Senior Alex Zhai is vying for his third straight spot on America's International Mathematical Olympiad team. Gargoyle photo by Sindha Agha (click to enlarge)

FOR THE FIFTH consecutive year, Alex Zhai has made it to the United States of America Mathematical Olympiad, also known as the USAMO.

Taking the USAMO exam is the next-to-last step in the process of determining who will represent the United States at the International Math Olympiad. Zhai will take the six-question, nine-hour exam on April 29 and 30. He is vying for his third straight spot on the U.S. team.

The senior qualified for the USAMO as a result of his scores on both the American Invitational Mathematics Examination II (AIME II, given April 2) and the American Mathematics Contest 12 (AMC 12, given Feb. 12).

Zhai has been invited to participate in the USAMO every year since he was a subfreshman.

In the USAMO selection process, each student has an “index,” calculated by adding the AMC score to 10 times the AIME score. This year, an index of 204 qualified students to take the USAMO.

Zhai's index was a near-perfect 290. He scored a perfect 150 on the AMC, followed by 14 out of a possible 15 on the AIME II. He missed a perfect index by just 10 points. Last year he had an index of 280 (150 AMC, 13 AIME).

A total of 8,624 students took the AIME this year: 5,476 on March 18 (AIME I), and 3,148 on April 2 (AIME II). Only 486 of those students made the USAMO cut, including just 25 from Illinois.

Besides Zhai, five other Uni students took the AIME II after qualifying on the AMC 12: seniors Geoffrey Beck, Ethan Berl, and Mike Renner, and juniors Allan Luo and Brian Wang. The national average on the AIME I was 4.93; the average AIME II score was 5.31.

Zhai was the only Uni student to advance to the USAMO, bringing him one step closer to representing the United States again at the International Mathematical Olympiad.

The top 12 scorers on the USAMO will be invited to a two-day Olympiad Award Ceremony in Washington, D.C., June 8 and 9.

While in Washington, the USAMO honorees will take one last exam, which will determine the six students who will represent the United States in this year's IMO, to be held July 10-22 in Madrid, Spain.

Zhai, a senior, has been a member of the U.S. IMO team for the past two summers. Last year, he 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 in his first IMO, held in Ljubljana, Slovenia.

THE ROAD TO THE 2008 INTERNATIONAL MATHEMATICAL OLYMPIAD

Alex Zhai has now reached the next-to-last step in the Mathematical Association of America's process for selecting a six-member team to represent the United States in the 2008 International Mathematical Olympiad in Madrid, Spain. Here is the road Alex and other American students must travel if they want to take part in the 49th IMO. All descriptions below are from the American Mathematics Competitions site. Follow the provided links to see the original material.

• 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.
• 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 final six will be determined by yet another exam, which the students will take during their time in Washington. 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.