Mildorf Mock AIME
Mock AIME Series
Thomas Mildorf
November 24, 2005
The following are five problem sets designed to be used for preparation for the American Invitation Math Exam. Part of my philosophy is that one should train by working problems that are more difficult than one is likely to encounter, so I have made these mock contests extremely difficult.
The idea is that, once you become acclimated to them, the real AIMEs will seem easier, and you will approach them with justifiable confidence. Therefore, do not be discouraged when working your way through this document. It is expected that you will find these problems and solutions extremely challenging. Although there is no fixed set of rules for practicing, you might try working each batch of problems under standard AIME conditions. Essentially, that means no calculators are allowed, the testing period is 3 consecutive hours, all answers are integers from 000 to 999 inclusive, and there are no penalties for guessing. An appoximation of the cover of the actual AIME phamphlet preceeds each problem set1 ; the cover will list the official testing parameters, including any slight changes from past years. Although in the AMC could change the rules, as they have for the AMC10/12 contests, they have been consistent when arbitrating the AIME. That said, the rules for
USAMO qualification have recently been in flux. For further information, see the AMC website http://www.unl.edu/amc/. The five contests begin on pages 3, 17, 29, 40, and 50. Within each contest, I have provided the problems, followed by the answers without solutions, followed by complete solutions for every problem.2 I believe this format should allow for maximum flexibility in individual practice style. I have checked most of the document fairly thoroughly, but it is possible that mistakes remain. This is a work in progress distributed for personal educational use only. In particular, any publication of all or part of this manuscript without prior contest of the author is
Thomas Mildorf
November 24, 2005
The following are five problem sets designed to be used for preparation for the American Invitation Math Exam. Part of my philosophy is that one should train by working problems that are more difficult than one is likely to encounter, so I have made these mock contests extremely difficult.
The idea is that, once you become acclimated to them, the real AIMEs will seem easier, and you will approach them with justifiable confidence. Therefore, do not be discouraged when working your way through this document. It is expected that you will find these problems and solutions extremely challenging. Although there is no fixed set of rules for practicing, you might try working each batch of problems under standard AIME conditions. Essentially, that means no calculators are allowed, the testing period is 3 consecutive hours, all answers are integers from 000 to 999 inclusive, and there are no penalties for guessing. An appoximation of the cover of the actual AIME phamphlet preceeds each problem set1 ; the cover will list the official testing parameters, including any slight changes from past years. Although in the AMC could change the rules, as they have for the AMC10/12 contests, they have been consistent when arbitrating the AIME. That said, the rules for
USAMO qualification have recently been in flux. For further information, see the AMC website http://www.unl.edu/amc/. The five contests begin on pages 3, 17, 29, 40, and 50. Within each contest, I have provided the problems, followed by the answers without solutions, followed by complete solutions for every problem.2 I believe this format should allow for maximum flexibility in individual practice style. I have checked most of the document fairly thoroughly, but it is possible that mistakes remain. This is a work in progress distributed for personal educational use only. In particular, any publication of all or part of this manuscript without prior contest of the author is