RMO: syllabus, mock tests and practice
Regional Mathematical Olympiad previous-year question papers, solutions and written-answer tests, including regional and KV/JNV sets.
- Syllabus years
- 2026-27
- Mock tests
- 43
- Downloads
- 67
About the RMO exam
How the exam works
RMO is a proof-based mathematics Olympiad stage. The current schedule specifies six questions and three hours. Write complete reasoning and proofs; qualification is governed by HBCSE's current selection rules.
Who can apply
The 2026 IOQM portal lists Classes 8–12 and birth dates 1 August 2007–31 July 2014, subject to its complete eligibility rules. RMO and INMO require qualification or a specifically permitted exemption under the current selection policy. These are 2026-cycle rules; do not assume the same birth-date window for the next IOQM edition.
When it happens
Next RMO: 15 November 2026, 13:00–16:00 IST. MTA(I)'s current portal says RMO registration opens 2 November 2026 for eligible IOQM qualifiers. Check your regional cutoff and registration notice. INMO follows on 17 January 2027, 12:00–16:30. Checked 1 November 2026.
How to register
IOQM accepts centre-based and individual online registration during its published window. The 2026 fee was ₹300, or ₹180 for KV/JNV pupils. Eligible candidates must separately register for RMO/INMO as instructed; the MTA(I) FAQ says no further exam payment is involved. Keep your enrolment number, date of birth, photo and school/identity documents ready. Verify the current notice before starting a new-cycle application.
Official website, syllabus and past papers
The mathematics syllabus centres on algebra, geometry, number theory and combinatorics, with non-routine problem solving. Use the official syllabus and stage-specific source papers.
RMO syllabus
RMO syllabus, All classes · 2026-27
Number Theory
- Divisibility, Primes and Factorisation: Prove results about divisibility, primes, prime factorisation and the number and sum of divisors, with clearly written arguments.
- GCD, LCM and Euclidean Algorithm: Use the Euclidean algorithm, Bezout's identity and properties of gcd and lcm in proofs.
- Congruences and Modular Arithmetic: Work with congruences, residues, Fermat's little theorem and Euler's theorem to prove divisibility and find remainders.
- Diophantine Equations: Solve and prove results on integer equations using factoring, parity, modular restrictions and descent.
- Number Bases and Digit Problems: Prove statements about digits, bases and digit sums.
Algebra
- Polynomials and Roots: Study polynomial identities, factorisation, remainder and factor theorems, and relations between roots and coefficients.
- Quadratic Equations and Expressions: Use the discriminant, nature of roots and completing the square to solve and prove statements about quadratics.
- Systems of Equations: Solve and analyse systems of linear and non-linear equations, using symmetry and substitution.
- Inequalities: Prove inequalities using AM-GM, Cauchy-Schwarz and rearrangement, and find extremal values.
- Sequences, Series and Recurrences: Work with arithmetic and geometric progressions, finite series and simple recurrence relations.
- Functions and Functional Equations: Analyse functions defined by relations and solve simple functional equations with justification.
- Complex Numbers: Learn the algebra and geometry of complex numbers, including modulus, conjugates and roots of unity.
- Mathematical Induction: Learn the principle of mathematical induction and use it to prove statements for all natural numbers.
Geometry
- Triangles: Congruence, Similarity and Area: Prove results using congruence, similarity, the Pythagoras theorem, angle bisector theorem and area relations.
- Circles and Cyclic Quadrilaterals: Prove results with angle chasing, tangents, power of a point and cyclic quadrilaterals.
- Triangle Centres and Special Lines: Study the centroid, incentre, circumcentre, orthocentre, medians and altitudes and prove their properties.
- Trigonometry in Geometry: Use trigonometric identities and the sine and cosine rules in geometric proofs and computations.
- Coordinate Geometry and Vectors: Use coordinates and vectors, including an introduction to three-dimensional geometry, to prove and compute.
Combinatorics
- Counting, Permutations and Combinations: Use counting rules, arrangements, selections and inclusion-exclusion with a proof of why the count is correct.
- Pigeonhole Principle: Use the pigeonhole principle and its generalisations in existence proofs.
- Recursion and Recurrence Relations: Set up and solve recurrences that arise in counting problems.
- Elementary Graph Theory: Study graphs, degrees, paths, trees and connectedness, and prove simple results.
- Invariants, Colouring and Extremal Arguments: Use invariants, colouring and extremal principles to prove that something is possible or impossible.
- Probability: Compute probabilities using counting and conditional probability at an introductory level.
Rounds and levels
- Previous Year Papers: Original RMO papers, grouped by year and regional set.
More exams on SkillStar
RMO: questions parents ask
- What is in the RMO syllabus for 2026-27?
- 24 topics in Number Theory, Algebra, Geometry and Combinatorics, laid out subject by subject on this page. On SkillStar your child can tick off each topic as they learn it.
- Are there RMO mock tests on SkillStar?
- Yes, 43 mock tests. Each one is marked the moment your child finishes, with a question-by-question review, and can be taken again as often as they like.
- Can I download RMO papers?
- Yes. The RMO Downloads tab on SkillStar has 67 files for this exam.
- How does my child start RMO practice?
- Sign up free as a parent, add your child with their class, and pick RMO from the exam list. Every new family gets welcome credits, lots of content costs nothing, and anything paid shows its price in credits before you decide.
- Is SkillStar the official RMO website?
- No. SkillStar is an independent practice platform and is not affiliated with, or endorsed by, the organisers of these exams. Exam names belong to their respective owners. Check dates, fees and registration with the RMO organisers.
SkillStar is an independent practice platform and is not affiliated with, or endorsed by, the organisers of these exams. Exam names belong to their respective owners.