AMC 12 Practice Test Guide 2026 June — American Mathematics Competition Prep

About the AMC 12

The AMC 12 is administered twice each year — as the AMC 12A (typically in November) and the AMC 12B (typically in December). Both versions are equivalent in difficulty and structure, giving eligible students two opportunities to achieve a qualifying score. The contest is open to students in grades 12 and below who are under 19.5 years of age on the day of the competition.

First held in 1950 as the Annual High School Examination, the AMC 12 is now taken by hundreds of thousands of students each year across the United States and internationally. It serves as the first step in the MAA's American Mathematics Competitions series, which ultimately identifies students for the U.S. team at the International Mathematical Olympiad (IMO).

The AMC 12 tests mathematical reasoning and problem-solving across a wide range of high school topics. Unlike standardized tests such as the SAT or ACT, the AMC 12 is designed to challenge even the strongest math students — top scores typically require both deep conceptual understanding and efficient problem-solving technique.

Topics Covered on the AMC 12

The AMC 12 covers the full range of high school mathematics through precalculus, including topics beyond the typical AMC 10 syllabus. Problems are arranged roughly in order of increasing difficulty, with the first 10 questions generally accessible to well-prepared students and the final 5–10 requiring olympiad-level insight.

Core Topic Areas

• Algebra: Polynomials, equations, inequalities, sequences and series, functions, logarithms, and complex numbers. Expect non-routine applications of algebraic identities and clever substitutions.
• Geometry: Plane geometry (triangles, circles, polygons), coordinate geometry, 3D geometry (surface area, volume), and trigonometry. AMC 12 geometry problems often require creative use of similarity, power of a point, and angle chasing.
• Number Theory: Divisibility, prime factorization, modular arithmetic, floor/ceiling functions, Diophantine equations, and number-theoretic functions like Euler's totient. Number theory problems can appear at any difficulty level.
• Counting and Probability: Combinatorics (permutations, combinations, stars and bars, inclusion-exclusion), probability (conditional probability, expected value, geometric probability), and counting arguments.
• Complex Numbers: Unique to the AMC 12 (not AMC 10), problems may involve De Moivre's theorem, roots of unity, and geometric interpretations of complex number operations.
• Precalculus Concepts: Conic sections, trigonometric identities, parametric equations, and basic limits may appear in harder problems.

Difficulty Distribution

Questions 1–10 are generally straightforward; problems 11–20 require solid problem-solving skills; problems 21–30 are genuinely hard and often involve multiple insights or elegant tricks. Most students who qualify for AIME solve roughly 15–20 problems correctly.

AMC 10 vs AMC 12 — Key Differences

Students in grades 10 and below may choose to take either the AMC 10 or the AMC 12 (or both, on their respective dates). Understanding the differences helps students select the right contest and set realistic goals.

Students eligible for the AMC 10 often find the AMC 12 harder but qualify for AIME at a slightly lower score threshold. Strong grade 10 students may benefit from attempting the AMC 12 to compete for USAMO rather than USAJMO eligibility, since USAMO is a stronger credential for college admissions.

AIME Qualification — What Score Do You Need?

Qualifying for the AIME is the primary goal for most serious AMC 12 participants. The AIME qualification threshold varies slightly from year to year based on the difficulty of the exam, but as a reliable benchmark:

• AMC 12A/12B AIME cutoff: Typically 96–100 points (approximately 16–17 correct answers with no wrong answers, or equivalent combinations)
• The MAA invites roughly the top 5% of AMC 12 scorers to the AIME each year
• In some years, the cutoff has been as low as 93 or as high as 102 depending on problem difficulty

Your combined score for USAMO qualification is computed as: AMC 12 score + 10 × AIME score. For example, a student scoring 100 on the AMC 12 and 7 on the AIME earns a USAMO index of 170. USAMO cutoffs typically fall around 215–230, meaning top performers need both a strong AMC 12 result and a solid AIME performance.

Students who score above 100 on the AMC 12 but fall slightly below the AIME cutoff should consider reviewing their strategic approach — a score of 96 represents roughly 16 correct answers with no wrong answers, which is achievable with focused preparation on problems 1–20.

Effective AMC 12 Preparation Strategies

1. Work Official Past Exams Under Timed Conditions

The MAA has released official AMC 12 exams dating back to 2000 (as AMC 12A/12B), plus earlier AMH exams from 1950–1999. Working through these under strict 75-minute time limits is essential. After each exam, score yourself honestly — then spend at least as long reviewing solutions as you did taking the test.

2. Use the Art of Problem Solving (AoPS) Resources

The AoPS Wiki contains detailed solutions to nearly every AMC 12 problem ever written. The AoPS forums allow students to discuss problems, see multiple solution approaches, and learn from more experienced competitors. The AoPS textbooks (Introduction to Algebra, Introduction to Number Theory, Intermediate Algebra, etc.) provide structured curriculum for AMC-level topics.

3. Topic-Based Practice

Identify your weakest topics by analyzing your performance across multiple practice exams. If number theory problems consistently cost you points, dedicate focused study sessions to modular arithmetic, Euler's theorem, and classic number theory problem types. AoPS's AMC 12 practice problems can help you drill specific topic areas.

4. Learn Core Theorems and Techniques

Certain tools appear repeatedly on the AMC 12: the Cauchy-Schwarz inequality, AM-GM inequality, Vieta's formulas, the Pythagorean theorem in disguise, modular arithmetic shortcuts, stars and bars, inclusion-exclusion, and the Chinese Remainder Theorem. Fluency with these reduces the cognitive load of hard problems.

5. Simulate Full Test Conditions

Print out a past exam, sit at a quiet desk, set a 75-minute timer, and work with only pencil and scratch paper — no calculator, no phone. The AMC 12 does not permit calculators, and test-day conditions differ significantly from casual practice.

Tips for AMC 12 Test Day

• Read the problem carefully: Many errors on the AMC 12 come from misreading — confirm what quantity the problem asks for before computing.
• Work forward from easy problems: Build confidence and accumulate points on problems 1–15 before spending time on problems 25–30.
• Manage time actively: If a problem is taking more than 3–4 minutes with no progress, skip and return later. Time management is a learnable skill.
• Use answer choices strategically: On multiple-choice problems, working backward from the answers (plugging in answer choices) or using process of elimination can be faster than a direct solution.
• Check units and reasonableness: For numerical answers, quickly verify that your answer is dimensionally consistent and plausible given the problem setup.
• Do not leave answers blank if you can eliminate options: With 1 eliminated, expected value of guessing becomes positive. With 2 eliminated, it is strongly positive.