FOR THE THIRD straight year, Alex Zhai is one of the top 12 scorers on the United States of America Mathematical Olympiad exam.

The USAMO is the next-to-last step in the process of selecting the six U.S. team members for the International Math Olympiad, "the world's toughest math contest."

Zhai scored 29 out of a possible 42 points to tie for ninth. The past two years he earned the second-highest USAMO score. He has advanced to the USAMO every year since he was a subfreshman.

"I actually thought this year's USAMO was pretty much — the whole process — wasn't that different from other years," Zhai said. "I guess this year I didn't do as well, but I don't think I got any worse. I knew how to do five of the [six] problems [which would have earned him 35 points and tied him for second again]. I'm not sure exactly what happened with one of my solutions."

The 12 USAMO winners will take a final test June 7 and 8 to determine who makes the six-member U.S. team that will compete in the 49th IMO, scheduled for July 10 to 22 in Madrid, Spain.

Zhai has been a member of the last two U.S. IMO teams. He won a silver medal in 2006 and a gold medal last year. In both IMOs, the U.S. team placed fifth overall. At the 2007 IMO, held in Hanoi, Vietnam, Zhai placed seventh individually. The 2006 U.S. team is the subject of the recently released documentary film "Hard Problems."

The Uni senior has already qualified for the 24-member U.S. Physics Team. In fact, he will leave Saturday for an 11-day physics training camp at the University of Maryland at College Park. If he is one of the top five students at the camp, he will be named to the U.S. traveling team, which will compete in this summer's International Physics Olympiad, July 20 to 29 in Hanoi.

A total of 505 students qualified to take the six-question 2008 USAMO exam, which was given April 29 and 30 over the course of nine hours. The exam tests the ability of students to think creatively and elegantly about mathematical problems.

Here are the 12 USAMO winners:

• David Benjamin, Harrison High School, West Lafayette, Ind.
• Taoran Chen, Bayside High School, Flushing, N.Y.
• Paul Christiano, The Harker School, San Jose, Calif.
• Samuel Elder, Poudre High School, Fort Collins, Colo.
• Shaunak Kishore, Unionville High School, Kennett Square, Pa.
• Delong Meng, Baton Rouge Magnet High School, Baton Rouge, La.
• Evan O’Dorney, Berkeley Math Circle, Berkeley, Calif.
• Qinxuan Pan, Thomas Sprigg Wootton High School, Rockville, Md.
• David Rolnick, home school, Rupert, Vt.
• Colin Sandon, Essex High School, Essex Junction, Vt.
• Krishanu Sankar, Horace Mann School, Riverdale, N.Y.
• ALEX ZHAI, UNI HIGH, Urbana, Ill.

The Mathematical Association of America sponsors the series of math contests that culminates in the selection of a U.S. IMO team. More than 225,000 students took the first contest (AMC 10 and/or AMC 12). About 8,600 advanced to the second contest (AIME), and only 505 made it to the USAMO.

An awards ceremony for the 12 USAMO winners will be held in Washington, D.C., at the MAA's headquarters on June 8 and at both the National Academy of Sciences and U.S. Department of State buildings on June 9.

The U.S. IMO team will consist of the six students with the highest combined scores from the USAMO exam and the June 7-8 team selection test. These students will then spend June 10 to July 3 at the University of Nebraska at Lincoln preparing for the IMO.

"I actually feel more experienced in my math," Zhai said. "There's still a certain level of problem that's kind of hard for me in certain subjects. For most of this year I wanted to take a break from Olympiad problems, and I did other math. But I guess I'm starting to get excited about those problems again."

THE ROAD TO THE 2008 INTERNATIONAL MATHEMATICAL OLYMPIAD

The USAMO is the first step in a talent-identification process, sponsored by the Mathematical Association of America, that ends in the selection of a six-member team to represent the United States in the International Mathematical Olympiad. Last year, Alex Zhai won a gold medal and placed seventh individually at the 48th IMO, held in Hanoi, Vietnam. As a team, the U.S. placed fifth in the world. In July 2006, Zhai won a silver medal at the 47th IMO, held in Ljubljana, Slovenia. Here is the road Alex and other American students must travel if they want to take part in this year's IMO, which will take place in Madrid, Spain. All descriptions below are from the American Mathematics Competitions site.

• Feb. 12: American Mathematics Contest 10/AMC 12
  Both the AMC 10 and AMC 12 are 25-question, 75-minute multiple-choice examinations in secondary school mathematics containing problems that can be understood and solved with precalculus concepts. The AMC 10 is for students in grades 10 and below, while the AMC 12 is for students in grades 12 and below.
• April 2: American Invitational Mathematics Examination
  All students who took the AMC 12 and achieved a score of 100 or more out of a possible 150 are invited to take the AIME. All students who took the AMC 10 and had a score of 120 or were in the top 1 percent also qualify for the AIME. The AIME is a 15-question, three-hour examination in which each answer is an integer number from 0 to 999. The questions on the AIME are much more difficult, and students are very unlikely to obtain the correct answer by guessing. As with the AMC 10 and AMC 12, all problems on the AIME can be solved by precalculus methods.
• April 29 & 30: United States of America Mathematical Olympiad
  The USAMO is a six-question, two-day, nine-hour essay/proof examination. All problems can be solved with precalculus methods. Approximately 500 of the top-scoring participants in the American Mathematics Competitions (based on a weighted average) are invited to take the USAMO. U. S. citizens and students legally residing in the United States and Canada (with qualifying scores) are eligible to take the USAMO. Only 12 winners will be selected.
• June 7 & 8: Team Selection Test
  The 12 USAMO winners will take the Team Selection Test to qualify for the six-person U.S. IMO squad.

• June 8 & 9: Olympiad Awards Ceremony
  The 12 top scoring USAMO students are invited to a two-day Olympiad Awards Ceremony in Washington, D.C., sponsored by the MAA, the Akamai Foundation, the Microsoft Corporation, and the Matilda Wilson Foundation. Six of these 12 students will comprise the United States team that competes in the International Mathematical Olympiad. The IMO began in 1959; the USA has participated since 1974.
• June 10 to July 3: Mathematical Olympiad Summer Program
  Located at the University of Nebraska at Lincoln, MOSP provides a mathematics program for a select group of very promising students who have risen to the top on the American Mathematics Competitions. The MOSP gives all participants, including the six IMO team members and two alternates, extensive practice in solving mathematical problems that require deeper analysis than those solved by students in even the best American high schools. Full days of classes and extensive problem sets give students thorough preparation in several important areas of mathematics that are traditionally emphasized more in other countries than in the United States. The MOSP ensures that the IMO record of the United States properly reflects the energy and creativity of its brightest students.
• July 10 to 22: 49th International Mathematical Olympiad
  This year's IMO will take place in Madrid, Spain. Each year since 1974, a small team of exceptionally talented high school students has represented the United States at the IMO, a rigorous two-day competition including problems that would challenge most professional mathematicians. In addition to comprehensive mathematical knowledge, success on the IMO requires truly exceptional mathematical creativity and inventiveness.