assignment of maths class 9

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

NCERT Solutions for Class 9 Maths – Class 9 Maths NCERT Solutions

If you are searching for NCERT Solutions for Class 9 Maths , you have reached the correct place. LearnCBSE.in has created most accurate and detailed solutions for Class 9 Maths NCERT solutions. NCERT Class 9 Maths Solutions includes all the questions provided as per new revised syllabus in Class 9 math NCERT textbook.  You can download PDFs of Maths NCERT Solutions Class 9 without LOGIN. You can also practice Extra Questions for Class 9 Maths  on LearnCBSE.in

NCERT Class 9 Maths Solutions –  NCERT Solutions Class 9 Maths

• 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 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
• Chapter 15 Probability
• Class 9 Maths (Download PDF)

There are 15 chapters in class 9 maths. These chapters lay a foundation for the chapters that will come in class 10. This pdf is accessible to everyone and they can use this pdf based on their convenience. Here below we are helping you with the overview of each and every chapter appearing in the textbook.

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 Questions

NCERT 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 Questions

NCERT 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 Questions

NCERT 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 Questions

NCERT 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 Questions

NCERT 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 Questions

NCERT 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 Questions

NCERT 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 Answers

NCERT 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 Questions

NCERT 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 Solutions

NCERT 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 Questions

NCERT 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 solutions

NCERT Solutions for Class 9 Maths Chapter 15

• Class 9 Maths Probability Exercise 15.1
• Probability Class 9 Extra Questions
• Class 9 Probability Important Questions

Maths NCERT Solutions

In this article, we will provide you all the necessary information regarding Class 9th Maths NCERT Solutions. NCERT Maths Class 9 Textbook Solutions is solved by expert teachers provide you a strong foundation in the subject Maths. The 9th CBSE Maths Solutions are solved keeping various parameters in mind such as stepwise marks, formulas, mark distribution, etc., This in turn, helps you not to lose even a single mark.

It is important to build a strong base in maths. This is one subject that will be useful for every student irrespective of their branch. And thus we are helping you with NCERT Solutions of Class 9 Maths. This pdf can guide you to all the solutions given in the NCERT textbook along with the exercise.

Maths plays a major role in every student’s life. Working on NCERT Solutions Class 9 Maths Notes will not only help you to score good marks in the grade 9 but also helps you to clear the toughest competitive exams like JEE, NEET, JEE Advanced etc., Further it is CBSE Class 9 Maths Solutions will also be helpful to clear the exams like Olympiad, NTSE, through which you can easily avail scholarship and make your education journey hassle free. Read on to find out everything about NCERT Class 9th Maths Solutions to secure colorful marks in CBSE grade 9.

CBSE Class 9 Maths Unit Wise Weightage

NCERT Solutions for Class 9 Maths PDF Download

Browse all 9th NCERT Maths Solutions from your mobile or desktop and gain more marks in your exams. You can also go through the Chapterwise Important Questions for Class 9 Maths which will help you in extra practice and exams. This consists of 1 mark Questions, 2 Mark Numericals Questions, 3 Marks Numerical Questions, 4 Marks Questions, Word Problems, and previous year questions (VSAQ, SAQ, LAQ, and Value-Based Questions) from all chapters in class 9 maths designed according to CBSE Class 9 Maths Syllabus are laid in a sequential manner will help in scoring more marks in your Board Examinations.

Class 9 Maths Chapter 1 Number Systems

This chapter is an extension of the number line you have studied in the previous standards. You will also get know how to place various types of numbers on the number line in this chapter. A total of 6 exercises in this chapter guides you through the representation of terminating or non terminating of the recurring decimals on the number line. Along with the rational numbers, you will also learn where to put the square roots of 2 and 3 on the number line. There are also laws of rational exponents and Integral powers taught in this chapter.

Class 9 Maths Chapter 2 Polynomials

This chapter guides you through algebraic expressions called polynomial and various terminologies related to it. There is plenty to learn in this chapter about the definition and examples of polynomials, coefficient, degrees, and terms in a polynomial. Different types of polynomials like quadratic polynomials, linear constant, cubic polynomials, factor theorems, factorization theorem are taught in this chapter.

Class 9 Maths Chapter 3 Coordinate Geometry

A total of 3 exercises in this chapter will help you understand coordinate geometry in detail. Along with there are concepts like concepts of a Cartesian plane, terms, and various terms associated with the coordinate plane are learned in this chapter. You will also learn about plotting a point in the XY plane and naming process of this point.

Class 9 Maths Chapter 4 Linear Equations in Two Variables

This chapter will introduce to a new equation, ax + by + c = 0 in two variables. The questions in this chapter will be related to proving that a linear number has infinite solutions, using ba graph to plot linear equation, and justifying any point on a line. A total of 4 exercises are there for your practice and understanding.

Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

The chapter begins with the introduction of Indian geometry as it has some base in Euclid’s geometry. The Introduction of Euclid’s geometry in this chapter helps you with a process of defining geometrical terms and shapes. There are a total of 2 exercises where you will dwell into the relationship between theorems, postulates, and axioms.

Class 9 Maths Chapter 6 Lines and Angles

This chapter in the NCERT textbook also has 2 exercises in it. There are various theorems on angles and lines in this chapter that can be asked in for proof. The first theorem which will be asked for proof is “If the two lines are intersecting each other, then the vertically opposite angles formed will be equal”. Also, the second proof that is asked is, “The sum of all the angles formed in a triangle is 180°”. There are other theorems also given, but these are based on only these two theorems.

Class 9 Maths Chapter 7 Triangles

The contents in this chapter will help in understanding the congruence of triangles along with the rules of congruence. This chapter also has two theorems in it and a total of 5 exercises for students to practice. These two theorems are given as proof while the other is used in the problems or applications. Besides this, there are many properties of inequalities and triangles in this chapter for students to learn.

Class 9 Maths Chapter 8 Quadrilaterals

This chapter is very interesting for students to learn and there are only 2 exercises in it. The questions in this chapter are related to the properties related to quadrilateral and their combinations with the triangles.

Class 9 Maths Chapter 9 Areas of Triangles and Parallelogram

This chapter is important to understand the meaning of the area with this, the areas of the triangle, parallelogram, and their combinations are asked in this chapter along with their proofs. There are also examples of the an which are used as a proof of theorems in this chapter.

Class 9 Maths Chapter 10 Circles

In this chapter, you will get to learn some interesting topics like equal chords and their distance from the center, the chord of a point and angle subtended by it, angles which are subtended by an arc of a circle, and cyclic quadrilaterals. There are also theorems in this chapter which are helpful to prove questions based on quadrilaterals, triangles, and circles.

Class 9 Maths Chapter 11 Constructions

This chapter will help you learn two different categories of construction. One of them is the construction of a triangle along with its base, difference or sum of the remaining two sides, and one base angle with base angle and parameters are given. The other is the construction of bisectors for the line segments and measuring angles that include 45/60/90, etc.

Class 9 Maths Chapter 12 Heron’s Formula

This chapter joins the long list NCERT chapters that also has 2 exercises in it. In this chapter, you will be learning the concepts that are an extension of concepts related to the area of a triangle. Furthermore, you will get to learn about finding the area of triangles, quadrilaterals, and various types of polygons. Along with the, is there is also knowledge of formula for the plane figures given in the chapter.

Class 9 Maths Chapter 13 Surface Areas and Volume

Every one of you has already studied mensuration in previous standards. Thus, you must be aware of surface areas and this chapter is on that. Along with this, this chapter also has a volume of cubes, cylinders, cuboids, cones, hemispheres, and spheres. Also, in this chapter, you will get to know about the conversion of one figure into another, and comparing volumes of two figures.

Class 9 Maths Chapter 14 Statistics

In this chapter, you will get the knowledge about the descriptive statistics and the collection of data based on different aspects of life. This is useful for interpretation and stating the inferences from the data. This chapter gives the basic knowledge of the collection of data as the data is available in raw form. As you move forward and study 5 exercises you will learn about presenting data in tabular form by keeping them together in regular intervals, polygon, histogram, or bar graph drawing. You will also get to the topics like mean, median, and mode and finding the central tendency with the raw data.

Class 9 Maths Chapter 15 Probability

Probability in this book is based on the observation approach or finding the frequency. Questions in this chapter are very intuitive as they are based on daily life or day to day situations. For example, incidents like throwing dice, coin tossing, the probability for a deck of cards and simple events. If you are curious this chapter can be very interesting for you to learn and understand.

There may be a few times where you feel you are stuck and not getting the desired solutions. This is where we can you with NCERT solutions for class 9 maths. You can use this article as a reference for all the chapters in the NCERT book.

FAQs on NCERT Solutions for Class 9 Maths

1.  How do I study for the CBSE Class 9 Maths Solutions?

Practice the CBSE 9th Maths Solutions and try covering all the topics and questions carefully.

2. How could I learn Class 9 maths in an efficient and fast way?

The best way to learn fast is to solve NCERT. NCERT has few questions but has great importance in papers. If you can solve the whole NCERT with examples, you can easily score well. If you ample time try referring to RD Sharma too as it’s the best book.

3. Can I get solved math questions for the Class 9 CBSE?

Yes, you can get solved math questions for Class 9 CBSE Exams from our page. Access the direct links available on our page and download them for free of cost.

4.  Which is the best maths guide for 9th CBSE?

NCERT Solutions for Class 9 Maths will help you aid your preparation. Get a good grip over the subject by practicing more and more NCERT Solutions prevailing on our page.

5. How can I download the NCERT Solution Book for the CBSE Class 9 Maths?

Aspirants can download the CBSE Class 9 Maths NCERT Solutions by tapping on the direct links available. Lay a stronger foundation of the concepts by referring to the NCERT Solutions.

6. How long should a student of Class 9 practice math?

It’s not about the time limit. Try practicing as much as you can and revise the complete syllabus of Class 9 Maths for the exams to score well.

Now that you are provided all the necessary information regarding NCERT Solutions for class 9 Maths and we hope this detailed article on Class 9 Maths NCERT Solutions is helpful. If you have any doubt regarding this article or NCERT Class 9 Maths Solutions, leave your comments in the comment section below and we will get back to you as soon as possible.

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NCERT Solutions for Class 9 Maths Exercises

• NCERT Solutions
• Maths All Exercises

NCERT Solutions for Class 9 Maths Exercises - PDF Solutions

Class 9 Maths has a vivid CBSE syllabus covering excellent topics in Mathematics. The CBSE board has formulated the syllabus for the development of respective mathematical concepts and skills among the students. To prepare these chapters, refer to the NCERT Class 9 Maths All Exercises Solutions developed by the subject experts of Vedantu and learn how the fundamental questions can be solved accurately.

Learn the best approaches to solve such problems and score more in the exams.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Students can register and get access to the best and reliable source of study materials specially made by master teachers at Vedantu. You can download NCERT Solutions Class 9 Maths to help you to revise the complete Syllabus and score more marks in your examinations. Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution for Class 9 Science , Maths solutions, and solutions of other subjects that are available on Vedantu only.

NCERT Solutions for Class 9 Maths - Chapter-wise List

Given below are the chapter-wise NCERT Solutions for Class 9 Maths . These solutions are provided by the Maths experts at Vedantu in a detailed manner. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

NCERT Solutions for Class 9 Maths Chapter 1

NCERT Solutions for Class 9 Maths Chapter 2

Ncert solutions for class 9 maths chapter 3, ncert solutions for class 9 maths chapter 4, ncert solutions for class 9 maths chapter 5, ncert solutions for class 9 maths chapter 6, ncert solutions for class 9 maths chapter 7, ncert solutions for class 9 maths chapter 8, ncert solutions for class 9 maths chapter 9, ncert solutions for class 9 maths chapter 10, ncert solutions for class 9 maths chapter 11, ncert solutions for class 9 maths chapter 12, ncert solutions for class 9 maths chapter 13, ncert solutions for class 9 maths chapter 14, ncert solutions for class 9 maths chapter 15.

NCERT Solutions for Class 9 Maths All Exercises

What could be better if you get the simpler and readymade solutions of your Class 9 NCERT textbook exercises ? Moreover, all these are created by an experienced subject matter expert. Can you imagine how beneficial these could be? Sounds amazing, right! You must opt for these NCERT solutions for Class 9 Maths All Exercises right away. You can download NCERT solutions Class 9 Maths All Exercises from Vedantu official website (vedantu.com) by registering yourself with your phone number/ email address. You can also access the same study materials from Vedantu app as well. In that case, you need to download the Vedantu app first from Google play store.

You will get Class 9 Maths All Exercises NCERT solutions written in a simple and lucid manner. Solve all the problems/questions given in the exercises and evaluate your performance with these 100% accurate solutions so that you can learn how to write answers to the questions from any perspective during the final exam. Each of the answers in the Maths All Exercises NCERT solutions Class 9 is student-friendly and customized by the experts.

These NCERT solutions Class 9 Maths All Exercises contain step-by-step answers to all the questions from the exercise which are considered as an invaluable aid to the students when it comes to regular study, exam preparation or doing homework. Class 9 Maths All Exercises NCERT solutions will clear all your doubts in very less time. Hence your confidence will be boosted. By practising the questions from these books, you will be able to improve your time management skills. That will help you in solving all the questions in the stipulated time frame during the final exam.

NCERT Solutions for Class 9 Maths All Exercises are designed as per the latest CBSE curriculum and guidelines. Vedantu’s study materials are updated regularly as per the latest changes. Hence students of Class 9 who are referring to these materials will be able to score the best marks in the final exam. Once you start using these materials, the preparation for Class 9 exam and scoring the highest percentile amongst your peers will seem like a cakewalk at the end of the day.

NCERT Solutions for Class 9 Maths Chapter 1 Number System

6 exercises are included in the NCERT Solutions for Class 9 Maths Chapter 1 which are Exercise 1.1 to 1.6. Most of the questions are application based and a few are memory-based questions to test students’ application skills and cognizance.

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

Chapter 2 of NCERT Solutions for Class 9 Maths includes 5 exercises. The majority of questions are practical and application-based which allows you to improve the understanding of the chapter.

Class 9 Maths NCERT Solutions Chapter 3 Coordinate Geometry

With 3 exercises comprising both long and short questions, the exercises of NCERT Class 9 Solutions Maths for Chapter 3 are designed to test your application skills as well as cognizance.

NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

NCERT 9th class Maths book solutions include 4 exercises with 16 questions in total. This chapter includes application-based questions to test your understanding of the chapter.

NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid's Geometry

Chapter 5 of Class 9 Maths NCERT Solutions has 2 exercises. The questions are based on analysis to test your analytical skills and cognizance.

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles

NCERT Solution Class 9 Maths of Chapter 6 includes 3 exercises.

NCERT Solutions for Class 9 Maths Chapter 7 Triangles

NCERT Solution Class 9 Maths of Chapter 7 includes 5 exercises . These questions are designed to test your cognizance.

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals

NCERT Solution Class 9 Maths of Chapter 8 includes 2 exercises. These questions are based on your application skills and analysis skills.

NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles

NCERT Solution Class 9 Maths of Chapter 9 includes 4 questions to test your application skills, numerical skills and memory skills.

NCERT Solutions for Class 9 Maths Chapter 10 Circles

9th class Maths book solutions Chapter 10 includes 6 exercises and solutions to all 35 questions given in your NCERT Textbook. These questions are based on your numerical abilities, application skills, and memory skills.

NCERT Solutions for Class 9 Maths Chapter 11 Constructions

NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula

NCERT Solution Class 9 Maths of Chapter 12 includes 2 exercises designed on your ability to decipher and apply the formula.

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes

NCERT Solution Class 9 Maths of Chapter 13 includes 9 exercises and these questions will test your understanding ability and memory skills (required to retain the different formulae).

NCERT Solutions for Class 9 Maths Chapter 14 Statistics

NCERT Solution Class 9 Maths of Chapter 14 contains 4 exercises. The questions judge your comprehensive ability and analytical skills.

NCERT Solutions Class 9 Maths Chapter 15 Probability

NCERT Solution Class 9 Maths Chapter 15 comprises just a single exercise that will assess your comprehensive ability. To prepare for the exams, make sure to read the chapter thoroughly and practise all the exercise questions. This will help you to score better.

CBSE Class 9 Maths Chapter-Wise Marks Weightage 

Internal Assessment for CBSE Class 9 Maths

Importance of CBSE Chapter Wise List of Class 9 Maths All Exercises

The experts have formulated the exercise solutions following the latest CBSE syllabus of Class 9 Maths so that students can find them conveniently here. The 9th Maths All Exercises Book Answers for all the exercises have been simplified so that students can easily grab hold of the concepts and use them to develop their answering skills.

The Maths chapters included in this syllabus are all crucial for the conceptual development of the students. They will need these fundamental concepts and skills in the future to study advanced Mathematics in higher classes. Hence, the foundation needs to be strong enough to carry these skills.

This is where the solutions can act as the right guide for the students to develop such skills in a profound way.

Download NCERT Maths All Exercises Book Class 9 Solutions PDF

Perform the NCERT Maths All Exercises Book Class 9 Solutions PDF free download to complete your study material. Find out how the experts have skillfully solved all the questions utilising mathematical principles. Develop your skills accordingly and learn how to ace the Class 9 Maths exams .

Important Related Links for CBSE Class 9 Maths

Important Questions for CBSE Class 9 Math

RS Aggarwal Class 9 Solutions for Math book

NCERT Solutions for Class 9 Maths

CBSE Class 9 Maths Revision Notes

FAQs on NCERT Solutions for Class 9 Maths Exercises

1. How can I prepare all the Class 9 Maths chapters?

Complete preparing a chapter by solving its exercises. Compare your answers to the solutions to find the preparation gaps to fix them. Proceed to the next chapter. This is how you can complete the whole syllabus.

2. How many chapters are there in Class 9 Maths?

There are 15 chapters in the CBSE Class 9 Maths syllabus.

3. What is the best way to remember the Class 9 Maths formulas?

The best way to remember the Class 9 Maths formulas is to prepare and apply them. The more your practice the easier you can remember them all.

4. How can I revise the Class 9 Maths exercises before an exam?

Follow the solutions and revise the answers before an exam and reduce your preparation time.

5. Can I use the exercise solutions for doubt resolution?

The answers in the solutions can be used to resolve your doubts related to the exercise problems. All the answers are accurate and follow the latest CBSE guidelines .

NCERT Solutions for Class 9

Cbse study materials for class 9, cbse study materials.

Class 9 Maths

Class 9 Maths is an interesting subject, and it is the turning point in the lives of many students. Understanding class 9 Maths will help students to score good marks in higher classes, as the topics covered are the foundation of higher education. BYJU’S offers revision notes for all chapters of class 9 Maths, which will help students to revise all the necessary definitions, concepts, formulas, theorems, and examples quickly and helps to attain good marks in the final examination.

Students can also refer to the class 9 Maths index page to get the comprehensive notes for the sub-topics of each chapter. Class 9 Maths notes are extremely helpful for the students to learn the concepts in-depth. Below is the list of chapter-wise notes of class 9 Maths.

Class 9 Maths Chapter Wise Notes

Go through the chapter-wise class 9 Maths notes to get thoroughly acquainted with the concepts.

Class 9 Maths Study Materials

Check out all the study materials for class 9 Maths. Click on the below links to access resources like important questions, NCERT solutions for class 9 Maths, Exemplar solutions, books, Class 9 Maths MCQs. These resources are extremely helpful for class 9 students, and they can learn the class 9 Maths concepts effectively.

Maths is a very extensive subject and it needs a lot of practice to score good marks in exams. Students are suggested to practice Maths problems from textbooks, reference books, previous year question papers and sample papers. Practising more questions of class 9 Maths will help students write the correct answers in the given time.

Stay tuned with BYJU’S – The Learning App to get complete assistance for class 9 Maths. Also, register now to access many video lessons along with several study materials.

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• Competitive Exams

Class 9 Maths

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Number System, Polynomials, Coordinate Geometry, Linear Equations, Triangles and Quadrilaterals, Lines and Angles, Circles, Mensuration, Statistics, Probability, Logical Reasoning

Rational Numbers, Polynomials, Coordinate Geometry, Linear Equations, Lines and Angles, Triangles and Quadrilaterals, Circles, Mensuration, Statistics, Probability

Operations on Real Numbers, Functions, Polynomials and Equations, Sequences of Numbers, Elements of Combinatorics, Synthetic and Analytic Plane Geometry

Simple Equations, Rational Numbers, Indices, System of Equations, Polynomials, Divisiblity, Prime and Composite Numbers, Square Numbers, Even and Odd Numbers, GCD and LCM, Permutation and Combination, Probability, Pythagorean Theorem, Pigeonhole Principle, Journey Problem, Profit and Loss, Circles, Geometry

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• CBSE Class 9

NCERT Class 9 Maths And Science Lab Manual: Download Exercise-Wise PDFs

Cbse class 9 maths and science lab manual: this article has all the links to download the cbse class 9 maths and science lab manuals, all in one place. students can easily download the pdfs as well. .

CBSE Class 9 Maths And Science Lab Manual: The Central Board Of Secondary Education is a national-level board of education for public and private schools, controlled by the government of India. 

Why CBSE Class 9 Maths And Science Lab Manual Is Important?

• Guide for procedures: The manual acts as a roadmap to conduct the experiments smoothly by looking at the instructions. This ensures consistency and reduces errors. 
• Background Knowledge: Labv manuals provide sufficient theory and background information for the experiments. 
• Preparation and efficiency: The manual provides a list of required materials and estimated time for completion. 
• Effective Learning: With the help of the manual, students can easily get practical knowledge and can clear their concepts with the help of it. 
• Supports student learning: Lab manuals support students' learning by providing lab objectives, materials required, estimated completion time and step-by-step instructions for lab activities, and review questions to reinforce concepts. 

CBSE Class 9 Maths And Science Practical Lab Manual Syllabus 2024-25

Theory And Practical Syllabus For Class 9 Mathematics 2024-25 

Course Structure

Class 9 Science Experiments Syllabus 2024-25

Practicals should be conducted alongside the concepts taught in theory classes.

(LIST OF EXPERIMENTS)

1. Preparation of

a) a true solution of common salt, sugar and alum

b) a suspension of soil, chalk powder and fine sand in water

• transparency
• filtration criterion

2. Preparation of

a) A mixture

b) A compound

• appearance, i.e., homogeneity and heterogeneity
• behaviour towards a magnet
• behaviour towards carbon disulphide as a solvent
• effect of heat

3. Perform the following reactions and classify them as physical or chemical changes:

a) Iron with copper sulphate solution in water

b) Burning of magnesium ribbon in air

c) Zinc with dilute sulphuric acid

d) Heating of copper sulphate crystals

e) Sodium sulphate with barium chloride in the form of their solutions in water

4. Preparation of stained temporary mounts of

(a) onion peel, and

(b) human cheek cells & to record observations and draw their labelled diagrams. 

5. Identification of Parenchyma, Collenchyma and Sclerenchyma tissues in plants, striped, smooth and cardiac muscle fibres and nerve cells in animals, from prepared slides. Draw their labelled diagrams.

6. Determination of the melting point of ice and the boiling point of water.

7. Verification of the Laws of reflection of sound.

8. Determination of the density of a solid (denser than water) by using a spring balance and a measuring cylinder.

• Strongly salty water with the weight of water displaced by it by taking at least two different solids.

10. Determination of the speed of a pulse propagated through a stretched string/slinky (helical spring).

11. Verification of the law of conservation of mass in a chemical reaction.

• NCERT Class 10 Science Lab Manual: Download Exercise-Wise FREE PDFs
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Class 9 Mathematics Polynomials Assignments

We have provided below free printable Class 9 Mathematics Polynomials Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 9 Mathematics Polynomials . These Assignments for Grade 9 Mathematics Polynomials cover all important topics which can come in your standard 9 tests and examinations. Free printable Assignments for CBSE Class 9 Mathematics Polynomials , school and class assignments, and practice test papers have been designed by our highly experienced class 9 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Polynomials Class 9 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Polynomials Class 9. Students can click on the links below and download all Pdf Assignments for Mathematics Polynomials class 9 for free. All latest Kendriya Vidyalaya Class 9 Mathematics Polynomials Assignments with Answers and test papers are given below.

Mathematics Polynomials Class 9 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 9 Mathematics Polynomials . Students and teachers can download and save all free Mathematics Polynomials assignments in Pdf for grade 9th. Our expert faculty have covered Class 9 important questions and answers for Mathematics Polynomials as per the latest syllabus for the current academic year. All test papers and question banks for Class 9 Mathematics Polynomials and CBSE Assignments for Mathematics Polynomials Class 9 will be really helpful for standard 9th students to prepare for the class tests and school examinations. Class 9th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 9 Mathematics Polynomials Download in Pdf

Advantages of Class 9 Mathematics Polynomials Assignments

• As we have the best and largest collection of Mathematics Polynomials assignments for Grade 9, you will be able to easily get full list of solved important questions which can come in your examinations.
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Assignments For Class 9 Mathematics Polynomials

Assignments for Class 9 Mathematics Polynomials have been developed for Standard 9 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 9 Mathematics Polynomials from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 9 Mathematics Polynomials. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Polynomials book and get good marks in class 9 exams.

Key Concepts for Class 9 Mathematics Polynomials

Constants : A symbol having a fixed numerical value is called a constant. Example : 7, 3, -2, 3/7, etc. are all constants.

Variables :   A symbol which may be assigned different numerical values is known as variable. Example :  C = 2π r         C – circumference of circle                                        r – radius of circle Where 2 & π are constants. while C and r are variable

Algebraic expressions : A combination of constants and variables. Connected by some or all of the operations +, -, X and ÷ is known as algebraic expression Example : 4 + 9x – 5x 2 y + 3/8, xy etc

Terms : The several parts of an algebraic expression separated by ‘+’ or ‘-‘ operations are called the terms of the expression Example : x 2 + 2x 2 y + 4xy 2 + y 3 + 7 is an algebraic expression containing 5 terms x 2 , 3x 3 y, – 4xy 2 , y3 & 7

Polynomials : An algebraic expression in which the variables involved have only non-negative integral powers is called a polynomial. (i) 5x 3 – 4x 2 – 6x – 3 is a polynomial in variable x. (ii) 5 + 8x 3/2 + 4x -2 is an expression but not a polynomial Polynomials are denoted by p (x), q (x) and r (x) etc.

Coefficients : In the polynomial x 3 + 3x 2 + 1, coefficient of x 3 , x 2 , x are 1,3,3 respectively and we also say that +1 is the constant term in it.

Degree of a polynomial in one variable : In case of a polynomial in one variable the highest power of the variable is called the degree of the polynomial. Classification of polynomials on the basis of degree.

       degree     Polynomial            Example (a)       1           Linear                       x + 1, 2x + 3 etc. (b)       2           Quadratic etc.         ax 2 + bx + c etc. (c)       3           Cubic etc.                x 3 – 3x 2 + 1 etc (d)     4            Biquadratic              x 4 – 1

Classification of polynomials on the basis of no. of terms          No. of terms      Polynomial & Examples. (i)          1                           Monomial – 5, 3x, 1/3, y etc. (ii)         2                           Binomial – (3 + 6x), (x – 5y) etc. (iii)        3                           Trinomial – 2x 2 + 4x + 2 etc.

Constant polynomial : A polynomial containing one term only, consisting a constant term is called a constant polynomial the degree of non-zero constant polynomial is zero.

Zero polynomial : A polynomial consisting of one term, namely zero only is called a zero polynomial. The degree of zero polynomial is not defined.

Zeroes of a polynomial : Let p (x) be a polynomial. If p (a) = 0, then we say that α is a zero of the polynomial of p(x). Remark : Finding the zeroes of polynomial p(x) means solving the equation p(x) = 0.

Remainder theorem : Let f (x) be a polynomial of degree n ≥ 1 and let a be any real number. When f (x) is divided by (x – α) then the remainder is (α)

Factor theorem : Let f (x) be a polynomial of degree n > 1 and let a be any real number. (i) if (α) = 0 then (x – α) is factor of f (x) (ii) if (x – α) is a factor of f (x) then f (a) = 0

Factor : A polynomial p (x) is called factor of q (x), if p (x) divides q (x) exactly.

Factorization : To express a given polynomial as the product of polynomials each of degree less than that of the given polynomial such that no such a factor has a factor of lower degree, is called factorization. Example : x 2 – 16 = (x + 4) (x – 4)

Methods of Factorization : Factorization by taking out the common factor e.g.    36q 3 b – 60a 2 bc = 12a 2 (3a – 5c)    Factorizing by grouping    ab + bc + ax + cx = (ab + bc) + (ax + cx)                                   = (a + c) + x(a + c)                                   = (a + c) (b + x)

Factorization of quadratic trinomials by middle term splitting method. x 2 + bc + c = x 2 + (p + q) x + pq                     = ( x + p) ( x + q)

Identity : Identity is a equation (trigonometric, algebraic ) which is true for every value of variable.

Some algebraic identities useful in factorization: (i) (x + y) 2 = x 2 + 2xy + y 2 (ii) (x + y) 2 = x 2 – 2xy + y 2 (iii) x 2 – y 2 = (x – y) (x +y) (iv) (x +a) (x + b) = x 2 + (a + b) x + ab (v) (x + y + z) 2 = x 2 + y 2 + z 2 + 2xy + 2yz + 2zx (vi) (x +y) 3 = x 3 + y 3 + 3xy (x – y) (vii) (x – y) 3 = x 3 – y 3 – 3xy (x – y) (viii) x 3 + y 3 + z 3 – 3xyz = (x + y + z)(x 2 + y 2 + z 2 – xy – yz -zx)         x 3 + y 3 + z 3 = 3xyz if x + y + z = 0

Class 9 Mathematics Polynomials Assignments

Class 9 Mathematics Polynomials Important Questions and Answers

Question. Write the degree of each of the following polynomial.

(i) 2x – √5

(ii) 3 – x + x 2 – 6x 3

(vi) 8x 4 – 36x + 5x 7

(v) x 9 – x 5 + 3x 10 + 8

(vi) 2 – 3x 2

Question. If x/y + y/x = -1 where x ≠ 0, y ≠ 0 then find the value of x 3 – y 3

Question. The zeroes of the polynomial p(x) = 3x 2 – 1 are (a) 1/3 (b) 1/√3 (c) -1/√3 (d) 1/√3 and -1/√3

1/√3 & -1/√3

Question. Find the zeros of the polynomials given below :

(i) p (x) = x – 5

(ii) q (x) = x + 4

x = – 4

(iii) h (x) = 6x – 1

(vi) p (x) = ax + b

x = – b/a

(v) r (x) = x 2 + 3x

x = 0, x = – 3

(vi) l (x) = x 2 + 2x + 1

x = – 1, – 1

Question. Which of the following expressions is polynomial? (i) x 5 – 2x 3 + x + 7 (ii) y 3 – √3y (iii) 5√z – 6 (iv) x – (1/x) (v) x108 – 1 (vi) 2vx – 27 (vii) x – 2 + 2x – 1 + 3

(i), (ii), (v)

Question. Find the remainder when f (x) = 12x 3 – 13x 2 – 5x + 7 is divided by (3x + 2)?

remainder = 1

Question. Factorize :

(i) 9x 2 – 16y 2

(3x + 4y) (3x – 4y)

(ii) x 3 – x

x (x + 1) (x – 1)

Question. Find the value of a for which (x – a )is a factor of the polynomial. f(x) = x 5 – a 2 x 3 + 2x + a – 3

Question. Factorize following expressions.

(i) x 2 + 9 x + 18

(x + 6) (x + 3)

(ii) x 2 – 4x – 21

(x -7) (x + 3)

(iii) x 2 – 9x + 18

(x – 6) (x – 3)

(iv) x 2 – 19x + 78

(x – 6) (x – 13)

Question. Calculate (997) 2 using algebraic identities

Question. Factorize:

(i) a (a – 1) – b (b – 1)

(a-b) (a+b-1)

Question. Calculate 103 X 107 using algebraic identities

Question. Expand (2a + 3b + 4c) 2

4a 2 + 9b 2 + 16c 2 + 12zb + 12bc + 16ac

Question. Factorize 4x 2 + y 2 + z 2 – 4xy – 2yz + 4xz

(2x – y + z) 2

Question. Expand

(i) (4a + 5b) 2

64a 3 + 125b 3 + 240a 2 b + 300qb 2

(ii) (5x – 3y) 3

125x 3 – 27y 3 + 225x 2 y + 135xy 2

Question. Evaluate

(ii) (106) 3

Question. Factorize the following expressions.

(i) 5x 2 – 20 xy

5x (x – 4y)

(ii) 5a (b + c) – 7b (b + c)

(b + c) (5a – 7b)

(iii) x (x – y) 2 + 3x 2 y (x – y)

x (x – y) (x – y)

(iv) 6ab – b 2 + 12ac – 3bc

(b +2c) (6a – b)

(v) x 2 + 1/x 2 + 2 – 2x – (2/x)

Question. Degree of zero polynomial is (a) 1 (b) 0 (c) not defined (d) none of these

(c) not defined

Question. Factorize a 3 + 27b 3 + 8c 3 – 18abc

(a + 3b + 2c) (a 2 + 9b 2 +4c 2 – 3ab – 6bc – 2ac)

Question. Factorize (p – q) 3 (q -r) 3 (r – p) 3

3(p – q) (q – r) (r – p)

Question. Find the product (3x – 5y – 4) (9x 2 + 25y 2 + 15xy + 12x – 20y + 16)

27x 3 – 125y 3 – 64 – 180xy.

Question. Factorize

(i) x 3 + 64

(x + 4) (x 2 – 4x + 16)

(ii) 27x 3 + 125y 3

(3x + 5y) (9x 2 – 15xy + 25y) 2

(iii) 8a 3 – 27b 3

(2a = 3b) (4a 2 + 6ab + 9b 2 )

(iv) 1- 64a 3

(1 – 4a) (1 + 4a + 16a 2 )

Question. Which of the following expression is a polynomial?

Question. If (x + 2) and (x – 1) are factors of (x 2 + 10x 2 + mx + n) then find value of m & n?

m = 7, n = -18

Question. If if x + y + z = 9 and xy + yz + zx = 23 then find the value of (x 3 + y 3 + z 3 – 3xyz)?

Question. For what value of k is the polynomial p (x) = 2x 3 – kx 2 + 3x + 10 exactly divisible by (x + 2)? (a) -1/3 (b) 1/3 (c) 3 (d) -3

Question. Find the value of (368) 2 – (368) 2

Assignments for Class 9 Mathematics Polynomials as per CBSE NCERT pattern

All students studying in Grade 9 Mathematics Polynomials should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics Polynomials exam for standard 9. We have made sure that all topics given in your textbook for Mathematics Polynomials which is suggested in Class 9 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

Some advantages of Free Assignments for Class 9 Mathematics Polynomials

• Solving Assignments for Mathematics Polynomials Class 9 helps to further enhance understanding of the topics given in your text book which will help you to get better marks
• By solving one assignments given in your class by Mathematics Polynomials teacher for class 9 will help you to keep in touch with the topic thus reducing dependence on last minute studies
• You will be able to understand the type of questions which are expected in your Mathematics Polynomials class test
• You will be able to revise all topics given in the ebook for Class 9 Mathematics Polynomials as all questions have been provided in the question banks
• NCERT Class 9 Mathematics Polynomials Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
• Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 9 Mathematics Polynomials teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 9 Mathematics Polynomials Assignments PDF.

You can download free assignments for class 9 Mathematics Polynomials from https://www.assignmentsbag.com

You can get free PDF downloadable assignments for Grade 9 Mathematics Polynomials from our website which has been developed by teachers after doing extensive research in each topic.

On our website we have provided assignments for all subjects in Grade 9, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

You can easily get question banks, topic wise notes and questions and other useful study material from https://www.assignmentsbag.com without any charge

Yes all test papers for Mathematics Polynomials Class 9 are available for free, no charge has been put so that the students can benefit from it. And offcourse all is available for download in PDF format and with a single click you can download all assignments.

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What   is Cartesian coordinate system

Answer: A system which involves the x-axis and y-axis on the two dimensional surface is called a cartesian coordinate system.

What we call the horizontal line in Cartesian coordinate system.

Answer: Horizontal line is called the x - axis.

What we call the vertical   line in Cartesian coordinate system.

Answer: Vertical Line is called the y - axis.

Which point is called the origin and what are its coordinates.

Answer: The point of intersection of x - axis and y - axis is called the Origin. Coordinates of origin are (0,0)

What is the point on x – axis.

Answer: Any point on the x - axis is (a, 0)

What is the point on y-axis.

Answer:  Any point on the y - axis is (0, b)

What do you mean by ordinates.

Answer: Point on y - axis is called ordinate.

What do you mean by abscissa.

Answer: Point on the x-axis is called abscissa.

Write the coordinates of the points given in the following graph. Also write In which quadrant or on which axis the following points lie.

Answer: 

A(3, 4) lie in I quadrant

B(-4, 3) lie in II quadrant

C(-2. -3) lie in III quadrant

D(3, -2) lie in IV quadrant

E(2, 0) lie on the x-axis

F(-2, 0) lie on the x-axis

G(0, 2) lie on y-axis

H(0, -2) lie on y-axis

Write the abscissa and ordinate of the following points

(-3, 5),     (0, 9),    (-5, 0),     (3,3),    (7, -9),   (12, 13)

Abscissa:  -3, 0, -5, 3, 7, 12

Ordinate:  5, 9, 0, 3, -9, 13

Write the coordinates of the point :

a) Whose ordinate is -5 and which lies on y- axis.

b) Which lies on x-axis and y – axes both.

c) Whose abscissa is -3 and which lies on x – axis.

b) Point on the x-axis is (a, 0) and Point on the y-axis is (0, b)

  Question 13:

What is the perpendicular distance of the point (3, 4) from

           a)   x – axis           b) Y – axis

a) 4 unit   b) 3 unit

What is the perpendicular distance of the point (7, 26) from

a) 26 unit   b) 7 unit

Name the quadrant in which abscissa and ordinate have different sign.

Ans: In II and IV quadrant abscissa and ordinate have different sign.

Plot the points P(1,0), Q(4,0), and S(1, 3). Find the coordinates of point R such that PQRS is a square. Also find the area of the square.     

Coordinates of R(4, 3),  Area of square PQRS = 9 square units)

Mark the points A(2, 2), B(2, -2), C(-2, -2) and D(-2, 2) on the graph paper and join these points in order. Identify the figure so obtained. Also find the area of the figure.  

Square, Area = 16cm 2 ]

Plot the points P(-1, 0), Q(0, 1) and R(2, 3) on the graph paper and check whether they are collinear or not.

Answer: If P, Q, R all points lie on a straight line then points are collinear.

If the points A(0, -6), B(0, 2 and C (a, 3) lie on the y-axis, then find the value of a.

Answer: For points on the y-axis the abscissa is "0" So the value of a = 0

From the given graph write :

a) The coordinates of the points B and F

b) The abscissas of points D and H

c) The ordinates of the points A and C

d) The perpendicular distance of the point G from x-axis 

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