Ncert Solutions for Class 9 Maths

Class 9 Maths NCERT Solutions Updated PDF Download

NCERT Solutions for Class 9 Maths has answers to all of the problems in the Class 9 NCERT textbook. This Ncert Solutions created by Utopper Subject Experts will help you for getting good marks in your exams. Students can use the links at the bottom of this page to get PDFs of solutions to these problems for each chapter. These NCERT Solutions for Class 9 cover all of the topics in the NCERT textbook, such as the Number System, Coordinate Geometry, Polynomials, Euclid’s Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, Probability, etc.

Students can practice all kinds of questions from each chapter with the help of these Solutions of NCERT Books for Class 9 Maths. Our experts have set up the CBSE Class 9 Maths Solutions in a well-organized way so that you can find more than one way to solve each problem and fully understand the concepts. Students are told to do a lot of practice with all of these answers before their tests. It will also help them build a base for classes at a higher level. 

Class 9 Maths Ncert Solutions – Download Free PDFs

Class 9 NCERT Solutions maths are extremely important for students because they help them grasp the fundamentals of the subject and provide a solid basis for future study. Class 9 is a continuation of Class 9, and students are exposed to relatively advanced material compared to their previous classes. NCERT books are the best study materials for Class 9 subjects that students may obtain. The textbook adequately describes all of the ideas a 7th student must master.  Therefore, students with a strong understanding of NCERT Solutions Class 9 can easily pass their CBSE Board or NCERT board exams. 

Our subject experts put together the NCERT Solutions for Class 9 to answer all of your questions about Math, Science, and Social Science in one place. Students who want to do well on the CBSE Class 9 Exam will find that these Solutions for Class 9 NCERT are a great way to learn all of the Maths, Science, and Social Science concepts on the syllabus. The NCERT Solutions are clearly explained with clear graphs and worked-out examples that make it easy to learn. It helps students build a strong understanding of ideas, which is a big part of how well they do on competitive exams later on.

NCERT Solutions for Class 9 Maths – All Chapters

The chapter-by-chapter NCERT Solutions for Class 9 provide students with the key to unlocking their problem-solving skills. Students’ academic careers might be significantly affected by adopting an appropriate learning method. Students can use these solutions not just to get the proper solution but also to determine whether their answers are correct. The ultimate goal of delivering the best NCERT Solutions is to aid students in gaining a thorough understanding of the themes and concepts. 

Ncert Solutions For Class 9 Maths

NCERT Solutions for Class 9 Maths are created and prepared by a team of experienced teachers and subject matter experts, whereas private solutions are written by a single author or possibly two. Therefore, the quality of the content flow in NCERT books is superior to that of any other publisher. Utilize these solutions to attempt to answer all of the questions. Simply read the NCERT books thoroughly, and you may quickly locate the answers to the questions.

If you click on the name of the chapter whose solutions you wish to view, you will be taken to the page for that chapter. Then, you can review the detailed, step-by-step CBSE 9th-grade mathematics questions and answers for every single question in that chapter. 

In class 9, you must learn 15 chapters of mathematics. The following are notable chapters and their respective subjects:

NCERT Solutions for Class 9 Maths Chapter-wise Links :

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

Some Important Chapters Present in the NCERT Class 9 Maths Solutions

Class 9 Maths NCERT Solutions Chapter 1: Number System

This chapter is a continuation of Number Line, which you covered in previous grades. This chapter will also instruct you on how to position different kinds of numbers on a number line. The placement of the square roots of 2 and 3 on the number line, rational numbers, the laws of rational exponents, and integral powers will also be covered in Class 9 Chapter 1.

This chapter covers subjects such as terminating decimals and their respective examples, non-rational numbers, rationalization, and laws of exponents. You must study natural numbers, whole numbers, integers, and so forth. Exercises include questions and examples for practice. Discover the properties and attributes of rational and irrational numbers. The rules of radicals must also be learned from this chapter.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Number systems Exercise 1.1
• Class 9 Maths Number systems Exercise 1.2
• Class 9 Maths Number systems Exercise 1.3
• Class 9 Maths Number systems Exercise 1.4
• Class 9 Maths Number Systems Exercise 1.5
• Class 9 Maths Number Systems Exercise 1.6

NCERT Solutions Class 9 Maths Chapter 2 – Polynomials

This chapter introduces polynomial algebraic expressions and their accompanying nomenclature. This chapter discusses the definition and examples of polynomials as well as their coefficients, degrees, and terms. In addition to quadratic polynomials, linear constants, cubic polynomials, factor theorems, and factorization theorems, NCERT Class 9 Chapter 2 will focus on the many forms of polynomials.

Among the topics discussed in this chapter are polynomial coefficients, polynomial degrees, cubic polynomials, quadratic polynomials, and linear polynomials. Learn all the definitions and formulas and answer as many questions as possible from this chapter. Acquire knowledge of zero polynomials and apply each theorem. You may also answer more questions using the NCERT solutions for Class 9 Mathematics. The factor and remainder theorems are essential concepts, and you must practice them using the solutions.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Polynomials Exercise 2.1
• Class 9 Maths Polynomials Exercise 2.2
• Class 9 Maths Polynomials Exercise 2.3
• Class 9 Maths Polynomials Exercise 2.4
• Class 9 Maths Polynomials Exercise 2.5

NCERT Solutions Class 9 Maths Chapter 3 – Coordinate Geometry

This chapter has three activities that will help you gain a deeper understanding of coordinate geometry. This chapter will introduce you to the Cartesian plane and related terminology. You will also learn how to plot and label a point in the XY plane.

Important subjects discussed in this chapter include cartesian coordinates, point coordinates, and graphing points on a plane, among others. Learn how to write points in various quadrants, all four quadrant signs, etc. Additionally, you should understand how to plot a graph and a point on the Cartesian plane. Solve as many problems as possible and practice the examples to familiarise yourself with the exercise problems.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Coordinate Geometry Exercise 3.1
• Class 9 Maths Coordinate Geometry Exercise 3.2
• Class 9 Maths Coordinate Geometry Exercise 3.3

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

Chapter 4 of the 9th-grade mathematics textbook will show you how to express a linear equation using a graph plot and how to solve linear equations with two variables.

Students must practice chapter-related questions and master the formulas thoroughly. Learn how to graphically describe a linear equation with two variables. You must be knowledgeable about the following chapter topics: On a graph, lines passing through the origin parallel to the coordinate axes and the solution of the linear equation in two variables. Practice and solve exercise problems Also review the examples before beginning to solve the exercise questions.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Linear Equations in Two Variables Exercise 4.1
• Class 9 Maths Linear Equations in Two Variables Exercise 4.2
• Class 9 Maths Linear Equations in Two Variables Exercise 4.3
• Class 9 Maths Linear Equations in Two Variables Exercise 4.4

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

This chapter presents several geometrical terms and shapes. This chapter has two tasks that teach the link between theorems, postulates, and axioms.

Students must demonstrate the connections between axioms and theorems. This chapter is crucial in the ninth-grade NCERT. Master each postulate and theorem. Examine the examples to better comprehend the ideas. This chapter is simple, and you should do well on it. This chapter contains only two exercises, and you should be thorough with both.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Introduction to Euclid Geometry Exercise 5.1
• Class 9 Chapter 5 Introduction to Euclid’s Geometry Ex  5.2

NCERT Solutions Class 9 Maths Chapter 6 – Lines and Angles

Chapter 6 of the ninth-grade mathematics textbook contains various theorems and strategies for proving these theorems based on angles and lines. Two exercises are covered in this chapter.

The sum of the angles of a triangle is always 1800, the sum of two inside opposite angles yields an outside angle, etc. are some of the subjects presented in this chapter. As you are already aware, this is one of the most crucial chapters, so you must study it with extreme care. You must complete and practice all of the exercises’ questions. This chapter covers fundamental concepts such as linear pairs, lines parallel to the same line, etc. Learn the types and characteristics of triangles and angles. You must have a firm grasp of the concepts presented in this chapter, and you can utilize the NCERT Class 9 Maths solutions to study the aforementioned topics.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Lines and Angles Exercise 6.1
• Class 9 Maths Lines and Angles Exercise 6.2
• Class 9 Maths Lines and Angles Exercise 6.3

NCERT Solutions Class 9 Maths Chapter 7 – Triangles

Students will learn about congruence rules, triangle properties, and inequalities in Chapter 7 of NCERT Mathematics for Class 9.

This chapter is really significant. To achieve a high score, you must complete this chapter and practice all the topics’ questions and examples. Important subjects in this chapter include sides of

triangles, the hypotenuse theorem, and proving SSS, ASA, and SAS congruence. Learn all triangle properties, triangle inequalities, and LHS and RHS congruence criteria.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Triangles Exercise 7.1
• Class 9 Maths Triangles Exercise 7.2
• Class 9 Maths Triangles Exercise 7.3
• Class 9 Maths Triangles Exercise 7.4
• Class 9 Maths Chapter 7 Triangles Ex 7.5

NCERT Solutions Class 9 Maths Chapter 8 – Quadrilaterals

This chapter will assist you in comprehending the properties of quadrilaterals and their conjunction with triangles.

Students are also required to prove theorems and formulas in this chapter. You must become familiar with quadrilateral kinds and formulas. There will be both short answer and extended response questions based on this chapter. Learn how to calculate the angles of quadrilaterals and then practice with the exercises’ problems.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Quadrilaterals Exercise 8.1
• Class 9 Maths Quadrilaterals Exercise 8.2

NCERT Solutions Class 9 Maths Chapter 9 – Areas of Triangles and Parallelogram

This chapter of ninth-grade mathematics is crucial for understanding area and how to calculate the area of triangles and parallelograms.

This chapter is also essential. You can do well on your exam if you study this chapter thoroughly. This chapter contains three exercises, and you must complete all of them. As many instances as possible from this chapter should be practiced. You will be required to prove the conditions of the provided diagrams and determine whether or not they are satisfied. This chapter contains numerous theorems; therefore, it must be studied and practiced thoroughly.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Areas of Parallelograms and Triangles Exercise 9.1
• Class 9 Maths Areas of Parallelograms and Triangles Exercise 9.2
• Class 9 Maths Areas of Parallelograms and Triangles Exercise 9.3
• Class 9 Chapter 9 Areas of Parallelograms and Triangles Ex 9.4

NCERT Solutions Class 9 Maths Chapter 10 – Circles

Class 9 Chapter 10 is both an important and interesting chapter for the pupils. It will assist you in understanding circles, chords, and subtended angles, as well as calculating the distance between a chord and the circle’s center.

Discover the meaning of a circle. You must also master formulas for calculating the circle’s area, perimeter, circumference, etc. Certain theorems and proofs must be learned and practiced. Before beginning the practice questions, review the properties and solve examples.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Circles Exercise 10.1
• Class 9 Maths Circles Exercise 10.2
• Class 9 Maths Circles Exercise 10.3
• Class 9 Maths Circles Exercise 10.4
• Class 9 Maths Circles Exercise 10.5
• Class 9 Chapter 10 Circles Ex 10.6

NCERT Solutions Class 9 Maths Chapter 11 – Constructions

This is a very essential chapter that focuses primarily on triangle construction, bisectors on line segments, and measuring angles such as 45°, 60°, and 90°.

This chapter is extremely essential, and its questions will have more weight than those from prior chapters. This will cover subjects such as the creation of triangles and the bisection of line segments.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Constructions Exercise 11.1
• Class 9 Maths Constructions Exercise 11.2

NCERT Solutions Class 9 Maths Chapter 12 Heron’s Formula

The chapter talks about Heron’s formula, which lets you figure out the area of a triangle when you know the lengths of all three sides. With this method, you don’t have to figure out the triangle’s angles or other distances. This formula can be used to find the area of triangles, quadrilaterals, and other polygons by dividing them into triangles. In this chapter, there are two exercises that help the student understand how to solve problems using Heron’s formula.

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

How to find the area of a quadrilateral using Heron’s formula (without proof) and how to use it to find the area of a triangle. 

Important Formulas –

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

Area of a triangle by Heron’s Formula = A = √s(s−a)(s−b)(s−c)

​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

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Heron’s Formula Exercise 12.1
• Class 9 Maths Heron’s Formula Exercise 12.2

NCERT Solutions Class 9 Maths Chapter 13 – Surface Areas and Volume

In prior grades, every one of you had already studied measurement. Consequently, you must understand surface areas, which are covered in this chapter. The volume of cubes, cylinders, cuboids, cones, hemispheres, and spheres is another essential topic. This chapter will also teach you how to convert one figure to another and compare the volumes of two figures.

Cube, cuboid, and spherical surface areas as well as volumes. Discover how to calculate the total and lateral surface areas of cubes and cuboids. Important topics that you must learn and practice include the following: right circular cone, right circular cylinder, and volume and capacity questions.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Surface Areas and Volumes Exercise 13.1
• Class 9 Maths Surface Areas and Volumes Exercise 13.2
• Class 9 Maths Surface Areas and Volumes Exercise 13.3
• Class 9 Maths Surface Areas and Volumes Exercise 13.4
• Class 9 Maths Surface Areas and Volumes Exercise 13.5
• Class 9 Maths Surface Areas and Volumes Exercise 13.6
• Class 9 Maths Surface Areas and Volumes Exercise 13.7
• Class 9 Maths Surface Areas and Volumes Exercise 13.8
• Class 9 Chapter 13 Surface Areas and Volumes Ex 13.9

NCERT Solutions Class 9 Maths Chapter 14 – Statistics

This chapter provides instructions on descriptive statistics and data collection. This is helpful for interpreting all types of data and presenting the results acquired.

This chapter will teach you how to handle the gathering, interpretation, and analysis of data. You must master sorting and grouping data. Among the topics you must study and practice for the exam are bar graphs, frequency polygons, and histograms, among others. You must also understand the mean, mode, and median. Solve exercise questions and practice graphics.

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Statistics Exercise 14.1
• Class 9 Maths Statistics Exercise 14.2
• Class 9 Maths Statistics Exercise 14.3
• Class 9 Maths Statistics Exercise 14.4

NCERT Solutions Class 9 Maths Chapter 15 – Probability

It is crucial to complete Chapter 15 of Class 9 Mathematics since all of the problems in this chapter are engaging and based on real-world events. This will make understanding Probability significantly simpler.

This chapter is also crucial, and students must practice accordingly. Consequently, students who utilize the NCERT solutions for Class 9 will receive high marks. 

Links to exercise solutions for the topics covered in this chapter can be found here.

• Class 9 Maths Probability Exercise 15.1

CBSE Class 9 Maths Unit Wise Weightage

CBSE Class 9 Maths Unit-wise Weightage
UNIT NO	UNIT Name	Scoring Marks
UNIT I	Number Systems	8
UNIT II	Algebra	17
UNIT III	Coordinate Geometry	4
UNIT IV	Geometry	28
UNIT V	Mensuration	13
UNIT VI	Statistics & Probability	10
	Total	80 Marks

NCERT Solutions Class 9 Maths Chapter-wise List

Chapter 1 Number systems

Chapter 2 Polynomials

Chapter 3 Coordinate Geometry

Chapter 4 Linear Equations in Two Variables

Chapter 5 Introduction to Euclid Geometry

Chapter 6 Lines and Angles

Chapter 7 Triangles

Chapter 8 Quadrilaterals

Chapter 9 Areas of Parallelograms and Triangles

Chapter 10 Circles

Chapter 11 Constructions

Chapter 12 Heron’s Formula

Chapter 13 Surface Areas and Volumes

Chapter 14 Statistics

Chapter 15 Probability

Benefits of NCERT Solution of Class 9 Maths

NCERT Solutions for Class 9 Maths are the key to success for every student because they help them build on their core knowledge and become experts in every subject. Some of the good things about the Class 9 Ncert solutions are as follows:

• The answers are made according to the rules and format set by the CBSE board. This gives the students an idea of how the questions will be set up on the final exams.
• Some expert teachers with years of experience in this field put together the solutions, so you can be sure that there are no mistakes in them. The students can be sure that the solutions are good.
• The answers are given to the questions that are most likely to show up on the tests. This helps the students prepare well.

Key features of NCERT Solutions for Class 9 Maths

Here are a few advantages of referring to Utopper’s NCERT Solutions:

• These solutions are grade-appropriate and use easily-understood language so that children can comprehend them without difficulty.
• These solutions have been produced by the nation’s leading specialists, allowing you to study from highly qualified instructors with minimal effort.
• All solutions are crafted with the most recent recommendations in mind.
• The PDF will serve as a one-stop shop for all of your educational needs.
• It will assist you in establishing a solid basis for higher study.
• You will receive practice tests to evaluate your knowledge and learning.
• These solutions have been created by a group of Utopper specialists who have taken into account the grade level of the pupils. Students should not worry about the accuracy of the solutions because they will receive the most accurate responses to the problems.
• If students practice these solutions beforehand, they will be able to complete the curriculum well ahead of schedule. In addition, the Class 9 All Subject Question Answer PDF will assist students to have a deeper understanding of questions that may be asked in final exams. 

Class 9 NCERT Solutions – Marks Weightage

All topics in Class 9 are worth a total of 100 marks, 20 of which come from an internal evaluation and 80 from the summative assessment administered at the conclusion of the school year by schools in accordance with the requirements of the CBSE. The internal evaluation consists of a weighted average of the grades earned on examinations, projects, and other assignments. The final examination for each subject is worth 80 marks and is weighted differently for each chapter and topic. A student’s ability to intelligently judge their readiness for tests might be aided by adhering to suitable plans. 

Internal Assessment	Summative Assessment	Total
20	80	100

Other Related Study Material for Class 9 :

• NCERT Class 9 Science Solutions
• NCERT Class 9 Maths Solutions
• NCERT Class 9 Textbooks
• NCERT Class 9 Science Book
• NCERT Class 9 Maths Book
• NCERT Syllabus

Importance of Class 9 NCERT Solutions for All Subjects

Class 9 students have a great deal of homework to complete. Their curriculum comprises of numerous subjects, including mathematics, physics, English grammar, Hindi composition, and social studies. In order to outperform the rest of the class, pupils must have a solid understanding of these disciplines. After finishing the chapters, students might seek out extra study materials to further their understanding.

Choosing Utopper’s NCERT solutions will assist students to solve difficult questions and gain an understanding of the curriculum. In addition, students will be able to comprehend the essential concepts taught in Class 9 NCERT Solutions. Thus, individuals can develop a study plan that will aid them throughout their final exams.

These NCERT solutions are unquestionable of great assistance to students who wish to complete the Class 9 curriculum and do well on their tests. These solutions were developed by subject matter specialists at Utopper in accordance with CBSE guidelines. Therefore, students can utilize these solutions as references to enhance their own skills in order to perform well on exams.