Mathematics Olympiad
Build problem-solving confidence from school-level Olympiads to the national selection pathway and the International Mathematical Olympiad. Verified patterns, clearly labelled rounds and past-paper resources—together in one place.
Two different routes to mathematical excellence
Important: SOF IMO and the International Mathematical Olympiad are separate competitions. Similar names should not be confused.
National Mathematical Olympiad Programme
Begin with IOQM, advance through proof-based RMO and INMO, and—by selection—train for India’s International Mathematical Olympiad team.
SOF International Mathematics Olympiad
School-registered, class-wise multiple-choice examinations. Level 1 is for Classes 1–12; qualifying students in Classes 3–12 can enter Level 2.
National pathway: exam pattern at every stage
From numeric answers to full mathematical proofs. Stages 4 and 5 are selective training processes rather than open-entry school tests.
IOQM
30 numeric-answer questions; 100 marks; 3 hours; OMR; no negative marking.
Classes 8–12 subject to the official eligibility criteria.RMO
6 proof-based problems; 3 hours.
Students qualify from IOQM according to the announced regional criteria.INMO
6 proof-based problems; 4½ hours.
Selection from RMO and any official additional routes as notified.IMOTC & TST
Invitational training camp followed by Team Selection Tests; the format is notified for each cycle.
Not a single common written paper with fixed MCQ marks.PDC
Final training and preparation for the selected national team.
Not an open registration exam.International IMO
2 competition days; 3 proof problems and 4½ hours per day; 42 marks maximum.
Up to six contestants per national team.Level 1 and Level 2: classwise pattern
Each paper is a 60-minute objective examination. SOF Level 1 has sections for Logical Reasoning, Mathematical Reasoning, Everyday Mathematics and Achievers; Level 2 has a different structure.
| Class | Level | Questions | Total marks | Sections / eligibility |
|---|---|---|---|---|
| 1–4 | Level 1 | 35 | 40 | 10 Logical + 10 Mathematical + 10 Everyday + 5 Achievers |
| 5–12 | Level 1 | 50 | 60 | 15 Logical + 20 Mathematical + 10 Everyday + 5 Achievers |
| 3–4 | Level 2 | 35 | 40 | 30 Mathematics + 5 Achievers; for qualified students only |
| 5–10 | Level 2 | 50 | 60 | 45 Mathematics + 5 Achievers; for qualified students only |
| 11–12 | Level 2 | 50 | 60 | 25 Mathematics + 20 Mathematical Reasoning / Applied Mathematics + 5 Achievers |
Level 1 · Who can appear?
Students of Classes 1–12 participate via their schools. Questions are objective and aligned with each class’s stated syllabus. For Classes 1–4, the five Achievers questions carry two marks each; for Classes 5–12, they carry three marks each.
Level 2 · How do students qualify?
Open only to eligible Level 1 qualifiers in Classes 3–12. SOF lists routes including classwise top 5% internationally, specified zonal ranks and eligible school class toppers; consult the current official criteria. There is no Level 2 for Classes 1–2.
Previous-year papers and answer keys
Open labelled files from your existing Olympiad archive. Papers, provisional keys and written solutions are distinguished. Some historical material follows an older selection structure.
IOQM
Numeric-answer questions · 2023–2026
RMO
Proof-based papers and solutions · Regional selection
INMO
National proof papers and solutions · 2023–2026
SOF IMO & International IMO
Official sample papers and international competition archive
Historical RMO year folders (1994–2018) · Expand archive
A better way to prepare for Olympiad mathematics
These four subject areas matter throughout the national proof pathway; early-stage school papers also build logical and quantitative habits.
Number theory
Divisibility, remainders, primes, Diophantine equations.
Algebra
Identities, inequalities, polynomials, functional reasoning.
Geometry
Angles, circles, similarity, constructions, clear proofs.
Combinatorics
Counting, invariants, arrangements, extremal arguments.