[/quote]
,
high-quality questions. This test was created by multiple 130+ scorers, and we have tried our very best to produce the highest quality test possible. We've blended the question types in a good distribution, and maintained a realistic difficulty. (something most AOPS mocks fail at)
of integer numbers, we define 
as the sum of the elements of 
and 
whose intersection is empty, whose union is the set 
and such that the product 
is a perfect square.
be a positive integer. Do there exist distinct 
and 
,
or 
,
divides 
?
in triangle 
.
,
,
be the feet of the internal angle bisectors of 
,
,
respectively.
be the incenter of triangle 
,
be the foot of the perpendicular from 
.
is cyclic, then the center of its circumscribed circle lies on segment 
.
be positive integers. Julia and Florian play a game on a 
board. Julia
where 
and 
are integers.
and![\[(x-y)[f(x)+f(y)]\leqslant f(x^2-y^2), \forall x,y \in \mathbb{R}\]](http://latex.artofproblemsolving.com/8/0/b/80bb1d7a992c9683a0c2a07b2febe6271f4e60f5.png)
and 
Prove that
,
be the orthocenter of it and 
be any point on the side 
.
are on the segments 
,
and 
are cyclic. The segments 
and 
intersect at 
is a point on 
such that 
is tangent to the circumcircle of triangle 
at 
and 
intersect at 
.
and 
where 
.
is called 
if there exists a permutation 
of the numbers 
,
and 
have different parities for every 
;
the sum 
is a quadratic residue modulo 
.
Y by eibc, ninjaforce, vrondoS, crazylizard, scannose
Hi AOPS community,
We are excited to announce that Westford Academy (located in Westford, MA) will be hosting its first ever math competition for middle school students (grades 5-8).
Based in Massachusetts, this tournament hosts ambitious and mathematically skilled students in grades 5–8 to compete against other middle school math teams while fostering their problem-solving skills and preparing them to continue enriching their STEM skills in high school and in the future.
This competition will be held on April 12, 2025 from 12:00 PM to 5:00 PM and will feature 3 rounds (team, speed, and accuracy). The problems will be of similar difficulty for AMC 8-10 and were written by USA(J)MO and AIME qualifiers.
If you are in the Massachusetts area and are curious about Mathematics, we cordially invite you to sign up by scanning the QR code on the attached flyer. Please note that teams consist of 4-6 competitors, but if you prefer to register as an individual competitor, you will be randomly placed on a team of other individual competitors. Feel free to refer the attached flyer and website as needed.
https://sites.google.com/westfordk12.us/wamt/home?authuser=2
We are excited to announce that Westford Academy (located in Westford, MA) will be hosting its first ever math competition for middle school students (grades 5-8).
Based in Massachusetts, this tournament hosts ambitious and mathematically skilled students in grades 5–8 to compete against other middle school math teams while fostering their problem-solving skills and preparing them to continue enriching their STEM skills in high school and in the future.
This competition will be held on April 12, 2025 from 12:00 PM to 5:00 PM and will feature 3 rounds (team, speed, and accuracy). The problems will be of similar difficulty for AMC 8-10 and were written by USA(J)MO and AIME qualifiers.
If you are in the Massachusetts area and are curious about Mathematics, we cordially invite you to sign up by scanning the QR code on the attached flyer. Please note that teams consist of 4-6 competitors, but if you prefer to register as an individual competitor, you will be randomly placed on a team of other individual competitors. Feel free to refer the attached flyer and website as needed.
https://sites.google.com/westfordk12.us/wamt/home?authuser=2
Attachments:
