6 Best Mathcounts For 11th Graders That Build Higher-Level Math Skills

Your 11th grader is acing their math classes, but you can tell they’re getting bored and need a bigger challenge. You might remember the fun and energy of middle school Mathcounts and wonder what the next step is for a serious high school student. Navigating the world of advanced math competitions can feel like learning a new language, but finding the right fit can ignite a lifelong passion for problem-solving.

AMC 12: The Gateway to National Competitions

Is your child ready to see how their math skills stack up on a national level? The American Mathematics Competition 12 (AMC 12) is the place to start. It’s the most well-known and accessible high-level high school math contest, offered right at your student’s school.

The test itself is a 75-minute sprint through 25 multiple-choice questions. While it covers standard high school topics like algebra, geometry, and trigonometry, the problems require a level of creative thinking far beyond typical classroom exercises. This isn’t about memorizing formulas; it’s about seeing clever connections and solving puzzles.

Think of the AMC 12 as the foundational qualifier for the entire U.S. math olympiad system. It’s the essential first step for any 11th grader serious about math competitions. A strong performance here opens the door to more prestigious, invitation-only events and is a fantastic credential for college applications.

AIME: For High-Scoring AMC Participants

If your student does exceptionally well on the AMC 12—typically scoring in the top 5%—they’ll receive an invitation to the American Invitational Mathematics Examination (AIME). This is where things get serious, and it’s a huge confidence booster for any teen to earn a spot.

The AIME represents a significant leap in difficulty. It’s a three-hour exam with 15 questions where every answer is an integer from 0 to 999. There’s no multiple-choice safety net, so guessing is impossible. Success on the AIME requires not just knowledge, but true mathematical ingenuity and persistence.

Participating in the AIME signals a student’s transition from a strong math student to a dedicated problem solver. A high score is a mark of distinction recognized by top STEM universities nationwide. It demonstrates a capacity for deep, rigorous thinking that simply can’t be shown on a standard report card.

Art of Problem Solving for Advanced Training

You’ve found the competitions, but how does your child prepare for problems they’ve never seen before? Art of Problem Solving (AoPS) is not a competition itself, but it is the single most effective training ground for students aiming to excel in them. Think of it as the specialized coaching and conditioning a serious athlete needs to compete at a high level.

AoPS offers a complete ecosystem for advanced learners, including challenging textbooks, self-paced online courses, and instructor-led classes. Their curriculum is built from the ground up to teach the non-standard problem-solving techniques that are essential for contest math. The online community also provides a place for students to collaborate with and learn from motivated peers around the world.

While AoPS courses are an investment, they provide a level of depth that is virtually impossible to find elsewhere. Consider starting with one of their subject-specific books or a shorter summer course to see if the demanding style fits your child’s learning process. For the student who is truly passionate, AoPS provides the tools to unlock their full potential.

HMMT for Elite Collaborative Problem Solving

Does your child thrive in a high-energy, collaborative environment? The Harvard-MIT Mathematics Tournament (HMMT) is one of the most prestigious and challenging team-based competitions in the world. It’s an exciting, intense event run entirely by students from Harvard and MIT.

Teams of students travel to either the Harvard or MIT campus to tackle incredibly difficult problems. The tournament includes individual rounds, but the main events are the Team Round and the famous Guts Round, where teams race to solve problems in sets against the clock. The atmosphere is less like a quiet exam and more like a major sporting event.

HMMT is for the truly advanced student who wants to experience problem-solving at an elite level alongside equally passionate peers. Getting onto a team can be a challenge in itself, often requiring high AMC and AIME scores. The experience, however, is invaluable for showing students what it’s like to be part of a top-tier intellectual community.

ARML: The Premier National Team Competition

Imagine the "World Series of math competitions," and you have the American Regions Mathematics League (ARML). This is a massive annual event where teams of 15 students representing schools, cities, or entire states compete simultaneously at university campuses across the country.

ARML is the ultimate test of mathematical teamwork. The competition includes rounds that require strategic collaboration, a "Power Question" where the team must write a full, proof-based argument, and lightning-fast relay races. It teaches students how to communicate complex ideas, trust their teammates, and perform under pressure.

Because it often involves travel, ARML is a significant commitment of time and resources. However, it provides an unforgettable social and competitive experience. It’s a fantastic goal for a school’s math club to build toward, fostering a sense of community and shared purpose that can define a student’s high school experience.

USAMTS for Developing Proof-Writing Skills

Is your child more of a deep, methodical thinker than a speed demon? The USA Mathematical Talent Search (USAMTS) is a completely unique, free competition that is perfect for them. Instead of a timed test, students are given a set of five incredibly challenging problems and have a full month to solve them.

The real value of USAMTS is its focus on proof-writing. Students must not only find the answer but also write a clear, logical, and rigorous explanation of how they got there. This is the single most important skill for success in university-level mathematics and advanced STEM fields, yet it’s rarely taught in high school.

USAMTS is ideal for the self-motivated student who enjoys sinking their teeth into a really hard problem over time. It’s a fantastic, low-pressure way to build the foundational skills needed for the USA Mathematical Olympiad (USAMO) without the anxiety of a timed environment. It rewards depth and clarity over speed.

Choosing Between Individual and Team Events

As you explore these options, a key question will emerge: is my child more motivated by individual achievement or by team success? There is no right answer, and many students enjoy a mix of both, but understanding their preference is key to picking the right opportunities.

• Individual Competitions (AMC 12, AIME, USAMTS): These are perfect for the student who loves the personal challenge of cracking a tough problem. They build focus, resilience, and self-reliance. Success is a direct measure of their own preparation and insight, which can be incredibly validating.
• Team Competitions (HMMT, ARML): These events teach skills that go beyond math. Students learn to lead, listen, and build on each other’s ideas. They discover that a team can often solve problems that no single member could solve alone. These shared experiences often build lasting friendships and mimic the collaborative nature of modern workplaces.

Don’t force a fit. An introverted deep thinker might find a massive team event overwhelming, while a social learner might feel isolated in a purely individual contest. Start with what feels most exciting to them.

Building a Math Competition Training Plan

Success in these competitions doesn’t happen by accident; it comes from consistent, focused preparation. A good plan transforms a student’s raw talent into polished, reliable skill.

First, use the AMC 12 as your foundation. Have your child take a few past exams under timed conditions. This will serve as a diagnostic, showing you exactly which areas (like geometry, number theory, or combinatorics) need the most work.

Next, integrate structured learning with a resource like the Art of Problem Solving books or online courses. It’s not enough to just do thousands of problems; they need to learn the underlying theorems and creative techniques behind the solutions. A balanced plan should include both learning new concepts and practicing their application.

Finally, establish a sustainable routine. An hour a day is far more effective than cramming for seven hours on a Saturday. Build in practice tests to develop pacing and stamina, but also schedule breaks to avoid burnout. The goal is to build a lasting intellectual habit, not just to prepare for a single test.

Ultimately, the best competition is the one that challenges and excites your child, pushing them to see mathematics not as a school subject, but as a creative and dynamic field of exploration. This journey is less about the final score and more about developing a resilient, curious, and powerful mind. That’s an investment that will pay dividends for the rest of their life.