Calculus for JEE Advanced Preparation: Check important tips to prepare

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.

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.

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.

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

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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