Hello students! Looking for the perfect solutions material for Class 9? Say goodbye to math worries because we’ve got you covered with top-quality NCERT Solutions for Class 9 Maths. But wait, there’s more! Need some extra practice to ace those exams? We’ve got a treasure trove of extra problem sets just waiting for you at the end of each chapter. You will find our solutions and illustrations interesting and exciting and they will be instrumental in preparing you for your exams.
NCERT Solutions Class 9 Maths (Chapter-Wise)
| 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 |
NCERT Solutions for Class 9 Maths – Summary of Each Chapter
Chapter 1 Number Systems:
The chapter explains natural numbers, whole numbers, rational numbers, irrational numbers, real numbers, representing irrational numbers on the number line, real numbers and their decimal expansions, terminating decimals, non-terminating recurring decimals and non-terminating non-recurring decimal expansions. The section on operations on real numbers is important because it shows you how to find the square root for any given positive real number x geometrically. The chapter ends with some identities related to square roots and laws of exponents for real numbers.
Chapter 2 Polynomials
The most important topics are the remainder theorem, factor theorem and algebraic identities. Understand the proofs of these theorems and do not just memorise. Then practise problems based on these topics. Our extra problem set is an excellent place to begin if you want extra practice.
Chapter 3 Coordinate Geometry
This chapter introduces the cartesian system, the conventions associated with it and teaches you how to accurately plot points on the cartesian system. This should be an easy chapter for you to master once you start practising.
Chapter 4 Linear Equations in Two Variables
This chapter first includes a recap on linear equations and then introduces linear equations in two variables. The second half of the chapter shows you how to find solutions to linear equations in two variables.
Chapter 5 Introduction to Euclid’s Geometry
The chapter delves into the historical evolution of geometry, tracing its roots in ancient civilizations like Egypt, Babylonia, India, and Greece. It discusses the practical applications of geometry in land measurement, construction, and ritualistic practices. Euclid’s “Elements” is introduced as a pivotal work that laid the groundwork for deductive reasoning and formal proofs in geometry. The most important part of the chapter are Euclid’s definitions, axioms, and postulates, which you will need to learn thoroughly in order to solve problems.
Chapter 6 Lines and Angles
The chapter starts with some basic geometry definitions which you recommend you know thoroughly before you proceed. Learn the following axioms and theorems well:
1. 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 as the Linear pair axiom.
2. If two lines intersect each other, then the vertically opposite angles are equal.
3. Lines which are parallel to a given line are parallel to each other.
Then practise problems based on the above axioms and theorems. The exercise problems and extra problem set we have given you are an excellent place to start.
Chapter 7 Triangles
This chapter introduces you to the concept on congruency at the beginning and then introduces you to criteria for congruency of triangles namely, SAS, ASA, AAS, SSS and RHS. It also includes a couple of important theorems which you will be using a lot. The vital thing here is that you need to understand the proofs behind all the congruency criteria and theorems instead of just memorising.
Chapter 8 Quadrilaterals
Have the theorems related to quadrilaterals and parallelograms at your fingertips as you will be expected to apply these to solve problems. Learn how to use a combination of these theorems to solve problems. Same goes for the mid-point theorem in triangles. Solving geometry problems of this type takes skill, which will come with lots of practise. We recommend you practise many different types of problems on your own. This will help train your eye and you will be able to solve unknown problems on your own. We recommend you start with the textbook solutions and the extra problem set we have designed. Try the problems by yourself before looking at the solutions.
Chapter 9 Circles
All theorems related to circles given in the chapter are equally important. You will need to use multiple theorems at once to solve problems. Wondering how to go about learning to solve problems on your own? Start by understanding the proofs of the theorems themselves. Practise drawing out the figures on your own and practise the proofs until they are like second nature to you. Then move onto the exercises and extra problem sets we have included.
Chapter 10 Heron’s Formula
In this chapter you will be required to memorise the Heron’s Formula and solve different types of problems using it. There can be many different types of problems on this topic and we have included many typical problems in the extra problem set to give you a taste of what exam problems might look like.
Chapter 11 Surface Areas and Volumes
Learn how to derive the formulae for the surface area and volume of cones, spheres and hemispheres. Then, learn how to use the formulae to solve problems. Also, revise the chapter on mensuration from previous classes as you will be required to know the formulae for cubes, cuboids, cylinders etc.
Chapter 12 Statistics
Practise drawing bar graphs, histograms and frequency polygons and learn to interpret them to answer questions correctly. Our textbook exercise solutions and extra problem set is an excellent place to start practising.
Frequently Asked Questions on NCERT Solutions for Class 9 Maths
In this complete and updated solutions material for Class 9 Maths, our experts have solved the problems step-by-step in a clear and logical manner to help you understand and to help retention. They have also included attractive illustrations, which complement the explanations nicely. If you need extra practise, we have even included extra problem sets at the end of each chapter.
Free PDFs of the solutions have also been included for you to study!
Begin by thoroughly understanding the key concepts outlined in the textbook and studying the solved examples provided for each chapter. This will show you the problem-solving techniques. Then try solving the exercise problems independently, referring to the solutions only when necessary. This approach allows you to gauge your understanding of the material. Additionally, challenge yourself further by tackling the extra problem sets we have provided at the end of each chapter.
If you need extra help, never fear! We have expert teacher-mentors on staff who will coach and counsel you and thoroughly prepare for your exams. The training they provide will be personalized and as per your convenience! Sounds good? Let us assign you a friendly teacher-mentor who will take care of all your needs. Reach out to us anytime and let us help you out! Cheers! Book an appointment now!
