Become Super at Calculus
Calculus forms a major chunk of the questions in almost all the exams of maths that you appear for after 10th grade. This topic of mathematics has a wide range of applications not only in academics but also in real life. Irrespective of the field whether it be related to science or not, calculus has some use in that field. But for the time being, being students our primary concern should be to be able to efficiently solve questions from calculus in exams. Following are some tricks mentioned, which if followed, might help you in gaining edge over others who don’t.
Understand the Definition
So what does differentiation of a function implies? d/dx ? Thats correct but how did we arrive to that expression? How do we define a derivative of something and what does that mean? This is one point which generally most of the students tend to ignore but in exams like JEE there will be many questions that will require the use of definition and your standard formulae won’t work. So make sure you are clear with the concept of every topic (integration,differentiation, limits,etc). e.g. differentiation in simple words involves calculating slope of two infinitesimally close points.
Remember standard Formulae
Lot of questions (not all) especially the ones having trigonometric terms in them, require manipulation and substitution in the function onto which an operation has to be performed so that the function gets simplified or the steps required to arrive at the solution becomes easy. For this you should know that particular formulae to be used, the question can be solved without any formula too but it will be time-consuming and lots of steps will be involved. You definitely don’t want to regret losing marks in a simple question just because you were too lazy to learn the formulae. So make sure you have a list prepared.
Knowing the nature of the functions
Functions is one of the most important topic under calculus. In almost all the questions you will be given a function and the set of operations to be performed on it. For this it is important to know the nature of the function as in whether the function is increasing or decreasing, odd or even, its point of maxima and minima,etc. This will also help in plotting the graph of the function. It is only after you understand the function that you will get an insight of the problem and will help you solve the problem efficiently.
Use graphs whenever possible
This might sound unconventional but use of graphs in the problem will be something that you should start practising from now on. The graph of the function need not be completely accurate but a rough idea of what the function will behave like. Once you have plotted the graph you can get many information from it without doing any calculations. Graphs will help a lot in problems of application of derivative and area under the curve.
Integration according to many is the toughest part of calculus as there are large number of algorithms for obtaining solution to the problem depending on the type of function. So one needs to practise as many problems in integration as possible because only then will you get the knowledge of the method to use for a particular problem. Also one should know the methods like use of partial fractions, integration by parts and integration by reduction methods.
Application of derivatives/integrals
This includes problems involving finding maxima-minima, area under the curve and slope of complex curves. These topics together hold a significant weightage in JEE both mains and advance every student planning to give these exams must be thorough with the types of problems and the methods to solve the same.
This is the most important trick that you need to remember in order to ace any topic especially calculus. Once you have gained an insight for every concept, the next step should be to practise as many problems as possible. Take a good reference book, mark some questions (make sure that you practise questions of each type and difficulty) and start solving them. This will not only boost your confidence but also it will help you in remembering the formulae and methods of problem solving.
Calculus is a challenging topic but it isn’t a difficult one. It all depends on the way we approach the topic and the amount of practise done. If the aforementioned points are taken care of, solving calculus problems will be a cake walk for you. You can find some more tips and tricks to ace calculus.
All the best!