Effective Strategies for Preparing for National and International Math Contests

Preparing for math contests is a journey filled with both excitement and challenges. From the moment you decide to participate, there’s a rush of anticipation as you dive into problem-solving and mathematical exploration. The excitement stems from the opportunity to test your skills against some of the brightest minds, nationally and internationally. It’s a chance to showcase your mathematical prowess and push the boundaries of your understanding.

But this journey is not without its hurdles. The challenges of preparing for math contests can be significant. They require dedication, perseverance, and a willingness to tackle complex problems that may initially seem insurmountable. The path to success is often paved with countless hours of studying, practicing, and refining problem-solving techniques. There are moments of frustration and self-doubt, but overcoming these obstacles can add to the sense of accomplishment when you finally crack a particularly challenging problem.

National and international math contests are crucial in shaping mathematical understanding and problem-solving skills. They provide a platform for students to apply theoretical knowledge to problems in the real world and develop critical thinking abilities. Participating in these contests exposes students to a variety of mathematical concepts and techniques that may not be covered in standard curricula. They learn to approach problems from different angles, think creatively, and communicate their solutions effectively.

Moreover, math contests foster a spirit of collaboration and camaraderie among participants. Competing alongside peers sharing a passion for mathematics creates a supportive environment for exchanging ideas and forming friendships. The sense of community that emerges from these contests is invaluable, as it encourages students to push each other to new heights and celebrate each other’s successes.

Ultimately, the significance of national and international math contests extends far beyond the competition itself. They inspire a lifelong love of learning, instill confidence in one’s abilities, and cultivate the skills needed to tackle the challenges of tomorrow. Whether vying for the top spot or simply aiming to improve your skills, preparing for math contests is a rewarding and transformative experience.

Understanding math contests

Overview of math contests

Various national and international math contests

1. International Mathematical Olympiad (IMO):

  • Format: Each country typically sends a team of six high school students to compete. They solve challenging mathematical problems over two days, with three daily problems.
  • Level: Extremely high, considered the pinnacle of high school math competitions.
  • Content: Pure mathematics, covering topics like number theory, algebra, geometry, and combinatorics.
  • Unique and challenging aspects: Problems presented in the IMO often require creative insights and innovative problem-solving techniques. Participants must be well-versed in various mathematical concepts and have strong problem-solving skills.

2. Putnam mathematical competition (USA):

  • Format: A six-hour exam with 12 challenging problems, typically divided into two sessions.
  • Level: Very high, targeting undergraduate students.
  • Content: Problems are often proof-based and require deep mathematical insight, covering a wide range of topics, including calculus, algebra, geometry, and number theory.
  • Unique and challenging aspects: The Putnam Competition emphasizes problem-solving skills and the ability to construct rigorous proofs under time pressure. It’s known for its difficulty and the prestige associated with high scores.

3. European Girls’ Mathematical Olympiad (EGMO):

  • Format: This is similar to the IMO but exclusively for female participants. Teams from various countries compete over two days.
  • Level: High, aimed at high school girls.
  • Content: Problems cover various areas of mathematics, similar to the IMO.
  • Unique, challenging aspects: EGMO provides a platform for female mathematicians to showcase their talents and encourages gender diversity in mathematics competitions.
  • The problems are carefully crafted to challenge participants while promoting collaboration and creativity.

4. Mathematical Kangaroo (International):

  • Format: A multiple-choice competition with varying difficulty levels based on age groups.
  • Level: Elementary and middle school students.
  • Content: Problems are designed to test mathematical intuition and encourage problem-solving skills in a fun and engaging way. They cover basic arithmetic, logic, and geometric concepts.
  • Unique and challenging aspects: The Mathematical Kangaroo promotes interest in mathematics among young students through accessible and engaging problems. While less intense than other competitions, it provides a valuable opportunity for students to develop their mathematical skills in a low-pressure environment.

5. USA Mathematical Olympiad (USAMO):

  • Format: Six proof-based questions are administered over two days.
  • Level: High school students who have performed exceptionally well in previous competitions.
  • Content: The problems are challenging and require rigorous proofs, often spanning various areas of mathematics, such as algebra, number theory, geometry, and combinatorics.
  • Unique and challenging aspects: USAMO problems demand deep mathematical understanding and the ability to construct clear and concise proofs. Success in USAMO requires mathematical creativity, problem-solving skills, and rigorous logical thinking.

Personal experiences and insights

Participating in math competitions can be an enriching experience regardless of the level of competition. They foster critical thinking, creativity, and perseverance, which are essential for success in mathematics and beyond. These competitions’ challenges test one’s mathematical abilities and encourage collaboration, as participants often work together to solve complex problems. Moreover, the camaraderie among contestants and the thrill of tackling challenging problems make math competitions a memorable and rewarding experience for many students.

Importance of participation

Participating in math contests offers a myriad of benefits that extend beyond just solving problems. Firstly, it fosters personal growth by honing problem-solving skills, fostering resilience in the face of challenges, and promoting a growth mindset. These qualities are invaluable for navigating academic and professional endeavors.

Moreover, involvement in math contests can significantly bolster college applications. Admissions committees recognize the dedication, passion, and intellectual rigor demonstrated through such participation. It showcases an applicant’s commitment to excellence and can set them apart in a competitive admissions landscape.

Career opportunities are also enhanced by engagement in math contests. The skills acquired—critical thinking, logical reasoning, and mathematical proficiency—are highly sought after in fields such as engineering, finance, and technology. Additionally, success in math competitions can open doors to prestigious internships, scholarships, and job opportunities.

Skills and knowledge gained through contest participation encompass more than just mathematical concepts. Participants develop time management skills, work collaboratively in team events, and refine their communication abilities by explaining solutions. These transferable skills are invaluable in academia and the workforce, enriching one’s educational and professional journey.

Pupil feeling happy after getting excellent mark

Strategies for effective preparation

Building a solid mathematical foundation

Understanding fundamental concepts and theories in mathematics is crucial for several reasons. Firstly, it provides a solid foundation upon which more complex mathematical ideas can be built. Like a house needs a solid foundation to support its structure, advanced mathematical concepts rely on a clear understanding of basics like arithmetic, algebra, geometry, and calculus.

Secondly, mathematical concepts are interconnected. A firm grasp of fundamentals enables individuals to see the relationships between different areas of mathematics and to apply concepts across various disciplines, from physics to economics to computer science.

Moreover, mathematical literacy is essential in many areas of life, from managing personal finances to analyzing data professionally. Individuals may struggle to make informed decisions or solve problems effectively without a solid understanding of basic mathematical concepts.

Regular practice is the key to reinforcing mathematical foundations. It can involve solving problems, working through exercises, and engaging with mathematical concepts in different contexts. Additionally, seeking advanced coursework can deepen understanding and expose learners to more sophisticated applications of mathematical principles.

Other strategies include:

  • Seeking guidance—Consulting teachers, tutors, or online resources to clarify challenging topics can provide valuable insights and help reinforce understanding.
  • Using technology – Utilizing mathematical software or online tools can make practice more interactive and facilitate the exploration of complex concepts.
  • Teaching others – Explaining mathematical concepts to others can solidify understanding and uncover any gaps in knowledge.
  • Studying real-world applications – Connecting mathematical concepts to real-world problems can make them more tangible and enhance understanding.
  • Consistent review – Regularly revisiting previously learned concepts helps prevent forgetting and reinforces retention.

Targeted practice and problem-solving

Approaches to targeted practice:

  • Solving past contest problems – Past contest problems are a valuable resource as they expose students to the types of questions that may appear in future contests. Solving these problems allows you to identify recurring patterns, understand standard problem-solving techniques, and gauge your proficiency in various topics. Additionally, analyzing solutions to past problems helps in learning new problem-solving strategies and understanding different approaches to solving a problem.
  • Simulating contest conditions—Simulating contest conditions involves setting a timer and working on problems under time pressure, similar to actual contest conditions. It helps improve speed and accuracy and develops the ability to manage time effectively during a contest. Practicing under timed conditions also helps simulate the stress and pressure experienced during a real contest, thus preparing you mentally for the event.
  • Focusing on weak areas—Identify your weak areas or topics that you find challenging and dedicate more practice time to them. By improving your weaknesses, you can strengthen your problem-solving skills and increase your chance of performing well in future contests.
  • Seeking feedback—After solving problems, seek feedback from peers, mentors, or online communities. Discussing solutions with others helps you gain new perspectives, learn alternative approaches, and correct any misconceptions. Constructive feedback can also highlight areas for improvement and effectively guide your practice efforts.
  • Continuous learning—Engage in constant learning by studying advanced concepts, exploring new problem-solving techniques, and staying updated with the latest developments in your field of interest. This will help you expand your problem-solving toolkit and enhance your ability to tackle complex mathematical problems.

Personal methods for approaching complex problems and developing problem-solving strategies:

  • Breaking down problems—Break down complex problems into smaller, more manageable components. Doing so makes understanding the problem and identifying potential solution approaches easier. Start by analyzing the problem statement, identifying key concepts, and outlining a plan of attack.
  • Visualizing solution – Visualize the problem and potential solution strategies using diagrams, graphs, or illustrations. Visual representations can help understand complex relationships, identify patterns, and devise effective problem-solving strategies.
  • Using analogies –Draw analogies between the current problem and similar problems you have encountered. Recognizing similarities between problems allows you to apply and adapt familiar problem-solving techniques to the current situation.
  • Experimenting with different approaches – Try approaching the problem from different angles and experimenting with various solution strategies. It helps you explore alternative solutions, discover new problem-solving techniques, and find the most efficient approach to solving the problem.
  • Iterative problem-solving—Break the problem-solving process into iterative steps, continuously clarifying your approach based on feedback and insights gained along the way. Iterate through different solution attempts, analyze their effectiveness, and adjust your strategy until you arrive at a satisfactory solution.
  • Practice reflective thinking. After solving a problem, Reflect on your problem-solving process. Analyze the effectiveness of your approach, identify areas that need improvement, and consider how you can apply lessons learned to future endeavors. Reflective thinking helps you refine problem-solving skills and develop a deeper understanding of problem-solving techniques.

Time management and planning

Strategies for creating and adhering to a study schedule leading up to the contests:

  • Set clear goals – Define your objectives for the contests. Determine which topics or areas to focus on and set realistic targets for your study sessions.
  • Prioritize tasks – Identify your most important commitments, such as schoolwork and extracurricular activities. Allocate time for these tasks first and then schedule study sessions around them.
  • Break down study material – Divide the contest material into smaller, manageable chunks. This approach will make it easier to digest and help prevent you from becoming overwhelmed.
  • Use a calendar or planner—Use a calendar or planner to schedule study sessions and allocate specific time slots for each subject or topic. Stick to the schedule as much as possible.
  • Stay organized—Organize your study materials, notes, and resources to maximize efficiency during study sessions and minimize time wasted searching for materials.
  • Stay consistent. Establish a routine and commit to regular study sessions. Consistency effectively helps retain information and improve skills.
  • Take breaks—Remember to schedule breaks during study sessions to avoid burnout. Short breaks can help refresh your mind and improve overall productivity.
  • Seek support – If you’re struggling with specific concepts, seek help from teachers, peers, or online resources. Collaboration and support can enhance your understanding and performance.

Personal insights on balancing contest preparation, schoolwork, and other commitments:

  • Time management—Effective time management is crucial. Breaking down the day into blocks dedicated to different tasks will enable you to stay on track and not neglect essential responsibilities.
  • Flexibility – While having a schedule is important, it’s also essential to be flexible. Unexpected events or changes in priorities may cause you to adjust your study plan. Being adaptable will allow you to handle these situations without feeling overwhelmed.
  • Self-care—Taking care of your physical and mental well-being is essential, especially during periods of intense studying. Prioritize adequate sleep, exercise, and relaxation to maintain optimal performance and prevent burnout.
  • Communication – Keep lines of communication open with teachers, parents, or mentors about your commitments and schedule. They can provide valuable support and understanding, helping alleviate potential conflicts.
  • Reflection—Regularly reflect on your progress and adjust your study strategies. Pay attention to what methods are most effective for you, and don’t be afraid to experiment with new approaches.

Seeking guidance and collaboration

The crucial role of mentors, teachers, and peers in preparing for math contests:

  • Mentors—Mentors provide guidance, support, and expertise in navigating the intricacies of math contests. They offer valuable insights, strategies, and techniques honed through their experiences. Mentors can help students understand advanced concepts, tackle challenging problems, and develop effective problem-solving skills. They can be role models and sources of inspiration, motivating students to strive for excellence.
  • Teachers – Teachers play a fundamental role in laying the foundation for math contest preparation. They impart essential mathematical knowledge, teach problem-solving methodologies, and offer personalized assistance to students. Teachers can help you identify individual strengths and weaknesses, tailor instruction accordingly, and provide constructive feedback to enhance learning. Their encouragement and mentorship contribute significantly to students’ confidence and readiness for math contests.
  • Peers – Peer collaboration fosters a supportive learning environment where students can collectively exchange ideas, discuss strategies, and tackle problems. Interacting with peers encourages active engagement, promotes critical thinking, and cultivates teamwork skills. Peer discussions stimulate intellectual curiosity and broaden perspectives, leading to deeper understanding and innovative problem-solving approaches. Peer encouragement and camaraderie motivate students to persevere through challenges and strive for continuous improvement.

Benefits of group study and collaborative problem-solving:

  • Diverse perspectives – Group study exposes individuals to diverse problem-solving approaches and perspectives, enriching their understanding of mathematical concepts.
  • Peer support – Collaborating with peers creates a supportive network where students can seek help, clarify doubts, and share insights, fostering a sense of camaraderie and mutual encouragement.
  • Enhanced learning – Interactive discussions and collaborative problem-solving sessions promote active learning, retention of knowledge, and deeper comprehension of mathematical concepts.
  • Skill development – Group study cultivates essential skills such as communication, teamwork, and leadership, which are valuable in math contests and various academic and professional life aspects.

One example:

During high school, the math club may have organized weekly study sessions where students could collaboratively tackle challenging problems from past math contests. Students could improve their problem-solving skills through lively discussions and collaborative problem-solving and develop strong bonds with fellow enthusiasts.

The students learned that where diverse perspectives were, they led to creative solutions and peer support and encouraged us to persevere through intricate problems. These group study sessions prepared us for math contests and fostered a lifelong love for mathematics and teamwork.

Asian schoolboy solving geometry problem on blackboard

Psychological preparation and mindset

Overcoming anxiety and building confidence

Managing pre-contest anxiety and maintaining a positive mindset:

  • Visualization – Imagine yourself performing well and achieving your goals.
  • Deep breathing exercises – Practice breathing deeply to calm your nerves and reduce anxiety.
  • Positive self-talk – Rather than focusing on negative thoughts, replace them with positive affirmations to boost confidence.
  • Focus on the present – Stay focused on the task rather than worrying about the outcome.
  • Establish a routine – Create a pre-contest routine to help you feel prepared and confident.
  • Stay organized – Break down your preparation into manageable tasks to avoid feeling overwhelmed.
  • Seek support – Surround yourself with friends, family, or coaches who can encourage and support you.

Personal strategies for building confidence and staying motivated:

  • Set specific goals – Define clear, achievable goals to give yourself direction and motivation.
  • Celebrate progress – Acknowledge and celebrate small victories to boost morale.
  • Stay positive – Maintain a positive attitude when you face challenges or setbacks.
  • Visualize success – Picture yourself achieving your goals to reinforce your confidence and motivation.
  • Practice self-care – Take care of yourself physically and mentally by getting enough rest, eating healthily, and managing stress.
  • Stay inspired—Surround yourself with sources of inspiration, such as books, music, or motivational speeches.
  • Reflect on past successes – Remind yourself of past achievements to build confidence in your abilities.

By combining these techniques and personal strategies, you can effectively manage pre-contest anxiety, maintain a positive mindset, build confidence, and stay motivated throughout preparation.

Learning from mistakes and setbacks

Analyzing past mistakes and learning from unsuccessful contest experiences

Analyzing past mistakes and learning from unsuccessful contest experiences is vital for personal and professional growth. Here’s why:

  • Identifying patterns – Examining past mistakes helps us recognize recurring patterns or behaviors that lead to failure. This awareness enables us to make necessary adjustments and avoid similar pitfalls in the future.
  • Gaining insight – Reflecting on unsuccessful experiences provides valuable insights into what went wrong, why it happened, and what could have been done differently. This understanding deepens our knowledge and enhances our decision-making skills.
  • Building resilience – Setbacks are inevitable in any competitive endeavor. Embracing failures as learning opportunities fosters resilience and mental toughness, enabling us to bounce back more robust and more determined than before.
  • Fostering growth – Learning from mistakes cultivates a growth mindset, where setbacks are viewed as stepping stones to success rather than roadblocks. Each failure becomes an opportunity for self-improvement and personal development.

Final preparations and contest day strategies

Last-minute review and relaxation techniques

Tips on balancing final review and mental preparation in the days leading up to the contest

  • Create a study schedule—Plan your final review sessions, allocating specific time slots for each subject or topic. Make sure to include breaks for relaxation and mental rejuvenation.
  • Prioritize topics – Focus on reviewing the most important or challenging topics first. This ensures you allocate sufficient time to areas where you need the most improvement.
  • Practice mindfulness and relaxation techniques – Use mindfulness meditation, deep breathing exercises, or yoga daily to help manage stress and promote relaxation.
  • Stay active. Regular physical activity, like walking, jogging, or yoga, can boost your mood, reduce anxiety, and improve concentration.
  • Get adequate sleep – Do your best to get at least 7 hours of quality sleep each day so your brain can consolidate information and recharge for the next day.
  • Maintain a healthy diet. Fuel your body and brain with nutritious foods like fruits, vegetables, whole grains, lean proteins, and healthy fats. Avoid excessive caffeine and sugary snacks, which can lead to energy crashes and decreased focus.
  • Take regular breaks – Break up each study session with a short break to avoid burnout and maintain productivity. Use these breaks to relax, stretch, or engage in enjoyable activities.
  • Visualize success—Spend a couple of minutes each day visualizing yourself performing well in the contest. Picture yourself confidently answering questions or completing tasks with ease.
  • Stay positive – Maintain a positive attitude and remind yourself of your strengths and accomplishments. Avoid dwelling on past mistakes or negative thoughts.
  • Review, but don’t overdo it – While it’s essential to review material, avoid cramming or studying late into the night before the contest. Trust in the preparation you’ve done leading up to this point.

Personal routines or rituals followed the day before and the day of the contest.

The day before the contest:

  • Review key concepts and formulas but avoid studying intensely.
  • Engage in relaxing activities such as reading a book, taking a leisurely walk, or spending time with friends or family.
  • Eat a balanced dinner, avoiding heavy or greasy foods that could disrupt sleep.
  • Prepare your contest materials (e.g., pens, pencils, calculator) and ensure you have everything you need for the next day.
  • Relax before bed with calming activities such as listening to soothing music and practicing deep breathing exercises.

The day of the contest:

  • Start your day with a nutritious breakfast to fuel your body and brain.
  • Review any last-minute notes or reminders, but avoid studying new material.
  • Arrive at the contest location early to avoid rushing and allow time to settle in.
  • Take a few moments to center yourself with deep breathing exercises or mindfulness techniques.
  • Trust in your preparation and approach the contest with confidence and a positive attitude.
  • After the contest, relax and celebrate your efforts, regardless of the outcome.
  1. Strategies for success during the contest

Tips for effectively managing time, handling complex problems, and maximizing scores during the contest.

Time management:

  • Prioritize tasks based on their importance and urgency.
  • Break tasks into smaller, manageable chunks.
  • Use time-blocking techniques to allocate time for specific activities.
  • Minimize distractions and stay focused on the task at hand.

Handling difficult problems:

  • Stay calm and approach problems systematically.
  • Break down complex problems into smaller, more manageable parts.
  • Use problem-solving strategies like trial and error, brainstorming, and seeking help when needed.
  • Don’t hesitate to skip complex problems and come back to them later if time permits.

Maximizing scores:

  • Understand the scoring criteria and allocate time accordingly.
  • Double-check your work for errors and ensure accuracy.
  • Use all available resources, such as reference materials and tools, wisely.
  • Stay confident, trust your instincts, and be open to revising your answers if necessary.


Preparing for national and international math contests requires more than raw knowledge; it demands strategic approaches. Strategies help in efficient time management, problem-solving techniques, and mental preparation. They enhance focus, confidence, and adaptability, which are crucial for navigating diverse problem types and formats. Ultimately, strategies can be the differentiating factor between success and underperformance in these highly competitive arenas.

Math contests can be challenging but incredibly rewarding experiences that help you grow as a problem solver and critical thinker. So, for fellow students, approach math contests with determination, strategy, and a positive mindset. Believe in yourselves, strategize your approach, and enthusiastically embrace the challenges. With the right mindset, you can conquer any mathematical puzzle that comes your way!

Apex College Prep is a leading K-12 after-school educational company in California. We are dedicated to giving students the skills and confidence to succeed as they prepare for and apply to college. Contact us here.