RMO Pre-Exam Review: Avoiding Common Pitfalls + Strategies for Common Question Types

The RMO exam is coming up on 9 April 2026, so we’ve put together a summary of pre-exam tips and problem-solving strategies just for you. We recommend that you read through it carefully before the exam to identify any gaps in your knowledge. If there’s anything you don’t understand, be sure to review it or ask your teacher for help.

1. Pay attention to details to avoid losing points due to careless mistakes

① Read the questions carefully: While reading, highlight key conditions or list them separately. Make sure you clearly identify which data and relationships belong to which part of the problem.

② Use scratch paper effectively: Organize your scratch paper by designating a separate area for each problem to facilitate checking and organizing your thought process.

③ Write neatly: Avoid misreading data due to illegible handwriting.

④ Pay attention to calculations: For numbers exceeding two digits, it’s best to perform long division by hand without skipping steps. You can eliminate obvious errors by estimating or checking the last digit; for example, 49 × 41 must be a four-digit number close to 50 × 40 = 2000, and the last digit of 37 × 29 must be 3.

⑤ Thoroughly review your work: First, if a result clearly contradicts quantitative relationships or common sense, re-examine your problem-solving approach. Second, use review techniques—try substituting the given conditions into the problem to verify if they all hold true. If time permits, recalculate using different methods.

2. Don’t panic when faced with complex problems: Pay attention to common mathematical concepts and techniques

① Start with the simple cases to identify patterns: For particularly complex problems involving large numbers, begin by examining the simplest cases and then look for patterns. (For example, to find the remainder when 5 to the 2025th power is divided by 7, you can start with 5 to the first power, list the first few relatively simple remainders, and thus identify a pattern.)

② Learn to think in reverse: When the total number or total area is known but the specific value is difficult to calculate, you can convert the problem into finding other parts and then subtracting them.

③ Use variables (algebra): When you need a number but don’t know it, you can introduce a variable. Use “x” to represent the unknown quantity and try to set up equations or inequalities. For problems where the answer is an integer, you can break down the number into parts and combine them to find the solution.

④ Extreme Thinking: When finding maximum or minimum values, try assuming the possible maximum value first, then gradually verify and adjust.

⑤ Special Value Method: When a problem has no fixed requirements for data or the position, size, or shape of a figure—and multiple possibilities exist—try assuming one or more of the most special positions or values to calculate the answer directly.

⑥ Identify Invariants: For problems involving ratios, try to identify invariants and solve the problem from the perspective of these invariants. For problems involving differences, try solving them by assuming the difference remains constant. For problems involving moving points, look for invariant areas or lengths; for example, in a parallelogram, no matter where a point is located, connecting it to the four fixed points will always form a half-parallelogram with a constant area.

Try to write out the process and list all the information you can—the process helps us think through the problem.

3. Common Approaches to Specific Problems

① Geometry Problems:

Finding angles: Especially when encountering sides of equal length, construct an isosceles or equilateral triangle.

Finding areas: Various proportional models (bird’s head, swallowtail, kite, etc.)—make full use of the conversion between area ratios and side length ratios.

Finding Lengths: Especially when a right angle is present, or when one can be constructed—use the Pythagorean Theorem.

Additionally, whether finding angles or lengths, you can adopt a strategy of first making an educated guess and then proving it.

② Number Theory:

Prime factorization, divisibility by 3 and 9 (including sums of digits and random grouping), place value, remainder problems (starting with simple cases), squares and cubes (considering powers)—so prime factorization is often required.

Based on past trends in exam questions, the current year may appear in the test. For example, 2026 = 2 × 1013 (where 1013 is a prime number), and its prime factorization can be directly applied in number theory problems.

③ Calculations:

Consecutive multiplication or addition/subtraction; construct identical numbers to simplify fractions or cancel out terms through addition or subtraction. Typical examples include chained simplification, fraction decomposition, and integer decomposition.

4. Special Note

Since all RMO problems are multiple-choice and even blank answers are worth one point, setting aside the element of luck, if you really don’t know how to solve a problem and must guess, try to eliminate a few incorrect options first before guessing. For example, if your analysis shows that the result must be a multiple of 3, you can eliminate any options that are not multiples of 3. This increases your chances of guessing correctly. Based on mathematical expectation (ignoring individual luck), for 4-point questions, if you cannot eliminate any options, it’s better to leave it blank; if you can eliminate one or more options, you should make a guess. For 6-point questions, you should always try to make a guess—it’s better than leaving it blank.

5. Summary
Finally, we wish every student the best of luck in performing at their best during the exam and achieving the results they hope for.

At 6:30 p.m. on the evening of the exam, we will host a live review session on YouTube. If you can still recall any questions after the exam, please share them with your teacher so that everyone can check their answers more quickly and listen to the explanations. This will help you gain valuable experience for the next exam!

Good luck on your exams!