7 Best AMCs for Competition Readiness That Build Foundational Skills

Your child has a spark for math, a knack for seeing patterns and solving puzzles that goes beyond their daily homework. You see the potential and hear whispers about things like the American Mathematics Competitions (AMC), but the path forward seems foggy. The goal isn’t just to chase a score, but to nurture that spark into a confident, resilient love for problem-solving that will serve them for life.

Choosing the Right AMC Prep for Your Student

So, you’re ready to explore the world of competition math. It can feel like a daunting landscape of books, websites, and classes, each promising to be the key to success. The most important thing to remember is that you’re not looking for the single "best" resource, but the best resource for your child’s specific stage and learning style.

Before you invest time or money, take a moment to assess where your student truly is. Are they a 6th grader who enjoys a good logic puzzle but hasn’t ventured beyond school curriculum? Or are they an 8th grader who is already self-studying algebra and asking for more challenges? A resource that’s too difficult can lead to frustration and burnout, while one that’s too easy won’t build the skills they need.

The key is to match the tool to the task. Some resources are designed for building deep, foundational understanding from the ground up, which is a slow and deliberate process. Others are for targeted practice to shore up weak spots, and still others are for simulating the high-pressure environment of the actual test. The right approach often involves a mix of these, tailored to your child’s journey.

AoPS Intro Series for Deep Conceptual Learning

You’ve noticed your child doesn’t just want to know how to get the answer; they want to know why the formula works. This curiosity is the sign that they’re ready to move beyond memorization and into true mathematical thinking. This is where the Art of Problem Solving (AoPS) Introduction series of textbooks shines.

These books, covering subjects like Introduction to Algebra or Introduction to Geometry, are the gold standard for a reason. They don’t just present facts; they guide students to discover concepts for themselves through carefully sequenced, challenging problems. This method builds a flexible, robust understanding that is essential for the creative problem-solving required on the AMC.

Be aware, this is not a light undertaking. Think of it as a full, rigorous curriculum, not a quick test-prep guide. It’s best suited for self-motivated middle or early high school students who are ready for a significant challenge. The investment here is deep conceptual mastery that pays dividends far beyond a single competition.

AoPS Alcumus for Adaptive, Targeted Practice

Your student has been working through a curriculum, but you’re not sure if the concepts are truly sticking. Or perhaps you know they’re solid on geometry but consistently struggle with number theory problems. This is where a tool for targeted, intelligent practice becomes invaluable.

Alcumus, the free online learning system from AoPS, is brilliant for this. It’s an adaptive platform, meaning it adjusts the difficulty and topic of the problems it presents based on your child’s answers. If they’re acing a topic, it will serve up harder problems. If they’re struggling, it will offer foundational questions to help them rebuild that skill.

Think of Alcumus as a personalized math coach. It’s an incredibly efficient way to identify and fill conceptual gaps without the need for endless, generic worksheets. It’s a perfect complement to any curriculum, allowing students to turn their knowledge into a reliable, practiced skill in a fun, game-like environment.

MAA Past Exams for Authentic Test Simulation

The competition date is circled on the calendar. Your student has put in the work learning the concepts and practicing problems. Now, the challenge shifts from knowing the math to performing under pressure.

The single most effective way to prepare for this is to use past exams, which are made available by the Mathematical Association of America (MAA), the organization that administers the AMC. Working through these official tests is the closest you can get to the real experience. It teaches crucial skills beyond the math itself: pacing, time management, and strategic guessing.

To get the most out of these, treat them like a dress rehearsal. Set a timer for the official time limit (75 minutes for AMC 10/12, 40 for AMC 8) and create a quiet, test-like environment. Afterward, the real work begins. Review every single problem—not just the ones they got wrong, but also the ones they guessed on—to understand the logic and identify patterns in their mistakes. This practice transforms knowledge into performance.

Brilliant.org for Interactive Problem Solving

Does your child’s eyes glaze over at the sight of a dense textbook? For many kids, especially visual and kinesthetic learners, the path to mathematical intuition is through hands-on, interactive exploration.

Brilliant.org is a fantastic resource for building this kind of flexible thinking. It’s less of a structured curriculum and more of a "mental gymnasium." Through beautiful, interactive puzzles, it allows students to discover complex ideas in logic, number theory, and geometry by doing and exploring. It lowers the barrier to entry for tough topics and makes learning feel like a game.

This is an excellent tool for a younger student (say, 5th to 7th grade) to build a love for logical reasoning before they’re ready for formal contest preparation. It can also serve as a great supplement for an older student to keep their practice fresh, fun, and engaging, preventing the burnout that can come from drills alone.

"Competition Math" for Middle School Strategy

Your middle schooler is excited about the idea of a math competition, but the imposing size of an AoPS textbook feels like too much, too soon. You need a bridge—something that can take their solid school-math skills and teach them how to apply them in a contest setting.

Books like Competition Math for Middle School are designed for precisely this purpose. They are more direct than a discovery-based curriculum, focusing on the specific types of problems and the key strategies needed for contests like MathCounts and the AMC 8. They explicitly teach tactics like "look for a pattern," "draw a picture," or "work backwards."

This approach can be perfect for students who thrive with a clear roadmap and a toolkit of strategies they can immediately apply. It’s a practical, focused way to build confidence and introduce them to the world of competitive math without the steep learning curve of a full, proof-based curriculum.

Khan Academy to Solidify Core Math Concepts

In the midst of tackling a tricky AMC 10 problem, your child suddenly looks up, confused about how to factor a quadratic. It’s a common scenario: the advanced problem-solving exposes a small crack in their foundational, school-level knowledge.

This is where Khan Academy is an indispensable, and completely free, resource. It is not a competition math program. Its strength is in providing clear, step-by-step instruction on the entire standard K-12 math curriculum. If there are any gaps in your child’s understanding of algebra, geometry, or trigonometry, Khan Academy is the most efficient way to patch them.

A solid foundation is non-negotiable. Before diving deep into contest-specific material, ensure your student has mastered the prerequisite school math. Use Khan Academy as a diagnostic tool and a library for review. A few hours spent shoring up the fundamentals here will save dozens of hours of frustration down the road.

MathCounts Handbooks for Creative Problem Sets

Your student needs more practice, but you’re worried they’ll get bored doing the same style of multiple-choice questions over and over. To develop true mathematical flexibility, they need to be exposed to a wide variety of creative, multi-step problems.

The MathCounts School Handbooks are a free, publicly available goldmine for this. Each year, MathCounts releases a new handbook packed with hundreds of brilliant problems that are tiered by difficulty. The problems are famous for their creativity and elegance, often requiring a clever insight rather than a brute-force calculation.

This is an excellent source of material for a math club or for any middle schooler looking to sharpen their problem-solving skills. Working through these handbooks builds mental agility and exposes students to the kind of "out of the box" thinking that is rewarded on the AMC and other advanced competitions.

Ultimately, remember that the goal is not just about a score or a qualification. It’s about nurturing a lifelong confidence in tackling hard problems. Choose the resource that best fits your child’s journey right now, celebrate their effort and curiosity, and enjoy the process of watching them grow.