Algebra… The study of the one and only ‘x’, the ever unknown variable. Just kidding, algebra is much more than just all this. Although many books differ in what they classify algebra as, I am going to use algebra to basically cover the theory of equations, complex numbers, matrices, sequences and series, and a few minor chapters. Time’s of prime importance and so, let’s be on our way to discuss this essential unit of JEE-Mathematics syllabus.
Chapter – Wise Analysis
- Theory of Equations : Here, we shall be mainly dealing with quadratic equations and their applications. However, the same concepts can be used for higher order equations, such as cubic or biquadratic equations. Be prepared for questions on higher order polynomials! They are pretty common. Many neat tricks can be used in this chapter, like the Descartes Rule of Signs, especially for higher order polynomials. Don’t hesitate to solve questions graphically. Graphs help in visualization and boost speed and accuracy. Questions based on location of roots are easily solvable by graphical approach. Another important concept is how a quadratic equation represents a parabola and related properties. Practice a lot from this chapter to master it.
- Principal of Mathematical Induction : An introduction to how mathematical proofs work. This chapter has no importance for JEE-Main or JEE-Advanced for the simple fact that questions based on this chapter are mainly subjective in nature. However, the method of induction should be known to all, atleast for their boards. No special preparation of this chapter needed for JEE.
- Mathematical Reasoning : Another chapter with no importance in JEE-Advanced. However, a couple of sure shot questions are to be expected from this chapter in JEE-Main. The most important part of this chapter is Boolean logic. Practice it well. Keep in mind that there are a few parallels – ^ is like the AND gate, ~ is like NOT gate and so on.
- Complex Numbers : The most important chapter of algebra, complex number holds a huge weightage in JEE. While easier questions are asked in JEE-Main, you’ll find hardly any direct questions of this chapter in JEE-Advanced. While the basic definitions and concepts are enough for JEE-Main, questions asked in JEE-Advanced require geometrical interpretation of complex numbers. Euler’s formula is of prime importance here. Practice a lot of questions of this chapter or you shall regret.
- Determinants & Matrices : I would not use this word for any chapter except this. It’s a boring one, especially the determinant part. Learn the basic properties of determinant manipulation and how to open determinants. That’s all for determinants. As far as matrices are concerned, properties of inverse, adjoint and transpose matrices are important. Also, there are a few named matrices like orthogonal, singular, unitary, etc. Make sure you know what each of these matrices are.
Books for Algebra
All the Best,