Summer is a great time to explore cool problems to keep your skills sharp!  Schedule a class today!

Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
3 M G
BBookmark  VNew Topic kLocked
Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
3 M G
BBookmark  VNew Topic kLocked
G
Topic
First Poster
Last Poster
k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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 Self-Paced

Prealgebra 1
Tuesday, May 13 - Aug 26
Thursday, May 29 - Sep 11
Sunday, Jun 15 - Oct 12
Monday, Jun 30 - Oct 20
Wednesday, Jul 16 - Oct 29

Prealgebra 2 Self-Paced

Prealgebra 2
Wednesday, May 7 - Aug 20
Monday, Jun 2 - Sep 22
Sunday, Jun 29 - Oct 26
Friday, Jul 25 - Nov 21

Introduction to Algebra A Self-Paced

Introduction to Algebra A
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
Tuesday, Jul 15 - Oct 28

Introduction to Counting & Probability Self-Paced

Introduction to Counting & Probability
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19

Introduction to Number Theory
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30

Introduction to Algebra B Self-Paced

Introduction to Algebra B
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14

Introduction to Geometry
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19

Paradoxes and Infinity
Mon, Tue, Wed, & Thurs, Jul 14 - Jul 16 (meets every day of the week!)

Intermediate: Grades 8-12

Intermediate Algebra
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22

Intermediate Counting & Probability
Wednesday, May 21 - Sep 17
Sunday, Jun 22 - Nov 2

Intermediate Number Theory
Sunday, Jun 1 - Aug 24
Wednesday, Jun 18 - Sep 3

Precalculus
Friday, May 16 - Oct 24
Sunday, Jun 1 - Nov 9
Monday, Jun 30 - Dec 8

Advanced: Grades 9-12

Olympiad Geometry
Tuesday, Jun 10 - Aug 26

Calculus
Tuesday, May 27 - Nov 11
Wednesday, Jun 25 - Dec 17

Group Theory
Thursday, Jun 12 - Sep 11

Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

MATHCOUNTS/AMC 8 Advanced
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21

AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22

AMC 12 Final Fives
Sunday, May 18 - Jun 15

AIME Problem Series A
Thursday, May 22 - Jul 31

AIME Problem Series B
Sunday, Jun 22 - Sep 21

F=ma Problem Series
Wednesday, Jun 11 - Aug 27

WOOT Programs
Visit the pages linked for full schedule details for each of these programs!


MathWOOT Level 1
MathWOOT Level 2
ChemWOOT
CodeWOOT
PhysicsWOOT

Programming

Introduction to Programming with Python
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22

Intermediate Programming with Python
Sunday, Jun 1 - Aug 24
Monday, Jun 30 - Sep 22

USACO Bronze Problem Series
Tuesday, May 13 - Jul 29
Sunday, Jun 22 - Sep 1

Physics

Introduction to Physics
Wednesday, May 21 - Aug 6
Sunday, Jun 15 - Sep 14
Monday, Jun 23 - Sep 15

Physics 1: Mechanics
Thursday, May 22 - Oct 30
Monday, Jun 23 - Dec 15

Relativity
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)
0 replies
jlacosta
May 1, 2025
0 replies
Frustration with Olympiad Geo
gulab_jamun   1
N 22 minutes ago by GallopingUnicorn45
Ok, so right now, I am doing the EGMO book by Evan Chen, but when it comes to problems, there are some that just genuinely frustrate me and I don't know how to deal with them. For example, I've spent 1.5 hrs on the second to last question in chapter 2, and used all the hints, and I still am stuck. It just frustrates me incredibly. Any tips on managing this? (or.... am I js crashing out too much?)
1 reply
1 viewing
gulab_jamun
an hour ago
GallopingUnicorn45
22 minutes ago
Sequences of real numbers
brian22   92
N 3 hours ago by NicoN9
Source: USAJMO 2015 Problem 1
Given a sequence of real numbers, a move consists of choosing two terms and replacing each with their arithmetic mean. Show that there exists a sequence of 2015 distinct real numbers such that after one initial move is applied to the sequence -- no matter what move -- there is always a way to continue with a finite sequence of moves so as to obtain in the end a constant sequence.
92 replies
brian22
Apr 28, 2015
NicoN9
3 hours ago
Trigo or Complex no.?
hzbrl   3
N Today at 8:26 AM by GreenKeeper
(a) Let $y=\cos \phi+\cos 2 \phi$, where $\phi=\frac{2 \pi}{5}$. Verify by direct substitution that $y$ satisfies the quadratic equation $2 y^2=3 y+2$ and deduce that the value of $y$ is $-\frac{1}{2}$.
(b) Let $\theta=\frac{2 \pi}{17}$. Show that $\sum_{k=0}^{16} \cos k \theta=0$
(c) If $z=\cos \theta+\cos 2 \theta+\cos 4 \theta+\cos 8 \theta$, show that the value of $z$ is $-(1-\sqrt{17}) / 4$.



I could solve (a) and (b). Can anyone help me with the 3rd part please?
3 replies
hzbrl
May 27, 2025
GreenKeeper
Today at 8:26 AM
Close to JMO, but not close enough
isache   11
N Today at 6:13 AM by LearnMath_105
Im currently a freshman in hs, and i rlly wanna make jmo in sophmore yr. Ive been cooking at in-person competitions recently (ucsd hmc, scmc, smt, mathcounts) but I keep fumbling jmo. this yr i had a 133.5 on 10b and a 9 on aime. How do i get that up by 20 points to a 240?
11 replies
isache
Yesterday at 11:37 PM
LearnMath_105
Today at 6:13 AM
k Bring Back Downvotes
heheman   79
N Today at 5:48 AM by heheman
i would like to start a petition to bring back downvote, it you agree then write "bbd $    $" in threads
79 replies
3 viewing
heheman
Yesterday at 7:21 PM
heheman
Today at 5:48 AM
3rd AKhIMO for university students, P3
UzbekMathematician   1
N Today at 3:07 AM by pineconee
Source: AKhIMO 2025, P3
Two points are chosen randomly - independently with uniform probability - from a semicircular arc with radius 1. A third point is chosen randomly - independently with uniform probability - from the diameter that connects the endpoints of the arc. What is expected value of the area of the triangle with the three chosen points as its vertices?
1 reply
UzbekMathematician
Yesterday at 1:57 PM
pineconee
Today at 3:07 AM
D1038 : A generalization of Jensen
Dattier   4
N Yesterday at 11:21 PM by Dattier
Source: les dattes à Dattier
Let $f \in C^1([0,1]), g \in C^2(f([0;1]))$.

Is it true that

$$\min(|g''|)\times \min(|f'|^2) \leq 24 \times\left|\int_0^1g(f(x)) \text{d}x- g(\int_0^1 f(x) \text{d}x) \right| \leq \max(|g''|)\times \max(|f'|^2)$$?
4 replies
Dattier
Yesterday at 12:15 PM
Dattier
Yesterday at 11:21 PM
3rd AKhIMO for University Students, P2
UzbekMathematician   1
N Yesterday at 9:40 PM by grupyorum
Source: AKhIMO 2025, P2
Find all possible values of $gcd(a^{2m}+1, a^n+1)$, where $a, m, n$ are positive integers and $n$ is odd.
1 reply
UzbekMathematician
Yesterday at 1:48 PM
grupyorum
Yesterday at 9:40 PM
Problem 2, Grade 12th RMO Shortlist - Year 2002
sticknycu   5
N Yesterday at 4:07 PM by P_Fazioli
Let $A \in M_2(C), A \neq O_2, A \neq I_2, n \in \mathbb{N}^*$ and $S_n = \{ X \in M_2(C) | X^n = A \}$.
Show:
a) $S_n$ with multiplication of matrixes operation is making an isomorphic-group structure with $U_n$.
b) $A^2 = A$.

Marian Andronache
5 replies
sticknycu
Jan 3, 2020
P_Fazioli
Yesterday at 4:07 PM
3rd AKhIMO for University Students, P1
UzbekMathematician   1
N Yesterday at 3:42 PM by KAME06
Source: AKhIMO 2025, P1
There are two circles in the $xy-$plane centered on the $y-$axis which are tangent to both the parabola $y=x^2$ and the line $y=2025$. Determine the lengths of the circles' diameters.
1 reply
UzbekMathematician
Yesterday at 1:44 PM
KAME06
Yesterday at 3:42 PM
3rd AKhIMO for university students, p4
UzbekMathematician   1
N Yesterday at 2:29 PM by grupyorum
Source: AKhIMO 2025, P4
Define a sequence $a_1, a_2, a_3, ... $ by $a_1=2, a_2=5$ and $a_{n+2}=f(a_n, a_{n+1})$ for all $n \ge 1$, where $$f(x,y)=5(x+y)+2\sqrt{6x^2+15xy+6y^2}.$$Show that $a_n$ is an integer for all $n\ge 1$.
1 reply
UzbekMathematician
Yesterday at 2:03 PM
grupyorum
Yesterday at 2:29 PM
Double Integral
namesis   3
N Yesterday at 2:27 PM by Mathzeus1024
The area of integration, $D$, is defined in plane polar coordinates $(r, \phi)$ by the inequality
$r-2 \leq r \leq r_1$, where $r_1 = 1 + \cos(\phi)$ and $r_2 = 3/2$.

Evaluate:

$\iint_D \frac{x+y+xy}{x^2 + y^2} dx dy $

I tried evaluating the integral in polar, with $r$ from $\frac{3}{2}$ to $1+ \cos \phi$ and $\phi$ from $- \frac{\pi}{3}$ to $ \frac{\pi}{3}$ but in vain.
3 replies
namesis
Dec 16, 2015
Mathzeus1024
Yesterday at 2:27 PM
Japanese Olympiad
parkjungmin   8
N Yesterday at 2:22 PM by parkjungmin
It's about the Japanese Olympiad

I can't solve it no matter how much I think about it.

If there are people who are good at math

Please help me.
8 replies
parkjungmin
May 10, 2025
parkjungmin
Yesterday at 2:22 PM
3rd AKhIMO for university students, P5
UzbekMathematician   0
Yesterday at 2:10 PM
Source: AKhIMO 2025, P5
Show that for every positive integer $n$ there exist nonnegative integers $p, q$ and integers $a_1, a_2, ... , a_p, b_1, b_2, ... , b_q \ge 2$ such that $$ n=\frac{(a_1^3-1)(a_2^3-1)...(a_p^3-1)}{(b_1^3-1)(b_2^3-1)...(b_q^3-1)} $$
0 replies
UzbekMathematician
Yesterday at 2:10 PM
0 replies
Mock Olympiad Geometry Contest #2
wu2481632   120
N Jun 21, 2017 by wu2481632
"If it is GGG, it will be GG..."

The contest is over!

Welcome, everyone! Over the last few weeks, I have had the pleasure of creating another olympiad geometry contest. My first one can be found here.

As users last time complained about the difficulty of 1/4, I've intentionally made 1/4 around JMO 1/4 level; 2/5/3/6 are closer to USAMO than USAJMO.

I'd like to thank users Generic_Username, AlgebraFC, MathSlayer4444, InCtrl, champion999, joey8189681, braniac1 for being there to support me in the creation of this contest. As well as complaining about the difficulty of drawing the diagrams, they also provided moral support and, in some cases, testsolved problems.

I have already recruited enough testsolvers, and I'd like to thank all who signed up to do so. Their usernames can be found below. Unfortunately, as JMO day I demonstrated, I still don't consider myself adequately good at bash to grade bash solutions, so I need people willing to grade ugly, ugly solutions. PM me if you want to grade bash solutions, or just post below!

See this post about time limits.

Signups for grading bashes

Submission Rules

Testsolvers

Day 1 Leaderboard

Day 2 Leaderboard

Complete Leaderboard

Congratulations to EulerMacaroni, tastymath75025, SAUDITYA, rkm0959, mofumofu, and huricane for winning the contest with perfect scores, and congratulations to PcelicaMaja and B.J.W.T for earning second place!
120 replies
wu2481632
May 20, 2017
wu2481632
Jun 21, 2017
Mock Olympiad Geometry Contest #2
G H J
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
wu2481632
4239 posts
#1 • 45 Y
Y by AIME12345, JasperL, kingofgeedorah, 62861, Magikarp1, Generic_Username, budu, mathisawesome2169, checkmatetang, laegolas, speck, Mudkipswims42, rkm0959, skipiano, itised, zxcv1337, anantmudgal09, ThisIsASentence, algebra_star1234, PiDude314, champion999, Plasma_Vortex, artsolver, atmchallenge, Kaladesh, PcelicaMaja, CaptainFlint, AlgebraFC, brianapa, huricane, Problem_Penetrator, leequack, kk108, countdown1234, mathwizard888, soojoong, MinionSV, don2001, niyu, parmenides51, amar_04, AmirKhusrau, OlympusHero, myh2910, Adventure10
"If it is GGG, it will be GG..."

The contest is over!

Welcome, everyone! Over the last few weeks, I have had the pleasure of creating another olympiad geometry contest. My first one can be found here.

As users last time complained about the difficulty of 1/4, I've intentionally made 1/4 around JMO 1/4 level; 2/5/3/6 are closer to USAMO than USAJMO.

I'd like to thank users Generic_Username, AlgebraFC, MathSlayer4444, InCtrl, champion999, joey8189681, braniac1 for being there to support me in the creation of this contest. As well as complaining about the difficulty of drawing the diagrams, they also provided moral support and, in some cases, testsolved problems.

I have already recruited enough testsolvers, and I'd like to thank all who signed up to do so. Their usernames can be found below. Unfortunately, as JMO day I demonstrated, I still don't consider myself adequately good at bash to grade bash solutions, so I need people willing to grade ugly, ugly solutions. PM me if you want to grade bash solutions, or just post below!

See this post about time limits.

Signups for grading bashes

Submission Rules

Testsolvers

Day 1 Leaderboard

Day 2 Leaderboard

Complete Leaderboard

Congratulations to EulerMacaroni, tastymath75025, SAUDITYA, rkm0959, mofumofu, and huricane for winning the contest with perfect scores, and congratulations to PcelicaMaja and B.J.W.T for earning second place!
Attachments:
MockOlympiadGeometryContest2Day1.pdf (96kb)
MockOlympiadGeometryContest2Day2.pdf (87kb)
This post has been edited 36 times. Last edited by wu2481632, Jun 21, 2017, 4:09 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
62861
3564 posts
#2 • 12 Y
Y by Magikarp1, wu2481632, kingofgeedorah, Mudkipswims42, itised, ThisIsASentence, Vedant10, rkm0959, eisirrational, DaniyalQazi2, Adventure10, Mango247
Signups (1)
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Achillys
137 posts
#3 • 3 Y
Y by kingofgeedorah, Adventure10, Mango247
Signups (2)
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
whatshisbucket
975 posts
#4 • 14 Y
Y by kingofgeedorah, wu2481632, RYang, algebra_star1234, Math1331Math, 62861, Mudkipswims42, tenplusten, ThisIsASentence, atmchallenge, jasonhu4, eisirrational, OlympusHero, Adventure10
Signups (3)

I failed to coordinate bash anything on the last one, so I seek redemption.
This post has been edited 2 times. Last edited by whatshisbucket, May 21, 2017, 12:04 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
AIME12345
1129 posts
#5 • 5 Y
Y by kingofgeedorah, soojoong, dchen, Adventure10, Mango247
Signups (4)
This post has been edited 1 time. Last edited by AIME12345, May 20, 2017, 11:56 PM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
zxcv1337
1631 posts
#6 • 2 Y
Y by Adventure10, Mango247
:D
Signups (4)
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Makorn
869 posts
#7 • 3 Y
Y by BobsonJoe, Adventure10, Mango247
Signups (6)
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
katniss123
41 posts
#8 • 1 Y
Y by Adventure10
Signups (7)
This post has been edited 1 time. Last edited by katniss123, May 21, 2017, 12:25 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
algebra_star1234
2467 posts
#9 • 2 Y
Y by Adventure10, Mango247
Signups (8)
This post has been edited 1 time. Last edited by algebra_star1234, May 21, 2017, 1:36 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Math1331Math
5317 posts
#10 • 2 Y
Y by Adventure10, Mango247
Signups (9)
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
techguy2
1297 posts
#11 • 2 Y
Y by Adventure10, Mango247
Signups (10)

oops should do more mocks
This post has been edited 1 time. Last edited by techguy2, May 21, 2017, 1:51 AM
Reason: oops too many typos
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Makorn
869 posts
#12 • 3 Y
Y by BobsonJoe, Adventure10, Mango247
110 signups in 2 hours whoa
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
wu2481632
4239 posts
#13 • 4 Y
Y by champion999, Kagebaka, Adventure10, Mango247
Makorn wrote:
110 signups in 2 hours whoa

yes, i too wish that i had 110 signups :(
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
pslv
165 posts
#14 • 2 Y
Y by Adventure10, Mango247
could anyone please add me?
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
wu2481632
4239 posts
#15 • 3 Y
Y by champion999, Adventure10, Mango247
Signups (11)
Z K Y
G
H
=
a