NCERT Solutions for Class 9 Maths: The Class 9 Maths textbook solutions of exercises for all 15 chapters are included in this article. After an in-depth analysis, our expert panel has drafted the solutions so that students of class 9 can easily refer to them during their exams or to complete their homework. NCERT Solutions for Class 9 are written in a manner that is simple to follow and understand.
Latest Update: Due to the spread of Coronavirus, the officials of CBSE have deleted some of the concepts in CBSE Class 9. So students who are preparing for Class 9 Annual Examinations can skip those topics for their preparation. Check
CBSE Class 9 Maths Deleted Topics.
As you go through the article, you can download chapter wise resources and also check out NCERT Solutions for other subjects in Class 9. You can easily download the PDF without any signup and can refer to them without the internet. Scroll down and get access to the list of all the chapter links and PDFs for Class 9 Maths Solutions.
NCERT Solutions For Class 9 Maths
The list contains solutions to all the questions in the NCERT Book for Class 9 Maths in the order that is present within the textbook. Practicing these sums will create a strong foundation to understand math and help you solve additional problems of the same variety.
NCERT/CBSE Class 9 Maths consists of a total of 15 chapters. Students can click on the chapter-wise links to download the particular chapter solutions.
- NCERT Solutions for Class 9 Maths Chapter 1: Number Systems
- NCERT Solutions for Class 9 Maths Chapter 2: Polynomials
- NCERT Solutions for Class 9 Maths Chapter 3: Coordinate Geometry
- NCERT Solutions for Class 9 Maths Chapter 4: Linear Equations in Two Variables
- NCERT Solutions for Class 9 Maths Chapter 5: Introduction to Euclid’s Geometry
- NCERT Solutions for Class 9 Maths Chapter 6: Lines and Angles
- NCERT Solutions for Class 9 Maths Chapter 7: Triangles
- NCERT Solutions for Class 9 Maths Chapter 8: Quadrilaterals
- NCERT Solutions for Class 9 Maths Chapter 9: Areas of Parallelograms and Triangles
- NCERT Solutions for Class 9 Maths Chapter 10: Circles
- NCERT Solutions for Class 9 Maths Chapter 11: Constructions
- NCERT Solutions for Class 9 Maths Chapter 12: Heron’s Formula
- NCERT Solutions for Class 9 Maths Chapter 13: Surface Areas and Volumes
- NCERT Solutions for Class 9 Maths Chapter 14: Statistics
- NCERT Solutions for Class 9 Maths Chapter 15: Probability
Advantages Of Embibe’s NCERT Solutions For Class 9 Maths
Grade 9 Maths NCERT exercise solutions provided here are prepared by our academic experts at Embibe. Students can refer to Class 9 Maths NCERT 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 related problems.
- 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.
- Complete Assignments: After the completion of the lessons, students are given assignments to solve 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 Are NCERT Solutions For Class 9 Maths 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 Grade 9 Maths solutions will help you a lot. Solving the exercise will help you identify your mistakes and to improve upon them.
NCERT Class 9 Maths Chapter Description
Let’s look at all the chapters within the Std 9 Maths textbook, in brief, to get an idea about what to expect from them. For each chapter, the answers are also linked so you can directly download them and start studying as well.
NCERT Solutions For Class 9 Maths: Chapter 1 Number Systems
If we want to measure our height, we would use feet or meters. If we want to calculate values or measure objects in a very exact manner, we cannot use natural numbers. We have to use special types of numbers, such as rational numbers, irrational numbers, and integers. This chapter helps you understand these different kinds of numbers and how to use them to solve problems.
|Download – NCERT Solutions For Class 9 Maths Chapter 1 PDF|
NCERT Solutions For Class 9 Maths: Chapter 2 Polynomials
After understanding coefficients and variables, students learn polynomials, which are terms that are linked together using addition or subtraction. Let’s understand polynomials using this expression – “2x – 3y + a” where the value of x is unknown, and y also symbolizes an unknown number. Some are constant (does not change), others are variable (changes or varies with the situation).
|Download – NCERT Solutions For Class 9 Maths Chapter 2 PDF|
NCERT Solutions For Class 9 Maths: Chapter 3 Coordinate Geometry
If you take your house as the center (a dot), then you can start plotting different paths, to your nearest neighbors, a grocery store around you, etc. If you define your house’s coordinates as (0,0), then similarly, you can plot the nearby objects with ease and measure distances between buildings. This concept is called “Coordinate Geometry”. It helps us to make graphs, which later on help in understanding complex algebra in later chapters. The concepts within the chapter include the cartesian plane, x-axis and y-axis, origin, quadrants, and abscissa.
|Download – NCERT Solutions For Class 9 Maths Chapter 3 PDF|
NCERT Solutions For Class 9 Maths: Chapter 4 Linear Equations In Two Variables
Linear equations with two variables allow us to do interesting things with them. We can learn how to find the values of variables from these sorts of equations. For instance, if apples and oranges are two variables x and y. If the given equation is x+y = 20, we can determine the total value of both apples and oranges, but not individual values.
|Download – NCERT Solutions For Class 9 Maths Chapter 4 PDF|
NCERT Solutions For Class 9 Maths: Chapter 5 Introduction To Euclid’s Geometry
The word Geometry is formed of two greek words “Geo” and “Metron” which means Earth and to measure. The man who gave the earth its first primer on geometry was Euclid, whose work “Elements” from 325 B.C. is still used today.
In this chapter, we learn about some basic shapes and terms within geometry, and also have a deeper look into axioms (definitions), postulates (laws), and theorems. These are some building blocks of geometry that help us understand more complex geometry that will come in later chapters.
|Download – NCERT Solutions For Class 9 Maths Chapter 5 PDF|
NCERT Solutions For Class 9 Maths: Chapter 6 Line And Angles
We begin studying geometry with some basic elements of geometry such as points, lines, and angles. For instance, two separate points at any place can form a line, and when two lines intersect at a point or emerge from a single point, they form an angle. We see lines and angles everywhere around us: in all buildings, objects, and other complex structures. Learning these concepts will help you form a strong understanding of geometry.
|Download – NCERT Solutions For Class 9 Maths Chapter 6 PDF|
NCERT Solutions For Class 9 Maths: Chapter 7 Triangles
In the previous chapter, we talked about two points forming a line. In this chapter, we explore how connecting any 3 points form a triangle. Depending on the position of those 3 points, triangles can have different angles within them that help us identify different types of triangles. By understanding these basics, students will be able to learn some theorems associated with triangles in this chapter.
|Download – NCERT Solutions For Class 9 Maths Chapter 7 PDF|
NCERT Solutions For Class 9 Maths: Chapter 8 Quadrilaterals
After learning about structures formed by any 2 points (lines) and 3 points (triangles), we will learn about quadrilaterals, which are structures formed by connecting any 4 points. The chapter goes further into different types of quadrilaterals such as trapeziums, parallelograms, squares, rectangles, rhombuses, and kites. Learning about these different types of quadrilaterals allows us to understand the theorems associated with them and widen our understanding of geometry.
|Download – NCERT Solutions For Class 9 Maths Chapter 8 PDF|
NCERT Solutions For Class 9 Maths: Chapter 9 Areas Of Parallelograms And Triangles
Combining our understanding of parallelograms and triangles from previous chapters, this chapter studies the relationship between both of these structures and the area they occupy. The majority of the chapter is about several theorems formed on the basis of these structures and is necessary for learning about more complex structures later on in geometry.
|Download – NCERT Solutions For Class 9 Maths Chapter 9 PDF|
NCERT Solutions For Class 9 Maths: Chapter 10 Circles
After learning about lines and the shapes formed by using lines, we come to circles – some of the most common shapes seen around us in coins, dishes, wheels, and even the sun. We learn how to identify circles in the world of geometry and we understand a very commonly used irrational number – Pi (π). In this chapter, we also understand how we can use more symmetrical shapes and lines with circles and understand how to calculate their area with the help of Pi.
|Download – NCERT Solutions For Class 9 Maths Chapter 10 PDF|
NCERT Solutions For Class 9 Maths: Chapter 11 Constructions
In this chapter, students get a chance to apply the knowledge of different shapes to construct different types of triangles using several different rules and some common tools used for geometry. By the end of this chapter, students will get a better understanding of how to construct shapes using theorems and rules learned in the earlier chapters.
|Download – NCERT Solutions For Class 9 Maths Chapter 11 PDF|
NCERT Solutions For Class 9 Maths: Chapter 12 Heron’s Formula
Geometry is useful for so many things. One of them is finding areas of shapes. While we have understood how to determine the area of circles through Pi and so on, we will explore how Heron’s formula can help us find the area of triangles and other quadrilaterals by dividing them into triangles.
|Download – NCERT Solutions For Class 9 Maths Chapter 12 PDF|
NCERT Solutions For Class 9 Maths: Chapter 13 Surface Areas And Volumes
We learned how to determine areas in a two dimensional (2-D) manner in earlier chapters. In this one, we delve into the 3-D aspect of geometry and determine the surface area of cuboids and cylinders. Simple formulas and application of geometrical concepts can help in understanding this and also how to determine the volume of such shapes.
|Download – NCERT Solutions For Class 9 Maths Chapter 13 PDF|
Maths NCERT Solutions For Class 9: Chapter 14 Statistics
After studying Geometry, we explore another critical field in mathematics that is utilized in economics, business, and taken into account before any crucial decision is taken – Statistics. In Statistics, we collect data and learn how to represent it in ways that are understandable easily in a visual manner. We also learn how to determine the mean, median, and mode of a data set, and frequency distribution of data.
|Download – NCERT Solutions For Class 9 Maths Chapter 14 PDF|
NCERT Solutions For Class 9 Maths: Chapter 15 Probability
Is it possible to predict the future? Not really, but it is possible to mathematically predict the likelihood of an event occurring, which is known as probability. Through the understanding of basic formulas and some interesting problems, students will be able to determine probability in a mathematical way. It is an important chapter that will be more useful as you explore maths in higher education.
|Download – NCERT Solutions For Class 9 Maths Chapter 15 PDF|
Deleted Portions For Class 9 Maths Exams by CBSE
Due to the Covid-19 pandemic, some questions/topics have been deleted from the syllabus for the 2020-21 year final exams. While preparing for exams, students can avoid studying these topics.
|Number Systems||– Representation of terminating / non-terminating recurring decimals on the number line through successive magnification.|
– Definition of nth root of a real number.
– Explanation of every real number being represented by a unique point on the number line.
|Polynomials||– Motivate and State the Remainder Theorem with examples. |
– Statement and proof of the Factor Theorem – x3 + y3 + z3 – 3xyz
|Linear Equations in Two Variables||– Examples and problems related to ratio and proportions|
|Triangle||– Proof of the Theorem: Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).|
– Triangle inequalities and the relation between ‘angle and facing side’ inequalities in triangles.
|Circles||– Proof of the Theorem: There is one and only one circle passing through three given non-collinear points. If a line segment joining two points subtends an equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.|
|Heron’s Formula||– Application of Heron’s Formula in finding the area of a quadrilateral.|
|Statistics||– Histograms (with varying base lengths), frequency polygons. |
– Mean, median and mode of ungrouped data.
Some Important Questions For Class 9 Maths
|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 centre.|
|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.|
How To Prepare For CBSE Class 9 Mathematics With Embibe?
For getting excellent scores in Class 9 Mathematics, it is crucial to go through all the chapters, solve all exercises, and practice as much as possible. Embibe 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 free Class 9 Mock Tests. These will surely help in improving your score. Embibe offers a unique way to practice class 9 mathematics that ensures 3 things:
- Complete coverage of all topics
- Explanation for all questions
- Consistent score improvement
There are 3 ways to improve your scores in Class 9 Maths with Embibe:
Full Syllabus Tests
It is very flexible to take tests on Embibe. You have the option of taking topic-wise tests (geometry, algebra, etc.), chapter-wise tests (e.g. number systems, probability) as well as full tests that cover the entire syllabus.
At the end of each test, you will get a detailed analysis (you have to unlock the Advanced Feedback Analysis) that shows areas/chapters/topics which you can improve. So after recognizing these problem areas, you can practice those topics on Embibe.
Get Quick Answers to Your Queries on Embibe Ask
If you encounter some problems or topics during your study that you cannot fully understand, you can get help at Embibe Ask. Here, you can either type out your question or post an image of your query. At the same time, you can also check out queries posted by other students. All of these features are available to you for free. So, try out this feature the next time you face any problem while studying.
Frequently Asked Questions About CBSE Class 9 Maths Solutions
Check the frequently asked questions on NCERT Grade 9th Maths Solutions from below:
A: 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.
A: 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.
A: 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.
A: Of course. Ideally, you should attempt to solve them first. If you can’t, then refer to the solutions provided. Rather than learning the exact exercise problems, it is important to understand the concepts and develop problem-solving skills on your own. The solutions are merely for reference.
A: Practice is the key to score improvement. After going through the chapter, you should go through and refer to the solutions provided on this page. After doing that, you can go to embibe.com and start practicing the same chapters and attempt mock tests. By doing so, you will definitely get more confidence about improving your score.
A: The textbook exercises cover almost all the concepts covered in the textbook. However, practicing more problems expands your understanding of the concepts and then you can count solve any problem from any topic in the textbook easily.
A: This article contains chapter-wise links to both text-book solutions and detailed explanations by experts from Embibe. You can click on the download link and download the PDF file to refer to it anytime even without internet access.
A: Students can download the class 9 NCERT solution from this page. Click on the respective chapter-wise link to download the PDF solutions.
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.3972 Views