Mathematics for JEE Advanced

By Aman Goel

Mathematics is the most important section for JEE Advanced. You would notice that every topper or good rank holders in JEE Advanced have strong Mathematics. Students generally find mathematics tough because it requires lot of practice. Also, you need to mug up a good number of formulas. If you want to score good marks in JEE advanced then make sure that your maths section is strong enough.

JEE Advanced consists of mainly Trigonometry, Algebra and Complex Number, Coordinate Geometry and 3D Geometry, Calculus, Vectors, in the syllabus.

Topics in Mathematics

So let’s go through each topic briefly:

• Concepts of Trigonometry is required in almost every part of mathematics. It should be understood properly as JEE advanced generally don’t ask simple and direct question on trigonometry. They will make you use the application of trigonometry in some other topics. For trigonometry, I would say just try to remember all the formulas and basic properties. In addition to that, just try and practice few problems specifically on Trigonometry as it will make you better in analysing the problem.
• Algebra is a very vast topic. It contains lots of small topics like matrices, permutations, Quadratic equation etc. Although these topics are small and easy for JEE advanced but sometimes tricky questions are also being asked from these topics. All these topics should be learnt properly during the starting phase of the preparation as these topics are not that much tough and also you can get some more time for revision at the end. Also, it contains some topics like probability and complex numbers. They are the scoring part in JEE advanced. They should be understood properly as JEE advanced generally asks easy questions from probability and you should not make any error while solving them. Most importantly, just revise all the topics before going to exam.
• Coordinate geometry requires lots of mugging. You have to remember various formulas and properties. Circle and Parabola are the most important topics in coordinate geometry and should be mastered because all the further topics are derived from them only. You should learn all their properties and should practice a variety of questions so that you can gain confidence. Just try to clear all the doubts and build your basics. You can perform well in this part as the questions which are generally asked from this topic are not so difficult but are lengthy which again can be solved in time if you do sufficient practice.
• Calculus is the most important topic in entire mathematics. I would say if you want to score really good marks in JEE Advanced, your Calculus should be very strong as this topic generally don’t have much variation in questions and you can solve every problem. But it requires some tricks, concepts and lots of practice. Just memorise all the basic formulas of integration because sometimes students do the question wrong just because they apply the wrong formula. This mistake is done by lots of students even if they are good in remembering formulas just because of the lack of practice. So make sure, you revise all the formulas of the entire mathematics syllabus before appearing for the exam.
• Vector is a small but scoring topic. First of all just go through all the subtopics and practice some problems. For this topic, previous year questions are important as sometimes they ask questions similar to what they have asked before.

Also, there are some other smaller topics like Logarithms, Exponentials etc. which should be studied at the beginning because they are extensively used in Mathematics.

Some Tips To Score Better Marks

As mentioned before, Mathematics is the subject in which practice is the essential attribute. In the other subjects sometimes you might understand some topics very easily just by seeing or reading it. But in mathematics, even if you understand any concept you should practice some problems of it. A large number of students get fewer marks only because of lack of practice. One important thing while practising questions is, do not see the solution of the problem until and unless you have tried it in every possible way because without doing that, you will not get the idea of your preparation level. Also if you put in all your efforts in solving any particular problem, either you’ll be able to solve it or you will remember the mistake that you were making, after seeing the solution. In both the cases, your concept will get clear and the chances of making mistakes will also minimize till an extend.

Also, while preparing just try to make the short notes or summary of what you’ve studied after each chapter. Just make a separate notebook and try to write all the tricks, properties and formulas used in any particular chapter. This will not only help you in remembering them but it will also save your time while doing the revision.

Some Reference Books

First of all just solve all the study material provided by your coaching institute. There are various reference books available for almost every topic but there are few reference books which are really good and they will help you a lot.

For Trigonometry and coordinate geometry, you can refer to S.L. Looney. This book will help you in understanding your basic concepts as each topic is explained from the scratch. Hall and Knight is the perfect book if you are seeking to understand Algebra in a better way. It has different types of questions which will help you in understanding various concepts. For calculus, you can refer to S.K. Goyal. Also, if you have any problems in drawing graph of various functions, you can refer to any of the Arihant publication like playing with graphs.

Along with that, you should practice all the previous year questions as they will help you in checking your level of preparation.

Summing up, I would say, just don’t take too much stress. Work hard and just give your 100 percent.

About the Author:

Aman Goel is 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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