The Complete Guide to the American Mathematics Competition (AMC)

The American Mathematics Competition is a prestigious series of exams organized by the Mathematical Association of America (MAA), aimed at fostering mathematical talent and cultivating problem-solving skills among high school students. It offers a unique opportunity to test one's mathematical prowess, engage in friendly competition, and gain recognition for exceptional achievements in the field.

Competition Levels: AMC 10, AMC 12, AIME, and USAMO

If you’ve read about the AMC, you might wonder about the differences between the levels. The AMC 10 is for students who are in Grades 10 or below, while the AMC 12 is for students who are Grades 12 or below. There is also the option for middle schoolers to take the AMC 8, which is for students in Grade 8 or below. For each competition, there are age limits that correlate with the grade levels.

The AIME, short for the American Invitational Mathematics Examination, is the next step after the AMC; the top 2.5% scores of the AMC 10 and the top 5% of the AMC 12 scores are able to qualify. Furthermore, the top 200 scorers on the AIME and on the AMC are then invited to take USA's national math olympiad (USAMO if you took the AMC 12, or USAJMO if you took the AMC 10). Getting to this point is extremely hard, and only the top participants in the country (top 200 to be precise) can qualify. From there, the members of the USA Math Olympiad team are selected. Only the truly, truly top students in the nation will get to this point.

The Case for Taking the AMC

You may ask, “Why take the AMC at all?” Well, here are a few benefits of taking this challenging math test:

• IMPROVE YOUR PROBLEM-SOLVING SKILLS: Problems that you will see on the AMC differ from problems you’ll see at school in that they emphasize creative problem-solving skills, with questions that probe deeper than just surface-level knowledge. Students will have to apply what they know in complex and unique ways, different from what they typically see in a school setting. This means that preparing and taking the AMC will challenge students to push themselves to their limits.
• QUALIFY FOR THE AIME: Qualifying for the AIME is a pretty significant achievement, and you should feel proud of yourself if you do so! Taking the AMC is the only way to qualify for this test, so you should definitely consider giving it a try.
• STAND OUT IN COLLEGE ADMISSIONS: Even if you don’t qualify for the AIME, scoring well on the AMC will catch colleges’ eyes. While colleges also look at standardized tests such as the SAT, contests like the AMC are not only more difficult but are pre-selective, which means that being in the top 10% of AMC scorers will put you in a smaller pool of people than being in the top 1% of SAT scorers. Many prestigious universities, such as MIT, Carnegie Mellon, and Caltech, also ask for your AMC score if you have taken it.

Format of the AMC 10/12

The AMC 10 and 12 are both 75 minutes, with 25 questions. The questions are multiple choice, with 5 possible answers. The scoring is designed to discourage random guessing, so it’s only strategic to guess if you’ve eliminated a few of the answers. The rules for scoring are as follows:

• Correct answers: 6 points
• Answers left blank: 1.5 points
• Incorrect answers: 0 points

There are two different versions for both AMC tests: A, and B. You are allowed to take both of the versions, but not the same version in both the AMC 10 and AMC 12. This is because questions on the AMC 10 are often reused on the AMC 12 in the same version of the test.

Difficulty and Preparation Resources

If you’re worried about whether or not you have the math skills, do not! The AMC tests only the usual high school-level math: algebra, geometry, etc. Calculus knowledge is not required. The difficulty level of the test comes from the critical, out-of-the-box thinking needed to solve the problems, not the content in the problems itself. To help you prepare, here are several resources:

• Past AMC 10 and 12 exams, answers and explanations: The best way to prepare is just to take a lot of practice tests and get used to the style of the questions. This is useful for taking practice tests to get a feel for the timing and level of difficulty.
• Art of Problem Solving textbooks: Many sites recommend these books, which go over a lot of high school level math topics as well as useful theorems that can be used to solve problems. Volume 1 is a recommended read for students taking the AMC 10, and Volume 2 is recommended for students taking the AMC 12.