At your level, the most important part of Mathematics in JEE preparation is practice. It is practice that gives or takes away edge from you. Concept building in Mathematics plays a role too but practice plays a more important part. In Physics, its the other way round. Now, everyone can solve problems since they have access to all kinds of practice material for JEE preparation. However, you have to be smart with the choice of material for JEE preparation.
Being smart in no way means practising less. But, it becomes largely important for you to introduce variety to the problems you do. Your practice should not become very redundant. This will bore you off and more importantly take your time. How do you know whether a material repeats problems or not, without even actually trying them? Well, that’s impossible. But, here’s a careful list of books to help you with selection:
Topic-wise books in Mathematics for JEE:
Shantinarayan – Calculus
This book played a very important role during my JEE preparation. I happened to get hold of the book from my school library in my 11th standard itself. Luckily enough, I knew a bit about integration and I used to like it. This book however made me love integration. It offers a good variety of problems.
GN Berman – Calculus
This is another great book for calculus. This can be solved for all it’s forms. It captures many challenging problems in itself. Not only for solving, but this is also a good reference material too.
Govorov – Functions & Quadratic Equations –
This book covers Inequalities and Quadratic Equations at their best. Want to practise questions on functions? This is the book to turn to.
S.L. Loney – Trigonometry
This is the most religiously practised book for Trigonometry. There is a reason behind it: Problems put forth are thought out really well so far as their sequencing goes. I can confidently say that a thorough practice of this book can make life very easy for you.
S.L. Loney – Coordinate geometry
This is not as religiously followed as its trigonometric counterpart. But, it comprises of potential JEE problems too. Complicated problems are hardly an issue in Coordinate Geometry, it’s the basic ones that are difficult. This book makes you work on your understanding of something as basic as definition of a conic.
R.S. Aggarwal – Mathematics Overall
This book introduces you to various problems having different trick points. JEE Algebra can be practised form this book. This is not a very difficult book but, it will help you check your capability through simpler problems & examples.
Hall & Knight – for higher Algebra
As can be seen, it is a book on higher algebra. But, a wide range of questions from your level can be found too. Great for Sequences and Series, refer when you have run out of practice problems in Algebra.
NCERT – Mathematics Overall
There are books which you can solve for JEE preparation, there are ones which you should solve, then there are NCERT books, which you must solve. There have been direct questions from NCERT. In fact, NCERT should be solved for all the JEE subjects. Adding to the compulsion of it, I’d like to point out that NCERT books are rich in content.
They love NCERT, so you’ll have to love it too.
Playing with graphs – Graphs
They may put forth a complex function, f(x) for you and ask all kinds of questions on it. There are two basic methods of solving this. And like always one is better than the other. One is where you treat the function traditionally and solve every single question separately. Other which I’d recommend is to draw the function. Once you have drawn its graph, you know everything about the function. This book can help you a great deal with drawing graphs.