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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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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]
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All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
May 1, 2025
0 replies
Jane street swag package? USA(J)MO
arfekete   10
N 8 minutes ago by Martin2001
Hey! People are starting to get their swag packages from Jane Street for qualifying for USA(J)MO, and after some initial discussion on what we got, people are getting different things. Out of curiosity, I was wondering how they decide who gets what.
Please enter the following info:

- USAMO or USAJMO
- Grade
- Score
- Award/Medal/HM
- MOP (yes or no, if yes then color)
- List of items you got in your package

I will reply with my info as an example.
10 replies
arfekete
Yesterday at 4:34 PM
Martin2001
8 minutes ago
Will I fail again
hashbrown2009   1
N 43 minutes ago by Inaaya
so this year I got 34 on JMO 772 774 and got docked 1 point from top honors + mop

I just got info that I pretty much cannot do math for the rest of summer due to family reasons, and the only time I have is winter break

do you guys think it's enough time to practice/grind to qualify mop through USAMO, or should I tell my parents to reschedule the stuff because I really want to make mop

(Note: I'm aiming for like 25+ on USAMO so at least silver but I'm not sure that's realistic given the circumstances i'm in)
1 reply
hashbrown2009
an hour ago
Inaaya
43 minutes ago
USAMO Medals
YauYauFilter   46
N an hour ago by Inaaya
YauYauFilter
Apr 24, 2025
Inaaya
an hour ago
MOP Emails Out! (not clickbait)
Mathandski   101
N Today at 5:42 AM by Craftybutterfly
What an emotional roller coaster the past 34 days have been.

Congrats to all that qualified!
101 replies
1 viewing
Mathandski
Apr 22, 2025
Craftybutterfly
Today at 5:42 AM
No more topics!
System
worthawholebean   10
N Apr 29, 2025 by daijobu
Source: AIME 2008II Problem 14
Let $ a$ and $ b$ be positive real numbers with $ a\ge b$. Let $ \rho$ be the maximum possible value of $ \frac{a}{b}$ for which the system of equations
\[ a^2+y^2=b^2+x^2=(a-x)^2+(b-y)^2\]has a solution in $ (x,y)$ satisfying $ 0\le x<a$ and $ 0\le y<b$. Then $ \rho^2$ can be expressed as a fraction $ \frac{m}{n}$, where $ m$ and $ n$ are relatively prime positive integers. Find $ m+n$.
10 replies
worthawholebean
Apr 3, 2008
daijobu
Apr 29, 2025
System
G H J
Source: AIME 2008II Problem 14
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worthawholebean
3017 posts
#1 • 1 Y
Y by Adventure10
Let $ a$ and $ b$ be positive real numbers with $ a\ge b$. Let $ \rho$ be the maximum possible value of $ \frac{a}{b}$ for which the system of equations
\[ a^2+y^2=b^2+x^2=(a-x)^2+(b-y)^2\]has a solution in $ (x,y)$ satisfying $ 0\le x<a$ and $ 0\le y<b$. Then $ \rho^2$ can be expressed as a fraction $ \frac{m}{n}$, where $ m$ and $ n$ are relatively prime positive integers. Find $ m+n$.
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calc rulz
1126 posts
#2 • 3 Y
Y by Adventure10, Mango247, and 1 other user
Click to reveal hidden text

EDIT: Hmm I think I switched a and b, but the answer is still the same.
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beta
3001 posts
#3 • 2 Y
Y by Adventure10, Mango247
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krustyteklown
641 posts
#4 • 1 Y
Y by Adventure10
These solutions are very nice. I was thinking geometric during the test too, but stuck to normal conic section curves and such.
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K81o7
2417 posts
#5 • 2 Y
Y by Adventure10 and 1 other user
Non-geometric...
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seasonal squirrel
57 posts
#6 • 2 Y
Y by Adventure10, Mango247
i was going through the AOPS wiki and I noticed that K81o7's solution has a small typing error in it. He actually says that the minimum value is 4/3, not the maximum. This doesn't affect the validity of his solution however i do want it to be corrected.
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Mudkipswims42
8867 posts
#7 • 1 Y
Y by Adventure10
calc rulz wrote:
Click to reveal hidden text

EDIT: Hmm I think I switched a and b, but the answer is still the same.


Sorry for the bump, but wouldn't in this solution $f(\theta)$ be maximized at $\theta=0$? This gives a value of $p=\dfrac{2}{\sqrt{3}}$ which matches the other solutions...
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ayushk
362 posts
#8 • 1 Y
Y by Adventure10
He switched $a,b$, which changes the problem a bit.
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yojan_sushi
330 posts
#9 • 3 Y
Y by dknj11902, Adventure10, Mango247
For a non-calculus way to maximize the function in calc rulz's post:
Click to reveal hidden text

This method also applies to maximizing/minimizing functions like $f(x)=\frac{x^2+4x+13}{3x^2+2x+3}$ for $x$ in the reals. See #48 here: http://holbrook.bergen.org/oldcomp/2015/Grade8.pdf
The solution is here: http://holbrook.bergen.org/oldcomp/2015/Grade8sol.pdf
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277546
1607 posts
#10
Y by
Non-Calculus Solution
This post has been edited 2 times. Last edited by 277546, Mar 3, 2020, 7:40 AM
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daijobu
527 posts
#11
Y by
Video Solution
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N Quick Reply
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