NCERT Solutions for Class 9 Maths: Are you looking for NCERT solutions for Class 9 Maths problems? Do not look anywhere else. In this article, we have provided answers to all the exercise questions/problems of the CBSE NCERT Class 9 Mathematics textbook. The Class 9 Maths exercise solutions provided here are prepared by our academic experts at Embibe. Students can refer to the Class 9 Maths solutions to complete their homework and also for exam preparation. The problems are solved in a simplified and organized manner to help you have a better understanding of the concepts and the related problems.
The CSBE NCERT Class 9 Maths solutions are available for all the chapters as PDF. Students can download the solutions as PDF without any signup formalities and study at their own convenience. Thus, scroll down and click on the respective chapter-wise links to download the NCERT Solutions for Class 9 Maths PDF for free.
Chapter-Wise NCERT Solutions For Class 9 Maths
The CBSE Class 9 Maths consists of a total of 15 chapters. Students can click on the chapter-wise links to land on the chapter pages and download the NCERT Class 10 Maths Solutions.
- a. Chapter 1: Number Systems
- b. Chapter 2: Polynomials
- c. Chapter 3: Coordinate Geometry
- d. Chapter 4: Linear Equations in Two Variables
- e. Chapter 5: Introduction to Euclid’s Geometry
- f. Chapter 6: Lines and Angles
- g. Chapter 7: Triangles
- h. Chapter 8: Quadrilaterals
- i. Chapter 9: Areas of Parallelograms and Triangles
- j. Chapter 10: Circles
- k. Chapter 11: Constructions
- l. Chapter 12: Heron’s Formula
- m. Chapter 13: Surface Areas and Volumes
- n. Chapter 14: Statistics
- o. Chapter 15: Probability
Advantages Of NCERT Solutions For Class 9 Maths
Go through the advantages of referring to the NCERT Solutions For Class 10 Maths:
- Reference Material to Solve Exercise Problems: The NCERT Class 9 Maths Solutions provided here will guide you in solving the exercise problems. The simple and step-by-step approach of the NCERT solutions will help you to easily follow the problem-solving procedures.
- For Practice and Revision: The NCERT Solutions provided will help students to do exam-focused practice covering all the important topics. Besides that, the NCERT solutions will also act as a great material for quick revision during exams.
- Better Understanding: The simplified, precise approach followed in these solutions will help students understand the problem-solving technique and related concepts. This in-depth and hands-on experience in solving the exercise problems will, in turn, boost your confidence and performance.
- To Complete Assignments: After the completion of the lessons, students are given assignments to solve the exercise problems. At times, students may get stuck in some questions. The NCERT solutions will guide you in this regard.
- To Ace Competitive Exams: The proper understanding of the concepts will not only be helpful in acing the upcoming exams but also lay a good foundation for your future academic journey. The NCERT textbooks will also act as a basic reference to crack various competitive exams. Be it cracking Government job exams, JEE, NEET, UPSC, and any other exam, NCERT books will be the basic reference. Hence, you must finish them thoroughly. This includes the exercise questions as well.
Why Is Class 9 Maths NCERT Solution Important?
Mathematics is usually seen as a very challenging subject among students. In reality, maths is not tough in nature. The difference lies in the approach of studying and dealing with problems. All you need is a proper understanding of the subjects and regular practice.
The most important part is to solve the problems on your own rather than to just glance through the steps. Negligence at the initial stage may turn into fear. So, don’t give it a chance to hijack you. If you practice and follow the right approach you will love the subject. This habit will not only help you ace Class 9 final exams but will also help you to face the Class 10 Maths exam with confidence.
In this process of understanding the concepts and solving problems, the NCERT Class 9 Maths solutions will help you a lot. Solving the exercise will help you identify your mistakes and to improve upon them.
CBSE NCERT Solutions For Class 9 Maths: Chapter Descriptions
Let’s look at what each of these chapters is about. Read the description of the Class 9 Maths to have a glimpse of each chapter.
NCERT Solutions For Class 9: Chapter 1 Number Systems
Imagine you are standing at position A and you decide to start walking in a straight line ahead. Say you take a walk of 1 m distance ahead. Now imagine if you are walking in a straight line. How much you can cover 2m, 3m, 5m, 10m, 100m, 1km, 100 km…? Will it end somewhere? The answer is: no, you can cover as much distance as you want to. There is no end. That’s why there is something called infinity represented by the symbol ‘∞’. So, in a number system, it starts from 0 (your current position), 1, 2, 3, 4, 5, goes on up to ∞.
|Exercise 1.1||4 Questions|
|Exercise 1.2||4 Questions|
|Exercise 1.3||9 Questions|
|Exercise 1.4||2 Questions|
|Exercise 1.5||5 Questions|
|Exercise 1.6||3 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 1 PDF|
NCERT Solutions For Class 9: Chapter 2 Polynomials
In order to understand polynomial, let’s consider this expression – 2x – 3y + a. Now in this expression, the x is something which we don’t know. y is also a symbol to represent an unknown quantity. Now there are two kinds of unknown quantities, one is varying (called as a variable) while other is constant. We usually represent variables as x, y, z while constant as a,b,c. Now anything like 2x – 3y + a which changes based on the variables like x and y can be called as Polynomials. We can represent this polynomial as f(x). Hence f(x) = 2x – 3y + a.
|Exercise 2.1||5 Questions|
|Exercise 2.2||4 Questions|
|Exercise 2.3||3 Questions|
|Exercise 2.4||5 Questions|
|Exercise 2.5||16 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 2 PDF|
NCERT Solutions For Class 9: Chapter 3 Coordinate Geometry
In this chapter, you will learn about how a point can be identified in a plane or space. When we talk about the point in space, we call it 3D geometry. While when we talk about a point in a plane, we call it as coordinate geometry. But why do you need to study this chapter? In order to understand the importance of this chapter, look at this example. If there is a girl standing on the streets, then how you will define her location? We will imagine a map having a north-south direction where the streets will be drawn. After having the reference you can easily point the location of the girl. Coordinate Geometry has many applications. One famous application is Maps.
|Exercise 3.1||2 Questions|
|Exercise 3.2||2 Questions|
|Exercise 3.3||2 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 3 PDF|
NCERT Solutions For Class 9: Chapter 4 Linear Equations In Two Variables
Linear Equation is the equation that has a degree of one. Equations like x + y = 3 and x + 2y – z =7 are linear equations. But here we are talking only about the linear equation in two variables. Hence we will not call the x + 2y – z = 7 as a linear equation in two variables since it has three variables x, y, and z. After understanding which kind of equations are linear equations in two variables, you can now proceed on to find out how we will form the equations from a problem.
So, assume that there are two kinds of fruits – apple and orange. The total number of apples and oranges is 20. But the number of apple and orange is unknown. Hence, we can form an equation: x + y = 20. Where x is the number of apple and y is the number of oranges. Now in order to find the number of apple and oranges, you need to have one more equation that has the relationship between apple and orange (in other words contains x and y). For example, if we know that the number of apples is twice that of the oranges then we can form an equation as x = 2y. We can now solve the above equations and thus, calculate the number of apples and oranges.
|Exercise 4.1||2 Questions|
|Exercise 4.2||4 Questions|
|Exercise 4.3||8 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 4 PDF|
NCERT Solutions For Class 9: Chapter 5 Introduction To Euclid’s Geometry
Throughout history, humans have used the knowledge of geometry to construct the pyramids, houses, statues, and drainage systems. Euclid was a Greek mathematician, who studied geometry. He defined point, line, straight line, surface, plane surface. In this chapter, you will also learn about Axioms and Postulates. Postulates are the assumptions that are specific to geometry. While the Axioms are the assumptions not specific to the geometry.
|Exercise 5.1||7 Questions|
|Exercise 5.2||2 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 5 PDF|
NCERT Solutions For Class 9: Chapter 6 Line And Angles
A line can only be formed by two or more points. The line segment can be defined as a line that has two endpoints. While the ray is the line with only one endpoint while the other point is free. If three or more lines are on the same line then they are called collinear points. An angle is also formed when two rays are originated from the same source but they are going in different directions.
|Exercise 6.1||6 Questions|
|Exercise 6.2||6 Questions|
|Exercise 6.3||6 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 6 PDF|
NCERT Solutions For Class 9: Chapter 7 Triangles
A triangle is formed when three intersecting lines are crossing each other. In this chapter, you will learn about the congruence of the triangle. Congruence means two objects having the same figure. The congruence of triangles means that there is more than 1 triangle that is similar in size and shape. One easy way to find out whether the two triangles are congruent or not is by finding the angle and the sides. If both are the same then they are called congruent triangles.
|Exercise 7.1||8 Questions|
|Exercise 7.2||8 Questions|
|Exercise 7.3||5 Questions|
|Exercise 7.4||6 Questions|
|Exercise 7.5||4 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 7 PDF|
NCERT Solutions For Class 9: Chapter 8 Quadrilaterals
A quadrilateral is a figure having four angles and four sides. The sum of all the angles of the quadrilateral is 360 degrees. There are different types of quadrilateral: trapezium, parallelogram, square, rectangle, rhombus, and kite. In this chapter, you will learn about the various theorems and properties of a quadrilateral. On the basis of these theorems, you will be able to solve various questions in this chapter.
|Exercise 8.1||12 Questions|
|Exercise 8.2||7 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 8 PDF|
NCERT Solutions For Class 9: Chapter 9 Areas Of Parallelograms And Triangles
In this chapter, you will learn about different figures lying on the same base or between the same parallels. There will be some activities that you need to perform. You will learn that parallelograms, as well as triangles on the same base and between the same parallels, are equal in area. This chapter is filled with theorems and you need to understand each of the theorems in order to solve the exercises.
|Exercise 9.1||1 Question|
|Exercise 9.2||6 Questions|
|Exercise 9.3||16 Questions|
|Exercise 9.4||8 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 9 PDF|
NCERT Solutions For Class 9: Chapter 10 Circles
The collections of all the points on a plane having a fixed distance from a certain point will lead to the formation of a circle. The fixed point is called the center while the fixed distance is called the radius. The circle divides the plane into three parts: inside the circle, on the circle, and outside the circle. If you take any two-point on the circle then the line formed by joining these two lines is called chords. If the line is passing through the center of the circle then the chord is called the diameter.
|Exercise 10.1||2 Questions|
|Exercise 10.2||2 Questions|
|Exercise 10.3||3 Questions|
|Exercise 10.4||6 Questions|
|Exercise 10.5||12 Questions|
|Exercise 10.6||10 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 10 PDF|
NCERT Solutions For Class 9: Chapter 11 Constructions
This chapter is more practical-oriented. Here students will be taking the geometry box, and with the help of a compass and various tools will be learning how to draw two lines at a different angle. Moving forward, you will also be drawing triangles when its base length, side length, and base angles are given. You will learn to draw the perpendicular bisector of a given line segment, construct an angle of 60°, construct a triangle given its base, a base angle and the sum of the other two sides, construct a triangle given its base, a base angle and the difference of the other two sides, construct a triangle given its perimeter and its two base angles.
|Exercise 11.1||5 Questions|
|Exercise 11.2||5 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 11 PDF|
NCERT Solutions For Class 9: Chapter 12 Heron’s Formula
Heron’s formula is used to find the area of the triangle. In this chapter, you will learn how this formula came into the picture. You will also learn how to calculate the area of the quadrilateral whose sides and one diagonal are given using Heron’s formula. The application of Heron’s formula can be used in various outdoor geometries.
|Exercise 12.1||6 Questions|
|Exercise 12.2||9 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 12 PDF|
NCERT Solutions For Class 9: Chapter 13 Surface Areas And Volumes
A cuboid is formed by six different rectangles. So if you want to find the surface area of the cuboid then you need to find the area of all the rectangles. After finding the areas of all the surfaces, you need to add them which will give you the Surface area of the cuboid. Similarly, you will also discover the surface area of a cylinder. A cylinder is formed by many circles. So if you take the area of one circle and multiply with the length and height of the rectangle that is formed when you unfold the cylinder, it will give you the surface area of the cylinder.
|Exercise 13.1||8 Questions|
|Exercise 13.2||11 Questions|
|Exercise 13.3||8 Questions|
|Exercise 13.4||9 Questions|
|Exercise 13.5||9 Questions|
|Exercise 13.6||8 Questions|
|Exercise 13.7||9 Questions|
|Exercise 13.8||10 Questions|
|Exercise 13.9||3 Questions|
|Download Class 9 Maths NCERT Solutions – Chapter 13 PDF|
NCERT Solutions For Class 9: Chapter 14 Statistics
Statistics deals with the representation of data. Data can be facts or figures which can be numerical. In this chapter, you will be performing various exercises on the given data. You will learn tally, graphical representation of data like bar graphs, histogram, frequency polygons. Going forward you will learn measures of central tendency of ungrouped data which are nothing but mean, median, and mode.
|Exercise 14.1||2 questions|
|Exercise 14.2||9 questions|
|Exercise 14.3||9 questions|
|Exercise 14.4||6 questions|
|Download Class 9 Maths NCERT Solutions – Chapter 14 PDF|
NCERT Solutions For Class 9: Chapter 15 Probability
In this chapter, you will be learning about how likely an event will occur. An event for an experiment is the collection of some outcomes of the experiment. You will also learn how and when to use the empirical formula. In this chapter, you will be given various scenarios where you will be asked to calculate the probability of the occurrence. This chapter is very much important as it will help you in higher studies.
|Exercise 15.1||10 Question|
|Download Class 9 Maths NCERT Solutions – Chapter 15 PDF|
FAQs On Class 9 Maths NCERT Solutions
Check the frequently asked questions on NCERT Class 9 Maths Solutions from below:
A1. The Class 9 Maths NCERT Solutions provide answers to all the exercise questions. The problems are solved in a simple and step-by-step manner to help students. This will help you understand the concepts and problem-solving methods. You can use it for practice and revision during exams.
A2. Yes, you can refer to the solutions to solve and practice the exercise questions which will help you learn and understand the problem-solving methods. Good practice and proper understanding will help you to ace not only the board exams but also the competitive exams such as JEE, BITSAT, State CET, government exams, etc.
A3. The NCERT Solutions at Embibe is always available on our website. There are no restrictions, and students can study whenever they wish to. The solutions are free and also available for download.
A4. Yes, as Mathematics is an application-based subject, students will have to solve the questions. Firstly, students must try and solve the problems on their own. In case they are not able to, they can use the solutions for reference and learn the problem-solving method.
A5. A total of 15 chapters are there in the NCERT Class Maths textbook. The chapters are Chapter 1 – Number System, Chapter 2 – Polynomials, Chapter 3 – Coordinate Geometry, Chapter 4 – Linear Equations in Two Variables, Chapter 5 – Introduction to Euclid’s Geometry, Chapter 6 – Lines and Angles, Chapter 7 – Variables, Chapter 8 – Quadrilaterals, 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 and Chapter 15 –
A6. Referring to the NCERT textbook and solving all the exercise questions will help you score good marks. NCERT textbook is one of the most comprehensive study resources. Proper understanding, regular practice, and improving on your weaker areas will help you score the best marks in board exams.
A7. Yes, we have provided the solutions to all the Class 9 Maths exercise questions here in this article. Download the solutions for free.
A9. Students can download the class 9 NCERT solution from this page. Click on the respective chapter-wise link to download the PDF solutions.
We have now provided you with NCERT Solutions For Class 9 Maths. It is advisable that you use this as reference material and learn the problem-solving process only when you are unable to solve the questions on your own. You can also practice model test papers and previous year papers for better practice and understanding of the subject.
At Embibe, you can solve free Class 9 Practice Questions for Science and Maths and go through the solutions if necessary. You can also attempt a free Class 9 Mock Test. These will surely help in improving your score.
We hope this article helps you. if you have any queries, feel free to post them below in the comment section. We will get back to you as soon as possible. Visit embibe.com for more NCERT solutions.1753 Views