The AMC 10 and AMC 12 are the most prestigious high school math contests in the US, and the first step on the path to the International Mathematical Olympiad (IMO).
This guide covers the format, scoring, cutoffs, and how to prepare, whether it’s your first time or you’re pushing for an AIME qualification.
💡 Rishab’s take: The AMC rewards speed and pattern recognition over deep theory. The highest-return prep is working old papers under the real 75-minute clock until the recurring problem types feel automatic — that beats grinding textbooks.
Rishab Jain
What Is the AMC 10 and AMC 12?
The AMC 10 and AMC 12 are math contests built to test problem-solving, not memorization. The AMC 10 is open to students in grades 10 and below, and the AMC 12 is open to students in grades 12 and below.
Questions cover algebra, geometry, number theory, and combinatorics, with a mix of easier and harder problems. The reward is for clever approaches, not for plugging into formulas.
Why Participate in the AMC 10/12?
- Boost college applications: A strong score is a clear, recognized signal of math ability.
- Scholarships and recognition: High scorers earn distinctions and qualify for further awards.
- A pathway to bigger competitions: Doing well qualifies you for the AIME (American Invitational Mathematics Examination), which leads to the USA(J)MO and, eventually, the IMO.
- Sharper problem-solving: The prep itself builds analytical thinking that pays off well beyond the contest.
AMC 10/12 Format and Scoring
- Duration: 75 minutes
- Questions: 25 multiple-choice questions
- Scoring:
- +6 points for each correct answer
- +1.5 points for each question left blank
- 0 points for each incorrect answer
The highest possible score is 150 points. There is no penalty for a wrong answer, but a blank is worth 1.5 points, so a careless guess can actually cost you. More on that below.
AMC 10/12 Cutoff Scores
Cutoffs to advance to the AIME are set each year by percentile, so the exact number moves with the difficulty of the test:
- AMC 10: roughly the top 2.5% of scorers qualify. Recent cutoffs have landed around 100 to 110.
- AMC 12: roughly the top 5% qualify, and the cutoff is usually lower than the AMC 10’s.
Preparation Strategies
- Know the syllabus
- The AMC 10 covers math through 10th grade; the AMC 12 goes through 12th grade. Focus your review on:
- Algebra (equations, inequalities, sequences)
- Geometry (circles, triangles, coordinate geometry)
- Combinatorics (counting, permutations, combinations)
- Number theory (divisibility, primes, modular arithmetic)
- Probability (basic principles, expected value)
- The AMC 10 covers math through 10th grade; the AMC 12 goes through 12th grade. Focus your review on:
- Build a study plan
- Set aside time each week. Start with easier problems to build confidence, then work up to harder ones.
- Do past papers, then analyze them
- Past AMC 10/12 exams are on the official MAA website. The real gains come from studying the problems you missed, not just racking up attempts.
- Use strong resources
- A few that work well:
- Art of Problem Solving (AoPS): courses and practice material built specifically for the AMC.
- The AoPS online community: an active forum where students work through problems together.
- Books: Introduction to Geometry by AoPS, and Competition Math for Middle School by Jason Batterson for the fundamentals.
- A few that work well:
- Manage your time on test day
- You have about 3 minutes per question on average. Don’t let one hard problem eat your clock; move on and come back.
- Guess only when the odds are in your favor
- A blank is worth 1.5 points. A random guess among five options averages only about 1.2, so it actually costs you. Only guess when you can eliminate at least two choices, which pushes the average above 1.5 and makes the guess worth it.
During the Exam
- Stay calm: Nerves slow you down. A few slow breaths before you start help more than you’d think.
- Work the easy ones first: Bank the points you’re sure of, then spend your remaining time on the hard problems.
- Check your work: Use any leftover time to re-verify answers, especially ones you rushed.
Beyond Math: Take On Science Competitions Too
If you like problem-solving, why stop at the AMC? The same instincts carry straight into science and engineering competitions. ScienceFair.io helps high and middle school students plan, build, and present a competitive STEM project, from the first idea to the final judging.
Book a consultation call to talk through your project and get a plan that fits where you’re starting from, or browse ScienceFair.io’s coaching to see how it works.
What ScienceFair.io offers
- AI Discovery Engine: generate research ideas drawn from thousands of past projects.
- Step-by-step research guide: a clear path from a rough idea to a finished project.
- Tuner: sharpen your project title and abstract so your work stands out to judges.
- AI judging tool: practice the Q&A with simulated judge questions before the real thing.
- Expert coaching: one-on-one mentorship from past winners through the A-Z Science Fair Masterclass and coaching calls.
Explore the tools at ScienceFair.io and start building a project that can win.
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