The USA Mathematical Talent Search (USAMTS) is a free mathematics competition open to all United States middle and high school students.
As opposed to most mathematics competitions, which typically place considerable emphasis on solving problems quickly, each round of the USAMTS allows students a full month to work out their solutions to five problems. With the exception of the first problem of every round, which is a puzzle, carefully written justifications are required for each problem. The problems range in difficulty from being within the reach of most high school students to challenging for the best students in the nation. Students may use any materials—books, calculators, computers—but all the work must be their own. The USAMTS is run on the honor system—it is an individual competition, whose competitive role is secondary (although there are prizes).
If interested, you would register and participate on your own. There are 2 more rounds if you are interested. Make sure to discuss with your parents and completely read all of the rules before registering.