Introduction
Being a high schooler in the world of competition math can be confusing. Where do you begin? What do you do? How do you stand out? One of the most renowned starting points is the AMC, and it has helped thousands of students stand out in top university applications.
The AMC? I’ve never heard of it. This post covers what the AMC and USAMTS are and points you to resources to succeed in them. Let’s go.
How to Qualify for Math Olympiads with the AMC
American Mathematics Competitions (AMC)
The American Mathematics Competitions date back to the 1950s. Each exam now has 25 questions, and the program is split into the AMC 8, AMC 10, and AMC 12. You can take the exam if you’re in the grade matching the number or below, and each has slightly different standards.
The AMC 8 is for middle schoolers getting into competition math, with introductory concepts at the middle school level. Students who’ve done MATHCOUNTS tend to perform best, but the stakes are low: top performers earn certificates of recognition.
The AMC 10 and AMC 12, in the high school division, work a bit differently. They still have 25 questions in increasing difficulty, but the problems are much harder (especially the AMC 12) and cover higher-level math. Scoring is 6 points for a correct answer, 1.5 points for a blank, and 0 for a wrong answer, so guessing blindly can cost you relative to leaving a question blank. High scorers earn distinctions such as the Honor Roll and Distinguished Honor Roll.
The bigger reason the AMC 10 and 12 are so coveted is that they’re the gateway to the AIME (American Invitational Mathematics Examination). Scoring well on the AIME leads to qualifying for the USAMO (USA Mathematical Olympiad), and doing well there leads to MOP (the Mathematical Olympiad Program), a summer program that can lead to representing the U.S. at the International Mathematical Olympiad.
Students who make it to the final stage, or even a stage or two behind it, are among the nation’s brightest young mathematicians, which makes the AMC a prestigious starting point. The math in these competitions is often unorthodox and requires thinking beyond what’s taught in school, which is why prep can get expensive.
But there’s good news. A free guide created by a former International Mathematical Olympiad winner in partnership with Rishab Jain breaks down the strategies for you. If you like math at all, the AMC is almost certainly for you, and this guide is a good place to start.
Bonus: USAMTS
I know what some of you are thinking. I hate timed tests, and the whole concept of the AMC makes my brain want to explode. Maybe not in those words, but plenty of students feel it. So listen up.
The USAMTS (USA Mathematical Talent Search) is administered by the Art of Problem Solving Initiative. It’s a proof-based contest that gives you about a month to solve five problems, rigorously proving your work on four of them (the first is usually a puzzle). This repeats over three rounds, for 15 problems total.
15 problems? Three rounds? Piece of cake! Not quite. At the high school level, these can be some of the most difficult, unintuitive problems you’ll ever face, and at first you may not even be sure what a problem is asking. Still, it’s a great option, especially if you prefer untimed, proof-based work.
Great, so this is different from the AMC. How do I even start studying for it?
It may not be as different as you think. Like the AMC, USAMTS tests a high-level understanding of lower-level concepts across a limited number of problems. So the usual study habits, like working through curated content on a topic, still apply, just tweaked for this setting.
What I’d recommend: take the entry-level areas (number theory, probability and counting, algebra, geometry, and so on) and work your way up to the hardest problems in each. The beautiful thing about studying math is that once you can solve the hardest problems and catch your silly mistakes, you can handle anything the exam throws at you.
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