Here are some helpful links for past tests:

**Middle school** level ( AMC 8, Mathcounts)

Mathcounts

Mathcounts current year

AMC 8

**AMC 10/12** level:

AMC 10

AMC 12

**AIME** level and harder:

AIME

Math Prize for Girls

HMMT

PUMaC

**Other**: If you want to prepare for ARML or Alabama Local Competitions:

ARML

Alabama Local

**Learning Tools:**

Alcumus (will need AoPS account)

**AoPS Mocks:**

AoPS Community Members’ Past Mock AMC’s

Mock AIME’s

Mock Test Forum on AoPS

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)

FAMAT (Florida)

Purple Comet

John Hopkins

**At least AMC-AIME level:**

Duke

Caltech-Harvery Mudd

Carnegie Mellon

Stanford

Online Math Open (Easy AMC to hard IMO)

**Overly Hard Middle School**

Exeter Math Club Competition

Math Open at Andover

**Olympiads:**

USAMO

IMO ShortList

**Easier Olympiad:**

British

Canadian

**Other Olympiad:**

European Girls Math Olympiad

China Girls Math Olympiad

**Calculus Practice Problems:**

MIT Integration Bee

Black Pen Red Pen

HMMT Feb pre-2012

**Algorithms/Computer Science:**

Carnegie Mellon (there are many more actually programming competitions)

**Physics:**

F=MA

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