Picture this: you’re halfway through the AMC 10, the clock is ticking, and you’re stuck on a geometry problem that looks nothing like anything you’ve seen in class. Your heart rate jumps. Do you keep pushing? Skip and come back? Change approaches completely?
The students who thrive in moments like this aren’t just “good at math.” They’ve built a toolbox of problem-solving habits, mental strategies, and competition-ready techniques. This ScholarComp guide explores essential skills and shows you how to develop them step by step.
This article is part of the “Getting Started in Mathematics” series, but stands on its own. If you’re brand-new, you might also like Getting Started in Mathematics Competitions: A Complete Beginner’s Guide. Here, we’ll focus on skills: what they are, why they matter, and how you can grow them from where you are right now.
Every competition problem rests on basic concepts. Competitions like AMC, MATHCOUNTS, and Math Kangaroo combine those basics in unfamiliar ways. If your foundation is shaky, you’ll feel lost when a problem looks “weird.”
Foundations go beyond memorizing formulas; they include number sense, algebra, geometry, and logical thinking. Key skills for competitions include:
Consider a student named Maya preparing for MATHCOUNTS. She can "plug numbers" into formulas but freezes when asked for "the number of factors of 360." After focusing on prime factorization and practice, those questions become routine.
Start with a self-assessment: select 10–15 problems from past AMC, MATHCOUNTS, or school math units. Identify which topics feel fuzzy, then:
Good foundations are like a strong floor: they support every step you take in competition math.
Competitions test how you think, not just what you know. Students who practice problem-solving habits find clever paths faster.
For example, when asked for the largest of three consecutive integers summing to 72, a competitor may notice the middle number is one-third of the sum: 24, making the largest 25. Spotting patterns saves time.
Key strategies to develop include:
During an AMC 8 practice, Alex tried brute-force methods but improved after incorporating visualization strategies, solving problems faster with fewer guesses.
When practicing, focus on how you think, not just if you got it right. After solving problems:
Over time, these strategies will become automatic, making problems feel less random.
Timed competitions require quick thinking, but careless mistakes can hurt your score. Both speed and accuracy can be trained.
Speed means using smarter approaches. For instance, instead of long multiplication for 49 × 51, you can use the difference of squares: 50² − 1 = 2499.
Ryan, practicing for Math Kangaroo, reduced arithmetic errors after focusing on mental math tricks and finding patterns instead of relying on long multiplication.
Follow this path:
After each timed session, carefully review mistakes, categorizing them to identify focus areas for improvement.
Even prepared students can freeze during competitions. Mindset and test-taking strategies are crucial.
Smart pacing is essential, especially on tests like the AMC 10. A common mistake is spending too long on mid-level problems instead of moving on to easier ones.
Leah learned to quickly scan problems, marking approachable ones and not spending more than 2–3 minutes stuck. Her score improved significantly.
Experiment with these rules:
Competition nerves are normal. Build stress-response routines before practice:
Mock contests with peers can help normalize the pressure of real events.
Rapid improvement often stems from how competitors respond after practice or contests. Do they analyze their performance?
Two students scoring 15 on the AMC 8 illustrate this. One moves on; the other reviews missed problems thoroughly, analyzing their reasoning and summarizing lessons learned. The latter gains many new techniques over time.
Build a reflection routine by:
Some problems are designed to be tough. Diego, after a week on a number theory problem, sought help from his math club, leading to breakthroughs. His persistence paid off.
To cultivate persistence:
Consider these action steps for the coming week:
As you explore competitions like AMC, MATHCOUNTS, or Math Kangaroo, remember that the skills you build are cumulative. Each problem, reflection, and strategy is an investment in your future self as a mathematician.
Ready to keep going? Explore more resources on ScholarComp, discuss specific skill goals with your teacher or coach, and seek out challenges that excite you. With the right skills and a growth-focused mindset, you won’t just be “taking” math competitions—you’ll be becoming the thinker they aim to discover.
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