CBSE Class 12 Mathematics important concepts for JEE Main 2022

CBSE Class 12 Mathematics is the foundation for calculating complex engineering and scientific problems. In the JEE Main 2022 examination, almost every question was solely based on mathematical formulae and applications. This section needs to be practised very well to obtain the best marks. There are a handful of chapters included in the JEE Mathematics. 

Moreover, unlike Physics and Chemistry, there is nothing like the least important or most important topics based on the level of importance to cover in mathematics. Because all the topics are interlinked to one another, the JEE aspirants must study all the chapters and every concept included in them. Also, they cannot skip between chapters since all are equally important.

In this informative article, let us learn the topics and how to schedule and study them to achieve good grades in the examination.

JEE Mathematics Syllabus

Most topics that appear on JEE Main are from CBSE Class 12. The students should be able to differentiate between each topic and know what the formulae are to solve the problems given in these topics. There are five most common chapters asked in previous years’ JEE examinations. They are as follows:

1. Calculus
2. Coordinate Geometry
3. 3D Geometry and Vectors
4. Algebra
5. Trigonometry

Let us have a wide look at all of them in detail.

Calculus

Due to the level of difficulty of this chapter, it is very crucial for both JEE Main and JEE Advanced examinations. This chapter has a wide variety of formulae and concepts to cover by the students. It is possible that in all the engineering entrance exams, a few questions from this chapter are asked without any denial.

This unit plays a key role in understanding all the other concepts of Mathematics, and the students will not have to worry about the examination if they are thorough with this one. This chapter requires strong development and understanding to achieve higher grades. Therefore, it is essential to have a neat preparation in this unit. The following are some of the important subtopics included in this chapter:

• Limits
• Differentiability and Continuity
• Relationship between Differentiability and Continuity
• Integration
• Differentiation
• Definite Integrals
• Integration by Parts
• Properties of Definite Integrals
• Rate Measurements
• Maxima and Minima
• Tangents and Normal
• Area under curves
• Differentiation Equations

Coordinate Geometry

A coordinate system is considered a system capable of utilising one or more coordinates or numbers. It illustrates the geometrical elements and position of points on a manifold, which is a Euclidean Space, uniquely. The basic purpose of this unit in JEE Main is to make the students understand some of the geometrical shapes like a parabola, hyperbola, ellipse, circle, etc.

The questions asked from this unit are primarily of application of different formulae discussed in this chapter, which makes it very interesting and engaging for the students. Due to this, they can score higher marks in this chapter than any others in JEE Maths. It is easy to obtain the maximum marks from this particular unit.

The aspirants of Mathematics should have to focus more on the following topics to attain higher marks:

• Circle
• Ellipse
• Parabola
• Hyperbola
• Straight lines

Among them, Circles and Straight lines are the most fundamental ones. 

3D Geometry and Vectors

This unit in Class 12 Mathematics is a bit complex since most of the topics in this chapter are conceptual. In JEE 2022, the weightage given to this chapter compared to the Co-ordinate Geometry is somewhat similar. This chapter includes some parts of Geometry and Complex numbers in it.

The students of JEE Mathematics must understand specific complex vector concepts and 3D Geometry to attain excellent grades from questions asked in this unit. So, a proper understanding of the topics mentioned above is a must. The JEE aspirants have to try developing a strong foundation on the basics and concentrate more on this chapter through visual understanding.

Algebra

Algebra plays a vital role in all the mathematical entrance and final examinations. The usage of this unit in all those examinations is humongous. Algebra is an interesting unit covering certain topics, namely Matrices, Logarithms, Determinants, and Quadratic Equations. All these have been very popular among students since primary school to understand the concepts very easily. For some students, it is even their favourite unit in Mathematics.

Moreover, in both JEE Main and JEE Advanced exams, questions on the topic of Complex numbers merged with the Vectors have been asked continuously. In the JEE Advanced exam, the aspirants can expect a passage-type question from determinants and matrices. It might be one of the easiest to answer.

In addition to this, it is possible to have questions from Permutations and Combinations. Some of the Formula-based questions are usually asked from Series and Sequence and Binomial Theorem. Therefore, by practising regularly, students can easily avoid silly mistakes, which open up a gateway to obtaining maximum marks in all these topics.

Trigonometry

Trigonometry is a very fundamental topic for the JEE Main examination. The following are the three most imperative topics the JEE aspirants should have their focus on:

• Trigonometric functions
• Inverse Trigonometry
• Trigonometric ratios

Moreover, for the JEE Maths aspirants to benefit from this chapter, they should have a firm understanding of all the basic concepts since a good amount of questions have been asked from this particular unit.

Therefore, memorising all these concepts and trigonometric formulae would play a key role in scoring well in this unit. Apart from that, it is also equally important to learn their graphs and substitutions.

Maths section in JEE Main 2019

The JEE Main 2019 examination level was set on moderate because it contains many questions that were neither difficult nor easy to answer. This section consists of more calculations with the candidates found hard to manage within the given time frame. It took a longer time than usual.

Furthermore, while breaking up the no. of questions and from which topics they were from:

• Algebra – 9 questions
• Calculus – 9 questions
• Coordinate geometry- 8 questions
• Probability – 4 questions
• Statistics – 4 questions
• Mathematical reasoning – 4 questions

Based on difficulty levels, 13 questions were easy and took less time to answer. Meanwhile, the other 13 questions were moderate and took a little more time to finish. Furthermore, four questions were difficult, and candidates took more time to accomplish them. 

To be more precise with the topics and concepts that were asked in the JEE Main 2019 Examination under the Mathematics section, let us have a look at the following tabulation:

So, from this, the important chapters covered in the JEE Main 2019 question paper are:

• Probability and Statistics
• Application of Derivatives
• Binomial Theorem
• 3D Geometry
• Circle
• Matrices and Determinants
• Complex Numbers
• Integration

Maths section in JEE Main 2018

The level of the Maths section in JEE 2018 was difficult. The candidates felt they needed more time to do the calculations because they were very lengthy, and the time given was not enough. In the exam, 20 questions were asked from the syllabus of 11th grade, whereas ten were from the 12th grade. Therefore, there were 30 questions, out of which ten were easy, 13 were moderate, and seven were difficult.

The following table provides the details of important questions that were asked, with the distribution of marks.

How to score excellent marks in JEE Main Mathematics

• Build your concepts

• Attend regular classes without skipping
• Make notes of what was taught in class
• Revise and practise the questions
• Mark important question

• Practise strategy

• Try to solve example problems
• Solve at least 200 questions from each chapter
• Buy or collect previous years’ question papers and solve them frequently

• Revision strategy

• Solve the questions given by your tutor after revising each topic
• Analyse the areas where you went wrong
• Correct your mistakes and make sure not to follow them in future tests
• Try to solve over 30 to40 questions in a fixed time frame

Conclusion

The aspirants of JEE 2022 should be able to practice a lot to obtain higher marks in this particular section. The accuracy and speed of solving the problems will gradually improve once they practice them regularly. The learners should not memorise the concepts, but instead, a deep understanding is much needed. They can memorise the formulas but not the concepts and theorems.

The aspirants must try to master all the vital topics by visualising, understanding, and applying them to real-world problems, which will give them top-notch knowledge of all the necessary concepts and help them lead a better life in terms of Engineering and Science.

FAQs

1. How easy or difficult is the JEE Main exam?

JEE Main is considered one of the toughest and the most competitive exams in India, especially in the field of Science and Engineering. There are over 12 lakhs students who appear for this exam every year. The numbers only go up every year, as there are always new aspirants getting to appear for them to get selected in India’s topmost Engineering universities.

The main objective of this exam is to filter the most brilliant intellects throughout the whole country and help them achieve their goal of studying at esteemed institutions. Some of India’s best educational institutions are IITs, NITs, etc.

2. How many attempts can a student take to pass this exam?

The latest update on JEE Main 2022 declares that a student can take up to two chances to clear this examination. The aspirants are not given any more chances, which indicates the quality of this examination compared to other entrance exams. Here, the students would be denied to write the third time, which is both a pro and a con. The NTA conducts the JEE Main exam in April and May of 2022.

3. What is the minimum mark required to be able to qualify in JEE Main?

To qualify for the JEE Mains Examinations, the aspirants must have at least 75 % in their 12 Grade. They must have a pass mark in 10+2 or equivalent exam from an authorised board with a minimum of 50 % aggregate marks.

4. How to crack JEE Main without any private coaching?

The aspirants should have attained the habit of practising mock tests and past years’ question papers to maintain their continuity in the subjects. It will also help them with speed and accuracy while solving each question.

5. How many students get seats in IITs?

There are lakhs and lakhs of students (over 12 lakhs) who appear for JEE Main examination, out of which only 20,000 to 25,000 can write JEE Advanced exam. Only 10,000 top-ranked candidates are selected to pursue their higher education in the 23 IITs in India.

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