Everything You Need to Know About the American Mathematics Competitions (AMC)

Swarnali Saha

Swarnali Saha

Founder, Welcome2Maths | 15+ years as a Math Teacher & Life Skills Coach

As a math coach, I often help students navigate competitive exams, and the American Mathematics Competitions (AMC) frequently stands out. Known for fostering problem-solving skills, the AMC is a gateway to advanced mathematics and prestigious opportunities like the AIME and USAMO.

In this blog, I’ll cover everything you need to know about AMC, highlight its unique aspects, compare it with Olympiad exams, and share how I prepare students for such challenges through one-on-one live sessions.

Fast Calculation Course

What Is AMC in Math?

The American Mathematics Competitions (AMC), organized by the Mathematical Association of America (MAA), is a series of exams aimed at identifying and nurturing mathematically talented students. It is divided into three levels:

  • AMC 8: For middle school students (grade 8 and below).
  • AMC 10: For high school sophomores and younger.
  • AMC 12: For high school seniors and younger.

The exams challenge students to think critically and creatively, focusing on topics like algebra, geometry, number theory, and combinatorics.

AMC vs. Olympiad Exams: What's the Difference?

The American Mathematics Competitions (AMC) and Olympiad exams both aim to identify and nurture mathematical talent, but they differ in focus, structure, and problem-solving requirements. Here's how they compare:

The AMC focuses on problem-solving and reasoning, with questions designed to test speed and accuracy. The exams consist of multiple-choice questions where students must select the correct answer from the given options. In contrast, Olympiad exams also include multiple-choice questions but require detailed solutions to arrive at the answers, emphasizing deep conceptual understanding and analytical thinking.

In terms of levels, AMC offers structured exams like AMC 8, AMC 10, and AMC 12, which lead to advanced competitions such as AIME and USAMO. Olympiad exams, such as the SOF Math Olympiad and RMO, cater to a global audience and can culminate in prestigious competitions like the International Mathematical Olympiad (IMO).

Time management plays a critical role in AMC, as the exams are strictly timed and require quick calculations. Olympiad exams, while also timed, provide slightly more room to solve complex problems as they demand step-by-step reasoning and explanatory solutions. Scoring in AMC often includes penalties for incorrect answers in higher levels, making strategic answering essential, whereas Olympiad exams typically focus on rewarding accuracy without penalizing wrong attempts.

Overall, AMC helps sharpen quick thinking and decision-making skills, while Olympiad exams encourage in-depth problem-solving and logical reasoning. As a math coach, I prepare students for both by tailoring strategies to suit the unique requirements of each competition.

What Topics Are Covered in AMC?

AMC exams test a variety of topics designed to challenge and expand mathematical thinking. Here’s an overview with examples:

  1. Algebra: Equations, inequalities, and functions.
    • Example: Solve for x x x: 2 x + 3 = 15 2x + 3 = 15 2x+3=15.
  2. Geometry: Properties of shapes, angles, and theorems.
    • Example: In a triangle, the sides are 3, 4, and 5. What is its area?
  3. Number Theory: Divisibility, primes, and modular arithmetic.
    • Example: Find the remainder when 1234 1234 1234 is divided by 7 7 7.
  4. Combinatorics and Probability: Counting principles and likelihood.
    • Example: How many ways can you arrange the letters in “MATH”?
  5. Logical Reasoning: Patterns and problem-solving strategies.
    • Example: If x x x is a prime number greater than 10, what could x + 2 x + 2 x+2 be?

Practicing questions like these builds the confidence and precision needed to excel in AMC.

How Do I Prepare Students for AMC and Competitive Exams?

Through one-on-one live sessions, I help students master problem-solving for competitive exams like AMC, Olympiads, and logical reasoning contests. My approach includes:

  1. Customized Lesson Plans: Tailored to each student’s skill level and goals.
  2. Practice with Real Problems: Using previous AMC and Olympiad questions to build familiarity.
  3. Mastering Calculations: With my Master Calculation Course, students learn techniques to perform rapid, accurate calculations—essential for timed exams.
  4. Building Logical Thinking: Developing strategies to approach unfamiliar problems confidently.

Why Is AMC Important?

AMC is more than just an exam—it’s an opportunity to:

  • Enhance problem-solving and critical-thinking skills.
  • Stand out in college applications, especially for STEM fields.
  • Progress to advanced contests like AIME, USAMO, and IMO.

It’s a great platform for students who aspire to excel in math and compete internationally.

Fast Calculation Course

Conclusion

The American Mathematics Competitions provide a unique opportunity for students to explore the beauty of mathematics and challenge their limits. Whether you’re preparing for AMC, Olympiad exams, or looking to boost your logical reasoning skills, the right guidance can make all the difference.

At Welcome2Maths, I’ve helped students achieve their goals through structured coaching and courses like the Master Calculation Course, ensuring they’re ready to tackle any challenge.

If you’re interested in one-on-one guidance or have questions about AMC, feel free to reach out. Let’s unlock your potential in math together!

Originally published May 2, 2019