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American Mathematical Competitions

Overview of Math Olympiads in United States

The American Mathematics Competitions (AMC) are the first of a series of competitions in middle school and high school mathematics that lead to the United States team for the International Mathematical Olympiad (IMO).

AMC has three levels:

  • AMC 8 - grade 8 and below
  • AMC 10 - grades 10 and below
  • AMC 12 - grades 12 and below

The AMCs lead to International Math Olympiad (IMO), world's most prestigious math contest at school level. The basic route is as follows

  1. AMC 10 or AMC 12 ===>American Invitational Mathematics Examination (AIME)
  2. AIME ===> United States of America Mathematical Olympiad (USAMO).
  3. USAMO (typically around 30 students) ===> Mathematical Olympiad Summer Program (MOSP or more commonly, MOP)
  4. Six students are selected from the top twelve scorers on the USAMO (through the Team Selection Test (TST)) to form the United States Math Team that goes to International Math Olympiad (held in June-July).
When?A Tuesday in NovemberA Tuesday in February or 15 days laterA Tuesday in February or 15 days later
Time (min)407575
ScoreCorrect +1
Incorrect 0
Not Attempted 0
Correct +6
Incorrect 0
Not Attempted +1.5
Correct +6
Incorrect 0
Not Attempted +1.5
Next LevelOnly awards, no next levelAIME if scores 120+AIME if scores 100+

How to Prepare for AMC

The American Math Contest is designed to encourage independent and critical thinking in young mind. Hence the problems are non-standard in nature. Hence key factors of AMC training are

  1. Strong foundation of mathematical concepts.
  2. Plenty of problem practice

All problems in AMC (or other Math olympiads) can be (and should be) solved without calculus. Though most problems are interdisciplinary in nature (that is use several concepts from secondary mathematics) 33% problems are from Geometry making it the single most important topic in AMC. The trend actually continues at all higher level olympiads, For example in IMO, 2 out of 6 problems are from Geometry.


We suggest two types of books/resources for AMC preparation. The first kind is for concept building. The second is for problem solving. Nothing beats the old Russian books as far as Math Olympiads are concerned. In fact American Math Olympiads are largely 'copies' of Russian Math Olympiads and Math Circles.

Starting Point

  • Mathematical Circles; A Russian Experience by Fomin
  • Lines and Curves by Vasiliyev
  • AMC 8 Problems

Both of these are outstanding books for concept building as well as problem solving. Lines and Curves present a novel method to introduce geometry to young people. Mathematical Circles covers most of the topics asked at AMC (or even higher levels). They are two light weight books for a great beginning.

Next Level

  • Challenges and Thrills of Pre College Mathematics by Venkatchala
  • Elementary Algebra and Higher Algebra by Hall and Knight
  • AMC 10 and AMC 12 Problems

Challenges and Thrills of Pre College Mathematics covers all the necessary topics of AMC. Hall and Knight's work are classics. They are useful for conceptual strengthening of skills in Algebra

Our Courses use several other resources in conjunction with these basic books. For example the outstanding articles of 'Quant', Mathematical Gems (Dolciani Series), Excursions into Mathematics or books by Martin Gardener are regularly used in a selective manner. Nowadays, thanks to internet, resource for math olympiad is unlimited. Hence the critical task is to point at selective few resources and fully utilize them.

There can be no quick-fix book for Math Olympiads. It is better to avoid undue sales gimmick and focus on classics. The sole purpose of math olympiads is to facilitate deep mathematical learning in young minds. This depth cannot be achieved in one day.

Am I ready for AMC?

The only way to understand whether you are ready for AMC (8, 10 or 12), or figure out your strengths and weaknesses, is to give a diagnosis test (AMC like test). You may either take an original AMC or take our diagnosis test. We will send you a report on the basis of this test with a review of your strengths and weaknesses.

You may request for a diagnosis test here (fill in the form).

Some Important Links:

Math Olympiad Program

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Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.