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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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 events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/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.

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0 replies
jlacosta
Apr 2, 2025
0 replies
9 Fun Proof Endings
elasticwealth   51
N 20 minutes ago by steve4916
It seems like AOPS is going through a stressful phase right now.

Let's lighten the mood by voting on the best proof endings!
51 replies
elasticwealth
Yesterday at 12:26 AM
steve4916
20 minutes ago
2025 ELMOCOUNTS - Mock MATHCOUNTS Nationals
vincentwant   122
N 29 minutes ago by steve4916
text totally not copied over from wmc (thanks jason <3)
Quick Links:
[list=disc]
[*] National: (Sprint) (Target) (Team) (Sprint + Target Submission) (Team Submission) [/*]
[*] Miscellaneous: (Leaderboard) (Sprint + Target Private Discussion Forum) (Team Discussion Forum)[/*]
[/list]
-----
Eddison Chen (KS '22 '24), Aarush Goradia (CO '24), Ethan Imanuel (NJ '24), Benjamin Jiang (FL '23 '24), Rayoon Kim (PA '23 '24), Jason Lee (NC '23 '24), Puranjay Madupu (AZ '23 '24), Andy Mo (OH '23 '24), George Paret (FL '24), Arjun Raman (IN '24), Vincent Wang (TX '24), Channing Yang (TX '23 '24), and Jefferson Zhou (MN '23 '24) present:



[center]IMAGE[/center]

[center]Image credits to Simon Joeng.[/center]

2024 MATHCOUNTS Nationals alumni from all across the nation have come together to administer the first-ever ELMOCOUNTS Competition, a mock written by the 2024 Nationals alumni given to the 2025 Nationals participants. By providing the next generation of mathletes with free, high quality practice, we're here to boast how strong of an alumni community MATHCOUNTS has, as well as foster interest in the beautiful art that is problem writing!

The tests and their corresponding submissions forms will be released here, on this thread, on Monday, April 21, 2025. The deadline is May 10, 2025. Tests can be administered asynchronously at your home or school, and your answers should be submitted to the corresponding submission form. If you include your AoPS username in your submission, you will be granted access to the private discussion forum on AoPS, where you can discuss the tests even before the deadline.
[list=disc]
[*] "How do I know these tests are worth my time?" [/*]
[*] "Who can participate?" [/*]
[*] "How do I sign up?" [/*]
[*] "What if I have multiple students?" [/*]
[*] "What if a problem is ambiguous, incorrect, etc.?" [/*]
[*] "Will there be solutions?" [/*]
[*] "Will there be a Countdown Round administered?" [/*]
[/list]
If you have any other questions, feel free to email us at elmocounts2025@gmail.com (or PM me)!
122 replies
vincentwant
Apr 20, 2025
steve4916
29 minutes ago
A nice inequality
KhuongTrang   0
3 hours ago
[quote=KhuongTrang]Problem. Let $a,b,c\ge 0: ab+bc+ca>0.$ Prove that$$\color{blue}{\frac{\left(2ab+ca+cb\right)^{2}}{a^{2}+4ab+b^{2}}+\frac{\left(2bc+ab+ac\right)^{2}}{b^{2}+4bc+c^{2}}+\frac{\left(2ca+bc+ba\right)^{2}}{c^{2}+4ca+a^{2}}\ge \frac{8(ab+bc+ca)}{3}.}$$[/quote]

0 replies
KhuongTrang
3 hours ago
0 replies
Inequalities
sqing   6
N 3 hours ago by lbh_qys
Let $x,y\ge 0$ such that $ 13(x^3+y^3) \leq 125(1+xy)$. Prove that
$$  k(x+y)-xy\leq  5(2k-5)$$Where $k\geq 5.6797. $
$$  6(x+y)-xy\leq 35$$
6 replies
sqing
Apr 20, 2025
lbh_qys
3 hours ago
Inequalities
sqing   0
3 hours ago
Let $ a,b \in [0 ,1] . $ Prove that
$$\frac{a}{ 1-ab+b }+\frac{b }{ 1-ab+a } \leq 2$$$$ \frac{a}{ 1+ab+b^2 }+\frac{b }{ 1+ab+a^2 }+\frac{ab }{2+ab }  \leq 1$$$$\frac{a}{ 1-ab+b^2 }+\frac{b }{ 1-ab+a^2 }+\frac{1 }{1+ab  }\leq \frac{5}{2}$$$$\frac{a}{ 1-ab+b^2 }+\frac{b }{ 1-ab+a^2 }+\frac{1 }{1+2ab  }\leq \frac{7}{3}$$$$\frac{a}{ 1+ab+b^2 }+\frac{b }{ 1+ab+a^2 } +\frac{ab }{1+ab }\leq \frac{7}{6 }$$
0 replies
sqing
3 hours ago
0 replies
Inequalities from SXTX
sqing   20
N 4 hours ago by sqing
T702. Let $ a,b,c>0 $ and $ a+2b+3c=\sqrt{13}. $ Prove that $$ \sqrt{a^2+1} +2\sqrt{b^2+1} +3\sqrt{c^2+1} \geq 7$$S
T703. Let $ a,b $ be real numbers such that $ a+b\neq 0. $. Find the minimum of $ a^2+b^2+(\frac{1-ab}{a+b} )^2.$
T704. Let $ a,b,c>0 $ and $ a+b+c=3. $ Prove that $$ \frac{a^2+7}{(c+a)(a+b)} + \frac{b^2+7}{(a+b)(b+c)} +\frac{c^2+7}{(b+c)(c+a)}  \geq 6$$S
20 replies
sqing
Feb 18, 2025
sqing
4 hours ago
An FE. Who woulda thunk it?
nikenissan   115
N 5 hours ago by Ilikeminecraft
Source: 2021 USAJMO Problem 1
Let $\mathbb{N}$ denote the set of positive integers. Find all functions $f : \mathbb{N} \rightarrow \mathbb{N}$ such that for positive integers $a$ and $b,$ \[f(a^2 + b^2) = f(a)f(b) \text{ and } f(a^2) = f(a)^2.\]
115 replies
nikenissan
Apr 15, 2021
Ilikeminecraft
5 hours ago
average FE
KevinYang2.71   81
N 5 hours ago by Ilikeminecraft
Source: USAJMO 2024/5
Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ that satisfy
\[
f(x^2-y)+2yf(x)=f(f(x))+f(y)
\]for all $x,y\in\mathbb{R}$.

Proposed by Carl Schildkraut
81 replies
KevinYang2.71
Mar 21, 2024
Ilikeminecraft
5 hours ago
Theory of Equations
P162008   3
N 5 hours ago by P162008
Let $a,b,c,d$ and $e\in [-2,2]$ such that $\sum_{cyc} a = 0, \sum_{cyc} a^3 = 0, \sum_{cyc} a^5 = 10.$ Find the value of $\sum_{cyc} a^2.$
3 replies
P162008
Apr 23, 2025
P162008
5 hours ago
Fun & Simple puzzle
Kscv   7
N 5 hours ago by vanstraelen
$\angle DCA=45^{\circ},$ $\angle BDC=15^{\circ},$ $\overline{AC}=\overline{CB}$

$\angle ADC=?$
7 replies
Kscv
Apr 13, 2025
vanstraelen
5 hours ago
A problem involving modulus from JEE coaching
AshAuktober   7
N Today at 5:55 AM by Jhonyboy
Solve over $\mathbb{R}$:
$$|x-1|+|x+2| = 3x.$$
(There are two ways to do this, one being bashing out cases. Try to find the other.)
7 replies
AshAuktober
Apr 21, 2025
Jhonyboy
Today at 5:55 AM
FB = BK , circumcircle and altitude related (In the World of Mathematics 516)
parmenides51   5
N Today at 4:05 AM by jasperE3
Let $BT$ be the altitude and $H$ be the intersection point of the altitudes of triangle $ABC$. Point $N$ is symmetric to $H$ with respect to $BC$. The circumcircle of triangle $ATN$ intersects $BC$ at points $F$ and $K$. Prove that $FB = BK$.

(V. Starodub, Kyiv)
5 replies
parmenides51
Apr 19, 2020
jasperE3
Today at 4:05 AM
Polynomial Limit
P162008   0
Today at 1:47 AM
Let $p = \lim_{y\to\infty} \left(\frac{2}{y^2} \left(\lim_{z\to\infty} \frac{1}{z^4} \left(\lim_{x\to\infty} \frac{((y^2 + y + 1)x^k + 1)^{z^2 + z + 1} - ((z^2 + z + 1)x^k + 1)^{y^2 + y + 1}}{x^{2k}}\right)\right)\right)^y$ where $k \in N$ and $q = \lim_{n\to\infty} \left(\frac{\binom{2n}{n}. n!}{n^n}\right)^{1/n}$ where $n \in N$. Find the value of $p.q.$
0 replies
P162008
Today at 1:47 AM
0 replies
Octagon Problem
Shiyul   4
N Today at 1:43 AM by Sid-darth-vater
The vertices of octagon $ABCDEFGH$ lie on the same circle. If $AB = BC = CD = DE = 11$ and $EF = FG = GH = HA = sqrt2$, what is the area of octagon $ABCDEFGH$?

I approached this problem by noticing that the area of the octagon is the area of the eight isoceles triangles with lengths $r$, $r$, and $sqrt2$ or 11. However, I didn't know how to find the radius. Can anyone give me a hint?
4 replies
Shiyul
Yesterday at 11:41 PM
Sid-darth-vater
Today at 1:43 AM
Mop Qual stuff
HopefullyMcNats2025   65
N Apr 1, 2025 by fake123
How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard
65 replies
HopefullyMcNats2025
Mar 30, 2025
fake123
Apr 1, 2025
Mop Qual stuff
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HopefullyMcNats2025
45 posts
#1 • 3 Y
Y by RainbowJessa, Exponent11, cubres
How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard
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Pengu14
577 posts
#2 • 2 Y
Y by RainbowJessa, cubres
HopefullyMcNats2025 wrote:
How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard

MOP basically guarantees MIT/harvard
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HopefullyMcNats2025
45 posts
#3 • 3 Y
Y by elasticwealth, RainbowJessa, cubres
Not true at all
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mdk2013
625 posts
#4 • 2 Y
Y by RainbowJessa, cubres
Pengu14 wrote:
HopefullyMcNats2025 wrote:
How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard

MOP basically guarantees MIT/harvard

def not true, a big portion of college apps comes from writing and literature
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hashbrown2009
182 posts
#5 • 1 Y
Y by cubres
mdk2013 wrote:
Pengu14 wrote:
HopefullyMcNats2025 wrote:
How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard

MOP basically guarantees MIT/harvard

def not true, a big portion of college apps comes from writing and literature

While I agree MOP doesn't guarantee, your statement isn't accurate either. They say it is but it actually is only like 40% of the percent. the other 60% comes from extra-curriculars, volunteer service, your grades and your achievements.
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Shan3t
273 posts
#6 • 1 Y
Y by cubres
Pengu14 wrote:
HopefullyMcNats2025 wrote:
How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard

MOP basically guarantees MIT/harvard

idk if this is true.

Mit/Harvard looks 4 science, coding, literature, etc. But if ur like a GOD at maths, aka Luke Robitaille level, you can definitely make those colleges.
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Pengu14
577 posts
#7 • 1 Y
Y by cubres
mdk2013 wrote:
Pengu14 wrote:
HopefullyMcNats2025 wrote:
How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard

MOP basically guarantees MIT/harvard

def not true, a big portion of college apps comes from writing and literature

I meant it in the sense that around 95% of MOPpers get into MIT. Also, why would literature matter at all for college apps?
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mdk2013
625 posts
#8 • 2 Y
Y by Exponent11, cubres
why am i writing about college apps when im not even a teen, excuse my mistakes
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LearnMath_105
149 posts
#9 • 1 Y
Y by cubres
Not sure about harvard but from what I've heard its a near lock for MIT as long as your GPA isn't bad
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Pengu14
577 posts
#10 • 1 Y
Y by cubres
Shan3t wrote:
Pengu14 wrote:
HopefullyMcNats2025 wrote:
How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard

MOP basically guarantees MIT/harvard

idk if this is true.

Mit/Harvard looks 4 science, coding, literature, etc. But if ur like a GOD at maths, aka Luke Robitaille level, you can definitely make those colleges.

They look for achievements and dedication in things you’re passionate about.
This post has been edited 1 time. Last edited by Pengu14, Mar 30, 2025, 11:46 PM
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scannose
1004 posts
#11 • 1 Y
Y by cubres
it should at the very least increase your chances by a lot
mit does value qualification for mop, and they should admit you as long as your gpa is good and nothing else is problematic (although what counts as a "good" gpa is debatable)
i've also heard that mit doesn't care that much about essays, but from how my source turned out last time take this will possibly less than a grain of salt
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hashbrown2009
182 posts
#12 • 1 Y
Y by cubres
Shan3t wrote:
Pengu14 wrote:
HopefullyMcNats2025 wrote:
How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard

MOP basically guarantees MIT/harvard

idk if this is true.

Mit/Harvard looks 4 science, coding, literature, etc. But if ur like a GOD at maths, aka Luke Robitaille level, you can definitely make those colleges.

Note that nearly all people who apply for MIT, Princeton, Harvard etc. who have made MOP usually apply for math or computer science and nearly all make it in, according to statistics of the MOPpers.

Edit: Also, please note that very few people are as good as Luke Robitaille, so don't use him as a comparison.
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HopefullyMcNats2025
45 posts
#13 • 1 Y
Y by cubres
I would say no one aside from Evan Chen, because luke made imo gold medal in 9th and won mc 2x in a row, his achievements are unique to him mostly
This post has been edited 1 time. Last edited by HopefullyMcNats2025, Mar 30, 2025, 11:55 PM
Reason: Typo
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Pengu14
577 posts
#14 • 1 Y
Y by cubres
HopefullyMcNats2025 wrote:
I would say no one aside from Evan Chen, because luke made imo gold medal in 9th and won mc 2x in a row, his achievements are unique to him mostly

dotted is also most likely going to be a 4x gold medalist
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awesomeming327.
1699 posts
#15 • 7 Y
Y by scannose, Pengu14, Marcus_Zhang, aidan0626, Radio2, cubres, aidensharp
If you really love math competitions, you should do it regardless of whether it looks good on a college application. This is because if you end up not making MOP, you'll feel sad but rewarded by the experience overall, as opposed to only feeling sad.

But for what it's worth, making MOP is nearly a direct ticket.
This post has been edited 1 time. Last edited by awesomeming327., Mar 31, 2025, 12:04 AM
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