Final Sprint for the 2026 AIME: A Complete Prep Blueprint with Key Topics, Pitfalls, and Past Problems

The countdown to the 2026 AIME (American Invitational Mathematics Examination) has officially begun. For students who have already qualified, the quality of preparation in this final stage will play a decisive role in determining their ultimate score.

With a major rule change in 2026—the weight of AIME scores in the USAMO / USA(J)MO qualification index increasing from 10× to 20×—every single point on the AIME is now more valuable than ever before.

AIME is not merely a test of mathematical knowledge. It is a comprehensive assessment of time management, problem-solving adaptability, and psychological resilience. In the limited time remaining, targeted and strategic preparation matters far more than unfocused practice.

I. 2026 AIME Competition Schedule

Exam Dates and Format

The 2026 AIME will be administered in two separate sessions:

• AIME I: February 6, 2026 (Thursday), 13:00–16:00

• AIME II: February 12, 2026 (Wednesday), 13:00–16:00

• Registration Deadline: January 27, 2026

2026 AIME Overview

Major Rule Update

Starting in 2026, the AIME score weight in USAMO and USAJMO qualification has doubled, fundamentally changing the competitive landscape.

The new qualification formulas are:

• USAMO Index = AMC 12 Score + 20 × AIME Score

• USAJMO Index = AMC 10 Score + 20 × AIME Score

Under this system, AIME now contributes approximately two-thirds of the total qualification index, making it the single most critical component for advancement.

II. Problem Difficulty Distribution and Time Management Strategy

AIME problems follow a clear gradient of increasing difficulty. Understanding this structure and allocating time strategically is essential for achieving a strong score.

Difficulty Breakdown and Recommended Strategy

Although the average time per problem is 12 minutes, effective allocation should follow a “fast start, flexible finish” principle.
The first five problems must be completed efficiently and accurately, while the middle section (Problems 6–10) determines whether a student reaches competitive score thresholds.

III. In-Depth Analysis of the Four Core Content Areas

1. Algebra (35%–40%)

Algebra is the most heavily tested area on the AIME.

High-frequency topics include:

• Higher-degree equations and Vieta’s formulas

• Complex numbers and roots of unity

• Inequalities

• Sequences and recursive relations

• Functional equations

Key preparation focus:

• Combining complex numbers with trigonometric identities

• Analyzing periodicity and closed forms of recursive sequences

• Flexible use of inequalities such as Cauchy-Schwarz and AM-GM

Common pitfalls:
Sign errors and incomplete case analysis are frequent causes of lost points. Multi-step algebraic solutions should always be checked with boundary values.

2. Geometry (30%–35%)

AIME geometry spans plane, coordinate, and solid geometry.

Core challenges:

• Interactions among triangle centers (circumcenter, incenter, centroid, orthocenter)

• Power of a point, radical axis, homothety

• Hybrid approaches combining geometry with trigonometry or complex numbers

Strategic insight:
Rather than relying on obscure theorems, AIME geometry emphasizes fundamental properties and trigonometric methods. Identifying key angles and applying the Law of Sines or Cosines is often decisive in higher-numbered problems.

3. Number Theory (15%–20%)

Number theory dominates many of the final five problems.

Essential advanced topics:

• Modular arithmetic and the Chinese Remainder Theorem

• Higher-order congruences

• Fermat’s Little Theorem and Euler’s Theorem

• Lifting The Exponent (LTE) Lemma

Preparation advice:
These problems require long logical chains and careful construction. Modular reduction, base-representation methods, and structural observations are common solution paths.

4. Combinatorics (10%–15%)

Despite its smaller share, combinatorics is one of the most conceptually demanding areas.

Key difficulty areas:

• Recurrence relations

• Generating functions and combinatorial identities

• Complex probability and geometric probability

Effective approach:
Most combinatorics problems require building an abstract model—often reducible to classical frameworks such as balls-and-bins, path counting, or state transitions. Developing strong combinatorial intuition is critical.

IV. Three-Stage Final Preparation Plan

Stage 1: Diagnostic Review (Now to Late January)

• Complete one full AIME from the past three years under timed conditions

• Analyze accuracy by topic area

• Identify weak modules and review high-frequency concepts

Stage 2: Targeted Reinforcement (Late January to Early February)

• Conduct focused training on weaker sections

• Practice relevant problems from 2015–2020 AIME, especially Problems 1–10

• Build an error log categorized by knowledge gaps, calculation errors, or flawed reasoning

Stage 3: Full Mock Exams (Early February to Exam Day)

• Take one full mock exam every 2–3 days

• Fine-tune personal time allocation strategy

• Practice recognizing entry points for difficult problems

V. Exam-Day Techniques and Common Mistakes

Core Problem-Solving Techniques

• Pattern exploration: Start with small cases to identify structure

• Special-value substitution: Try values like 0, 1, or −1

• Diagram support: Accurate drawings for geometry and state diagrams for combinatorics

• Symmetry analysis: Symmetric structures often yield integer or special results

Common Errors and Prevention

Psychological Preparation

AIME is intentionally challenging—even top students rarely solve all 15 problems. Maintaining composure is essential. Secure accuracy on solvable problems first, then attempt partial progress on harder ones.

With less than a month remaining until the 2026 AIME, every day matters. A structured plan, steady pace, and calm mindset will ultimately matter just as much as mathematical ability.