IOQM syllabus 2026
There is no separate IOQM syllabus. HBCSE asks olympiad students to know all of NCERT Class 8, 9 and 10 maths, plus more depth in four areas: algebra, geometry, number theory and combinatorics. Calculus is not part of it.
Where the syllabus comes from
HBCSE, which runs India’s mathematical olympiad programme, publishes one olympiad syllabus for IOQM, RMO, INMO and the international rounds. The topics stay the same from round to round; HBCSE notes that the difficulty rises from RMO to INMO to the IMO. (source: HBCSE)
Algebra
Equations and what their solutions look like, inequalities, sequences (arithmetic, geometric and harmonic progressions), powers and indices, the binomial theorem, polynomials, complex numbers and functional equations.
Starts from Class 8 and 9 linear equations and identities.
Try this algebra problem
In the sequence of odd numbers 1, 3, 5, 7, …, what is the position of 41? (1 is the 1st, 3 is the 2nd, 5 is the 3rd, …)
See the answer
21. The n-th odd number is 2n − 1. Solve 2n − 1 = 41, so n = 21.
Geometry
Triangles, quadrilaterals and circles and their properties, constructions, when lines meet at a point or points lie on a line (Ceva and Menelaus), trigonometry up to the sine and cosine rules, coordinate geometry and vectors.
Starts from Class 9 and 10 triangles, circles and the Pythagoras theorem.
Try this geometry problem
A right triangle has hypotenuse 10 and one leg 6. Find the other leg.
See the answer
8. By Pythagoras, 6² + b² = 10², so b² = 64 and b = 8.
Number theory
Divisibility, highest common factors and the Euclidean algorithm, prime factorisation, remainders and congruences, the Chinese remainder theorem, Fermat’s and Wilson’s theorems, Euler’s phi function, Pythagorean triples and equations in whole numbers.
Starts from Class 6 to 8 factors, multiples and divisibility rules.
Combinatorics (counting)
Counting without listing, the pigeonhole principle and its uses, counting by building from smaller cases (recursion) and a first look at graphs (points joined by lines).
The least like school maths of the four, and the one where young students can shine early.
Try this combinatorics problem
There are 4 roads from town A to town B and 3 roads from B to C. How many ways can you travel from A to C through B?
See the answer
12. Each of the 4 roads to B can be followed by any of the 3 roads to C: 4 × 3 = 12.
What to learn first
For a Class 8 or 9 student: counting and number theory first, because they need the least school maths and reward clear thinking straight away. Then geometry, alongside school. Algebra last, as school algebra catches up. Keep one area “live” each week rather than finishing one area before starting the next.
Questions parents ask
Is calculus in the IOQM syllabus?
No. Calculus is not among the olympiad topics HBCSE lists. The paper is algebra, geometry, number theory and combinatorics.
What is the IOQM syllabus for Class 9?
The same as for every class: there is one paper for Class 8 to 12. A Class 9 student should be strong on NCERT Class 8 and 9 maths and start the olympiad topics in each area; the Class 10 topics can come during the year.
Can questions come from outside the list?
Yes. HBCSE says the list is not exhaustive and RMO and INMO problems may use topics not stated. In practice the problems need clever use of simple ideas more than advanced topics.
Practise all four areas at Level 5
Kiwimath’s IOQM level has topics for each area. Your child can start with the one they like best.
Start the IOQM level Free during early access.
Sources
All checked on . Organisers change dates; if one of these differs from what your school tells you, trust the school and the organiser, and write to hello@kiwimaths.com so we can fix this page.
- Syllabus for Mathematical OlympiadHBCSE (the organiser)
- Mathematical Olympiads 2026-2027 brochureHBCSE (the organiser)