AMC Past Papers with Answers - Practise Online

The American Mathematics Competitions (AMC) are a series of mathematics contests run by the Mathematical Association of America (MAA) for middle and high school students. The three entry-level papers, the AMC 8, AMC 10 and AMC 12, are 25-question multiple-choice tests that reward problem solving rather than routine calculation, and they are taken by students in the United States and at registered schools and centres in many other countries.

AMC past papers are widely used for competition practice because the format has stayed stable for many years. This page covers the AMC levels, exam format, scoring and A and B versions.

Overview

The AMC series has a long history. The paper now called the AMC 12 began in 1950 as the American High School Mathematics Examination (AHSME), and the AMC 8 was known as the American Junior High School Mathematics Examination (AJHSME) until the 1999-2000 school year. The AMC 10 was added in 2000 for younger high school students.

The competitions are organised by the MAA in the United States. Schools, colleges and approved testing centres register with the MAA and act as competition sites, which is how students outside the United States usually take part.

The AMC is also the first step of a larger pathway. Strong AMC 10 and AMC 12 scores can lead to an invitation to the AIME (American Invitational Mathematics Examination), and from there to the USAJMO or USAMO, which are part of how the United States selects its team for the International Mathematical Olympiad. Edupiad covers the AMC 8, AMC 10 and AMC 12 only. It does not include AIME, USAJMO or USAMO papers.

Note that the AMC described here is not the same contest as the Australian Mathematics Competition, which is also often called "AMC". The two are run by different organisations and use different papers.

AMC levels and grades

A student may take the AMC 12 while still in Grade 10 or below, but cannot take the AMC 10 once they are in Grade 11. The AMC 8 also has an age limit set by the MAA.

Versions A and B

Since 2002, the AMC 10 and AMC 12 have been offered twice each year, as Version A (AMC 10A and AMC 12A) and Version B (AMC 10B and AMC 12B), on two different dates. The A and B papers are different sets of questions of similar difficulty. A student can sit one paper on each date, for example the AMC 10A and then the AMC 10B.

The AMC 8 has only one paper per year, with no A or B version.

The 2021 school year was an exception. The MAA moved the AMC 10 and AMC 12 from February to November that year, so there are four papers for each of AMC 10 and AMC 12 dated 2021: the spring Version A and Version B, plus a Fall Version A and Fall Version B. On Edupiad these fall papers are listed separately.

AMC exam format and scoring

Calculators are not allowed on any AMC paper. Questions get harder as the paper goes on.

The scoring difference matters. On the AMC 8 there is no reward for leaving a question blank, so students should answer every question. On the AMC 10 and AMC 12, a blank earns 1.5 points while a wrong answer earns nothing, so a pure guess costs you 1.5 points on average compared with skipping. Guessing only makes sense when you can rule out several options.

When is the AMC held

The AMC 10 and AMC 12 are held every year in November, with the A and B dates about a week apart. Since 2022, the AMC 8 has been held in January. Students register through their school or a local AMC competition site, not directly as individuals in most countries, and registration usually closes several weeks before the test dates. The exact dates and deadlines change each year, so check the MAA website.

The MAA has revised the rules for the AIME from 2027, including how students qualify. If you are aiming beyond the AMC, read the current MAA rules rather than older guides.

How to prepare with AMC past papers

• Start with the first 15 questions. These cover core topics in arithmetic, algebra, geometry, counting and number theory. Getting them right quickly and reliably is worth more than attempting the hardest problems.
• Practise under real time. 40 minutes for 25 questions (AMC 8) or 75 minutes for 25 questions (AMC 10/12) leaves little time per question. Timed practice teaches you when to move on.
• Train your blank-or-answer decision. On the AMC 10 and AMC 12, review each wrong answer and ask whether skipping would have scored more. Students who stop careless guessing often gain several points.
• Mix A and B versions. Since each year has two papers for AMC 10 and AMC 12, past papers give you plenty of material at the right level.

On Edupiad you can take AMC 8, AMC 10 and AMC 12 past papers online with a timer, get automatic marking when you submit, and review your answer to each question. Available years and solutions depend on what has been added to the library.

Frequently asked questions

Is the AMC hard?

The early questions suit students who know their school maths well, but the later ones are genuinely challenging. Most students score well below the maximum.

What grade is the AMC 8 for?

The AMC 8 is for students in Grade 8 and below. There is no minimum grade.

What is the difference between AMC 10A and AMC 10B?

They are two different papers with the same format and similar difficulty, held on different dates in November. A student can take one on each date.

Does the AMC have negative marking?

There is no deduction for wrong answers. On the AMC 10 and AMC 12, however, a blank earns 1.5 points and a wrong answer earns 0, so guessing has a cost compared with leaving the question blank.

Does Edupiad have AIME papers?

No. Edupiad offers AMC 8, AMC 10 and AMC 12 papers only. The AIME, USAJMO and USAMO are later stages of the MAA pathway and are not on Edupiad.

Is the AMC the same as the Australian Mathematics Competition?

No. The AMC 8, 10 and 12 are run by the MAA in the United States. The Australian Mathematics Competition is a separate contest run by the Australian Maths Trust.

Sources

• MAA American Mathematics Competitions
• American Mathematics Competitions - Wikipedia
• American Invitational Mathematics Examination - Wikipedia