AMC 10/12 | Olympiad Insider

Introduction to the AMC 10/12

What is the AMC 10/12?

The AMC 10 and 12 are national mathematics competitions for students who are younger than or enrolled in Grade 10 and 12, respectively. It is written and scored by the Mathematical Association of America (MAA) and proctored by a local school or learning center. Calculators and graphing devices are not permitted. Each year, there is an A and B version. Each version has its own cutoffs for AIME qualification and other distinctions. Students are allowed (and encouraged) to take both, as it allows them another chance to get a high score.

Summary

What is tested on the competition?

The AMC 10 includes topics in the high school curriculum through Algebra II and Geometry. In addition, number theory and combinatorics (counting and probability) are also tested.

The AMC 12 tests the entire high school curriculum, with the exception of Calculus. Topics on the AMC 12 include all the topics tested on the AMC 10, plus trigonometry and advanced Algebra.

An approximation of the topic distribution on the AMC 10/12 is below.

How is the test scored?

The AMC 10/12 are scored in a way that penalizes guessing.

Correct Answer: 6 points awarded

Blank Answer: 1.5 points awarded

Incorrect Answer: 0 points awarded

Total: 150 possible points.

Because there are five answer choices for each problem, the expected value for guessing at random is 1.2 points, which is less than the 1.5 points awarded for blank answers. Therefore, you should not guess unless you can eliminate at least 1-2 answers (which raise your expected value to 1.5 and 2 points, respectively.).

Are there awards?

The awarding criteria for performance on the AMC 10/12 is below.

Perfect Score: This is a huge accomplishment, usually achieved by less than ten participants annually.

Honor Roll of Distinction: This award is given to the top 1% of scorers. Cutoffs vary by year, but is usually between 120 and 136.5 for the AMC 10 and between 127.5 and 139.5 for the AMC 12.

Distinction: This award is given to the top 5% of contestants. Cutoffs can also vary by year, and is usually between 100 and 115 for both the AMC 10 and 12.

AIME Qualification: Passing this special threshold allows the student to continue his or her journey in the AMC series, by qualifying the student to take the American Invitational Math Exam (AIME), the second round of the competition. The MAA invites at least the top 2.5% of AMC 10 scorers and at least the top 5% of AMC 12 scorers. However, in recent years, the MAA has invited many more students, making the AIME floor usually around the top 6% of the AMC 10 and the top 12% of the AMC 12. In recent years, the AIME cutoff for the AMC 10 has ranged from 94.5 to 105, and 85.5 to 93 for the AMC 12. To learn more about qualifying for the AIME, read this blog post.

What can I do to prepare for the AMC 10/12?

To prepare for the AMC 10 or AMC 12, learning the content tested is the first step. Most topics covered are not covered in traditional school math classes, and even those that are will be explored at a deeper level in competitions. The quickest way to methodically attain a basic understanding in these topics is the AoPS book Volume One by Sandor Lehoczky and Richard Rusczyk. Volume One is the perfect introduction to competition math, exploring introductory-level ideas in Algebra, Geometry, Combinatorics, and Number Theory. Volume One provides the foundation for a student to solve around 14-17 problems on the AMC 10. For the AMC 12, the book Volume Two, by the same authors, will prove fruitful. Volume Two explores deeper mathematical concepts, such as Fibonacci Numbers, Pascal's Identity, and Diophantine equations.