How to prepare for JEE Advanced from class 11th

So you got 96% in your 11th test conducted by your school. You are entering in class 12th. The usual clamor for the preparation for JEE has started in the family and in your friend circle. You don’t care much because you have done wonderful with your 11th. So you start solving problems of JEE related to the syllabus of class 11th. The first question you encounter is finding the possible number of real roots of a polynomial with degree 4. You are stumped. This is not what you studied in class 11th. All you did was few equations of degree 2. Then what is this?

The reason for this is difference between the “depth” of some of the topics in 11th versus the syllabus of JEE Advanced comprising the 11th topic. Since 12th syllabus is pretty vast, you do not have time to go through 11th chapters once again. This creates problems because not doing 11th topics well will reduce your chances further.

Had it not been better if you knew the topics which are hardly touched by your NCERT books? Let me list some of the topics which you need to go through in depth before you can call them “complete”. The chapters in NCERT hardly touch the surface of these topics.

Theory of Equation

In your 11th book, there is a chapter on quadratic equation. This is such a small chapter that you can finish it in 2-3 hours irrespective of your intelligence. Yes, try that if you haven’t.

However, JEE is notorious for going deep into this. Theory of equations is a very important topic both from calculus and algebra point of view. It literally has no bound. The rules governing nature of roots, sum and product of roots, sign of roots, sum of series of various forms of roots, relation between the roots of an equation and its derivative, and nature of equation between two values of x, convergence or divergence of equation with x tending to infinity, division of an expression, finding highest common factors (HCF), and many more phenomenon are huge in number. The syllabus does great injustice to this one of the most important topics for JEE main and advanced.

Complex number

The NCERT book for 11th combines quadratic equation and complex number in one chapter which can be studies in one sitting. The real scope of complex number in JEE is humongous. This is one of the toughest topics for students. JEE question setters just love this chapter. Playing with arguments of a complex number with different sign of real and imaginary part, using geometry with complex numbers, and twisting all-pervading and unpronounceable De-Moivre’s theorem are some of the ways JEE questions complicate the already complex topic.

Conic Section

The content in conic section in NCERT book is pretty small. They cover just the basic of conic sections. It doesn’t cover tangents, normal, pole & polar, combination of various conics, other forms of conics etc. Once again, JEE loves conic sections, especially JEE Advanced. They have almost abandoned the poor straight line and circle to favour conic section.

What should you do?

While nobody expects CBSE to go deeper into such topics as they are not meant for coaching you for JEE but treatment of theory of equation, complex number, and conic sections given in the 11th textbook is too shallow. There are few more chapters but they cover about 50% or more (at least concept wise).

Hence to prepare well for JEE and do not get overburdened with your 11th topics in your 2nd year, focus on theory of equation and complex number in great details. You must make it sure to cover the gap between CBSE syllabus and JEE standard. You can go through any of the JEE books (Cengage, Arihant, Eduwiser etc.) and study complex numbers and theory of equation in details, solve each and every question, and note down the lessons learnt, important formula, important concepts etc. so that this comes handy for last minute preparation.

Conic section is time consuming. It will require discipline and hours of practice to get expertise. Thankfully since the syllabus of 11th is small compared to 12th, you get more time to study. Use this time to achieve a certain level of expertise before you go to class 12th. Class 12th syllabus is huge. Coupled with the pressure of board, it is highly unlikely that you will have to time to study the 11th syllabus in details in your second year.

Work through these topics and do better in JEE.

~ Pankaj Priyadarshi

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