It would be sinful on my part to even claim that JEE Advanced has a one-size-fits-all formula with which a student can crack the ‘elite’ examination. You will see various topics and unique questions across the years. However, some amount of general advice will always keep you in good stead while attacking sums from certain topics. These are more like generic tips and tricks that can be applied to every numerical from a certain chapter in JEE Advanced. With this thing in our mind, let’s try to devise a systematic method to go about approaching Calculus, a chapter that usually has a meaty weightage in JEE Advanced.
Calculus: An Integral Part Of JEE-Advanced Maths
Now, it becomes rather difficult to tackle Calculus if we do not segregate the topic into its primary branches. Thus, I’ll broadly classify Calculus into five parts – pure differentiation, pure integration, application of differentiation, definite integration, differential equations.
Before we move to the actual approach to Calculus, just a tiny word of advice: Among these topics differential equations happens to carry the most disproportionate amount of weightage (and also happens to be the topic which will essentially swamp you during engineering), so do give it a lot of attention during problem-solving practice.
First of all, I would suggest you first tackle the problems on integration. Though it is understandable that differentiation seems easier but that is only on the surface, because JEE will obviously not ask you questions like ‘differentiate a fifth-degree polynomial’ (that’s a bad example but it will suffice). The questions for differentiation in JEE Advanced will be trickier than you think and, more importantly, they are time-consuming. All we are doing here is following the golden rule of JEE paper solving: Do what earns you the most number of marks in the least amount of time.
Another unique characteristic of integration problems is the rapid way they fall apart. The entire question will mostly hinge on you noticing one important thing in the sum. Once you pick on that one golden thread in the Pandora’s box, everything magically falls apart. Thus, it can be said that sums on integration may be more rewarding than differentiation related sums (obviously, this is taking into account the fact that you have studied enough integration to know how to decimate a sum).
Once into integration, keep pure integration for the last. Same logic as before, it takes time and may not yield any result despite a lot of trying. Go for differential equations and applications of integration (like finding the area under a curve and definite integrals) first as they generally are bound to be easier and also because there are a lot of shortcuts to solve these kinds of problems. Some of these can be solved merely by observation if you are adept enough. Hence those are the questions you should tackle first.
Then move on to pure integration and crack the nut if you can. Many times it happens that after solving some questions on definite integrals, we start getting a hang of how to solve indefinite integrals. Thus, this approach takes care of that as well.
Having addressed integration, move on to differentiation. Even here, like before, try to tackle the application questions before the pure differentiation questions. For most of the questions, differentiation will involve a lot of calculations, involving terms of many high powers. Thus, it is advisable that you leave ample amount of rough space specifically for these questions.
The general advice that I would give for solving such sums is clarity of solving. The problem being that once you go to an advanced step in solving, it is a kind of a ‘point of no return’. There is no practical way in which you can go back to start and solve again, maybe with a new method or otherwise.
Thus, the most important tip that I would give here is space management. If need be, write more steps if it gives you any semblance of clarity. This thing will go a long way when it comes to the D-Day.
That is all from my side for this topic. However, and I can’t possibly stress this enough, these are merely guidelines and while solving the JEE Advanced paper, you shall have to be dynamic and alert. If you feel a pure differentiation sum can be easily cracked, go for it without batting an eyelid. After all, every aspirant is different and has got different comfort zones. Take my advice, sure! but make a game plan for yourself. That will be the deciding factor to get that coveted rank.
Before JEE-Advanced, though, you have to tackle JEE-Main, an exam which is an altogether different ball-game. Read about the best way to approach JEE-Main here.
Cheers and all the best guys!