# NCERT Solutions for Class 9 Maths

## NCERT Solutions For Class 9 Maths

ToppersCBSE.com is presenting best NCERT Solutions for Class 9 Maths. We have created most accurate and detailed solutions for Class 9 Maths NCERT solutions. Class 9 Maths NCERT Solutions cover all the questions provided as per new revised syllabus in Class 9 math NCERT textbook. Students can download PDFs of NCERT book solutions for class 9 maths without any Registration or Login. These Solutions of NCERT Class 9 Maths cover all the topics included in the textbook-like Number System, Coordinate Geometry, Polynomials, Euclid’s Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, Probability, etc.The CBSE Class 9 Maths Solutions have been prepared by our experts in a well-structured format with easiest way of solving numerials.The students are suggested to practise all these solutions thoroughly for their exams. It will also help them in building a foundation for higher-level classes.

### NCERT Solutions For Class 8 Maths (Chapter-wise)

• Chapter 1 Number systems
• Chapter 2 Polynomials
• Chapter 3 Coordinate Geometry
• Chapter 4 Linear Equations in Two Variables
• Chapter 5 Introduction to Euclid Geometry
• Chapter 6 Lines and Angles
• Chapter 7 Triangles
• Chapter 9 Areas of Parallelograms and Triangles
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Heron’s Formula
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability

In Class 9 math, there are 15 Chapters. Each Chapter has some different concepts. Basics of Class 9 math is used in Maths of class 10 also. So it is very important to have proper knowledge of all basics. Strong base of Mathematics is deciding factor of future of a student.

NCERT Solutions for Class 9 Maths Chapter 1

• Class 9 Maths Number systems Exercise 1.1
• Class 9 Maths Number systems Exercise 1.2
• Class 9 Maths Number systems Exercise 1.3
• Class 9 Maths Number systems Exercise 1.4
• Class 9 Maths Number Systems Exercise 1.5
• Class 9 Maths Number Systems Exercise 1.6
• Number Systems Class 9 Extra Questions

NCERT Solutions for Class 9 Maths Chapter 2

• Class 9 Maths Polynomials Exercise 2.1
• Class 9 Maths Polynomials Exercise 2.2
• Class 9 Maths Polynomials Exercise 2.3
• Class 9 Maths Polynomials Exercise 2.4
• Class 9 Maths Polynomials Exercise 2.5
• Polynomials Class 9 Extra QuestionsNCERT Solutions for Class 9 Maths Chapter 3
• Class 9 Maths Coordinate Geometry Exercise 3.1
• Class 9 Maths Coordinate Geometry Exercise 3.2
• Class 9 Maths Coordinate Geometry Exercise 3.3
• Coordinate Geometry Class 9 Extra QuestionsNCERT Solutions for Class 9 Maths Chapter 4
• Class 9 Maths Linear Equations in Two Variables Exercise 4.1
• Class 9 Maths Linear Equations in Two Variables Exercise 4.2
• Class 9 Maths Linear Equations in Two Variables Exercise 4.3
• Class 9 Maths Linear Equations in Two Variables Exercise 4.4
• Linear Equations for Two Variables Class 9 Extra Questions
• Linear Equations in Two Variables Class 9 Word Problems and Important Questions
• NCERT Solutions for Class 9 Maths Chapter 5
• Class 9 Maths Introduction to Euclid Geometry Exercise 5.1
• Chapter 5 Introduction to Euclid’s Geometry Ex 5.2
• Introduction to Euclid’s Geometry Class 9 Extra QuestionsNCERT Solutions for Class 9 Maths Chapter 6• Class 9 Maths Lines and Angles Exercise 6.1• Class 9 Maths Lines and Angles Exercise 6.2• Class 9 Maths Lines and Angles Exercise 6.3• Lines and Angles Class 9 Extra QuestionsNCERT Solutions for Class 9 Maths Chapter 7• Class 9 Maths Triangles Exercise 7.1• Class 9 Maths Triangles Exercise 7.2• Class 9 Maths Triangles Exercise 7.3• Class 9 Maths Triangles Exercise 7.4• Chapter 7 Triangles Ex 7.5• Triangles Class 9 Extra QuestionsNCERT Solutions for Class 9 Maths Chapter 8• Class 9 Maths Quadrilaterals Exercise 8.1• Class 9 Maths Quadrilaterals Exercise 8.2• Quadrilaterals Class 9 Extra Questions• Quadrilaterals Class 9 Maths Important QuestionsNCERT Solutions for Class 9 Maths Chapter 9• Class 9 Maths Areas of Parallelograms and Triangles Exercise 9.1• Class 9 Maths Areas of Parallelograms and Triangles Exercise 9.2• Class 9 Maths Areas of Parallelograms and Triangles Exercise 9.3• Chapter 9 Areas of Parallelograms and Triangles Ex 9.4• Areas of Parallelograms and Triangles Class 9 Extra QuestionsNCERT Solutions for Class 9 Maths Chapter 10• Class 9 Maths Circles Exercise 10.1• Class 9 Maths Circles Exercise 10.2• Class 9 Maths Circles Exercise 10.3• Class 9 Maths Circles Exercise 10.4• Class 9 Maths Circles Exercise 10.5• Chapter 10 Circles Ex 10.6• Circles Class 9 Extra Questions• Circles Class 9 Maths Important Questions with AnswersNCERT Solutions for Class 9 Maths Chapter 11• Class 9 Maths Constructions Exercise 11.1• Class 9 Maths Constructions Exercise 11.2• Constructions Class 9 Extra Questions• Class 9 Maths Constructions Important QuestionsNCERT Solutions for Class 9 Maths Chapter 12• Class 9 Maths Heron’s Formula Exercise 12.1• Class 9 Maths Heron’s Formula Exercise 12.2• Heron’s Formula Class 9 Extra Questions• Class 9 Areas of Parallelograms and Triangles Worksheets with SolutionsNCERT Solutions for Class 9 Maths Chapter 13• Class 9 Maths Surface Areas and Volumes Exercise 13.1• Class 9 Maths Surface Areas and Volumes Exercise 13.2• Class 9 Maths Surface Areas and Volumes Exercise 13.3• Class 9 Maths Surface Areas and Volumes Exercise 13.4• Class 9 Maths Surface Areas and Volumes Exercise 13.5• Class 9 Maths Surface Areas and Volumes Exercise 13.6• Class 9 Maths Surface Areas and Volumes Exercise 13.7• Class 9 Maths Surface Areas and Volumes Exercise 13.8• Chapter 13 Surface Areas and Volumes Ex 13.9• Surface Areas and Volumes Class 9 Extra Questions• Surface Areas and Volumes Word Problems and Important QuestionsNCERT Solutions for Class 9 Maths Chapter 14• Class 9 Maths Statistics Exercise 14.1• Class 9 Maths Statistics Exercise 14.2• Class 9 Maths Statistics Exercise 14.3• Class 9 Maths Statistics Exercise 14.4• Statistics Class 9 Extra Questions• Maths Class 9 Statistics Important Questions with solutionsNCERT Solutions for Class 9 Maths Chapter 15• Class 9 Maths Probability Exercise 15.1• Probability Class 9 Extra Questions• Class 9 Probability Important Questions

## Features of NCERT Solutions for Class 8 Maths

• NCERT solutions of math are very easy to understand.
• Available free of cost for the students.
• Is exercise of chapter is covered separately in our NCERT solutions for Class 8 math.
• NCERT solutions will help the students to make their basic knowledge better.
• Exercises are formulated by our expert tutor to help exam preparations to attend good marks in the subject.
• Solutions are explained step by step manner.
• Formulas are mentioned to help students recall them easily.

### NCERT Solutions For Class 8 Maths – Demo Pages     In addition, students are given access to additional online study materials and resources, available on TOPPERSCBSE, such as notes, books, question papers, exemplar problems, worksheets, etc. Students are also can be benefited by practicing Class 8 Sample Papers to get an idea of the question pattern in the final exam.

#### NCERT Exercise-wise Solutions for Class 8 Maths

Basic idea about each chapter is given below indicating the various concepts and number of exercises. Students are advised to go through these NCERT Solutions Class 8. All the solutions are in line with the CBSE guidelines and presented in a step wise manner so that students can understand the logic behind every problem while practicing.

### Chapter 1 Rational Numbers

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 1 Exercises

• Exercise 1.1
• Exercise 1.2

### Chapter 2 Linear Equations in One Variable

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

NCERT Solutions for Class 8 Maths Chapter 2 Exercises

• Exercise 2.1
• Exercise 2.2
• Exercise 2.3
• Exercise 2.4
• Exercise 2.5
• Exercise 2.6

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 3 Exercises

• Exercise 3.1
• Exercise 3.2
• Exercise 3.3
• Exercise 3.4

### Chapter 4 Practical Geometry

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 4 Exercises

• Exercise 4.1
• Exercise 4.2
• Exercise 4.3
• Exercise 4.4
• Exercise 4.5

### Chapter 5 Data Handling

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 3 Exercises

• Exercise 5.1
• Exercise 5.2
• Exercise 5.3

### Chapter 6 Square and Square Roots

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

NCERT Solutions for Class 8 Maths Chapter 6 Exercises

• Exercise 6.1
• Exercise 6.2
• Exercise 6.3
• Exercise 6.4

### Chapter 7 Cube and Cube Roots

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 7 Exercises

• Exercise 7.1
• Exercise 7.2

### Chapter 8 Comparing Quantities

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 8 Exercises

• Exercise 8.1
• Exercise 8.2
• Exercise 8.3

### Chapter 9 Algebraic Expressions and Identities

This chapter, Algebraic Expressions and Identities, helps the students in understanding the concepts covered in the chapter. The terms, factors and coefficients related to Algebraic Expressions are discussed in the chapter. A brief on the basics of monomials, binomials and polynomials are also given in the chapter. Students learn the addition, subtraction and multiplication of Algebraic Expression. The concept of Identity is also covered in the chapter. The 5 exercises in the chapter cover all the concepts present in Algebraic Expressions and Identities.

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 9 Exercises

• Exercise 9.1
• Exercise 9.2
• Exercise 9.3
• Exercise 9.4
• Exercise 9.5

### Chapter 10 Visualizing Solid Shapes

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 10 Exercises

• Exercise 10.1
• Exercise 10.2
• Exercise 10.3

### Chapter 11 Mensuration

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 11 Exercises

• Exercise 11.1
• Exercise 11.2
• Exercise 11.3
• Exercise 11.4

### Chapter 12 Exponents and Powers

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 12 Exercises

• Exercise 12.1
• Exercise 12.2

### Chapter 13 Direct and Inverse Proportions

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 13 Exercises

• Exercise 13.1
• Exercise 13.2

### Chapter 14 Factorization

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

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 14 Exercises

• Exercise 14.1
• Exercise 14.2
• Exercise 14.3
• Exercise 14.4

### Chapter 15 Introduction to Graphs

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

NCERT Solutions for Class 8 Maths Chapter 15 Exercises

• Exercise 15.1
• Exercise 15.2
• Exercise 15.3

### Chapter 16 Playing with Numbers

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

NCERT Solutions for Class 8 Maths Chapter 16 Exercises

• Exercise 16.1
• Exercise 16.2

In Chapter 15, Visualising Solid Shapes of NCERT textbook deals with the plane figures and solids, faces, edges, vertices, nets for building 3-D shapes, drawing solids on a flat surface, oblique sketches, isometric sketches. Some more concepts covered in this chapter are visualising solid objects, viewing different sections of a solid, then another way is by shadow play.

Here you can find exercises solution links for the topics covered in this chapter.

NCERT Solutions for Class 8 Maths Chapter 15 Exercises

• Exercise 15.1
• Exercise 15.2
• Exercise 15.3
• Exercise 15.4

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