JEE is without doubt one of the most difficult exams of the country. Be it JEE-Main or JEE-Advanced, you have to work really hard to be able to solve the question paper comfortably. Now, an exam such as this is all about putting your analytical skills & knowledge of concepts to tests & not about memory, right? Well, wrong, I’d say. And ‘What about JEE mathematics?’, one may ask. It’d still be the same.
If you carefully browse through JEE mathematics archives, you’ll find that there have been questions which test your ability to remember. They have been heartless in these situations in the past. They never have hesitated in asking a problem that might involve a non-standard value cosine (22.50). Of course, you can go ahead and work this value out through a simple trigonometric identity or sometimes a simple multiplication. Consider however, the case where you have this value memorized. You clearly will have an edge over others who do not. This is one example where you can save time & take it from me, Time is the key!!
During my JEE prep, my instructor asked me to remember values that tend to repeat in some form or the other. I will try and list a few down for you ( to the best of my memory 😛 ).
Things to Remember for JEE Mathematics
Squares of Integers from 1 to 30
This always tops the list of things to remember for JEE Mathematics. These always come handy during any exam, especially in algebra. Take the case where discriminant of a quadratic equation is 361. For those of you who don’t already know, 361 is a perfect square of 19.
You may cross a geometry problem that asks you to draw the diagram first. Now this may involve a triangle too. It is likely that the triangle is right angled. You will be really lucky if the sides are a Pythagorean triplet and even luckier if you have them in your mind. Now figure out how 40, 41 & 9 are related?
Values of Cube Roots of Unity
Many a times while solving a problem, a rather complicated irrational term may present itself (only later to realise that it was our very own ‘ω’). They may ask you to operate on this value which becomes so easy with the ‘ω-realisation‘.
Non-Standard Trigonometric values
Do you know the value of cosine (15) or tan (22.5) ? It’d be really helpful if you do. You may encounter them in problems involving trigonometry’s combination with algebra or series & sequences. There have been problems with direct use of these values.
Standard Integration Formulae
There are many integration formulae which look very different from each other but, are solutions to the same problem. You will save a lot of your time, if you are able to identify the similarity. This will be easy if you remember them.
Solution of Triangles
As tedious as they may seem, you should memorise the important formulae from this topic. Don’t bank on your derivation skills on the big day. You won’t have time for that during exams.
Conic Sections Formulae
This is one of the most scoring topics in JEE Mathematics. You don’t want to miss on scoring in these topics. These formulae should appear in front of your eyes as soon as you know the conic. This can only be achieved through practice with these formulae memorised.
It is definitely an advantage if you memorise these ‘Things to Remember’. It is important, however, to derive them, from scratch, at least once before memorising them. After all there is no substitute to simple hard work!