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The OMO, a series of free team-based math competitions
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Online Math Open
The OMO, a series of free team-based math competitions
The OMO, a series of free team-based math competitions
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k a February Highlights and 2025 AoPS Online Class Information
jlacosta 0
Feb 2, 2025
We love to share what you can look forward to this month! The AIME I and AIME II competitions are happening on February 6th and 12th, respectively. Join our Math Jams the day after each competition where we will go over all the problems and the useful strategies to solve them!
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.
Introductory: Grades 5-10
Prealgebra 1
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.
Introductory: Grades 5-10
Prealgebra 1
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
0 replies
2014-2015 Fall OMO #26
v_Enhance 14
N
Feb 9, 2025
by abeot
Let
be a triangle with
,
,
. Let
,
,
be the midpoints of arcs
,
,
(not containing the opposite vertices) respectively on the circumcircle of
. Let
be the midpoint of arc
containing point
. Suppose lines
and
meet at
, while lines
and
meet at
. Find the square of the distance from
to
.
Proposed by Michael Kural






















Proposed by Michael Kural
14 replies
2018-2019 Fall OMO Problem 30
trumpeter 17
N
Jan 10, 2025
by qwerty123456asdfgzxcvb
Let
be an acute triangle with
, and circumradius
. Let
have circumcenter
, symmedian point
, and nine-point center
. Consider all non-degenerate hyperbolas
with perpendicular asymptotes passing through
. Of these
, exactly one has the property that there exists a point
such that
is tangent to
and
. Let
be the reflection of
over
. If
meets
at
, then the length of
can be expressed in the form
, where
are positive integers such that
is not divisible by the square of any prime. Compute
.
Proposed by Vincent Huang

























Proposed by Vincent Huang
17 replies
2013-2014 Fall OMO #26
v_Enhance 8
N
Jan 8, 2025
by OronSH
Let
be a triangle with
,
, and
. Denote the reflections of
across
by
, respectively, and let
be the circumcenter of triangle
. Let
be a point such that
, and let
and
be the midpoints of the major and minor arcs
of the circumcircle of triangle
. Find
.
Proposed by Michael Kural
















Proposed by Michael Kural
8 replies
2012-2013 Winter OMO #22
v_Enhance 2
N
Dec 28, 2024
by NicoN9
In triangle
,
,
, and
. Let
be the point on segment
satisfying
, and let
be the unique point such that
and line
is tangent to the circumcircle of
. Find the length of segment
.
Ray Li












Ray Li
2 replies
2012-2013 Winter OMO #11
v_Enhance 2
N
Dec 26, 2024
by NicoN9
Let
,
, and
be distinct points on a line with
. Square
and equilateral triangle
are drawn on the same side of line
. What is the degree measure of the acute angle formed by lines
and
?
Ray Li









Ray Li
2 replies
2011-2012 Winter OMO #22
Zhero 4
N
Dec 24, 2024
by NicoN9
Find the largest prime number
such that when
is written in base
, it has at least
trailing zeroes.
Author: Alex Zhu




Author: Alex Zhu
4 replies
2013-2014 Fall OMO #29
v_Enhance 22
N
Dec 11, 2024
by eg4334
Kevin has
cookies, each labeled with a unique nonempty subset of
. Each day, he chooses one cookie uniformly at random out of the cookies not yet eaten. Then, he eats that cookie, and all remaining cookies that are labeled with a subset of that cookie (for example, if he chooses the cookie labeled with
, he eats that cookie as well as the cookies with
and
). The expected value of the number of days that Kevin eats a cookie before all cookies are gone can be expressed in the form
, where
and
are relatively prime positive integers. Find
.
Proposed by Ray Li









Proposed by Ray Li
22 replies
2012-2013 Winter OMO #38
v_Enhance 11
N
Oct 29, 2024
by PEKKA
Triangle
has sides
,
, and
. Let
be the points on segments
, respectively, such that
and
. Suppose lines
and
intersect at
and the circumcircles of
and
intersect at a second point
. If the length of segment
can be expressed in the form
for positive integers
, where
is not divisible by the square of any prime, find
.
Victor Wang



















Victor Wang
11 replies
2015-2016 Fall OMO #12
pi37 14
N
Aug 7, 2024
by eg4334
Let
,
,
be the distinct roots of the polynomial
.
The cubic polynomial
is monic and has distinct roots
,
,
.
What is the sum of the coefficients of
?
Proposed by Evan Chen




The cubic polynomial




What is the sum of the coefficients of

Proposed by Evan Chen
14 replies
2017-2018 Fall OMO Problem 18
trumpeter 6
N
Aug 5, 2024
by ryanbear
Let
be real nonzero numbers such that
and
Compute the largest possible value of
.
Proposed by Tristan Shin


![\[\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{abc}=1.\]](http://latex.artofproblemsolving.com/6/d/a/6da709be271e908a29f5a90b71e5ff8f499c6fbb.png)

Proposed by Tristan Shin
6 replies
