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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)!

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[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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0 replies
jlacosta
May 1, 2025
0 replies
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2-var inequality
sqing   2
N 2 minutes ago by sqing
Source: Own
Let $ a,b>0, ab^2+a+2b\geq4 $. Prove that$$ \frac{a}{2a+b^2}+\frac{2}{a+2}\leq 1$$
2 replies
1 viewing
sqing
Today at 6:16 AM
sqing
2 minutes ago
J
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Inspired by 2022 MARBLE - Mock ARML
sqing   0
9 minutes ago
Source: Own
Let $ a,b,c\geq 0 , \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}= 5 $ and $ \frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=32. $ Prove that $$\frac{1}{2}>ab+bc+ca \geq \frac{49}{34}$$Let $ a,b,c\geq 0 ,ab+bc+ca = \frac{49}{34} $ and $ \frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=32. $ Prove that $$\frac{51}{10}>\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}\geq5$$Let $ a,b,c\geq 0 ,ab+bc+ca = \frac{49}{34} $ and $ \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}=5. $ Prove that $$\frac{63}{2}<\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\leq32$$
0 replies
sqing
9 minutes ago
0 replies
J
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Inequality on non-nagative numbers
TUAN2k8   2
N 11 minutes ago by pooh123
Source: My book
Let $a,b,c$ be non-nagative real numbers such that $a+b+c=3$.
Prove that $ab+bc+ca-abc \leq \frac{9}{4}$.
2 replies
TUAN2k8
an hour ago
pooh123
11 minutes ago
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Inequality
Sappat   8
N 19 minutes ago by skellyrah
Let $a,b,c$ be real numbers such that $a^2+b^2+c^2=1$. Prove that
$\frac{a^2}{1+2bc}+\frac{b^2}{1+2ca}+\frac{c^2}{1+2ab}\geq\frac{3}{5}$
8 replies
Sappat
Feb 7, 2018
skellyrah
19 minutes ago
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Mathcamp 2011
AwesomeToad   62
N Aug 1, 2011 by MAPARENT
Anyone thinking of going?

Applications come out in about a month.

I'll probably apply, yay :)

Also is anyone from MathPath in previous years planning on going?
62 replies
AwesomeToad
Dec 29, 2010
MAPARENT
Aug 1, 2011
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MATHCAMP 2010 - Who is applying/going this summer?
mathlearner   148
N Jun 7, 2010 by hcs
Just thought I'd start a thread to see who is going where this summer .. I didn't see any other identical threads for this year ...
148 replies
mathlearner
Apr 1, 2010
hcs
Jun 7, 2010
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Who has been accepted and/or plans on attending PROMYS 2010?
mathlearner   3
N May 9, 2010 by DanZ
I realize I am in the Mathcamp forum, but I couldn't find a forum for either PROMYS OR ROSS in the Camps and Other Programs section. Anyway, I just thought I'd start a thread to see who is going to PROMYS .. so if you were accepted, please feel free to post here. (If someone knows of somewhere I should move this thread to, please let me know, and I'll try to repost there).
3 replies
mathlearner
May 9, 2010
DanZ
May 9, 2010
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USAJMO Qualification
v_Enhance   82
N Apr 20, 2010 by BarbieRocks
Source: What, really? I made it?
I decided to make this a separate thread from the already existing USAMO thread.

YAYS I QUALIFIED FOR USAJMO AS AN EIGHTH GRADER :D :rotfl:

I thought my index was 190.5, so either the cutoff was WAY below our forum predictions or I actually did better than I think I did.

Maybe it was just that I had an unclear erasure on a problem which I changed the right answer to the wrong one and it got accepted by sheer dumb luck? :D

Wow, I had given up for the year, thinking that I had failed and that I could now slow down and start reading through AoPS Vol II. Now I have to cram like crazy for JMO. But you have no idea how broadly I'm smiling after feeling I died on the AIME. :D

Anyone else qualify, maybe with a low index like me?
82 replies
v_Enhance
Apr 8, 2010
BarbieRocks
Apr 20, 2010
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MAA is lowing USAMO index??
dinoboy   38
N Apr 18, 2010 by Zhero
Just heard the rumor. How can this happen? The list already has 277 people.
38 replies
dinoboy
Apr 16, 2010
Zhero
Apr 18, 2010
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USAMO Qualification Error???
wsjradha   7
N Apr 8, 2010 by Kent Merryfield
Source: Lost AMC 12 scores
I got a 117 AMC 12 and 10 AIME (also 123 AMC 10), but I am not on the USAMO list, nor have I received a USAMO email, even though my index is a 217 (with 208.5 as the cutoff). I took the AMC 10A and AIME at my school but the AMC 12B at the local college. I have gotten a USAJMO qualification email. My teacher sent me a copy of the AIME school report for this year, so I did not make any bubbling errors. What should I do?

See also: meenamathgirl's post perhaps she is in the same situation
7 replies
wsjradha
Apr 8, 2010
Kent Merryfield
Apr 8, 2010
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Predictions for 2010 USAMO Index
andrewma08   31
N Apr 8, 2010 by andrewma08
Hi,
I'm a freshman in high school that was wondering about your thoughts/opinions on the USAMO Index. I got a 100.5 on the AMC 12B and an 11 on AIME. This puts me up to an index of 210.5. Is that enough to pass?
31 replies
andrewma08
Mar 17, 2010
andrewma08
Apr 8, 2010
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USAMO qualifiers?
Bijection   13
N Apr 2, 2010 by moplam
When are the emails sent and the list posted?
13 replies
Bijection
Apr 2, 2010
moplam
Apr 2, 2010
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2 var inequalities
sqing   0
Apr 24, 2025
Source: Own
Let $ a,b> 0 $ and $ a+b\leq 3ab . $ Prove that
$$ \frac{ a + b }{ a^2(1+ 3b^2)} \leq \frac{3}{2}$$$$ \frac{ a - ab+ b }{ a^2(1+ 3b^2)} \leq 1$$$$ \frac{ a + 3ab+ b }{ a^2(1+ 3b^2)} \leq 3$$$$ \frac{ a -2ab+ b }{ a^2(1+ b^2)}\leq \sqrt{\frac{5}{2}}-\frac{1}{2}$$$$ \frac{ a +ab+ b }{ a^2(1+ b^2)} \leq 2(\sqrt{10}-1)$$$$ \frac{ a -2a^2b^2+ b }{ a^2(1+ b^2)}\leq \frac{\sqrt{82}-5}{2}$$
0 replies
sqing
Apr 24, 2025
0 replies
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2 var inequalities
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sqing
42235 posts
sqing
#1 h  Apr 24, 2025, 2:54 PM
Y by
Let $ a,b> 0 $ and $ a+b\leq 3ab . $ Prove that
$$ \frac{ a + b }{ a^2(1+ 3b^2)} \leq \frac{3}{2}$$$$ \frac{ a - ab+ b }{ a^2(1+ 3b^2)} \leq 1$$$$ \frac{ a + 3ab+ b }{ a^2(1+ 3b^2)} \leq 3$$$$ \frac{ a -2ab+ b }{ a^2(1+ b^2)}\leq \sqrt{\frac{5}{2}}-\frac{1}{2}$$$$ \frac{ a +ab+ b }{ a^2(1+ b^2)} \leq 2(\sqrt{10}-1)$$$$ \frac{ a -2a^2b^2+ b }{ a^2(1+ b^2)}\leq \frac{\sqrt{82}-5}{2}$$
This post has been edited 1 time. Last edited by sqing, Apr 24, 2025, 2:54 PM
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