OmegaLearnHow to Prepare for the USAMO Math Olympiad
HighWhat is the USAMO?
Format
Six proof-based problems over two days: three problems in 4.5 hours each day. Each is graded from 0 to 7, for a maximum score of 42.
Who qualifies
Invitation is based on a USAMO index (AMC score plus ten times your AIME score). The AMC 12 path leads to the USAMO and the AMC 10 path to the USAJMO.
Where to take it
It is proctored at your school or a testing center over the two scheduled days in the spring.
Problem distribution
Each day pairs an accessible P1/P4 with a hard P3/P6, drawn across algebra, combinatorics, number theory, and geometry. Combinatorics is the least templated and most decisive at the top; geometry and inequalities are the most drillable.
Official Information
USAMO & USAJMO (MAA)
The official MAA page for the USA Mathematical Olympiad with dates, eligibility, and rules.
View โUSAMO Guide
A comprehensive community guide to preparing for and succeeding on the USAMO, from problem selection through proof writing.
View โUSAMO (AoPS Wiki)
The AoPS wiki overview of the USAMO, with history, format details, and links to every past exam.
View โRecommended Books
For number theory and combinatorics, the free Modern Olympiad Number Theory and Olympiad Combinatorics (see Handouts) are widely considered the standard references. The books below are strong supplements for geometry, algebra, and inequalities, but they are secondary to those two.
Euclidean Geometry in Mathematical Olympiads ยท Evan Chen
A rigorous, proof-based geometry text written for olympiad competitors aiming at the USA(J)MO and IMO.
View on Amazon โProblem-Solving Strategies ยท Arthur Engel
A classic, comprehensive guide to the problem-solving techniques used across olympiad math.
View on Amazon โ104 Number Theory Problems ยท Andreescu, Andrica & Feng
104 challenging number theory problems from USA IMO team training, essential for olympiad prep.
View on Amazon โGeometry Revisited ยท Coxeter & Greitzer
A classic olympiad geometry text covering the powerful techniques and theorems used on the USAMO.
View on Amazon โMathematical Olympiad Challenges ยท Andreescu & Gelca
A curated problem collection with detailed solutions for olympiad-level competitors.
View on Amazon โMathematical Olympiad Treasures ยท Andreescu & Enescu
Olympiad problems with full solutions and discussion of the key ideas behind each approach.
View on Amazon โInequalities ยท Zdravko Cvetkovski
A thorough treatment of inequality techniques for olympiad math, from AM-GM to SOS and beyond.
View on Amazon โ102 Combinatorial Problems ยท Andreescu & Feng
102 problems from USA IMO team training covering the full range of olympiad combinatorics.
View on Amazon โHandouts & Topic Sets
Modern Olympiad Number Theory (MONT) ยท Aditya Khurmi
Free and widely regarded as the standard olympiad number theory reference: it develops modular arithmetic, orders and primitive roots, quadratic residues, lifting the exponent, and Diophantine methods from scratch with USAMO/IMO-level problems. Everything else is supplementary to this.
Download PDF โOlympiad Combinatorics ยท Pranav Sriram
Free and the de facto standard for olympiad combinatorics: chapters on extremal principle, invariants and monovariants, algorithms, counting in two ways, and probabilistic methods, each ending in graded problem sets. The core combinatorics text โ treat other books as supplements.
Download โEvan Chen's Olympiad Page
An extensive collection of olympiad handouts, lecture notes, and problem sets for USA(J)MO-level students.
Explore โThe OTIS Excerpts ยท Evan Chen
Free problem sets and expository notes from Evan Chen's OTIS olympiad training program.
Download PDF โOlympiad Number Theory Through Challenging Problems
A free AoPS handout covering divisibility, modular arithmetic, and Diophantine equations at the olympiad level.
Download PDF โA Beautiful Journey Through Olympiad Geometry
A free, full-length geometry textbook covering projective geometry, inversion, and classical theorems.
View book โAoPS Olympiad Handouts
A forum index of hundreds of olympiad handouts organized by topic on the AoPS community.
Browse โBig List of Olympiad Handouts
An extensive collection of olympiad handouts organized by algebra, combinatorics, geometry, and number theory.
View on Dropbox โPast Exams & Practice
Official USAMO Problems & Solutions (AoPS Wiki)
Every past USAMO with full solutions. Practice writing complete proofs under the real 4.5-hour limit.
View on AoPS โOfficial USAJMO Problems & Solutions (AoPS Wiki)
Every past USAJMO with solutions, a strong stepping stone toward USAMO-level problems.
View on AoPS โAoPS Contest Collections
Archive of problems and solutions from major national and international olympiads on the AoPS platform.
Browse โAoPS Olympiad Archive
A comprehensive index of olympiad problems from around the world, organized by competition.
Browse โUSA Olympiad Problem Collections
A blog compiling problems and solutions from major national olympiads including the USAMO.
View blog โCourses & Online Classes
OTIS (Olympiad Training for Individual Study) ยท Evan Chen
One of the most popular and elite training programs for USAMO preparation. OTIS runs on a problem-first, mastery-based model: students select topic units, work curated problem sets pitched at USA(J)MO difficulty, and submit written solutions for feedback. The single most recommended structured path to the USAMO.
View program โArt of Problem Solving ยท Class Catalog
Online courses through olympiad level, including WOOT for advanced olympiad training.
View catalog โAwesomeMath Academy
Intensive online courses and summer programs for high-performing students at the olympiad level.
Browse courses โEveraise Academy
A free summer olympiad program with rigorous courses in number theory, combinatorics, geometry, and more.
Visit everaise.org โIDEA MATH
Advanced math curriculum and courses designed for top AIME, USAMO, and olympiad competitors.
View courses โ