RMO — Regional Mathematics Olympiad
Competition mathematics for the Regional (and Pre-RMO) Olympiad — Number Theory, Algebra, Combinatorics, and Geometry.
Number Theory
Algebra
Polynomials & Inequalities
Polynomial roots, factorisation, AM-GM, Cauchy-Schwarz, and algebraic inequalities
Practise →Functional Equations
Techniques for solving functional equations, substitution strategies, and olympiad-style problems
Practise →Combinatorics
Geometry
Euclidean Geometry
Circle theorems, concurrency, collinearity, angle chasing, and triangle centres
Practise →Transformations & Advanced Geometry
Reflections, rotations, inversions, projective techniques, and trigonometric Ceva/Menelaus
Practise →The Regional Mathematical Olympiad (RMO) is the stage of the Indian mathematical olympiad pathway that follows the pre-regional round and leads to the Indian National Mathematical Olympiad (INMO). It is a serious test of mathematical problem-solving and proof-writing.
Unlike multiple-choice exams, RMO asks for full written solutions to challenging problems in number theory, algebra, combinatorics and geometry. Practising rigorous problem-solving is the key to success.
| Stage | Follows the pre-regional round; leads to INMO |
| Answer type | Full written solutions (proof-based) |
| Core topics | Number Theory, Algebra, Combinatorics, Geometry |
| Note | Calculus is not part of the syllabus |
- Number Theory — divisibility, congruences, Diophantine equations
- Algebra — inequalities, polynomials, functional equations
- Combinatorics — counting arguments, pigeonhole, invariants
- Geometry — synthetic geometry, circles, classical theorems
- Practise writing complete, rigorous proofs — partial reasoning earns partial marks.
- Build depth in each of the four topic areas through hard problems.
- Study elegant model solutions to learn proof techniques.
- Time yourself solving a few problems in a sitting to build stamina.
How is RMO different from PRMO?
PRMO asks for short numerical answers, while RMO requires full written, proof-based solutions to harder problems.
Which topics does RMO cover?
Number Theory, Algebra, Combinatorics and Geometry — without calculus.
What comes after RMO?
Students who clear RMO advance to the Indian National Mathematical Olympiad (INMO).
How do I prepare for RMO?
Practise rigorous proof-based problems and study model solutions across all four topics.
Are these RMO practice questions free?
Yes. All RMO practice on Safe Learning for Kids is free, with explanations.