# NCERT Solutions for Class 8 Maths

Looking for NCERT Solutions for Class 8 Maths that will solve your maths problems in a jiffy? Don’t worry because your search ends here. GeeksforGeeks have Maths solutions to all your Maths questions.

NCERT Solutions for Class 8 Maths consists of the chapter-wise solutions to all the problems provided in the NCERT textbook for Class 8 Mathematics. GeeksforGeeks has created a detailed chapter-wise solution for the NCERT book of class 8 that contains problems on various topics like Rational Numbers, Linear Equations, Quadrilaterals, Data Handling, and many more. Each chapter in this solution thoroughly covers every exercise along with a detailed step-by-step explanation of the solutions.

NCERT Solutions for Class 8 Maths are incredibly useful for students studying for CBSE exams as well as state or national competitive tests like Olympiads. The CBSE examinations adhere to the structure established by the NCERT texts.

There are 16 chapters altogether in this book. As a student, you must constantly revise and practice all of the solutions. Begin by answering the problems in the NCERT book, and then check at these class 8 maths NCERT solutions.

To improve the basic knowledge of students, we have also covered 1500+ Most asked Questions of Mathematics, Chapterwise Important Formulas, and many more based on the new Class 8th CBSE curriculum. These notes and other study materials provide a helping hand for students to prepare for their Final Examinations.

## Chapter 1: Rational Numbers

This chapter helps to learn about the properties of real numbers, rational numbers, the representation of a rational number on a number line, and additive and multiplicative identity. Here in NCERT solutions for class 8 maths chapter 1, we have covered NCERT Problems based on Rational numbers mainly discussing the characteristics of all the real numbers, integers, whole numbers, rational numbers, and natural numbers.

This chapter consists of two exercises only in which the problems in Exercise 1.1 are related to the properties of the rational numbers (closure, commutativity, associativity, etc). However, in Exercise 1.2 the problems are related to the advanced concepts of the rational number like the representation of rational numbers on a number line and determining any numbers of rational numbers between any two rational numbers.

**NCERT Solutions for Class 8 Maths of Chapter 1 are here:**

- NCERT Maths Solutions Class 8 Exercise 1.1 – 11 Questions (11 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 1.2 – 7 Questions (7 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 1 at GeeksforGeeks:**

## Chapter 2: Linear Equations in One Variable

The **linear equations in one variable** deal with the expression defined in one variable only and its algebraic operations. This chapter contains six different exercises that have problems based on the linear equations in one variable and their application.

There are 65 well-structured questions in Chapter 2 linear equations in one variable, which may be divided into 20 simple calculation sums, 38 intermediate levels, and 7 difficult problems. Exercises 2.1, 2.2, 2.3, and 2.4 are designed to determine the solution of the linear equation. However, Exercises 2.5 and 2.6 are based on the topic equations reducible to the linear form.

**NCERT Solutions for Class 8 Maths of Chapter 2 are here:**

- NCERT Maths Solutions Class 8 Exercise 2.1 – 12 Questions (12 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 2.2 – 16 Questions (6 Long Answers and 10 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 2.3 – 10 Questions (3 Long Answers and 7 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 2.4 – 10 Questions (4 Long Answers and 6 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 2.5 – 10 Questions (1 Long Answer and 9 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 2.6 – 7 Questions (1 Long Answer and 6 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 2 at GeeksforGeeks:**

## Chapter 3: Understanding Quadrilaterals

This chapter covers **all types of quadrilaterals** such as** polygonal shapes** like **squares**, **rectangles**, **triangles**, **pentagons**, **hexagons**, etc.

In total, this chapter contains four exercises that include a total of 31 questions, out of which 7 are easy, 16 are medium and 8 are difficult problems. Exercise 3.1 covers the problems on the definition of various polygons and their properties, Exercise 3.2 is based on the concept of the **Angle sum property of a polygon**. However, Exercise 3.3 covers the elements and the properties of quadrilaterals like trapezium, kite, and parallelogram, and Exercise 3.4 is designed to learn some special types of parallelogram like square, rectangle, and rhombus.

**NCERT Solutions for Class 8 Maths of Chapter 3 are here:**

- NCERT Maths Solutions Class 8 Exercise 3.1 – 7 Questions (1 Long answer and 6 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 3.2 – 6 Questions (6 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 3.3 – 12 Questions (6 Long answers and 6 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 3.4 – 6 Questions (1 Long answer and 5 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 3 at GeeksforGeeks:**

- CBSE Class 8 Maths Notes Chapter 3
- Class 8 RD Sharma Solutions Understanding Quadrilaterals Chapter 1, Chapter 2 and Chapter 3
- All important formulas for Chapter 3

## Chapter 4: Practical Geometry

The chapter on **practical geometry** helps to learn the construction of quadrilaterals when different parameters of it are known. Geometry may be visualized and realized in the actual world with the help of practical geometry. This can be applied in architecture, sculpture, dimension calculations, and other areas.

This chapter contains a total of five exercises only, with 8 questions in total. Each question is divided into 3-4 subparts with easy, to difficult questions. Exercise 4.1 covers the problem for the case when the lengths of four sides and a diagonal are given. Similarly, Exercises 4.2, 4.3, and 4.4 are based on the topics when two diagonals and three sides are known, two adjacent sides and three angles are given and three sides and two included angles are provided. However, Exercise 4.5 contains problems based on some special cases.

**NCERT Solutions for Class 8 Maths of Chapter 4 are here:**

- NCERT Maths Solutions Class 8 Exercise 4.1 – 1 Questions (1 Long Answer)
- NCERT Maths Solutions Class 8 Exercise 4.2 – 1 Questions (1 Long Answer)
- NCERT Maths Solutions Class 8 Exercise 4.3 – 1 Questions (1 Long Answer)
- NCERT Maths Solutions Class 8 Exercise 4.4 – 1 Questions (1 Long Answer)
- NCERT Maths Solutions Class 8 Exercise 4.5 – 4 Questions (4 Long Answers)

**More resources for CBSE Class 8 Maths Chapter 4 at GeeksforGeeks:**

## Chapter 5: Data Handling

**Data handling** is a method of organizing data or information systematically using diagrams like pictographs, pie charts, bar graphs, and histograms. Students learn about data organization and representation in this chapter. Data handling is the process of organizing data in a systematic manner.

This chapter consists of only three exercises. Exercise 5.1 is based on the basic concept of representing, organizing, and grouping the data provided while Exercise 5.2 helps to make a pie chart for the given data. Moreover, Exercise 5.3 coves the topic that helps to understand the basic concept of probability.

**NCERT Solutions for Class 8 Maths of Chapter 5 are here:**

- NCERT Maths Solutions Class 8 Exercise 5.1 – 5 Questions (5 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 5.2 – 5 Questions (3 Long Answers and 2 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 5.3 – 6 Questions (2 Long Answers and 4 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 5 at GeeksforGeeks:**

- CBSE Class 8 Maths Notes Chapter 5
- Class 8 RD Sharma Solutions Data Handling Chapter 1, Chapter 2, Chapter 3 and Chapter 4
- All important formulas for Chapter 5

## Chapter 6: Squares and Square Roots

As the name of the chapter says, **Squares and square roots** this chapter gives the knowledge of the concept to determine the squares and square roots of a number. The different properties and the pattern followed to find a square number are discussed in four exercises.

Exercises 6.1 and 6.2 are based on the basic idea of the square numbers and different ways to determine them. Though Exercises 6.4 and 6.5 are focused on the concept of the determination of the square root of a number.

**NCERT Solutions for Class 8 Maths of Chapter 6 are here:**

- NCERT Maths Solutions Class 8 Exercise 6.1 – 9 Questions (9 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 6.2 – 2 Questions (2 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 6.3 – 10 Questions (3 Long Answers and 7 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 6.4 – 9 Questions (3 Long Answers and 6 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 6 at GeeksforGeeks:**

## Chapter 7: Cubes and Cube roots

Again, as the title of the chapter suggest **Cubes and Cube roots** this chapter helps to understand the concept to determine the cubes and cube root of a number. The different patterns followed to find a cube and cube root of a number are discussed in only two exercises.

Exercises 7.1 contains the problem to determine whether the given number is a perfect cube or not. And Exercises 7.2 focused on the idea of the cube root and the determination of the cube root of a number.

**NCERT Solutions for Class 8 Maths of Chapter 7 are here:**

- NCERT Maths Solutions Class 8 Exercise 7.1 – 4 Questions (4 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 7.2 – 3 Questions (2 Long Questions and 1 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 6 at GeeksforGeeks:**

## Chapter 8: Comparing Quantities

This chapter gives a basic understanding of the topics such as **increased and decreased percentage**, market price, selling price, cost price, discount, discount price, profit or loss, interest, etc.

Total there are three exercises in this chapter, Exercise 8.1 based on the topics of** ratios and percentage**, and Exercises 8.2 and 8.3 covers a wide range of concepts such as percentage, profit or loss, tax, and** **compound interest.

**NCERT Solutions for Class 8 Maths of Chapter 8 are here:**

- NCERT Maths Solutions Class 8 Exercise 8.1 – 6 Questions (1 Long Answer and 5 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 8.2 – 10 Questions (4 Long Answers and 6 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 8.3 – 12 Questions (6 Long Answers and 6 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 8 at GeeksforGeeks:**

- CBSE Class 8 Maths Notes Chapter 8
- Class 8 RD Sharma Solutions Comparing Quantities Chapter 1, Chapter 2, and Chapter 3
- All important formulas for Chapter 8

## Chapter 9: Algebraic Expressions and Identities

The chapter **Algebraic Expressions and Identities** briefs the basics of monomials, binomials, and polynomials in an algebraic expression. **Multiplying different polynomials**, and solving questions using** algebraic identities** are essential topics covered in this chapter.

There are 25 well-structured questions in Chapter 9 algebraic expressions and identities, including 8 basic identity-based problems, 12 intermediate problems, and 5 hard questions. Exercises 9.1 and 9.2 covers the basic concepts of terms related to polynomials and operations on the expressions. Exercise 9.3 and 9.4 are based on the multiplications of polynomials while Exercise 9.5 discussed the standard algebraic identities.

**NCERT Solutions for Class 8 Maths of Chapter 9 are here:**

- NCERT Maths Solutions Class 8 Exercise 9.1 – 4 Questions (4 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 9.2 – 5 Questions (5 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 9.3 – 5 Questions (5 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 9.4 – 3 Questions (3 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 9.5 Set 1, Set 2 – 8 Questions (8 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 9 at GeeksforGeeks:**

- CBSE Class 8 Maths Notes Chapter 9
- Class 8 RD Sharma Solutions Chapter 1 and Chapter 2
- All important formulas for Chapter 9

## Chapter 10: Visualising Solid Shapes

This chapter provides the understanding of different solids shapes when visualized in different dimensions and various terms used to describe their properties. The chapter covered in three different exercises consists of a total of 15 Questions. Out of which 10 are easy, 3 are moderate and 2 are easy to-level questions.

Here exercises 10.1 and 10.2 are based on the concept of the **visualisation of different solid shapes **at different positions and the mapping spaces around the observer. Though, Exercise 10.3 discussed the terms like faces, edges, vertices, and the relation between them, related to a solid shape.

**NCERT Solutions for Class 8 Maths of Chapter 10 are here:**

- NCERT Maths Solutions Class 8 Exercise 10.1 – 4 Questions (4 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 10.2 – 4 Questions (1 Long Answer and 3 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 10.3 – 8 Questions (8 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 10 at GeeksforGeeks:**

## Chapter 11: Mensuration

**Mensuration **is the chapter that deals with the measurement or the calculations related to determining the **area**, **perimeter**, volume of various geometrical figures like squares, cubes, rectangles, cuboids, cylinders, and triangles, etc.

This chapter consists of only four exercises in which Exercises 11.1 and 11.2 deal with problems related to the areas of different geometrical shapes, combinations of shapes, and everyday life examples. However, Exercises 11.3 and 11.4 discussed the terminology related to 3-Dimensional shapes.

**NCERT Solutions for Class 8 Maths of Chapter 11 are here:**

- NCERT Maths Solutions Class 8 Exercise 11.1 – 5 Questions (5 Long Answers)
- NCERT Maths Solutions Class 8 Exercise 11.2 – 11 Questions (11 Long Answers)
- NCERT Maths Solutions Class 8 Exercise 11.3 – 10 Questions (8 Long Answers and 2 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 11.4 – 8 Questions (6 Long Answers and 2 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 11 at GeeksforGeeks:**

- CBSE Class 8 Maths Notes Chapter 11
- Class 8 RD Sharma Solutions Mensuration Chapter 1, Chapter 2 and Chapter 3
- All important formulas for Chapter 11

## Chapter 12: Exponents and Powers

The chapter Exponents and powers cover the primary concepts such as laws of exponents and their applications. The main topics covered in this chapter are expressing numbers in the form of exponents and applying the laws of negative exponents.

In class 8 maths chapter 12 exponents and powers, there are 11 questions, four of which are based on exponent laws, three of which are medium level, and two of which are difficult. Exercise 12.1 is specifically based on the laws of exponents, and Exercise 12.2 deals with the problems using the applications of power to write large numbers in exponents and vice-versa.

NCERT Solutions for Class 8 Maths of Chapter 12 are here:

- NCERT Maths Solutions Class 8 Exercise 12.1 – 7 Questions (7 Long Answers)
- NCERT Maths Solutions Class 8 Exercise 12.2 – 4 Questions (4 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 12 at GeeksforGeeks:**

## Chapter 13: Direct and Inverse Proportions

This chapter gives a detailed explanation of** inverse and direct proportions** through problems discussed in two exercises. This chapter covers various types of questions on direct proportion, identifying inverse proportion. And determining the value of quantities following this relationship, the important topics explained in class 8 maths NCERT solutions chapter 13.

There are 21 well-structured problems in Chapter 13 on direct and inverse proportion. There are five simple relationship identification questions, ten moderately tough questions, and six lengthy answer-type sums. Exercise 13.1 contains problems to determine the direct proportions between any quantity and Exercise 13.2 deals with the questions from the indirect inverse.

**NCERT Solutions for Class 8 Maths of Chapter 13 are here:**

- NCERT Maths Solutions Class 8 Exercise 13.1 – 10 Questions (10 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 13.2 – 11 Questions (11 Long Answers)

**More resources for CBSE Class 8 Maths Chapter 13 at GeeksforGeeks:**

- CBSE Class 8 Maths Notes Chapter 13
- Class 8 RD Sharma Solutions Direct and Inverse Proportions Chapter 1 and Chapter 2
- All important formulas for Chapter 13

## Chapter 14: Factorisation

Class 8 mathematics chapter 14 **factorization **teaches students how to factor algebraic equations using numerous methods and the steps required to divide different types of polynomials. Factorization is an important topic since it is an integral part of mathematics. This chapter comprises the problems on the factors of natural numbers and algebraic expressions, factorisation by regrouping terms, factorisation using identities, and division of algebraic expressions.

The chapter includes four exercises out of which exercises 14.1 and 14.2 are based on the topic factorisations and their application while exercises 14.3 and 14.4 emphasize the division of algebraic expressions.

**NCERT Solutions for Class 8 Maths of Chapter 14 are here:**

- NCERT Maths Solutions Class 8 Exercise 14.1 – 3 Questions (3 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 14.2 – 5 Questions (5 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 14.3 – 5 Questions (5 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 14.4 – 21 Questions (21 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 14 at GeeksforGeeks:**

## Chapter 15: Introduction to Graphs

The chapter **Introduction to Graphs** is all about the basic understanding of the graphs, kinds of graphs, etc. Other topics include linear graphs and how to apply them to daily life problems.

Chapter 15 introduction to graphs consists of a total of 13 problems. 7 are difficult to level analytical questions, 2 are moderate and 4 are easy problems. Exercise 15.1 deals with problems from introduction to graphs and terminology related to it while problems in Exercises 15.2 and 15.3 provided emphasis on the construction of different types of graphs and their applications.

**NCERT Solutions for Class 8 Maths of Chapter 15 are here:**

- NCERT Maths Solutions Class 8 Exercise 15.1 – 7 Questions (7 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 15.2 – 4 Questions (4 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 15.3 – 2 Questions (2 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 15 at GeeksforGeeks:**

## Chapter 16: Playing with Numbers

All the above-mentioned chapters basically helped to learn about various kinds of numbers and their different properties likewise in this chapter the concept of numbers is discussed in a more general way. Chapter 16 of Maths for class 8 Playing with numbers allows students to explore the properties of numbers in an interactive manner. This chapter assists students in determining the divisibility of integers by providing a list of pointers and methods for increasing calculation speed.

Chapter 16 playing with numbers consists of total 14 problems. Out of which, 5 are easy-to-level problems based on games, 7 are moderate-level questions based on divisibility tests, while the rests two are difficult-to-level questions. Exercise 16.1 and 16.2 contains fun activities, puzzles, etc. such as divisibility tests to determine any missing number in a series of numbers.

**NCERT Solutions for Class 8 Maths of Chapter 16 are here:**

- NCERT Maths Solutions Class 8 Exercise 16.1 – 10 Questions (10 Short Answers)
- NCERT Maths Solutions Class 8 Exercise 16.2 – 4 Questions (4 Short Answers)

**More resources for CBSE Class 8 Maths Chapter 16 at GeeksforGeeks:**

**Important Resources for CBSE Class 8th provided by GeeksforGeeks:-**

**CBSE Class 8 Maths Notes****RD Sharma Solutions Maths Class 8****CBSE Class 8 Maths Formulas****CBSE Physics Class 8 Notes****CBSE Class 8 Chemistry Notes**

## Frequently Asked Questions (FAQs)

**Question 1: What are some important formulas from Class 8 Maths NCERT?**

**Answer:**

Here is the list of some important formulas covered in NCERT solutions from Mensuration and Algebra, for class 8 maths are given below:

Important Mensuration formulas:

- TSA of Cuboid = 2(lb + bh +lh)
- TSA of Cube = 6a
^{2}- TSA of Right Circular Cone = πr (l + r)
- CSA of Solid Shapes
- CSA of Cuboid = 2(l + b)
- CSA of Cube = 4a
^{2}- CSA of Right Circular Cone = πrl
- Volume of Cuboid = lbh
- Volume of Cube = a
^{3}- Volume of Right Circular Cone = ⅓ × πr
^{2}h

Important Algebraic Expressions

- (x + a)(x + b) = x
^{2}+ (a + b)x + ab- (x – a)(x – b) = x
^{2}– (a + b)x + ab- (x – a)(x + b) = x
^{2}+ (b – a)x – ab

**Question 2: Why it is important to study Class 8 maths Notes for CBSE Exams?**

**Answer:**

Making notes when studying the NCERT Solutions Class 8 Maths is usually a good idea because they serve as guides for pupils while revising the amounts. Furthermore, notes aid students in recalling topics involved in a problem at a glance. This cuts down on the amount of time it takes to go over an issue during an exam.

**Question 3: Why are NCERT Solutions for Class 8 Maths Important?**

**Answer:**

NCERT Solutions for Class 8 Math are essential since they allow students to double-check their responses to exercise problems. These NCERT answers for class 8 math are self-explanatory and give pupils a full overview of the procedures they must take to obtain the correct answer using the most effective way.

**Question 4: How are NCERT Solutions for Class 8 Maths Promoting Problem Solving in Students?**

**Answer:**

NCERT solutions for class 8 maths teach how to break down a question into smaller sections to understand it. Students can not only develop a problem-solving approach but also improve their mathematics skills by applying these approaches.

**Question 5: How Many Chapters are there in Class 8 Maths NCERT Solutions?**

**Answer:**

The NCERT solutions for class 8 maths contain 16 chapters. Mensuration, graphs, factorization, exponents, and other topics covered in this chapter create the foundation for higher levels. Because mathematics is a subject in which all subjects are interconnected, it is critical to be well-versed in all of these chapters in order to prevent misunderstanding in higher grades.

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