Even before I had participated in any formal tournaments or competitions, I knew that I took a liking to mathematics. My first experience in competitive math was MATHCOUNTS, in sixth grade, and since then I have participated in dozens of tournaments at the middle and high school level. To see any collegiate math classes I've taken, please refer to my past coursework.
All of this experience in scholastic level math allowed me to take on a position as a local community tutor in high school and teach the youth in my area.
American Regions Mathematics League (ARML)
ARML hosts an annual, prestigious math tournament in the early summer. The competition usually hosts almost 2000 students (primarily high school but a few exceptional junior high students as well). After being invited to the Lehigh Valley ARML team during my junior year of high school, I went to bi-weekly practices for about 5 months prior to the competition in the summer of 2007. I was selected captain of Ice Team (Lehigh Valley's second division team) and competed in the ARML competition during the summer of 2007; the Ice Team finished 17th out of 79 teams. Historically, Lehigh Valley has been one of the known leaders in the ARML competitions (in-depth results for 2007 season and Lehigh Valley's other seasons are available here).
Here are some sample ARML questions.
Harvard-MIT Mathematics Tournament
During the February of my junior year in high school, I competed in the annual HMMT. The HMMT is a joint effort of student organizations from both Harvard and MIT, held at Harvard and at MIT on alternate years. Each of the roughly 900 competitors either chooses two "subjects" (such as Calculus, Geometry, Algebra, etc.) which to study or takes the General Math examination on the tournament day. I took the general math examination and scored 51 points out of the 80 possible (archived results, practice examinations, and tournament information is all available at HMMT website).
Here are some sample HMMT questions.
AMC 8, AMC 12, AIME
The American Math Competitions (AMC) releases examinations for the 8th, 10th, and 12th grade level each year. Fortunately, my middle school offered the AMC 8 and my high school administered the AMC 12. I had the best AMC 8 performance in the county, and my AMC 12 performance allowed me to take the invite-only AIME later that year. Unfortunately, I did not perform well enough to move on to the USAMO, a proof-intensive prestigious math competition.
Lehigh Valley Math Competition
Don Davis of Lehigh Valley hosts a math competition each spring consisting of 40 questions. The top scorers each year are invited to be a part of the Lehigh Valley ARML team, one of the leading ARML teams in the country. I have competed in this competition four times, finishing 4th place (in my grade) twice. During my junior year, my score qualified me to compete in the ARML competition for Lehigh Valley.
Here are some sample Lehigh Valley Math Competition questions.
U-Pitt High School Integration Bee
My father and I had attended the Pitt college integration bee for a few years, and had thought that it would be a wonderful opportunities for high school students as well to compete in a similar competition. Fortunately, Pitt professor Jon Rubin took it into his own hands to start a high school level integration bee. I have competed in this bee ever since its inception, winning third and second place in 10th and 11th grade respectively, but was never able to clench the first place title.
Marywood Math Competition
Marywood High School hosts an annual math contest for high schoolers towards the end of march. I competed in this competition during my sophomore and junior years in high school, winning first place both times. Not only was prize money a good incentive for this competition, but this contest kept me on my feet for the national ARML tournament later in my junior year.
Here are some sample Marywood Math Competition questions.
Gannon University Applied Math contest
Gannon University hosts an applied math, or engineering/math contest to sophomores and juniors in high school. Not only can the contestants walk away with bragging rights, but Gannon offers scholarship of varying amounts to the top three performers at this annual competition. I finished first place as a 10th grader, but wasn't able to exercise the scholarship as I enrolled in Carnegie Mellon for undergraduate study.
During my 7th and 8th grade middle school years I competed the nationally recognized MATHCOUNTS competition. MATHCOUNTS was my first introduction to competitive math, and I loved it. From the regular after school team practices to the anxious feeling of a tournament, there was something I enjoyed about competing which has stuck with me. Although I was never able to progress out of the regional level of MATHCOUNTS, the two times I made it to the countdown round were some of the most memorable experiences I have from middle school.
My middle and high schools offered, through a program known as SAL, a variety of competitions from science tournaments to english contents. The ones I looked forward to the most, naturally, were the math competitions such as Equations and Calcusolve. Having competed in dozens of SAL competitions, I even wrote some of the problems for the math competitions that our school would host. Competing in low pressure, regional competitions such as SAL events was a good break from big tournaments such as ARML or HMMT, and would help me brush up on my math as well.