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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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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 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.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

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!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 2, 2025
0 replies
U.S.J.A.M.O tips from a superstar!
K-Cliquey   23
N 4 minutes ago by sultanine
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.
23 replies
K-Cliquey
Today at 4:56 AM
sultanine
4 minutes ago
Proof Question
MathRook7817   3
N 5 hours ago by Jack_w
Prove or disprove the assertion that when $1/n$ is written in decimal form with n being a natural number, that it's decimal either terminates or is eventually periodic.

I saw this question somewhere and I thinks it's interesting.
3 replies
MathRook7817
Today at 2:19 AM
Jack_w
5 hours ago
Inequalities
lgx57   2
N 6 hours ago by sqing
Let $0 < a,b,c < 1$. Prove that

$$a(1-b)+b(1-c)+c(1-a)<1$$
2 replies
lgx57
Today at 7:43 AM
sqing
6 hours ago
solve the system of equations
Havu   1
N 6 hours ago by Mathzeus1024
Solve the system of equations:
\[\begin{cases}
3x^2-2xy+3y^2+\dfrac{2}{x^2-2xy+y^2}=8\\
2x+\dfrac{1}{x-y}=4
\end{cases}\]
1 reply
Havu
Today at 7:52 AM
Mathzeus1024
6 hours ago
Inequalities
sqing   7
N Today at 8:12 AM by sqing
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
$$\left(\frac{2}{a}+\frac{1}{b}-1\right)\left(\frac{2}{a}-\frac{1}{b}+1\right)\ge \frac{13}{3}$$
7 replies
sqing
Mar 15, 2025
sqing
Today at 8:12 AM
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
Quadratic Equation Problems
Saucepan_man02   7
N Today at 5:53 AM by soryn
P1) Let $\alpha < \beta <	\gamma$ be the roots of $ax^3+bx^2+cx+d=0$ with $7a+3b>0, 3a+2b<0$ and $\alpha(\beta+1)+\beta(\gamma+1)+\gamma(1+\alpha)=0$.
If [.] denotes the greatest integer function, then the number of possible values of $[|3 \alpha |] + [|6 \beta|] +
 [|9 \gamma |]$ is equal to
7 replies
Saucepan_man02
Mar 3, 2025
soryn
Today at 5:53 AM
Trash Trig Sum
P_Groudon   4
N Today at 5:41 AM by invisibleman
Find the smallest positive integer $n$ such that $$\sum_{k=0}^{298}\sin(k^2 + 2k + 2)\sin(2k + 2) = \frac{\cos(1) - \cos(n)}{2},$$where degrees are used.
4 replies
P_Groudon
Monday at 5:34 PM
invisibleman
Today at 5:41 AM
Chessboard
Ecrin_eren   2
N Today at 5:24 AM by Ecrin_eren
On an 8×8 checkerboard, what is the minimum number of squares that must be marked (including the marked ones) so that every square has exactly one marked neighbor? (We define neighbors as squares that share a common edge, and a square is not considered a neighbor of itself.)

2 replies
Ecrin_eren
Yesterday at 8:55 PM
Ecrin_eren
Today at 5:24 AM
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
Good luck on olympiads tomorrow!
observer04   4
N Today at 4:56 AM by rhydon516
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
4 replies
observer04
Today at 1:27 AM
rhydon516
Today at 4:56 AM
Inequality
BaCaPhe   1
N Today at 4:43 AM by lbh_qys
$\begin{array}{l}
a,b,c \ge 1,ab + bc + ca \ge 4 + abc\\
{a^2} + {b^2} + {c^2} \ge 9?
\end{array}$
I tried:
$\begin{array}{l}
 * {\text{In three numbers }}a,b,c \ge 1,{\text{ at least 2 numbers }} \ge {\text{2 or}} \le {\text{2}}\\
{\text{WLOG assume they are }}a{\text{ and }}b \Rightarrow \left( {a - 2} \right)\left( {b - 2} \right) \ge 0 \Leftrightarrow 4c + abc \ge 2ac + 2bc\\
 \Leftrightarrow 2ac + 2bc \le 4c - 4 + 4 + abc \le 4c - 4 + ab + bc + ca \Leftrightarrow ac + bc \le 4c - 4 + ab
\end{array}$
How do I process further?
1 reply
BaCaPhe
Today at 3:13 AM
lbh_qys
Today at 4:43 AM
Inequalities
sqing   21
N Today at 4:36 AM by sqing
Let $ a,b>0 $ and $ \frac{1}{a}+\frac{1}{b}=1. $ Prove that
$$(a^2-a+1)(b^2-b+1) \geq 9$$$$ (a^2-a+b+1)(b^2-b+a+1) \geq 25$$Let $ a,b>0 $ and $ \frac{1}{a}+\frac{1}{b}=\frac{2}{3}. $ Prove that
$$(a+8)(a^2-a+b+2)(b^2-b+5)\geq1331$$$$(a+10)(a^2-a+b+4)(b^2-b+7)\geq2197$$
21 replies
sqing
Mar 10, 2025
sqing
Today at 4:36 AM
Inequalities
sqing   6
N Today at 4:16 AM by sqing
Let $ a,b $ be real numbers such that $ a + b  \geq  |ab + 1|. $ Prove that$$ a^3 + b^3 \geq |a^3 b^3 + 1|$$Let $ a,b $ be real numbers such that $ 2(a + b ) \geq  |ab + 1|. $ Prove that$$26( a^3 + b^3) \geq |a^3 b^3 + 1|$$Let $ a,b $ be real numbers such that $ 4(a + b) \geq 3|ab + 1|. $ Prove that$$148(a^3 + b^3) \geq27 |a^3 b^3 + 1|$$
6 replies
sqing
Mar 8, 2025
sqing
Today at 4:16 AM
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
AMC 10.........
G H J
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BAM10
68 posts
#1
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
#2
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
#3
Y by
Dunno, opposite way for me. I got 80-something on AMC 10 (cutoff mid 90's) and got 37 on MATHCOUNTS chapter
Z K Y
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Airbus320-214
77 posts
#4
Y by
Practice past problems of amc 10/12
Z K Y
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nxchman
21 posts
#5
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
#6
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
1052 posts
#7
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
#8
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
#9
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
#10
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
#11
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
#12
Y by
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
#13
Y by
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
#14
Y by
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
#15
Y by
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
#16
Y by
lol im in 7thn but i also got 34 on chapter and 20 on the amc8 loll
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