Key To Excel in Algebra

This is the most difficult topic of maths for most students and even top ranker's.This is due to the vast and different varieties of questions . Algebra comprises 35% of the JEE paper and usually is the section that examiner wishes to make difficult .Lots of practice is needed in this area to get a good rank . Refer to as many different books and Institute Material for this section .Read plenty of solved Examples as this will help you on how to approach the various questions.

Topics In Algebra 

• Quadratic Equations- A simple topic in Algebra .Questions of this topic are sometimes asked mixing concepts of calculus .Focus Majorly on Location of roots. Practice previous year questions and this topic becomes Cake walk for most .
• Logarithm -The easiest topic of algebra .Graph of log and Inequality are very important .Though questions from this topic might not be asked directly and are usually mixed along with calculus .Make sure that you are comfortable with properties of log especially the base changing .
• Permutation And Combination-This is usually a difficult topic of algebra for most students.Make sure that you are clear with concepts before approaching problems .Grouping and Distribution ,Derrangement,Circular Permutations must be practiced a lot .Questions involving Recursion must also be covered ,since JEE has started asking this in recent times. Practice  as many questions as you can from this chapter .
• Binomial Theorem - This is a Cake Walk chapter ,if you know the properties and have a basic idea of calculus .Give emphasis on Multinomial Theorem and various identities of this chapter 
• Complex Number - This was the most difficult topic of algebra for me .It has many concepts whose application is way too much and used in almost all chapters be it Integration and Bionomial Theroem . Euler Theorem , Cube Roots of unity are most frequently asked .Triangle Inequality gives way to a large number of problems .Geometrical problems involving Solutions of Triangle,Coordinate Geometry must be practiced well. Practise this chapter from various sources specially the geometry part. The problems of this chapter are difficult since they are often multi-conceptual containing a lot of concepts from other chapters so to master this chapter you should be thorough with other chapters as well.
• Probability- This Chapter is contains 50% of the questions which can be solved just be knowing PNC .The rest of the Questions are mainly based on Bayes Theorem and Total Probability Theorem .Solve the Previous Year Questions since quite many similar type of questions are asked .Overall This is an Easy Chapter .
• Sequences And Series- The sequences part is usually cake walk and formula based .For the sequences mainly VN method is used .Questions on Inequality of series has become JEE Favorite topic in recent years .In recent years JEE has been asking questions of Sequences and Series mixing it with Definite Integration .
• Determinants- It is also an Easy topic for JEE ,but may not be for Your Boards where you need to simplify it a lot before expanding . If You are familiar with the Properties of Determinants the chapter is very easy .Give special emphasis on questions on where determinants simplify as a product of 2 determinants and those where we consider the co-factor determinant of a given determinant.
• Matrices-  It is an easy chapter and most of the questions are direct .Try to build up speed and accuracy while finding adjoint and multiplying 2 matrices. Refer to Cayley-Hamilton Theorem from internet, it is quite helpful .Solving equations and Cramer's rule are quite important in this chapter .

 BOOKS

For Algebra ,one must practice a lot and that too from multiple sources. Solve your institute material and various books .Understand various approaches by reading plenty of solved examples.

• A textbook for Algebra -SK Goyal (Highly Recommended)

  

 This book is highly relevant and according to the latest pattern and trends of questions asked by JEE .It illustrates most of the concepts of algebra with proper solved examples and unsolved excersises at the last .

• A Das Gupta is an old Classic book. It mainly has problems from each chapter of mathematics some of which have been excluded from the current syllabus. The focus on Algebra in the Book is quite high is recommended for JEE .Many of the problems are solved illustrating the ideas used to solve problems. It also contains chapter-wise tests so that you know your level of preparation in that chapter.(Recommended)

• Cengage Series for Algebra -(Highly Recommended)

Once again Cengage series is one of the most suited books for JEE and for algebra it is not behind.Contains large number of questions but it slightly on the easier side as compared to the other 2 books .Contains proper theory and solved examples.

• Higher Algebra by Hall and Knight - (Recommended)

One of the Best books for Algebra read throughout the world .Very good for Sequences and Series and Binomial theorem .

ARCHIVE

• Previous Year's Papers of JEE Advanced are a gem. It would also help you to know where you stand and what type of questions are generally asked in the exam and whether your preparation is enough or not. This book is with solutions and appropriate for both JEE Main and Advanced.
(Highly Recommended)

    

Revision for Algebra 

• Vikas Gupta and Pankaj Joshi is the best book for REVISION purposes.
(Highly Recommended)

   
This book is best for revision purpose, The most important part of JEE preparation is revision of the concepts you have already learnt. For this purpose you need a book which has around 50 good questions from each chapter and the problems should cover almost all the important concepts. Hence this book is ideal for this purpose.