on the basic definition of the quadrilaterals and its different types. Solve lots of example questions and revise the term regularly. 

Sum Of The Measures Of The Exterior Angles Of A Polygon can be sometimes tricky so make sure you pay close attention to this topic and practice a lot of questions.

Practical Geometry (Chapter 4)

The chapter 4 of NCERT Class 8 Maths focuses on the geometry portions such as drawing a triangle and quadrilateral.

This chapter deals with various interesting constructions based on different criteria. The entire lesson 4 has been distributed among 3 sections:-

4.1 Introduction:- In the intro section of the chapter practical geometry is trying to give a brief on how the past study of constructing a triangle will be useful here.

By recalling the measure requirements to draw a triangle, the intro section asks a question whether we can use four measurements to draw a unique closed figure: Quadrilateral.

4.2 Constructing A Quadrilateral:- In order to construct a quadrilateral, there are several criteria and this section has covered all those criteria and conditions. The section 4.2 has been divided into 4 sub sections: (4.2.1) When the lengths of four sides and a diagonal are given, (4.2.2) When two diagonals and three sides are given, (4.2.3) When two adjacent sides and three angles are known, (4.2.4) When three sides and two included angles are given.

4.3 Some Special Cases:- The special cases deal with the possibilities to draw a quadrilateral, if we have only one measurement given or less number of measurements given compared to we have used earlier to construct a quadrilateral.

Practical Geometry Chapter 4 Exercises

➤Exercise 4.1 – 1 Question (1 Long Answer)

➤Exercise 4.2 – 1 Question (1 Long Answer)

➤Exercise 4.3 – 1 Question (1 Long Answer)

➤Exercise 4.4 – 1 Question (1 Long Answer)

➤Exercise 4.5 – 4 Questions (4 Long Answers)

Study Tips for Class 8 Practical Geometry

Questions in this type of chapter are word problems that contain the measurements too. So, the key is to grab the key points a question is trying to convey.

Read the question carefully, if not understandable at once, read them time and again unless you get what the question is trying to ask. 

Once you understand the question, your basic knowledge of constructions will be enough to answer the question.

Data Handling (Chapter 5)

When we collect the information for the analysis purpose we call it data. Data is collected in a systematic manner so that the analysis process could be seamless. 

The process of collecting data in a systematic manner is called data handling.

This topic has a broad area but, here in this chapter students will get a chance to study the basics and fundamentals of data handling. 

The terms such as raw data, frequency, pie chart, histogram, etc. have been covered. 

There are 3 exercises containing 16 questions which provide students with enough questions to practice. 

The topic Data handling has been elaborated in the following sections:-

5.1 Looking For Information:- This section is dedicated to teach students how they can collect data, and where they can do this for which purpose. As well as how we can represent the data using various methods are also mentioned such as:- A Pictograph, A bar graph, Double bar graph.

5.2 Organising Data:- In general the data we see or collect are in the raw form, in other word they are unorganised. So, section 5.2 is with the purpose of helping students to learn how to organise the collected data.

Tally Marks have been used in this section to teach students how to organise data. Also, the term: frequency has been explained here.

5.3 Grouping Data:- We can surely organise and represent the data in various organising or representing methods however, these methods are ideal for less number of data. But for the large amount of data, we have to group them to make it short and precise. Also, grouping data is quite a convenient way to make groups of observations.

5.4 Circle Graph Or Pie Chart:- By introducing the circle graph or pie chart, this section helps students to identify how a circle graph looks like.

 

A circle graph has a quality that is it represents the relationship between a whole and its parts. This kind of chart is also called a pie chart.

With some real life examples, this section helps students to draw a pie chart.

5.5 Chance And Probability:- This section contains the topic that is a beginning part of topic probability. However, here in this section a learner will be able to grasp the concepts of random experiment and outcomes. Also, based on the data how likely an event can occur.

A formula for probability of an event is:

 

Data Handling Chapter 5 Exercises

➤ Exercise 5.1 – 5 Questions (5 Short Answers)

➤ Exercise 5.2 – 5 Questions (3 Long Answers, 2 Short Answers)

➤ Exercise 5.3 – 6 Questions (2 Long Answers, 4 Short Answers)

Study Tips for Class 8 Data Handling

This lesson is quite interesting as well as simple to comprehend. You no need to worry about this, as you begin solving some examples and exercises, you will be able to grasp the concepts much easier.

Squares and Square Roots (Chapter 6)

As per the definition of Square: When numbers can be expressed as the product of the number with itself, it is called square. For example:- 8 × 8 = 64 = 82

So, chapter 6 is very helpful to learn about the squares and square roots. Referring to the NCERT Class 8 Mathematics book, students will be able to learn the definition, its types, methods of finding or solving the square and square roots.

The whole chapter 6 has been distributed into 5 sections:-

6.1 Introduction:- By giving the intro of this chapter, the section 6.1 deals with the definition of square numbers as well as an intro of what perfect squares are.

6.2 Properties Of Square Numbers:- What are the properties of square numbers? Not sure? With suitable examples, section 6.2 has helped students to understand the properties of square numbers. For instance: if a number has 1 or 9 in the unit’s place, then it’s square ends in 1.

6.3 Some More Interesting Patterns:- The section 6.3 is really interesting because there are various interesting patterns has been explained such as; pattern between two consecutive square numbers, Adding odd numbers, Adding triangular numbers, A sum of consecutive natural numbers, Product of two consecutive even or odd natural numbers, Some more patterns in square numbers.

6.4 Finding The Square Of A Number:- After covering the fundamentals of square number, this section deals with finding the square number. Various terms such as Other patterns in squares, Pythagorean triplets have been covered with suitable examples.

6.5 Square Roots:- Square root is known as the process of finding the number when the square of a number is known. For example: Area of a square is 144 cm2. In this section, the students will be able to grasp the various methods to find the square roots such as:- Finding square root through repeated subtraction, through prime factorisation, through division method.

Squares and Square Roots Chapter 6 Exercises

➤ Exercise 6.1 – 9 Questions (9 Short Answers)

➤ Exercise 6.2 – 2 Questions (2 Short Answers)

➤ Exercise 6.3 – 10 Questions (3 Long Answers, 7 Short Answers)

➤ Exercise 6.4 – 9 Questions (3 Long Answers, 6 Short Answers)

Study Tips for Class 8 Squares and Square Roots

The Squares and Square Roots are extremely important topics to cover as it plays an important role in further classes. Due to several properties, you may feel stuck, so make sure you go through them one by one. 

Understand one property at a time, solve an ample amount of questions on one property and then get forward in the chapter. 

Also, sometimes, it’s tricky to solve a question of square and square roots so, understand all the methods of finding the Squares and Square Roots.

Cubes and Cube Roots (Chapter 7)

The Cubes and Cube Roots are an extended version of Square and Square roots. Hence, prior knowledge of Squares and Square roots are important for this chapter to begin. 

However, this chapter covers the topic from the very basics: Definitions, property, and methods to solve the questions based on the cube and cube roots.

There are only 2 exercises and 7 questions in this lesson that help students to develop a good command on cube and cube roots.

7.1 Introduction:- Intro part of this chapter tells a story on how one of India’s great mathematical geniuses, S. Ramanujan pointed out something interesting in the number 1729. Furthermore, this section gives students a brief of what they can expect from this lesson.

7.2 Cubes:- Cube is a part of geometry which has solid figures and all sides equal. By giving an overview of the cube and how it looks and what its properties are, this chapter explains students' about perfect cubes or cube numbers. In addition to that, the section deals with Some interesting patterns where consecutive odd numbers are added, factorisation of the numbers and their cubes are done.

7.3 Cube Roots:- By taking an example of how finding the square root is the inverse operation of squaring, the same applies with cube roots: It is the inverse operation of the cube. 

The cube root has its symbol and it is denoted as: 

Apart from this, the section has two main methods to consider focusing on: Finding Cube root through prime factorisation method and Cube root of a cube number

Cubes and Cube Roots Chapter 7 Exercises

➤ Exercise 7.1 – 4 Questions (4 Short Answers)

➤ Exercise 7.2 – 3 Questions (2 Long Answers,1 Short Answer)

Study Tips for Class 8 Cubes and Cube Roots

Similarly to the Squares and Square roots, the cube and cube roots are important to understand as there are lots of questions in which these terms are used.

Hence, the study tips for this chapter is to practice lots of questions from the prescribed NCERT Book as well as from the reference textbooks. 

NCERT Class 8 Maths Exemplar Book can be a great study resource for solving advanced level maths questions.

Comparing Quantities (Chapter 8)

With three exercises and 28 questions, the chapter 8 comparing quantities helps students to learn the most important and daily life used topics: Ratios and Percentages, Finding the Increase or Decrease Per cent, market value, sales value, discount etc.

Since it is a bit of a huge topic, it has been divided into 9 parts. Each part covers one important topic. For example:- 

8.1 Recalling Ratios And Percentages:- Since, this is the very first section, it helps students to recall what they have studied so far about comparing quantities.

This section’s main focus is to present some examples and enable the students to revise the topics ratios and percentages.

8.2 Finding The Increase Or Decrease percent:- Section 8.2 contains one question related to the price of a scooter where the solver has to find the increased price of a scooter after one year. As per this example, Finding The Increase Or Decrease percent is an important thing to learn. So, it is vital to have a thorough knowledge of this section.

8.3 Finding Discounts:- Discount price has been introduced here, as per the formula of Discount = Marked price – Sale price. Meaning if a product has mentioned some amount of money but the shopkeeper gives that product on reduced price then, it will be known as Discount. It is also an ideal topic to learn properly as it is being used by all of us on a regular basis.

8.4 Prices Related To Buying And Selling (profit And Loss):- Overhead charges are an additional amount when one has to pay for a product. The overhead charges can be due to repairing expenses, labour charges, transportation etc. In that case a buyer will have a loss as they have to pay more price for the product. Thus, in this section, Finding cost price/selling price, profit %/loss% are covered in detail with suitable examples.

8.5 Sales Tax/Value Added Tax:- The concept of Sales Tax and VAT (Value Added Tax) have been covered in section 8.5. Students can refer to the given example in this section to understand and practice the questions.

8.6 Compound Interest:- It is quite an interesting and important topic to study because it is used in our day to day life. Also, the term compound interest can be a bit lengthy to find so, the proper and simple methods have been mentioned in section 8.6. With the example given in this section, students will be able to learn how to find compound Interest?

8.7 Deducing A Formula For Compound Interest:- By using the simple interest formula we can calculate the compound interest but, when it comes to the longer time period, the process could be lengthy. So, there is a Formula For Compound Interest that makes the process very short. The formula of compound interest is - 

Where P is Principal Amount, R is ration, and n is the no. of times the interest is compounded annually.

8.8 Rate Compounded Annually Or Half Yearly (semi Annually):- What if one needs to calculate the Rate Compounded Annually Or Half Yearly? For this condition, the section 8.8 contains a detailed brief and a few solid examples. Referring to which, a student can learn the methods to calculate Rate Compounded Annually Or Half Yearly. 

8.9 Applications Of Compound Interest Formula:- In the real world situations, there are several moment when we need to use the compound interest formula such as Increase (or decrease) in population, the growth of a bacteria when rate of growth is known, the value of an item, if its price fluctuate in the intermediate years.

Comparing Quantities Chapter 8 Exercises

➤ Exercise 8.1 – 6 Questions (1 Long Answer, 5 Short Answers)

➤ Exercise 8.2 – 10 Questions (4 Long Answers, 6 Short Answers)

➤ Exercise 8.3 – 12 Questions (6 Long Answers, 6 Short Answers)

Study Tips for Class 8 Comparing Quantities

Learn formulas and the ways it has been derived. Doing so will help you understand the Comparing Quantities in detail. This is a single chapter but there are various important topics. Make sure you go through them often and revise all the formulas time and again.

In case you find solving the questions a bit difficult refer to our NCERT Solutions for class 8 Maths.

Algebraic Expressions and Identities (Chapter 9)

In this chapter, Algebraic Expressions and Identities, students are taught all the topics related to the algebraic expressions. 

The chapter begins with the definition of expressions, terms, factors, And Coefficients, Monomials, Binomials, And Polynomials, Like and Unlike terms, etc. This is a bit lengthy lesson where multiple topics are explained individually.

The whole chapter is distributed among 12 sections:-

9.1 What Are Expressions?:- This includes the definition of expressions which have already been covered in the previous class. Also, the element that forms an expression has been covered: Variable and Constant. 

9.2 Terms, Factors And Coefficients:- Expressions are formed by adding the terms. The terms themselves can be formed as the product of factors and the numerical factor of an expression is known as coefficients. All of these definitions are from the NCERT Class 8th Maths Book chapter number, section 9.2.

9.3 Monomials, Binomials And Polynomials:- As the name suggests Monomials, Binomials And Polynomials. There are certain differences between these names: Monomials are known as for the expression having single term only, Binomials, when an expression has two terms, and Polynomials, when an algebraic expression has many terms.

9.4 Like And Unlike Terms:- Recall the basic definition of like and unlike terms which you have studied in algebraic expression to understand the given example in this section.

9.5 Addition And Subtraction Of Algebraic Expressions:- By continuing the earlier studied topics of algebraic expression, in this section a few good examples have been given to solve the Addition And Subtraction Of Algebraic Expressions.

9.6 Multiplication Of Algebraic Expressions: Introduction:- The Multiplication Of Algebraic Expressions has been introduced in this section, where patterns of dots are used to elaborate the process of multiplication of algebraic expressions. Furthermore, the section concludes that when quantities are given through algebraic expressions, we need to find their product.

9.7 Multiplying A Monomial By A Monomial:- In order to multiply a monomial by a monomial, we use rules of exponents and powers. About this thing, section 9.7 contains one solid example.

9.8 Multiplying A Monomial By A Polynomial: To multiply a monomial by a polynomial distributive law is being used. This topic has been further extended in this section: (9.8.1) Multiplying a monomial by a binomial, (9.8.2) Multiplying a monomial by a trinomial.

9.9 Multiplying A Polynomial By A Polynomial:- In multiplication of polynomials with polynomials, the like terms play a crucial role and hence students should always look for this term, if any, and combine them. The section has two subsections: (9.9.1) Multiplying a binomial by a binomial, (9.9.2) Multiplying a binomial by a trinomial. An example of binomial and trinomial is given in this image -

9.10 What Is An Identity?:- By taking a simple equation, the section has tried to explain the identity. As per their outcome, if LHS = RHS, for any value of a, Such an equality, true for every value of the variable in it, is called an identity.

9.11 Standard Identities:- There are three most important standard identities in algebraic expression which have extreme levels of application. Such standard identities are: (a + b) 2 = a2 + 2ab + b2 , (ii) (a – b)2 = a2 – 2ab + b2, (iii) (a + b) (a – b) = a2 – b2.

9.12 Applying Identities:- All of the above mentioned identities have real application, and so these are used in solving many problems on multiplication of binomial expressions. These identities are known as simple alternative methods of solving the problems of algebraic expressions. The section has elaborated its application in detail by referring to the several example problems.

Algebraic Expressions and Identities Chapter 9 Exercises

➤ Exercise 9.1 – 4 Questions (4 Short Answers)

➤ Exercise 9.2 – 5 Questions (5 Short Answers)

➤ Exercise 9.3 – 5 Questions (5 Short Answers)

➤ Exercise 9.4 – 3 Questions (3 Short Answers)

➤ Exercise 9.5 – 8 Questions (8 Short Answers)

Study Tips for Class 8 Algebraic Expressions and Identities 

The only tip for this lesson is to give a quick revision to all the basics of Algebraic expression you have already studied in the earlier classes.

Visualising Solid Shapes (Chapter 10)

This chapter comprises 3 chapters and 16 questions to learn the Visualising Solid Shapes. Views Of 3d-Shapes, Mapping Space around us, faces, edges, and vertices are explained in this lesson. The main idea of this lesson is to help students understand the 3D shapes and objects that are around us.

The chapter is divided into 4 sections:-

10.1 Introduction:- In the previous class 7, the plane shapes and solid shapes were introduced. Although, those concepts are for 2D shapes but, here in this chapter the world of 3D and its shapes will explore the students.

10.2 Views Of 3d-Shapes:- A 3D object can be drawn from multiple positions as they have different perspectives; such as Top View, Front, Side. This section is quite fun to study.

10.3 Mapping Space Around Us:- The section 10.3 has covered the method of reading a map and what are the key points to keep in mind to map a space around us. This topic has been elaborated in detail here in this section.

10.4 Faces, Edges And Vertices:- This section is a bit advanced as students can get to know about the faces, edges and vertices here. All these are parts of a 3D shape. The difference between polyhedrons and non-polyhedrons have been covered here as well. Euler’s formula has been given.

Euler’s formula:- F + V = E + 2, where F is the number of faces, V the number of vertices, and E the number of edges

Visualising Solid Shapes Chapter 10 Exercises

➤ Exercise 10.1 – 4 Questions (4 Short Answers)

➤ Exercise 10.2 – 4 Questions (3 Short Answers, 1 Long Answer)

➤ Exercise 10.3 – 8 Questions (8 Short Answers)

Study Tips for Class 8 Visualising Solid Shapes 

This chapter may look a bit tricky as there are lots of 3D figures to study. However, a constant effort and regular revision of the terms such as Faces, Edges And Vertices are good enough to score better marks in this chapter.

Mensuration (Chapter 11)

In the previous class 7th, the sneak peek of this topic has been already given. Therefore, here in this chapter the topics have been recalled as well as in various sections the method and formulas to find the areas of Trapezium, General Quadrilateral, Polygon, etc. have been covered.

34 questions are distributed among 4 exercises. Let’s see each section and their topics to be able to solve all the 34 questions.

11.1 Introduction:- This part is a brief of what topics and terms students have covered. Also, the upcoming that a learner will learn in this lesson has been mentioned. The surface area and volume of solids such as cube, cuboid and

Cylinders are also discussed here in this lesson.

11.2 Let Us Recall:- This section has recalled the previous classes' learning of various figures, areas and perimeter. An screenshot from the NCERT Class 8th Maths Book is given here:-

11.3 Area Of Trapezium:- The section is full of questions and their step by step answers. Here in section 11.3, area of trapezium, a question is given and a figure is also mentioned. As student can refer this section to know the area of trapezium 

Where, a and b is base and h is height.

11.4 Area Of A General Quadrilateral:- Students get a chance in this section to find out the Area Of A General Quadrilateral: . 

In order to derive the formula, a general quadrilateral is splitted into two triangles by drawing one of its diagonals.

11.5 Area Of A Polygon:- The method used in finding the Area Of A General Quadrilateral, the same method will be applied in finding an area of a polygon. Various examples have been mentioned in this section to allow learners to practice many questions to understand the concepts better.

11.6 Solid Shapes:- Some shapes have two or more than two identical faces. In the previous class, students have already covered two dimensional figures that can be identified as the faces of three dimensional shapes. But here this topic has been broadened.

11.7 Surface Area Of Cube, Cuboid, and Cylinder:- Here in this section, the students will be able to know the formula of Cuboid: 2(lb+bh+hl), where l, b and h are the length, breadth and height of a cuboid. Cube: 6a2, a is the side of the cube. Cylinder: 2πr (r+h), r is the radius of the circular base and h is the height of the cylinder. As well as the method of solving the questions based on these formulas are given in the exercises.

11.8 Volume Of Cube, Cuboid, and Cylinder:- The definition of volume says, Amount of space occupied by a three dimensional object is called its volume. Hence, this section has covered the derivation of formulas of Volume Of Cube, Cuboid, and Cylinder.

• Volume of cuboid = area of the base × height
• volume of cube = l × l × l = l3
• Volume of cylinder = area of base × height = πr2 × h = πr2h

11.9 Volume And Capacity:- This section 11.9 begins with the basic difference between Volume And Capacity, which is not much. As per the NCERT Book,

1. Volume refers to the amount of space occupied by an object.

1. Capacity refers to the quantity that a container holds.

Mensuration Chapter 11 Exercises

➤ Exercise 11.1 – 5 Questions (5 Long Answers)

➤ Exercise 11.2 – 11 Questions (11 Long Answers)

➤ Exercise 11.3 – 10 Questions (2 Short Answers, 8 Long Answers)

➤ Exercise 11.4 – 8 Questions (2 Short Answers, 6 Long Answers)

Study Tips for Class 8 Mensuration 

Developing a good grip on the mensuration formulas are key to score better marks. You are advised here to go through each section of Chapter 11 and understand the derivation of formulas so that you can better visualise the questions from the next time.

Exponents and Powers (Chapter 12)

 Laws of exponents, use of exponents, comparison of numbers, etc are covered in chapter 13. There are a total of 2 exercises and 11 questions in this chapter. With the help of the various sections given in the NCERT Class 8th Maths Book, students can develop a better grip on the given topics.

12.1 Introduction:- In the introduction section, the power and exponents have been described by taking an example of Mass of earth that is 5,970,000,000,000, 000, 000, 000, 000 kg. However, using exponents, it can be written as 5.97 × 1024 kg. Here is a visual representation of what exponents and power look like: 

12.2 Powers With Negative Exponents:- for any non-zero integer a, where m is a positive integer. a–m is the multiplicative inverse of am.

12.3 Laws Of Exponents:- The law states, for any non-zero integer a, am × an = a m+ n , where m and n are natural numbers. With the help of suitable examples, the topic has been made clear to the students.

12.4 Use Of Exponents To Express Small Numbers In Standard Form:- This section includes the method to express small numbers in standard form. Furthermore, the topic has been extended to a subsection: (12.4.1) Comparing very large and very small numbers.

Exponents and Powers Chapter 12 Exercises

➤ Exercise 12.1 – 7 Questions (7 Short Answers)

➤ Exercise 12.2 – 4 Questions (4 Short Answers)

Study Tips for Class 8 Exponents and Powers

It is quite a useful mathematical term that all students should master. Here, the study tip is to go through each section one by one, read all the written text and practice the solved examples.

Direct and Indirect proportions (Chapter 13)

2 exercises and 21 questions are available in chapter 13 to help students grasp the concept of Direct and Indirect proportions. This chapter has been divided into 3 sections:- 

13.1 Introduction:- The intro part includes a real life scenario to allow students to understand the context of this topic. As well as variations in quantity has been mentioned too.

13.2 Direct Proportion:- In the simplest form, the direct proportion can be defined when two quantities x and y increase or decrease together in such a way that the ratio of their corresponding values remains constant. With the help of a few great examples the direct proportion has been explained.

13.3 Inverse Proportion:- When two quantities may change in such a manner that if one quantity increases, the other quantity decreases and vice versa, note that the product remains constant. It is known as Inverse Proportion. By giving a real life situation, the inverse proportion has been explained.

Direct and Indirect proportions Chapter 13 Exercises

➤ Exercise 13.1 – 10 Questions (10 Short Answers)

➤ Exercise 13.2 – 11 Questions (11 Long Answers)

Study Tips for Class 8 Direct and Indirect proportions

This concept has various real life applications and so you must pay attention to the concepts. The study tip for this lesson is to clear your understanding in the definition of Direct and Indirect proportions and don’t forget to practice the solved example questions.

Factorisation (Chapter 14)

Till this chapter students have already gained a good command on the algebraic expression as well as natural numbers. So, chapter 14 aims to guide students to learn the factorisation with the help of 4 exercises. 

14.1 Introduction:- The very first section of introduction includes the basic Factors of natural numbers, algebraic expressions. Proper examples have been given to help students to cover the topics thoroughly.

14.2 What Is Factorisation?:- When an algebraic expression is written as a product of factors, where factors can be numbers, algebraic variables or algebraic expressions. In this section, the various factorisation methods have been mentioned: Method of common factors, Factorisation by regrouping terms, Factorisation using identities, Factors of the form ( x + a) ( x + b).

14.3 Division Of Algebraic Expressions:- Before this point, all class 8 students have learned the methods to add and subtract algebraic expressions. But, division of algebraic expression has not been covered. So, this section is dedicated to teach Division Of Algebraic Expressions using various methods: Division of a monomial by another monomial, Division of a polynomial by a monomial. 

14.4 Division Of Algebraic Expressions Continued (polynomial ÷ Polynomial):- In this section, example 15 & 16 has elaborated the methods to factorise and divide the Algebraic Expressions.

14.5 Can You Find The Error?:- Since, students make many mistakes while solving algebra exercises, thus, this section ensures students do not make such mistakes.

Factorisation Chapter 14 Exercises

➤ Exercise 14.1 – 3 Questions (3 Short Answers)

➤ Exercise 14.2 – 5 Questions (5 Short Answers)

➤ Exercise 14.3 – 5 Questions (5 Short Answers)

➤ Exercise 14.4 – 21 Questions (21 Short Answers)

Study Tips for Class 8 Factorisation

Factorisation is being used at a wide level, a student must master this to handle the algebra questions with ease. There is no shortcut for this chapter to study except lots of practice. However, command on some basic algebraic expressions and Exponents and Powers can help you to ease the factorisation process.

Introduction to Graphs (Chapter 15)

This chapter contains 3 lessons and 13 exercises that help students to cover the topics related to graphs: bar graphs, pie graphs, line graphs and linear graphs. Not only this but, this chapter also guides students to know how to locate a point and coordinate in a graph.

This whole chapter is divided into 3 sections:-

15.1 Introduction:- The intro part informs learners why we need to use the graph. By answering this question, section 15.1 says, the graph is a useful method to show the data in visual form to grasp the information faster and easier. Apart from graphs, data can be shown in table form, but information will not be as clear and easier to grasp as it can be in graphs. In this section, various types of graphs have been covered: A Bar graph, A Pie graph (or a circle-graph), A histogram, A line graph.

15.2 Linear Graphs:- A line graph is a set of line segments which is joined consecutively. However, sometimes the graph may be completely unbroken, such a graph is called linear graphs. After the definition of linear graphs in this section, it further explains about Location of a point & Coordinates.

15.3 Some Applications:- Section 15.3 covers the term independent variable as well as dependent variable. Apart from this, the section is dedicated to teach us how we can use the graphs in real life. In simple terms: The graph can be used to show the relation between dependent variable and independent.

Introduction to Graphs Chapter 15 Exercises

➤ Exercise 15.1 – 7 Questions (7 Long Answers)

➤ Exercise 15.2 – 4 Questions (4 Short Answers)

➤ Exercise 15.3 – 2 Questions (2 Short Answers)

Study Tips for Class 8 Introduction to Graphs

Understand the bar graph, pie graph and histogram completely then move to the topic of line graph, x-coordinate and y-coordinate. A good knowledge of these terms will help you master the lesson as well as in scoring higher marks.

Playing with Numbers (Chapter 16 )

Till this chapter, students have already covered so much about the numbers: Integers, Whole Numbers, rational numbers, Natural Numbers. But the need of this chapter is to get in depth of the number in more detail. Learn justifying tests of divisibility through this lesson.

There are 2 lessons and 14 questions to learn and practice the problems. Chapter 16 has been explained in 5 sections:-

16.1 Introduction:- It includes the topics which this chapter is going to explain as well as what has been taught so far in this subject.

16.2 Numbers In General Form:- This section helps students know how the 2 digit and 3 digit numbers are written in general form. Such as, two digit number ab will be written as ab = 10a + b. As well as some questions have been given to ensure students have understood completely.

16.3 Games With Numbers:- This section is a bit interesting as students get to learn about numbers in an interesting manner. Section 16.3 covers the method to reverse the 2-digit as well as 3-digit numbers. In addition to that the methods to form the 2 digit numbers and 3 digit numbers are mentioned.

16.4 Letters For Digits:- There are some puzzles in this section. Such as the given image contains a sum where students need to find the digit for the letter Q.

16.5 Tests Of Divisibility:- This section may seem known to you as it has been already covered in class 6. However, here in this section 16.5 why the methods of divisibility work has been answered with some suitable examples.

Also, the test of divisibility by 10, 5, 2, 9 & 3, etc. have been covered.

Playing with Numbers Chapter 16 Exercises

➤ Exercise 16.1 – 10 Questions (Short Answers)

➤ Exercise 16.2 – 4 Questions (Short Answers)

Study Tips for Class 8 Playing with Numbers

Don’t forget to revise the Integers, Whole Numbers, rational numbers, Natural Numbers and their properties.

CBSE Class 8 Maths Chapter -Wise Marks Weightage

There are a total of 16 chapters and each has some weightage. Thus, knowing them is extremely important. Here’s the table that contains the chapter wise marks weightage.

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

Benefits of Using NCERT Solutions for Class 8 Maths

There are numerous benefits of using NCERT Solutions for class 8 Maths including easy understanding of the concepts and step by step answers to all the questions. Apart from these, followings are the benefits of using NCERT Maths solutions of class 8:-

1. The Solutions help students to cover the whole syllabus with ease.
2. It enhances the accuracy, since the subject matter experts have developed these NCERT Solutions.
3. Eases the exam preparation process due to having crystal clear and step by step answers to all the chapter wise questions.