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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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Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

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
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k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
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k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
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Good luck on olympiads tomorrow!
observer04   5
N 9 minutes ago by ElectricWolverine
Hello mortals!

For those of you that qualified for the USAMO / USAJMO, I have a message for you! Remember to have fun! And enjoy the experience! Personally, I did not qualify for the USAMO / USAJMO! But I am still eager to try the high quality thought-provoking problems! As I once said... it's not all about the score!

Furthermore, for those like myself who failed along the way, it's A-OK! Don't worry, fellows! Remember to smile and enjoy your lives! There is more than math out there!


Warmest Regards
5 replies
observer04
Today at 1:27 AM
ElectricWolverine
9 minutes ago
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U.S.J.A.M.O tips from a superstar!
K-Cliquey   25
N 11 minutes ago by Reaper177
Source: smart people
Hi every body. I know it is very stressful because the U.S.J.A.M.O. is soon, I just want to make sure everyone pays attention to their mental health. Every day, remember mental health is more important than U.S.J.A.M.Ο.

And I used to be worse than my friend at U.S.J.A.M.O., but I improve, so here are my tips for making sure mental health on the U.S.J.A.M.O.


1. Drink water. You are not cactus.


2. Don't drink too much water. Or else you will pee.


3. Get protein. I recommend cow meat.


4. (I am serious) Have a girlfriend or a boyfriend. I got rejected 8 times before I met Lennon Court, but he is my best emotional support on the U.S.J.A.M.O. now. It is good emotional support.


5. Sleep early. I know you guys are scared of dreaming about bad U.S.J.A.M.O. grade, but just think about #4 so you can get mental healthy from sleep instead of nightmare.


6. Social to your friends! They are also good mental healthy support.



Now, most importantly, ADD YOUR TIPS TO THIS LIST. PLEASE COMMENT DOWN BELOW YOUR TIPS FOR GOOD MENTAL HEALTH. We are a TEAM to have good MENTAL HEALTH.
25 replies
K-Cliquey
Today at 4:56 AM
Reaper177
11 minutes ago
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inequality
senku23   3
N 27 minutes ago by SunnyEvan
Let x,y,z in R+ prove that 8(x^3+y^3+z^3)2≥9(x^2+yz)(y^2+zx)(z^2+xy).
3 replies
senku23
3 hours ago
SunnyEvan
27 minutes ago
J
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Cool Number Theory
Fermat_Fanatic108   1
N an hour ago by Fermat_Fanatic108
For an integer with 5 digits $n=abcde$ (where $a, b, c, d, e$ are the digits and $a\neq 0$) we define the \textit{permutation sum} as the value $$bcdea+cdeab+deabc+eabcd$$For example the permutation sum of 20253 is $$02532+25320+53202+32025=113079$$Let $m$ and $n$ be two fivedigit integers with the same permutation sum.
Prove that $m=n$.
1 reply
Fermat_Fanatic108
an hour ago
Fermat_Fanatic108
an hour ago
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ratio chasing inside a triangle, segment trisecting
parmenides51   10
N an hour ago by sangsidhya
Source: CRMO 2012 Region 2 p5
Let $ABC$ be a triangle. Let $D, E$ be a points on the segment $BC$ such that $BD =DE = EC$. Let $F$ be the mid-point of $AC$. Let $BF$ intersect $AD$ in $P$ and $AE$ in $Q$ respectively. Determine $BP:PQ$.
10 replies
parmenides51
Sep 30, 2018
sangsidhya
an hour ago
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Geo: incircle, escircle, isotomic conjugate
XAN4   0
an hour ago
Source: Own
For $\triangle{ABC}$, Its incircle $\odot I$ and $A-$escircle $\odot I_A$ are tangent to $BC$ at $D$ and $E$ respectively. $AI$ intersects line $BC$ at $J$. Line $AD$ intersects $\odot I$ at $F$, and line $AE$ intersects $\odot I_A$ at $G$. Line $FG$ intersects $BC$ at $H$. Prove that $BJ=CH$.
0 replies
XAN4
an hour ago
0 replies
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f(x)+f(x+y) \leq f(xy)+f(y)
augustin_p   7
N an hour ago by MuradSafarli
Source: Estonia TST 2022
Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ that satisfy the following condition for any real numbers $x{}$ and $y$ $$f(x)+f(x+y) \leq f(xy)+f(y).$$
7 replies
augustin_p
Jul 12, 2023
MuradSafarli
an hour ago
J
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Integer equation in 3 variables
Kimchiks926   2
N an hour ago by MuradSafarli
Source: Latvian TST for Baltic Way 2019 Problem 15
Determine all tuples of integers $(a,b,c)$ such that:
$$(a-b)^3(a+b)^2 = c^2 + 2(a-b) + 1$$
2 replies
Kimchiks926
May 29, 2020
MuradSafarli
an hour ago
J
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Interesting inequality
sqing   1
N an hour ago by sqing
Source: Own
Let $ a,b,c\geq 2 . $ Prove that
$$(a^2-1)(b-\frac{3}{2})(c^2-1) - \frac{9}{4}abc\geq -15$$$$(a^2-1)(b-\frac{3}{2})(c^2-1) - 2abc\geq -\frac{73}{6}$$$$(a^2-1)(b-\frac{3}{2})(c^2-1) - abc\geq -\frac{7}{2}$$$$(a^2-2)(b-\frac{3}{2})(c^2-2) - abc\geq -6$$
1 reply
sqing
an hour ago
sqing
an hour ago
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Hard problem involving circumcenter and concurrent lines
GeoMetrix   6
N an hour ago by bin_sherlo
Source: AQGO 2020 Problem 3
Let $\triangle{ABC}$ be a triangle with circumcenter $O$. Let $M,N$ be the midpoints of $\overline{AB}$ and $\overline{AC}$ respectively and let $T$ be the projection of $O$ on $\overline{MN}$. Let $D$ be the projection of $A$ on $\overline{BC}$. Let $\overline{TD}$ intersect $\odot(BOC)$ at points $U$ and $V$. Let $\odot(AUV)$ intersct $\overline{MN}$ at points $X,Y$. Let $\overline{AY}$ intersect $\odot(AMN)$ at $R$ and $\overline{AX}$ intersect $\odot(AMN)$ at $S$. Then show that $\overline{AO},\overline{RS},\overline{MN}$ are concurrent.

Proposed by GeoMetrix
6 replies
+1 w
GeoMetrix
Jun 20, 2020
bin_sherlo
an hour ago
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Oi! These lines concur
Rg230403   17
N an hour ago by L13832
Source: LMAO 2021 P5, LMAOSL G3(simplified)
Let $I, O$ and $\Gamma$ respectively be the incentre, circumcentre and circumcircle of triangle $ABC$. Points $A_1, A_2$ are chosen on $\Gamma$, such that $AA_1 = AI = AA_2$, and point $A'$ is the foot of the altitude from $I$ to $A_1A_2$. If $B', C'$ are similarly defined, prove that lines $AA', BB'$ and $CC'$ concurr on $OI$.
Original Version from SL
Proposed by Mahavir Gandhi
17 replies
Rg230403
May 10, 2021
L13832
an hour ago
J
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Differentiable functional
bakerbakura   2
N 2 hours ago by Gryphos
Find all differentiable functions $ f;\mathbb{R}\to\mathbb{R}$ such that, for all real numbers $ a,b,t$ with $ 0<t<1$, $ t^2f(a)+(1-t^2)f(b)\geq f(ta+(1-t)b)$
2 replies
bakerbakura
Jan 11, 2010
Gryphos
2 hours ago
J
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College Math Competitions
gavinhaominwang   6
N Today at 7:41 AM by xHypotenuse
What are the major competitions that take place at college? For example HMMT.
6 replies
gavinhaominwang
Today at 1:39 AM
xHypotenuse
Today at 7:41 AM
J
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Trapezoid ABCD
tenniskidperson3   51
N Today at 5:15 AM by Curious_Droid
Source: 2009 USAMO problem 5
Trapezoid $ ABCD$, with $ \overline{AB}||\overline{CD}$, is inscribed in circle $ \omega$ and point $ G$ lies inside triangle $ BCD$. Rays $ AG$ and $ BG$ meet $ \omega$ again at points $ P$ and $ Q$, respectively. Let the line through $ G$ parallel to $ \overline{AB}$ intersects $ \overline{BD}$ and $ \overline{BC}$ at points $ R$ and $ S$, respectively. Prove that quadrilateral $ PQRS$ is cyclic if and only if $ \overline{BG}$ bisects $ \angle CBD$.
51 replies
tenniskidperson3
Apr 30, 2009
Curious_Droid
Today at 5:15 AM
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AMC 10.........
BAM10   15
N Yesterday at 10:46 PM by jkim0656
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?
15 replies
BAM10
Mar 2, 2025
jkim0656
Yesterday at 10:46 PM
J
AMC 10.........
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Reveal topic tags
AMC 10
AMC 8
MATHCOUNTS
AIME
L
G H BBookmark kLocked kLocked NReply
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BAM10
68 posts
BAM10
#1 h  Mar 2, 2025, 8:02 PM
Y by
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?
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orangebear
610 posts
orangebear
#2 h  Mar 2, 2025, 8:04 PM
Y by
Yeah you can last year I got a 19 on AMC and a 31 on mathcounts chapter and I qualified for AIME.
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CYW
326 posts
CYW
#3 h  Mar 2, 2025, 9:06 PM
Y by
Dunno, opposite way for me. I got 80-something on AMC 10 (cutoff mid 90's) and got 37 on MATHCOUNTS chapter
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Airbus320-214
77 posts
Airbus320-214
#4 h  Mar 3, 2025, 3:07 AM
Y by
Practice past problems of amc 10/12
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nxchman
21 posts
nxchman
#5 h  Mar 3, 2025, 9:09 PM
Y by
BAM10 wrote:
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?

Im in the same boat lol. Im in 8th grade and I never took amc 10, but this year I got 22 on amc 8.
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iwillregretthisnamelater
1 post
iwillregretthisnamelater
#6 h  Yesterday at 1:59 AM
Y by
I’m in 6th grade and I got 20 on amc 8 and 38 on chapter and i flunked the amc 10 so hard
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sadas123
1053 posts
sadas123
#7 h  Yesterday at 2:04 AM
Y by
iwillregretthisnamelater wrote:
I’m in 6th grade and I got 20 on amc 8 and 38 on chapter and i flunked the amc 10 so hard

Same except I am a 6th grader that got 24 on AMC 8 and a 37 on mathcounts chapter :(
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jb2015007
1703 posts
jb2015007
#8 h  Yesterday at 2:09 AM
Y by
orangebear wrote:
Yeah you can last year I got a 19 on AMC and a 31 on mathcounts chapter and I qualified for AIME.

bruh i got a 51 on AMC 10 and got a 35 on mc chapter
(im better now relax im mocking 90+)
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ChickensEatGrass
26 posts
ChickensEatGrass
#9 h  Yesterday at 2:19 AM
Y by
I'm an 8th grader and I got 25 on amc8 but only 40 on chapter, I made aime barely this year but I got like problem 4 wrong on 10a :wallbash_red:
so yes with your stats you have a decent chance, just study more and do past mocks, you can find them here on aops.
try to aim for at least 100. This year's cutoff for 10a was really low (94.5) but most years it's higher.
because you are in alg2, I'd recommend doing some geometry because there are several of those problems. maybe also start trig because they can provide faster solutions to them. but alg2 is a good start.
And make sure to not make sillies!!!!!!!!!! but I cant rlly say anything about that because i myself make 100000000 sillies every day :whistling:
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giratina3
432 posts
giratina3
#10 h  Yesterday at 11:35 AM
Y by
I’m somebody who got 41 on chapter and 21 on AMC8 but didn’t qualify for AIME :stretcher:
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hashbrown2009
105 posts
hashbrown2009
#11 h  Yesterday at 1:54 PM
Y by
Honestly it depends
I qualified for AIME in 5th grade (9th grade now) with 106.5
but that year I got like 16 on AMC8 lol I sold
also I pre-prepped for MathCounts and did mocks
averaged like 36-40
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Andyluo
851 posts
Andyluo
#12 h  Yesterday at 4:23 PM
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Both completely different skill sets

my scores last year were

AMC 8: 17
chapter: 41 (My MATHCOUNTS skills were more developed)
AMC 10: 81

This year:

AMC 8: 21
Chapter: 43
AMC 10: 135

imo just take mocks + learn the theory from aops
mathdash good too
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BAM10
68 posts
BAM10
#13 h  Yesterday at 9:39 PM
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thx for the help. I have taken a couple mocks.

2020 10a: 84.5
2020 10b: 99
2021 10a: 87.5

Im finding that I can the first 10-15 pretty easily but I silly a lot a can't get many after #15. How can I help these problems?
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Pengu14
407 posts
Pengu14
#14 h  Yesterday at 10:10 PM
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BAM10 wrote:
thx for the help. I have taken a couple mocks.

2020 10a: 84.5
2020 10b: 99
2021 10a: 87.5

Im finding that I can the first 10-15 pretty easily but I silly a lot a can't get many after #15. How can I help these problems?

Can you solve the problems with unlimited time? If not, you should probably read AOPS vol 1 since you might be lacking theory.
This post has been edited 1 time. Last edited by Pengu14, Yesterday at 10:11 PM
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gavinhaominwang
71 posts
gavinhaominwang
#15 h  Yesterday at 10:23 PM
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If you are talking about qualifying for aime this year, anyone that can take the test can qualify for aime. They just have to work hard.
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jkim0656
272 posts
jkim0656
#16 h  Yesterday at 10:46 PM
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lol im in 7thn but i also got 34 on chapter and 20 on the amc8 loll
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