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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

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Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
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0 replies
jlacosta
Mar 2, 2025
0 replies
J
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The return of American geo
brianzjk   77
N 5 minutes ago by Ilikeminecraft
Source: USAJMO 2023/6
Isosceles triangle $ABC$, with $AB=AC$, is inscribed in circle $\omega$. Let $D$ be an arbitrary point inside $BC$ such that $BD\neq DC$. Ray $AD$ intersects $\omega$ again at $E$ (other than $A$). Point $F$ (other than $E$) is chosen on $\omega$ such that $\angle DFE = 90^\circ$. Line $FE$ intersects rays $AB$ and $AC$ at points $X$ and $Y$, respectively. Prove that $\angle XDE = \angle EDY$.

Proposed by Anton Trygub
77 replies
+1 w
brianzjk
Mar 23, 2023
Ilikeminecraft
5 minutes ago
J
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Apply for Team USA at the International Math Competition (IMC)!
peace09   53
N 5 minutes ago by stjwyl
The International Math Competition (IMC) is essentially the elementary and middle school equivalent of the IMO, with individual and team rounds featuring both short-answer and proof-based problems. See past problems here.

Team USA is looking for 6th graders and below with AIME qualification or AMC 8 DHR (or equivalent), and for 9th graders and below with JMO or Mathcounts Nationals qualification. If you think you meet said criteria, fill out the initial form here.

Here are a couple quick links for further information:
[list=disc]
[*] Dr. Tao Hong's website, which contains a detailed recap of the 2024 competition (and previous years'), as well as Team USA's historical results. (You may recognize a couple names... @channing421 @vrondoS et al.: back me up here :P)
[*] My journal, which gives an insider's perspective on the camp :ninja:
[/list]
53 replies
peace09
Aug 13, 2024
stjwyl
5 minutes ago
J
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OTIS Mock AIME 2025 airs Dec 19th
v_Enhance   39
N 16 minutes ago by MonkeyLuffy
Source: https://web.evanchen.cc/mockaime.html
Satisfactory. Keep cooking.
IMAGE

Problems are posted at https://web.evanchen.cc/mockaime.html#current now!

Like last year, we're running the OTIS Mock AIME 2025 again, except this time there will actually be both a I and a II because we had enough problems to pull it off. However, the two versions will feel quite different from each other:

[list]
[*] The OTIS Mock AIME I is going to be tough. It will definitely be harder than the actual AIME, by perhaps 2 to 4 problems. But more tangibly, it will also have significant artistic license. Problems will freely assume IMO-style background throughout the test, and intentionally stretch the boundary of what constitutes an “AIME problem”.
[*] The OTIS Mock AIME II is meant to be more practically useful. It will adhere more closely to the difficulty and style of the real AIME. There will inevitably still be some more IMO-flavored problems, but they’ll appear later in the ordering.
[/list]
Like last time, all 30 problems are set by current and past OTIS students.

Details are written out at https://web.evanchen.cc/mockaime.html, but to highlight important info:
[list]
[*] Free, obviously. Anyone can participate.
[*]Both tests will release sometime Dec 19th. You can do either/both.
[*]If you'd like to submit for scoring, you should do so by January 20th at 23:59 Pacific time (same deadline for both). Please hold off on public spoilers before then.
[*]Solutions, statistics, and maybe some high scores will be published shortly after that.
[/list]
Feel free to post questions, hype comments, etc. in this thread.
39 replies
v_Enhance
Dec 6, 2024
MonkeyLuffy
16 minutes ago
J
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Gunn Math Competition
the_math_prodigy   12
N 25 minutes ago by the_math_prodigy
Gunn Math Circle is excited to host the fourth annual Gunn Math Competition (GMC)! GMC will take place at Gunn High School in Palo Alto, California on Sunday, March 30th. Gather a team of up to four and compete for over $7,500 in prizes! The contest features three rounds: Individual, Guts, and Team. We welcome participants of all skill levels, with separate Beginner and Advanced divisions for all students.

Registration is free and now open at compete.gunnmathcircle.org. The deadline to sign up is March 27th.

Special Guest Speaker: Po-Shen Loh!!!
We are honored to welcome Po-Shen Loh, a world-renowned mathematician, Carnegie Mellon professor, and former coach of the USA International Math Olympiad team. He will deliver a 30-minute talk to both students and parents, offering deep insights into mathematical thinking and problem-solving in the age of AI!

View competition manual, schedule, prize pool at compete.gunnmathcircle.org . Stay updated by joining our Discord discord.gg/fqcxukv3Dq server. For any questions, reach out at ghsmathcircle@gmail.com or ask in Discord.
12 replies
the_math_prodigy
Mar 8, 2025
the_math_prodigy
25 minutes ago
J
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Geometry problem for enthusiasts
Raul_S_Baz   1
N Yesterday at 5:45 PM by Raul_S_Baz
IMAGE
1 reply
Raul_S_Baz
Yesterday at 4:51 PM
Raul_S_Baz
Yesterday at 5:45 PM
J
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Inequalities
sqing   3
N Yesterday at 4:24 PM by DAVROS
Let $a,b,c\ge \frac{1}{2}$ and $\left(\frac{1}{a}+\frac{1}{b}-\frac{1}{c}\right)\left(\frac{1}{a}-\frac{1}{b}+\frac{1}{c}\right)\le 1. $ Prove that
$$a+b+c\geq 2$$Let $a,b,c\ge \frac{1}{2}$ and $ \left(a+\frac{1}{a}+\frac{1}{b}-\frac{1}{c}\right)\left(a+\frac{1}{a}-\frac{1}{b}+\frac{1}{c}\right)\le \frac{9}{2}. $ Prove that
$$a^2+b^2+c^2\geq 1$$Let $a,b\ge \frac{1}{2}$ and $ \left( \frac{1}{a}-\frac{1}{b}+2\right)\left( \frac{1}{b}-\frac{1}{a}+2\right) \le \frac{20}{9}. $ Prove that
$$ a+b\geq 2$$Let $a,b\ge \frac{1}{2}$ and $a^2+b^2=1. $ Prove that
$$\left(\frac{2}{a}+\frac{1}{b}-1\right)\left(\frac{2}{a}-\frac{1}{b}+1\right)\ge \frac{13}{3}$$
3 replies
sqing
Mar 15, 2025
DAVROS
Yesterday at 4:24 PM
J
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Classic geometry problem
Raul_S_Baz   2
N Yesterday at 4:10 PM by Raul_S_Baz
IMAGE
2 replies
Raul_S_Baz
Mar 4, 2025
Raul_S_Baz
Yesterday at 4:10 PM
J
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complement counting but less rigorous
dotscom26   1
N Yesterday at 3:47 PM by dotscom26
A set of teams held a round-robin tournament in which every team played every other team exactly once. Every team won $10$ games and lost $10$ games; there were no ties. How many sets of three teams $\{A, B, C, D\}$ were there in which $A$ beat $B$, $B$ beat $C$, $C$ beat $D$ and $D$ beat $A?$
1 reply
dotscom26
Yesterday at 3:29 PM
dotscom26
Yesterday at 3:47 PM
J
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Trig Multiplication
szhang7   2
N Yesterday at 3:46 PM by szhang7
Find the exact value of $(2-\sin^2(\frac{\pi}{7}))(2-\sin^2(\frac{2\pi}{7}))(2-\sin^2(\frac{3\pi}{7}))$.
2 replies
szhang7
Sunday at 3:50 PM
szhang7
Yesterday at 3:46 PM
J
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Inequalites
Mario16   17
N Yesterday at 3:21 PM by sqing
If a+b+c=3 ;a,b,c>=0 prove that 1/(5+a^2)+1/(5+b^2)+1/(5+c^2)<=1/2
17 replies
Mario16
Feb 1, 2021
sqing
Yesterday at 3:21 PM
J
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inequalities
LuvThoConBoiRoi   8
N Yesterday at 2:18 PM by sqing
With $a,b,c$ are all real positive number that: $abc=a+b+c+2$. Prove that:
$\frac{1}{a+b} + \frac{1}{b+c} + \frac{1}{c+a} \leq \frac{3}{4}$
8 replies
LuvThoConBoiRoi
Aug 1, 2019
sqing
Yesterday at 2:18 PM
J
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Inequality with integers and indices
Michael Niland   4
N Yesterday at 1:44 PM by krish6_9
Without using a calculator, show that $2^{\frac{1}{2}}$ $< 3^{\frac{1}{3}}$, and for a positive integer $n\geq3$, prove that

$n^{\frac{1}{n}}$ $>(n+1)^{\frac{1}{n+1}}$.
4 replies
Michael Niland
Yesterday at 6:52 AM
krish6_9
Yesterday at 1:44 PM
J
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Complex + Radical Evaluation
Saucepan_man02   1
N Yesterday at 1:30 PM by MathRook7817
Evaluate: (without calculators)
$$ (\sqrt{6 - 2 \sqrt{5}} + i \sqrt{2 \sqrt{5} + 10})^5 + (\sqrt{6 - 2 \sqrt{5}} - i \sqrt{2 \sqrt{5} + 10})^5$$
1 reply
Saucepan_man02
Yesterday at 1:08 PM
MathRook7817
Yesterday at 1:30 PM
J
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Inequalities
sqing   6
N Yesterday at 9:22 AM by sqing
Let $ a, b\geq 0 $ and $ \frac {a^2+a+1}{b^2-b+1}+\frac {b^2+b+1}{a^2-a+1} \geq 3 $. Prove that
$$ a+b+a^2+b^2 \geq 28-6\sqrt{21}$$Let $ a, b\geq 0 $ and $ \frac {a^2+a+1}{b^2-b+1}+\frac {b^2+b+1}{a^2-a+1} \geq 4 $. Prove that
$$ a+b+a^2+b^2 \geq 10-4\sqrt 5$$Let $ a, b\geq 0 $ and $ \frac {a^2+a+1}{b^2-b+1}+\frac {b^2+b+1}{a^2-a+1} \geq 5 $. Prove that
$$ a+b+a^2+b^2 \geq \frac {2(26-5\sqrt{13})}{9} $$Let $ a, b\geq 0 $ and $\frac {a^2+a+1}{b^2-b+1}+\frac {b^2+b+1}{a^2-a+1}\geq 3+ \sqrt {5} $. Prove that
$$ a+b+a^2+b^2 \geq 2$$
6 replies
sqing
Mar 14, 2025
sqing
Yesterday at 9:22 AM
J
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J
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AIME Math History
hashbrown2009   81
N Mar 14, 2025 by stjwyl
Idk why but I wanted to see how good ppl are
Post all your AIME scores ever (if you qualified for USA(J)MO, you may put that score, too)

(Note: Please do not post fake scores. I legit want to see how good ppl are and see how good I am)
I'll start:

5th grade: AIME : 2 lol
6th grade: AIME : 5
7th grade: AIME : 8
8th grade : AIME : 13 USAJMO: 18
9th grade (rn): AIME: 11 (sold)
81 replies
hashbrown2009
Feb 20, 2025
stjwyl
Mar 14, 2025
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AIME Math History
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Reveal topic tags
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G H BBookmark kLocked kLocked NReply
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Ruegerbyrd
1032 posts
Ruegerbyrd
#70 h  Mar 3, 2025, 12:43 AM
Y by
Never qualified :(
mocked from 0-7
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Airbus320-214
77 posts
Airbus320-214
#71 h  Mar 3, 2025, 3:03 AM
Y by
elasticwealth wrote:
9th: 4
10th: 10 (we don’t talk abt jmo)
11th: 11 (hoping for mop)

Nice I also got 10 this year, also G10
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Airbus320-214
77 posts
Airbus320-214
#72 h  Mar 3, 2025, 3:04 AM
Y by
BS2012 wrote:
7th: 84
8th: 118.5, 9 (when you silly a 246.5 index down to a 208.5)
9th: 144, 13

Bro, 13 was insane
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shawnzeng
179 posts
shawnzeng
#73 h  Mar 13, 2025, 3:39 AM
Y by
6th grade: no qual
7th grade : 7 on AIME (We don't talk about what I got on A, 130.5 on B)
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MathPerson12321
3614 posts
MathPerson12321
#74 h  Mar 13, 2025, 3:47 AM
Y by
started comp math in 6th
6th and 7th: um 10 scores sucked
8th: 94.5 on a so 9 points off
9th: made borderline aime and sold both
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arfekete
241 posts
arfekete
#75 h  Mar 13, 2025, 7:46 PM
Y by
Started comp math in 10th, made AIME with exactly the cutoff (93 on 10A)
10th: 8
11th: 9
12th: 12 (current)
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FliX0onbo
272 posts
FliX0onbo
#76 h  Mar 13, 2025, 9:02 PM
Y by
7th: Only MathCounts
8th: 6
9th: 9 (144 10A & 10B :headbash:)
9th JMO: TBD
This post has been edited 1 time. Last edited by FliX0onbo, Mar 13, 2025, 9:03 PM
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stjwyl
1222 posts
stjwyl
#77 h  Mar 13, 2025, 9:49 PM
Y by
i got 96 in 5th grade and made AIME
got 1 on AIME that year

:/
sold and goofed next two years and didnt make AIME
made aime this year (8th) and got 7 on it
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eugenewang1
10 posts
eugenewang1
#78 h  Mar 14, 2025, 12:24 AM
Y by
no qual 8th -> 9 9th
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MathPerson12321
3614 posts
MathPerson12321
#79 h  Mar 14, 2025, 12:31 AM
Y by
FliX0onbo wrote:
7th: Only MathCounts
8th: 6
9th: 9 (144 10A & 10B :headbash:)
9th JMO: TBD

wdym tbd
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Pengu14
405 posts
Pengu14
#80 h  Mar 14, 2025, 12:43 AM
Y by
MathPerson12321 wrote:
FliX0onbo wrote:
7th: Only MathCounts
8th: 6
9th: 9 (144 10A & 10B :headbash:)
9th JMO: TBD

wdym tbd

The JMO is next week

TBD means to be decided
This post has been edited 1 time. Last edited by Pengu14, Mar 14, 2025, 12:44 AM
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sadas123
1030 posts
sadas123
#82 h  Mar 14, 2025, 1:59 AM
Y by
5th grade:12 AMC 8 lol AMC 10 MOCKED* AMC 10 A and B in 5th grade (103.5/105) AIME MOCKED* (4)
6th grade:24 AMC 8 and 7 or 8 on AIME I forgot lol I don't know why (118.5/132)
6th grade is all real
This post has been edited 1 time. Last edited by sadas123, Mar 14, 2025, 2:02 AM
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derekwang2048
1188 posts
derekwang2048
#83 h  Mar 14, 2025, 3:49 AM
Y by
bro sadas tell the truth
did you get 4 or 7 or 9 on aime
and 120 or whatever on AMC 10
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MathPerson12321
3614 posts
MathPerson12321
#84 h  Mar 14, 2025, 4:13 AM
Y by
sadas123 wrote:
5th grade:12 AMC 8 lol AMC 10 MOCKED* AMC 10 A and B in 5th grade (103.5/105) AIME MOCKED* (4)
6th grade:24 AMC 8 and 7 or 8 on AIME I forgot lol I don't know why (118.5/132)
6th grade is all real

this is reasonable they prob js sold amc8 in 5th
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stjwyl
1222 posts
stjwyl
#86 h  Mar 14, 2025, 11:35 PM
Y by
derekwang2048 wrote:
bro sadas tell the truth
did you get 4 or 7 or 9 on aime
and 120 or whatever on AMC 10

who knows
bro gon say "omg guys i sold on aime i got -2" or smth
or gon say "omg guys i cooked on aime i got a 12 missed jmo cutoff by 1 tho !!1!!!1!!!"
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