Training and Preparation
This page features training materials, including preparation tips and a comprehensive collection of problems from previous editions of the International Youth Math Challenge, dating back to IYMC 2018.
General Information
Our team frequently receives the questions "How should I prepare for the competition?" and "What books would you recommend?". Diverse skills are required to approach the IYMC problems, including the following key skills that you will train throughout the competition:
- Creativity and problem-solving skills (e.g., logical reasoning).
- General mathematical knowledge (e.g., definitions).
- Science reading comprehension (i.e., Pre-Final Round).
- Mental calculation skills without tools (i.e., Final Round).
- Analytical thinking and pattern recognition (e.g., identifying relationships)
- Ability to apply theoretical knowledge (e.g., using theorems).
- Time management skills (i.e., Pre-Final & Final Round).
- Adaptability to different formats (e.g., multiple-choice or proof-based).
There are multiple problems and questions in each round (Qualification, Rre-Final, and Final Round) from a variety of mathematical areas, including the following:
- Algebra
- Number Theory
- Calculus
- Geometry
- Statistics
- Combinatorics
Additionally, the Pre-Final Round usually includes special-creativity problems, which require you to read a scientific article. The Final Round can also include questions related to the previous problems (e.g., the scientific article) from the Pre-Final Round and Qualification Round. Consider checking out this page to understand better how IYMC differs from other competition formats and what to expect:
- About IYMC (How IYMC differs from other competitions and what to expect.)
Preparation Tips for Participants
Below, you will find a set of tips designed to help you prepare for the International Youth Math Challenge. These recommendations are tailored to support your success in the competition and enhance your mathematical skills:
- Know the Competition Format
Start by understanding the structure and requirements of each round: the Qualification Round focuses on foundational math problems, the Pre-Final Round includes creativity and reading comprehension tasks, and the Final Round tests quick problem-solving under time pressure. Reviewing past IYMC problems will help you grasp the diversity and difficulty level of each round.
- Focus on the Core Topics
The problems in IYMC come from a range of mathematical areas, including algebra, geometry, number theory, and calculus. Make sure you are comfortable with the fundamental concepts, definitions and techniques in these topics to build a solid foundation for tackling problems.
- Train Your Problem-Solving Skills
Work on improving your creativity, logical reasoning, and analytical thinking by solving proof-based questions (i.e., by using the book recommendations below). These skills will help you approach even the most challenging IYMC problems effectively.
- Learn from Mistakes
Reflecting on your mistakes and learning from them is an essential part of growth in any competition. First, try to solve the problems as far as possible. Then, compare them to a fiven solution and evaluate at which steps you made mistakes and correct them accordingly.
- Use the Available Resources
Take advantage of past IYMC problem sets, recommended math books, and online platforms to sharpen your skills. Additionally, the IYMC team is available to provide assistance and guidance; do not hesitate to contact us for support.
- Prepare for Scientific Reading (Pre-Final Round)
The Pre-Final Round often features problems inspired by scientific articles. Practice reading and summarizing scientific texts, focusing on extracting relevant mathematical ideas, and connecting them to broader concepts. Reading papers from previous years and current papers from the arXiv will help.
- Simulate Timed Problem-Solving (Final Round)
Time management is essential for the Pre-Final and even more the Final Round. Practice solving problems within set time limits to develop a sense of pacing.
- Practice Mental Math (Final Round)
Mental calculation without tools is beneficial for various rounds, especially in the Final Round. Regularly solve problems that require quick calculations to enhance your speed and accuracy under time constraints.
- Collaborate and Learn from Others
Join study groups, math clubs, or connect with IYMC Ambassadors to discuss strategies and share insights. Collaboration can help you explore new problem-solving approaches and stay motivated throughout your preparation.
- Enjoy the Learning Experience
Keep in mind that IYMC prioritizes learning and expanding your knowledge while participating. Engage with each problem, and treat every challenge as an opportunity to expand your understanding of mathematics.
Book Recommendations
Most standard school and university books from your preferred institution are useful and contain all information required to approach the problems. For reference, please have a look at the following list of scripts that address mathematical problem-solving in an intuitive and entertaining way:
- Terence Tao (2006). Solving Mathematical Problems: A Personal Perspective. OUP Oxford. View
- George Pólya (2015). How to Solve It: New Aspect of Mathematical Method. Pinc. Press. View
- Titu Andreescu (2003). Mathematical Olympiad Treasures. Birkhauser. View
- Paul Zeitz (1999). The Art and Craft of Problem Solving. John Wiley & Sons. View
- Titu Andreescu and Zuming Feng (2006). 104 Number Theory Problems. Birkhauser. View
- Alexander Soifer (2009). Mathematics as Problem Solving. Springer. View
- Shyam Sunder Gupta (2023). Creative Puzzles to Ignite Your Mind. Springer. View
- Ellina Grigorieva (2015). Methods of Solving Nonstandard Problems. Springer. View
- Ravi Vakil (1997). A Mathematical Mosaic: Patterns & Problem Solving. Brendan Kelly Pub. View
- Edward Scheinerman (2000). Mathematics: A Discrete Introduction. Brooks Cole. View
IYMC Problems of 2023
IYMC Problems of 2022
IYMC Problems of 2021
IYMC Problems of 2020
IYMC Problems of 2019
IYMC Problems of 2018
