Mathematics Tips for JEE Algebra – Part 3
JEE Algebra covers the following topics (for JEE Advanced):
Logarithms, Sequences & Series, Quadratic Equations & Inequalities, Binomial Theorem, Permutations & Combinations, Probability, Complex Numbers, Matrices and Determinants
Algebra at the JEE level is very interesting. All topics are more or less independent of each other. The number of formulae to be remembered per topic are on the lower side. However, a large number of interesting & challenging questions can be constructed in Algebra. Especially in topics like Permutations & Combinations, Probability and Complex number algebra.
Logarithms, Sequences and Series, Quadratic Equations & inequalities, Binomial Theorem are the easier topics. The next set of topics is slightly more difficult.
Sequences & Series and Binomial Theorem appear in NCERT books (class XI). Logarithms and Quadratic Equations & Inequalities do not and have to be done from other sources.
This post deals with Tips for JEE Algebra for the easy topics (Algebra A)
Logarithms for JEE has only 5 to 6 formulae that you must understand.
Log of products, division, exponents, change of base, Log with respect to a given base or it’s nth power & log of 1 are key things to know.
It is also critical to know the basics. The base cannot be negative. The number whose log is being taken should not be negative either.
A basic fact that gets used a lot in Logarithms is the identity x = a Loga x. This follows directly from the definition of logarithm. But a lot of students get confused with this simple identity.
After getting familiar with the above facts in detail, it is recommended that you solve a number of questions on logarithms. Questions are usually of the form where you are given a complicated equation or inequality (expressed in Logarithms) and have to simplify it or solve for a variable.
Usually, most questions can be easily cracked using the rules of Logs as far as JEE Algebra is concerned.
Sequences and Series
Another stand-alone and easy topic for JEE.
It is essential to know formulae for general & nth term of the usual culprits (AP, GP, HP & AGP).
Also one must know summation formulae and the techniques used to arrive at these.
Knowing summation formulae of specialized series like Σn, Σn2, Σn3, Σn4 is mandatory.
One must be familiar with difference series (where you can get an AP, GP, HP or AGP by writing the series twice, shifting by one term & subtracting), difference of difference series.
Apart from this, no real twists occur in questions related to Sequences & Series in JEE Algebra.
Quadratic Equations & Inequalities
An easy JEE topic with just a few formulae.
Know the basic formulae (solution to quadratic, sum of roots, product of roots etc.) well.
The impact of changing roots on the equation must be understood (taking reciprocal roots, squares, cubes etc.).
Plotting sign of expression with x on the number line for quadratic & higher inequalities should be clear. General rules for inequalities (multiplication by a negative number etc.) must be clear.
We also recommend understanding the basic rules for any general polynomial equation. For e.g. number of roots, nature of irrational & complex roots, relation between sign changes & real roots, significance of the coefficients of xn-1, xn-2 etc. Note however, that this is slightly beyond the scope of JEE Algebra.
This is an interesting topic from the perspective of JEE as well as higher mathematics.
It is used a lot in other topics as well. This topic should be studied well.
One must know the following (at minimum):
The basic expansion and rth term of (x+y)n, (1+x)n, (1-x)n are of-course important.
Sums of series of the combinatorial nCr obtained by putting x = 1, x = -1, x = 2 etc. in (1+x)n are important. Also understand how to obtain the sum of other series of nCr (like nCr2). The general case of putting x = a (and y = b) is important too.
Obtaining the coefficient of rth terms (or term independent of x) in product of two expressions must also be understood.
Finding the largest term in a given expression (the method of doing so) must be clearly understood.
Finally, we also recommend knowing the expansion for negative and fractional indices as well.
We recommend solving a lot of questions (especially from past JEE papers) for these topics for full practice. One should not miss out on any question asked in JEE Mains or Advanced from any of these topics.
With the above tips for JEE Algebra, we hope your preparation for these easy topics will be thorough and strong.
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