For Class 9 CBSE students, start with the NCERT textbook for Class 9. The key is to understand, not memorize. Remember, these are your formative years and building a strong foundation is important. Get a general idea of the syllabus and then go through the book. Make sure you understand each and every concept presented in the book from the beginning. Do not try to rush through it. Understand the theory that is presented in every chapter starting from the beginning. Then, try the problems first on your own. Only look at the solutions if you’re stuck. This way you will be able to see where you stand and where your problem areas are.
Regarding the book, the concepts are explained from scratch and in detail. It starts off with Chapter 1 on number systems. It explains the theory behind different kinds of number system with illustrations, thus making it very easy to understand. There are both worked out examples and exercises for you to solve after every section. It covers all the basics of number systems and is sufficient for a Class 9 student. It teaches you many tricks for solving problems, which will come in handy later on. The Chapter ends by giving you a taste of how geometry is applied to calculate the square roots of positive real numbers, which I found to be very interesting! This Chapter contains the best explanation on number systems I have ever seen. So, I would recommend studying Chapter 1 and practice all the problems in detail.
Chapter 2 is about polynomials. I would highly on studying this Chapter in detail as it will lay the foundation for a bunch of things that you will study later on in your student career. One of the things I like about this Chapter is that it starts from the basic level, which not many books do. Make sure you understand the worked out examples after every section. Try to solve them on your own. Only look at the solutions if you get stuck. This will help build confidence. After finishing with the basics, it talks about the Remainder Theorem which I would say is a very important topic. You will learn to divide a polynomial by another polynomial, which like I said is a very important topic. I have seen questions on college entrance exams which are based on this topic. So, make sure you understand it thoroughly! It is followed by another important topic which you will see later on again in your students career is the Factor Theorem. Then there is some basic algebra and very typical problems which you must be familiar with. Note: do not try to memorize anything. Understand the theory and practice and you will be fine!
Chapter 3 deals with coordinate geometry. This is an extremely important topic which many of you (specially science and engineering aspirants) will encounter throughout your student careers and maybe even n the professional world. So it’s important to analyze the basics of it! The basics are very well-explained in the chapter, starting with the cartesian system. The main thing the chapter teaches you is how to read points on the x-y plane. It might take some time to get used to it, specially as a Class 9 student. But never fear, you will get the hang of it soon! Chapter 3 is relatively simple, when compared to the first couple of chapters!
Chapter 4 talks about linear equations in 2 variables. You have probably encountered this topic in earlier classes, so it shouldn’t be that hard for u. It talks about finding multiple solutions for linear equations with 2 variables. Then it talks about graphing linear equations with 2 variables. It also does a very good job of explaining equations parallel to the x and y axes. This last concept might take sometime to understand. But it’s a very important concept. So, make sure you understand it perfectly. You will need to draw and interpret complicated graphs in higher classes. Learn these topics thoroughly.
Chapter 5 is about the basics of Euclid’s geometry. It starts from scratch and does a very good job of explaining the basics. It consists some of the best theory I have seen on the topic. A lot of you already have a good understanding of the basics of Euclidian geometry. Nevertheless, I would strongly advise going through the theory in detail. It might even set straight any misconceptions you might have.
Chapter 6 talks about lines and angles. It starts from the basics and contains excellent theory. Once again, you have seen a lot of this stuff already, but going through the chapter in detail will refresh your memory and get rid of any misconceptions! It contains many different kinds of problems on lines and angles. Solve both the worked out problems and the exercises as well because you will encounter more complicated problems later on that make use of these concepts. The chapter ends with some stuff on some properties of triangles which lays the foundation for the next chapter. Do not underestimate these topics. You will be surprised at how useful they will prove to be later on!
Chapter 7 focuses on triangles. It starts with congruency : Again, I cannot stress enough on how important these concepts are, even for higher classes. The book does a very good job of explaining these concepts. That is followed by applying congruency concepts to general properties of isosceles triangles which is followed by more congruency concepts. You probably have a good grasp of these concepts already, but nevertheless go through them. It ends with some general concepts regarding triangles followed by exercises which are good for brushing up your concepts. Both the theory and exercises are excellent.
Chapter 8 is about quadrilaterals. It starts from the basics and contains a lot of good theory. There are a lot of theorems which you probably have seen in earlier classes which are good for revision. That is followed by the mid-point theorem and it’s applications. All the proofs and theory are presented in a organized and detailed manner. Solve all the problems. They are meant to further improve your concepts.
Chapter 9 consists of methods used in calculations of areas used in calculating areas of parallelograms and triangles. You have probably seen most of this stuff before also, but still go through the theory. The chapter will clear all your concepts regarding calculating areas of different shapes and sizes and combinations of triangles and parallelograms which you will find useful in later classes as well. This chapter contains a lot of problems at the end. Practice them. They will give you confidence!
Chapter 10 deals with circles. This is another topic you will need to understand thoroughly. You will see a lot of this stuff in this chapter in higher classes. The chapter presents the material very thoroughly from the basic level and in a very organized manner. It contains pretty much all you need to know about circles, so study the theory thoroughly and practice the problems including the worked out problems. You will find yourself referring to this chapter again and again in higher classes, so keep that in mind and study the chapter thoroughly.
Chapter 11 deals with geometric constructions. It’s absolutely essential that you fully internalize the material in this chapter because the chapter on constructions in class 10 will build on the material of this chapter. There a lot of construction methods explained from the very basics in this chapter. Understand them thoroughly and you will be well prepared for the material in class 10.
Chapter 12 is relatively brief and talks about Heron’s formula and different applications of it. It’s relatively easy, however, do not neglect it. You will have to get used to memorizing formulae of this type in higher classes.
Chapter 13 is about calculating surface areas and volumes of cuboids, cubes, right circular cylinders, right circular cones and spheres. The proofs of all the formulae are shown in a very elegant manner with illustrations and I would highly advise understanding them. This chapter is very important as it forms the basis for the Surfaces Areas and Volumes chapter in Class 10. So make sure you understand it thoroughly.
Chapter 14 deals with statistics. As someone who has learnt and used statistics throughout his student career, I would recommend getting a good grasp of statistics. Even in Class 10 there is a Chapter on statistics that will build on this chapter. So, it’s important to have a good understanding of it. It starts off with the very basics, the understanding of which is essential for a student learning about statistics for the first time. Then it introduces you to graphical representation of data in a very organized and methodical manner. It ends with the concepts of mean, median and mode. It has many worked out problems which are good for understanding the material as well as for practice. Remember mastering even the basics of statistics requires practice. Solve the problems at the end of the chapter. It will clear any conceptual difficulties you might be having.
Chapter 15 introduces you to probability. I will start out by saying, a lot of students have difficulties with this topic. I will advice on thoroughly understanding the concepts from the basic level as the concepts build on each other. You will encounter more advanced concepts on probability in Class 10, so take your time and get a thorough understanding of this Chapter. It teaches you the basics of probability in a very elegant, organized and lucid manner. Read it from front to back and you’ll be prepared for Class 10! Good luck!
Note: If you do not want to buy the solutions book, there are plenty of resources online which you can use to look at the solutions for free. In fact, you can even download the textbook itself although I highly recommend buying it.
Same with Class 10 CBSE students. Only go through the NCERT textbook for Class 10 once you are done with the one for Class 9. I would highly suggest revising the Class 9 textbook alongside as many concepts in the textbook for Class 10 build on the concepts presented in the textbook for Class 9. I will write about the NCERT textbook for Class 10 now, so read on!
Chapter 1 consists of a very detailed discussion of basic theorems pertaining to numbers as well as worked out examples. It starts from the basics and has some of the best theory that I have seen on this topic. Understand this chapter thoroughly because you can expect multiple questions on this topic in your Class 10 mathematics paper and it will come in handy in higher classes as well.
Chapter 2 continues the discussion on polynomials in the Class 9 textbook. It does a very good job of teaching you how to graph higher degree polynomials which will definitely come in handy in higher classes, so I would recommend understanding and studying it thoroughly. It also explains a bunch of theorems and includes examples after each explanation, studying which will clear your doubts. It also lays the foundation for the chapter on Quadratic Equations. If you need to, revise the chapter on polynomials in the Class 9 textbook side by side. Take your time understanding the material. Like I said, it will come in handy later on.
Chapter 3 talks about pairs of linear equations in 2 variables which is again a continuation of the Linear Equations chapter in the Class 9 textbook. You have probably seen a lot of this material before, but nevertheless go through the chapter in detail. A lot of important concepts are very well-explained in this chapter. It also contains word problems which are very important, so make sure you understand them well.
Chapter 4 focuses on quadratic equations which is a type of polynomial. So make sure you fully understand Chapter 2 before starting this Chapter. A lot of this Chapter teaches you how to do algebraic manipulations which most of you already have previous experience, so it shouldn’t be too hard.
Chapter 5 introduces the topic of arithmetic progression. It is absolutely essential to understand the basics of it properly because you will study it in much greater detail in Class 11 and for competitive exams as well. You will find all the basic formulae along with their derivations explained thoroughly in this chapter. There are problems of many different kinds, both worked out and otherwise, practicing which will give you confidence.
Chapter 6 continues the discussion on triangles started in the Class 9 textbook. Revise the chapter on triangles in the Class 9 textbook. Chapter 6 starts off with a very good theoretical discussion on similarity. It has a lot of theorems and also has very good worked out examples which I recommend you understand and practice thoroughly because you will see similar questions in the exam. This is a very important chapter. It will take some time to internalize the material. However, the book does a very good job of explaining everything, so go through the material thoroughly and revise everything again and again. Also, practice the problems at the end of each section.
Chapter 7 continues the discussion on coordinate geometry started in the Class 9 textbook, so revise the chapter in the Class 9 textbook before starting this chapter. This chapter is very important not only for your board exams, but also for Classes 11 and 12. So, make sure you understand everything properly. Again, practice the exercises at the end of each section.
Chapter 8 starts with the very basics of trigonometry. This chapter is again something you will see throughout student career and maybe even after that, so it’s very important to have a very good understanding of it. There a lot of basic concepts in this chapter which need thorough understanding. So make sure you understand the basics well! Some of the material uses concepts from earlier chapters, so revise them if you need to. You will have to memorize some stuff in this chapter, so keep that in mind.
Chapter 9 teaches you to apply various concepts of trigonometry to solve problems. They are mostly variations of the same concept, so it shouldn’t be that hard.
Chapter 10 is a continuation of the chapter on circles in Class 9, so I would suggest revising the concepts you learnt in Class 9. Again, understand the theory and practice the theorems and problems. You will see similar questions in the exam.
Chapter 11 is about constructions and build on the Chapter on constructions in Class 9. I would suggest revising it. I would suggest practicing the construction methods presented in Chapter 11 thoroughly because in the exam you will not get a lot of time to think.
Chapter 12 starts off with relatively simple stuff such as how to calculate areas of sectors and segments of circles which are mostly intuitive. Then it shows you how to calculate areas of combinations of plane figures. The latter topic is very important and you can expect problems like the ones presented in the chapter.
Chapter 13 teaches you how to calculate surface areas and volumes of a combination of solids. This is a very important topic and you will encounter questions like these in your board exams as well as later on in your student life. Go through the theory and practice the problems for the sections on both surface area and volume calculations. Another type of problem it does a very good job of explaining is the conversion of solids from one shape to another, which is again a very important concept. The chapter ends with a bunch of formulae involving the frustum of a cone. Understand the formulae are derived and practice the problem, both worked out and at the end of the section. This is also an important concept and you can expect similar problems to appear in the exam.
Chapter 14 builds on the concepts of statistics presented in the Class 9 textbook. It will take a lot of practice to get used to the concepts presented in this Chapter. So, make sure you start early. When working with tables guard against mistakes due to carelessness. The Chapter ends by introducing you to different of graphical representations of data. The explanation of all the theory in the chapter is good and there are lots of problems. Once again, practice. You will get stuck in the exam, if you don’t practice.
Chapter 15 is the last chapter in the book which continues the discussion of probability introduced in Class 9. The theory is very good and easy to understand for beginners. The concepts are pretty intuitive and although they might take you some time to internalize, are not hard.
