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Maths

A Step-by-Step Guide to Maths for IIT-JEE

The JEE Maths syllabus is huge, and you know it. Maybe you're behind. Maybe you've started three times and lost the thread each time. Either way, you're staring at a mountain and wondering where the path even begins.

Here's the path. Follow it and you can cover the whole syllabus in six months — faster if you're hungry for it.

I'll be honest with you. This plan is hard to stick to. But it works. I've run it with my own students and watched it pay off. All I ask is that you put in the hours.

Before we begin

Two promises first. Make them now, before you read the plan.

One — give Maths two hours every single day. Life happens. You'll get sick, you'll travel, a function will eat your evening. Fine. But never let two days pass without solving Maths. Momentum is the whole game here.

Two — stop hoarding books. Don't buy every JEE Maths book on the shelf. Pick a couple of standard texts and one solid question bank, then get rid of the rest. A pile of unused books isn't preparation. It's anxiety on a shelf.

For topic-wise theory, the Cengage series or Arihant both work well. For drilling problems, pick one good question bank and stay loyal to it. Classics like S. L. Loney and I. A. Maron are beautiful books, but they drift a little from what JEE asks today. Solve them if you enjoy them — just don't make them your spine.

Two more rules that save months:

  • Don't chase proofs. JEE won't ask you to prove a theorem. Learn the result, learn where it applies, and use it. This isn't a license to mindlessly memorise — keep asking why — it's a warning not to bleed weeks over derivations no one will test.
  • Close every topic the same way. Finish the theory. Solve the question bank. Mark the problems that beat you. When you revise, you only re-solve those marked ones. Then glance at past-year questions from that topic and move on. Relentless, then next.

The plan, in one line

The whole strategy fits in a single mantra:

Start easy. Build confidence. Boost speed. Cross the line.

Below is a month-by-month breakdown. Cover the topics in this order — the order is doing real work for you. Take a short break now. Come back when you can actually focus, then read on.

Month 1 — Start easy

These topics are gentle on purpose. The goal this month is to begin well and set a rhythm. There's a second reason they sit up front: JEE loves to bolt these onto harder chapters to build clever questions.

  • Logarithms. Quick to learn. Shows up glued to Calculus later.
  • Trigonometry. JEE rarely asks pure trig, but trig functions are everywhere in the paper. Go up to solution of triangles — and leave inverse trig functions for now.
  • Quadratic Equations. With trig in hand, take these on. JEE frames genuinely interesting questions here, and the ideas come back again and again. Do it properly.
  • Sequences and Series. A short one — three days, maybe. Pay real attention to the AM–GM inequality. For nn non-negative numbers it says

a1+a2+⋯+ann≥a1a2⋯ann,\frac{a_1 + a_2 + \cdots + a_n}{n} \ge \sqrt[n]{a_1 a_2 \cdots a_n},

with equality only when every term is equal. JEE builds whole problems on that single line.

  • Binomial Theorem. Breathe out. This one's a treat after the grind. Enjoy it — but not too much. Finish fast and get ready to climb.

Before you leave Month 1, revise. Re-solve the problems you marked as hard. Then shift gears.

Month 2 — Accelerate into Calculus

Now the real work starts. This is the heart of the syllabus.

  • Functions. Drill domain and range until they're automatic, and learn each standard function cold. You'll meet graphs properly here — and graphs are how the toppers solve fast. Don't skip the inverse of a function.
  • Inverse Trigonometric Functions. Remember the ones we parked in Month 1? Finish them now.
  • Limits, Continuity and Differentiability. These blend straight into Functions. If your graphs are strong, this month feels easy.
  • Methods of Differentiation. A satisfying topic — you may get hooked on the techniques. A few you'll just have to commit to memory. Stick to the schedule and resist solving every problem in sight. You can always differentiate more later.

Month 3 — The month of Integration

  • Indefinite Integration. This is the most memory-heavy stretch in Calculus. Certain integrals are cracked by certain set methods, and you need those by heart.
  • Definite Integration. Students prefer this over its messier sibling — and so does JEE.
  • Area Under Curves. A JEE favourite. Expect one or two questions almost every year.
  • Application of Derivatives. Lean into maxima–minima, the Mean Value Theorem, and errors. Anything that touches the real world tends to show up in the paper.

Month 4 — Time to co-ordinate

Ease off the throttle a little. The hardest climbing is behind you. If you've reached this point on schedule, you're doing genuinely well — keep going, you're not done.

  • Straight Lines. Give locus and the family of straight lines special care.
  • Circle. Circles pour concepts into the rest of coordinate geometry, and they feed into complex numbers too. Do this one thoroughly.
  • Vectors. Yes, conic sections can wait. Clear vectors first — you'll find a lot of it already feels familiar.
  • 3D Geometry. One or two questions, usually on the friendlier side. A firm grip on straight lines carries you most of the way.
  • Permutations and Combinations. An abstract topic. Some students find it pure intuition; others fight it the whole way. I was in the second camp. If it's draining you, push it later or let it go — the marks aren't worth a spiral.

Month 5 — Consolidate

The topics this month borrow from chapters you've already done. They'll sharpen your older work and hand you new angles on it.

  • Matrices and Determinants. Fairly easy. You can clear most of it on your own.
  • Complex Numbers. Some students do this early. I push it late — by now you've got the maturity to handle it, and you'll see it quietly pulling in locus, functions, trigonometry, the circle, all at once.
  • Differential Equations. An important one for JEE. Focus hard on actually solving the equations.
  • Probability. Odds are you're already decent at this. One question at most. If you're shaky, it's fine to leave it.

Month 6 — Wrap up for the showdown

  • Conic Sections. Parabola, ellipse, hyperbola — the same ideas with small twists each time. JEE has leaned toward easier questions here lately.
  • Mathematical Reasoning. Easy, important, and newer to the syllabus. Recent papers almost always carry a question or two.

Any spare hours from here go into one thing: revision and more problems. There's no Month 7. There's just sharpening.

A few honest notes

Your turn. Don't just nod along — open your notebook and write today's date at the top of Month 1. Now sketch the next 30 days: which of those five topics lands on which week, and which two hours of each day belong to Maths. Be specific. A plan you can see is a plan you'll keep.

Check: if your week has Logarithms and Trigonometry penciled into real dates with real time slots, you're ready. If it's still vague, you'll drift — go back and pin the hours down before you start.

Mark your hard problems. Revise only those. Cover the topics in order. Two hours a day, no two days off. That's the entire system — simple to read, hard to live, and it works if you let it.

You've got six months and a map. Start easy, and start today.