IOQM preparation

What IOQM is

IOQM is the first of six stages run by HBCSE for the National Board for Higher Mathematics. Students who do well are invited to the Regional Mathematical Olympiad (RMO), then the Indian National Mathematical Olympiad (INMO), then a month-long training camp, where India’s team of six for the International Mathematical Olympiad is chosen. The paper itself is set and run by the Mathematics Teachers’ Association (India). (source: HBCSE)

The IOQM 2026 paper was on Sunday 6 September 2026, 10 am to 1 pm. If your child is starting now, they are preparing for IOQM 2027, whose date is not out yet.

The pattern

Thirty questions in three hours, in English or Hindi. Every answer is a whole number from 0 to 99, marked on an OMR sheet, and there is no negative marking. (source: HBCSE)

Six minutes a question on average, but the last ten are worth half the paper. Strong students bank the first twenty with care, then spend what is left on the 5-mark questions.

From IOQM to RMO

A student needs at least 10% of the IOQM marks to be considered. Then, in each region, the top 200 students from Class 8 to 11 go through, plus 5 more girls from that group, and the top 40 from Class 12. Ties at the last place all go through. (source: HBCSE)

So a Class 8 student competes with Class 11 students for the same places. That is why an early first attempt is worth making: the paper is practice for the next four years.

A preparation plan by class

1. Class 6 and 7: foundation first

   IOQM is not open yet, so this is the time for NCERT maths done properly, puzzles that need an idea, and the habit of a notebook of mistakes. NMTC and Math Kangaroo are good practice contests. (source: ioqm.in)

2. Class 8: the first attempt

   Cover the four areas at a basic level: linear equations and identities, triangles and circles, divisibility and remainders, counting and arrangements. Sit IOQM for the experience; aim to get the first ten questions right.

3. Class 9 and 10: the serious years

   Go deeper in each area (quadratics and inequalities, similar triangles and circle theorems, modular arithmetic, the pigeonhole principle). From six months out, one past paper every two weeks, timed, then every miss redone without looking.

4. Class 11 and 12: RMO in view

   IOQM should feel familiar. Most of the time now goes into writing full solutions, because RMO asks for proofs. Class 12 students compete in their own group for RMO places.

The topics, in plain words

Four areas: algebra (equations, inequalities, sequences, polynomials), geometry (triangles, circles, lengths and angles), number theory (divisibility, primes, remainders) and combinatorics (counting, arrangements, the pigeonhole principle). The IOQM syllabus, area by area.

How Kiwimath’s IOQM level works

Level 5 is the IOQM level. Its topics are Algebra, Algebra meets number theory, Combinatorics, Combinatorial Geometry, Geometry, Number Theory. Each topic is a ladder of skills: a right answer moves your child to the next skill, a wrong one brings another problem on the same idea when there is one, and hints come in steps (a nudge, then a strategy, then a worked step) rather than as the answer. A skill counts as mastered after it is solved without hints on two different days, and spaced review brings it back before it is forgotten.

We do not have an IOQM mock test yet. Until we do, HBCSE’s own past papers are the best timed practice, and they are free. For untimed warm-ups, try our three IOQM-style sets.

Past papers

HBCSE publishes past olympiad papers and solutions on its site: past papers and sample questions. Work them timed, three hours at a sitting, and only in the last few months; earlier, they teach the format more than the maths. Where each paper is, and how to use it.

Warm-up problems

Ten Level 4 problems, the kind a Class 8 student meets on the way to IOQM. Every answer is a whole number, as in the real paper.