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NCERT Solutions for Class 9 Maths: Download PDF
NCERT Solutions for Class 9 Maths: The Class 9 students often face difficulties while preparing for the exam. Therefore, while solving the questions and exercise, a chapter-wise NCERT Solution for Class 9 Maths will offer practical problem-solving strategies for them. Therefore, Embibe has provided comprehensive solutions for all chapters from this textbook, which can be downloaded in a PDF format for offline reference.
These Class 9 Mathematics solution offers chapter-wise questions and solution for the candidates to gain good marks in their final exam of CBSE Class 9. NCERT Solutions for Mathematics Class 9 have been provided in PDF form for 11 chapters from Number System to Probability. Read this article to get the complete details about NCERT Class 9 Maths Solutions and the steps to download.
| Latest Update: 👉 The CBSE Term 1 results are expected to be released in March 2022. 👉 The board has released the CBSE Class 12 Term 2 exam date sheets! The Term 2 examination will commence from April 26, 2022. |
Chapterwise CBSE NCERT Solutions for Class 9 Maths
NCERT Class 9 Maths book consists of 15 chapters. The following list contains links to solutions for all questions from every chapter in the NCERT Books for Class 9 Maths. Moreover, our reliable 9th CBSE Maths Guide PDF document will create a strong foundation to understand the subject and help you solve additional problems of the same variety. Students can click on the chapter-wise links to download the particular chapter solutions.
Advantages of Embibe’s NCERT Solutions for Class 9 Maths
Students can refer to NCERT Class 9th Maths Guide as an aid to quickly finish their homework and exam preparation. In this Std 9 Practice Work solutions PDF, the problems are solved in a simple and orderly manner to help you better understand the related concepts. The main benefits of using this NCERT solution for Class 9 Maths PDF are pointed out as follows:
1– Reference Material to Solve Exercise Problems: The class 9 Maths NCERT solutions provided here will guide you in solving the exercise problems. The simple and step-by-step and straightforward approach of the NCERT solutions will help you follow the problem-solving procedures easily.
2- For Practice and Revision: The NCERT Solutions provided will help students follow a CBSE exam-focused practice methodology as it covers all the important topics given in the textbook. Besides that, the NCERT solutions will also act as excellent material for quick revision during exams.
3- Better Understanding: These solutions follow a simplified yet precise approach in solving the problems. This will help students understand the problem-solving technique and related concepts easily. This in-depth and hands-on experience in solving exercise problems will, in turn, boost the confidence and overall performance of students.
4- Complete Homework/Assignments: At times, students get stuck while solving some tricky exercise questions for their homework or class assignments. The NCERT solutions will act as a guide to help them out in such situations and will save them from wasting excessive time and effort in the initial learning stage. Wards may have to refer to the solutions multiple times until they become familiar with difficult or confusing concepts. But eventually, they will learn the concepts and formulas by heart.
5- To Ace Competitive Exams: The proper understanding of the concepts will help ace the upcoming exams and lay a good foundation for your future academic journey. The NCERT textbooks will also be 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 Solutions for CBSE Class 9 Maths Important?
Mathematics is usually seen as a very challenging subject by CBSE class 9 students. In reality, Maths is not tough. All you need is some guidance on the proper understanding of the concepts, techniques to solve problems and regular practice. In these two domains, i.e., understanding the concepts and solving problems, the NCERT Grade 9 Maths solutions will help you a lot. Referring to the solutions will help you identify your mistakes and improve upon them. Eventually, you will develop a better understanding of the subject and the skill to remember and use these techniques without any reference. This habit will help you ace Class 9 final exams and help you to face the Class 10 Maths exam with confidence.
NCERT Class 9 Maths Chapter Description
NCERT Class 9 Maths Solutions are available as a free PDF download from Embibe. Subject matter experts with in-depth expertise and years of experience create these solutions. The Class 9 Maths NCERT Solutions PDF follows the most recent NCERT standards and exam format, making it a credible exam preparation resource. You may also save the NCERT Solutions for Class 9 Maths PDF to your computer and use it for a fast review before the examinations. Furthermore, among the many online resources available for the Class 9 Maths Syllabus, Class 9th Maths NCERT answers are regarded as one of the most reliable ways to prepare for your Class 9 exams.
To assist you in answering the questions in the CBSE Maths Class 9 textbook, get the NCERT solution Class 9th Maths as a free PDF download.
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.
Practice 9th CBSE Exam Questions
NCERT Solutions for Class 9 Maths Chapter 1: Number Systems (Term I)
If we want to measure our height, we would use feet or metres. If we want to calculate values or measure objects accurately, we cannot use natural numbers. We have to use special numbers, such as rational numbers, irrational numbers, and integers. This chapter helps you understand these different kinds of numbers and how to solve problems.
Types of Exercise Questions in Class 9 Maths Chapter 1
(i) Exercise 1.1 – 4 Questions (4 short answers)
(ii) Exercise 1.2 – 4 Questions (4 short answers)
(iii) Exercise 1.3 – 9 Questions (8 short answers, 1 long answer)
(iv) Exercise 1.4 – 2 Questions (2 long answers)
(v) Exercise 1.5 – 5 Questions (4 short answers, 1 long answer)
(vi) Exercise 1.6 – 3 Questions (3 short answers)
NCERT Solutions for Class 9 Maths Chapter 2: Polynomials (Term II)
After understanding coefficients and variables, students learn polynomials, which 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).
Types of Exercise Questions in Class 9 Maths Chapter 2
(i) Exercise 2.1 – 5 Questions (5 short answers)
(ii) Exercise 2.2 – 4 Questions (4 short answers)
(iii) Exercise 2.3 – 3 Questions (3 short answers)
(iv) Exercise 2.4 – 5 Questions (4 short answers, 1 long answer)
(v) Exercise 2.5 – 16 Questions (9 short answers, 5 long answers, 2 very long answers)
NCERT Solutions for Class 9 Maths Chapter 3: Coordinate Geometry (Term I)
If you take your house as the centre (a dot), you can start plotting different paths to your nearest neighbours, a grocery store around you, etc. If you define your house’s coordinates as (0,0), you can similarly plot the nearby objects with ease and measure distances between buildings. This concept is called “Coordinate Geometry”. It helps us make graphs, which will help us understand complex algebra in later chapters. The concepts within the chapter include the cartesian plane, x-axis and y-axis, origin, quadrants, and abscissa.
Types of Exercise Questions in Class 9 Maths Chapter 3
(i) Exercise 3.1 – 2 Questions (1 short answer, 1 long answer)
(ii) Exercise 3.2 – 2 Questions (2 short answers)
(iii) Exercise 3.3 – 2 Questions (1 short answer, 1 long answer)
NCERT Solutions for Class 9 Maths Chapter 4: Linear Equations in Two Variables (Term I)
Types of Exercise Questions in Class 9 Maths Chapter 4
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, 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.
(i) Exercise 4.1 – 2 Questions (2 short answers)
(ii) Exercise 4.2 – 4 Questions (3 short answers, 1 long answer )
(iii) Exercise 4.3 – 8 Questions (4 short answers, 4 long answers)
(iv) Exercise 4.4 – 2 Questions (2 long answers)
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 will 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 will help us understand more complex geometry that will come in later chapters.
Types of Exercise Questions in Class 9 Maths Chapter 5
(i) Exercise 5.1 – 7 Questions (4 short answers, 3 long answers)
(ii) Exercise 5.2 – 2 Questions (1 short answer, 1 long answer)
NCERT Solutions for Class 9 Maths Chapter 6: Line And Angles (Term I)
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.
Types of Exercise Questions in Class 9 Maths Chapter 6
(i) Exercise 6.1 – 6 Questions (5 short answers, 1 long answer)
(ii) Exercise 6.2 – 6 Questions (3 short answers, 3 long answers)
(iii) Exercise 6.3 – 6 Questions (5 short answers, 1 long answer)
NCERT Solutions for Class 9 Maths Chapter 7: Triangles (Term I)
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.
Types of Exercise Questions in Class 9 Maths Chapter 7
(i) Exercise 7.1 – 8 Questions (6 short answers, 2 long answers)
(ii) Exercise 7.2 – 8 Questions (6 short answers, 2 long answers)
(iii) Exercise 7.3 – 5 Questions (3 short answers, 2 long answers)
(iv) Exercise 7.4 – 6 Questions (5 short answers, 1 long answer)
(v) Exercise 7.5 – 4 Questions (3 short answers, 1 long answer)
NCERT Solutions for Class 9 Maths Chapter 8: Quadrilaterals (Term II)
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 quadrilaterals, such as trapeziums, parallelograms, squares, rectangles, rhombuses, and kites. Learning about these different quadrilaterals allows us to understand the theorems associated with them and widen our understanding of geometry.
Types of Exercise Questions in Class 9 Maths Chapter 8
(i) Exercise 8.1 – 12 Questions (2 short answers, 6 long answers, 4 very long answers)
(ii) Exercise 8.2 – 7 Questions (2 short answers, 2 long answers, 3 very long answers)
Attempt 9th CBSE Exam Mock Tests
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.
Types of Exercise Questions in Class 9 Maths Chapter 9
(i) Exercise 9.1 – 1 Question (1 short answer)
(ii)Exercise 9.2 – 6 Questions (5 short answers, 1 long answer)
(iii) Exercise 9.3 – 16 Questions (12 short answers, 4 long answers)
(iv) Exercise 9.4 – 8 Questions (4 short answers, 1 long answer, 3 very long answers)
NCERT Solutions for Class 9 Maths Chapter 10: Circles (Term II)
After learning about lines and the shapes formed by using lines, we come to circles – one 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.
Types of Exercise Questions in Class 9 Maths Chapter 10
(i) Exercise 10.1 – 2 Questions (2 short answers)
(ii) Exercise 10.2 – 2 Questions (2 long answers)
(iii) Exercise 10.3 – 3 Questions (3 long answers)
(iv) Exercise 10.4 – 6 Questions (6 long answers)
(v) Exercise 10.5 – 12 Questions (12 long answers)
(vi) Exercise 10.6 – 10 Questions (10 long answers)
NCERT Solutions for Class 9 Maths Chapter 11: Constructions (Term II)
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.
Types of Exercise Questions in Class 9 Maths Chapter 11
(i) Exercise 11.1 – 5 Questions (2 short answers, 2 long answers, 1 very long answer)
(ii) Exercise 11.2 – 5 Questions (5 very long answers)
NCERT Solutions for Class 9 Maths Chapter 12: Heron’s Formula (Term I)
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.
Types of Exercise Questions in Class 9 Maths Chapter 12
(i) Exercise 12.1 – 6 Questions (2 short answers, 2 long answers, 2 very long answers)
(ii) Exercise 12.2 – 9 Questions (4 long answers, 5 very long answers)
NCERT Solutions for Class 9 Maths Chapter 13: Surface Areas and Volumes (Term II)
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 applications of geometrical concepts can help in understanding this and also how to determine the volume of such shapes.
Types of Exercise Questions in Class 9 Maths Chapter 13
(i) Exercise 13.1 – 8 questions
(ii) Exercise 13.2 – 11 questions
(iii) Exercise 13.3 – 8 questions
(iv) Exercise 13.4 – 9 questions
(v) Exercise 13.5 – 9 questions
(vi) Exercise 13.6 – 8 questions
(vii) Exercise 13.7 – 9 questions
(viii) Exercise 13.8 – 10 questions
(ix) Exercise 13.9 – 3 questions
NCERT Solutions for Class 9 Maths Chapter 14: Statistics (Term I)
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 made – Statistics. In Statistics, we collect data and learn how to represent it in understandable ways 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.
Types of Exercise Questions in Class 9 Maths Chapter 14
(i) Exercise 14.1 – 2 questions (2 short answers)
(ii) Exercise 14.2 – 9 questions (9 long answers)
(iii) Exercise 14.3 – 9 questions (6 short answers, 3 long answers)
(iv) Exercise 14.4 – 6 questions (2 short answers, 4 long answers)
NCERT Solutions for Class 9 Maths Chapter 15: Probability (Term II)
Is it possible to predict the future? Not really, but it is possible to mathematically predict the likelihood of an event occurring, known as probability. Students will mathematically determine probability by understanding basic formulas and some interesting problems. It is an important chapter that will be more useful as you explore maths in higher education.
Types of Exercise Questions in Class 9 Maths Chapter 15
(i) Exercise 15.1 – 10 Question (4 short answers, 3 long answers, 3 very long answers)
CBSE Class 9 Maths Unit wise Weightage
CBSE Class 9 exams will be conducted as per the new assessment policy. Students appearing for the CBSE Class 9 Maths exams should be completely aware of the syllabus, exam pattern to ace the examination. CBSE has released the rationalised syllabus for Term I and II based on which the exams will be conducted.
CBSE has released the rationalised syllabus for Term I and II based on which the exams will be conducted.
CBSE Class 9 Maths Unit-wise Weightage Term I
| Unit Name | Marks |
| Unit 1: Number systems | 08 |
| Unit 2: Algebra | 05 |
| Unit 3: Coordinate Geometry | 04 |
| Unit 4: Geometry | 13 |
| Unit 5: Mensuration | 4 |
| Unit 6: Statistics and Probability | 6 |
| Total | 40 |
| Internal Assessment | 10 |
| Total | 50 |
Internal Assessment Class 9 Term I
Internal assessment of Class 9 Term I carries 10 marks. The details of the weightage are listed as follows.
| Internal Assessment | Marks |
| Periodic Tests | 03 |
| Multiple Assessments | 02 |
| Portfolio | 02 |
| Student Enrichment Activities-practical work | 03 |
| Total Marks | 10 |
CBSE Class 9 Maths Unit-wise Weightage Term II
Check the Unit wise weightage for CBSE Class 9 Maths Term II from the below-mentioned table.
| Unit Name | Marks |
| Unit 1: Algebra (Cont.) | 12 |
| Unit 2: Geometry (Cont.) | 15 |
| Unit 3: Mensuration (Cont.) | 09 |
| Unit 6: Statistics and Probability | 04 |
| Total | 40 |
| Internal Assessment | 10 |
| Total | 50 |
Internal Assessment Class 9 Term II
Internal assessment of Class 9 Term II carries 10 marks. The details of the weightage are listed as follows.
| Internal Assessment | Marks |
| Periodic Tests | 03 |
| Multiple Assessments | 02 |
| Portfolio | 02 |
| Student Enrichment Activities-practical work | 03 |
| Total Marks | 10 |
Some Important Questions for Class 9 Maths
| 1. Prove the statement: Equal chords of a circle are equidistant from the centre. |
| 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 a base length of 11 cm and a 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 the 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 being 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
FAQs on CBSE NCERT Solutions for Class 9 Maths
Check the frequently asked questions on NCERT 9th Grade Maths Solutions PDF from below:
Q.1: Is there any time restriction in accessing the NCERT Solutions?
Ans: 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.
Q.2: How can I download NCERT Solutions for Grade 9 Maths exercise questions?
Ans: Students can download the Class 9 NCERT solutions from this page. Click on the respective chapter-wise link to download the PDF solutions.
Q.3: How can I improve my score in Mathematics with NCERT solutions?
Ans: 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 practising the same chapters and attempt mock tests. By doing so, you will definitely get more confidence about improving your score.
Q.4: Will CBSE NCERT Class 9 Maths textbook help me to prepare for competitive exams?
Ans: 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.
Q.5: Is the CBSE NCERT textbook enough for getting good marks in the exam?
Ans: The textbook exercises cover almost all the concepts in the textbook. However, practicing more problems expands your understanding of the concepts, and then you can solve any problem from any topic in the textbook easily.
Q.6: Is it mandatory to solve practice problems in the exercise?
Ans: 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.
Q.7:How to download CBSE Class 9th Maths guide?
Ans: This article contains chapter-wise links to both textbook 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.
Q8. How will referring to the 9th Class Maths solution PDF will help me?
A: The NCERT Class 9th Maths Guide 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.
So, now you have all the CBSE Class 9 Maths Solutions. Make the best use of these resources. Also, solve the free Class 9 practice questions and take Class 9 mock tests on Embibe. Practice questions and mock tests are available for Maths and Science. These will be of great help to you in your preparation for the final exam as well as various Olympiad exams.
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.
