RMO Previous Papers

RMO Previous Year Papers

RMO (Regional Mathematical Olympiad) is the second stage and a crucial milestone for any student aiming to represent India at the International Mathematical Olympiad (IMO). Conducted by Regional Coordinators under the Homi Bhabha Centre for Science Education (HBCSE) and the National Board for Higher Mathematics (NBHM), RMO is open to students from Classes 8 to 12 who have qualified IOQM. India is divided into 25 geographical regions for RMO, plus separate non-geographical regions for the Kendriya Vidyalaya Sangathan (KVS) and Navodaya Vidyalaya Samiti (NVS) networks, and only 30 Category A students (Classes 8 to 11) and 6 Category B students (Class 12) per region qualify for the next stage, INMO, making strong preparation essential. Solving RMO previous papers helps you understand the types of proofs expected, the depth of mathematical reasoning required, and the topics that appear most frequently.

RMO is fundamentally different from IOQM. It is a fully descriptive, proof-based exam. There are no integer-type answers, no OMR sheets, and no multiple choice options. Answers must be written as complete mathematical solutions with clear logical steps. Download the RMO previous papers PDF to practise at your own pace, or use them as timed 3-hour mock sessions under real exam conditions.

How to Download RMO Previous Papers PDF

Getting your RMO previous papers PDF from the official sources is straightforward and free. Just follow these simple steps.

1. Visit the official HBCSE Olympiads portal at olympiads.hbcse.tifr.res.in or the MTAI website at mtai.org.

2. Navigate to the Past Papers or Mathematical Olympiad section.

3. Click the link for the year and region you want to practise and save the PDF on your laptop.

4. Print the paper and set a strict 3-hour timer before you begin.

5. Attempt all 6 questions in writing with complete proofs, just as in the real exam.

6. After finishing, compare your solutions against the official answer key or community solutions on Art of Problem Solving (artofproblemsolving.com) to evaluate the quality of your proofs.

RMO papers from 2018 onwards are widely available in the public domain. Since RMO was not held as a separate stage during the 2020-21 and 2021-22 cycles due to COVID-19 disruptions, the available archive for recent years covers 2018, 2019, and 2022 to 2025. Together, these papers give you a thorough picture of the exam's depth, style, and difficulty range.

Benefits of Solving RMO Previous Years Papers

Working through past RMO papers gives you advantages no other resource can match.

• Understand proof structure and style: RMO problems require complete written proofs, not just answers. Past papers show you exactly how problems are framed and what level of logical rigor is expected in a solution.
• Improve time management: RMO gives you 3 hours for 6 problems with no time limits per question. Practice teaches you how to allocate roughly 30 minutes per question and when to move on from a problem that is not yielding.
• Judge difficulty and question depth: Learn to identify which questions are approachable early and which are designed to challenge the strongest students. Attempting easier questions fully first and returning to harder ones is a proven strategy.
• Spot topic trends: Geometry, Algebra, Number Theory, and Combinatorics each appear in predictable proportions across years. Solving multiple years of papers reveals which topics dominate and which styles of problems repeat.
• Strengthen proof-writing skills: Each paper you attempt and review teaches you new techniques and helps you write cleaner, more rigorous proofs. This skill matters more than raw mathematical knowledge in RMO.
• Build stamina for long-form solutions: Writing six complete proofs in three hours is physically and mentally demanding. Only repeated timed practice builds the stamina required.

Pair your paper-solving with detailed solution review from the HBCSE website and community resources like Art of Problem Solving for the best results.

RMO Exam Pattern & Marking Scheme

Understanding the RMO exam pattern is the first step before solving any paper. RMO is an offline, pen-and-paper exam requiring fully written mathematical proofs. It is conducted simultaneously across all regions on the same day.

RMO Exam Pattern

The table below shows the RMO exam structure. All six questions are of equal marks and require complete descriptive solutions. There are no multiple choice options and no calculators are allowed.

There are no sectional time limits. Candidates can attempt questions in any order within the 3-hour window. The exam is conducted in English, Hindi, and other regional languages as determined by each Regional Coordinator. RMO papers are the same for all classes (8 to 12) within a region.

RMO Marking Scheme

The table below shows how marks are awarded in RMO. Unlike IOQM, partial credit is available for incomplete but substantially correct solutions.

There is no negative marking in RMO. Partial credit makes it important to always write down whatever relevant progress you can make on every question, even if you cannot complete the full proof. A well-argued partial solution can score 5 to 14 marks, which can be the difference between qualifying and not qualifying for INMO.

RMO Exam Analysis Over the Years

A year-wise look at RMO helps you plan smarter.

The RMO exam analysis shows that Geometry is consistently the most prominent topic and appears in two or more questions in almost every year. Number Theory problems require careful case analysis and modular arithmetic. Algebra problems often involve inequalities or functional equations. Combinatorics problems reward creative counting arguments. Students who score full marks on at least three questions and partial marks on the rest typically qualify for INMO.

RMO Preparation Tips

Smart preparation beats long preparation. Use these RMO preparation tips to plan your study schedule.

• Study proof techniques before solving papers: Learn mathematical induction, contradiction, construction, pigeonhole, infinite descent, and modular arithmetic as standalone techniques before applying them in timed conditions.
• Master Geometry deeply: Circle theorems, triangle centres, power of a point, radical axes, and projective geometry are essential. RMO geometry problems demand both intuition and rigorous proof.
• Build Number Theory systematically: Divisibility, Bezout's lemma, Euler's theorem, quadratic residues, and Vieta jumping are high-frequency RMO techniques that must be second nature.
• Practise Algebra proof problems: Inequalities (AM-GM, Cauchy-Schwarz, SOS), functional equations, and polynomial problems appear regularly and require clean algebraic proof writing.
• Solve every problem completely in writing: Even for problems you can solve mentally, write out the full proof on paper. RMO evaluators assess logical flow and completeness, not just the final answer.
• Review solutions critically: After each timed attempt, compare your proofs with official or community solutions and identify every logical gap. Keeping a proof-error notebook builds precision over time.
• Use Art of Problem Solving (AoPS): The AoPS community archives every RMO paper with detailed community solutions and alternate approaches, making it the best free resource for solution review.

For beginners, focus first on Geometry and Number Theory proofs before attempting full papers under timed conditions. Repeat aspirants should focus on Algebra and Combinatorics to fill gaps, and target full-score solutions rather than partial attempts across many questions.