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Contests & Programs AMC and other contests, summer programs, etc.
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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
May 1, 2025
0 replies
Goals for 2025-2026
Airbus320-214   2
N 2 hours ago by AshAuktober
Please write down your goal/goals for competitions here for 2025-2026.
2 replies
Airbus320-214
3 hours ago
AshAuktober
2 hours ago
MOP Emails Out! (not clickbait)
Mathandski   104
N 2 hours ago by ohiorizzler1434
What an emotional roller coaster the past 34 days have been.

Congrats to all that qualified!
104 replies
Mathandski
Apr 22, 2025
ohiorizzler1434
2 hours ago
Past USAMO Medals
sdpandit   2
N 5 hours ago by sdpandit
Does anyone know where to find lists of USAMO medalists from past years? I can find the 2025 list on their website, but they don't seem to keep lists from previous years and I can't find it anywhere else. Thanks!
2 replies
sdpandit
May 8, 2025
sdpandit
5 hours ago
Geo is back??
GoodMorning   137
N 5 hours ago by Siddharthmaybe
Source: 2023 USAJMO Problem 2/USAMO Problem 1
In an acute triangle $ABC$, let $M$ be the midpoint of $\overline{BC}$. Let $P$ be the foot of the perpendicular from $C$ to $AM$. Suppose that the circumcircle of triangle $ABP$ intersects line $BC$ at two distinct points $B$ and $Q$. Let $N$ be the midpoint of $\overline{AQ}$. Prove that $NB=NC$.

Proposed by Holden Mui
137 replies
GoodMorning
Mar 23, 2023
Siddharthmaybe
5 hours ago
Tetrahedron
4everwise   3
N Yesterday at 10:43 PM by aidan0626
Four balls of radius 1 are mutually tangent, three resting on the floor and the fourth resting on the others. A tetrahedron, each of whose edges have length $s$, is circumscribed around the balls. Then $s$ equals

$\text{(A)} \ 4\sqrt 2 \qquad \text{(B)} \ 4\sqrt 3 \qquad \text{(C)} \ 2\sqrt 6 \qquad \text{(D)} \ 1+2\sqrt 6 \qquad \text{(E)} \ 2+2\sqrt 6$
3 replies
4everwise
Jan 1, 2006
aidan0626
Yesterday at 10:43 PM
Concurrent in a pyramid
vanstraelen   0
Yesterday at 7:13 AM

Given a pyramid $(T,ABCD)$ where $ABCD$ is a parallelogram.
The intersection of the diagonals of the base is point $S$.
Point $A$ is connected to the midpoint of $[CT]$, point $B$ to the midpoint of $[DT]$,
point $C$ to the midpoint of $[AT]$ and point $D$ to the midpoint of $[BT]$.
a) Prove: the four lines are concurrent in a point $P$.
b) Calulate $\frac{TS}{TP}$.
0 replies
vanstraelen
Yesterday at 7:13 AM
0 replies
Triangle on a tetrahedron
vanstraelen   2
N Friday at 7:51 PM by ReticulatedPython

Given a regular tetrahedron $(A,BCD)$ with edges $l$.
Construct at the apex $A$ three perpendiculars to the three lateral faces.
Take a point on each perpendicular at a distance $l$ from the apex such that these three points lie above the apex.
Calculate the lenghts of the sides of the triangle.
2 replies
vanstraelen
Friday at 2:43 PM
ReticulatedPython
Friday at 7:51 PM
shadow of a cylinder, shadow of a cone
vanstraelen   2
N Friday at 6:33 PM by vanstraelen

a) Given is a right cylinder of height $2R$ and radius $R$.
The sun shines on this solid at an angle of $45^{\circ}$.
What is the area of the shadow that this solid casts on the plane of the botom base?

b) Given is a right cone of height $2R$ and radius $R$.
The sun shines on this solid at an angle of $45^{\circ}$.
What is the area of the shadow that this solid casts on the plane of the base?
2 replies
vanstraelen
Friday at 3:08 PM
vanstraelen
Friday at 6:33 PM
Cube Sphere
vanstraelen   4
N Friday at 2:37 PM by pieMax2713

Given the cube $\left(\begin{array}{ll} EFGH \\ ABCD \end{array}\right)$ with edge $6$ cm.
Find the volume of the sphere passing through $A,B,C,D$ and tangent to the plane $(EFGH)$.
4 replies
vanstraelen
Friday at 1:10 PM
pieMax2713
Friday at 2:37 PM
parallelogram in a tetrahedron
vanstraelen   1
N Friday at 12:19 PM by vanstraelen
Given a tetrahedron $ABCD$ and a plane $\mu$, parallel with the edges $AC$ and $BD$.
$AB \cap \mu=P$.
a) Prove: the intersection of the tetrahedron with the plane is a parallelogram.
b) If $\left|AC\right|=14,\left|BD\right|=7$ and $\frac{\left|PA\right|}{\left|PB\right|}=\frac{3}{4}$,
calculates the lenghts of the sides of this parallelogram.
1 reply
vanstraelen
May 5, 2025
vanstraelen
Friday at 12:19 PM
Regular tetrahedron
vanstraelen   7
N May 6, 2025 by ReticulatedPython
Given the points $O(0,0,0),A(1,0,0),B(\frac{1}{2},\frac{\sqrt{3}}{2},0)$
a) Determine the point $C$, above the xy-plane, such that the pyramid $OABC$ is a regular tetrahedron.
b) Calculate the volume.
c) Calculate the radius of the inscribed sphere and the radius of the circumscribed sphere.
7 replies
vanstraelen
May 4, 2025
ReticulatedPython
May 6, 2025
volume 9f a pentagonal base pyramid circumscribed around a right circular cone
FOL   1
N May 6, 2025 by Mathzeus1024
A pentagonal base pyramid is circumscribed around a right circular cone, whose height is equal to the radius of the base. The total surface area of the pyramid is d times greater than that of the cone. Find the volume of the pyramid if the lateral surface area of the cone is equal to $\pi\sqrt{2}$.
1 reply
FOL
Jul 22, 2023
Mathzeus1024
May 6, 2025
Geometry books
T.Mousavidin   4
N Apr 30, 2025 by compoly2010
Hello, I wanted to ask if anybody knows some good books for geometry that has these topics in:
Desargues's Theorem, Projective geometry, 3D geometry,
4 replies
T.Mousavidin
Apr 29, 2025
compoly2010
Apr 30, 2025
Tetrahedrons and spheres
ReticulatedPython   4
N Apr 28, 2025 by soryn
Let $OABC$ be a tetrahedron such that $\angle{AOB}=\angle{AOC}=\angle{BOC}=90^\circ.$ A sphere of radius $r$ is circumscribed about tetrahedron $OABC.$ Given that $OA=a$, $OB=b$, and $OC=c$, prove that $$r^2+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \ge \frac{9\sqrt[3]{4}}{4}$$with equality at $a=b=c=\sqrt[3]{2}.$
4 replies
ReticulatedPython
Apr 21, 2025
soryn
Apr 28, 2025
AIME/AMC 10 Overlap and Preparation
AlphaBetaTheta   2
N Jan 2, 2011 by MCL
I've been trying to prepare for the amc 10 to qualify for the aime. I've heard that 1-5 on aime should be done for practice. Which years on the aime would help me the most in my preparation?
2 replies
AlphaBetaTheta
Jan 2, 2011
MCL
Jan 2, 2011
AIME/AMC 10 Overlap and Preparation
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AlphaBetaTheta
182 posts
#1 • 2 Y
Y by Adventure10, Mango247
I've been trying to prepare for the amc 10 to qualify for the aime. I've heard that 1-5 on aime should be done for practice. Which years on the aime would help me the most in my preparation?
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luie1168e
1295 posts
#2 • 2 Y
Y by Adventure10, Mango247
AlphaBetaTheta wrote:
I've been trying to prepare for the amc 10 to qualify for the aime. I've heard that 1-5 on aime should be done for practice. Which years on the aime would help me the most in my preparation?

In my opinion,in the time where aime 2 doesn't exist,the 1-5 problem is harder, but i think all the kind of problem would help also... but i think doing the harder AMC 12 problem might help because sometime #15-20 in AMC 12 meant to #20-25 AMC 10!
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MCL
1259 posts
#3 • 3 Y
Y by Adventure10, Mango247, and 1 other user
Try the AIME of 1989. I managed to get the first ten questions right because they were much easier than the average AIME.
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