Senior Alex Zhai recently scored a perfect 150 on the American Mathematics Contest 12 exam, and he barely broke a sweat. This is par for the course for Uni's resident math prodigy, who has represented the United States twice at the International Mathematical Olympiad. This is the second straight year he has scored 150 on the AMC, which consists of 25 multiple-choice questions and a 75-minute time limit. In 2007, Zhai was one of only 20 American students who recorded a perfect score out of 126,000 people who took the exam. (Six foreign students also had perfect scores.) The Gargoyle catches up with Alex to get his reaction to the AMC results and find out his thoughts about a possible third IMO appearance.

What's your reaction to the perfect score? Did you set that as a goal?

I didn't really set this as a goal, since I knew I would be able to do all of the problems. It was mainly a matter of not making any careless mistakes.

What kind of preparation did you do for the AMC?

Mostly it was drawing on a lot of experience accumulated from previous years that allowed me to do well. This year, I didn't really practice for either the AMC or the next round, the AIME, because I feel I've already learned everything that I can learn from those problems. I have been helping other students prepare, though, so that could have kept me in practice.

How would you describe the AMC in terms of difficulty and type of material covered? How challenging is it?

The AMC covers standard high school math plus a few additional concepts that might not be covered in every school. The first few problems are routine calculations, but they quickly become more involved, and the AMC really tests that students can take a situation and understand the essence of what is going on. Generally, you don't need to know obscure formulas or techniques to do well.

How would you assess the evolution of your performance over the past five years of taking the AMC? What have you learned about your own mathematical abilities?

I think that in my subbie, freshman, and sophomore years, I steadily improved and gained experience, which allowed me to solve the harder problems of the test. I started not to pay as much attention to the AMC after sophomore year, because at that point I could pretty much do all the problems. But this year, I finished with a considerable amount of time left, and I think it does reflect an increase in thinking efficiency over the years.

What are your math goals for the remainder of the year?

As far as contests go, the focus will be the USA Math Olympiad and the International Math Olympiad. I don't like setting specific numbers as goals, but I'd like to try to get a perfect score on the IMO. I'm not actually sure about that goal yet. More importantly, I think, I want to be able to do some of the very hard Olympiad problems that I can still learn a lot from. I just focus on improving, and I think that if you improve at math in general, the results will follow. I also hope to learn some more college math, although I don't have specific goals for that.

How much time do you spend on math outside of your course work?

It's hard to quantify, because I like to read math books or work on math problems whenever I have nothing else to do. I would estimate that over the past four years, I've spent at least an average of one hour per day doing something math-related.

THE ROAD TO THE 2008 INTERNATIONAL MATHEMATICAL OLYMPIAD

The AMC 12 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. 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 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.