Paths to the Math Olympiad (AMC 8 vs. MATHCOUNTS)
The AMC 8 and MATHCOUNTS are two of the most popular math competitions for U.S. middle school students. The AMC 8 is a single 40-minute test of 25 multiple-choice questions, while MATHCOUNTS is a season of in-person contests for grades 6-8 that runs from school to chapter, state, and national competitions, with individual and team rounds. Neither leads straight to the math olympiad: that path runs through the AMC 10 or AMC 12 and the AIME, and on to the U.S. Math Olympiad Team, which has placed first at the International Mathematical Olympiad five times since 2015.
In this article, we point you to official AMC 8 practice problems from the Mathematical Association of America (MAA), for those seeking to enhance their quantitative abilities or advance to higher levels. For students also interested in broader preparation, we will also discuss the MATHCOUNTS competition and how their practice problems compare with the types of questions found in the AMC 8. We'll also discuss how these competitions fit into rigorous math olympiads and how students can begin preparing from a young age for a chance to participate in high school tournaments.
What elementary and middle-school math competitions are available?
The many competitions available to younger students include Math Olympiads for Elementary and Middle Schools (MOEMS), MATHCOUNTS, and the American Mathematics Competitions (AMC) series, including AMC 8. Of these, the AMC series is the one that leads, through the AMC 10 and AMC 12, to the American Invitational Mathematics Examination (AIME) and the U.S. math olympiads.
What is the MOEMS Math Olympiad?
The Math Olympiad run by Math Olympiads for Elementary and Middle Schools (MOEMS) is a problem-solving contest for students in grades 4-8, taken by more than 120,000 students in the U.S. and 39 other countries each year. It isn’t part of the selection for the U.S. Math Olympiad Team, but it helps young students build the problem-solving skills that later contests demand. The purpose of this international math olympiad is to ignite enthusiasm, encourage the creative exploration of mathematics, and strengthen students’ abilities in quantitative problem-solving.
Each year, the competition runs from November to March, with five monthly contests given to teams of up to 35 students. Each contest has five problems and a 30-minute limit, and schools can give it on paper or online. Test responses are then submitted to MOEMS for official evaluation and scoring. Achieving a top score can provide valuable experience for students interested in advancing through elite mathematical circles and possibly joining the ranks of the official international competition in the future.
The Math Olympiad has two divisions: Division E for students in grades 4-6 and Division M for students in grades 6-8, so sixth graders can enter either one.
It’s important to note that MOEMS and this Math Olympiad are distinct from the USA Mathematical Olympiad (USAMO), which invites top students after the AMC 10 or AMC 12 and the American Invitational Mathematics Examination (AIME). The USA Mathematical Talent Search (USAMTS) is another way to qualify for the AIME. The USA Mathematical Olympiad serves as one of the primary pathways for exceptional students seeking a spot on the official U.S. Math Olympiad Team, which represents the country at international events.
What is MATHCOUNTS?
MATHCOUNTS is a nationwide math competition for U.S. students in grades 6-8, held each year at school, chapter, state, and national events. Founded in 1983 by the National Society of Professional Engineers, the National Council of Teachers of Mathematics, and CNA Insurance, and sponsored today by companies including RTX, Northrop Grumman, and Lockheed Martin, MATHCOUNTS is designed to foster advanced problem-solving skills and mathematical excellence among students. Much like the Olympiads and the prestigious U.S. Math Olympiad Team selection process, MATHCOUNTS engages participants through multiple levels of challenging and interactive “bee” style contests.
MATHCOUNTS contests are held in person, and calculators are allowed in some rounds but not others. MATHCOUNTS problems span a diverse range of topics, including algebra, geometry, number theory, counting, and probability, offering students rigorous practice and preparation for future contests.
The MATHCOUNTS competition is structured into four progressive stages: school, chapter, state, and national. With each stage, MATHCOUNTS problems become increasingly complex, ensuring that only the most talented mathematicians advance.
Top-performing individuals and teams from chapter competitions progress to their respective state MATHCOUNTS contests. At the state level, the top four individuals earn a place at the MATHCOUNTS National Competition, where they compete as their state’s team, coached by the coach of the winning team at the state competition. At nationals, every competitor takes the Sprint Round (30 problems in 40 minutes, no calculator) and the Target Round (four pairs of problems, six minutes per pair, with a calculator) individually, and each state’s four students work together in the Team Round (10 problems in 20 minutes). Nationals also include the Countdown Round, with up to 45 seconds per problem.
By participating in MATHCOUNTS and tackling advanced problems, students build a strong foundation that prepares them for higher-level competitions and potentially leads to selection for elite groups.
What is the AMC 8?
The AMC 8 mathematics competition is a key event in the American Mathematics Competitions (AMC) series, designed to challenge middle school students with advanced problem-solving skills. Part of a suite of contests provided by the Mathematical Association of America, the AMC 8 stands out as the most advanced entry-level math contest on this list, requiring a solid understanding of mathematics. For many students, preparation through Math Olympiad and MATHCOUNTS serves as excellent groundwork before tackling AMC 8 problems.
Aimed at students in grade 8 and below who are under 15.5 years old on the day of the competition, the AMC 8 is a fast-paced 40-minute test given once a year, in January, through schools and other sites registered with the MAA. Results come out a few weeks after the competition. The competition includes 25 multiple-choice AMC 8 problems, covering a variety of mathematics topics such as elementary geometry, probability, counting, proportional reasoning, data interpretation with graphs and tables, as well as coordinate geometry and basic algebra. The test is typically proctored by a teacher or school administrator to ensure a fair environment.
AMC 8 problems are renowned for encouraging creative problem-solving, often permitting several different solution strategies for the same question. Success not only demonstrates mathematical knowledge but also highlights a student’s adaptability and general reasoning abilities.
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The AMC 8 doesn’t qualify students for any later contest, so students who do well on it usually move on to the AMC 10 or AMC 12. Top AMC 10 and AMC 12 scorers are invited to the American Invitational Mathematics Examination (AIME), and top AIME scorers go on to the United States of America Junior Mathematical Olympiad (USAJMO) or the United States of America Mathematical Olympiad (USAMO). Outstanding achievers may even become eligible for selection to represent the U.S. at the International Mathematical Olympiad (IMO).
AMC 8 vs. MATHCOUNTS: Key differences
The AMC 8 and MATHCOUNTS differ more in format than in topic: both cover algebra, geometry, counting, and probability. The AMC 8 is one 40-minute test of 25 multiple-choice questions, taken individually once a year. MATHCOUNTS is a season of contests for grades 6-8, with a 40-minute, 30-problem Sprint Round, a Target Round, and a Team Round, and the best students advance from school to chapter, state, and national competitions. Students can do both: MATHCOUNTS builds speed and teamwork, and the AMC 8 is the first step in the MAA series that leads to the AIME.
AMC 8 math problem samples
Curious about tackling challenging AMC 8 problems? Test your problem-solving skills with the official problems from the 2023 AMC 8, published by the MAA and linked below. They give you a real sense of what the AMC 8 exam is like. Set a 40-minute timer and try all 25 on your own before you look up any solutions.
Find AMC 8 sample problems in this official practice PDF from the Mathematical Association of America.
Final thoughts
Remember, it’s never too early to start practicing your math skills, as there are several options for young, motivated students to explore and develop a passion for competitive problem-solving that can extend into high school and beyond. Whether your goal is to excel in national math competitions like the AMC or MATHCOUNTS, eventually advance to the international level, or simply improve your math knowledge and speed, completing practice problem sets (and timing yourself) is the best way to prepare.
The AMC 8 serves as an introduction to the world of math competitions at the middle school level, and it’s known for featuring elite math challenges. Don’t be discouraged if you don’t answer all AMC 8 practice problems correctly on your first attempt: questions on the AMC are meant to be tough and engaging. Many students find that the AMC exams are among the most challenging math contests they’ve faced so far, but working through problems is also what makes preparing for this exam so rewarding.
