AMC 10 & AMC 12 Competition Instructions

What the AMC 10 and AMC 12 are

Both contests are 25-question, 75-minute multiple-choice papers designed to develop and reward problem-solving skill. The AMC 10 is built around mathematics typically met by the end of Grade 10, while the AMC 12 covers the full high-school curriculum. They are the entry point of the American Mathematics Competitions sequence, and a strong result on either paper is what earns an invitation to the AIME. Beyond qualification, the papers give students a genuine reason to think analytically and to build a positive, confident relationship with mathematics.

Eligibility

Eligibility is set by both grade and age on the day of the competition:

• AMC 10 — open to students in Grade 10 and below who are under 17.5 years old on the competition date.
• AMC 12 — open to students in Grade 12 and below who are under 19.5 years old on the competition date.

A student in Grade 10 or below may choose either paper; a student in Grade 11 or 12 takes the AMC 12. Students with a real appetite for problem-solving are encouraged to enter the harder paper they are eligible for.

The A and B versions

Each contest is offered in two versions every year — AMC 10 A and AMC 10 B, AMC 12 A and AMC 12 B — sat on separate dates. The A and B papers share the same number of questions, the same scoring and the same rules; only the dates and the specific questions differ, while difficulty and topic spread are kept equivalent. A student may take one version or both. Where a student sits both A and B, the better of the two scores is the one used.

Format and scoring

Both papers are 25 multiple-choice questions to be answered in 75 minutes, with no calculator permitted. Scoring rewards accuracy and discourages guessing:

• +6 for each correct answer
• +1.5 for each question left blank
• 0 for each incorrect answer

The maximum possible score is 150. Because a blank question is worth more than a wrong guess on the questions you cannot narrow down, deciding when to leave a question is part of the strategy.

AMC 10 vs AMC 12 at a glance

	AMC 10	AMC 12
Grade	Grade 10 and below	Grade 12 and below
Age on competition day	Under 17.5	Under 19.5
Questions / time	25 questions / 75 minutes	25 questions / 75 minutes
Versions	A and B	A and B
Maximum score	150	150
Mathematics covered	Elementary algebra; basic geometry, area and volume; number theory; probability	Full high-school curriculum, including trigonometry and advanced algebra (no calculus)

What the mathematics covers

The AMC 10 draws on elementary algebra; basic geometry, including the Pythagorean theorem and area and volume; elementary number theory; and elementary probability. Trigonometry and advanced algebra are not required. The AMC 12 covers everything on the AMC 10 and extends across the entire high-school curriculum, including trigonometry and advanced algebra. Neither paper requires calculus.

How AIME qualification works

The AMC 10 and AMC 12 are the gateway to the AIME (American Invitational Mathematics Examination). Top scorers on each paper are invited to sit the AIME; where a student has taken more than one paper, their best score is the one that counts toward qualification. The AIME is a 15-question, integer-answer exam, and results there feed forward into selection for the USA(J)MO. In short, a high AMC 10 or AMC 12 score is the first step on the route that leads to national olympiad selection.