USA(J)MO Grading Poll

by elasticwealth, Apr 23, 2025, 3:17 AM

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Please vote honestly. If you did not compete in the USA(J)MO, please do not vote.

AMC

USA(J)MO

USAMO

poll

0 on JMO P2

by dogeA, Apr 22, 2025, 8:53 PM

I got a 0 on this problem but I'm not really sure why, as I should be at least on the right track? Can someone tell me why I got a 0?

Attachments:

This post has been edited 2 times. Last edited by dogeA, Yesterday at 8:56 PM

AMC

USA(J)MO

USAJMO

Metals cutoff prediction; mop colors prediction

by mulberrykid, Apr 22, 2025, 8:23 PM

For USAMO and JMO,

what will the cutoff for different metals:

1. Gold: ?
2. Silver:?
3. Bronze:?

JMO:
Honors: ?
High Honors:?

MOP colors:
Black:?
Blue:?
Green:?
Orange:?
Red: ?

USA(J)MO scores will be released today

by profhong, Apr 22, 2025, 5:21 PM

The awards will be out next week.
Best luck!

AMC

USA(J)MO

legit

SL Difficulty Level

by MajesticCheese, Apr 20, 2025, 8:58 PM

Is there a rough difficulty comparison between IMO shortlist questions and USAMO questions? For example,

SL 1, 2, 3 -> USAMO P1
SL 4, 5, 6 -> USAMO P2
SL 7, 8, 9 -> USAMO P3

(This is just my guess; probably not correct)

Also feel free to compare it with other competitions(like the jmo) as well! :-D

AMC and JMO qual question

by HungryCalculator, Apr 17, 2025, 12:05 AM

Say that on the AMC 10, you do better on the A than the B, but you still qualify for AIME thru both. Then after your AIME, it turns out that you didn’t make JMO through the A+AIME index but you did pass the threshold for the B+AIME index.

does MAA consider your B+AIME index over the A+AIME index and consider you a JMO qualifier even tho Your A test score was higher?

usamOOK geometry

by KevinYang2.71, Mar 21, 2025, 12:00 PM

Let $H$ be the orthocenter of acute triangle $ABC$ , let $F$ be the foot of the altitude from $C$ to $AB$ , and let $P$ be the reflection of $H$ across $BC$ . Suppose that the circumcircle of triangle $AFP$ intersects line $BC$ at two distinct points $X$ and $Y$ . Prove that $C$ is the midpoint of $XY$ .

Prove a polynomial has a nonreal root

by KevinYang2.71, Mar 20, 2025, 12:00 PM

Let $n$ and $k$ be positive integers with $k<n$ . Let $P(x)$ be a polynomial of degree $n$ with real coefficients, nonzero constant term, and no repeated roots. Suppose that for any real numbers $a_0,\,a_1,\,\ldots,\,a_k$ such that the polynomial $a_kx^k+\cdots+a_1x+a_0$ divides $P(x)$ , the product $a_0a_1\cdots a_k$ is zero. Prove that $P(x)$ has a nonreal root.

AMC

USA(J)MO

USAMO

p^k divides term of sequence

by KevinYang2.71, Mar 20, 2024, 4:01 AM

Let $a(n)$ be the sequence defined by $a(1)=2$ and $a(n+1)=(a(n))^{n+1}-1$ for each integer $n\geq 1$ . Suppose that $p>2$ is a prime and $k$ is a positive integer. Prove that some term of the sequence $a(n)$ is divisible by $p^k$ .

Proposed by John Berman

This post has been edited 1 time. Last edited by KevinYang2.71, Mar 21, 2024, 3:11 PM

Subset coloring

by v_Enhance, Apr 28, 2015, 9:13 PM

Let $S = \left\{ 1,2,\dots,n \right\}$ , where $n \ge 1$ . Each of the $2^n$ subsets of $S$ is to be colored red or blue. (The subset itself is assigned a color and not its individual elements.) For any set $T \subseteq S$ , we then write $f(T)$ for the number of subsets of $T$ that are blue.

Determine the number of colorings that satisfy the following condition: for any subsets $T_1$ and $T_2$ of $S$ , $f(T_1)f(T_2) = f(T_1 \cup T_2)f(T_1 \cap T_2).$