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.
AMC 10? AMC 12? AIME? USAMO? What’s the Difference?
If you’ve read about the AMC. 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.
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?” That’s a great question. 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, since typically only people who are decent at math to begin with will take the test, 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. Correct answers give you 6 points and answers left blank give you 1.5 points; however, incorrect answers give you zero points. This is to discourage random guessing, so it’s only strategic to guess if you’ve eliminated a few of the answers.
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. So you can take the AMC 10A and 10B, or the AMC 10A and 12B, but not the AMC 10A and 12A. This is because questions on the AMC 10 are often reused on the AMC 12 in the same version of the test.
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.
List of Resources to Help Prepare for the AMC 10/12
Past AMC 10 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. Here is a link to past AMC 10 exams, which is useful for taking practice tests to get a feel for the timing and level of difficulty.
Past AMC 12 exams, answers and explanations: Same as above, these are practice tests for the AMC 12.
Many sites recommend the Art of Problem Solving textbooks, 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.
Summer camps are a great way to hone your problem-solving skills and gain exposure to more difficult math questions. Some possible summer camps include PROMYS, AwesomeMath, and others.
There are many YouTube videos that cover skills that would be helpful while taking the AMC, such as the ones in this playlist. This is a great, free resource for students looking for related content.
AMC Trainer: Contains problems similar to ones often seen on the AMC, allows for practice on a daily basis.
The Puzzlr: They offer a free crash course for AMC 10 preparation.
Conclusion
Whether you are a novice or a seasoned participant, we hope this complete guide has inspired you to embark on your AMC journey with confidence and enthusiasm. Let the American Mathematics Competition be a platform for personal growth, a testament to your mathematical abilities, and a gateway to endless opportunities.
Remember, mathematics has the power to shape the world and transform lives. Embrace the challenge, believe in your abilities, and let the AMC be the catalyst for unlocking your mathematical potential. Good luck, and may your journey be filled with excitement, growth, and countless "aha!" moments.
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