Algebra for JEE Advanced Preparation: Check important tips to prepare

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

Algebra is one of the most important topics of Mathematics in JEE. In fact, in the preparation of JEE, this is the starting point. Algebra like most of the other topics in Math doesn’t involve as much theory as application. There are very few formulae and definitions that you need to know, and won’t take much time in knowing either. But after that, your prowess on the topic depends on how much you practice it. By doing this, you will develop fluency in the topic and will get to know all the tricks and loopholes thoroughly.

Let us first note what all algebra covers:

Complex Number, Quadratic Equations, Series and Progressions (Includes Arithmetic, Geometric, Harmonic and Miscellaneous Series), Logarithms, Permutations and Combinations, Binomial Theorem, Matrices and Determinants, Probability.

From the above topics, Quadratic Equations, Matrices, and Determinants, Probability have heavy weightage. So, you should definitely focus on these chapters as they will be very helpful in getting you more marks. The rest of the chapters are relatively easy and you won’t face many problems in understanding.

Algebra is the most diverse topic. You have to learn each topic very efficiently and practice a lot of problems in order to perform well in Algebra.

Now, coming to the chapter-wise analysis:

Quadratic Equations

Quadratic equations fetch direct questions too and are also easy to grasp. Make sure you know all the concepts. This would be easy if you practice past years’ problems well. Beware of getting negative square roots. Learn the properties of inequality well. This can be tricky when multiple-choice questions are asked. So, practice few questions and be careful during exams. Make sure you understand how to make graphs of quadratic equations as it will be very helpful to determine signs of the roots.

Series and Progressions

Series and Progressions is another section that is mixed with other concepts and then asked in the examination. This is one of the easiest topics to understand but questions can be a bit tricky. You should understand the series properties carefully. Make sure you practice a variety of problems. Learn how to solve a_n series problems. If you are stuck on a question, try to think out of the box and apply various methods. Remember the standard GP, HP formulas as students tend to forget them quickly.

Logarithms

This chapter is the simplest one but the base change formula is important. Direct questions are asked rarely but they can test you in say a different way but integrating this chapter with other chapters of algebra. Don’t get afraid by seeing large terms, they are actually the easiest ones.

Permutations and Combinations / Probability

Permutations and Combinations along with Probability is the most important section in Algebra. JEE Advanced exam fetches a lot of questions on them. These chapters are rank deciders for those who aim for a very good rank in JEE Advanced.

A permutation is an ordered arrangement of the numbers, terms, etc., of a set of specified groups. A combination is also a way of selecting certain things out of a larger group. But here order does not matter, unlike permutation.

This is one of the most difficult chapters for JEE. Make sure you practice a lot of problems and learn the standard tricks.

For probability, I would recommend first solve problems from NCERT and then move to JEE problems. Generally, questions from probability are not that tough if you know which formula will be applied where. Practice questions on every theorem till you get comfortable. This chapter needs a lot of practice to be confident while giving JEE paper.

Binomial Theorem

Binomial Theorem is also a mark fetching topic as the questions on this topic are quite easy. The binomial theorem is used for expanding binomial expressions (a+b) raised to any given power without direct multiplication. Make sure you practice enough problems for having good speed and accuracy during exams.

Matrices and Determinants

Matrices and Determinants mostly give direct questions and you can solve them easily. Questions from determinants are quite simple and can be solved using their properties. Remember the properties. Be fast in expanding it (this will be achieved by practising), it will save your time during exams. However, if you are stuck somewhere, try its expansion. Sometimes, scary questions are the easiest ones. Few questions from matrices are a bit tricky. Learn the properties of matrices, their multiplication, and inverse properties well and solve a lot of questions from this to be comfortable.

Complex Number

Complex Numbers are also important as this fetches questions in JEE almost every year. As the name suggests, this chapter is a bit complex. Try to study this chapter after co-ordinate geometry and you will find it easy to visualize what is happening (real and imaginary number concepts). This chapter contains a large number of concepts. Solve a lot of problems just after learning any concept. Learn to apply the triangular inequality property well. Also, visualize any complex number by making quadrants. This will be helpful for knowing the tangent of the angle.

Algebra requires you to practice a lot of problems and if you are quick, then you will be benefited from exams. Remember the standard formulas and practice a lot. Since there is a very limited number of formulas in algebra, make a note of all the important ones in one place. Not the basic ones which you will remember obviously, but the ones which you always seem to forget uncannily. There are always a few. Keep updating your list and constantly revising. Algebra will have questions more often than not which involve several topics so fluency in all and application is crucial. 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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