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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
J
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Area problem
MTA_2024   0
4 hours ago
Let $\omega$ be a circle inscribed inside a rhombus $ABCD$. Let $P$ and $Q$ be variable points on $AB$ and $AD$ respectively, such as $PQ$ is always the tangent line to $\omega$.
Prove that for any position of $P$ and $Q$ the area of triangle $\triangle CPQ$ is the same.
0 replies
MTA_2024
4 hours ago
0 replies
J
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Four Semicircles
worthawholebean   5
N Today at 4:18 AM by e___
Three semicircles of radius $ 1$ are constructed on diameter $ AB$ of a semicircle of radius $ 2$. The centers of the small semicircles divide $ \overline{AB}$ into four line segments of equal length, as shown. What is the area of the shaded region that lies within the large semicircle but outside the smaller semicircles?
IMAGE$ \textbf{(A)}\ \pi-\sqrt3 \qquad \textbf{(B)}\ \pi-\sqrt2 \qquad \textbf{(C)}\ \frac{\pi+\sqrt2}{2} \qquad \textbf{(D)}\ \frac{\pi+\sqrt3}{2}$
$ \textbf{(E)}\ \frac{7}{6}\pi-\frac{\sqrt3}{2}$
5 replies
worthawholebean
Jan 5, 2009
e___
Today at 4:18 AM
J
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Find the value
yt12   1
N Today at 4:15 AM by soryn
Find the value of $\tan^6 ( \frac{\pi}{18}) + \tan^6(\frac{5 \pi}{18}) + \tan^6(\frac{7 \pi}{18})$
1 reply
yt12
Today at 3:33 AM
soryn
Today at 4:15 AM
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2021 SMT Guts Round 5 p17-20 - Stanford Math Tournament
parmenides51   3
N Today at 3:58 AM by SatisfiedMagma
p17. Let the roots of the polynomial $f(x) = 3x^3 + 2x^2 + x + 8 = 0$ be $p, q$, and $r$. What is the sum $\frac{1}{p} +\frac{1}{q} +\frac{1}{r}$ ?


p18. Two students are playing a game. They take a deck of five cards numbered $1$ through $5$, shuffle them, and then place them in a stack facedown, turning over the top card next to the stack. They then take turns either drawing the card at the top of the stack into their hand, showing the drawn card to the other player, or drawing the card that is faceup, replacing it with the card on the top of the pile. This is repeated until all cards are drawn, and the player with the largest sum for their cards wins. What is the probability that the player who goes second wins, assuming optimal play?


p19. Compute the sum of all primes $p$ such that $2^p + p^2$ is also prime.


p20. In how many ways can one color the $8$ vertices of an octagon each red, black, and white, such that no two adjacent sides are the same color?


PS. You should use hide for answers. Collected here.
3 replies
parmenides51
Feb 11, 2022
SatisfiedMagma
Today at 3:58 AM
J
No more topics!
H
J
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Nice algebra problem
Silverfalcon   3
N Nov 4, 2017 by nbgb
Determine all pairs of integers $(x,y)$ which satisfy the equation

\[ 6x^2-3xy-13x+5y = -11 \]
3 replies
Silverfalcon
Jan 27, 2006
nbgb
Nov 4, 2017
J
Nice algebra problem
G H J
Reveal topic tags
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Silverfalcon
5006 posts
Silverfalcon
#1 h  Jan 27, 2006, 11:07 PM • 2 Y
Y by Adventure10, Mango247
Determine all pairs of integers $(x,y)$ which satisfy the equation

\[ 6x^2-3xy-13x+5y = -11 \]
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Silverfalcon
5006 posts
Silverfalcon
#2 h  Jan 27, 2006, 11:10 PM • 2 Y
Y by Adventure10, Mango247
My solution
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nbgb
5 posts
nbgb
#3 h  Nov 4, 2017, 10:47 AM • 2 Y
Y by Adventure10, Mango247
(-5 + 3 x) (-1 + 2 x - y)=-6
KARA
trivial
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nbgb
5 posts
nbgb
#4 h  Nov 4, 2017, 11:24 AM • 2 Y
Y by Adventure10, Mango247
{(-5 + 3 x) == -2, (-1 + 2 x - y) == 3}
{(-5 + 3 x) == 1, (-1 + 2 x - y) == -6}
 :-D
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