So you’re in Class 11 and starting to prepare for competitive exams. Or maybe, you have long-since started your preparations, which most students at this stage do. Either way, I would strongly recommend you understand the material and solve the problems in the NCERT textbook from front and back. You will thus have a strong foundation on which to build on!
Chapter 1 starts off right from the basics of sets. This is a very important topic which you will use a lot later on and the book does a very good job of explaining the material in an elegant and easy-to-understand way. The theory is a lot better than many other books I have seen, so I would suggest studying the theory thoroughly and solving the worked out problems as well the problems at the end of section, which will give you confidence. You will learn about the different kinds of sets in this chapter, which is very important. That is followed by a very thorough discussion of different kinds of sets, Venn diagrams, operations on sets, complements of sets in a detailed and organized way. It also shows you how to solve word problems, which are very important. Take your time to solve the miscellaneous worked out examples and problem at the end of the chapter. In short the Chapter contains a wealth of information and sample problems. So, study them thoroughly.
Chapter 2 is on relations and functions which will form the basis of other topics later on. The first section presents some additional concepts related to sets which the rest of the chapter will build on. Again, the presentation and organization of the concepts are excellent and I will highly recommend that you go through it. It very clearly explains the transition from relations to functions. It also teaches you graphical representation of certain functions, some of which you might have seen before. Some basic algebra of functions are also shown. Read and understand this chapter thoroughly. The explanations of the concepts are very good and it shows you how one concept leads to another.
Chapter 3 is on trigonometric functions, a little of which you have seen in earlier classes. Again it does a very good job of explaining everything from the basics. It shows you how the signs of the different trigonometric functions are derived in such a way that you will never forget them. Same with graphing the functions. Then it moves onto trigonometric identities and equations. There’s plenty of problems for practice. The chapter helps to build your concepts bit by bit. Understanding everything in the chapter will give you a very good understanding of the topic.
Chapter 4 explains the theory on the principle of mathematical induction very succinctly and contains both excellent worked out and end of chapter problems. Practice them and you’re good.
Chapter 5 explains complex numbers again starting from the very basics and I highly recommend going through the chapter in detail as this topics are very important for competitive exams. The style of presentation of the material of this chapter is ideal for beginners. You have encountered quadratic equations in earlier classes. The chapter ends by succinctly showing you how to solve complex quadratic equations. Again, practice the problems, both the worked out and end of chapter ones.
Chapter 6 deals with linear inequalities. It starts with showing you how to algebraically solve linear inequalities in one variable and how to graphically represent the solution. It continues with showing you how to graphically represent linear inequalities in 2 variables. The theory in the chapter is really good and learning the theory well prove to be useful later on when dealing with topics like calculus.
Chapter 7 is on permutations and combinations. This is a very confusing topic, but the chapter starts from the very basics and does a very good job of explaining the material. If you read the chapter from front to back, you will develop a very good understanding of the topic. All the formulae are very elegantly derived and solving the example problems and exercises will further clear your concepts.
Chapter 8 on binomial theorem presents the theory in a simple, compact and straightforward manner starting with Pascal’s triangle. Both the worked out problems and exercises will give you good practice.
Chapter 9 is on sequences and series. It does an excellent job of explaining the material right from the beginning. It also talks about arithmetic progression (A.P) and geometric progression (G.P). Then it shows you how to deal with other kinds of series and ends with a lot of different kinds of problems. In short, this chapter is excellent for learning the basics of this topic.
Chapter 10 is on straight lines. It starts with a brief discussion on coordinate geometry which you have probably seen in earlier classes. Then it starts the discussion of straight lines from the very basics. It’s excellent for beginners. I would suggest you start with this chapter and then refer to other books (more on this later) for the more advanced stuff which you will need for competitive exams.
Chapter 11 is on conic sections. You will learn about the basics of circles, ellipses, parabolas and hyperbolas. This chapter is good for learning the basics, so that you have a solid foundation when referring to other books for competitive exams, so I highly suggest you go through the theory and practice all the problems. It’s an excellent place to start.
Chapter 12 introduces you to three dimensional geometry which is a very interesting and important topic. The theory in each section and the following exercises are good for learning the basics. Once again, I would suggest that learn this chapter very well and you will be prepared for the chapter on three dimensional geometry in Class 12.
Chapter 13 introduces to the all important topic of calculus which most of you will need throughout your student lives. So it’s absolutely essential to have a sound understanding of this topic right from the very basics, which this chapter will help you do. The concept of limits are very well explained and illustrated with examples and is ideal for beginners. The second half of the chapter talks about derivatives and is an excellent place to start learning about derivatives. The worked out examples and exercises will further clear your concepts.
Chapter 14 talks about mathematical reasoning. The book deals with it in a very organized and logical manner. In this chapter you will learn to apply logic and is mostly intuitive. The chapter does a very good of of explaining the material. You will learn to logically interpret different statements. Some of you might see stuff like later on in your student lives and in standardized exams like the GRE, GMAT etc, so it’s important to get a good grasp of it. Go through through the chapter, practice the problems and you’re mostly good.
Chapter 15 continues the discussion on statistics from where it left off in Class 10. So make sure you revise those concepts before starting this chapter. This chapter shows you how to calculate different parameters from given data in an organized and logical manner. It will take a bit of practice, but the chapter contains all that you need to know. Understand the theory, practice the problems and you’re good.
Chapter 16 is on probability and resumes from where it left off in Class 10. Revise the chapter on sets (Chapter 1 of this book)because you will need those concepts in this chapter. The chapter talks about sets and events as a prelude to the discussion on probability, so make sure you understand those concepts thoroughly. After reading the chapter do the problems and then you will be prepared for the chapter on probability in Class 12.
So, you’ve finished Class 11 and looking for guidance on how to handle Class 12 mathematics! Once again, I recommend you start with the NCERT textbook which I will talk about now!
Chapter 1 is on relations and functions and discusses relations in more detail than what you learnt in Class 11. Then it continues the discussion on functions started in Class 11 as well. Do not neglect these topics. You will see questions from these topics in your board exams and competitive exams as well. The chapter explains a lot concepts very well which you will not find in many other books. It also contains a ton of worked out examples and exercises, so make sure you practice them as well.
Chapter 2 is on inverse trigonometric functions. Make sure you revise the chapter on trigonometry in the class 11 textbook before you start this chapter. The graphs of all the inverse functions are explained very well. The theoretical explanations are also very good. Practice the sample problems in the chapter before you move onto harder problems in other books. I will talk more about which books to solve later.
Chapter 3 on matrices starts from the very basics and has a lot of really good theory and in great detail. So make sure you study it well. It contains some of the best theory I’ve seen on this topic. Many of you will study this stuff in much more detail later on during your student lives. Expect multiple questions from this topic in competitive exams. So, make sure you understand it well. Practice the problems in this chapter before you move onto other books.
Chapter 4 is on determinants and does a very good job of explaining the basics and there are very good sample problems. Study the theory and practice the problems. They will give you a solid foundation on which to build on.
Chapter 5 is on continuity and differentiability. It continues the discussion on differentiation of functions started in Class 11. It starts with a discussion of continuity of functions and then moves onto differentiability. It is essential that you learn how to graph the functions as shown in the chapter, so practice them well. Also memorize the differentiation formulae as most of you will need them not just for competitive exams, but throughout your student lives. Also, practice the problems. There is a very good chance that you will see similar problems in competitive exams. The theory in the chapter ends with a discussion on the mean value theorem which is another important topic, so make sure you learn it well.
Chapter 6 is about the application of derivatives. This chapter is of utmost importance. You will encounter situations in all your math/science subjects not just in your board and competitive exams, but throughout your student lives where you will need to use derivatives. So, make sure you understand the theory and solve all the different kinds problems in this chapter thoroughly. The chapter builds on the previous chapter, so keep that in mind.
Chapter 7 is on integrals and is also an extremely important topic. There are a lot of important techniques and formulae in the chapter which you should have at your fingertips, so take your time and make sure you learn the techniques and memorize all the formulae. It also has many sample problems, which are excellent for practice.
Chapter 8 is on applications of integrals. The chapter doesn’t have much material but you will have to learn thoroughly as you will be required to know how to use integrals to solve different types of problems not just in math but also in physics and chemistry and later on in your student careers as well. The chapter teaches you how to calculate areas under different kinds of curves, areas between different curves etc. Practice the problems. You will see similar stuff in your exams.
Chapter 9 deals with differential equations which is again a very important topic which most of you will need throughout your student and maybe even your professional lives. It starts by teaching you about the order and degree of a differential equation. Then it talks about the general and particular solutions of a differential equation and how to find a differential equation whose general solution is given. After that, it teaches you methods on how to solve different kinds of differential equations. Learn and practicing the methods thoroughly will give you a very solid foundation.
Chapter 10 is on vector algebra, some of which you have already have come across. This chapter is relatively simple. Nevertheless, studying this chapter thoroughly will prove to be of immense help both in your exams and later on. The worked out examples and the problems at the end of each chapter will give you good practice.
Chapter 11 continues the discussion on three dimensional geometry. It shows you how to tackle three dimensional geometry using concepts of vector algebra which you learnt in the previous chapter. It contains a lot of formulae which you should memorize and know how to derive. There’s a lot of material but if you have learnt the previous chapter well, it shouldn’t be much of a problem.
Chapter 12 is on linear programming. In this chapter you will learn how to maximize or minimize a linear function subject to certain conditions imposed by a set of linear inequalities where all the values are non-negative. Learn how to present the information given to you graphically and half the job is done. Practice the problems in the chapter and you’re good.
Chapter 13 builds on the concepts you learnt in earlier classes and introduces the concepts of conditional probability and random variables and probability distributions. These concepts will seem difficult when you’re learning about them for the first time, but the book does an excellent job of explaining the concepts from scratch. Read the theory in detail. Brush up your concepts on sets from the Class 11 textbook. You will need them in this chapter. Take your time with this chapter. It’s extremely important for not just your boards but also competitive exams. Also, practice the problems. You will see similar problems in your exams.
