Stay ahead of learning milestones! Enroll in a class over the summer!

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
Coolabra
Titibuuu   3
N 13 minutes ago by sqing
Let \( a, b, c \) be distinct real numbers such that
\[
a + b + c + \frac{1}{abc} = \frac{19}{2}
\]Find the maximum possible value of \( a \).
3 replies
+2 w
Titibuuu
Today at 2:21 AM
sqing
13 minutes ago
interesting functional
Pomegranat   1
N 22 minutes ago by NicoN9
Source: I don't know sorry
Find all functions \( f : \mathbb{R}^+ \to \mathbb{R}^+ \) such that for all positive real numbers \( x \) and \( y \), the following equation holds:
\[
\frac{x + f(y)}{x f(y)} = f\left( \frac{1}{y} + f\left( \frac{1}{x} \right) \right)
\]
1 reply
Pomegranat
an hour ago
NicoN9
22 minutes ago
Is the result of this is the same as cauchy?
ItzsleepyXD   0
22 minutes ago
Source: curiosity
Prove or disprove that for all continuous or monotonic function $f : \mathbb{R}^2 \to \mathbb{R}$ .The solution to $$f(a,x)+f(b,y)=f(a+b,x+y) \text{ for all }a,b,x,y \in \mathbb{R}$$is only $f(x,y)=cx+dy$ for some $c,d \in \mathbb{R}$
0 replies
ItzsleepyXD
22 minutes ago
0 replies
a fractions problem
kjhgyuio   1
N 25 minutes ago by Ash_the_Bash07
.........
1 reply
kjhgyuio
an hour ago
Ash_the_Bash07
25 minutes ago
No more topics!
wu2481632 Mock Geometry Olympiad problems
wu2481632   14
N Apr 7, 2025 by bin_sherlo
To avoid clogging the fora with a horde of geometry problems, I'll post them all here.

Day I

Day II

Enjoy the problems!
14 replies
wu2481632
Mar 13, 2017
bin_sherlo
Apr 7, 2025
wu2481632 Mock Geometry Olympiad problems
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 • 16 Y
Y by laegolas, MathAwesome123, 62861, claserken, efang, Generic_Username, lucasxia01, rkm0959, anantmudgal09, soojoong, CQYIMO42, mhq, parmenides51, Adventure10, Mango247, Bet667
To avoid clogging the fora with a horde of geometry problems, I'll post them all here.

Day I

Day II

Enjoy the problems!
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
liberator
95 posts
#2 • 12 Y
Y by AlgebraFC, j___d, laegolas, GoJensenOrGoHome, atmchallenge, claserken, lucasxia01, rkm0959, anantmudgal09, Aryan-23, Adventure10, MS_asdfgzxcvb
Problem 1
Problem 2
Problem 3 (my original solution by complex bash
Problem 3 (better solution)
Problem 4 (barybash)
Problem 5
Problem 6
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
#3 • 1 Y
Y by Adventure10
Surprisingly, nobody found our solution for #2, so I'm not exactly sure it's completely correct, so I'll post it here to check.

Solution
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
#4 • 2 Y
Y by Adventure10, Mango247
Also, as only a barybash has been posted for #4, I thought it appropriate to post a synthetic solution.

4
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
#5 • 1 Y
Y by Adventure10
Oops, sorry about a third post -- but no one has found the Major Hint solution for #6, which I believe is the shortest.
This post has been edited 1 time. Last edited by wu2481632, Mar 14, 2017, 12:41 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
gianteel
73 posts
#6 • 3 Y
Y by Aryan-23, Adventure10, Mango247
Unless I'm misreading, I think there's a quick solution to #6 which involves inverting about $P$? The diagram attached should outline a solution.
Attachments:
This post has been edited 1 time. Last edited by gianteel, Mar 14, 2017, 2:25 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
bobthesmartypants
4337 posts
#7 • 2 Y
Y by 62861, Adventure10
These problems seem to consist entirely of Projective and Inversive geometry. :maybe:
zacchro would be pleased :lol:
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
#8 • 2 Y
Y by Adventure10, Mango247
bobthesmartypants wrote:
These problems seem to consist entirely of Projective and Inversive geometry. :maybe:
zacchro would be pleased :lol:

help i solved 1,4,5 without projective or inversive tools
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
rkm0959
1721 posts
#9 • 4 Y
Y by anantmudgal09, themathfreak, Adventure10, Mango247
Sketch, because I don't have access to computer rn

1. Angle Chase, easy

2. Prove Gamma and BFEC are orthogonal -> T1 T2 lie on (BFEC) so use radical axis on (ABC), Gamma and (BFEC) to get BC S1S2 T1T2 concurrent. Now use brokard a lot of times. Angle chase to get XY to be a diameter of Gamma, then brokard again.

3. 1:00 am rip

4. Prove LH=r by a simple length bash - AH and AL is easy to calculate. The rest is angle chase.

5. Extend DP and DQ to meet (DS1S2) at P', Q'.
Then one can get, by PoP that AEDBP' and AFDCQ' are cyclic. The rest is ratio bash to prove that PQ and P'Q' are parallel.

6. Easily get that A1B1 A2B2 O12O21 concur at a point T on AB such that (A,B;P,T)=-1. This implies that O12O21 passes through a point T' such that (O1,O2;T',P)=-1. Now notice that A1P and A2P are polars of O1 and O2 wrt (A1A2P) and etc. We can use harmonic quad/pencil to prove that A1A2 passes through T' and we are done.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
anantmudgal09
1980 posts
#10 • 2 Y
Y by Adventure10, Mango247
I post my submitted solutions in all their glory. Especially the over complicated one for #3 and the faster one for #4.

1

2

3

4

5

6

6 (later version)
This post has been edited 3 times. Last edited by anantmudgal09, Mar 14, 2017, 2:02 PM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
rkm0959
1721 posts
#11 • 2 Y
Y by Adventure10, Mango247
Problem 1 is straightforward, I won't post the solution.

Problem 2

Problem 4

Problem 5

Problem 6
This post has been edited 3 times. Last edited by rkm0959, Mar 15, 2017, 4:39 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Vfire
1354 posts
#12 • 2 Y
Y by Adventure10, Mango247
Problem 5
This post has been edited 3 times. Last edited by Vfire, May 24, 2018, 4:15 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
awesomeming327.
1717 posts
#13
Y by
Solution to P3 using elementary methods
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
bin_sherlo
720 posts
#14 • 2 Y
Y by GeoKing, MS_asdfgzxcvb
Problem 5
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
bin_sherlo
720 posts
#15
Y by
Problem 3
Z K Y
N Quick Reply
G
H
=
a