AMC 10/AIME Study Forum
by PatTheKing806, Mar 27, 2025, 11:34 PM
Me (PatTheKing806) and EaZ_Shadow have created a AMC 10/AIME Study Forum! Hopefully, this forum wont die quickly. To signup, do /join or \join.
Click here to join! (or do some pushups)

People should join this forum if they are wanting to do well on the AMC 10 next year, trying get into AIME, or loves math!
This post has been edited 2 times. Last edited by PatTheKing806, Mar 27, 2025, 11:35 PM
Tennessee Math Tournament (TMT) Online 2025
by TennesseeMathTournament, Mar 9, 2025, 7:30 PM
Hello everyone! We are excited to announce a new competition, the Tennessee Math Tournament, created by the Tennessee Math Coalition! Anyone can participate in the virtual competition for free.
The testing window is from March 22nd to April 12th, 2025. Virtual competitors may participate in the competition at any time during that window.
The virtual competition consists of three rounds: Individual, Bullet, and Team. The Individual Round is 60 minutes long and consists of 30 questions (AMC 10 level). The Bullet Round is 20 minutes long and consists of 80 questions (Mathcounts Chapter level). The Team Round is 30 minutes long and consists of 16 questions (AMC 12 level). Virtual competitors may compete in teams of four, or choose to not participate in the team round.
To register and see more information, click here!
If you have any questions, please email connect@tnmathcoalition.org or reply to this thread!
Thank you to our lead sponsor, Jane Street!

The testing window is from March 22nd to April 12th, 2025. Virtual competitors may participate in the competition at any time during that window.
The virtual competition consists of three rounds: Individual, Bullet, and Team. The Individual Round is 60 minutes long and consists of 30 questions (AMC 10 level). The Bullet Round is 20 minutes long and consists of 80 questions (Mathcounts Chapter level). The Team Round is 30 minutes long and consists of 16 questions (AMC 12 level). Virtual competitors may compete in teams of four, or choose to not participate in the team round.
To register and see more information, click here!
If you have any questions, please email connect@tnmathcoalition.org or reply to this thread!
Thank you to our lead sponsor, Jane Street!

This post has been edited 4 times. Last edited by TennesseeMathTournament, Mar 24, 2025, 2:48 AM
[TEST RELEASED] Mock Geometry Test for College Competitions
by Bluesoul, Feb 24, 2025, 9:42 AM
Hi AOPSers,
I have finished writing a mock geometry test for fun and practice for the real college competitions like HMMT/PUMaC/CMIMC... There would be 10 questions and you should finish the test in 60 minutes, the test would be close to the actual test (hopefully). You could sign up under this thread, PM me your answers!. The submission would close on March 31st at 11:59PM PST.
I would create a private discussion forum so everyone could discuss after finishing the test. This is the first mock I've written, please sign up and enjoy geometry!!
~Bluesoul
Discussion forum: Discussion forum
Leaderboard
I have finished writing a mock geometry test for fun and practice for the real college competitions like HMMT/PUMaC/CMIMC... There would be 10 questions and you should finish the test in 60 minutes, the test would be close to the actual test (hopefully). You could sign up under this thread, PM me your answers!. The submission would close on March 31st at 11:59PM PST.
I would create a private discussion forum so everyone could discuss after finishing the test. This is the first mock I've written, please sign up and enjoy geometry!!
~Bluesoul
Discussion forum: Discussion forum
Leaderboard
Quantum-Phantom: 9
QuestionSourcer: 6
SirAppel: 6
NL008: 6
megahertz13: 6
scannose:4
Anonymous: 3
ethanzhang1001: 3
nats123: 3
bjump: 2
Anonymous: 2
Sadas123: 1
Soupboy0: 1
QuestionSourcer: 6
SirAppel: 6
NL008: 6
megahertz13: 6
scannose:4
Anonymous: 3
ethanzhang1001: 3
nats123: 3
bjump: 2
Anonymous: 2
Sadas123: 1
Soupboy0: 1
Attachments:
This post has been edited 13 times. Last edited by Bluesoul, Saturday at 6:23 PM
PROM^2 for Girls 2025
by mathisfun17, Feb 22, 2025, 12:26 AM
Hi everyone!
The Princeton International School of Math and Science (PRISMS) Math Team is delighted that
for Girls, PRISMS Online Math Meet for Girls, is happening this spring! https://www.prismsus.org/events/prom/home/index
We warmly invite all middle school girls to join us! This is a fantastic opportunity for young girls to connect with others interested in math as well as prepare for future math contests.
This contest will take place online from 12:00 pm to 3:00 pm EST on Saturday, April 26th, 2025.
The competition will include a team and individual round as well as activities like origami. You can see a detailed schedule here. https://prismsus.org/events/prom/experience/schedule.
Registration is FREE, there are cash prizes for participants who place in the top 10 and cool gifts for all participants.
1st place individual: $500 cash
2nd place individual: $300 cash
3rd place individual: $100 cash
4th-10th place individual: $50 cash each
Some FAQs:
Q: How difficult are the questions?
A: The problem difficulty is around AMC 8 or Mathcounts level.
Q: Are there any example problems?
A: You can find some archived here: https://www.prismsus.org/events/prom/achieve/achieve
Registration is open now. https://www.prismsus.org/events/prom/register/register. Email us at prom2@prismsus.org with any questions.
The PRISMS Peregrines Math Team welcomes you!
The Princeton International School of Math and Science (PRISMS) Math Team is delighted that

We warmly invite all middle school girls to join us! This is a fantastic opportunity for young girls to connect with others interested in math as well as prepare for future math contests.
This contest will take place online from 12:00 pm to 3:00 pm EST on Saturday, April 26th, 2025.
The competition will include a team and individual round as well as activities like origami. You can see a detailed schedule here. https://prismsus.org/events/prom/experience/schedule.
Registration is FREE, there are cash prizes for participants who place in the top 10 and cool gifts for all participants.
1st place individual: $500 cash
2nd place individual: $300 cash
3rd place individual: $100 cash
4th-10th place individual: $50 cash each
Some FAQs:
Q: How difficult are the questions?
A: The problem difficulty is around AMC 8 or Mathcounts level.
Q: Are there any example problems?
A: You can find some archived here: https://www.prismsus.org/events/prom/achieve/achieve
Registration is open now. https://www.prismsus.org/events/prom/register/register. Email us at prom2@prismsus.org with any questions.
The PRISMS Peregrines Math Team welcomes you!
This post has been edited 1 time. Last edited by mathisfun17, Feb 22, 2025, 12:27 AM
2025 INTEGIRLS NYC/NJ Math Competition
by sargamsujit, Jan 28, 2025, 11:40 PM
NYC/NJ INTEGIRLS will be hosting our second annual math competition on May 3rd, 2025 from 9:30 AM to 4:30 PM EST at Rutgers University. Last year, we proudly organized the largest math competition for girls globally, welcoming over 500 participants from across the tristate area. Join other female-identifying and non-binary "STEMinists" in solving problems, socializing, playing games, and more! If you are interested in competing, please register at https://forms.gle/jqwEiq5PgqefetLj7
Find our website at https://nyc.nj.integirls.org/
Eligibility: This competition is open to all female-identifying and non-binary students in 8th grade or under. The competition is also completely free, including registration and lunch.
System: We will have two divisions: a middle school division and an elementary school division. There will be an individual round and team round. There will be prizes for the top competitors in each division!
Problem Difficulty: Our amazing team of problem writers is working hard to ensure that there will be problems for problem-solvers of all levels! The elementary school problems will range from introductory to AMC 8 level, while the middle school problems will be for more advanced problem-solvers. Team round problems will cover various difficulty levels.
Platform: This contest will be held in person at Rutgers University. Competitors will all receive free merchandise, raffle tickets, and the chance to win exclusive gift prizes!
Find our website at https://nyc.nj.integirls.org/
Important Information
Eligibility: This competition is open to all female-identifying and non-binary students in 8th grade or under. The competition is also completely free, including registration and lunch.
System: We will have two divisions: a middle school division and an elementary school division. There will be an individual round and team round. There will be prizes for the top competitors in each division!
Problem Difficulty: Our amazing team of problem writers is working hard to ensure that there will be problems for problem-solvers of all levels! The elementary school problems will range from introductory to AMC 8 level, while the middle school problems will be for more advanced problem-solvers. Team round problems will cover various difficulty levels.
Platform: This contest will be held in person at Rutgers University. Competitors will all receive free merchandise, raffle tickets, and the chance to win exclusive gift prizes!
Prizes
Over $2,000 in awards, including plaques, medals, plushies, gift cards, toys, books, swag, and more for top competitors and teams
Over $2,000 in awards, including plaques, medals, plushies, gift cards, toys, books, swag, and more for top competitors and teams
Help Us Out
Please help us in sharing our competition and spreading the word! Our amazing team of officers has worked very hard to provide this educational opportunity to as many students as possible and we would appreciate it if you could help us spread the word!
Format credits go to Indy INTEGIRLS!
Format credits go to Indy INTEGIRLS!
This post has been edited 1 time. Last edited by sargamsujit, Jan 28, 2025, 11:40 PM
Congrats Team USA!
by MathyMathMan, Jul 21, 2024, 3:18 PM
Congratulations to the USA team for placing 1st at the 65th IMO that took place in Bath, United Kingdom.
The team members were:
Jordan Lefkowitz
Krishna Pothapragada
Jessica Wan
Alexander Wang
Qiao Zhang
Linus Tang
The team members were:
Jordan Lefkowitz
Krishna Pothapragada
Jessica Wan
Alexander Wang
Qiao Zhang
Linus Tang
IMO
L
Correlation between USAMO and CMO qualification
by rantaccountcs, Nov 2, 2023, 7:56 PM
Fixed point as P varies
by tenniskidperson3, Apr 19, 2016, 9:32 PM
The isosceles triangle
, with
, is inscribed in the circle
. Let
be a variable point on the arc
that does not contain
, and let
and
denote the incenters of triangles
and
, respectively.
Prove that as
varies, the circumcircle of triangle
passes through a fixed point.










Prove that as


USAJMO #5 - points on a circle
by hrithikguy, Apr 28, 2011, 10:10 PM
Points
lie on a circle
and point
lies outside the circle. The given points are such that (i) lines
and
are tangent to
, (ii)
are collinear, and (iii)
. Prove that
bisects
.










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