NCERT Solutions for Class 8 Maths

NCERT Solutions for class 8 maths helps students to get better marks in school. It is designed as per the latest syllabus of the Central Board of Secondary Education (CBSE) to match students' learning needs.

NCERT Solutions for class 8 maths provides comprehensive solutions and detailed explanations to the NCERT Class 8 Maths textbooks. The solutions include an explanation of formulas, graphs and figures along with doubt-clearing exercises. All the NCERT solutions for class 8 Maths are prepared by experts of Home-tutions having years of teaching experience for class 8 Maths CBSE board. Do solve all the questions asked in the NCERT textbook with the help of NCERT Solutions for class 8 prepared by HT in an easy and lucid language all NCERT Solutions are errorless and accurate. 

To score good marks in class 8 Maths one must have the right strategies, and it starts with understanding the correct weightage of chapters so that based on which you understand the chapters which are more important for exams.

CBSE Class 8 Maths Unit-Wise Marks Weightage

• Chapter 1 Weightage-08
• Chapter 2 Weightage-10
• Chapter 3 Weightage-13
• Chapter 4 Weightage-08
• Chapter 5 Weightage-11
• Chapter 6 Weightage-12
• Chapter 7 Weightage-06
• Chapter 8 Weightage-16
• Chapter 9 Weightage-12
• Chapter 10 Weightage-07
• Chapter 11 Weightage-15
• Chapter 12 Weightage-06
• Chapter 13 Weightage-08
• Chapter 14 Weightage-12
• Chapter 15 Weightage-12
• Chapter 16 Weightage-10

Once students understand the Weightage of the chapter now start preparing class 8 Maths by the following methods

1.  Never miss your Maths class in school or tuition if still, you have any work which you can’t avoid make sure you have backup planning for how you are going to cover the missing classes. Maths is a subject of concepts application always remember that if you are going to miss anyone’s class the next class is difficult to understand because all the classes are interlinked.
2.  While in class make sure you are making proper notes of what the teacher is teaching to you, class 8 Maths need proper notes of all chapters because you are going to learn many new concepts and application of formulas in the numerical.
3.  Always write the important formulas list of the chapter before solving the questions given in the NCERT exercise and try to remember all the formulas used in the chapter. Don’t jump directly to NCERT solutions for class 8 Maths make sure you have attempted enough times before taking help from a solution to any questions.
4.  Maths is a subject of practice and in-class 8 Maths you need to do lots of practice to score good marks in the final exam as well as to have a good foundation in Maths for higher classes. To solve all the questions given in the NCERT textbook exercise as well as solve questions from NCERT exemplars.

How can we help you to score the highest in maths by our NCERT Solutions for class 8 maths?

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Chapters covered in NCERT Solutions for class 8 maths

Here are all chapters included in NCERT, and we provide each chapter with solutions in both Hindi and English, so it is easy to access anyone. And if you want to join our tutors, why are you waiting for it!

• NCERT solutions for class 8 Maths Chapter 1 - Rational Numbers

Chapter 1 - Rational Numbers consist of 2 Exercise and the subtopics covered in this chapter are.

1.1 Introduction

1.2 Properties Of Rational Numbers

1.3 Representation Of Rational Numbers On The Number Line

1.4 Rational Numbers Between Two Rational Numbers

• Exercise 1.1 This exercise consists of 11 Questions & Solutions (11 Short Answers)
• Exercise 1.2 This exercise consists of 7 Questions & Solutions (7 Short Answers)

Rational numbers help us to measure certain things which are not possible through integers cannot. Rational numbers are used to measure quantities like time, the volume of liquids or the mass of objects. In this chapter, students will understand the application and concepts of properties of integers, natural and whole numbers. Euclid was a Greek Mathematician who started a new way of thinking. He is famous for his ‘Elements of Geometry’, but his important contribution to the number theory remained unknown to many people e.g. Euclid’s Lemma which is a restatement of the long division process, we have been using for last many years. This lemma was known for a long time but was first recorded in Book VII of Euclid’s Elements. Euclid’s Division Algorithm (EDA) is based on this lemma.

A lemma is a proven statement which is used to prove other statements.

An algorithm is a series of well-defined steps which gives a procedure for solving a type of problem.

• NCERT solutions for class 8 Maths Chapter 2 - Linear Equations in One Variable

Chapter 2 - Linear Equations in One Variable consists of 6 Exercises and the subtopics covered in this chapter are.

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 variable on both sides

2.5 Some more applications

2.6 Reducing equations to a simpler form

2.7 Equations reducible to the linear form

• Exercise 2.1 This exercise consists of 12 Questions & Solutions (12 Short Answers)
• Exercise 2.2 This exercise consists of 16 Questions & Solutions (6 Long Answers, 10 Short Answers)
• Exercise 2.3 This exercise consists of 10 Questions & Solutions (3 Long Answers, 7 Short Answers)
• Exercise 2.4 This exercise consists of 10 Questions & Solutions (4 Long Answers, 6 Short Answers)
• Exercise 2.5 This exercise consists of 10 Questions & Solutions (1 Long Answer, 9 Short Answers)
• Exercise 2.6 This exercise consists of 7 Questions & Solutions (1 Long Answer, 6 Short Answers)

In the previous class, we studied linear equations and their solution. Linear equations had their applications in day-to-day life. We will take up some illustrations from daily life and solve them by using the concept of linear equations. We will revive the facts studied earlier and there will be equations which may not be linear, to begin with, but they can be brought to a linear form by multiplying both sides of the equation by a suitable expression.

A linear equation may have for its solution any rational number. In earlier classes, we had studied linear equations which had just a number (constant term) on one side of the equation. In this class, we will have expressions on both sides of the equation. An equation is simply the mathematical way to describe a relationship between two variables. The variables may be physical quantities, perhaps temperature and position for instance, in which case the equation tells us how one quantity depends on the other, so how the temperature varies with position. The simplest kind of relationship that two such variables can have is a linear relationship. This means that to find one quantity from the other you multiply the first by some number, then add another number to the result. Put mathematically, if we call the quantities x and y, then they are related by the equation y = MXMX + c", where we can choose any values for m and c. This is a linear equation. Fortunately, in real physical problems, quantities often are related linearly, so this equation is very commonly used.

• NCERT solutions for class 8 Maths Chapter 3 - Understanding Quadrilaterals

Chapter 3 - Understanding Quadrilaterals consist of 4 Exercise and the subtopics covered in this chapter are.

3.1 introduction

3.2 polygons

3.3 sum of the measures of the exterior angles of a polygon

3.4 kinds of quadrilaterals 3.5 Some Special Parallelograms

• Exercise 3.1 7 Questions & Solutions (1 Long Answer, 6 Short Answers)
• Exercise 3.2 6 Questions & Solutions (6 Short Answers)
• Exercise 3.3 12 Questions & Solutions (6 Long Answers, 6 Short Answers)
• Exercise 3.4 6 Questions & Solutions (1 Long Answer, 5 Short Answers)

Important points in Chapter 3 - Understanding Quadrilaterals

1.  A closed figure bounded by three or more line segments is called a polygon.
2.  A polygon each of which interior angles are less than 180 is called a convex polygon otherwise it is called a concave polygon.
3.  A regular polygon is a polygon whose all sides and all angles are equal.
4.  A polygon is called an irregular polygon if all the sides are not equal.
5.  A parallelogram is a quadrilateral in which both the pairs of opposite sides are parallel.
6.  A quadrilateral in which at least one pair of opposite sides is parallel is called a trapezium.
7.  A parallelogram with a pair of adjacent sides equal is called a rhombus.
8.  A parallelogram in which one angle is the right angle is called a rectangle.
9.  A parallelogram with a pair of adjacent sides equal and all angles equal to a right angle is called a square.

a. Every parallelogram is a trapezium, but every trapezium is not a parallelogram.

b. Every rhombus is a parallelogram, but the converse is not true.

c. Every rectangle is a parallelogram but the converse is not true.

d. Every square is a parallelogram but the converse is not true.

e. Every square is a rhombus but the converse is not true.

f. Every square is a rectangle but the converse is not true.

• NCERT solutions for class 8 Maths Chapter 4 - Practical Geometry

Chapter 4 - Practical Geometry consists of 5 Exercises and the subtopics covered in this chapter are.

4.1 Introduction

4.2 Constructing a quadrilateral

4.3 Some special cases

• Exercise 4.1 1 Questions & Solutions (1 Long Answer)
• Exercise 4.2 1 Questions & Solutions (1 Long Answer) 
• Exercise 4.3 1 Questions & Solutions (1 Long Answer)
• Exercise 4.4 1 Questions & Solutions (1 Long Answer) 
• Exercise 4.5 4 Questions & Solutions (4 Long Answers)

In earlier classes, we had studied to construct a triangle when some of its elements (sides and angles) are given. In this class, we will learn how to construct a quadrilateral when a suitable number of measurements (of sides and angles) are given. Five measurements can determine a quadrilateral specifically. In the construction of quadrilaterals, students are advised to first make a rough sketch of the quadrilateral and then with the help of a rough sketch, the student should start the actual steps of construction.

During the construction of quadrilaterals concepts about the angle sum property of quadrilaterals and other properties of special quadrilaterals are also taken into account.

• NCERT solutions for class 8 Maths Chapter 5 - Data Handling

Chapter 5 - Data Handling consists of 3 Exercises and the subtopics covered in this chapter are.

5.1 looking for information

5.2 organising data

5.3 grouping data

5.4 circle graph or pie chart 5.5 chance and probability

• Exercise 5.1-5 Questions & Solutions (5 Short Answers)
• Exercise 5.2-5 Questions & Solutions (3 Long Answers, 2 Short Answers)
• Exercise 5.3-6 Questions & Solutions (2 Long Answers, 4 Short Answers)

Important Points on Data handling

Primary data: Data collected by an investigation or a group of investigations for a definite purpose is called primary data.

Secondary data: When data is collected from a source which already had the information stored, the data is called secondary data.

Raw data/ungrouped data: The data obtained in the original form are called raw/ ungrouped data.

Range: The difference between the maximum value and the minimum value of the variable is known as range.

Frequency: The count of tally marks or the number of observations in a particular class is its frequency.

Class-interval: It is a specific small range in which various scores fall.

Class limits: Every interval has two class limits. The smallest number of the interval is called the lower limit while the greatest number of the interval is called the upper limit.

Class-mark: The variate value which lies mid-way between lower and upper limits of classes is called the d-value or central value of the class mark.

Class size: The difference between the upper and the lower class limits is called the width or size of the class interval

Frequency distribution It is the representation of grouped data in which frequencies are distributed over several classes (intervals Frequency in any class is centred at its classmark mid-point).

• NCERT solutions for class 8 Maths Chapter 6 - Squares and Square Roots

Chapter 6 - Squares and Square Roots consist of 3 Exercise and the subtopics covered in this chapter are.

6.1 Introduction

6.2 Properties of Square Numbers

6.3 Some more interesting patterns

6.4 Finding the square of a number

6.5 Square roots

• Exercise 6.1-9 Questions & Solutions (9 Short Answers)
• Exercise 6.2-2 Questions & Solutions (2 Short Answers)
• Exercise 6.3-10 Questions & Solutions (3 Long Answers, 7 Short Answers)
• Exercise 6.4-9 Questions & Solutions (3 Long Answers, 6 Short Answers)

In this chapter, we will learn how to find the square of numbers, squares of numbers by different patterns, squares by simple methods etc. We shall also study the method for finding the square roots of perfect square numbers by the prime factorization method, square roots by the long division method of integers, rational numbers and decimals etc.

If the number is not a perfect square, we cannot find its square root as an integer. However, we will try to find a fraction or a decimal number whose square is approximately equal to the given number.

• NCERT solutions for class 8 Maths Chapter 7 - Cubes and Cube Roots

Chapter 7 - Cubes and Cube Roots consist of 2 Exercise and the subtopics covered in this chapter are.

7.1 Introduction

7.2 Cubes

7.3 Cube roots 

• Exercise 7.1-4 Questions & Solutions (4 Short Answers)
• Exercise 7.2-3 Questions & Solutions (2 Long Answers, 1 Short Answer)

Cubes and cube roots form an integral part of modern algebra. Applications of cube and cube roots are widespread in mathematics. Knowledge of cube and cube roots finds its usefulness in solving problems related to surface areas and volumes.

In this chapter, we will learn various methods of finding cubes and cube roots of integers, natural numbers and rational numbers.

C.B.S.E. Syllabus:

• Cubes and cube roots (only factor method for numbers containing at most 3 digits)
• Estimating cube roots. Learning the process of moving nearer to the required number.

• NCERT solutions for class 8 Maths Chapter 8 - Comparing Quantities

Chapter 8 - Comparing Quantities consists of 2 Exercises and the subtopics covered in this chapter are.

8.1 Recalling Ratios And Percentages

8.2 Finding The Increase Or Decrease in per cent

8.3 Finding Discounts

8.4 Prices Related To Buying And Selling (profit And Loss)

8.5 Sales Tax/Value Added 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

• Exercise 8.1-6 Questions & Solutions (1 Long Answers, 5 Short Answers)
• Exercise 8.2-10 Questions & Solutions (4 Long Answers, 6 Short Answers)
• Exercise 8.3-12 Questions & Solutions (6 Long Answers, 6 Short Answers)

• NCERT solutions for class 8 Maths Chapter 9 - Algebraic Expressions and Identities

Chapter 9 - Algebraic Expressions and Identities consist of 2 Exercises and the subtopics covered in this chapter are.

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: introduction

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

• Exercise 9.1-4 Questions & Solutions (4 Short Answers)
• Exercise 9.2-5 Questions & Solutions (5 Short Answers)
• Exercise 9.3-5 Questions & Solutions (5 Short Answers)
• Exercise 9.4-3 Questions & Solutions (3 Short Answers)
• Exercise 9.5-8 Questions & Solutions (8 Short Answers)

The algebraic expression has been studied in previous classes. We are familiar with the terms, monomials, binomials, trinomials etc. In this chapter, we will extend our study to the wide application of algebraic expressions in modern algebra. Different operations on algebraic expressions viz. addition, subtraction, multiplication and division will be studied in this chapter. Applications of standard identities will also be treated in this chapter.

C.B.S.E. Syllabus:

•  Multiplication and division of algebraic expression. (Coefficient should be integers)
•  Some common errors (e.g. 2 + x not equal to 2x, 7x + y not equal to 7xy).
•  Identities (a +- b)2 = a2 2ab + b2, a2 – b2 = (a – b) (a + b).
•  Factorization (simple cases only) as examples the following types:  a(x + y), (x +- y)2, a2 – b2, (x + a) (x + b)

• NCERT solutions for class 8 Maths Chapter 10 - Visualising Solid Shapes

Chapter 10 - Visualising Solid Shapes consist of 2 Exercise and the subtopics covered in this chapter are.

10.1 introduction

10.2 views of 3d-shapes

10.3 mapping space around us

10.4 faces, edges and vertices

• Exercise 10.1-4 Questions & Solutions (4 Short Answers)
• Exercise 10.2-4 Questions & Solutions (3 Short Answer, 1 Long Answers)
• Exercise 10.3-8 Questions & Solutions (8 Short Answers)

In earlier classes, we studied the concept of plane figures requiring two dimensions. Such figures are called 2-D figures. Solid shapes have three dimensions, viz. length, breadth and height. These figures are known as 3-D figures. Polyhedrons involving prism and pyramid will be studied in this chapter.

Euler’s formula which gives the relationship between faces, edges and vertices of solid will also be studied in this lesson.

C.B.S.E. Syllabus:

• Identify and Match pictures with objects [more complicated e.g. nested, joint –D and 3-D shapes (not more than 2)]. •Drawing 2-D representation of 3-D objects (Continued and extended) •Counting vertices, edges and faces and verifying Euler’s relation for 3-D figures with flat faces (cubes, cuboids, tetrahedrons, prisms and pyramids).

• NCERT solutions for class 8 Maths Chapter 11 – Mensuration

Chapter 11 – Mensuration consists of 2 Exercises and the subtopics covered in this chapter are.

11.1 introduction

11.2 let us recall

11.3 area of trapezium

11.4 area of a general quadrilateral

11.5 area of a polygon

11.6 solid shapes

11.7 surface area of cube, cuboid, and cylinder

11.8 volume of cube, cuboid, and cylinder

11.9 volume and capacity

• Exercise 11.1-5 Questions & Solutions (5 Long Answers)
• Exercise 11.2-11 Questions & Solutions (11 Long Answers)
• Exercise 11.3-10 Questions & Solutions (2 Short Answers, 8 Long Answers)
• Exercise 11.4-8 Questions & Solutions (2 Short Answers, 6 Long Answers)

• NCERT solutions for class 8 Maths Chapter 12 - Exponents and Powers

Chapter 12 - Exponents and Powers consist of 2 Exercise and the subtopics covered in this chapter are.

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 form

• Exercise 12.1-7 Questions & Solutions (7 Long Answers)
• Exercise 12.2-4 Questions & Solutions (4 Short Answers)

• NCERT solutions for class 8 Maths Chapter 13 - Direct and Inverse Proportions

Chapter 13 - Direct and Inverse Proportions consist of 2 Exercises and the subtopics covered in this chapter are.

13.1 introduction

13.2 direct proportion

13.3 inverse proportion

• Exercise 13.1-10 Questions & Solutions (10 Short Answers)
• Exercise 13.2-11 Questions & Solutions (11 Long Answers)

• NCERT solutions for class 8 Maths Chapter 14 – Factorisation

Chapter 14 – Factorisation consists of 2 Exercises and the subtopics covered in this chapter are.

14.2 what is factorisation?

14.3 division of algebraic expressions

14.4 division of algebraic expressions continued (polynomial ÷ polynomial)

14.5 can you find the error?

• Exercise 14.1-3 Questions & Solutions (3 Short Answers)
• Exercise 14.2-5 Questions & Solutions (5 Short Answers)
• Exercise 14.3-5 Questions & Solutions (5 Short Answers)
• Exercise 14.4-21 Questions & Solutions (21 Short Answers)

We know that a number can be factored into two or more two numbers. For example, let a non-prime number 21, we can factor the number 21 into two-part as 3 × 7 or 3 × 7. In this chapter, we will study factors and factorization.

FACTORING:

In factoring, we have to find the number of numbers from which by multiplication we will get the number itself. In this way, we will express the given complicated polynomials or numbers into a product of simpler polynomials or numbers. This is known as factorization.

We do this all the time with numbers. For instance, here are a variety of ways to factor in 24.

24 = (4) (6) 24 = (3) (8) 24 = (2) (4) (3)

24 = (2) (2) (4) (3) 24 = (–4) (–6) 24 = (–2) (4) (–3)

But many more ways we can factor 24, The basic rule or method to find the factor is the factor of prime numbers. We can factor number 24 as 2×2×2×3 = 23 × 3.

We know that if a number has only two factors number itself and one, It is known as a prime number.

If we have to factor a number completely into positive prime factors, there will only be one way of doing it. For this, we have to find each prime factor of this number. Number 24 is complete factories as 24 = 2×2×2×3 = 23 × 3.

• NCERT solutions for class 8 Maths Chapter 15 - Introduction to Graphs

Chapter 15 - Introduction to Graphs consists of 2 Exercises and the subtopics covered in this chapter are.

15.1 introduction

15.2 linear graphs

15.3 some applications

• Exercise 15.1-7 Questions & Solutions (7 Short Answers)
• Exercise 15.2-4 Questions & Solutions (4 Short Answers)
• Exercise 15.3-2 Questions & Solutions (2 Short Answers)

• NCERT solutions for class 8 Maths Chapter 16 - Playing with Numbers

Chapter 16 - Playing with Numbers consists of 2 Exercises and the subtopics covered in this chapter are.

16.1 introduction

16.2 numbers in general form

16.3 games with numbers

16.4 letters for digits

16.5 tests of divisibility

• Exercise 16.1-10 Questions & Solutions (10 Short Answers)
• Exercise 16.2-4 Questions & Solutions (4 Short Answers)

Why does NCERT is the most important book for class 8 maths?

This book contains a detailed solution to all the questions at the end of a chapter. It covers concepts that students find challenging in class 8 maths, making it an essential guide for students who want to crack the JEE Main and JEE Advanced

NCERT Solutions for class 8 maths are a compilation of questions and their solutions based on the latest textbooks prescribed by NCERT.