The American Mathematics Competition (AMC) is one of the most prestigious and challenging math contests in the United States, designed to inspire and recognize students with exceptional mathematical abilities. It offers an exciting opportunity to showcase your talent on a national stage. The AMC is a series of examinations ranging from the AMC 8 for middle school students to the AMC 10 and 12 for high schoolers. Winning or achieving a high score on the AMC can open doors to further prestigious competitions like the American Invitational Mathematics Examination (AIME) and the USA Mathematical Olympiad (USAMO), which can significantly enhance your academic portfolio. Beyond the accolades, participating in the AMC sharpens your problem-solving skills, deepens your understanding of mathematical concepts, and connects you with a community of like-minded peers who share your passion for math.
But winning the AMC is no small feat. It requires not just raw mathematical talent, but also strategic preparation, mental endurance, and a solid grasp of the exam’s unique format. That’s where this blog comes in. In the following sections, we’ll break down the key strategies and study techniques that will set you on the path to success. We’ll cover everything from mastering the essential content areas to managing your time effectively on exam day. Whether you’re a first-time participant or a seasoned competitor, this guide will provide the insights and tools you need to achieve your best possible performance in the AMC.
Eligibility and Registration
Before you take the AMC, you must make sure that you are eligible to take it and know how to register. There are three versions of the AMC; AMC 8, AMC 10, AMC 12. These are made for different grade levels.
Eligibility
The three different versions of the AMC have different eligibility requirements, shown below:
- AMC 8: Typically for students in grades 8 and below.
- AMC 10: For students in grades 10 and below and under 17.5 years of age on the day of the contest.
- AMC 12: For students in grades 12 and below and under 19.5 years of age on the day of the contest.
Note that for example, if you are in 9th grade, you may elect to participate in either the AMC 10 or the AMC 12.
Registration
School Registration: Schools typically handle the registration process for their students. It’s important for you to communicate with their math teacher or school administrator to ensure they are registered.
Alternative Registration: If a student’s school doesn’t offer the AMC, they can look for nearby schools or institutions that are hosting the exam. Some online math programs also administer the AMC.
Deadlines: Pay close attention to registration deadlines. Schools usually need to register a few weeks before the exam date, so it’s important to inquire and complete registration in advance.
Fees: There may be a small fee associated with registering for the AMC, either paid by the school or by the student’s family. Ensure that this is handled well before the deadline.
Exam Format
Multiple Choice Questions: The AMC exams consist of 25 multiple-choice questions with 5 answer choices each.
Scoring System:
- AMC 10 and 12: 6 points for each correct answer, 1.5 points for each unanswered question, and 0 points for each incorrect answer.
- AMC 8: 1 point for each correct answer, with no penalty for incorrect answers.
In expectation, you will get 1.2 points if you guess randomly. This means that there is a guessing penalty and it will benefit you to leave questions blank unless you can eliminate at least two choices.
Since higher levels of the competition require that you not only get a qualifying score for AIME, but still take into account the AMC (i.e. USAMO uses a combination of AMC and AIME scores to create a selection index), it is in your best interest to aggressively try to get points rather than conservatively leave questions blank in an effort to just get a qualifying score.
Resources
The best way to practice for the AMC is to look at previous exams and practice those questions. The Art of Problem Solving has a section with past exams for the AMC, as well as other math competitions.
Conclusions
If you are interested in mathematics, you have probably thought about doing research in the field at some point, as well as competitions that assess your skills in the subject. One way you can pursue this is by registering for the International Research Olympiad. This nonprofit competition had over 1000 participants last year and an in-person finals event at Harvard University. The Olympiad aims to meritocratically assess research capabilities.
Full disclosure: While I am on the board of the IRO, I do believe that it is a genuinely valuable competition. Board members are not compensated monetarily by the IRO.
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