The first thing that strikes us about JEE Math is the sheer extent of its syllabus. There ought to be some method to this madness! This article aims to outline a strategy and identify crucial and scoring topics for JEE.

One of the main themes I want to highlight is the idea of culmination topics–which will be clear as the article progresses. The concept is simple. In each class of topics, for example, Calculus, Algebra, Combinatorics and the like, the initial chapters will build ideas up. Each chapter will flow logically from the previous one. The final chapters will involve all the concepts that you have assimilated — and those are the ones that carry the maximum weight.

## The Trigo Family

Although not so significant by weight, Trigonometric identities is a prerequisite for several other chapters. You’ll also need to learn how to solve Trigonometric Equations with ease. Inverse Trigonometric Functions as a topic is fairly popular in the JEE and tends to be involved in a few quality crossovers with Calculus. Don’t be surprised if you see a Calculus question that requires deep knowledge of Inverse Trigonometry.

In my opinion, Solution of Triangles is more of an Olympiad topic. It’s not particularly a heavyweight, but having a basic idea of the results and some presence of mind will be helpful.

## Algebra

Once Quadratic Equations sets the stage, Sequences and Series will feature quite a bit in your preparation. Quite a few questions are asked in the JEE from it. The best part? It is easy to score marks in such topics since the problems are relatively easier.

Determinants and Matrices may appear cumbersome at this level, but this is a fairly straightforward and scoring topic for the JEE. Also, it is a powerful coding tool, so you will be seeing more of it later.

## Calculus

This class carries the most weight. Once the notion of a Function is introduced, discussions about Limits and their application to determine Continuity start making sense. Soon you go one step further to Differentiability and Methods of Differentiation. But the topic that actually tends to fetch a bulk of the marks in the JEE is Application of Derivatives – which is an apt conclusion.

Indefinite Integrals are challenging, but the JEE has not asked as many questions from here as from the topics that follow. Definite Integrals is definitely scoring – it’s not very tough and you often find very elegant solutions to problems! However, the examiner’s favourite is the ‘integrating act’ – Differential Equations and Area Under The Curve. Differential Equations, at the JEE level, have standard templates. Master that, and your score will shoot up!

## Combinatorics

This category is particularly enjoyable if you’re inclined towards CSE. And it helps that it includes a bunch of scoring topics for JEE. Once you acquaint yourself with the intricacies of Binomial Theorem and PnC, you are ready for the Main Event – Probability!

The beauty is that these chapters offer a lot of scope for creativity – you can have fun discovering multiple elegant methods and boost your JEE score while you’re at it.

All three topics can be considered scoring but Probability is the examiners’ favourite.

## Coordinate Geometry

Here is another one of the JEE Mains maths important topics. This starts off with Straight Lines and then moves on to discussions on Conic Sections. Parabola deserves a special mention here because of its simplicity – you don’t want to miss out on marks from here. Circle has significant weight as a topic too – you’ll notice that the questions are thematic and standard, so it’s easy to score as well.

The topic of Complex Numbers also falls into this category. It is more powerful than the regular 2D coordinate system and problems utilize the properties of all the curves you have studied. This makes it a quintessential Culmination Topic. Often the Geometrical Approach (cis θ) is much more elegant than the brute force x+ iy.

You won’t find a bulk of marks coming from Complex Numbers, but in a quality paper, mastery over this topic makes a huge difference. This is what separates toppers from dreamers.

Moving further on, Vectors and 3D Geometry are a more general application of the ideas we have built up so far. The problems are thematic and quite frequent, so these are scoring topics for JEE. In fact, quite a few JEE level problems from this topic are from school level books like RD Sharma or ML Agarwal.

## AND… Action!

Now we have identified a bunch of Culmination Topics which are going to build your score. The next question is, how do we go about consolidating?

An important observation is that Culmination Topics will be your strengths if and only if you’ve grasped what preceded it reasonably well. The key isn’t the mindless rote learning of results and formulae – rather, it is the conceptual clarity that matters.

The associated ideas should be intuitive, just like second nature! To get there, well-planned practice is a must.

Next, observe problems from the Culmination Topic in question. More often than not, you’ll identify themes. The problems won’t be exactly the same. There won’t be a set formula. If there were, writing this article would be pointless. What I mean is, the general plan of approach will more or less be the same.

The algorithm will be quite similar for most problems of a particular theme. A striking example is Linear Differential Equations. The plan is simple – get it into the format, find the integrating factor, multiply, and solve. Your ingenuity lies in the execution. Maybe you’ll have to make a clever substitution or multiply both sides by a function to even get to the format, or whatever.

So it’s crucial to identify the themes. Once you’ve done that, you’ll gain confidence as the general algorithm runs in your head. Problem after problem, you’ll tell yourself, “I got this.” That’s how scores are built!

It’s easy to score in JEE Mains maths important topics once you know exactly what you are doing, and why you are doing it.

Culmination topics are scoring topics because they solve real-life problems as well! This is engineering — you systematically apply the knowledge you have!

This systematization is the key to making the most of scoring topics for JEE. Take some time, you’ll find a way yourself. Good luck!

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