Aiming for MIT or Cambridge? AMC Math Competitions Are Essential

Free AoPS E-Books to Help Students Build Competition-Level Mathematical Thinking

For families pursuing the international university application track, especially those targeting MIT, Cambridge, and other world-leading institutions, the pressure is real. Strong standardized test scores alone are no longer enough. Top universities increasingly expect clear academic distinction, and in mathematics, the AMC (American Mathematics Competitions) are nearly unavoidable.

The AMC series is one of the most globally recognized mathematics competitions, widely regarded as an “unspoken benchmark” by elite universities in the U.S. and U.K. However, many parents struggle with AMC preparation:

• The difficulty curve is steep

• Resources are scattered

• Standard textbooks lag far behind competition requirements

• Blindly drilling problems wastes valuable time

In reality, there is a widely acknowledged “shortcut” in AMC preparation:
The Art of Problem Solving (AoPS) series—often called the “competition bible” by top students worldwide. These black-covered textbooks consistently rank at the top of AMC preparation resources and are frequently cited by successful applicants to top universities.

Today, we are sharing free AoPS e-book resources to help students systematically build competition-level mathematical logic, prepare efficiently for AMC exams, and avoid common detours.

Part I: Introduction to the AoPS Book Series

Unlike traditional textbooks that simply list formulas and concepts, AoPS emphasizes mathematical thinking and real problem-solving ability, making it exceptionally well-suited for AMC 8 / AMC 10 / AMC 12 preparation.

Whether a student is starting in Grade 5 or aiming for high scores in Grade 11, AoPS offers a one-stop preparation pathway.

Comprehensive Coverage Across Grades 5–11

The AoPS curriculum progresses in carefully structured stages, aligning with students’ developmental levels and competition goals:

• Foundational topics such as algebra and geometry to solidify core skills

• Advanced topics including number theory and combinatorics, targeting high-frequency AMC challenges

• Full coverage of all tested concepts across AMC 8, 10, and 12

Deep Thinking Training and Logical Framework Building

AoPS does not rely on rote memorization. Instead, it uses guided discovery and heuristic examples to encourage active thinking. Each problem is designed to connect prior knowledge, helping students understand how concepts relate, not just how to apply formulas.

Over time, students develop the ability to generalize, transfer, and extend ideas, which directly matches the core assessment goals of AMC competitions.

Strong Practical Focus with High-Quality Practice

AoPS problem sets are highly targeted and include numerous AMC-style variations and past-problem adaptations. Every problem comes with detailed, logically structured solutions that explain not only how to solve the problem, but why the method works—ensuring deep mastery rather than superficial familiarity.

Essential AoPS Mathematics Competition Books

The Art of Problem Solving, Volume 1

• Difficulty: Moderate

• Recommended for Grades 7–10

• Topics include exponents and logarithms, complex numbers, linear equations, ratios, number theory, and foundational proofs

Prealgebra

• Difficulty: Introductory

• Recommended for Grades 5–8 (AMC 8 level)

• Covers arithmetic, primes and divisibility, fractions, equations and inequalities, decimals, ratios, unit conversion, percentages, and square roots

• Can serve as a complete pre-algebra course

Introduction to Algebra

• Difficulty: Foundational

• Recommended for Grades 6–9

• Covers linear and quadratic equations, factoring techniques, complex numbers, inequalities, functions, polynomials, sequences, absolute value, exponents, and logarithms

Introduction to Geometry

• Difficulty: Intermediate

• Recommended for Grades 7–10 with basic algebra background

• Topics include similar and congruent triangles, quadrilaterals, polygons, circles, solid geometry, and geometric transformations

Introduction to Number Theory

• Difficulty: Intermediate

• Recommended for Grades 7–10

• Covers primes and composites, factors and multiples, prime factorization, modular arithmetic, divisibility rules, linear congruences, and number sense development

Introduction to Counting & Probability

• Difficulty: Intermediate

• Recommended for Grades 7–10

• Topics include permutations, combinations, Pascal’s Triangle, combinatorial identities, probability fundamentals, geometric probability, expected value, and the binomial theorem

Part II: Hanlin AMC Coaching Programs

Aiming for the top 1%, but concerned about gaps in foundations or insufficient advanced training? Hanlin offers tiered AMC programs designed for students at different levels, ensuring systematic progress toward high scores.

Hanlin AMC courses feature:

• Carefully developed proprietary materials

• Elite instructors with strong academic backgrounds

• High-frequency, competition-focused training models

All programs are designed to solidify foundations and push students toward top-percentile performance.

AMC & Euclid Course Overview