United States of America Junior Mathematical Olympiad
The United States of America Junior Mathematical Olympiad (USAJMO), along with the USAMO, are the third exams in the series of exams used to challenge bright students on the path toward choosing the team that represents the United States at the International Mathematics Olympiad (IMO).
About 60 top scorers of the USAJMO and USAMO are invited to participate in the Math Olympiad Summer Program (MOP), a challenging 3 to 4 week math program for the brightest students in the country.
The USAJMO is administered by the Mathematical Association of America (MAA). Art of Problem Solving (AoPS) is a proud sponsor of the MAA.
| USAJMO |
| Region: USA |
| Type: Proof |
| Difficulty: 6-7 |
| Difficulty Breakdown:
Problem 1/4: 6 |
Format
The USAJMO is a proof-based examination taken by approximately 250 of the highest scoring students in the AMC 10 and AIME exams. The competition takes place over 2 consecutive days. Each day, 3 problems are given to the students to work for 4.5 hours. Responses are assessed based on correctness, completeness, and clarity and are subsequently awarded between 0 and 7 points, making the maximum score 42. Since most students receive limited exposure to proofs in high school, scores in the single digits are common.
Curriculum
The USAJMO is best approached by students with a solid command of topics in algebra, geometry, number theory, and combinatorics and a host of rigorous methods such as induction and proof by contradiction. Students who do well on the USAJMO have considerable experience in both solving highly challenging problems and writing proofs. Following the general format of high school competitions, the USAJMO does not require calculus or related topics, though proofs using higher mathematics are accepted.
Resources
Links
- The MAA's official webpage for the AMC and its Invitational Competitions page
- The AoPS Wiki's USAJMO Problems and Solutions page
- The AoPS Contest's USAJMO, National Olympiads, and Team Selection Tests folders
- The AoPS Contests & Programs Forum for contest related discussions
- AoPS User created mock USAJMOs, an abundance of mocks designed to mimic real USAMO tests, compiled here in AoPS Contests
- Evan Chen's Math Contest Platitudes blog, a guide to contest preparation, and website
Books & Classes
- The Art of Problem Solving Volume 2 by Richard Rusczyk and Sandor Lehoczky
- Euclidean Geometry in Mathematical Olympiads and The OTIS Excerpts by Evan Chen
- USA Mathematical Olympiads 1972-1986 by Murray Klamkin (Editor) (ISBN 978-0883856345)
- Countdown: The Race for Beautiful Solutions at the International Mathematical Olympiad by Steve Olson (ISBN 0-618-56212-5)
- The AoPS Online School, including the Worldwide Online Olympiad Training (WOOT) program designed to help students train for the USAMO, other national Mathematics Olympiads, and the IMO.
- The AoPS Math Jams, some of which are devoted to discussing problems of the USAMO
