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Class 9 Mathematics Assignments

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

Mathematics Class 9 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 9 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 9th. Our expert faculty have covered Class 9 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 9 Mathematics and CBSE Assignments for Mathematics 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 Download in Pdf

More Assignments for Class 9 Mathematics

Advantages of Class 9 Mathematics Assignments

• As we have the best and largest collection of Mathematics assignments for Grade 9, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics textbooks for Class 9 .
• All Mathematics assignments for Class 9 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 9 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics chapter wise worksheets and assignments for free in Pdf
• Class 9 Mathematics question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 9 Mathematics students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Class 9 which you can download in Pdf

We provide here Standard 9 Mathematics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics in Grade 9, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Grade 9 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 9 for all subjects. You can download them all and use them offline without the internet.

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Class 9 Mathematics Quadrilateral Assignments

Class 9 Mathematics Linear Equations In Two Variables Assignments

RS Aggarwal Solutions Class 9 Chapter 3 Factorisation of Polynomials

RS Aggarwal Solutions for Class 9 Maths Book Chapter 3 Factorisation of Polynomials are available here. Study path has prepared solutions of all the exercises of the chapter by our expert math teachers to help you to get good marks in exams. This lesson has a ton of questions that are very important from the examination point of view.

We at Study Path solved each questions step by step with detailed explanations. Students must practice from practice these problems to score high marks in Maths. Below we have listed the Class 9 RS Aggarwal Solutions Chapter 3 Factorisation of Polynomials Exercise 3A, Ex 3B, Ex 3C, Ex 3D, 3E, Ex 3F, Ex 3G and Multiple Choice Questions (MCQs).

Class 9 RS Aggarwal Solutions Chapter 3 Factorisation of Polynomials

Class 9 rs aggarwal solutions chapter 3 ex 3a.

Class 9 RS Aggarwal Solutions Chapter 3 Ex 3B

Class 9 RS Aggarwal Solutions Chapter 3 Ex 3C

Class 9 RS Aggarwal Solutions Chapter 3 Ex 3D

Class 9 RS Aggarwal Solutions Chapter 3 Ex 3E

Class 9 RS Aggarwal Solutions Chapter 3 Ex 3F

Class 9 RS Aggarwal Solutions Chapter 3 Ex 3G

Class 9 RS Aggarwal Solutions Chapter 3 MCQs

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Basic concepts, definitions and formulas of mathematics, mathematics assignments for 9th standard to 10+2 standard, maths study material for 8th, 9th, 10th, 11th, 12th classes, Mathematics lesson plan for classes 8th,10th and 12th standard, Interesting maths riddles and maths magic, Class-wise mathematics study material for students from 8th to 12. A complete resource centre of mathematics for students and teachers

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Linear programming class xii chapter 12, math assignment class ix ch-3 | coordinate geometry, mathematics assignment  class ix  chapter 3  coordinate geometry.

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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It is very helpful for students.

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CBSE Worksheets for Class 9 Maths | MCQ Questions for Class 9 Maths

CBSE Worksheets for Class 9 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 9 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 9 Maths Worksheets for the students of Class 9. All our CBSE NCERT Class 9 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 9 Maths will be useful to test your conceptual understanding.

Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 9 Maths Number of Worksheets: 59

CBSE Class 9 Maths Worksheets PDF

All the CBSE Worksheets for Class 9 Maths provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 9 Maths important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 9 Maths Worksheet. CBSE Worksheets for Class 9 Math can also use like assignments for Class 9 Maths students.

• MCQ Questions for Class 9 Maths
• CBSE Worksheets for Class 9 Mathematics Area Assignment

Area of Triangles (Herons Formula)

• CBSE Worksheets for Class 9 Mathematics Area of Triangles (Herons Formula) Assignment

Areas of Parallelograms and Triangles

• CBSE Worksheets for Class 9 Mathematics Areas of Parallelograms and Triangles Assignment 1
• CBSE Worksheets for Class 9 Mathematics Areas of Parallelograms and Triangles Assignment 2
• CBSE Worksheets for Class 9 Mathematics Areas of Parallelograms and Triangles Assignment 3
• CBSE Worksheets for Class 9 Mathematics Circles Assignment 1
• CBSE Worksheets for Class 9 Mathematics Circles Assignment 2
• CBSE Worksheets for Class 9 Mathematics Circles Assignment 3

Constructions

• CBSE Worksheets for Class 9 Mathematics Constructions Assignment

Coordinate Geometry

• CBSE Worksheets for Class 9 Mathematics Coordinate Geometry Assignment 1
• CBSE Worksheets for Class 9 Mathematics Coordinate Geometry Assignment 2
• CBSE Worksheets for Class 9 Mathematics Coordinate Geometry Assignment 3

Euclids Geometry

• CBSE Worksheets for Class 9 Mathematics Euclids Geometry Assignment

Incentre of a Triangle

• CBSE Worksheets for Class 9 Mathematics Incentre of a Triangle Assignment 1
• CBSE Worksheets for Class 9 Mathematics Incentre of a Triangle Assignment 2
• CBSE Worksheets for Class 9 Mathematics Incentre of a Triangle Assignment 3
• CBSE Worksheets for Class 9 Mathematics Incentre of a Triangle Assignment 4

Lines and Angles

• CBSE Worksheets for Class 9 Mathematics Lines and Angles Assignment 1
• CBSE Worksheets for Class 9 Mathematics Lines and Angles Assignment 2
• CBSE Worksheets for Class 9 Mathematics Lines and Angles Assignment 3
• CBSE Worksheets for Class 9 Mathematics Lines and Angles Assignment 4
• CBSE Worksheets for Class 9 Mathematics Lines and Angles Assignment 5

Number System

• CBSE Worksheets for Class 9 Mathematics Number System Assignment 1
• CBSE Worksheets for Class 9 Mathematics Number System Assignment 2
• CBSE Worksheets for Class 9 Mathematics Number System Assignment 3
• CBSE Worksheets for Class 9 Mathematics Number System Assignment 4
• CBSE Worksheets for Class 9 Mathematics Number System Assignment 5
• CBSE Worksheets for Class 9 Mathematics Number System Assignment 6
• CBSE Worksheets for Class 9 Mathematics Number System Assignment 7

Polynomials

• CBSE Worksheets for Class 9 Mathematics Polynomials Assignment 1
• CBSE Worksheets for Class 9 Mathematics Polynomials Assignment 2
• CBSE Worksheets for Class 9 Mathematics Polynomials Assignment 3
• CBSE Worksheets for Class 9 Mathematics Polynomials Assignment 4
• CBSE Worksheets for Class 9 Mathematics Polynomials Assignment 5
• CBSE Worksheets for Class 9 Mathematics Polynomials Assignment 6
• CBSE Worksheets for Class 9 Mathematics Polynomials Assignment 7

Probability

• CBSE Worksheets for Class 9 Mathematics Probability Assignment 1
• CBSE Worksheets for Class 9 Mathematics Probability Assignment 2

Quadrilaterals

• CBSE Worksheets for Class 9 Mathematics Quadrilaterals Assignment 1
• CBSE Worksheets for Class 9 Mathematics Quadrilaterals Assignment 2
• CBSE Worksheets for Class 9 Mathematics Statistics Assignment 1
• CBSE Worksheets for Class 9 Mathematics Statistics Assignment 2

Surface areas and volumes

• CBSE Worksheets for Class 9 Mathematics Surface areas and volumes Assignment 1
• CBSE Worksheets for Class 9 Mathematics Surface areas and volumes Assignment 2
• CBSE Worksheets for Class 9 Mathematics Surface areas and volumes Assignment 3

Linear Equations in Two Variables

• CBSE Worksheets for Class 9 Mathematics Linear Equations in Two Variables Assignment 1
• CBSE Worksheets for Class 9 Mathematics Linear Equations in Two Variables Assignment 2
• CBSE Worksheets for Class 9 Mathematics Linear Equations in Two Variables Assignment 3
• CBSE Worksheets for Class 9 Mathematics Linear Equations in Two Variables Assignment 4
• CBSE Worksheets for Class 9 Mathematics Linear Equations in Two Variables Assignment 5
• CBSE Worksheets for Class 9 Mathematics Assignment 1
• CBSE Worksheets for Class 9 Mathematics Assignment 2
• CBSE Worksheets for Class 9 Mathematics Assignment 3
• CBSE Worksheets for Class 9 Mathematics Assignment 4
• CBSE Worksheets for Class 9 Mathematics Assignment 5
• CBSE Worksheets for Class 9 Mathematics Assignment 6
• CBSE Worksheets for Class 9 Mathematics Assignment 7
• CBSE Worksheets for Class 9 Mathematics Assignment 8
• CBSE Worksheets for Class 9 Mathematics Assignment 9

Advantages of CBSE Class 9 Maths Worksheets

• By practising NCERT CBSE Class 9 Maths Worksheet , students can improve their problem solving skills.
• Helps to develop the subject knowledge in a simple, fun and interactive way.
• No need for tuition or attend extra classes if students practise on worksheets daily.
• Working on CBSE worksheets are time-saving.
• Helps students to promote hands-on learning.
• One of the helpful resources used in classroom revision.
• CBSE Class 9 Maths Workbook Helps to improve subject-knowledge.
• CBSE Class 9 Math Worksheets encourages classroom activities.

Worksheets of CBSE Class 9 Maths are devised by experts of WorksheetsBuddy experts who have great experience and expertise in teaching Maths. So practising these worksheets will promote students problem-solving skills and subject knowledge in an interactive method. Students can also download CBSE Class 9 Maths Chapter wise question bank pdf and access it anytime, anywhere for free. Browse further to download free CBSE Class 9 Maths Worksheets PDF .

Grade 9 math worksheets

CBSE Worksheets For Class 9

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Class 9 Maths Notes, Solved Exercises Solutions, MCQ’s

These maths class 9 notes contain theory of each and every chapter, solutions to every exercise and review exercises which are great for reviewing giant exercises. It is a complete package of solutions to problems of your really tough book. You have these advantages of browsing notes from our website. Good quality notes, whole course notes at one place, fast loading website, friendly interface.

Math is an important part of our studies. Whatever field you like to go in, the mathematics is not going to leave you alone. So, start working on your mathematics skills. As an example, you will be saved from the fear and anxiety of doing math. Therefore, we provide maths class 9 notes. Some students enjoy doing math and others just feel it as a burden on them. The reason for becoming math a burden is that those students really don’t practice math. Conversely, It’s all about remembering formulas and applying them to different kind of problems in different ways. So, don’t be afraid and practice the math problems. And, lets take a look at maths class 9 notes.

Most of the time, after doing a mathematics problem we feel that maybe we have done it a wrong way. If we are not sure about the correctness of our solution than we don’t feel satisfied. Satisfaction becomes the most important thing after doing a lot of hard work. If you are not satisfied then you will be not sure and this creates the disappointment and that leads to hate to math. So, don’t hate math because we are going to provide you with some great solutions for your whole mathematics book (Maths class 9 notes).

We love to help you in your studies. We uploaded these notes because we feel happy when you download these notes from our website. Because, we believe in if you do good for someone, Allah rewards you. May Allah bless you with endless happiness.

This Post Has 157 Comments

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I’m really really thankful for the person who uploaded these notes . I’m studying from a good academy but still I always use these notes whenever I feel difficulty in solving any of maths problem . These notes have all the questions correctly and step by step solved so as a person who really Hates maths I just want to say that these notes helped me a lot through out my ninth class .thank you so much.

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AOA Sir! There is small mistake which is not a big mistake but i want to tell you that in Maths exercise 4.4 Q no1 part vi in second step the sign of conjugate is multiply please correct it to plus sign.Btw your app super hilarious fantastic. May god bless you trillions joys.

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This website is fantastic ❤️It’s so helpful…. But I request to the author to check the Question # 4..Part(ii) of Review Exercise 4…there is a mistake …

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Aoa there is a mistake in Qno 6 you write 289=64+BC but in next step you write 284=64+BC please correct it for no confusion in 2nd step it was 289 not 284

5.4 maths last question q=2 correct

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

Extra Questions for Class 9 Maths with Solutions Chapter Wise

August 18, 2019 by Veerendra

Extra Questions for Class 9 maths will help you with practice. We have selectively graded these extra questions for more practice. We request Students to solve these questions without going through solutions. If you face any difficulty in solving these Extra Questions, Please refer solutions.

Extra Questions for Class 9 Maths with Solutions

Here is the list of Extra Questions for Class 9 Maths with Answers based on latest NCERT syllabus prescribed by CBSE.

• Chapter 1 Number Systems Class 9 Extra Questions
• Chapter 2 Polynomials Class 9 Extra Questions
• Chapter 3 Coordinate Geometry Class 9 Extra Questions
• Chapter 4 Linear Equations for Two Variables Class 9 Extra Questions
• Chapter 5 Introduction to Euclid’s Geometry Class 9 Extra Questions
• Chapter 6 Lines and Angles Class 9 Extra Questions
• Chapter 7 Triangles Class 9 Extra Questions
• Chapter 8 Quadrilaterals Class 9 Extra Questions
• Chapter 9 Areas of Parallelograms and Triangles Class 9 Extra Questions
• Chapter 10 Circles Class 9 Extra Questions
• Chapter 11 Constructions Class 9 Extra Questions
• Chapter 12 Heron’s Formula Class 9 Extra Questions
• Chapter 13 Surface Areas and Volumes Class 9 Extra Questions
• Chapter 14 Statistics Class 9 Extra Questions
• Chapter 15 Probability Class 9 Extra Questions

NCERT Solutions for Class 9 Maths

Free resources.

NCERT Solutions

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• NCERT Solutions
• NCERT Class 9
• NCERT 9 Maths

NCERT Solutions for Class 9 Maths

Ncert solutions for class 9 maths – free pdf updated for 2023-24 session.

NCERT Solutions for Class 9 Maths includes solutions to all the questions given in the NCERT textbook for Class 9. The students can download PDFs of chapter-wise solutions to these problems from the links provided below on this page. These NCERT Solutions for Class 9   cover all the topics included in the NCERT textbook, like Number System, Coordinate Geometry, Polynomials, Euclid’s Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, Probability, etc.

With the help of these Solutions of NCERT Books for Class 9 Maths , students can practise all types of questions from the chapters. The  CBSE Class 9 Maths Solutions have been designed by our experts in a well-structured format to provide several possible methods of answering the problems and ensure a proper understanding of concepts. The students are suggested to practise all these solutions thoroughly for their exams. It will also help them in building a foundation for higher-level classes.

NCERT Solutions Class 9 Maths Chapters

• Chapter 1 Number System
• Chapter 2 Polynomials
• Chapter 3 Coordinate Geometry
• Chapter 4 Linear Equations in Two Variables
• Chapter 5 Introduction to Euclids Geometry
• Chapter 6 Lines and Angles
• Chapter 7 Triangles
• Chapter 8 Quadrilaterals
• Chapter 9 Circles
• Chapter 10 Heron’s Formula
• Chapter 11 Surface Areas and Volumes
• Chapter 12 Statistics

The following chapters have been removed from the NCERT Class 9 Maths textbook 2023-24. 

• Areas of Parallelograms and Triangles
• Constructions
• Probability

Along with NCERT Solutions , students are also provided with other online learning materials available at BYJU’S, such as notes, books, question papers, exemplar problems, worksheets etc. These materials are designed with respect to the CBSE syllabus and NCERT curriculum. Students are also advised to practise CBSE Class 9 Sample Papers to get an idea of the question pattern in the final exam.

15 chapters are present in the NCERT Solutions for Class 9 Maths . These chapters given in the NCERT Class 9 Maths lay a foundation for the chapters present in Class 10. The PDFs given at BYJU’S are accessible to everyone and can be downloaded by the students for free.

NCERT Solutions of Class 9 Maths Book Chapter Brief:

Students having trouble solving tough Math problems can refer to these CBSE Maths Class 9 Solutions of NCERT for better guidance and for quick review. Solving these exercises in each chapter will ensure positive results.

NCERT Solutions Class 9 Maths Chapter 1 Number System

This chapter discusses different topics, including rational numbers and irrational numbers. Students will also be learning the extended version of the number line and how to represent numbers (integers, rational and irrational) on it. A total of 6 exercises are present in this chapter that contains the problems based on all the topics asked in the chapter. This chapter also teaches students the representation of terminating/non-terminating recurring decimals (and successive magnification method) as well as the presentation of square roots of 2, 3 and other non-rational numbers on the number line. The chapter also deals with the laws of integral powers and rational exponents with positive real bases in the Number System.

Topics Covered in Class 9 Maths Chapter 1 Number System

Review of representation of natural numbers, integers, and rational numbers on the number line. Representation of terminating/non-terminating recurring decimals on the number line through successive magnification. Rational numbers as recurring/terminating decimals.

Examples of nonrecurring/non-terminating decimals such as √2, √3, √5 etc. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line, and conversely, every point on the number line represents a unique real number.

Existence of √x for a given positive real number x (visual proof to be emphasised). Definition of n th root of a real number.

Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing the learner to arrive at the general laws).

Rationalisation (with precise meaning) of real numbers of the type (and their combinations) \(\begin{array}{l}\frac{1}{a+b\sqrt{x}}\: and\: \frac{1}{\sqrt{x}+\sqrt{\sqrt{y}}}\end{array} \) where x and y are natural numbers, and a and b are integers.

Important Formulas – 

Operations on Real Numbers

√(a/b) = √a/√b

√ab = √a √b

(√a + √b) (√a – √b) = a – b

(a + √b) (a – √b) = a 2 – b

(√a + √b) (√c + √d) = √ac + √ad + √bc + √bd

(√a + √b) 2 = a + 2√ab + b

Laws of Exponents for Real Numbers

a m . a n = a m + n

(a m ) n = a mn

a m /a n = a m – n , m > n

a m b m = (ab) m

Also, access the following resources for Class 9 Chapter 1 Number System, at BYJU’S:

• NCERT Number System Class 9 Notes
• Number System Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Number Systems
• RD Sharma Solutions Number Systems Class 9

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NCERT Solutions Class 9 Maths Chapter 2 Polynomials

This chapter discusses a particular type of algebraic expression called polynomial and the terminology related to it. Polynomial is an expression that consists of variables and coefficients involving the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. The chapter also deals with the Remainder Theorem and the Factor Theorem with the uses of these theorems in the factorisation of polynomials. Students will be taught several examples as well as the definition of different terms like polynomials, degrees, coefficients, zeros and terms of a polynomial. A total of 5 exercises are present in this chapter, which includes problems related to all the topics mentioned in the chapter.

Topics Covered in Class 9 Maths Chapter 2 Polynomials

Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros/roots of a polynomial/equation. State and motivate the Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorisation of ax 2 + bx + c, a ≠ 0 where a, b, c are real numbers, and of cubic polynomials using the Factor Theorem.

Recall algebraic expressions and identities. Further identities of the type:

(x + y + z) 2 = x 2 + y 2 + z 2  + 2xy + 2yz + 2zx

(x ± y) 3  = x 3  ± y 3 ± 3xy (x ± y)

x 3  + y 3 + z 3 – 3xyz = (x + y + z) (x 2 + y 2 + z 2 – xy – yz – zx)

and their use in the factorisation of polynomials. Simple expressions are reducible to these polynomials.

Important Formulas –

(x + y) 2 = x 2 + 2xy + y 2

(x – y) 2 = x 2 – 2xy + y 2

x 2 – y 2 = (x + y) (x – y)

(x + y + z) 2 = x 2 + y 2 + z 2 + 2xy + 2yz + 2zx

(x + y) 3 = x 3 + y 3 + 3xy(x + y)

(x – y) 3 = x 3 – y 3 – 3xy(x – y)

x 3 + y 3 + z 3 – 3xyz = (x + y + z) (x 2 + y 2 + z 2 – xy – yz – zx)

Dividend = (Divisor × Quotient) + Remainder

Remainder Theorem

Let p(x) be any polynomial of degree greater than or equal to one, and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).

Factor Theorem

If p(x) is a polynomial of degree n > 1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x).

Also, access the following resources for Class 9 Chapter 2 Polynomials, at BYJU’S:

• NCERT Polynomials Class 9 Notes 
• Polynomials Class 9 Important Questions 
• NCERT Exemplar Solutions Class 9 Polynomials
• RD Sharma Solutions factorisation of Polynomials Class 9

NCERT Solutions Class 9 Maths Chapter 3 Coordinate Geometry

The chapter Coordinate Geometry includes the concepts of the cartesian plane, coordinates of a point in xy–plane, terms, and notations associated with the coordinate plane, including the x-axis, y-axis, x- coordinate, y-coordinate, origin, quadrants and more. Students, in this chapter, will also be studying the concepts of abscissa and ordinates of a point as well as plotting and naming a point in xy–plane. There are 3 exercises in this chapter that contain questions revolving around the topics mentioned in the chapter, helping the students get thorough with the concepts.

Topics Covered in Class 9 Maths Chapter 3 Coordinate Geometry

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane, graph of linear equations as examples; focus on linear equations of the type ax + by + c = 0 by writing it as y =mx + c and linking with the chapter on linear equations in two variables.

Important Points – 

• To locate the position of an object or a point in a plane, we require two perpendicular lines. One of them is horizontal, and the other is vertical.
• The plane is called the Cartesian, or coordinate plane, and the lines are called the coordinate axes.
• The horizontal line is called the x-axis, and the vertical line is called the y-axis.
• The coordinate axes divide the plane into four parts called quadrants.
• The point of intersection of the axes is called the origin.
• The distance of a point from the y-axis is called its x-coordinate, or abscissa, and the distance of the point from the x-axis is called its y-coordinate, or ordinate.

Also, access the following resources for Class 9 Chapter 3 Coordinate Geometry, at BYJU’S:

• NCERT Coordinate Geometry Class 9 Notes
• Coordinate Geometry Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Coordinate Geometry
• RD Sharma Solutions Coordinate Geometry Class 9

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

Along with recalling the knowledge of linear equations in one variable, this chapter will introduce the students to the linear equation in two variables, i.e. ax + by + c = 0. Students will also learn to plot the graph of a linear equation in two variables. There are 4 exercises in this chapter that consist of questions related to finding the solutions of a linear equation, plotting a linear equation on the graph and other topics discussed in the chapter.

Topics Covered in Class 9 Maths Chapter 4 Linear Equations in Two Variables:

Recall of linear equations in one variable. Introduction to the equation in two variables. Prove that a linear equation in two variables has infinitely many solutions, and justify their being written as ordered pairs of real numbers, plotting them and showing that they seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

Important Points –

• An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables.
• A linear equation in two variables has infinitely many solutions.
• The graph of every linear equation in two variables is a straight line.
• x = 0 is the equation of the y-axis, and y = 0 is the equation of the x-axis.
• The graph of x = a is a straight line parallel to the y-axis.
• The graph of y = a is a straight line parallel to the x-axis.
• An equation of the type y = mx represents a line passing through the origin.

Also, access the following resources for Class 9 Chapter 4 Linear Equations in Two Variables, at BYJU’S:

• NCERT Linear Equations in Two Variables Class 9 Notes
• Linear Equations in Two Variables Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Linear Equations in Two Variables
• RD Sharma Solutions Linear Equations in Two Variables Class 9

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

This chapter discusses Euclid’s approach to geometry and tries to link it with present-day geometry. Introduction to Euclid’s Geometry provides the students with a method of defining common geometrical shapes and terms. Students will be taken deeper into the topic of axioms, postulates and theorems with the two exercises present in the chapter.

Topics Covered in Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry:

History – Euclid and geometry in India. Euclid’s method of formalising observed phenomenon into rigorous mathematics with definitions, common/obvious notions, axioms/postulates, and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem. 1. Given two distinct points, there exists one and only one line through them. 2. (Prove) Two distinct lines cannot have more than one point in common.

Important Axioms and Postulates – 

Some of Euclid’s axioms are:

(1) Things which are equal to the same thing are equal to one another.

(2) If equals are added to equals, the wholes are equal.

(3) If equals are subtracted from equals, the remainders are equal.

(4) Things which coincide with one another are equal to one another.

(5) The whole is greater than the part.

(6) Things which are double of the same things are equal to one another.

(7) Things which are halves of the same thing are equal to one another.

Euclid’s Five Postulates

Postulate 1 – A straight line may be drawn from any one point to any other point.

Postulate 2 – A terminated line can be produced indefinitely.

Postulate 3 – A circle can be drawn with any centre and any radius.

Postulate 4 – All right angles are equal to one another.

Postulate 5 – If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

Also, access the following resources for Class 9 Chapter 5 Introduction to Euclid’s Geometry, at BYJU’S:

• NCERT Introduction to Euclid’s Geometry Class 9 Notes
• Introduction to Euclid’s Geometry Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Introduction to Euclid’s Geometry
• RD Sharma Solutions Introduction to Euclid’s Geometry Class 9

NCERT Solutions Class 9 Maths Chapter 6 Lines and Angles

This chapter revolves around the theorems present in the topics of Lines and Angles. Students might often be asked to prove the statements given in the questions. There are 3 exercises in the chapter, solving which students would be able to understand the concepts covered in the chapter thoroughly. There are four axioms and eight theorems covered in the chapter.

Topics Covered in Class 9 Maths Chapter 6 Lines and Angles:

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse. 2. (Prove) If two lines intersect, the vertically opposite angles are equal. 3. (Motivate) Results on corresponding angles, alternate angles, and interior angles when a transversal intersects two parallel lines. 4. (Motivate) Lines, which are parallel to a given line, are parallel. 5. (Prove) The sum of the angles of a triangle is 180°. 6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

• If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and vice versa. This property is called the Linear pair axiom.
• If two lines intersect each other, then the vertically opposite angles are equal.
• If a transversal intersects two parallel lines, then

(i) each pair of corresponding angles is equal,

(ii) each pair of alternate interior angles is equal,

(iii) each pair of interior angles on the same side of the transversal is supplementary.

• If a transversal intersects two lines such that, either

(i) any one pair of corresponding angles is equal, or

(ii) any one pair of alternate interior angles is equal, or

(iii) any one pair of interior angles on the same side of the transversal is supplementary, then the lines are parallel.

Also, access the following resources for Class 9 Chapter 6 Lines and Angles, at BYJU’S:

• NCERT Lines and Angles Class 9 Notes
• Lines and Angles Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Lines and Angles
• RD Sharma Solutions Lines and Angles Class 9

NCERT Solutions Class 9 Maths Chapter 7 Triangles

In this chapter, students will study in detail the congruence of triangles, rules of congruence, some properties of triangles and the inequalities in triangles. The chapter has a total of 5 exercises, in which the students are asked “to-prove” as well as application-level problems. With this chapter, students will also learn to prove the properties that they learnt in earlier classes. The chapter also teaches the students to apply the various congruence rules while solving the problems. There are about eight theorems covered in this chapter.

Topics Covered in Class 9 Maths Chapter 7 Triangles:

1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). 2. (Prove) 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). 3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to the three sides of the other triangle (SSS Congruence). 4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. 5. (Prove) The angles opposite to equal sides of a triangle are equal. 6. (Motivate) The sides opposite to equal angles of a triangle are equal. 7. (Motivate) Triangle inequalities and the relation between ‘angle and facing side’; inequalities in a triangle.

Important Axioms and Theorems –

Axiom 7.1 (SAS congruence rule) – Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.

Theorem 7.1 (ASA congruence rule) – Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.

Theorem 7.2 – Angles opposite to equal sides of an isosceles triangle are equal.

Theorem 7.3 – The sides opposite to equal angles of a triangle are equal.

Theorem 7.4 (SSS congruence rule) – If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

Theorem 7.5 (RHS congruence rule) – If in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.

Theorem 7.6 – If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater).

Theorem 7.7 – In any triangle, the side opposite to the larger (greater) angle is longer.

Theorem 7.8 – The sum of any two sides of a triangle is greater than the third side.

Also, access the following resources for Class 9 Chapter 7 Triangles, at BYJU’S:

• NCERT Triangles Class 9 Notes
• Triangles Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Triangles
• RD Sharma Solutions Triangles Class 9

NCERT Solutions Class 9 Maths Chapter 8 Quadrilaterals

A figure obtained by joining four points in order is called a quadrilateral. This chapter takes the students to the depth of the topics of Quadrilaterals. The chapter contains 2 exercises that contain only one theorem to prove. However, there are a total of nine theorems that can be used to solve the application or conceptual-level questions asked. The angle sum property of a quadrilateral, types of quadrilaterals, properties of a parallelogram, and the mid-point theorem are explained in this chapter to help the students in learning the concepts thoroughly.

Topics Covered in Class 9 Maths Chapter 8 Quadrilaterals:

1. (Prove) The diagonal divides a parallelogram into two congruent triangles. 2. (Motivate) In a parallelogram, opposite sides are equal and conversely. 3. (Motivate) In a parallelogram, opposite angles are equal and conversely. 4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides are parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each other conversely. 6. (Motivate) In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and (motivate) its converse.

Important Theorems –

A quadrilateral has four sides, four angles and four vertices.

Angle Sum Property of a Quadrilateral – The sum of the angles of a quadrilateral is 360 o .

Theorem 8.1 – A diagonal of a parallelogram divides it into two congruent triangles

Theorem 8.2 – In a parallelogram, opposite sides are equal.

Theorem 8.3 – If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

Theorem 8.4 – In a parallelogram, opposite angles are equal.

Theorem 8.5 – If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.

Theorem 8.6 – The diagonals of a parallelogram bisect each other.

Theorem 8.7 – If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Theorem 8.8 – A quadrilateral is a parallelogram if a pair of opposite sides are equal and parallel.

Theorem 8.9 – The line segment joining the mid-points of two sides of a triangle is parallel to the third side.

Theorem 8.10 – The line drawn through the mid-point of one side of a triangle, parallel to another side, bisects the third side.

Also, access the following resources for Class 9 Chapter 8 Quadrilaterals, at BYJU’S:

• NCERT Quadrilaterals Class 9 Notes
• Quadrilaterals Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Quadrilaterals
• RD Sharma Solutions Quadrilaterals Class 9

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

In this chapter, an attempt has been made to consolidate the knowledge about the formulae to find the areas of different figures by studying relationships between the areas of geometric figures, provided they lie on the same base and between the same parallels. This study will also be useful in understanding some results on the ‘similarity of triangles’. The chapter contains 4 exercises, of which most of the questions ask the students to prove the statements given.

Topics Covered in Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles:

Review the concept of area and recall the area of a rectangle. 1. (Prove) Parallelograms on the same base and between the same parallels have the same area. 2. (Motivate) Triangles on the same base and between the same parallels are equal in area and its converse.

Theorem 9.1 – Parallelograms on the same base and between the same parallels are equal in area.

Theorem 9.2 – Two triangles on the same base (or equal bases) and between the same parallels are equal in area.

Theorem 9.3 – Two triangles having the same base (or equal bases) and equal areas lie between the same parallels.

Also, access the following resources for Class 9 Chapter 9 Areas of Parallelograms and Triangles, at BYJU’S:

• NCERT Areas of Parallelograms and Triangles Class 9 Notes
• Areas of Parallelograms and Triangles Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Areas of Parallelograms and Triangles
• RD Sharma Solutions Areas of Parallelograms and Triangles Class 9

NCERT Solutions Class 9 Maths Chapter 10 Circles

A circle can be defined as a collection of all the points in a plane at a fixed distance from a fixed point in the plane. Topics like Angle Subtended by a Chord at a Point, Equal Chords and their respective distances from the Centre, the Angle Subtended by an Arc of a Circle, Cyclic Quadrilaterals and other terms related to circles are covered in this chapter. A total of twelve theorems are present in this chapter, learning which the students will get a clearer idea of the concepts taught. There are 6 exercises in this chapter which consist of questions from all the concepts present in the chapter.

Topics Covered in Class 9 Maths Chapter 10 Circles:

Through examples, arrive at definitions of circle-related concepts, radius, circumference, diameter, chord, arc, and subtended angle. 1. (Prove) Equal chords of a circle subtend equal angles at the centre and (motivate) its converse. 2. (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord, and conversely, the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. 3. (Motivate) There is one and only one circle passing through three given non-collinear points. 4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the centre(s) and conversely. 5. (Prove) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. 6. (Motivate) Angles in the same segment of a circle are equal. 7. (Motivate) If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the segment, the four points lie on a circle. 8. (Motivate) The sum of either pair of opposite angles of a cyclic quadrilateral is 180 0 and its converse.

Theorem 10.1 – Equal chords of a circle subtend equal angles at the centre.

Theorem 10.2 – If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.

Theorem 10.3 – The perpendicular from the centre of a circle to a chord bisects the chord.

Theorem 10.4 – The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

Theorem 10.5 – There is one and only one circle passing through three given non-collinear points.

Theorem 10.6 – Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).

Theorem 10.7 – Chords equidistant from the centre of a circle are equal in length.

Theorem 10.8 – The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Theorem 10.9 – Angles in the same segment of a circle are equal.

Theorem 10.10 – If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle (i.e. they are concyclic).

Theorem 10.11 – The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.

Theorem 10.12 – If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.

Also, access the following resources for Class 9 Chapter 10 Circles, at BYJU’S:

• NCERT Circles Class 9 Notes
• Circles Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Circles
• RD Sharma Solutions Circles Class 9

NCERT Solutions Class 9 Maths Chapter 11 Constructions

In this chapter, students will learn some basic constructions. The method learnt will then be used to construct certain kinds of triangles. There are 2 exercises present in this chapter, of which the first exercise deals with the construction of a certain angle or the bisector of a given angle. On the other hand, the second exercise deals with the constructions of triangles when different parameters are given.

Topics Covered in Class 9 Maths Chapter 11 Constructions:

1. Construction of bisectors of a line segment and angle, 60°, 90°, 45° angles etc., equilateral triangles. 2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle. 3. Construction of a triangle of given perimeter and base angles.

Construction 11.1 – To construct the bisector of a given angle.

Construction 11.2 – To construct the perpendicular bisector of a given line segment.

Construction 11.3 – To construct an angle of 600 at the initial point of a given ray.

Construction 11.4 – To construct a triangle, given its base, a base angle and the sum of the other two sides.

Construction 11.5 – To construct a triangle given its base, a base angle and the difference between the other two sides.

Construction 11.6 – To construct a triangle, given its perimeter and its two base angles.

Also, access the following resources for Class 9 Chapter 11 Constructions, at BYJU’S:

• NCERT Constructions Class 9 Notes
• Constructions Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Constructions
• RD Sharma Solutions Constructions Class 9

NCERT Solutions Class 9 Maths Chapter 12 Heron’s Formula

The chapter discusses Heron’s formula, which can be used to calculate the area of a triangle when the length of all three sides is given. In this method, there is no need to calculate the angles or other distances in the triangle. This formula can be used not only to find the area of triangles but also to find the areas of quadrilaterals and other polygons by dividing them into triangles. There are 2 exercises in this chapter which help the student understand the method of solving the problems based on Heron’s formula.

Topics Covered in Class 9 Maths Chapter 12 Heron’s Formula:

Area of a triangle using Heron’s formula (without proof) and its application in finding the area of a quadrilateral.

Area of a triangle = 1/2 × base × height

Where a, b and c are the sides of a triangle

s is the semi-perimeter, i.e. half of the perimeter of a triangle = (a + b + c)/2

Also, access the following resources for Class 9 Chapter 12 Heron’s Formula, at BYJU’S:

• NCERT Heron’s Formula Class 9 Notes
• Heron’s Formula Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Heron’s Formula
• RD Sharma Solutions Heron’s Formula Class 9

NCERT Solutions Class 9 Maths Chapter 13 Surface Areas and Volumes

In this chapter, students shall learn to find the surface areas and volumes of cuboids and cylinders in detail and broaden the study to some other solids, such as cones and spheres. This chapter is just an extended version of the chapter mensuration, in which the students learnt about the surface areas and volumes in earlier classes. There are 8 exercises in this chapter, and these exercises contain problems that are based on surface areas and volumes of different solids such as cubes, cuboids, spheres, cylinders, cones, and hemispheres.

Topics Covered in Class 9 Maths Chapter 13 Surface Areas and Volumes :

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

Surface Area of a Cuboid = 2(lb + bh + hl)

where l, b and h are, respectively, the three edges of the cuboid

Surface Area of a Cube = 6a 2

where a is the edge of the cube.

Curved Surface Area of a Cylinder = 2πrh

where r is the radius of the base of the cylinder and h is the height of the cylinder

Total Surface Area of a Cylinder = 2πr(r + h)

where h is the height of the cylinder and r is its radius

Curved Surface Area of a Cone = 1/2 × l × 2πr = πrl

where r is its base radius, and l is its slant height

Total Surface Area of a Cone = πrl + πr 2 = πr(l + r)

Surface Area of a Sphere = 4 π r 2

where r is the radius of the sphere.

Curved Surface Area of a Hemisphere = 2πr 2

where r is the radius of the sphere of which the hemisphere is a part.

Total Surface Area of a Hemisphere = 3πr 2

Volume of a Cuboid = base area × height = length × breadth × height

Volume of a Cube = edge × edge × edge = a 3

Volume of a Cylinder = πr 2 h

where r is the base radius, and h is the height of the cylinder.

Volume of a Cone = 1/3 πr 2 h

where r is the base radius, and h is the height of the cone.

Volume of a Sphere = 4/3 πr 3

Volume of a Hemisphere = 2/3 πr 3

where r is the radius of the hemisphere.

Also, access the following resources for Class 9 Chapter 13 Surface Areas and Volumes, at BYJU’S:

• NCERT Surface Areas and Volumes Class 9 Notes
• Surface Areas and Volumes Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Surface Areas and Volumes
• RD Sharma Solutions Surface Areas and Volumes Class 9

NCERT Solutions Class 9 Maths Chapter 14 Statistics

The branch of Mathematics in which the extraction of meaningful information is studied is known as Statistics. It can also be defined as the collection of data on different aspects of the life of people useful to the State. The chapter teaches about the different presentations of the data, including the frequency distribution as well. The chapter also helps the students learn the graphical representation of data using different graphs such as Bar graphs, Histograms, Frequency polygons, etc. The chapter also lets the students learn the measure of central tendency mean, median and mode of the raw data. A total of 4 exercises are present in the chapter that includes problems related to all these concepts.

Topics Covered in Class 9 Maths Chapter 14 Statistics:

Introduction to Statistics: Collection of data, presentation of data – tabular form, ungrouped/grouped, bar graphs, histograms (with varying base lengths), frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, and mode of ungrouped data.

Statistics deals with the collection, presentation, and analysis of data, as well as the drawing of meaningful conclusions from the data.

Mean – It is found by adding all the values of the observations and dividing it by the total number of observations. It is denoted by \(\begin{array}{l}\overline{x}\end{array} \) .

Median – It is the value of the middle-most observation (s).

If n is an odd number, the median = value of the [(n + 1)/2] th observation

If n is an even number, median = Mean of the values of the (n/2) th and [(n/2) + 1] th observations.

Mode – The mode is the most frequently occurring observation.

Also, access the following resources for Class 9 Chapter 14 Statistics, at BYJU’S:

• NCERT Statistics Class 9 Notes
• Statistics Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Statistics
• RD Sharma Solutions Statistics Class 9

NCERT Solutions Class 9 Maths Chapter 15 Probability

The collection of some outcomes of an experiment is known as an event of an experiment. The chances of occurrence of an event are known as probability. In this chapter, students will learn to measure the chance of occurrence of a particular outcome in an experiment. This chapter contains only 1 exercise. The problems covered in this exercise are based on real-life incidents, enhancing the interest of the students in solving the questions.

Topics Covered in Class 9 Maths Chapter 15 Probability:

History, Repeated experiments and observed frequency approach to probability. Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real-life situations and from examples used in the chapter on statistics).

The empirical probability P(E) of an event E happening is given by

P (E) = Number of trials in which the event happened/The total number of trials

Also, access the following resources for Class 9 Chapter 15 Probability, at BYJU’S:

• NCERT Probability Class 9 Notes
• Probability Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Probability
• RD Sharma Solutions Probability Class 9

Benefits of BYJU’S NCERT Maths Solutions for Class 9

• The solutions are given in easy steps so that students can easily understand them.
• Students can access these solutions for free and clear any doubts instantly.
• Exercise-wise PDFs are also provided for all chapters of CBSE 9th Class Maths.
• Detailed explanations also help students to develop problem-solving skills and help them to learn concepts more effectively.
• The questions are solved using the easiest method.
• Diagrams are also given to help students visualise the questions and solutions.

CBSE Class 9 Maths Unit-wise Weightage for 2023-24

Internal Assessment Class 9

During the exam preparation, students should first complete the units carrying more weightage and then move on to the lower weightage. This helps students to first cover the important concepts and improves their confidence level to perform well in the annual exam.

The students are advised to analyse all the concepts covered in the Syllabus of Class 9 Maths and prepare a proper preparation strategy. It’s merely impossible to score well in Maths by simply reading and memorising the concepts. Students should always try to understand the concept and logic given in any particular topic. The students are suggested to practise these NCERT Solutions Class 9 materials on a regular basis to develop a strong understanding of basic mathematics concepts.

Along with the NCERT Solutions, we have also provided a brief summary of important formulas and different methods of solving similar problems to help students understand the concepts thoroughly. Keep visiting BYJU’S to get more updated learning materials, and download the BYJU’S app for a better and personalised learning experience with engaging video lessons.

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NCERT Solutions for Class 9 Maths

NCERT Solutions for Class 9 Maths in Hindi and English Medium are given here along with class 9th Maths current syllabus. NCERT Solutions for Class 9 Maths in Hindi and English Medium have been updated for session 2024-25. We at Tiwari Academy have spared no effort in providing the best NCERT Solutions for Class 9 Maths keeping in mind needs of the students. Tiwari Academy’s NCERT Solutions are helpful to students by providing conceptual clarity and developing problem-solving ability. Class 9 Maths Syllabus for 2024-25 Chapter 1. Number Systems Chapter 2. Polynomials Chapter 3. Coordinate Geometry Chapter 4. Linear Equations in Two Variables Chapter 5. Introduction to Euclid’s Geometry Chapter 6. Lines and Angles Chapter 7. Triangles Chapter 8. Quadrilaterals Chapter 9. Circles Chapter 10. Heron’s Formula Chapter 11. Surface Areas and Volumes Chapter 12. Statistics For other State Boards Chapter 13. Surface Areas and Volumes Chapter 14. Statistics Chapter 15. Probability

NCERT Solutions of Class 9 Maths

The solutions and answers have been suitably modified and revised taking into account the guidelines of CBSE and State board 9th Maths curriculum 2024-25 . Your valuable feedback and Review would help us to improve further our answers. Class 9 Solution Apps Download Class 9 Math solutions can be found in various formats, including printed books, online resources, and mobile applications. Some websites like Tiwari Academy consider a sacred social responsibility by offering free access to NCERT solutions, so that education becomes accessible to one and all.

CBSE Syllabus for Class 9 Maths Revised for 2024-25

• CBSE Syllabus for Class 9 Maths

NCERT solutions are considered very useful for students as they are developed by subject experts based on curriculum prescribed by CBSE. If you are searching for the Class 9 Maths UP Board NCERT Solutions revised for 2024-25 exams, then do not worry. The good news is that Tiwari Academy has provided updated NCERT textbook solutions for Class 9 Mathematics here for all chapters. These are helpful in scoring more marks in the examination. They provide a solid foundation for understanding mathematical concepts and enable students to excel in their studies.

NCERT Solution Apps for 9th Class You can get to know about various concepts while solving Class 9 Maths NCERT Solutions , which will be useful in your higher classes. Get Class 9th Maths question answers for the new Academic year based on latest NCERT book syllabus.

Tiwari Academy’s Educational App sends notifications and reminders for important dates, exams and study schedules. These help students to stay organized and on track with their studies. Students can monitor their scores, completion of exercises and areas where they need improvement.

How to Score well in class 9 Maths Exams For a Class 9 student aiming to excel in Maths, a structured approach to learning and practice is the key. Start by thoroughly understanding the current syllabus and the fundamental concepts it covers.

Physical exercise, hobbies, or even short walks can be refreshing and help in maintaining focus during study sessions. A positive mindset and belief in your ability to learn and improve will go a long way in improving your overall personality. Regular self-assessment mathematics through quizzes or timed practice sessions can be beneficial. This not only helps in identifying areas that need more attention but also builds confidence.

NCERT Solutions for Class 9 Maths All Chapters

These Chapter Wise NCERT Solutions for Class 9 Maths App is well designed so that class 9 students can easily understand each sum’s solutions. The Class 9th NCERT Math textbook has a total of 12 chapters which are divided into six units. Solving Class 9th Maths solution in each chapter will ensure positive results. Chapters covered in the NCERT 9th Math textbook are Number System, Polynomials, Introduction to Euclids Geometry, Quadrilaterals, Surface Areas, Heron’s Formula, and Volumes, Statistics etc. 

NCERT Class 9 Maths Chapters Solutions

Students who are facing any trouble in solving tough Class 9th Maths problems can get best help from these CBSE Maths Class 9 Solutions of NCERT (https://ncert.nic.in/) textbooks. The syllabus contains 12 chapters with important topics. Here all solutions build your fundamental very clear and efficiency by solving theses exercise-wise solutions.

NCERT Solutions for Class 9 Maths Chapter 1 – Number System

NCERT Solutions for Class 9 Maths Chapter 1 introduce you different topics such as rational numbers and irrational numbers. You can learn how to represent the integers, rational and irrational numbers in a line. Here you get an overall knowledge of the number line.

Class 9 Maths Chapter 1 for CBSE Board Class 9 Maths Exercise 1.1 in English Class 9 Maths Exercise 1.2 in English Class 9 Maths Exercise 1.3 in English Class 9 Maths Exercise 1.4 in English Class 9 Maths Exercise 1.5 in English

Class 9 Maths Chapter 1 Solution for State Boards Class 9 Maths Chapter 1 Exercise 1.1 Class 9 Maths Chapter 1 Exercise 1.2 Class 9 Maths Chapter 1 Exercise 1.3 Class 9 Maths Chapter 1 Exercise 1.4 Class 9 Maths Chapter 1 Exercise 1.5 Class 9 Maths Chapter 1 Exercise 1.6

Class 9 Maths Chapter 1 in Hindi Medium Class 9 Maths Exercise 1.1 in Hindi Class 9 Maths Exercise 1.2 in Hindi Class 9 Maths Exercise 1.3 in Hindi Class 9 Maths Exercise 1.4 in Hindi Class 9 Maths Exercise 1.5 in Hindi

There are five exercises in this NCERT Solutions for Class 9 Maths Chapter 1 Number System, where you can also find all word problems based on 9th Class Maths NCERT Book. You can learn from these 9th Class Maths Book Solution, the representation of terminating and non-terminating recurring decimals, presentation of square roots of 2, 3, other non-rational numbers on the number line.

Topics to Study in Class 9 Maths Chapter 1 Number Systems Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers. 2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number. 3. Definition of nth root of a real number. 4. Rationalization (with precise meaning) of real numbers of the type 1/(a + b√x) and 1/(√x + √y) (and their combinations) where x and y are natural number and a and b are integers. 5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials

Get NCERT Solutions for Class 9 Maths Chapter 2 here with free of cost, and all solutions are solved by the professional Maths teacher. Class 9 Maths Chapter 2 for CBSE Board Class 9 Maths Exercise 2.1 in English Class 9 Maths Exercise 2.2 in English Class 9 Maths Exercise 2.3 in English Class 9 Maths Exercise 2.4 in English

Class 9 Maths Chapter 2 Solution for State Boards Class 9 Maths Chapter 2 Exercise 2.1 Class 9 Maths Chapter 2 Exercise 2.2 Class 9 Maths Chapter 2 Exercise 2.3 Class 9 Maths Chapter 2 Exercise 2.4 Class 9 Maths Chapter 2 Exercise 2.5

Class 9 Maths Chapter 2 in Hindi Medium Class 9 Maths Exercise 2.1 in Hindi Class 9 Maths Exercise 2.2 in Hindi Class 9 Maths Exercise 2.3 in Hindi Class 9 Maths Exercise 2.4 in Hindi

This chapter Polynomial consists of variables and coefficients, its operations of addition, subtraction, multiplication and also non-negative integer exponents of variables.

Topics of Class 9 Maths Chapter 2 Polynomials Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax² + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities: (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx (x + y)³ = x³ + y³ + 3xy(x + y) (x – y)³ = x³ – y³ – 3xy(x – y) x³ + y³ = (x + y)(x² – xy + y²) x³ – y³ = (x – y)(x² + xy + y²) x³ + y³ + z³ – 3xyz = (x + y)(x² + y² + z² – xy – yz – 2zx) and their use in factorization of polynomials.

NCERT Solutions for Class 9 Maths Chapter 3 – Coordinate Geometry

Students can get NCERT exercises solutions for Class 9 Maths Chapter 3 with free of cost. This chapter 3 introduced the concepts of the cartesian plane, coordinates of a point in the plane, terms, coordinate plan notations, x-axis, y-axis, x- coordinate, y-coordinate, quadrants, origin and many more.

Class 9 Maths Chapter 3 for CBSE Board Class 9 Maths Exercise 3.1 in English Class 9 Maths Exercise 3.2 in English

Class 9 Maths Chapter 3 for State Boards Class 9 Maths Chapter 3 Exercise 3.1 Class 9 Maths Chapter 3 Exercise 3.2 Class 9 Maths Chapter 3 Exercise 3.3

Class 9 Maths Chapter 3 in Hindi Medium Class 9 Maths Exercise 3.1 in Hindi Class 9 Maths Exercise 3.2 in Hindi

In NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry, students learn coordinate plane and the mutually perpendicular lines which are called axe. They downloads NCERT Solutions for Class 9 Maths PDF to learn offline anywhere. Get Chapter Number System Class 9 Maths Solutions in Hindi medium and English medium.

Class 9 Maths Chapter 3 Coordinate Geometry Main Points The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.

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

NCERT Solutions for Class 9 Maths Chapter 4 teaches you here about the knowledge of linear equations in one variable. In this chapter, know about linear equations in two variables, such as ax + by + c = 0. Learn here how to graph of a linear equation in two variables.

Class 9 Maths Chapter 4 for CBSE Board Class 9 Maths Exercise 4.1 in English Class 9 Maths Exercise 4.2 in English

Class 9 Maths Chapter 4 for State Boards Class 9 Maths Chapter 4 Exercise 4.1 Class 9 Maths Chapter 4 Exercise 4.2 Class 9 Maths Chapter 4 Exercise 4.3 Class 9 Maths Chapter 4 Exercise 4.4

Class 9 Maths Chapter 4 in Hindi Medium Class 9 Maths Exercise 4.1 in Hindi Class 9 Maths Exercise 4.2 in Hindi

There are only two exercises in this NCERT Solutions for Class 9 Maths Chapter 9 Linear Equations in Two Variables. Download NCERT Solutions for Class 9 Maths PDF free of cost and study at any time anywhere. Students take the benefits clearing all the concepts of each math sum. Download free unlimited Chapter Linear Equations in Two Variables Class 9 Maths Solutions in Hindi Medium and English Medium.

Topics to be covered in Class 9 Maths Chapter 4 Linear Equations in Two Variables Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c = 0. Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.

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

Get NCERT Solutions for Class 9 Maths Chapter 5 for all exercises. This chapter includes Euclid’s approach to geometry which is used the present-day geometry. In NCERT exercises for Class 9 Maths Introduction to Euclid’s Geometry defining common geometrical shapes and terms.

Class 9 Maths Chapter 5 for CBSE Board Class 9 Maths Exercise 5.1 in English

Class 9 Maths Chapter 5 for State Boards Class 9 Maths Chapter 5 Exercise 5.1 Class 9 Maths Chapter 5 Exercise 5.2

Class 9 Maths Chapter 5 in Hindi Medium Class 9 Maths Exercise 5.1 in Hindi

There is only one exercise in this 9th Class Maths Book Solution which teach you deeper knowledge relation between axiom, postulates, and theorems. Download here Chapter Euclid’s Geometry Class 9 Maths Solutions in Hindi medium and English medium.

Syllabus of Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom) 1. Given two distinct points, there exists one and only one line through them. (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

NCERT Solutions for Class 9 Maths Chapter 6 – Lines and Angles

NCERT Solutions for Class 9 Maths Chapter 6 revolves around the theorems present in the topics of Lines and Angles.

Class 9 Maths Chapter 6 Solutions for CBSE Board Class 9 Maths Exercise 6.1 in English Class 9 Maths Exercise 6.2 in English

Class 9 Maths Chapter 6 Solutions for State Boards Class 9 Maths Chapter 6 Exercise 6.1 Class 9 Maths Chapter 6 Exercise 6.2 Class 9 Maths Chapter 6 Exercise 6.3

Class 9 Maths Chapter 6 in Hindi Medium Class 9 Maths Exercise 6.1 in Hindi Class 9 Maths Exercise 6.2 in Hindi

9th Maths Book Solution are provided here are well-reviewed. Get free NCERT Solutions for Class 9 Maths in PDF for offline study. Practice these solutions thoroughly to get maximum marks in the final exam. Download Chapter Lines and Angles Class 9 Maths Solutions in Hindi medium and English medium.

Class 9 Maths Chapter 6 Lines and Angles Topics 1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse. 2. (Prove) If two lines intersect, vertically opposite angles are equal. 3. (Motivate) Lines which are parallel to a given line are parallel.

NCERT Solutions for Class 9 Maths Chapter 7 – Triangles

Get NCERT Solutions for Class 9 Maths Chapter 7 , and students will study detail knowledge about the triangle, congruence of triangles, rules of congruence, and its properties of triangles and many more.

Class 9 Maths Chapter 7 Solutions for CBSE Board Class 9 Maths Exercise 7.1 in English Class 9 Maths Exercise 7.2 in English Class 9 Maths Exercise 7.3 in English

Class 9 Maths Chapter 7 Solutions for State Boards Class 9 Maths Chapter 7 Exercise 7.1 Class 9 Maths Chapter 7 Exercise 7.2 Class 9 Maths Chapter 7 Exercise 7.3 Class 9 Maths Chapter 7 Exercise 7.4 Class 9 Maths Chapter 7 Exercise 7.5

Class 9 Maths Chapter 7 in Hindi Medium Class 9 Maths Exercise 7.1 in Hindi Class 9 Maths Exercise 7.2 in Hindi Class 9 Maths Exercise 7.3 in Hindi

In this 9th Maths Book Solution, we have to prove the properties of the triangle which you learn about in previous classes. Apply the various congruence rules while solving the problems. In this chapter, students learn about eight theorems. There are three exercises which cover in this NCERT Solutions for Class 9 Maths Chapter 7 Triangles. Get Chapter Triangles Class 9 Maths Solutions in Hindi medium and English medium.

Class 9 Maths Chapter 7 Triangles Main Points to Study 1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). 2. (Prove) 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). 3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence). 4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence) 5. (Prove) The angles opposite to equal sides of a triangle are equal. 6. (Motivate) The sides opposite to equal angles of a triangle are equal.

NCERT Solutions for Class 9 Maths Chapter 8 – Quadrilaterals

Find NCERT Solutions for Class 9 Maths Chapter 8 , which covers the topic Quadrilaterals. The joining four points in order is called a quadrilateral.

Class 9 Maths Chapter 8 for CBSE and State Boards Class 9 Maths Exercise 8.1 in English Class 9 Maths Exercise 8.2 in English

Class 9 Maths Chapter 8 in Hindi Medium Class 9 Maths Exercise 8.1 in Hindi Class 9 Maths Exercise 8.2 in Hindi

Class 9 Maths chapter 8 contains two exercises that contain only one theorem to prove. These Solutions include Angle sum property of a Quadrilateral, properties of a parallelogram, and types of quadrilaterals etc. Download here Chapter Quadrilaterals Class 9 Maths Solutions in Hindi medium and English medium.

Class 9 Maths Chapter 8 Quadrilaterals Focus Points 1. (Prove) The diagonal divides a parallelogram into two congruent triangles. 2. (Motivate) In a parallelogram opposite sides are equal, and conversely. 3. (Motivate) In a parallelogram opposite angles are equal, and conversely. 4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely. 6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

NCERT Solutions for Class 9 Maths Chapter 9 – Circles

Here get well explained NCERT Solutions for Class 9 Maths Chapter Circles with free of cost and no need to login and register to get solutions for all exercises. In this NCERT Solutions for Class 9 Maths Chapter 9 Circle, learn that circle is a collection of all the points in a plane at a fixed distance.

Class 9 Maths Chapter 9 for CBSE Board Class 9 Maths Exercise 9.1 in English Class 9 Maths Exercise 9.2 in English Class 9 Maths Exercise 9.3 in English

Class 9 Maths Chapter 9 Solutions for State Boards Class 9 Maths Chapter 9 Exercise 9.1 Class 9 Maths Chapter 9 Exercise 9.2 Class 9 Maths Chapter 9 Exercise 9.3 Class 9 Maths Chapter 9 Exercise 9.4

Class 9 Maths Chapter 9 in Hindi Medium Class 9 Maths Exercise 9.1 in Hindi Class 9 Maths Exercise 9.2 in Hindi Class 9 Maths Exercise 9.3 in Hindi

Get knowledge about circle including a Chord at a Point, Equal Chords. There are a total of twelve theorems present in this chapter. Download  NCERT Solutions for Class 9 Maths PDF without any cost and registration. Get Chapter 9 Circles Class 10 Maths Solutions in Hindi medium and English medium here.

Class 9 Maths Chapter 9 Circles Curriculum for 2024-25 1.(Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse. 2.(Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord. 3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely. 4. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle. 5. (Motivate) Angles in the same segment of a circle are equal. 6. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle. 7. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

NCERT Solutions for Class 9 Maths Chapter 10 – Heron’s Formula

Students get NCERT Solutions for Class 9 Maths Chapter 10 , which covers Heron’s formula which is used to calculate the area of a triangle with all three sides length is given. By the help of Heron’s Formula, find out distances in the triangle without calculating.

Class 9 Maths Chapter 10 for CBSE Board Class 9 Maths Exercise 10.1 in English

Class 9 Maths Chapter 10 for State Boards Class 9 Maths Chapter 10 Exercise 10.1 Class 9 Maths Chapter 10 Exercise 10.2 Class 9 Maths Chapter 10 Exercise 10.3 Class 9 Maths Chapter 10 Exercise 10.4 Class 9 Maths Chapter 10 Exercise 10.5 Class 9 Maths Chapter 10 Exercise 10.6

Class 9 Maths Chapter 10 in Hindi Medium Class 9 Maths Exercise 10.1 in Hindi

This formula is used to find out the areas of quadrilaterals, the area of triangles and other polygons. There is only one exercise in this NCERT Solutions for Class 9 Maths Chapter 10 Heron’s Formula. Download NCERT Solutions for Class 9 Maths Chapter 12 PDF and learn anytime in desktop or mobile while offline.

Class 9 Maths Chapter 10 Heron’s Formula Main Points To Study Area of a triangle using Heron’s formula (without proof)

NCERT Solutions for Class 9 Maths Chapter 11 – Surface Areas and Volumes

NCERT Solutions for Class 9 Maths Chapter 11 , learn to find the surface areas and volumes of cuboids and cylinders in details. In this NCERT Solutions for Class 9 Maths Chapter 11 Surface Areas and Volumes, learn the surface areas of some other solids such as cones and spheres.

Class 9 Maths Chapter 11 for CBSE Board Class 9 Maths Exercise 11.1 in English Class 9 Maths Exercise 11.2 in English Class 9 Maths Exercise 11.3 in English Class 9 Maths Exercise 11.4 in English

Class 9 Maths Chapter 11 Solutions for State Boards Class 9 Maths Chapter 11 Exercise 11.1 Class 9 Maths Chapter 11 Exercise 11.2

Class 9 Maths Chapter 11 in Hindi Medium Class 9 Maths Exercise 11.1 in Hindi Class 9 Maths Exercise 11.2 in Hindi Class 9 Maths Exercise 11.3 in Hindi Class 9 Maths Exercise 11.4 in Hindi

Here students get detailed knowledge about the surface areas and volumes in earlier classes. There are four exercises in chapter 11 that covers surface areas and volumes of different solids such as cubes, cuboids, hemispheres, spheres, cylinders, cones etc. Download NCERT Solutions for Class 9 Maths PDF here without paying any cost and required no login detail. Get Chapter Surface Areas and Volumes  Class 9 Maths Solutions in Hindi medium and English medium.

The Points to be covered in Class 9 Maths Chapter 11 Surface Areas and Volumes Surface areas and volumes of spheres (including hemispheres) and right circular cones.

NCERT Solutions for Class 9 Maths Chapter 12 – Statistics

These best easy NCERT Solutions for Class 9 Maths Chapter 12 , deals with Statistics which the extraction of meaningful information is studied is known as Statistics.

Class 9 Maths Chapter 12 for CBSE Board Class 9 Maths Exercise 12.1 in English

Class 9 Maths Chapter 12 Solutions for State Boards Class 9 Maths Chapter 12 Exercise 12.1 Class 9 Maths Chapter 12 Exercise 12.2

Class 9 Maths Chapter 12 in Hindi Medium Class 9 Maths Exercise 12.1 in Hindi

Statistics is used in our daily life such as aspects of the life of people, useful to the State etc. These NCERT Solutions for Class 9 Maths Chapter 12 Statistics teaches the different presentation of the data, including the frequency distribution too. Presentation data in tubular and row form and grouping them in a regular interval. Here learn to Mean, Mode and median as well. Get Chapter Statistics Class 9 Maths Solutions in Hindi medium and English medium.

Class 9 Maths Chapter 12 Statistics Main Points Bar graphs, histograms (with varying base lengths), and frequency polygons.

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

Tiwari Academy NCERT solutions on Surface Areas and Volumes based on state board syllabus, Hindi and English medium, 2024-25 session. Achieve mastery in geometry with Tiwari Academy’s expert NCERT Solutions for Class 9 Maths Exercise 13.8, tailored for students in the 2024-2025 session, available in both Hindi and English. Class 9 Maths Chapter 13 for State Boards Class 9 Maths Chapter 13 Exercise 13.1 Class 9 Maths Chapter 13 Exercise 13.2 Class 9 Maths Chapter 13 Exercise 13.3 Class 9 Maths Chapter 13 Exercise 13.4 Class 9 Maths Chapter 13 Exercise 13.5 Class 9 Maths Chapter 13 Exercise 13.6 Class 9 Maths Chapter 13 Exercise 13.7 Class 9 Maths Chapter 13 Exercise 13.8 Class 9 Maths Chapter 13 Exercise 13.9

NCERT Solutions for Class 9 Maths Chapter 14 Statistics

Access Class 9 Maths Chapter 14 Statistics solutions in Hindi and English. Perfect for CBSE students, our resources at Tiwari Academy are comprehensive and user-friendly. Class 9 Maths Chapter 1 Solution for State Boards Class 9 Maths Chapter 14 Exercise 14.1 Class 9 Maths Chapter 14 Exercise 14.2 Class 9 Maths Chapter 14 Exercise 14.3 Class 9 Maths Chapter 14 Exercise 14.4

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Master Class 9 Maths with Chapter 15 Probability solutions, available in English and Hindi. Excel in CBSE exams with Tiwari Academy’s expert resources. Clear, concise, and free – your key to understanding Probability concepts. Class 9 Maths Chapter 15 Solutions for State boards Class 9 Maths Chapter 15 Exercise 15.1

Importance of NCERT Solutions for Class 9 Maths

NCERT stands for National Council of Educational Research and Training. NCERT was formed to provide standardised textbooks along with research and training in the field of education system of India. NCERT Solutions for Class 9 Maths is very helpful will provide you with a detailed and in-depth understanding of all the questions and concepts of NCERT Textbooks. Excluding that there are so many other benefits of NCERT Solutions for Class 9 Maths.

Explain Each And Every Concept in Detail NCERT Solutions for Class 9 Maths explain each and every concept in detail and in easy language. It helps you and so important for better understanding and scoring good marks in 9 class exams.

Most Accurate Solutions All the NCERT Solutions for Class 9 Maths for all chapters are provided by the many years experienced teachers. All solutions are well-reviewed before provided. Students who have misguided by the wrong study materials before can study with these most accurate NCERT Solutions for Class 9 Maths.

Student can learn Offline NCERT Solutions for Class 9 Maths for all chapters PDFS are available, so learn these subjects offline also by just downloading these PDFs. You can study anywhere and anytime.

Clear all Doubts Class 9 Students who have confusion with many topics in class 9 Maths, they can learn with these NCERT Solutions for Class 9 Maths for all chapters. These solutions are given in easy method, and it clear your all doubts and concepts clear.

Created the Best Subject Experts in Field Class 9 Maths solution provided by an expert math teacher who has been created by the high-quality subject matter experts. So get more marks with these high-quality study materials. All solutions are designed by following extensive research on the Math subject. Be able to solve a wide range of problems at any difficulty level.

How are CBSE 9 Maths Solutions of NCERT Helpful for Final Exams?

CBSE 9 Maths Solutions of NCERT is sufficient to score more in 9th boards exams. With NCERT Solutions for Class 9 Maths , students will get complete guidance on every topics and sub-topics related to the respective chapter.

It is an effective and the best way to make students understand the subject and exclusively to perform well in the final exams. CBSE 9 Maths Solutions of NCERT are very helpful to get full marks in the final exam, but Just make sure you cover all the exercise and learn the theorems of the whole syllabus. Also, do not skip any topic of CBSE 9th Maths syllabus .

A panel of experts from Tiwari Academy held a workshop of two days and thoroughly discussed the content quality and made some suggestions . Amendments were carried out in the English as well as Hindi draft accordingly.

The final draft was thus prepared. The solutions are prepared according to new syllabus for 2024-25 having classical approach of constructions and geometrical chapters. Get here UP Board Secondary Education (High School) Solution, Sample Papers, Notes and other study material.

How to practice Class 9 Maths using NCERT Solutions?

According to new NCERT Textbooks published for academic session 2024-25, the syllabus for class 9 Maths is reduced significantly. That is why, the NCERT Solutions for class 9 Maths is also modified and revised as per new session. NCERT Solutions play a significant role in helping students score well in their Class 9 CBSE (Central Board of Secondary Education) Mathematics exams. Follow the steps given here to know how you can score well in exams using class 9 Maths solutions.

Step 1: Use NCERT Solutions for Comprehensive Coverage of class 9 Maths textbook.

Step 2: verify your answers and learn about the exam pattern., step 3: revise the syllabus and use class 9 maths ncert solution as a revision aid., step 4: make effective self study in 9th maths using ncert solutions., step 5: confined to new rationalised ncert textbooks and solve it using ncert solutions..

How many chapters are there in NCERT Class 9 Maths?

According to new syllabus, there are a total of 12 chapters present in the NCERT Class 9 Maths. 

• Chapter 1- Number System,
• Chapter 2- Polynomials, 
• Chapter 3- Coordinate Geometry, 
• Chapter 4- Linear Equations in Two Variables, 
• Chapter 5- Introduction to Euclid’s Geometry, 
• Chapter 6- Lines and Angles, 
• Chapter 7- Triangles, 
• Chapter 8- Quadrilaterals, 
• Chapter 9- Circles, 
• Chapter 10- Heron’s Formula, 
• Chapter 11- Surface Areas and Volumes, 
• Chapter 12- Statistics, 

These are the chapters in Class 9 of NCERT Maths. And you need to cover all the chapters to get full marks in your final exam.

How can I get more than 80% marks in Class 9 Maths Exams?

Most of the chapters in Class 9 Maths are easy to understand. If we try to learn by doing, the mathematics become simple and interesting subject otherwise it would be a burden for us. Get concentrated on your NCERT Textbook 2024-25 and start practicing with understanding to score well with less efforts. How to practice questions: Read the preface of the chapter and see the pattern of each example given before the exercises. Now taking the hints from these solved example, try to solve the questions of exercises by own. Don’t take help from teachers or online website when your are solving the questions. After trying many time if still not getting the correct answers, then consult your respective teacher or visit to Tiwari Academy to take help from PDF Solutions or videos solutions.

Is class 9 maths tough?

In real maths of class, 9th and 10th are both very easy. But practically you can say class 9th maths is tough for you because you introduced some new topics and topics in the advanced level study here. In previous classes like 8th, 7th and 6th, the maths you study is very basic and somehow simple. So your mindset is for that simple maths method with very fewer logics and formulas. Some student class 9 get confusion with the syllabus.

How can I perform best in Terminal exams of Class 9 Maths?

There are so many chapters in class 9 Maths which are easy and interesting to work with. When you are in energetic mood, start doing the chapter which you considered as difficult one but if you are tired and still want to practice mathematics, start with an easier chapter. Studying in this manner make the mathematics interesting and easier.

Sushant Mukherjee

Providing help in science for class 6 to 10. Adviser in Tiwari Academy for the science related subjects subject as well as videos contents. Ample teaching experience in schools. I am not only working for Tiwari Academy but also provide new ideas for the website and apps.

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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.

NCERT Books

NCERT Books for Class 9 Maths PDF Download [2020- 21 Edition Revised Syllabus]

NCERT Books Class 9 Maths : The National Council of Educational Research and Training (NCERT) publishes Maths textbooks for Class 9. The NCERT Class 9th Maths textbooks are well known for it’s updated and thoroughly revised syllabus. The NCERT Maths Books are based on the latest exam pattern and CBSE syllabus.

NCERT keeps on updating the Maths books with the help of the latest question papers of each year. The Class 9 Maths books of NCERT are very well known for its presentation. The use of NCERT Books Class 9 Maths is not only suitable for studying the regular syllabus of various boards but it can also be useful for the candidates appearing for various competitive exams, Engineering Entrance Exams, and Olympiads.

NCERT Class 9 Maths Books in English PDF Download

NCERT Class 9 Maths Books are provided in PDF form so that students can access it at any time anywhere. Class 9 NCERT Maths Books are created by the best professors who are experts in Maths and have good knowledge in the subject.

• Class 9 Maths NCERT Book English Medium
• Class 9 Maths NCERT Book Hindi Medium
• Class 9 Maths Proofs in Mathematics
• Class 9 Maths Introduction to Mathematical Modelling

NCERT Books for Class 9 Maths English Medium

NCERT Books for Class 9th Maths (Ganit) – Hindi Medium

• Class 9 Maths NCERT Book Introduction
• पाठ 1:  संख्या पद्धति
• पाठ 2:  बहुपद
• पाठ 3:  निर्देशांक ज्यामिति
• पाठ 4:  दो चरों वाले रैखिक समीकरण
• पाठ 5:  यूक्लिड की ज्यामिति का परिचय
• पाठ 6:  रेखाएँ और कोण
• पाठ 7:  त्रिभुज
• पाठ 8:  चतुर्भुज
• पाठ 9:  समांतर चतुर्भुजों और त्रिभुजों के क्षेत्रफल
• पाठ 10:  वृत
• पाठ 11:  रचनाएँ
• पाठ 12:  हीरोन का सूत्र
• पाठ 13:  पृष्ठीय क्षेत्रफल और आयतन
• पाठ 14:  सांख्यिकी
• पाठ 15:  प्रायिकता
• Proofs in Mathematics Hindi
• Class 9 Maths Hindi Medium Introduction to Mathematical Modelling

The NCERT syllabus mainly focuses on this book to make it student-friendly to make it useful for both the students and the competitive exam aspirants. The book covers a detailed Maths based on the syllabuses of various boards. NCERT Maths Books for Class 9 is perfectly compatible with almost every Indian education state and central boards.

We hope that this detailed article on NCERT Books Class 9 Maths helps you in your preparation and you crack the Class 9 exams or competitive exams with excellent scores.

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