Another Avenue for Seeking out Prospective Members for the Mega Society

by Ron Yannone



            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. (See (  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, begun 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.


Since 1995, I have been involved with the American Mathematics Competitions (AMC) committee to develop test questions for the AMC8, AMC10, AMC12 and AIME (American Invitational Mathematics Examination).  The AMC8, AMC10 and AMC12 are for the 8th, 10th, and 12th grade junior/high school level students.  The process is progressive, in that there is a call for problem/solution submittals by the TEAM (mostly college professors) for the various difficulty levels in each of these tests, then a review galley prepared for the TEAM to select/modify the best candidate problems/solutions, and then several more galley reviews to hone the tests to reflect the AMC “style” of conciseness, unambiguous wording, sufficient “distracters” used in the answer selections, solution clarity and creativeness, etc.


            The present collection of tests offered, in order of their difficulty, are the AMC8, AMC10, AMC12, AIME, USAMO (USA Mathematics Olympiad), Team Selection Test that screens for entry into the MOSP (Mathematical Olympiad Summer Program), and down-selection to the USA IMO (International Mathematics Olympiad) team.


                The AMC 8 is a 25 question, 40 minute multiple choice examination in junior high school (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 allowed.  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.


            The AMC10 is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators are allowed.  For the year 2002 there were two dates on which the contest may be taken: Contest A on February 10, 2004 and Contest B on February 25, 2004.  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 multiple-choice 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.  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 that seem liketricks”.  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.  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 fewer than 6% of all participants.  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 AMC12 is a 25 question, 75-minute multiple-choice examination in secondary school mathematics containing problems that can be understood and solved with pre-calculus concepts. Calculators are allowed. For the year 2004 there were two dates on which the contest may be taken: Contest A on February 10, 2004 and Contest B on February 25, 2004.  The main purpose of the AMC 12 is to spur interest in mathematics and to develop talent through solving challenging problems in a timed multiple-choice format.  Because the AMC 12 covers such a broad spectrum of knowledge and ability there is a wide range of scores.  The National Honor Roll cutoff score, 100 out of 150 possible points, is typically attained or surpassed by fewer than 3% of all participants.  For most students and schools only relative scores are significant, and so lists of top individual and team scores on regional and local levels are compiled. 


            The AIME (American Invitational Mathematics Examination) is an intermediate examination between the AMC 10 or AMC 12 and the USAMO.  All students who took the AMC 12 and achieved a score of 100 or more out of a possible 150 are invited to take the AIME.  All students who took the AMC 10 and were in the top 1% also qualify for the AIME.  The AIME is intended to provide further challenge and recognition, beyond that provided by the AMC 10 or AMC 12, to the many high school students in North America who have exceptional mathematical ability.  The top scoring USA American Mathematics Competitions participants (based on a weighted average) are invited to take the USAMO.  The AIME is a 15 question, 3-hour examination in which each answer is an integer number from 0 to 999.  The questions on the AIME are much more difficult and students are very unlikely to obtain the correct answer by guessing.  As with the AMC 10 and AMC 12 (and the USAMO), all problems on the AIME can be solved by pre-calculus methods.  The use of calculators is not allowed. The AIME provides the exceptional students who are invited to take it with yet another opportunity to challenge their mathematical abilities. Like all examinations, it is but a means towards furthering mathematical development and interest. The real value of the examination is in the learning that can come from the preparation beforehand and from further thought and discussion of the solutions.


The USAMO (United States of America Mathematics Olympiad) provides a means of identifying and encouraging the most creative secondary mathematics students in the country.  It serves to indicate the talent of those who may become leaders in the mathematical sciences of the next generation. The USAMO is part of a worldwide system of national mathematics competitions, a movement in which both educators and research mathematicians are engaged in recognizing and celebrating the imagination and resourcefulness of our youth. The USAMO is a six-question, two-day, 9-hour essay/proof examination.  All problems can be solved with pre-calculus methods.  Approximately 250 of the top scoring AMC participants (based on a weighted average) are invited to take the USAMO.  Participation on the USAMO will be limited to American citizens or permanent residents in other words, those seeking citizenship and currently possessing a U.S.A. Immigration “green card”.  The twelve top scoring USAMO students are invited to a two-day Olympiad Awards Ceremony in Washington, DC sponsored by the MAA, the Akamai Foundation, the Microsoft Corporation and the Matilda Wilson Foundation.  Six of these twelve students will comprise the United States team that competes in the “International Mathematical Olympiad (IMO). The IMO began in 1959; the USA has participated since 1974. The USA Mathematical Olympiad (USAMO) is a two-day, nine-hour, six-question, essay-proof examination.  Only USA citizens or permanent residents (currently possessing a USA green card) will be invited to officially take the USAMO. Selection for the USAMO will be made according to the following rules:


1.       The goal is to select about 250 of the top scorers from the prior AIME and AMC 12A, AMC 12B, AMC 10A and AMC 10B contests to participate in the USAMO.

2.       Selection will be based on the USAMO index which is defined as 10 times the student’s AIME score plus the student’s score on the AMC 12 or the AMC 10.

3.       The first selection will be the approximately 160 highest USAMO indices of students taking the AMC 12A or AMC 12B contest.

4.       The lowest AIME score among those 160 first selected will determine a floor value. The second selection of USAMO participants will be from the highest USAMO indices among students who took the AMC 10A or AMC 10B and the AIME, and got an AIME score at least as high as the floor value.

5.       The student with the highest USAMO index from each state, territory, or U.S. possession not already represented in the selection of the first and second groups will be invited to take the USAMO.

6.       To adjust for variations in contest difficulty, the number of students selected from A & B contests will be proportional to the number of students who took the (A & B) Contests.

7.       The selection process is designed to favor students who take the more mathematically comprehensive AMC 12A and AMC 12B contests.



The goal of the Mathematical Olympiad Summer Program (MOSP) is:


(1) To provide a mathematics program for about 25 very promising students who have risen to the top on the American Mathematics Competitions.

(2) To broaden students' view of mathematics, and better prepare them for possible participation on our International Mathematical Olympiad (IMO) team.

(3) To provide in depth enrichment in important mathematical topics to stimulate their continuing interest in mathematics and help prepare them for future study of mathematics.

(4) To coach the IMO team, which was selected on the basis of the USA Mathematical Olympiad and further IMO type testing taking place the first week of MOSP, to its highest level of performance in the IMO, and to achieve an atmosphere of comradeship and cooperation among the team and other participants which brings about feelings of cooperation and pride.


The rigorous curriculum and daily schedule of the MOSP is designed to achieve the goals of the program.  The MOSP will give approximately 25 students, including the six IMO team members and two alternates extensive practice in solving mathematical problems which require deeper analysis than those solved by students in even the best American high schools.  Full days of classes and extensive problem sets gives students thorough preparation in several important areas of mathematics which are traditionally emphasized more in other countries than in the United States.  These topics include combinatorics arguments and identities, generating functions, the Pigeonhole Principle, Ramsey's Theorems, graph theory, recurrence relations, telescoping sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities.  Acquaintance with and understanding of these topics is important for reasonable performance in an IMO.  The MOSP ensures that the IMO record of the United States properly reflects the energy and creativity of its brightest students.

Following the MOSP, the six-member USA team travels to the IMO site.  The Office of Naval Research has traditionally underwritten the MOSP instructional costs and participant support, while private sponsorship provides travel funds for the participants travel, and the University of Nebraska Lincoln provides its campus facilities and reduction in room and board fees.


            Each year since 1974, a small team of exceptionally talented high school students has represented the United States at the International Mathematical Olympiad (IMO), a rigorous two day competition including problems that would challenge most professional mathematicians. In addition to comprehensive mathematical knowledge, success on the IMO requires truly exceptional mathematical creativity and inventiveness. As an example, here is a problem from the 1998 IMO:


Let I be the incenter of triangle ABC. Let the incircle of ABC touch the sides BC, CA, and AB at K, L and M, respectively. The line through B parallel to MK meets the lines LM and LK at R and S, respectively. Prove that angle RIS is acute.


Following the 4-week Mathematical Olympiad Summer Program (MOSP), the U.S. Team and the adult leaders travel to the site of the International Mathematical Olympiad (IMO).  There, the most talented high school students from over 80 nations compete in an extremely challenging two-day examination.  The examination is constructed by the leaders of the participating teams from a pool of problems submitted earlier by the invited nations.  Both the construction of the examination and the subsequent grading of the papers are conducted in elaborate and highly democratic proceedings designed to preserve security and objectivity.  During the period of the IMO, the students are entertained by the host nation. In addition to visiting local points of interest in the host city, there is ample opportunity for informal interaction among the team members and leaders and their counterparts from the other participating countries.  The officers of the Mathematical Association of America (MAA) and the Committee on the American Mathematics Competitions (CAMC) endorse the following objectives of participation by the United States in the IMO:

(1) To provide opportunities for meetings and contacts among present and future mathematicians and scientists of different countries.

(2) To enrich the education and training for research in the mathematical sciences of 30 of our nation’s most talented students by means of an intensive four-week seminar in mathematics and problem solving beyond the standard syllabus.

(3) To stimulate and encourage mathematical excellence among the students and teachers of America’s high schools through the example set by these talented students and the favorable publicity the United States Team receives as a consequence of its participation in the IMO.

(4) To use this friendly competition as a forum for the exchange of mathematical and educational ideas that might prove helpful in setting priorities for secondary school mathematics in the United States.

(5) To foster unity of interest among all nations.  Mathematics, because of its universal nature, is ideally suited for this role.




          Another “avenue” to seek prospective members for the Mega Society is for me to contact the CAMC explaining my present role on the CAMC (since 1995) and as member/officer of the Mega Society – to entreat the CAMC to be a door-opener to allow the Mega Society to specifically distribute the Titan Test to, say, the top AIME scorers – and definitely the USAMO and USA IMO TEAM.  These candidates would likely have no problem in the non-verbal portion of the Titan Test.  Ideally, the CAMC might further “screen” those candidates mentioned herein who have scored very high on the SAT verbal portion as well.  This way, the Mega Society would almost be guaranteed promising, successful new members!


          The Mega Society would be highly blessed by having these exceptional youth as members.  These same youth would be superb proteges (male) and protegees (female) of some of the Mega Society’s leading adult-level hi-IQ test-makers – like Ron Hoeflin, Kevin Langdon, Chris Harding, . . . , Chris Cole, Phil Bloom, for example, to help prepare thrilling new tests for admission into the Mega Society.  With email accessibility by these talented youth, the Mega Society’s “presence” into the eventual colleges these students attend, would be make the Mega Society’s presence widespread.


          This elite group of youth would be a terrific thrust to help the Mega Society develop articles that are heavy on the math side – which in turn, would be read by junior/senior high school youth interested in mathematics.   Another aspect would be fantastic media for the concerned public about our Nation’s education system, as well as for the hundreds of thousands of potential junior/senior high school students in letting them know former students are members of the world’s most elite hi-IQ society.


         I hope this idea sparks other ideas with the members!  Ron Yannone