AMC 10 and AMC 12 Prep: A Complete Guide for Competitive Math Students

Each year, students at strong private schools and advanced math programs across North America sit one of the best-known high school math contests: the AMC 10 or AMC 12. For many families it starts with a teacher's comment or a line in the math department newsletter. Parents at schools such as Upper Canada College, Havergal College and Phillips Exeter Academy ask the same two things: should my child be doing the AMC, and how do we prepare? This guide covers what the contest tests, who it suits, and how to build a plan that produces real improvement.

What the AMC 10 and AMC 12 are, and who should write them

Both are 25-question, 75-minute multiple-choice contests run by the Mathematical Association of America. The AMC 10 is meant for students in Grade 10 or below, and the AMC 12 is open to every high school student. They are the first step on the route to the USA Mathematical Olympiad (USAMO) and, for the top scorers, the International Mathematical Olympiad (IMO).

The AMC suits students who like math beyond the regular curriculum, particularly those already in accelerated or advanced courses. Students in IB programs, AP schools or gifted math streams often find its problems both hard and satisfying. A student need not be chasing the Olympiad to gain from preparing: the problem-solving habits built through AMC study make students noticeably stronger in IB Math AA HL, AP Calculus BC and first-year university math.

When to start preparing

Plan on beginning structured preparation at least six months ahead. The most competitive students often start in Grade 7 or 8. Since the AMC is held every November, a Grade 9 or 10 student should start on foundations in the spring or early summer before the contest year.

A timeline that suits most students:

• 6 to 12 months out: Build a base in algebra, geometry, number theory and combinatorics. Practise with AMC 8 problems and early AMC 10 problems from 2000 to 2010.
• 3 to 6 months out: Work through recent AMC 10 or AMC 12 past papers. Reliably solve problems 1 through 15 before moving on to the harder ones at the end.
• 6 to 8 weeks out: Sit timed practice tests under real exam conditions. Go over every missed problem closely: look at the underlying idea and the point where your reasoning went off, not only the right answer.
• Final 2 weeks: Review lightly, concentrating on speed and accuracy for problems you can already solve. Do not try to learn new topics this close to the contest.

Experienced competition math educators say the most common mistake is skipping foundational review and diving straight into hard problems. A solid base brings far better results on the day.

Topics on the AMC 10 and AMC 12

The AMC 10 stays within Grade 10 math, so it has no trigonometry, advanced combinatorics or calculus. The AMC 12 has no such limit and may draw on all of high school math, including trigonometry and advanced algebra, but not calculus. Both reward creative problem-solving and mathematical reasoning more than rote calculation.

Here is how the main areas compare:

Topic Area	AMC 10	AMC 12
Algebra and Functions	High emphasis	High emphasis
Euclidean Geometry	High emphasis	High emphasis
Number Theory	Moderate	Moderate
Combinatorics and Probability	Moderate	High emphasis
Trigonometry	Not included	Moderate
Logarithms and Complex Numbers	Not included	Moderate

Successful AMC students usually have good geometric intuition and feel at ease with counting arguments. These are areas where focused work can produce large score gains fairly quickly.

Scoring and target scores

Each contest is marked out of 150 points. A correct answer earns 6 points, a blank earns 1.5 and a wrong answer earns 0. Because a blank is worth 1.5, a pure guess among five choices (worth 1.2 on average) is not worth making, but a guess after eliminating two or more choices is.

Many students aim for the AIME qualification cutoff. For the 2026-27 contest year the MAA has fixed it at 100 out of 150 on the AMC 10 (about 16 or 17 correct answers) and 85 out of 150 on the AMC 12 (about 14 correct answers). Qualifying for the AIME is a real academic achievement that universities in the US and Canada recognize in competitive admissions.

For students at top private schools and in advanced programs, aiming at AIME qualification usually takes 12 to 18 months of steady preparation. A student whose goal is to score above the 75th percentile can often get there with 3 to 6 months of focused work. Setting a realistic target score early makes the whole process more efficient.

Study resources and methods that work

The strongest preparation combines structured topic study with a large volume of problem practice. Competition math educators consistently recommend these resources:

• Art of Problem Solving (AoPS) books: The Introduction to Algebra, Introduction to Geometry, Introduction to Number Theory, and Introduction to Counting and Probability volumes are the standard for AMC preparation. Students aiming for AIME qualification should continue to the Intermediate series once the introductory books are mastered.
• AMC past papers: More than 20 years of papers are freely available. Doing them under timed conditions is the most direct and effective way to prepare.
• The AoPS online community: Its forums offer excellent problem discussions and peer support, well beyond what a textbook provides.
• One-on-one competition math tutoring: For students who need quicker progress or have specific topic gaps, an experienced competition tutor is the fastest route to real improvement. A skilled tutor can spot weaknesses in a few sessions that might take months to find through self-study.

Students at schools with strong math teams, such as Crescent School, Upper Canada College or Phillips Exeter Academy, often find that solving problems together with peers adds something that solo preparation lacks.

If your child is working toward AMC success or wants to build serious competition math skills, book a free consultation with Bosen Academics to talk about how our tutors can help, or browse our tutoring subjects.