Here are some helpful links for past tests:
Middle school level ( AMC 8, Mathcounts)
AMC 10/12 level:
AIME level and harder:
Other: If you want to prepare for ARML or Alabama Local Competitions:
Learning Tools:
Alcumus (will need AoPS account)
AoPS Mocks:
AoPS Community Members’ Past Mock AMC’s
Note not all mocks in the above link are high quality (i.e. nice problems had at least as hard as the actual contest). Some may be troll. Take with some skepticism of quality.
OTHER:
Lexington (AMC level)
Mu Alpha Theta (lower quality, easier problems)
At least AMC-AIME level:
Online Math Open (Easy AMC to hard IMO)
Overly Hard Middle School
Olympiads:
Easier Olympiad:
Other Olympiad:
Calculus Practice Problems:
Algorithms/Computer Science:
Carnegie Mellon (there are many more actually programming competitions)
Physics:
Xinke's Math Academy 