As a critical bridge between AMC and higher-level mathematics competitions, the AIME (American Invitational Mathematics Examination) is well known for both its difficulty and academic value.
In this article, we will take a clear and approachable look at what the AIME focuses on in 2026, the core mathematical areas it tests, and how students can reserve access to full solution analyses.
Key Features of the AIME Mathematics Competition
Unlike AMC multiple-choice exams, the AIME consists of 15 short-answer questions, each requiring complete logical reasoning and accurate final answers. There are no answer choices to rely on—every problem demands depth of thought and precise execution.
Overall, AIME questions emphasize conceptual understanding, flexible application of techniques, and rigorous problem-solving processes, mainly across the following four areas.
1. Algebra
AIME algebra problems rarely ask students to simply “solve an equation.” Instead, they focus on advanced algebraic manipulation, functional equations, and creative algebraic constructions.
For example, a problem may present a complicated rational or radical expression and ask for its integer part, or define a function with a special relationship and require the evaluation of a sum of function values.
Preparation Tips:
A strong command of AMC-level algebra techniques is essential. Beyond that, students should practice working with symmetric expressions, cyclic sums, and advanced algebraic identities that frequently appear in AIME problems.
2. Geometry
AIME geometry problems often involve complex plane-geometry figures, requiring the combined use of properties of circles, triangles, and classical theorems. In many cases, problems also integrate coordinate geometry or trigonometry.
For example, a problem may include a diagram with multiple intersecting circles and triangles and ask for the length of a segment that is not directly measurable. The key lies in drawing effective auxiliary lines and identifying hidden similarity or congruence relationships.
Preparation Tips:
Students should be fluent in common geometry theorems and models, such as Ceva’s Theorem and Menelaus’ Theorem, and practice breaking down complex diagrams into simpler, manageable components.
3. Number Theory
Number theory is one of the defining features—and challenges—of the AIME. Topics include divisibility, prime numbers, modular arithmetic, and Diophantine equations. While problems are often concise, they require highly rigorous and creative reasoning.
For instance, a problem might ask how many three-digit numbers satisfy a specific divisibility condition involving the number and the sum of its digits. Solving such problems requires systematic analysis and careful casework.
Preparation Tips:
Master fundamental tools such as modular arithmetic and the Euclidean algorithm, and develop familiarity with standard number-theory strategies through extensive practice and structured case analysis.
4. Combinatorics and Probability
Problems in this category often appear in real-life or game-based scenarios, asking students to count outcomes or compute probabilities accurately. Common techniques include case classification, the Principle of Inclusion and Exclusion, and recurrence relations.
Examples include counting the number of valid paths on a game board or determining how many codes satisfy a given set of constraints. Precision is essential to avoid overcounting or missing cases.
Preparation Tips:
Develop a clear understanding of the difference between permutations and combinations, and practice translating word problems into correct mathematical counting models.
Final Thoughts
Overall, AIME problems require students to move beyond AMC-level familiarity and develop deeper reasoning, complete solution structures, and rigorous mathematical writing. During daily practice, it is essential to write out every step clearly and logically—this habit not only improves accuracy but also strengthens problem-solving intuition.
For students preparing for AIME 2026, a clear understanding of these four core areas is the foundation for effective revision and high performance.