The American Mathematics Competitions (AMC) exams are hosted by the Mathematical Assosciation of America (MAA).  Their mission is to increase interest in mathematics and develop problem solving skills with challenging questions that are aligned with curriculum standards at all levels of difficulty. These competitions allow students to compete on a local and global level.

The following are the basics about the various exams:

• AMC 8: The AMC 8 is a 25 question, 40 minute multiple choice examination in junior high school (middle school) mathematics designed to promote the development and enhancement of problem solving skills. The examination provides an opportunity to apply the concepts taught at the junior high level to problems which not only range from easy to difficult but also cover a wide range of applications. Many problems are designed to challenge students and to offer problem solving experiences beyond those provided in most junior high school mathematics classes. Calculators are NOT allowed. The AMC 8 offers different levels of awards for high scoring students. Those who are in 6th grade are lower with a score of 15/25 recieve a Certificate of Merit. Then, the total top 5% (students who scored about 18/25) are awarded with the National Honor Roll, while the top 1% (about 22/25 or higher) have the National Distinction Honor Roll. The highest performing students are invited to participate in the AMC 10, which may lead to even more challenging tests. Last year, over 170,000 students participated in the AMC 8 worldwide. Everyone who participated, regardless of their score or the questions they were able to complete, was encouraged to learn more mathematics outside of their regular school curriculum. If your child participates this year, they too can grow just by taking the test.
• AMC 10: The AMC 10 covers mathematics normally associated with grades 9 and 10 and is for students under 17.5 years of age who are not enrolled in grades 11, 12 or equivalent. The contest is given in a convenient 75-minute interval, is 25 questions in length, with approximately 12 questions in common to both contests. The AMC 10 is administered in schools in February. The main purpose of the AMC 10 is to spur interest in mathematics and to develop talent through the excitement of solving challenging problems in a timed multiple-choice format. The problems range from the very easy to the extremely difficult. Students who participate in the AMC 10 should find that most of the problems are challenging but within their grasp. The contest is intended for everyone from the average student at a typical school who enjoys mathematics to the very best student at the most special school.
• AMC 12: The AMC 12 covers high school mathematics, and is for students in high school who are under 19.5 years of age. The contest is given in a convenient 75-minute interval, is 25 questions in length, with approximately 12 questions in common to both contests. The AMC 12 is administered in schools in February. The main purpose of the AMC 12 is to spur interest in mathematics and to develop talent through solving challenging problems in a timed multiple-choice format. What happens before and after the AMC 12 can have lasting educational value. Talents will be enhanced if one practices beforehand, by working through previous examinations, by participating in math leagues and, most importantly, by studying mathematics more intensely than one normally does in high school.
• AIME: The American Invitational Mathematics Examination (AIME) is a 15 question, 3 hour examination in which each answer is an integer number from 0 to 999. Students will qualify for the AIME and can participate in the AIME only they score 120 or above on finish in the top 1% of the AMC 10, or if a student scores 100 or above or finishes in the top 5% of the AMC 12. The AIME is intended to provide further challenge and recognition, beyond that provided by the AMC 10 or AMC 12, to the many high school students in North America who have exceptional mathematical ability. The questions on the AIME are much more difficult and students are very unlikely to obtain the correct answer by guessing. The AIME is administered in schools in March. The top scoring U.S. citizens and students legally residing in the United States and Canada (with qualifyng scores, based on a weighted average) are invited to take the USAMO. As with the AMC 10 and AMC 12 (and the USAMO), all problems on the AIME can be solved by pre-calculus methods. The use of calculators is not allowed.
• USAJMO/USAMO: The USAMO is a six question, two day, 9 hour essay/proof examination. The Junior Mathematical Olympiad or USAJMO contest better meets the level of young students. The USAJMO new contest bridges the computational solution process of the AIME and the proof orientation of the USAMO. Both are administered the last week of April. All problems can be solved with pre-calculus methods. Approximately 270 of the top scoring AMC 12 participants (based on a weighted average) are invited to take the USAMO. Approximately 230 of the top scoring AMC 10 participants (based on a weighted average) are invited to take the USAJMO. U.S. citizens and students legally residing in the United States and Canada (with qualifying scores) are eligible to take the USAMO and USAJMO.

For more in-depth descriptions of these tests please visit the AMC FAQs.