Calculus for JEE Advanced Preparation: Check important tips to prepare

Joint Entrance Exam - Advanced 2025 ( JEE Advanced )

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Exam On: 18 May '25

Updated on Oct 10, 2022 10:31 IST

Read the article below to check important tips for effective preparation of Calculus from JEE Advanced point of view.

Calculus is one of the most important chapters in Mathematics. It is an important section in mathematics due to its vastness and also the weightage that is given to it in JEE question paper. Around 35% to 40% of the JEE Advanced exam paper comprises Calculus. Due to such a huge weightage given to Calculus in JEE, for a serious IIT aspirant, it becomes mandatory to study this topic seriously to gain a good command over it for scoring high in JEE mathematics.

The topics which are covered under the Calculus section are Functions, Inverse Trigonometric Functions, Limits, Continuity, Differentiability, Methods of Differentiation, Indefinite Integration, Definite Integrals, Application of Derivatives, Area under Curves and Differential Equations.

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Once you are comfortable with this topic, your path to JEE becomes quite easier as you can score good marks in it. All you need is a good grasp of concepts and practice questions. Those who are confident in it give less time to this during revision saving time for other subjects.

Q:   How to prepare for JEE Advanced in 1 month?

A:
Preparing for JEE Advance in just one month can be a challenging task, but it's not impossible. Here are some tips to help you make the most of your time: Understand the Exam Pattern: Go through the JEE Advanced exam pattern, syllabus, and previous year's papers. This will help you understand the format of the exam, the types of questions, and the level of difficulty. Focus on Important Topics: Identify the important topics and subjects that carry maximum weightage in the JEE Advanced exam. You can prioritize them based on their weightage and focus on mastering them first. Practice with Mock Tests: Take as many mock tests as possible in the remaining time. This will help you get a better understanding of the exam pattern and the types of questions asked. Revise Formulas and Concepts: Revise all the important formulas, concepts, and theories. You can make notes, flashcards or use any other technique to help you memorize them. Solve Previous Year Papers: Solve previous year's papers and analyze your performance. This will help you identify your strengths and weaknesses and work on them accordingly. Stay Focused and Motivated: Stay focused and motivated throughout the preparation process. Avoid distractions and stay committed to your goal. Remember that one month is a short time to prepare for such a competitive exam, so make the most of the time you have, and stay consistent in your efforts. Best of luck!

Q:   What is JEE Advanced rank list?

A:

JEE Advanced rank lists are prepared based on the aggregate marks in JEE Advanced. Only candidates who appear for BOTH Paper 1 and Paper 2 will be considered for ranking. There will be no waiting list for ranking. The ranklist is used in JoSAA for allocation of seats in the IITs. JoSAA is held online only. All the candidates who are eligible for admission will have to participate in the joint seat allocation process by filling in their preferential choices of the courses and institutes. If the aggregate marks scored by two or more candidates are the same, then the following tie-break policy will be used for awarding ranks: Candidates having higher positive marks will be awarded a higher rank. If a tie exists then a higher rank will be assigned to the candidate who has obtained higher marks in Mathematics. If this does not break the tie, a higher rank will be assigned to the candidate who has obtained higher marks in Physics. If there is a tie even after this, candidates will be assigned the same rank.

Q:   What is a safe score for JEE Advanced to get an IIT?

A:

It is a very relatable thing. A good score in JEE Advanced will depend on various factors one of them being the cutoff. Further, the cutoff will depend on various factors like the difficulty level, paper pattern, number of seats in the IITs, number of candidtaes taking the exam and so on. Therefore, it is difficult to say what will be a safe score. However, 300+ is a safe score in JEE Advanced if the total marks in the paper is 360.

JEE Advanced 2024 cutoff has been the highest in the past 6 year. This year the cutoff marks has been 109 marks for the Common rank list (CRL) out of 360 marks. For the GEN-EWS and OBC-NCL rank list the cutoff marks is 98; for SC/ST/Common-PwD/GEN-EWS-PwD/OBC-NCL-PwD/SC-PwD/ST-PwD is 54 marks and for Preparatory course rank lists it is 27 marks.

JEE Advanced Question Papers

JEE Advanced Mock Test

JEE Advanced Exam Pattern

JEE Advanced Syllabus

How to study Calculus?

Functions

This is where you learn the fundamentals. Learn to find the domain, range, plotting graphs of different functions. Learn about knowing injection, surjection, bijection of different functions. Study this chapter well. You can make silly mistakes in this chapter. Read the questions carefully, see the given range and domain carefully while determining whether it is one-one onto or not. Be careful sometimes like having a negative number under square root or a number divisible by zero.

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You will also learn about Inverse Trigonometric Functions. Remember the properties by heart. Learn about their sign in different quadrants and their graphs.

Limits

This is one of the easiest chapters yet very important as you will find questions related to limit throughout the entire calculus. Learn about the series expansion and sandwich theorem as they come in handy sometimes. L’Hopital’s rule is very important. You might also give a try to series expansion. It is advisable to remember the exponential and logarithmic series.

Questions from this chapter are usually straightforward. You just have to figure out the zero by zero form or the infinity by infinity form and apply L'Hopital's rule. Practice questions related to it and you will be able to find limits of almost any question

Q:   What is JoSAA?

A:

JoSAA (Joint Seat Allocation Authority) has been set up by the Ministry of Human Resources Development (MHRD) to manage and regulate joint seat allocation for admissions to over 100 institutes including IITs, NITs, IIITs, and Other-Government Funded Technical Institutes (Other-GFTIs). Admissions to all these institutes will be done through a single platform. The idea behind introducing a single counselling platform was to reduce thousands of seats going vacant in engineering colleges across the country. The Joint seat allocation process was introduced to make the whole process of admissions smoother, effective, efficient, transparent and a lot faster. Candidates who qualify for the JEE Main or JEE Advanced must register for JoSAA 2025 to participate in the counselling and admission process for various renowned engineering institutes across India. The admission process for admissions in 23 IITs, 31 NITs, 25 IIITs, and 28 Other-Government Funded Technical Institutes (Other-GFTIs) is managed by The Joint Seat Allocation Authority (JoSAA). Candidates will be allotted seats in various rounds of JoSAA counselling. The seat allotment through JoSAA will be based on the merit of candidates and their preference for courses and colleges.

Q:   What should be my preparation strategy to crack JEE Advanced in one year?

A:

Determination and dedication are the two main Ds which one should have in plenty. It's the mind which helps you achieve whatever your dreams or goals are and at the same time acting on it. To preparae for JEE Advanced in one year, candidates must consider the following:

  • Make formulae sheets along with your preparation, you can also use 100 marks mind maps.
  • Keep marking tricky questions to look upon at the time of revision.
  • Always solve questions in time constraints.
  • It is not at all necessary to attempt questions in a specific order, start with the easiest.
  • You only have 1 year, focus on problem-solving tactics rather than analysis of questions.
  • If a reverse approach is easy then use it rather than following full solution procedure.
  • Go with few books, clear your basics and keep yourself attached to the school curriculum.
  • Study all three subjects daily, you may decide timings according to your convenience and do it consistently and eventually, you will surely secure a good rank. 9. Have faith in yourself.
  • There will be times when you would find it difficult to understand and manage things. Do not give up. That is the point where many aspirants give up and finally fail. Keep giving your best, even if you feel like you aren't getting any output. Remember, hard work pays forever.

Q:   How to score well in JEE Advanced?

A:

Here are the top 7 strategies that any students may follow to clear JEE Advanced exam with ease: 1. Solve As Many Numerical Problems as Possible JEE Advanced exam focuses on testing the candidates comprehension, reasoning and analytical ability. The questions asked in the three subjects of Physics Chemistry and Mathematics are of advanced level and focus on the application of the concepts rather than the concepts themselves. 2. Keep Track of Strengths and Weaknesses For scoring perfect marks, candidates must be prepared perfectly as well. This means keeping an eye on their strengths and weaknesses and trying to avoid making the same mistake twice. Errors occur when one is unsure of himself/herself, and uncertainty is the last thing any candidate would want while attempting questions in the exam. 3. Set Daily Targets Setting daily targets serves two purposes. One, the entire syllabus is divided into short-term goals that need to be achieved daily, and two, the focus of the students remains unwavering until the long-term goal is achieved. 4. Develop a Subject-wise Study Plan Different students have varied levels of command over different subjects. Someone may be good at Physics and Mathematics and need more effort in Chemistry or the other way round. 5. Keep a Positive Outlook JEE Advanced is not the end of the world, but that does not mean it should be taken lightly. Moreover, if a candidate appears for JEE Advanced then it is natural that they have qualified the JEE Main exam after beating Lacs of competitors. This means that a positive mindset can help achieve the steepest of goals under any circumstance. Hence, students should always keep a positive outlook for the best results. 6. Refer to Previous Years Question Papers 7. Attempt Mock Tests. Hope it helps.

Q:   JEE Advanced syllabus feels overwhelming. How to cope with it?

A:

JEE Advanced syllabus can sometimes feel like an infinite sea. So, candidates can get overwhelmed. Thus, here is what to do:

  • Firstly, it is crucial to keep yourself updated with the ongoing chapters in your class. It is highly recommended to read ahead of what you are being taught in class. This technique has been proven to be helpful for every person who believed themselves to be average and not incredibly smart.
  • Secondly, it is essential to mark the difficulty level of the questions when you attempt them for the very first time. This way, you can categorize them according to their level of difficulty. Then, it is recommended to revise the theory and revisit the marked questions. You should filter out the questions again accordingly to their level and mark them differently for Mains and advanced. (Note: This idea works for inorganic chemistry too but it must be learned by heart first.). Now, whenever you feel the need to revise any topic, just go through the marked questions. If you can do them, practice past year questions. In case you get stuck, you can always refer to your notes or clear your doubts during doubt sessions. This technique is believed to be the best method for effective learning. 

Q:   How many chapters should be covered for JEE Advanced for fast revision?

A:
The chapters that cover for JEE Advanced fast revision are: Physics Mechanics, Electricity and Magnetism, Optics Waves Thermodynamics Modern Physics Chemistry: Physical Chemistry (Mole Concept, Atomic Structure, Chemical Bonding, Thermodynamics Organic Chemistry (Basic Principles, Hydrocarbons, Alcohols, Phenols, Ethers, Aldehydes, Ketones, Carboxylic Acids, Amines Inorganic Chemistry (Periodic Table, Chemical Bonding, Coordination Compounds, p-Block Elements, d-Block Elements) Mathematics: Algebra (Quadratic Equations, Sequences and Series, Permutations and Combinations, Complex Numbers), Calculus (Limits, Continuity and Differentiability, Application of Derivatives, Indefinite and Definite Integrals Differential Equations Coordinate Geometry (Straight Lines, Circles, Parabola, Ellipse, Hyperbola), Vectors and 3D Geometry, Probability.

Continuity and Differentiability

If you have studied functions properly then you will find this chapter very easy. This chapter can be solved if you are accurate and quick at drawing graphs of functions. Few problems of continuity require graph drawing. Learn intermediate value theorem. In differentiation, just remember the formulas. Learn the formulas of differentiation - quotient rule, product rule, chain rule, differentiation of exponential and logarithmic functions, higher-order derivatives. Practice a few questions to get comfortable with it.

Integration and Definite integrals

One of the most important topics in calculus. There is a good number of questions on this topic. You have to remember the standard formulas of Integration and practice a lot of questions. You will find a variety of questions. You will be comfortable once you have practised sufficient problems. Learn how to use integration by parts, partial fraction method, substitution method, Newton Leibnitz formula. Most questions will be based on the properties of definite integrals Learn few tricks like solving any question by differentiating both sides. Practice a lot and you will love this topic.

Once you are good with definite integrals, another chapter Area under the curves will be very easy for you as it requires you to draw the graph of the given function and evaluate the integral between the given limit.

Application of Derivatives

Again, one of the most important topics. There will be a good number of questions from this chapter. You will have to remember few formulas like a tangent, normal, sub- tangent, subnormal. Learn about monotonicity, finding minima/maxima. Using the second derivative test is important sometimes Rolle's theorem, Lagrange's mean value theorem, the concept of maxima-minima, increasing and decreasing functions, inflexion points, etc are extremely important. This is a beautiful chapter and you will not face much difficulty if you have done your previous studies properly. You can score good marks in this topic.

Differential Equations

After learning the tougher topics earlier, when you will study this, you will find this chapter relatively easy. There are few formulas in this chapter like finding first-order Differential Equations and Bernoulli’s equation. Practice a few questions from this.

The weightage of Differential Equations in the JEE paper varies hugely. Also, this is the topic that you will also encounter during your engineering studies in college. So make sure to gain a good command of this topic. Doing so will not only help you in JEE but also in college.

To get confidence in Mathematics, practice is a must. However, this portion is so vast that you might miss out on some concepts after some time. Practice as many number of problems the application of derivatives and definite integrals. So, revise this part regularly and practice the standard problems. In the end, this will be one of the easiest and scoring topics. All the best.

About the Author:

Aman Goel is a co-founder at a Tech Start-up. He holds a BTech in Computer Science Engineering from IIT Bombay with a JEE Advanced AIR 33 (Year 2013).

During his free time, he enjoys writing articles/blogs. He is an Entrepreneur, Coder, Speed-cuber, gamer, and fan of Air crash investigation!

 

 

 

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If you match the eligibility requirements, you can apply for JEE Advanced after finishing your second intermediate (12th class). Clearing JEE Main and placing in the top 2.5 Lacs applicants are prerequisites for JEE Advanced. Your age, number of attempts, and results from your prior qualifying exams

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