NCERT Solutions for Class 9 Maths CBSE: Are you looking for NCERT solutions for Class 9 Maths? your search ends here. In this article, we have provided answers to all the exercise questions/problems of CBSE NCERT Class 9 Mathematics textbook. Class 9 Maths exercise solutions provided here are prepared by our academic experts at Embibe. Students can refer to 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 chapters as PDF. Students can download PDF solutions without any signup formalities and study at their own convenience. Thus, scroll down and click on the respective chapter-wise links to download free NCERT Solutions for Class 9 Maths PDF.
Solve NCERT Class 9 Maths Questions Here
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 Embibe’s 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.
Check Class 9 Maths CBSE Syllabus Here
CBSE NCERT Solutions For Class 9 Maths: Chapter Descriptions
In the sections below, you will find a brief description of each chapter. You can go through the description to have a glimpse of each chapter and to get an overview of the Class 9 Maths syllabus. We have also provided a direct download link to the NCERT solution PDF after the chapter description. Just click on the link to view and download the solution PDF.
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 ∞.
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Exercise 1.1 |
4 Questions |
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Exercise 1.2 |
4 Questions |
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Exercise 1.3 |
9 Questions |
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Exercise 1.4 |
2 Questions |
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Exercise 1.5 |
5 Questions |
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Exercise 1.6 |
3 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 2.1 |
5 Questions |
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Exercise 2.2 |
4 Questions |
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Exercise 2.3 |
3 Questions |
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Exercise 2.4 |
5 Questions |
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Exercise 2.5 |
16 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 3.1 |
2 Questions |
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Exercise 3.2 |
2 Questions |
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Exercise 3.3 |
2 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 4.1 |
2 Questions |
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Exercise 4.2 |
4 Questions |
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Exercise 4.3 |
8 Questions |
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Exercise 4.4 |
2 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 5.1 |
7 Questions |
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Exercise 5.2 |
2 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 6.1 |
6 Questions |
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Exercise 6.2 |
6 Questions |
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Exercise 6.3 |
6 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 7.1 |
8 Questions |
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Exercise 7.2 |
8 Questions |
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Exercise 7.3 |
5 Questions |
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Exercise 7.4 |
6 Questions |
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Exercise 7.5 |
4 Questions |
| Class 9 Maths NCERT Solutions – Download Chapter 7 PDF |
Download NCERT Class 9 Textbooks
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.
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Exercise 8.1 |
12 Questions |
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Exercise 8.2 |
7 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 9.1 |
1 Question |
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Exercise 9.2 |
6 Questions |
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Exercise 9.3 |
16 Questions |
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Exercise 9.4 |
8 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 10.1 |
2 Questions |
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Exercise 10.2 |
2 Questions |
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Exercise 10.3 |
3 Questions |
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Exercise 10.4 |
6 Questions |
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Exercise 10.5 |
12 Questions |
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Exercise 10.6 |
10 Questions |
| Class 9 Maths NCERT Solutions – Download Chapter 10 PDF |
NCERT Solutions For Class 9: Chapter 11 Constructions
This chapter is more practical-oriented. Here students can use the geometry boxes, 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.
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Exercise 11.1 |
5 Questions |
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Exercise 11.2 |
5 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 12.1 |
6 Questions |
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Exercise 12.2 |
9 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 13.1 |
8 Questions |
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Exercise 13.2 |
11 Questions |
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Exercise 13.3 |
8 Questions |
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Exercise 13.4 |
9 Questions |
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Exercise 13.5 |
9 Questions |
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Exercise 13.6 |
8 Questions |
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Exercise 13.7 |
9 Questions |
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Exercise 13.8 |
10 Questions |
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Exercise 13.9 |
3 Questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 14.1 |
2 questions |
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Exercise 14.2 |
9 questions |
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Exercise 14.3 |
9 questions |
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Exercise 14.4 |
6 questions |
| Class 9 Maths NCERT Solutions – Download 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.
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Exercise 15.1 |
10 Question |
| Class 9 Maths NCERT Solutions – Download Chapter 15 PDF |
How To Prepare For CBSE 9th Grade Maths?
To help the students understand the subject better and get better marks, we have listed some of the preparation tips for CBSE 9th grade Maths:
- Practice is the key to get good marks in Maths. To understand the subject better, you should practice problems regularly.
- While preparing for the exam, start with the topics that you can understand easily. Once you are done with these, move on to more difficult topics.
- Solve all the exercises in the NCERT textbook.
- Make a habit of solving test papers and previous years CBSE exam papers, especially before the exam.
- Make notes for important formulas and theorems.
- Refer to NCERT Solutions for Class 9 Maths by Embibe to clear your doubts.
Some Important Questions For Class 9 Maths
Some important questions for Class 9 Maths are provided below:
| 1. Prove the statement: Equal chords of a circle are equidistant from the center. |
| 2. Draw a right triangle with a base length of 10 cm and the sum of its hypotenuse and the other side is 20 cm. |
| 3. Calculate the area of a right-angled triangle with base length of 11 cm and height of 7 cm. |
| 4. Find the area of a triangular plot if its sides are in the ratio of 2:3:5 and its perimeter is 540 m. |
| 5. State Euclid’s fifth postulate. |
| 6. Calculate the area of the corresponding major segment of a circle of radius 20 cm if a chord of the circle makes an angle of 90° at the center. |
| 7. A bull is tied in the middle of a square lawn of grass with each side of 30 m with a rope of length 5 m. Find the increase in area of the lawn in which the bull can graze if the length of the rope is increased by 2.5 m. |
| 8. Find the solution: x + y = 58; y + z = 13; z + x = 34 |
| 9. A triangle ABC is given with a right angle at A and AL is perpendicular to BC. Prove that ∠BAL = ∠ACD. |
| 10. Find all the angles of a triangle if the exterior angles obtained on extending the base of a triangle both ways are 90° and 60°. |
| 11. Find the product: (x – 4y) (x + 2y) (3x + 5y2) |
| 12. Find the probability of getting heads if 2 coins are thrown together. |
| 13. If one of the angles in a parallelogram ABCD is 60°, find the measure of all the angles. |
| 14. Find the mode of the given values: 11, 3, 10, 8, 11, 6, 5, 8, 17, 1, and 9. |
| 15. Find the ratio of the volumes of two cylinders if their heights of are in the ratio of 4:2 and their radii are in the ratio of 5:6. |
Learn Class 9 Lessons Online With Embibe
With the entire country being under the lockdown, students have an opportunity to learn and study through online mode. The MHRD Ministry has launched the platform Diksha where students can watch videos and learn various topics and concepts.
Embibe also offers you a medium to learn and practice online. 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. Follow the steps given below to take a mock test or practice questions at Embibe:
- – 1st Step: Visit embibe.com. You can take the test or practice questions online without logging in but we advise you to log in to have the best experience.
- – 2nd Step: Click on the ‘Take a Test’ tab below the search field.
- – 3rd Step: Click on the ‘change your goal’ tab and select ‘Foundation-09’.
- – 4th Step: Choose the subject – Science or Maths.
- – 5th Step: To take the test on, click on ‘Start Test’. If you want to take a chapter-wise test, select the chapter of your choice from the menu.
- – 6th Step: You can click on the ‘Start Practice’ tab to practice Class 9 Maths questions.
Get Answers To Your Queries On Embibe Ask
Embibe presents a unique platform where you will get answers to all your academic queries. At Embibe Ask, you can ask any question or upload an image of your question and get solutions from our experts. You can also browse through the questions/queries uploaded by others. The best feature of Embibe Ask is you can access it for free! So go to Embibe Ask and get answers to your questions today.
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 –
Probability.
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.
Download Free NCERT Solutions For Class 9 Science PDF Here
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.
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.
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