MOEMS is a nonprofit public foundation providing opportunities for children to engage in creative
problem-solving activities that enhance a child’s ability to reason, to be logical, to be resourceful,
and occasionally to be ingenious.
"Tell me, I'll forget.
Show me, I'll remember.
Involve me, I'll understand."
A Chinese proverb
"Being able to solve a difficult problem is one of the most satisfying
experiences one may have. On the other hand, struggling with a difficult problem should indicate [that
the student] has found something worthwhile and new to learn. This should be viewed as a challenge
and an opportunity to grow. Learning how to solve a problem and to understand its underlying mathematical
concepts are the most important goals of mathematics education."
Richard Kalman
Executive Director, MOEMS
MOEMS is a nonprofit public foundation providing opportunities for children to engage in creative
problem-solving activities that enhance a child’s ability to reason, to be logical, to be resourceful,
and occasionally to be ingenious.
The Olympiad goals for students are for them to:
1. Develop enthusiasm for problem solving and mathematics;
2. Deepen understanding of mathematical concepts and strengthen the ability to use these concepts;
3. Consider concepts that they might not otherwise encounter; and
4. Enrich experiences in intellectually stimulating and significant mental activities.
Like most worthwhile goals, there is no easy road to becoming a capable problem solver. One must recognize that this is an important and desirable goal, and that it may take considerable time and effort to realize it.
Format: There are five monthly Olympiad contests, that are taken at the school. Each contests consists of five nonroutine problems per 30 minutes. When a problem introduces a more advanced concept, all necessary definitions are included. Calculators are NOT permitted. Sample contest here.
Awards: Individual: each participant - Certificate of Participation, the highest scorer - a trophy, top 50% Olympiad patch, top 10% - silver or gold pin; perfect scorers - bronze medallion. Team: top 10% - a plaque, the next 10% - a certificate.
The Math League was formed in 1977 by Steven R. Conrad and Daniel Flegler. In October 1985, they were
both honored by President Ronald Reagan as recipients of Presidential awards for "Excellence in
Mathematics Teaching." Mr. Conrad was the winner from New York, and Mr. Flegler the winner from New
Jersey. Mr. Flegler was the 1977 recipient of Princeton University's award for "Distinguished Secondary
School Teaching." They have co-authored 12 books.
The Math League has Math Contests for Grades 4 through 8, High School Students, and Algebra 1 students. Over 1 million students from the United States and Canada participate in Math League Contests each year. Every contest has questions from different areas of mathematics. The goal is to encourage student interest and confidence in mathematics through solving worthwhile problems. Many students first develop an interest in mathematics through problem-solving activities such as these contests. Schools compete in statewide or multi-state league competitions.
Math League's 7th, and 8th grade contests challenge students and schools in interschool league competitions. Students in each league compete for the highest scores, while schools compete for the highest team score: the total of the top 5 scores in each school. Each contest's questions cover material appropriate to each grade level. Questions may cover basic topics, as well as exponents, fractions, reciprocals, decimals, rates, ratios, percents, angle measurement, perimeter, area, circumference, basic roots, patterns, sequences, integers, triangles and right triangles, and other topics, depending on the grade level. Detailed solution sheets demonstrate the methods used to solve each problem. These contests encourage a variety of problem-solving skills and methods, allowing students to improve their abilities and understanding of mathematical connections, while having fun.
Format: 40 multiple-choice questions (3 pages) / 30 minutes. 1st page is usually straightforward, 2nd page - moderate, 3rd page - difficult. Calculators are allowed. Sample 7th Grade contest. Sample 8th Grade contest.
Awards: Certificates of Merit for high scoring students. A plaque to the highest scoring school in each region.
Math League's High School Contests are the best in high school mathematics competition. Students in each league compete for the highest scores, while schools compete for the highest team score: the total of the top 5 scores in each school. There are 6 rounds each year, with 6 questions per round; thus, there are 6 score reports per year for each league, showing each participating school's team scores, high scoring schools and students, and students with a perfect score. Each score report is accompanied by a newsletter, which includes comments and alternate solutions from teachers and students. All high school students in accredited schools are welcome to compete.
Problems are drawn from a wide range of high school topics: geometry, algebra, trigonometry, logarithms, series, sequences, exponents, roots, integers, real numbers, combinations, probability, coordinate geometry, and more. No knowledge of calculus is required to solve any of these problems. Detailed solution sheets demonstrate the methods used to solve each problem, including various approaches where appropriate.
Format: There are 6 contests through the school year. Each contests consists of 6 questions per 30 minutes. The last 2 questions are more difficult; the final question is very challenging. No knowledge beyond secondary school math is required; 2 to 4 questions only require knowledge of elementary algebra. Calculators are allowed. Sample contests: 1995, 1994, 1987, 1988.
Awards: Certificates of Merit for high scoring students. A plaque to the highest scoring school in each region.
Math League's Algebra Course 1 Contests are a great way to motivate students learning algebra for the first time. The questions range from basic algebra skills to more difficult problems, requiring creative solutions by applying Algebra Course 1 techniques. In addition to computational problems, a wide variety of word problems are included into each contest, to stress the value of applied algebra techniques. These contests are provided for intra-school competition only.
Format: 30 multiple-choice questions (3 pages) per 30 minutes. 1st page is straightforward, 2nd page - moderate, 3rd page - difficult. Calculators are allowed. Sample Contest.
Awards: Certificates of Merit for high scoring students. A book of Math Contests for highest scoring student.
The AMC held its first competition in 1950 and was sponsored by the Mathematics Association of America.
The overall success of the program is evidenced by its growth from 238 to over 5100 schools registered for competitions and
from 6,000 to over 413,000 students competing. The AMC offers a series of exams called AMC-8, AMC-10/12,
the American Invitational Mathematics Examination (AIME), and the USA Mathematics Olympiad (USAMO).
This series leads to selection of the team representing the US on the International Mathematics Olympiad (IMO).
The AMC 8 (formerly AJHSME) 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 that range from easy to difficult and 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.
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.
Students who score high on the AMC 8 may be invited to apply to exciting summer programs, such as MathPath. Perfect scores on the AMC 8 appear to be rarer than perfect scores on the SAT I math section (even by persons of the same young age).
Format: 25-question, 40-minute multiple choice examination. Problems range from easy to difficult and cover a wide range of applications. Calculators are allowed. Sample Questions.
Awards: Perfect scorers - Certificate of Distinction; student(s) in each school with the highest score - AMC 8 Winner Pin; the top three students for each school - Certificate for Outstanding Achievement; all high scoring students - AMC 8 Honor Roll Certificate.
The AMC-10 and AMC-12 are both 25 questions, 75 minute multiple choice examinations in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators are allowed.
Perfect scores on the AMC 12 are more difficult to attain that a score of 800 on the SAT I math section AND even rarer than a score of 800 on SAT II Math IIC subject test. Needless to state, high AMC-12 scores are taken very seriously by many college admission officers, for example, in MIT.
Format: 25-question, 75-minute multiple-choice contest. All problems can be solved by pre-calculus methods. Calculators are allowed. Sample questions: AMC10 2002, AMC10 2003, AMC12 2004.
Awards: A variety of national and intramural awards. AMC 10 students who rank in the top 1% nationally (or score at least 1 20) will qualify for the AIME.
IMPORTANT! Scoring system: The scoring system for these contests is different from all others, because THERE IS A PENALTY FOR GUESSING. Technically, it is implemented in the following way: every correct answer receives 6 points, every problem left blank receives 2.5 points, and every incorrect answer receives 0 points. To maximize your score on this contest, DO NOT GUESS UNLESS YOU CAN RELIABLY ELIMINATE 3 of 5 ANSWER CHOICES. Only a guess out of two is advantageous.
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 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. Similar to the AMC 10 and 12 and USAMO, all problems on the AIME can be solved using pre-calculus methods. The use of calculators is not allowed.
Format: 15 question, 3 hour examination. Each answer is an integer number from 0 to 999. All problems can be solved by pre-calculus methods. Calculators are not allowed. Sample questions: AIME 1998, AIME 1999, AIME 2003 practice Qs.
Awards: The top scoring U. S. citizens and students legally residing in the United States and Canada (with qualifyng scores, based on a weighted average) are invited to take the USAMO.