AMC 10 and AMC 12 Preparation: A Study Plan for Students and Parents

Every November, tens of thousands of high school students across North America write the AMC 10 or AMC 12, the opening round of the leading math contest series run by the Mathematical Association of America (MAA). For students at competitive private schools and advanced math programs, a strong result means more than personal pride. It can qualify them for the AIME (American Invitational Mathematics Examination), add weight to university applications, and open doors to selective summer programs. The leap from classroom math to contest math surprises many students, though. This guide explains how to prepare for the AMC 10 and AMC 12, with timelines, resources and strategies that experienced math educators recommend.

What the AMC 10 and AMC 12 are, and why they matter

Both exams are 75 minutes long with 25 multiple-choice questions. The AMC 10 is open to students in grade 10 and below; the AMC 12 is open to all students in grade 12 and below. The material goes well past the standard school curriculum and includes combinatorics, number theory, geometry and probability. Scoring is 6 points for each correct answer, 1.5 points for each blank and 0 points for each wrong answer, so the top score is 150.

Why do these contests matter to ambitious students? First, scoring 100 or more on the AMC 10, or 85 or more on the AMC 12, qualifies a student for the AIME (the 2026-27 fixed scores), a notable line on a university application. Second, admissions officers at top universities, including MIT, Caltech, Stanford and competitive Canadian engineering programs, treat AMC and AIME results as evidence of exceptional quantitative reasoning. Students at schools such as Phillips Exeter, UCC and Branksome Hall, and other academically demanding institutions, often take part through their school math teams.

How early to start

Begin structured preparation 6 to 12 months before the contest. For a student aiming at the November AMC, that means starting by the previous spring at the latest. A suggested schedule:

Timeline	Focus Area	Goal
12 months out	Foundation building	Master AMC-level algebra, geometry basics, and counting principles
6-9 months out	Topic deep dives	Study number theory, combinatorics, and intermediate geometry systematically
3-6 months out	Problem sets and past exams	Work through 2-3 past AMC papers per week under timed conditions
1-3 months out	Timed practice and strategy	Full timed mock exams, refine time management and skipping strategy
Final 2 weeks	Light review	Review mistake logs, avoid burnout, build confidence

Younger students heading toward the AMC 10 often do well to try the AMC 8 in grade 6 or 7 first. That gives them a feel for contest-style problems before the difficulty climbs.

Topics to study

The AMC exams draw on four main content areas, and a study plan should cover all of them. Here is how to set priorities.

Core topics for the AMC 10

• Algebra: Sequences, polynomials, inequalities, systems of equations and functional equations
• Geometry: Triangle properties, circle theorems, coordinate geometry, area methods, and similarity and congruence
• Counting and Probability: Permutations, combinations, casework, complementary counting and expected value
• Number Theory: Divisibility, modular arithmetic, prime factorization and the Euclidean algorithm

Extra topics for the AMC 12

• Trigonometry: Identities, the unit circle, the laws of sines and cosines, and links to complex numbers
• Advanced Algebra: Logarithms, sequences and series, polynomial roots and Vieta's formulas
• Complex Numbers and Functions: Complex arithmetic, roots of unity, polynomial functions and their graphs

Experienced competition math educators find that students moving from school math to AMC math have the biggest gaps in combinatorics and number theory. Most school curricula, even at advanced private schools, give these topics very little time.

Best resources for AMC preparation

Good resources matter. Competition math tutors recommend these tools for the AMC 10 and AMC 12:

1. Art of Problem Solving (AoPS) textbooks: "Introduction to Counting and Probability" and "Introduction to Number Theory" for the AMC 10, and the Intermediate series for the AMC 12. They are the standard way to build contest-style thinking.
2. Past AMC papers: The MAA has published past exams going back decades, and working through them is the single most effective preparation method. Aim to finish at least 15 to 20 full past papers before the contest.
3. The AoPS Online Community: Its forums hold detailed solutions and discussion for nearly every past AMC problem, so students can compare several ways of solving the same question.
4. A competition math tutor: For students aiming at AIME qualification, a tutor with contest experience can speed up progress a great deal. A skilled tutor finds blind spots, teaches elegant problem-solving techniques and keeps a student on schedule.

Test-taking strategies that raise AMC scores

Preparation is only half of it. Good test-day strategy can add 10 to 20 points. Experienced math educators suggest the following:

• Do not guess randomly. Wrong answers score 0 and blanks score 1.5, so random guessing lowers your score. Answer only when you can confidently rule out at least two choices.
• Move through the first 15 problems efficiently. Well-prepared students can usually handle problems 1 through 15. Try to finish them in about 40 minutes, which leaves 35 minutes for the harder ones.
• Skip with a plan. If a problem still looks time-consuming after 2 minutes of reading, skip it and come back. Many students lose points by sinking too much time into one problem and never reaching easier ones.
• Verify with a second method. On problems 1 through 10, a quick sanity check (trying the answer choices, estimating) catches careless slips that cost 6 points each.

Preparing for the AMC 10 or AMC 12 is among the most rewarding academic challenges a math-minded student can take on. With a structured plan, the right resources and steady practice, students can improve their scores considerably in a single preparation cycle. If your child loves competition math and would gain from an experienced math educator, book a free consultation with Bosen Academics. Our tutors include experienced classroom teachers, and you can see how we support contest math and advanced curriculum work.