IOQM, RMO and INMO Preparation: The Complete Indian Maths Olympiad Pathway

One pathway, not three separate exams

The Indian mathematics olympiad runs as a sequence. Students sit the Indian Olympiad Qualifier in Mathematics, those who qualify go on to the Regional Mathematical Olympiad, and from there the Indian National Mathematical Olympiad leads towards the training camp and international selection. Each stage exists to select for the next.

Most preparation treats these as three unrelated exams and teaches them in isolation. That is the wrong shape. A student who learns number theory only for IOQM finds the same material returning at RMO in a form that now demands a written proof rather than an integer. We teach the pathway as one journey, so nothing has to be unlearned.

The shift that catches students out

IOQM asks for integer answers. RMO asks for proofs. That single change is where most students stall, and it is not a change in difficulty so much as a change in what counts as an answer.

At IOQM, knowing that the answer is 17 is the whole job. At RMO, knowing the answer is worth very little; the marks are in the argument that gets there, written so that a grader who has never met you can follow each step and agree. Students who have spent years in multiple-choice and integer-answer formats have usually never been asked to do this, and discover the gap only under exam conditions.

Six weeks of this course are given to proof writing alone. Not to new mathematics, but to taking an idea the student already has and turning it into something a grader will award full marks for: stating the assumptions, justifying every step that is not obvious, handling the cases, and closing the argument properly.

The four pillars

Olympiad mathematics rests on four areas, and problems rarely announce which one they belong to.

Number theory is where many olympiad problems begin: divisibility, modular arithmetic, the behaviour of primes. We build it from first principles because a student who has only met modular arithmetic as a clock analogy will not get far with it.

Algebra covers polynomials, functional equations, inequalities and sequences. The inequality toolkit, particularly AM-GM and Cauchy-Schwarz, recurs so often at RMO that fluency with it is close to compulsory.

Geometry remains Euclidean and proof-based. Circles, cyclic quadrilaterals and the power of a point appear year after year in configurations that start to look familiar once a student has worked enough of them. We teach it with diagrams and synthetic arguments rather than reaching for coordinates, because the coordinate approach usually makes olympiad geometry harder, not easier.

Combinatorics is the area that rewards a clear idea over heavy calculation. Pigeonhole, invariants, extremal arguments and clever bijections turn problems that look impossible into problems that are nearly immediate, once the right way of seeing them is found.

How the classes run

Sessions are live and online, one-on-one or in small groups of two to six. The format is not lecture-then-homework. Students work problems during the session, with the teacher watching the attempt rather than only the answer, because the useful teaching moment is usually in the wrong turn rather than in the correct final line.

Past papers are used throughout rather than saved for the end. Olympiad problems repeat their ideas across years even when the specific problems differ, and a student who keeps a problem log begins to recognise those ideas rather than meeting each paper cold.

Who this suits

The course starts at a level a motivated Class 8 or 9 student can join without prior competition experience, and runs to INMO standard. What it assumes is not prior olympiad exposure but a particular tolerance: the willingness to sit with a single problem for an hour, make no progress, and come back to it. Students who need the reassurance of a worked method for every question tend to find olympiad mathematics frustrating, and that is worth knowing before starting rather than three months in.

Registration and current dates are handled by the organisers. We do not print dates here that could be out of date by the time you read them; check the official HBCSE olympiad site for the current cycle, and ask your school, since many students register through school rather than individually.