
STYLES OF MATH COMPETITION 
Math Olympiad
 To stimulate enthusiasm and a love for mathematics
 To introduce important mathematical concepts
 To teach major strategies for problem solving
 To develop mathematical flexibility in solving problems
 To strengthen mathematical intuition
 To foster mathematical creativity and ingenuity
 To provide for the satisfaction, joy, and thrill of meeting challenges
AMC 8
The AMC 8 is a 25 question, 40 minute multiple choice examination in middle school mathematics designed to promote the development and enhancement of problem solving skills.
The examination provides an opportunity to apply the concepts taught at the junior high level to problems which not only range from easy to difficult but also cover a wide range of applications. Many problems are designed to challenge students and to offer problem solving experiences beyond those provided in most junior high school mathematics classes. Calculators are not allowed starting in 2008. High scoring students are invited to participate in the AMC 10.
A special purpose of the AMC 8 is to demonstrate the broad range of topics available for the junior high school mathematics curriculum. This is done by competencies. The AMC 8 has the potential to increase the perceptions of the importance of problem solving activities in the mathematics curriculum by stimulating these activities both preceding and following the examination —specifically by studying the solutions manual.
Additional purposes of the AMC 8 are to promote excitement, enthusiasm and positive attitudes towards mathematics and to stimulate interest in continuing the study of mathematics beyond the minimum required for high school graduation. Developmentally, junior high school students are at a point where attitudes toward school and learning, and perceptions of themselves as learners of mathematics are solidified. It is important that they be provided opportunities that foster the development of positive attitudes towards mathematics and positive perceptions of themselves as learners of mathematics. The AMC 8 provides one such opportunity.
We encourage all students in grades 6, 7 and 8 to participate in the AMC 8. All USA, USA embassy, Canadian and foreign school students in grade 8 or below are eligible to participate.
AMC 8 Intramural Awards
 A Certificate of Distinction is given to all students who receive a perfect score.
 An AMC 8 Winner Pin is given to the student(s) in each school with the highest score.
 The top three students for each school section will receive respectively a gold, silver, or bronze Certificate for Outstanding Achievement.
 An AMC 8 Honor Roll Certificate is given to all high scoring students.
 An AMC 8 Merit Certificate is given to high scoring students who are in 6th grade or below.
The members of the Committee on the American Mathematics Competitions (CAMC) are dedicated to the goal of strengthening the mathematical capabilities of our nation's youth. The CAMC believes that one way to meet this goal is to identify, recognize and reward excellence in mathematics through a series of national contests called the American Mathematics Competitions. The AMC include: the American Mathematics Contest 8 (AMC 8) (formerly the American Junior High School Mathematics Examination) for students in grades 8 and below, begun in 1985; the American Mathematics Contest 10 (AMC 10), for students in grades 10 and below, new in 2000; the American Mathematics Contest 12 (AMC 12) (formerly the American High School Mathematics Examination) for students in grades 12 and below, begun in 1950; the American Invitational Mathematics Examination (AIME), begun in 1983; and the USA Mathematical Olympiad (USAMO), begun in 1972.
AMC 10
The AMC 10 is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with precalculus concepts. Calculators are not allowed starting in 2008.
 Purpose
The main purpose of the AMC 10 is to spur interest in mathematics and to develop talent through the excitement of solving challenging problems in a timed multiplechoice format. The problems range from the very easy to the extremely difficult. Students who participate in the AMC 10 should find that most of the problems are challenging but within their grasp. The contest is intended for everyone from the average student at a typical school who enjoys mathematics to the very best student at the most special school.
 Learning
Although the excitement of testing one's mettle is naturally directed toward the contest itself, it is what happens before and after the contests which can have lasting educational value. Talents are enhanced with practice beforehand. This might be done by working through previous examinations, by participating in math leagues and, most importantly, by studying mathematics more intensely than one normally does in high school.Learning will take place if students singly, jointly and, especially with their teachers, strive to solve those contest problems they did not see how to solve in the allotted time as well as to understand the solutions to those problems that they did not solve correctly. The problems on the AMC 10 are chosen so that the solutions illustrate important mathematical principles. Occasionally, problems are chosen so that certain subtle but significant confusions, as well as some common computational errors, will be identified by the wrong answers listed. These principles and confusions are highlighted in the carefully prepared solutions manual. Some problems have quick solutions which seem like "tricks". What appears to be a trick the first time it is encountered often becomes a technique for solving other problems. A student’s mathematical tool kit for solving problems can be greatly expanded by the acquisition of these techniques.
 Difficulty
Since the AMC 10/12 covers such a broad spectrum of knowledge and ability there is a wide range of scores. The National Honor Roll cut off score for the AMC 12, 100 out of 150 possible points, is typically attained or surpassed by about 5% of all participants. For many students and schools only relative scores are significant, and so lists of top individual and team scores on regional and local levels are compiled. These regional lists and information on score distributions appear in the yearly summary sent to all participating schools. The more valuable comparison students can make is between their own level of achievement and their levels in previous years. In particular, they are encouraged to begin taking the contests early in their mathematics studies and to look back with pride each year on how they have learned to answer questions that they could not have answered previously.
A special purpose of the AMC 10 is to help identify those few students with truly exceptional mathematics talent. Students who are among the very best deserve some indication of how they stand relative to other students in the country and around the world . The AMC 10 provides one such indication, and it is the first in a series of examinations. In this way the very best young mathematicians are recognized, encouraged and developed.
The AMC 10 is not an end in itself. Outstanding performance on it is neither necessary nor sufficient for becoming an outstanding mathematician. The ability to gain insights and do computations quickly are wonderful talents, but many eminent mathematicians are not quick in this way. Also, the multiplechoice format (necessary for the prompt scoring of over 400,000 examinations) benefits those who are shrewd at eliminating wrong answers and guessing, but this is not particularly a mathematical talent. In short, students who do not receive nationally recognized scores should not shrink from pursuing mathematics further, and those who do receive such high scores should not think that they have forever proved their mathematical merit. This examination, like all mathematical competitions, remains but a means for furthering mathematical development.
AMC 12
The AMC 12 is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with precalculus concepts. Calculators are not allowed starting in 2008.
 Purpose
The main purpose of the AMC 12 is to spur interest in mathematics and to develop talent through solving challenging problems in a timed multiplechoice format. What happens before and after the AMC 12 can have lasting educational value. Talents will be enhanced if one practices beforehand, by working through previous examinations, by participating in math leagues and, most importantly, by studying mathematics more intensely than one normally does in high school.
 Learning
Although the excitement of testing one's mettle is naturally directed toward the contest itself, it is what happens before and after the contests which can have lasting educational value. Talents are enhanced with practice beforehand. This might be done by working through previous examinations, by participating in math leagues and, most importantly, by studying mathematics more intensely than one normally does in high school. Learning will take place if students singly, jointly and, especially with their teachers, strive to solve those examination problems they did not see how to solve in the allotted time as well as to understand the solutions to those problems that they did not solve correctly. Occasionally, problems are chosen so that certain subtle but significant confusions, as well as some common computational errors, will be identified by the wrong answers listed. These principles and confusions are highlighted in the carefully prepared solutions manual.
 Difficulty
Since the AMC 10/12 covers such a broad spectrum of knowledge and ability there is a wide range of scores. The National Honor Roll cut off score for the AMC 12, 100 out of 150 possible points, is typically attained or surpassed by about 5% of all participants. For many students and schools only relative scores are significant, and so lists of top individual and team scores on regional and local levels are compiled. These regional lists and information on score distributions appear in the yearly summary sent to all participating schools. The more valuable comparison students can make is between their own level of achievement and their levels in previous years. In particular, they are encouraged to begin taking the contests early in their mathematics studies and to look back with pride each year on how they have learned to answer questions that they could not have answered previously.
A special purpose of the AMC 12 is to help identify those few students with truly exceptional mathematics talent. Students who are among the very best deserve some indication of how they stand relative to other students in the country and around the world . The AMC 12 is one in a series of examinations (followed in the United States by the American Invitational Examination and the USA Mathematical Olympiad) that culminate in participation in the International Mathematical Olympiad, the most prestigious and difficult secondary mathematics examination in the world.
The AMC 10/12 is not an end in itself. Outstanding performance on it is neither necessary nor sufficient for becoming an outstanding mathematician. The ability to gain insights and do computations quickly is wonderful talent, but many eminent mathematicians are not quick in this way. Also, the multiplechoice format (necessary for the prompt scoring of over 300,000 examinations) benefits those who are shrewd at eliminating wrong answers and guessing, but this is not particularly a mathematical talent. In short, students who do not receive nationally recognized scores should not shrink from pursuing mathematics further, and those who do receive such high scores should not think that they have forever proved their mathematical merit. This contest, and all other mathematical competitions, remains but one means for furthering mathematical development.
Math Prize for Girls Highlights
A centry ago, suffragettes gathered in Cooper Union's Great Hall, agitating for the right to vote for women. I believe they would have been bursting with pride if they could have seen the first annual Math Prize for Girls awards ceremony held in that hallowed and historic hall yesterday afternoon.
The winner was Elizabeth Synge from Massachusetts, taking home a prize check for $20,000 for top honors on a very challenging set of problems during yesterday's written test held at NYU's Courant Institute of Mathematics. This prize was yet another iimpressive accomplishment for Elizabeth, who previously had won high honors at an international competition in China last summer. You can read more about Elizabeth's background in The Boston Globe: http://tinyurl.com/esynge.

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