PRMO — Pre-Regional Math Olympiad
Competition mathematics for Classes VIII–XII. Practise Number Theory, Algebra, Combinatorics, and Geometry.
Number Theory
Divisibility & Primes
Divisibility rules, prime numbers, GCD, LCM, and the fundamental theorem of arithmetic
Practise →Modular Arithmetic
Congruences, Fermat's little theorem, Chinese remainder theorem, and number bases
Practise →Algebra
Polynomials
Roots, Vieta's formulas, polynomial identities, and factorisation
Practise →Inequalities
AM-GM, Cauchy-Schwarz, triangle inequality, and optimisation problems
Practise →Combinatorics
Counting Principles
Multiplication principle, addition principle, inclusion-exclusion, and pigeonhole
Practise →Permutations & Combinations
Arrangements, selections, binomial theorem, and Pascal's triangle
Practise →Geometry
Triangles & Circles
Congruence, similarity, angle in a circle, tangents, and power of a point
Practise →Coordinate Geometry
Distance, midpoint, slopes, conic sections, and loci
Practise →The Pre-Regional Mathematics Olympiad (PRMO) is the first stage of India's mathematical olympiad pathway, which progresses through the Regional Mathematical Olympiad (RMO), the Indian National Mathematical Olympiad (INMO) and ultimately the International Mathematical Olympiad (IMO).
It tests problem-solving ability in number theory, algebra, combinatorics and geometry — areas that go well beyond the routine school syllabus. Consistent practice with challenging problems is essential to clear this stage.
| Stage | First stage of the Maths Olympiad pathway (leads to RMO) |
| Eligibility | Classes 8 to 12 |
| Answer type | Short numerical answers (integers) |
| Core topics | Number Theory, Algebra, Combinatorics, Geometry |
| Note | Calculus is not part of the syllabus |
- Number Theory — divisibility, modular arithmetic, primes
- Algebra — polynomials, inequalities, functional relations
- Combinatorics — counting, pigeonhole, basic graph ideas
- Geometry — triangles, circles, and classical results
- Practise olympiad-style problems regularly — routine textbook questions are not enough.
- Master number theory and combinatorics, which are heavily represented.
- Learn standard techniques and theorems, then apply them to unfamiliar problems.
- Work through previous problems and study the elegant solutions.
What is PRMO?
It is the first stage of the Indian mathematical olympiad pathway, leading to the RMO and beyond.
Which topics does PRMO cover?
Number Theory, Algebra, Combinatorics and Geometry — calculus is not included.
Who can take PRMO?
It is aimed at students in Classes 8 to 12 with strong mathematical interest.
How do I prepare for PRMO?
Practise olympiad-level problems consistently and learn the standard problem-solving techniques.
Are these PRMO practice questions free?
Yes. All PRMO practice on Safe Learning for Kids is free, with explanations.