JEE Main Maths Session 2: Important Topics From Session 1 Exam

JEE Main 2022 Session 1 exams have been concluded and the JEE Main session 2 examinations are to be held from 21 to 30 July 2022. Since a few days are left, students need to prepare well for the upcoming exams. Mathematics is one of the trickiest and lengthiest papers in JEE exams. Moreover, its questions cover nearly every part of the JEE Main Maths syllabus in sessions 1 and 2, making it challenging to identify the most important Maths topics for the exam. 

However, there are some important topics, such as 3-D geometry, calculus, Vector algebra and so forth, that carry high weightage in exams. Once students know and master these topics, they can score optimum highest in Maths in both sessions, as session two is highly similar to the session one exam pattern. This is why students often prepare and take both sessions simultaneously. 

Candidates preparing for the JEE Mains 2022 examination should concentrate on the most important chapters and their weightage from the extensive JEE Mains syllabus. Many aspirants put in a lot of time and effort, but they don’t do the smart work required to pass the JEE Mains exam. Students who want to perform well in the JEE Mains exam should be familiar with the weightage of each chapter as well as previous year’s trends. Analysing the last year’s questions and sample papers, we compiled a list of essential topics requiring more attention from students preparing for Session 1 and Session 2.

The table below represents JEE Main Maths syllabus and its topic-wise weightage for session 2. 

According to the previous year’s Maths JEE Mains Session 2, analysis Calculus, 3D Geometry, and Vector Algebra were all weighted equally. Additionally, there were some tricky questions in Binomial Theorem, Permutation and Combinations, and Properties of Definite Integral and Differential Equations. There were a few complex questions in the Circle & Ellipse chapters. In both the sessions, the paper had similar difficulty and lengthiness. Based on the previous year’s trends topics/chapters weightage of JEE Main Maths, it’s simple to find the most important topics for preparation; however, these topics also include numerous important concepts and sub-topics. Henceforth, we have listed the essential JEE Maths Session 1 topics that will also be a part of session 2. 

Integral Calculus

Integral calculus helps to find a function’s anti-derivatives. The anti-derivatives of a function are also known as its integrals. The process of determining a function’s anti-derivative is referred to as integration. The opposite of finding derivatives is finding integrals. The integral of a function represents a set of curves. It covers a wide range of sub-topic, the most important ones for JEE both sessions are:

• Integration as Reverse Process of Differentiation
• Fundamental Formulae of Indefinite Integration (Trigonometric Functions)
• Some Special Integration
• Application of Special Integral Formula (Part 1)
• Integration by Parts

Differential Equation

A differential equation contains one or more functions and their derivatives. The function’ defines the function’s rate of change at a given point. The differential equation is mainly used to analyse the properties of the solutions that satisfy the equations. Explicit formulas are the most straightforward method of solving differential equations. The following are the essential sub-topics of Differential Equations for JEE exams.

• Bernoulli’s Equation
• Formation of Differential Equation & Solutions of a Differential Equation
• Linear Differential Equation
• Homogeneous Differential Equation

Coordinate Geometry

Co-ordinate Geometry (also known as Analytic Geometry) is a simple and enjoyable topic in the JEE Main curriculum. It has the highest weightage (from 17 to 20%) in the Maths section, making it easier for test-takers to achieve a good score in JEE Main. Co-ordinate Geometry explains the relationship between geometry and algebra using graphs with curves and lines. Check out the co-ordinate geometry topics that require more attention in JEE Mains. As per the previous trends, this topic holds great importance for both the sessions of JEE exam.

• Co-ordinate Axes
• Distance between two points
• Section Formula
• Centroid
• Incentre

Three-Dimensional Geometry

This topic primarily deals with 2-D and 3-D geometry. Two-dimensional geometry is concerned with the placement of a point in the x-y plane. In contrast, three-dimensional geometry is concerned with three orthogonal axes: x,y, and z. Therefore, 3-D geometry is nothing more than an extension of 2-D geometry in Three-dimensional geometry. JEE aspirants will tackle a few tricky questions on this topic in session one and session 2. Therefore, they know about the high weighing sub-topics of three-dimensional geometry, which is already given below:

• Introduction to 3D Coordinate System
• Section Formula, Direction Cosines and Direction Ratio
• Angle Between Two Lines
• Equations for a Line in Space
• Shortest Distance between Two Lines

Vector Algebra

Mastering the essential concepts of Vector algebra can get you eight marks more in JEE session one, and there are high chances for it to be a part of session two as well, just like in previous years. In its most basic form, Vector algebra is an algebra in which vectors represent all variables. The rules and hypotheses of this branch are based on the properties and behaviour of vectors. Students will learn various concepts by applying the fundamentals of vector algebra and working through the following JEE Mains topics. 

• Types of Vectors
• Component of Vector & Vector Joining Two Points
• Section Formula
• Direction Cosines and Direction Ratio
• Multiplication of a Vector by a Scalar

Statistics and Probability

Statistics and Probability are among the most fundamental concepts in JEE Mains Mathematics, whereby Probability is heavily influenced by chance. On the other hand, statistics is concerned primarily with the methods used to analyse various data types. Therefore, solving the essential questions in Statistics and Because Statics and Probability are one of the most crucial topics for the JEE Mains. Moreover, the previous year’s paper analysis represents both JEE sessions. Therefore, paying attention to its essential subtopics can provide students with a competitive advantage in the exam. 

• Mean
• Median
• Mode
• Dispersion (Range, Mean Deviation)
• Dispersion (Variance and Standard Deviation)

Trigonometry

It is evident from previous records that Trigonometry is repeated in both JEE Mains sessions; therefore, understanding its concepts and formulas is a must for JEE aspirants. The functions compute the bell curve and investigate regular periodicities in statistics. One of the many applications of trigonometry that can be found in various fields is the Fourier series. The essential subtopics of this calculus branch are listed here:

• Trigonometric Functions of Acute Angles
• Trigonometric Identities
• Measurement of Angle
• Trigonometric Ratio for Compound Angles (Part 1)
• Trigonometric Ratio for Compound Angles

Complex numbers and quadratic equations

This topic is also essential for competitive entrance examination preparation. This topic holds 7% weightage in  JEE Main. It is estimated that every year 1-2 questions come from Complex numbers and quadratic equations in both sessions of JEE Mains, either directly or indirectly. So while preparing this chapter, it’s a must for students to go through previous questions and grasp the concepts. This topic includes the following sub-topics:

• Complex Numbers
• Algebra of Complex Numbers
• Modulus & Conjugate of a Complex Number
• Argand Plane and Polar Representation
• Quadratic Equations

Matrices and determinants

It is one of the most fascinating, fundamental, and essential topics of JEE Mains. Every year, 2-3 problems from this topic are included in JEE Main and other entrance exams. Students will learn the following concepts while studying  Matrices and determinants.

• Matrices
• Types of Matrices
• Inverse Matrix
• Transpose of Matrix
• Determinant of Matrix

Mathematical Reasoning

Mathematical reasoning is one of the most straightforward to cover and is worth four marks. The field of Mathematical Logic is concerned with the concepts of reasoning. Once you learn this topic, you can answer all the questions from it, whether you are participating in the Session 1 exam or Session 2. JEE aspirants need to know the following to ace this particular topic in the exam.

• Truth Table
• Relation Between Set Notation and Truth Table
• Converse, Inverse, and Contrapositive
• Tautology And Contradiction
• Algebra of Statements

Sets, relations, and functions

Sets, relations, and functions are an essential part of calculus because they serve as the subject’s foundation (differential and integral). It carries 3.3-5% weight in the JEE Main exam, students can expect 1-2 problems from it each year, but the principle of this chapter will be used in many other areas of calculus. Therefore, Sets, relations, and functions make this a must-read chapter for anyone preparing for a JEE Mains, session 1 or 2. It includes the following sub-topics:

• Union of Sets, Properties of Union
• Subsets, Proper and Improper Subsets, Intervals
• Cardinal Number of some sets
• Domain, Range of Relation

Permutation and combinations

Permutations and combinations are ways to select objects from sets without making any replacements. If the order in which the subsets are chosen is important, it is a permutation; otherwise, it is a combination. This topic carries 3.3-5% weightage. At least a four marks question can be found in JEE Mains both session papers. Therefore, students should also cover this topic by solving questions based on the following subtopics:

• Permutation as an Arrangement
• Application of Permutation
• Geometrical Permutations
• Different Cases of Geometrical Arrangements

After completing the preceding topics, you can study Inverse Trigonometry, Heights and Distances, Application of Derivatives, Logarithm, Theory of Equations, Quadratic Equations. Additionally, Binomial Theorem, Locus, Hyperbola, Ellipse, and other relevant JEE Mains Maths can also be studied. They are undoubtedly included in Sessions 1 and 2 but carry lesser weightage than those mentioned above.

Conclusion

To understand mathematics, one must first understand its fundamental concepts. Then, those who want to master it will need to spend a lot of practice remembering the formulas. Additionally, Maths is crucial for the IIT JEE Mains exam regardless of the session. Therefore, the most straightforward way to perform well in the Joint Entrance Exam is to study Maths and other subjects such as Chemistry and Physics. Also, it’s best to pay more attention to the highest scoring sections, but learning the Maths concepts of low scoring sections is equally essential; as they say, many a little makes a mickle!

FAQs

1. How many marks will Trigonometry get me? How can I prepare for it?

Trigonometry is an integral part of the JEE Main exam that can get you four marks. The most important topics to learn are inverse trigonometry, trigonometric functions, and trigonometric ratios. Given how frequently questions from this chapter are asked, knowing a few basic trigonometric principles could be very useful to a JEE student. To score optimum in this chapter, you must memorise all trigonometric formulas, graphs, and substitutions.

2. Is NCERT sufficient for JEE Maths preparation? If not, what other books can I refer to?

NCERT textbooks are the best for a thorough understanding of the fundamentals. However, students should also consult the following reference books for more information and practice questions to perform well on the JEE Main exam:

• Play with Graphs by Amit M Agarwal (Arihant Publications)
• The Elements Of Coordinate Geometry by S L Loney
• Integral Calculus by Amit M Agarwal (Arihant Publications)
• Algebra by Dr S K Goyal Arihant Publications
• Plane Trigonometry by S L Loney
• Objective Mathematics by R D Sharma

3. Can taking mock tests help me to prepare for JEE Mains?

JEE Main Mock Tests are the most effective way to prepare for the exams. They are exact replicas of the actual exams. Taking mock tests can make you familiar with the exam environment and enable you to evaluate yourself and work on your shortcomings. Further, they reduce stress and build up confidence among aspirants like you.

4. Why is it essential for aspirants to know the JEE Main Syllabus and topic-wise weightage for JEE Mains 2022?

This is the most frequently asked question related to JEE Mains exam pattern. Many of the JEE Main 2022 topics are taken from NCERT Class 11 and 12 Physics, Chemistry, and Mathematics textbooks. Candidates aware of the chapter-by-chapter weightage of the syllabus for JEE Main 2022 can understand which topic needs more time and attention and which requires less. They have a full-proof strategy to better prepare for NTA JEE Main 2022. 

5. How can I cover Maths’ vast syllabus for my JEE Mains exam?

If you want to pass the IIT JEE 2022 with a high score, you must devise a strategy. Since the JEE Mains Maths syllabus is extensive, it isn’t easy to cover all material. On the other hand, the exam is simple to pass if you prepare ahead of time. You should concentrate on the important chapters and topics, leaving the less important ones for last. Examining JEE Main previous year’s questions will assist you in determining the importance of each topic. Also, it would be helpful if you analyse your strengths and weaknesses to understand what you know better and where you lag.

6. How can I understand Algebra precisely?

Algebra focuses on properties rather than formulas. When studying quadratic or equation theory, understand how symmetric sums of roots and equation transformations occur in an equation. Many complex number formulae can be better understood and memorised if interpreted geometrically. Probability, Binomial, Permutation, and Combination should all be taken simultaneously. Because they are less formula-based and more focused on problem-solving tactics, mark a few common issues to review.