So you’re an ISC student in Class 11 and wondering where to start learning and practicing maths from. I will recommend you start with Understanding ISC Mathematics Volume 1 by ML Aggarwal. I will write about the book now, so read on.
SECTION-A
Chapter 1 is called Sets. It contains all the terms and theory you need to know on sets. The theory and the terms are explained using examples and illustrations (when required) which will help you understand the material.
Chapter 2 is called Relations and Functions. Make sure you understand all the material in the previous chapter before you start this one. This chapter contains some material which is very important and which you will not find in other books. Everything is presented in an organized and easy-to-understand way. Make sure you internalize the part on relations before you move on to functions. You will learn this topic in more detail in Chapter 1 : Relations and Functions of Volume 1 of the Class 12 book Understanding ISC Mathematics by ML Aggarwal.
Chapter 3 is called Trigonometry. The beginning of the chapter contains some basic concepts which are important but omitted in most other books. This is a long chapter and explains everything from the very basics and in greater detail than other books. Practice all the problems in the chapter. There is a very good chance you will see similar problems in your Class 11 exams as well as competitive exams.
Chapter 4 is called Principle of Mathematical Induction. This chapter mostly contains problems which are very important for all your exams. It will take some time for you to internalize the techniques, so practice the problems time and time again until you are comfortable with them.
Chapter 5 is called Complex Numbers. This chapter contains everything you need to know on this topic at this stage. I particularly like the material on the Argand Plane. The chapter presents the material in a simple and easy-to-understand way, unlike some other books which overcomplicate it.
Chapter 6 is called Quadratic Equations. It contains good theory. The part on graphs of quadratic functions (Section 6.5) is very important, specially for competitive exams.
Chapter 7 is called Linear Inequalities. Study the parts on solutions of systems on linear inequalities in one variable (Section 7.2), graphical solution of linear inequalities and a system of linear inequalities in two variables (Section 7.3 and 7.4) and quadratic inequalities (Section 7.5). They are very important for competitive exams.
Chapter 8 is called Permutations and Combinations. This is a topic that a lot of students have trouble with, but the chapter contains everything you need to know and in detail for both your Class 11 and competitive exams.
Chapter 9 is called Binomial Theorem. There isn’t much theory in the chapter. You will learn by solving the problems.
Chapter 10 is called Sequences and Series. It starts from the basics and contains excellent theory on Arithmetic Progression (A.P), Geometric Progression (G.P), Arithmetico-Geometric series and some special series along with a wealth of worked out examples. All the techniques that you have to learn on this topic are well-explained in the book through worked out examples and are very important for your exams.
Not only are there a ton of worked out examples and exercises in each chapter, but also a chapter test at the end of each chapter which you should practice. The book contains answers to the exercises at the back. Good luck!
Understanding ISC Mathematics Volume 2 by ML Aggarwal picks up from where Volume 1 left off. I will talk about the book now. Hope you find it helpful!
SECTION-A (continued)
Chapter 11 is called Straight Lines. It starts with a recap on some basic concepts you might have learnt previously and then it starts with new material. The theory and problems in this chapter are among the best I have seen. All the formulae you need to know are listed in an extremely organized manner along with their proofs and problems based on them. This chapter will not only prepare you for your Class 11 exams, but competitive exams as well.
Chapter 12 is called Circles. You will use some of the formulae you learnt in Chapter 11, so revise them if you need to. You will need some concepts on Euclidean geometry which you learnt in previous classes, so revise them as well. Learn the theory and the proofs and practice the problems until you are comfortable with everything. You are bound to see similar questions in your exams (specially competitive exams).
Chapter 13 is called Limits and Derivatives. The first half of the chapter is on limits and the second half on derivatives. The chapter develops the concepts very well from the very beginning. However, this chapter leaves out L’Hôpital’s rule, which you will learn in Chapter 6 : Indeterminate Forms of Volume 1 of the Class 12 book Understanding ISC Mathematics by ML Aggarwal.
Chapter 14 is called Statistics. This chapter contains a lot of material and problem-solving techniques that you need to know on the topic as a beginner. It contains material and problems that I haven’t seen in other books. Get as much practice as you can. It will also prepare you for more advanced material on statistics which you will learn in SECTION-C, Chapter 1.
Chapter 15 is called Probability. The chapter is enough for what you need to know on probability in Class 11. Make sure you understand everything from the beginning as the material in the Class 12 book will build on these concepts.
SECTION-B
Chapter 1 is called Conic Sections. What I like about this chapter is that it explains parabolas, ellipses and hyperbolas from all possible angles and the theory along with the problems will mostly prepare you for your exams.
Chapter 2 is called Introduction to Three Dimensional Geometry. The most important part are the problems, most of which are important for your exams and which you won’t find in most other books. Practice them until you are able to handle similar problems easily. You will learn this in more detail in SECTION -B, Chapter 2 called Three Dimensional Geometry in the book Understanding ISC Mathematics Volume 2 for Class 12 by ML Aggarwal.
Chapter 3 is called Mathematical Reasoning. This is a vast and confusing field of study, but the book contains brief and to-the-point discussions on everything you need to know at this stage. This topic will appear confusing at first. Keep practicing until you are comfortable with it.
SECTION-C
Chapter 1 is called Statistics. It picks up from where it left off in SECTION-A, Chapter 14 and includes detailed discussions on the rest of the material you need to know at this stage. Study the part on estimation of partition values by graphical method from ogives (Section 1.5) well. They are important for your exams.
Chapter 2 is called Correlation Analysis. This chapter is relatively simple. There are some big formulae and lengthy problems which the book explains how to do step-by-step, which you should take your time to practice.
Chapter 3 is called Index Numbers and Moving Averages. This chapter is again not that hard. There are some simple methods and formulae which you should learn and practice. Understand how to obtain and interpret the graphs shown in the worked out examples on moving averages.
Good luck!
As an ISC student in Class 12 I would suggest you continue with ML Aggarwal’s book Understanding ISC Mathematics Volume 1 for Class 12:
SECTION-A
Chapter 1 is called Relations and Functions. This chapter picks up from where it left off in Chapter 2 in Volume 1 (Class 11). You will learn relations and functions in more detail and this chapter will prepare you for competitive exams as far as this topic is concerned.
Chapter 2 is called Inverse Trigonometric Functions. The chapter includes all the theory and graphs you need to know on the topic in a very organized manner. It will prepare you for your board exams and competitives as well.
Chapter 3 is called Matrices. Most of the properties of matrices you need to know at this stage are well-explained with examples. Get as much practice as you can. You will learn about adjoint of a square matrix and some theorems on matrices in the next chapter.
Chapter 4 is called Determinants. Again the properties of determinants you need to know for now are explained very well. It will take some time for you to get used to solving problems on determinants which the myriad of worked out examples in the chapter will help you with. It also contains some material on matrices to understand which you need to have an idea of determinants. It also talks about solution of systems of linear equations using matrices as well as determinants. Solve all the worked out examples and exercises well.
Chapter 5 is called Continuity and Differentiability. The discussion on continuity is excellent. The worked examples are designed to make you think and are representative of what you will see in the exams. The second part on differentiability is long and contains every single concept, formula, theorem and technique you need to know at this stage. There’s tons of worked out problems. Practice them until they become like second nature to you. You are bound to see similar problems in your exams (specially competitives).
Chapter 6 is called Indeterminate Forms. This is where you will learn about L’Hôpital’s rule which Chapter 13 on Limits and Derivatives in Understanding ISC Mathematics Volume 2 by ML Aggarwal for Class 11 left out. This is a short but extremely important chapter and you will certainly see similar problems in your exams.
Chapter 7 is called Applications of Derivatives. This chapter contains explanations and problems on all the different kinds of applications of derivatives that you need to know for now. You will use these concepts in other subjects as well, so make sure you study everything thoroughly.
Start with Understanding ISC Mathematics Volume 2 for Class 12 by ML Aggarwal only after you finish Volume 1. I will talk about Volume 2 now:
SECTION-A (Continued)
Chapter 8 is called Integrals. It starts with indefinite integrals and contains all the formulae and techniques to solve all the different kinds of integrals that you need to know for your exams. Then it starts the discussion of definite integrals by showing you how to calculate definite integrals as the limit of a sum (important) followed by the fundamental theorems of integral calculus (also very important). It also contains the properties of definite integrals along with proofs which you should know how to derive and how to apply as well. It will take a lot of practice to get used to all the techniques. There are a multitude of problems, so practice them as well.
Chapter 9 is called Differential Equations. It teaches you through worked out examples how to verify that a particular expression is a solution of a differential equation, finding the differential equations representing different curves, how to solve different types of differential equations and applications of differential equations. Practice all the problems to get used to all the different techniques.
Chapter 10 is called Probability. You learnt the basics of probability in Volume 2 of the Class 11 book. The chapter starts with a review of some laws on probability you learnt in Class 11 followed by conditional probability, multiplication theorem, the law of total probability, Baye’s theorem (important), random variables and probability distribution along with it’s mean and variance and Binomial distribution. This is a long chapter, but it contains everything you need to know which a lot of other books do not. So study it thoroughly.
SECTION-B
Chapter 1 is called Vectors. It starts from the very basics and explains vector algebra (important) in detail, scalar and vector products and scalar triple product (important). You may have seen some of this material before, nevertheless do not underestimate this chapter and study it in detail.
Chapter 2 is called Three Dimensional Geometry. You learnt a bit of this topic in Class 11. This chapter lists and explains all the material you need to know on this topic in a very organized manner with excellent worked-out examples and illustrations. So study it well.
Chapter 3 is called Applications of Integrals. This is a short and simple chapter which teaches you how to find areas of bounded regions and areas between two curves. Once again there are a lot of worked out examples of all types practicing which will teach you how to deal with problems like these.
SECTION-C
Chapter 1 is called Application of Calculus in Commerce and Economics. This chapter starts with some basic concepts related to economics and problems based on them. Then it introduces you to the concept of Marginal Functions which requires the application of calculus. This is a relatively simple chapter and shouldn’t give you much trouble.
Chapter 2 is called Linear Regression. You learnt about correlation analysis in Class 11. Here you will learn about the concept of regression. You will need some of the formulae from the Correlation Analysis chapter from Class 11. The concepts in this chapter are simple, but you will need practice to get comfortable with solving problems of this type.
Chapter 3 is called Linear Programming. This chapter shows you how to formulate and solve linear programming problems involving two variables. You will see similar problems in your exams, so practice them well.
Good luck!
