Here are some International Mathematical Contests. The following are mirrored files, so I am not the author of them. (In parentheses, the website from which they are taken.)

The Asian Pacific Mathematical Olympiad:

Pdf  files from: 1989, 1990 , 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1999, 2001, 2002.(Copyright Asian Pacific Competition.)
                     
The Austrian Polish Mathematical Competition:
 
Pdf  files from: 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001.(Copyright Poland in Mathematical Olympiads.)

The Baltic-Way Mathematical Competition:

 
Pdf  files from: 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001.(Copyright Poland in Mathematical Olympiads.)

                                   
The Balkan Mathematical Olympiad:
 
Pdf  files from:1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995,
1996, 1997, 1998, 1999, 2000, 2001, 2002.(Copyright Andrei Jorza.)
                                                                                                           
The USA Mathematical Olympiad:
 
Pdf files from: 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,
2001, 2002.(Copyright Kiran Kedlaya, 1989-2002.)

The International Mathematical Olympiad:
 
Pdf files from: 1986, 1987, 1988, 1989, 1990,1991, 1992, 1993,19941995, 1996, 1997, 1998, 1999, 2000, 2001, 2002. (Copyright Kiran Kedlaya,1986-2001.)

Here are some other Mathematical Contests (I personally typed all the files) :

The Romanian Mathematical Olympiad

Pdf files from:1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002(Solutions).                         

The Junior Balkan Mathematical Olympiad Romanian Selection Tests:

Files from: 2000(DVI/PDF/PS), 2001(DVI/PDF/PS), 2002(DVI/PDF/PS).


The Junior Balkan Mathematical Olympiad:

Files from:1999(DVI/PDF/PS), 2000(DVI/PDF/PS), 2001(DVI/PDF/PS),
2002(DVI/PDF/PS,solutions).

The Romanian Selection Tests for the:

43rd IMO PDF.

The American Selection Tests for the:

43rd IMO(DVI/PDF/PS).

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