Math in Motion: The AMC Challenge and its Impact on Students

The American Mathematics Competition (AMC) was administered to students during first and second period on November 6, 2024. The competition is split into two different tests: the AMC 10, taken by students in grades 10 and below, and the AMC 12, a slightly more advanced test taken by students in grades 12 and below. Additionally, the AMC 10/12 is split into the AMC 10/12 A and the AMC 10/12 B, which occur a few days later. All four exams challenge students with math problems that test their problem-solving skills, critical thinking, and knowledge of topics like algebra, geometry, and number theory. 

The AMC is one of the most popular math competitions in the nation, so it isn’t surprising that it is popular amongst Stuyvesant students. In an email interview, Senior Math Team teacher Glen Chew said, “The population [of test takers] is consistent with its interest in math, being that Stuy is a STEM school.” Another reason many students take the AMC 10 or the AMC 12 is to score high enough to qualify for the American Invitational Mathematics Examination (AIME). If one scores high enough on the AIME, they will be invited to take the USA Mathematical Olympiad (USAMO) or USA Junior Mathematical Olympiad (USAJMO).

Students who are enrolled in math team classes at Stuyvesant are required to take both the AMC A and the AMC B. Students on the math team are enrolled in a one-period class every morning to help prepare for this test. Sophomore Eriko Goto joked, “Unfortunately, as part of the math team, I was forced to/automatically signed up. [I] received multiple emails telling me I needed to register.”

The math team class introduces students to competitive math. Math Team Assistant Captain and junior Tanvir Ahmed shared, “I was first introduced to competitive math in high school through the math team class, which meets every morning. It was here that I met some very smart people and learned new techniques/topics in math, which inspired me to learn more as well as to do well on math competitions.” 

While challenging, the AMC is also a rewarding experience for many students. Goto shared, “I think the AMC has inspired my interest in ‘contest math.’ Since the AMC 10 was the first official math competition I took, it introduced me to the more problem-solving aspect of math compared to the more school-oriented aspect of it.”

Additionally, the math team class offers several resources to help with the AMC. “Also, the environment of the math team, meeting every morning first period, and through after school practices, I was able to naturally get better at math,” Ahmed added.

To prepare for this exam, Chew emphasizes the importance of practice and a curious mindset, recommending online resources to build their problem-solving skills. Chew added, “If a student doesn't have any experience, [they] can visit the website ArtOfProblemSolving.com (AOPS) for its massive archive in math/science competitions. Younger students should practice a little bit daily, and to always have the mindset of being curious and learning new ideas. As you get older, the material you study tends to deal with longer multi-stepped ideas that require a couple of days of thinking and lots of trial and error.”

Some students studied by practicing certain topics they were weak in. “I focused on studying geometry and sequences/series because I like it, and combinatorics because I hate it and need practice,” Goto revealed.

However, Math Team Assistant Captain and sophomore Corwin Eisenbeiss shared, “I don't really have a specific method I used to prepare for the AMC. The general approach is just to practice/mock AMCs repeatedly. These practices not only help you learn from the mistakes you might be susceptible to on the real AMC, they tell you what you can’t do, teaching you approaches or general theory that will help you solve problems in the future.”

However, the AMC and AIME aren’t solely based on how advanced one’s math knowledge is. Chew said, “I feel that a student looking to do well on the AMC/AIME shouldn't focus on math ‘skills,’ but rather math experience. With the internet, it is very easy to bombard your brain with examples, ideas, problems, from the various resources that already exist. So a critical skill would be able to experience these ideas and to look into the insight that might've been suggested in the problem.” Success with the AMC and the AIME relies more on gaining experience and insight into problem solving, rather than solely based on computation.

The AMC has 25 questions and a full score of 150. Correct answers are rewarded with six points, unanswered with one point five, and incorrect with zero. Therefore, students try to maximize their scores by choosing which questions to answer and which to leave blank. “A student who can qualify for the AIME typically knows that they would need a certain number of questions correct on an AIME to proceed further (the qualification formula uses the two scores from the AMC & AIME to decide if you advance further to take the USAMO/USAJMO),” Chew explained in his email. 

Along with problem-solving skills and math experience, luck is also a factor in this exam because there are strategic ways to guess. “First of all, you should know that the AMC and AIME, which are part of the qualification process for USAMO, have a large factor of luck, so you should not be discouraged if you don't do as well as you want on these,” Ahmed added.

Some students were worried about making careless mistakes and not having enough time to check their work. Eisenbeiss said, “The hardest part for me was definitely trying not to make avoidable mistakes. Many people will often get the correct answer on their first pass through the problem, but it is much harder to ensure that answer is correct. Considering the equal weight of each question, scoring high really requires you to minimize these errors, which sometimes soaks up an unreasonable amount of time.”

Nitpicking and thinking too strategically about the test also pose a challenge. Goto added, “For me, the hardest part of the [AMC 10] was staying awake and also choosing which problems to solve or guess in order to maximize my score.” Additionally, he planned out how he would take the test ahead of time. “I would recommend having a rough idea of how you are going to split your time. I allotted 40 minutes for questions 1-20, 25 minutes for questions 21-25, and 10 minutes to check my work. I would also recommend keeping your scrap work organized so you can refer back to it later,” Goto revealed.

Additionally, on the day of the test, it’s natural to feel at least a bit nervous before and even during the exam. Eisenbeiss admitted, “I know from experience that when I am really stressed during these exams, I perform really poorly and get derailed from my thinking in the contest. I occasionally glance at my time to gauge if I need to speed my work up or if I can afford to double check my solutions, but I tend to avoid looking at my time as it can be very stressful.”

The AIME benefits students since colleges recognize the AMC and AIME as prestigious exams. “Everything done for the AMC or in general, math, is a step into the study for future math in college. It will help with preparing the mind better for harder exams, and if there is any success in the competition it will help with the college application,” Chew said.

Some students take it as they are simply passionate about math. “I would like to continue expanding my knowledge of math and solving fun and interesting problems,” Goto added.

Additionally, students not enrolled in the math team can still take the AMC. Sophomore Kabir Madan shared, “A friend convinced me to study with them for the AMC, and I wanted to make AIME.” However, these students do feel a lack of community compared to what the math team has, and may believe it is difficult to compete against them. “So many of those kids are leagues ahead of me in math and are mostly doing their own thing. I’m not part of the math team and I’ve made my peace with that,” Madan said.

But the competition is not just between math team and non-math team students. It also exists within the math team itself. Ahmed said, “There definitely is a competitive culture, but I think it mostly affects me positively. Seeing higher-level math students in Stuy and out of Stuy inspires me to learn more math. After all, math is not just about the competitions; learning about new things can be just as rewarding.”

Students have different views on the exam, especially between those who are in math team and those who are not. Madan said, “I feel like students who are outside of math team view it in one of three ways. Either they don’t care, they take it for fun, or it’s do or die. In math team, it’s more like it’s important, but it’s not everything, because there are so many contests and opportunities to showcase your math skills.”

Eisenbeiss agreed that results shouldn’t be taken too negatively. “While I think doing well in a contest can definitely boost your confidence in math, doing poorly should not demotivate or detract from your confidence in your mathematical abilities. Many people mess up or make mistakes they normally would not have, so letting these annual contests define you doesn’t make sense,” he said.

The AMC 10 and AMC 12 offer students the opportunity to explore math beyond the classroom, build problem-solving skills, experiment with competition math, and help students find their interests. Teachers and students recognize this exam as a way to build confidence, foster collaboration, and ultimately inspire students. “It can really build a sense of community, similar to that of a sports team. It’s everything. It’s a challenge, an annoyance, a hobby, a frustration, sometimes it’s even very depressing,” Madan said. 

So if you’re thinking about participating, take the challenge. Whether you want to qualify for the AIME or just want to expand your knowledge of math, it will teach lifelong skills that will help with problem solving. “It's a once-in-a-lifetime opportunity to participate. You can also meet other students that might share some similar interests. I also feel that anything that might create some sort of epiphany or an ‘ah ha!’ moment is worthwhile and very rewarding,” Chew advised.