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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
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combo j3 :blobheart:
rhydon516   21
N 12 minutes ago by CatinoBarbaraCombinatoric
Source: USAJMO 2025/3
Let $m$ and $n$ be positive integers, and let $\mathcal R$ be a $2m\times 2n$ grid of unit squares.

A domino is a $1\times2$ or $2\times1$ rectangle. A subset $S$ of grid squares in $\mathcal R$ is domino-tileable if dominoes can be placed to cover every square of $S$ exactly once with no domino extending outside of $S$. Note: The empty set is domino tileable.

An up-right path is a path from the lower-left corner of $\mathcal R$ to the upper-right corner of $\mathcal R$ formed by exactly $2m+2n$ edges of the grid squares.

Determine, with proof, in terms of $m$ and $n$, the number of up-right paths that divide $\mathcal R$ into two domino-tileable subsets.
21 replies
rhydon516
Mar 20, 2025
CatinoBarbaraCombinatoric
12 minutes ago
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Tennessee Math Tournament (TMT) Online 2025
TennesseeMathTournament   35
N 41 minutes ago by athreyay
Hello everyone! We are excited to announce a new competition, the Tennessee Math Tournament, created by the Tennessee Math Coalition! Anyone can participate in the virtual competition for free.

The testing window is from March 22nd to April 5th, 2025. Virtual competitors may participate in the competition at any time during that window.

The virtual competition consists of three rounds: Individual, Bullet, and Team. The Individual Round is 60 minutes long and consists of 30 questions (AMC 10 level). The Bullet Round is 20 minutes long and consists of 80 questions (Mathcounts Chapter level). The Team Round is 30 minutes long and consists of 16 questions (AMC 12 level). Virtual competitors may compete in teams of four, or choose to not participate in the team round.

To register and see more information, click here!

If you have any questions, please email connect@tnmathcoalition.org or reply to this thread!

Thank you to our lead sponsor, Jane Street!

IMAGE
35 replies
TennesseeMathTournament
Mar 9, 2025
athreyay
41 minutes ago
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USA Canada math camp
Bread10   25
N an hour ago by akliu
How difficult is it to get into USA Canada math camp? What should be expected from an accepted applicant in terms of the qualifying quiz, essays and other awards or math context?
25 replies
Bread10
Mar 2, 2025
akliu
an hour ago
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funny title placeholder
pikapika007   47
N 2 hours ago by llddmmtt1
Source: USAJMO 2025/6
Let $S$ be a set of integers with the following properties:
[list]
[*] $\{ 1, 2, \dots, 2025 \} \subseteq S$.
[*] If $a, b \in S$ and $\gcd(a, b) = 1$, then $ab \in S$.
[*] If for some $s \in S$, $s + 1$ is composite, then all positive divisors of $s + 1$ are in $S$.
[/list]
Prove that $S$ contains all positive integers.
47 replies
pikapika007
Yesterday at 12:10 PM
llddmmtt1
2 hours ago
J
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Derivative of function R^2 to R^2
Sifan.C.Maths   0
Today at 7:09 AM
Source: Internet
Give a function $f:\mathbb{R}^2 \to \mathbb{R}^2: f(x,y)=(x^2+xy,y^2+x)$. Calculate the first and second derivative of the function at the point $(1,-1)$.
0 replies
Sifan.C.Maths
Today at 7:09 AM
0 replies
J
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some distribution
We2592   2
N Today at 6:46 AM by Tricky123
Let \( F(x) \) be a distribution function. Prove that for any \( h \neq 0 \), the function

\[ G(x) = \frac{1}{2h} \int_{x-h}^{x+h} F(t) \, dt \]
is also a distribution function.



how to approach?
2 replies
We2592
Yesterday at 1:07 PM
Tricky123
Today at 6:46 AM
J
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Equation with complex numbers on the unit circle
Tintarn   9
N Today at 4:30 AM by Fibonacci_math
Source: IMC 2024, Problem 1
Determine all pairs $(a,b) \in \mathbb{C} \times \mathbb{C}$ of complex numbers satisfying $|a|=|b|=1$ and $a+b+a\overline{b} \in \mathbb{R}$.
9 replies
Tintarn
Aug 7, 2024
Fibonacci_math
Today at 4:30 AM
J
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numerical analysis
ay19bme   1
N Today at 3:05 AM by YuLuo
...............
1 reply
ay19bme
Yesterday at 4:48 PM
YuLuo
Today at 3:05 AM
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distribution function
We2592   1
N Yesterday at 9:55 PM by alexheinis
Q)The distribution function $F(x)$ of a variate $X$ is defined as follows:
\[ F(x) = \begin{cases} A, & -\infty < x < -1, \\ B, & -1 \leq x < 0, \\ C, & 0 \leq x < 2, \\ D, & 2 \leq x < \infty. \end{cases} \]
where $A,B,C,D$ are constants. Determine the values of $A,B,C,D$ it being given that $P(X=0)=\frac{1}{6}$ and $P(X>1)=\frac{2}{3}$

how to solve
1 reply
We2592
Yesterday at 1:23 PM
alexheinis
Yesterday at 9:55 PM
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Complex roots
Sarbajit10598   7
N Yesterday at 5:57 PM by quasar_lord
Source: C.M.I entrance exam 2019
2.(a)Count the number of all the complex roots $\omega$ of the equation $z^{2019}-1=0$ which follows $$|\omega+1|\geq \sqrt{2+\sqrt{2}}$$(b) Solve for real $x$
$$\frac{8^x+27^x}{12^x+18^x}=\frac{7}{6}$$
7 replies
Sarbajit10598
May 15, 2019
quasar_lord
Yesterday at 5:57 PM
J
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CMI Entrance 19#3
bubu_2001   12
N Yesterday at 5:17 PM by quasar_lord
Evaluate $\int_{ 0 }^{ \infty } ( 1 + x^2 )^{-( m + 1 )} \mathrm{d}x$ where $m \in \mathbb{N} $
12 replies
bubu_2001
Oct 31, 2019
quasar_lord
Yesterday at 5:17 PM
J
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analysis
ay19bme   2
N Yesterday at 3:27 PM by ay19bme
..........
2 replies
ay19bme
Thursday at 8:06 PM
ay19bme
Yesterday at 3:27 PM
J
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Do these have a closed form?
Entrepreneur   0
Yesterday at 2:17 PM
Source: Own
$$\int_0^\infty\frac{t^{n-1}}{(t+\alpha)^2+m^2}dt.$$$$\int_0^\infty\frac{e^{nt}}{(t+\alpha)^2+m^2}dt.$$$$\int_0^\infty\frac{dx}{(1+x^a)^m(1+x^b)^n}.$$
0 replies
Entrepreneur
Yesterday at 2:17 PM
0 replies
J
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more rafinament limits integrals
teomihai   6
N Yesterday at 2:11 PM by teomihai
Let$ f:[0,1]->R$ continously function with $f'$ bounded
Find $$\lim_{n \rightarrow \infty}n(n\int_{0}^{1}x^{n}f(x)dx-f(1))$$
6 replies
teomihai
Yesterday at 4:55 AM
teomihai
Yesterday at 2:11 PM
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J
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Mathcounts States
RMarri_1018   9
N Yesterday at 11:36 AM by giratina3
As Mathcounts States has not started yet, I would like to ask a quick question. What would be the target goal to get to nationals in the state of Pennslyvania. I mock 34-38, so I want to know would that be enough to get me to CDR?
9 replies
RMarri_1018
Feb 24, 2025
giratina3
Yesterday at 11:36 AM
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Mathcounts States
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Reveal topic tags
MATHCOUNTS
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RMarri_1018
3 posts
RMarri_1018
#1 h  Feb 24, 2025, 9:44 PM
Y by
As Mathcounts States has not started yet, I would like to ask a quick question. What would be the target goal to get to nationals in the state of Pennslyvania. I mock 34-38, so I want to know would that be enough to get me to CDR?
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orangebear
611 posts
orangebear
#2 h  Feb 24, 2025, 9:50 PM
Y by
Since this years Pennsylvania team should be weak (As far as I know cuz all the 8th graders are gone and there were many of them) The cutoff for countdown should be 32-36 depending how hard the test is.
This post has been edited 2 times. Last edited by orangebear, Feb 24, 2025, 9:53 PM
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happypi31415
734 posts
happypi31415
#3 h  Feb 24, 2025, 10:38 PM
Y by
As a former MATHCOUNTS participant in PA (made nats once) i believe cutoff was around 30 for cdr both 2023 and 2024. However I don't think the team will be that strong this year b/c there were around 4 7th graders in top 20 (compare to 2023 where there were like 8) so it might be easier tbh
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RMarri_1018
3 posts
RMarri_1018
#4 h  Feb 26, 2025, 8:27 PM
Y by
Ok Thanks
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MichaelLin16
44 posts
MichaelLin16
#5 h  Mar 11, 2025, 9:45 PM
Y by
RMarri_1018 wrote:
As Mathcounts States has not started yet, I would like to ask a quick question. What would be the target goal to get to nationals in the state of Pennslyvania. I mock 34-38, so I want to know would that be enough to get me to CDR?

in florida mathcounts 35-36 or higher is enough to get into nats
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NS0004
169 posts
NS0004
#6 h  Mar 11, 2025, 9:53 PM
Y by
Probably will be less this year tho cuz the top ten didnt have too many 7th graders in florida...
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mathlover3141
5 posts
mathlover3141
#7 h  Mar 17, 2025, 8:19 PM
Y by
if it's an easy year and other people score higher you just need to not silly questions and you will also do well
if it's a normal/hard year then the cdr cutoff is usually 30 and the top 4 cutoff is around 33-35
expect hard questions so that you won't be surprised when you actually sit down and take the test
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Hanruz
6 posts
Hanruz
#18 h  Yesterday at 1:26 AM
Y by
Is discussion allowed now?
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c_double_sharp
291 posts
c_double_sharp
#19 h  Yesterday at 1:38 AM
Y by
Hanruz wrote:
Is discussion allowed now?

no.
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giratina3
443 posts
giratina3
#20 h  Yesterday at 11:36 AM
Y by
Hanruz wrote:
Is discussion allowed now?

Wait until April just to be safe :)
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