A number of interesting olympiads and contests are held every year.
BAMO (Bay Area Math Olympiad) There is more information here.
BAMM (Bay Area Math Meet)
American Mathematics Competitions (Includes AMC8, AMC10, AMC12, AIME, MOSP and USAMO)
IMO (The International Mathematical Olympiad)
SCVMA Math Field Day at San Jose State University
ARML (American Regional Mathematics League)
The Annual High School Math Contest at SCU.
San Jose JACL - Tokutomi Math Contest, given in January at Santa Teresa High School
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