Toppers handwritten notes a comprehensive package for the preparation of JEE Main & Advanced which is designed by Top 100 IIT-JEE Rankers. Through our hard work we have developed handwritten notes of students who topped previous JEE exams & secured AIR under 100.These are highly self explanatory notes for JEE main , JEE advanced & other regional exams.
Mathematics Volume I:- Vectors, 3D Geometry, Complex Numbers, Permutation & Combination, Binomial Theorem, Probability
Mathematics Volume II:- Function, Inverse Trigonometry, Limits, Continuity, Differentiability, Method Of Differentiation, Indefinite Integrals, Definite Integrals, Tangent & Normal
Mathematics Volume III:- Quadratic Equation, Trigonometric Equations, Solution Of Triangle, Application Of Derivatives, Application Of Integral, Differential Equation, Point & Straight Line, Circle, Conic Section, Parabola, Ellipse, Hyperbole
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IIT JEE Mathematics
Mathematics is the most vital part of the IIT JEE syllabus. It is in fact an indispensible part of human race. Physics, Chemistry and Mathematics have equal weightage in the JEE but Mathematics has an edge over the other two as, in case of a tie in the overall score of two or more candidates, the score in mathematics is considered to be the deciding factor. Mathematics is like a kin of science which lays the foundation for Physics and Chemistry. Various topics like calculus, differential equations and quadratic equations are used in almost all the questions of physics and chemistry.
The syllabus of IIT JEE Mathematics is a perfect blend of easy and difficult topics. Topics like probability, differential calculus, trigonometry, straight lines and circles in coordinate geometry, permutations and combinations in algebra are always easy to crack in IIT JEE. The success mantra of the JEE is practice and hard work. Gone are the days when students used to spend hours in attempting one question. Now it is an era of multiple choice questions. The JEE Mathematics questions test a student’s acquired knowledge as well as his aptitude.
There are various mathematics books for IIT JEE which explain all the important topics in detail. IIT JEE Math is not very tough but students fail to excel in it as their basics are not very clear. Mathematics is a creation of human mind that builds up the reasoning capability in humans. It is this branch which explains the logic behind the concepts. Mathematical concepts lay down the foundation for Physics as well as Chemistry. The topics which form a part of IIT mathematics syllabus include:
Algebra can be considered to be one of the simplest and the most scoring domain of IIT Mathematics. The topics are quite interesting and demand good computation speed. In algebra, it is important to have conceptual clarity along with good speed in order to fetch excellent scores in various competitive exams like the JEE. Some of the important areas covered under it include:
Vectors & 3D Geometry: In mathematics and linear algebra, vector algebra refers to algebraic operations in vector spaces. Most commonly, it refers to operations on Euclidean vectors. The major concepts vector includes are General Vector Space, Three dimensional Space, Multilinear Algebra and Matrices. This is easy and scoring topic in JEE paper. There are a lot of problems you will see in the JEE paper.
Complex numbers : as the name suggests, it’s a really complex chapter. Contains a large number of concepts. This chapter integrated with coordinate geometry serves as the source of a large number of questions. Be careful with this. Locus problems are asked from this chapter wherein the definitions are given in complex number notation and you are expected to decipher it. The triangle inequality is another important aspect.
Quadratic Equations : A rather simple chapter but very much interesting. Make sure you know all the basic concepts. This would be easy if you practice past years problems well.
Series & Progression : The so called Vn method is most important. Recursion problems are the favourite ones. Make sure you know the definitions well and are well equipped to apply them whenever needed.
Logarithms : Simplest one. But the base change formula is important. Direct questions are asked rarely but they can test you in say a different way but integrating this chapter with other chapters of algebra.
Permutations and Combinations : The most difficult chapter for me. I am still confused so I can’t really say anything but make sure that you solve a large number of problems. The knowledge of this topic is very useful while solving probability, which is considered as a very tricky and relatively tough chapter of mathematics.
Binomial Theorem : Easy one. Practice a handful of problems and you are done.
Matrices : Simplest chapter of algebra. But the paper setters know how to make you sweat in matrices problems. Check the paragraph that was asked in JEE 2010. It is the toughest problem from this chapter.
Probability : Not really difficult but not easy too. Practice board level problems in the beginning and then move on to tougher ones.
Differential Calculus & Integral Calculus:
Calculus is the most important topic for JEE (Main & Advanced) and it constitutes a major part of modern mathematics. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. The JEE Math comprises all sort of problems including the theoretical as well as application based. The major and important chapter included in calculus are:
Functions: A function is a relation for which each value from the set of the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair. The major topic function contains are types of Relations & Functions, Composition of Functions, Invertible Functions and Binary Operations.
Inverse Trigonometry: In this chapter, you will learn and use the inverse sine, cosine, and tangent functions and how to find the exact value of expressions involving the inverse sine, cosine, and tangent functions. Also, learn to find exact values of composite functions with inverse trigonometric functions. The basic concepts used in this chapter, will help you throughout the whole Calculus.
Limits: The concept of a limit is fundamental to Calculus. In fact, Calculus without limits is like Romeo without Juliet. It is at the heart of so many Calculus concepts like the derivative, the integral, etc. In mathematics, a limit is the value that a function or sequence “approaches” as the input or index approaches some value. Limits are essential to calculus and are used to define continuity, derivatives, and integrals.
Continuity & Differentiability: It is not only an easy topic but also fetches direct question in the examination. A person who has already done a good practice of this chapter is also likely to do well in the next topic of Differentiation. The lifeline of Differential Calculus is basically the topics which include the application of Derivatives i.e. Tangent and Normal and Maxima and Minima.
Methods of Differentiation: Techniques of Differentiation explores various rules including the product, quotient, chain, power, exponential and logarithmic rules. These methods are very helpful for solving various complex differentiation problems.
Indefinite Integrals: Integral or Improper integrals, which are integrals where either the limits of integration or the function contain something crazy, like an asymptotes. The limit here is not defined while integrating.
Definite Integral: The Definite Integral unit identifies how to use the definite integral to approximate area, the average value of a function and how to compute it using substitution. The Topics included are Approximating Area Using Rectangles, The Fundamental Theorem of Calculus, Computing Definite Integrals using Substitution, Definite Integrals As Net Change, Definite Integrals and Area and Average Value of a Function.
Tangents & Normal: Tangents and Normal is the introducing part in the Application of Derivatives. The chapter starts with basic concepts of equations of tangent and normal to general curves, angle of intersection between two curves and goes on to discuss more fundamental concepts. “Tangents and Normal” is one of the scoring topics of Differential Calculus in the Mathematics syllabus of IIT JEE. It requires a good understanding of graphs and further helps in the portion of Coordinate Geometry, another important unit in the syllabus.
Coordinate geometry is also an important component of IIT Math. It is basically a method of analyzing geometrical shapes and is one of the most scoring topics of the mathematics syllabus of IIT JEE and other engineering exams. Besides calculus, this is the only topic that can fetch you maximum marks. It is a vast topic and can further be divided into various parts like:
Basics : Cartesian coordinates, distance between two points, section formulae, shift of origin etc. They form the backbone of Co-ordinate geometry. Make sure to learn all formulas by heart. Locus problems form another set of problems from the point of JEE. Master them.
Straight lines : Equation of a straight line in various forms, angle between two lines, distance of a point from a line. Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines, centroid, orthocentre, incentre and circumcentre of a triangle. These are the topics as mentioned in JEE syllabus. Understand the various forms of a line and learn to apply the best form in a particular scenario. Family of straight lines is most important from the point of view of JEE problems. Also make sure to learn how and when to apply the parametric form of a straight line.
Circles : Equation of a circle in various forms, equations of tangent, normal and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.
It’s the simplest chapter. Understand the standard equations. This chapter contains a number of formulas such as – length of tangent from a point, equation of chord of contact, equation of chord with a given midpoint, equation of common tangent, finding radical axis, radical centre, etc. The formulas derived here are general and apply to ellipse, parabola and hyperbola as well. So better learn them by heart. The parametric form of a circle is very important.
Parabola : Most of the equations that are derived in Circles chapter will work here. Theparametric form is really important in all chapters of conics. An interesting topic is the reflection property of parabola which you might like to learn for solving paragraph type questions in JEE. Note that paragraphs are common from the chapters of coordinate geometry so better be prepared to se something new on JEE day. You won’t be given the same old beaten up problems.
Ellipse : Much of same as Circles. Again the parametric form is important. Auxiliary circle helps a lot in solving the questions of this chapter. Locus problems are frequently asked from this chapter. Parametric form will help you in solving locus problems.
Hyperbola : Much of same as Circles and ellipse. Simple but confusing. Conjugate hyperbola and asymptotes and their properties are important. Some people face problems in this chapter. Reason is that this chapter marks the end of coordinate geometry. So, usually people get bored till this time and tend to neglect it. But keep in mind that paper setters know all this. And they are ready to trap you. A good student cannot afford to miss any chapter.
Trigonometry: Trigonometry is a vital constituent of Mathematics in IIT JEE examination. Trigonometric functions and trigonometry ratios are some of the most imperative areas of trigonometry. Since the IIT JEE exam asks a good amount of questions on this topic, so getting the knack of the basic trigonometry can surely help an IIT JEE aspirant to smooth his way through the exam.
This branch of maths deals with triangles and the relationships between the sides and angles. The trigonometry functions are universal in parts of pure mathematics and applied mathematics which also lay the groundwork for many branches of science and technology. The IIT JEE Trigonometry problems range from the trigonometry basics to the applications of trigonometry.
If one prepares the topics efficiently, he can easily get a good AIR. So if you have practiced all types of IIT maths questions thoroughly it would help you in reaching the solution quickly rather than figuring out how to crack the question. The more one practices and learns the typical methods of solving different types of questions the faster he can crack IIT JEE mathematics questions.