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American Mathematics Competitions(Redirected from AMC)

The American Mathematics Competitions (AMC) consist of a series of increasingly difficult

tests for students in middle school and high school. The AMC sets the standard in the United

States for talented high school students of mathematics. The AMC curriculum is both

comprehensive and modern. AMC exams are so well designed that some top universities such

as MIT now ask students for their AMC scores. "AMC" is also used as an abbreviation for American

Math Contest, used to refer to the AMC 8, AMC 10, and AMC 12.

Contents [hide]

1 AMC C ontests

2 History

3 Curriculum

4 Chain

5 Resources5.1 Links

5.2 Recommended reading

5.3 Preparation C lasses

6 See also

AMC Contests

In order of increasing difficulty, AMC competitions are

AMC 8 — for students grades 8 and under.

AMC 10 — for students grades 10 and under.AMC 12 — for students grades 12 and under.

American Invitational Mathematics Examination (AIME) — high scorers from the AMC 10/12 exams.

United States of America Mathematics Olympiad (USAMO) — high AIME and AMC scorers.

The top students on the USAMO are invited to participate in the Mathematical Olympiad Summer

Program, where students train for possible inclusion on the U.S. IMO team.

History

The AMC contests started in 1950, but unlike the modern AMC, the AMC's had 50 questions, and

was only available in New York and were called the Annual High School Contest. Two years later,

the Annual High School Contest was avalible nationwide. The amount of questions also decreased

from 50 to 35 in a span of 17 years. In 1974, the Annual High School Contest was re-named the

Annual High School Mathematics Examination. In 1983, the AHSC was renamed the American High

School Examination, and the AIME was also introduced. In 1985, the American Junior High School

Examination (Now know as the AMC 8) was introduced. In 2000, the AHSME was split into the

AMC 10 and 12, reduced to only 25 questions, and 2 years later, the A and B version of the AMC's

were introduced.

Curriculum

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AMC tests mathematical problem solving with arithmetic, algebra, counting, geometry, number

theory, andprobability, with far more cross-over between the subject areas than in nearly all

classrooms. For example, most classrooms only have divisibility rules and little tidbits of number

theory, and consider number theory as not a whole branch of mathematics but just a bunch of 

short cuts. The AMCs use number theory in much deeper (although elementary, without analysis)

ways. Tests vary widely in difficulty. All three of the tests are designed such that no background

in calculus, analysis, or any other higher mathematics is needed to take the exams.

Chain

The AMC tests are the first in a series of test to select the American International Mathematical

Olympiadteam. High scoring students on the AMC 10 or 12 are allowed to take the American

Invitational Mathematics Examination. Students who have a high AMC index, or a high score on

both the AMCs and the AIME, are allowed to take the United States of America Mathematics

Olympiad, the national Olympiad of the United States. There, many high scorers go to the Math

Olympiad Summer Program, which is divided into three "colors" depending on how high ones

scored. The highest color, black, consists of twelve students, six of whom will form the United

States' IMO team.

Resources

Links

AMC homepage

About AMC

AMC Problems and Solutions

Mock AMC exams by AoPSers

Recommended reading

Introduction to Counting & Probability by Dr. David Patrick. Information

Introduction to Geometry by Richard Rusczyk. Information

The Art of Problem Solving Volume I by Sandor Lehoczky and Richard Rusczyk. Information .

The Art of Problem Solving Volume II by Sandor Lehoczky and Richard Rusczyk. Information .

Preparation Classes

Art of Problem Solving offers many helpful online classes  on topics covered by the AMC exams.

AoPS holds many free Math Jams, some of which are devoted to discussing problems on the

various AMC exams.

EPGY offers AMC contest preparation classes .