Math competitions like the AMC 10/12, Waterloo contests (Cayley, Fermat, Euclid), and MATHCOUNTS reward a type of mathematical thinking that regular classroom instruction does not always develop. Students who excel in school math sometimes struggle on competitions, not because they lack ability, but because contest math requires different preparation strategies.
Based on our work coaching students who have qualified for national-level competitions, here are five strategies that consistently produce results.
1. Should You Start with Problems or Theory?
Start with problems. The biggest mistake students make is trying to learn contest math the way they learn school math: read the theory, then do practice problems. Contest math works the other way. Attempt problems first, struggle with them, and then learn the theory you need to solve them. This approach, sometimes called problem-driven learning, builds the pattern recognition skills that separate good competitors from great ones.
Begin with past contest papers at the appropriate level. For AMC 10, start with problems 1 through 15 from recent years. For Waterloo contests, work through Cayley before attempting Euclid. Master the easier problems completely before moving to harder ones.
2. How Many Problems Should You Practice Each Week?
Quality matters more than quantity, but volume still matters. Aim for 15 to 20 problems per week during active preparation, with at least 5 of those being problems you cannot solve on the first attempt. The problems you struggle with are where the real learning happens.
Keep a “problem journal” where you write out full solutions to every difficult problem, including the ones you eventually looked up. Revisit this journal weekly. Students who review their past struggles consistently outperform those who only push forward to new material.
3. What Topics Should You Focus On?
Contest math draws heavily from a set of core topics that are underrepresented in school curricula:
- Number theory: divisibility, modular arithmetic, prime factorization
- Combinatorics: counting principles, probability, pigeonhole principle
- Geometry: circle theorems, similar triangles, coordinate geometry tricks
- Algebra: inequalities, sequences, functional equations
If a student is comfortable with all four areas, they will be able to attempt at least 80% of problems on a typical AMC or Waterloo contest.
4. How Important Is Time Management During Contests?
Extremely important. The AMC 10 gives 75 minutes for 25 problems, and the Euclid gives 2.5 hours for 10 multi-part problems. Many students who know how to solve a problem run out of time because they spend too long on one question. Practice under timed conditions at least once per week. Learn to recognize when you are stuck and move on, rather than grinding on a single problem while easier points go uncollected.
A practical rule: on the AMC, spend no more than 3 minutes on any single problem in the first pass. Return to skipped problems after completing everything you can solve quickly.
5. Should You Use a Tutor or Prep Course for Contest Math?
Self-study with good problem books (such as “The Art and Craft of Problem Solving” or the AMC/AIME preparation volumes) can take a motivated student a long way. However, one-on-one coaching accelerates progress significantly because a skilled contest math tutor can identify gaps in your problem-solving approach that you cannot see yourself. They can also introduce you to elegant techniques and shortcuts that might take months to discover independently.
Frequently Asked Questions
What age should my child start contest math?
Most students begin competitive math in grades 6 to 8, starting with competitions like MATHCOUNTS, the AMC 8, or the Waterloo Gauss contest. However, starting in grade 9 or 10 is not too late, especially for students with strong foundational skills.
Do math contest results help with university admissions?
Yes, particularly for STEM programs. Strong performance on the AMC/AIME, Euclid, or national olympiads signals genuine mathematical talent and is valued by admissions committees at competitive programs. A Euclid score in the top 25% or AMC qualification for AIME are meaningful achievements to include on applications.
How long does it take to see improvement in contest scores?
With consistent practice of 3 to 5 hours per week, most students see meaningful improvement within 3 to 4 months. Jumping from the AMC 10 to AMC 12 level, or from Cayley to Euclid level, typically takes 6 to 12 months of dedicated work.
Contest math is one of the most rewarding academic pursuits a student can take on. If your child is interested in competitive mathematics, contact Polaris Tutors to connect with an experienced contest math coach. Our team includes educators who have trained students for national and international math competitions.