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Middle School Math Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

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Middle School Math Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

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]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

Introductory: Grades 5-10

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Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)

0 replies

jlacosta

May 1, 2025

0 replies

Rational equation

soruz 1

Solve the equation:
$\frac{x+2}{1011} +\frac{x}{1010} +\frac{x-2}{1009} +\frac{x-4}{1008}...+\frac{x-2016}{2}=2020$ .

1 reply

soruz

Feb 23, 2022

Mathzeus1024

2 hours ago

9 How many squares do you have memorized

LXC007 102

How many squares have you memorized. I have 1-20

Edit: to clarify i mean positive squares from 1 so if you say ten you mean you memorized the squares 1,2,3,4,5,6,7,8,9 and 10

102 replies

LXC007

May 17, 2025

SapphireKitty

3 hours ago

Penrick Hates 2, 5, and 7

LilKirb 0

Penrick writes all positive integers starting from $1$ , but skips any number containing digits $2$ , $5,$ or $7$ . If the last number he writes is $3141$ , how many numbers has Penrick written in total?

Answer
Solution

0 replies

LilKirb

5 hours ago

0 replies

[PMO26 Qualis] I.3 Change every number

aops-g5-gethsemanea2 4

The arithmetic mean of $11$ integers is $10$ . After adding $20$ to each of the first four and subtracting $24$ from each of the last seven, what is the new mean?

$\text{(a) }2\qquad\text{(b) }3\qquad\text{(c) }4\qquad\text{(d) }6$

Answer confirmation

4 replies

aops-g5-gethsemanea2

Feb 9, 2025

Shinfu

Today at 3:48 AM

High School Math Grades 9-12, Ages 13-18

Grades 9-12, Ages 13-18

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High School Math Grades 9-12, Ages 13-18

Grades 9-12, Ages 13-18

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120,734 topics

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

La hire's with only euclidian

Kscv 2

How can I prove la hire's theorem with pure Euclidean geometry? Every single proof I see on the internet uses projective geometry which I have no idea of.

Can someone help me? I only need the proof for circles BTW.

2 replies

Kscv

Today at 6:03 AM

compoly2010

6 minutes ago

17th PMO Area stage #18

Kyj9981 0

Segment $CD$ is tangent to the circle with center $O$ , at $D$ . Point $A$ is in the interior of the circle, and segment $AC$ intersects the circle at $B$ . If $OA = 2$ , $AB = 4$ , $BC = 3$ , and $CD = 6$ , find the length of segment $OC$ .

IMAGE

Answer

0 replies

Kyj9981

8 minutes ago

0 replies

23rd PMO Qualifying stage #15

Kyj9981 0

In the figure below, $BC$ is the diameter of a semicircle centered at $O$ , which intersects $AB$ and
$AC$ at $D$ and $E$ respectively. Suppose that $AD = 9$ , $DB = 4$ , and $\angle ACD = \angle DOB$ . Find the
length of $AE$ .
IMAGE

Answer

0 replies

Kyj9981

17 minutes ago

0 replies

[Own problem] geometric sequence of logarithms

aops-g5-gethsemanea2 1

A geometric sequence has the property where the third term is $\log32$ more than the first term, and the fourth term is $\log(128\sqrt2)$ more than the second term. Find the first term.

1 reply

aops-g5-gethsemanea2

32 minutes ago

aops-g5-gethsemanea2

31 minutes ago

Contests & Programs AMC and other contests, summer programs, etc.

AMC and other contests, summer programs, etc.

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Contests & Programs AMC and other contests, summer programs, etc.

AMC and other contests, summer programs, etc.

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34,729 topics

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

An FE. Who woulda thunk it?

nikenissan 120

Source: 2021 USAJMO Problem 1

Let $\mathbb{N}$ denote the set of positive integers. Find all functions $f : \mathbb{N} \rightarrow \mathbb{N}$ such that for positive integers $a$ and $b,$ $f(a^2 + b^2) = f(a)f(b) \text{ and } f(a^2) = f(a)^2.$

120 replies

nikenissan

Apr 15, 2021

NerdyNashville

3 minutes ago

4th grader qual JMO

HCM2001 37

i mean.. whattttt??? just found out about this.. is he on aops? (i'm sure he is) where are you orz lol..
https://www.mathschool.com/blog/results/celebrating-success-douglas-zhang-is-rsm-s-youngest-usajmo-qualifier

37 replies

HCM2001

May 22, 2025

CatCatHead

4 hours ago

Zsigmondy's theorem

V0305 3

Is Zsigmondy's theorem allowed on the IMO, and is it allowed on the AMC series of proof competitions (e.g. USAJMO, USA TSTST)?

3 replies

1 viewing

V0305

Yesterday at 6:22 PM

CatCatHead

4 hours ago

[TEST RELEASED] OMMC Year 5

DottedCaculator 132

Test portal: https://ommc-test-portal-2025.vercel.app/

Hello to all creative problem solvers,

Do you want to work on a fun, untimed team math competition with amazing questions by MOPpers and IMO & EGMO medalists? $\phantom{You lost the game.}$
Do you want to have a chance to win thousands in cash and raffle prizes (no matter your skill level)?

Check out the fifth annual iteration of the

Online Monmouth Math Competition!

Online Monmouth Math Competition, or OMMC, is a 501c3 accredited nonprofit organization managed by adults, college students, and high schoolers which aims to give talented high school and middle school students an exciting way to develop their skills in mathematics.

Our website: https://www.ommcofficial.org/

This is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read carefully and thoroughly. Join our Discord or monitor this thread for updates and test releases.

How hard is it?

We plan to raffle out a TON of prizes over all competitors regardless of performance. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!

How are the problems?

You can check out our past problems and sample problems here:
https://www.ommcofficial.org/sample
https://www.ommcofficial.org/2022-documents
https://www.ommcofficial.org/2023-documents
https://www.ommcofficial.org/ommc-amc

How will the test be held?/How do I sign up?

Solo teams?

Test Policy

Timeline:
Main Round: May 17th - May 24th
Test Portal Released. The Main Round of the contest is held. The Main Round consists of 25 questions that each have a numerical answer. Teams will have the entire time interval to work on the questions. They can submit any time during the interval. Teams are free to edit their submissions before the period ends, even after they submit.

Final Round: May 26th - May 28th
The top placing teams will qualify for this invitational round (5-10 questions). The final round consists of 5-10 proof questions. Teams again will have the entire time interval to work on these questions and can submit their proofs any time during this interval. Teams are free to edit their submissions before the period ends, even after they submit.

Conclusion of Competition: Early June
Solutions will be released, winners announced, and prizes sent out to winners.

Scoring:

Prizes:

I have more questions. Whom do I ask?

We hope for your participation, and good luck!

OMMC staff

OMMC’S 2025 EVENTS ARE SPONSORED BY:

[list]
[*]Nontrivial Fellowship
[*]Citadel
[*]SPARC
[*]Jane Street
[*]And counting!
[/list]

132 replies

DottedCaculator

Apr 26, 2025

MathCosine

Today at 5:08 AM

High School Olympiads Regional, national, and international math olympiads

Regional, national, and international math olympiads

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High School Olympiads Regional, national, and international math olympiads

Regional, national, and international math olympiads

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313,107 topics

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

Serbian selection contest for the IMO 2025 - P5

OgnjenTesic 2

Source: Serbian selection contest for the IMO 2025

Determine the smallest positive real number $\alpha$ such that there exists a sequence of positive real numbers $(a_n)$ , $n \in \mathbb{N}$ , with the property that for every $n \in \mathbb{N}$ it holds that:
$a_1 + \cdots + a_{n+1} < \alpha \cdot a_n.$ Proposed by Pavle Martinović

2 replies

OgnjenTesic

May 22, 2025

GreenTea2593

5 minutes ago

centroid wanted, point that minimizes sum of squares of distances from sides

parmenides51 1

Source: Oliforum Contest V 2017 p9 https://artofproblemsolving.com/community/c2487525_oliforum_contes

Given a triangle $ABC$ , let $P$ be the point which minimizes the sum of squares of distances from the sides of the triangle. Let $D, E, F$ the projections of $P$ on the sides of the triangle $ABC$ . Show that $P$ is the barycenter of $DEF$ .

(Jack D’Aurizio)

1 reply

parmenides51

Sep 29, 2021

SuperBarsh

9 minutes ago

Inequality em981

oldbeginner 17

Source: Own

Let $a, b, c>0, a+b+c=3$ . Prove that
$\sqrt{a+\frac{9}{b+2c}}+\sqrt{b+\frac{9}{c+2a}}+\sqrt{c+\frac{9}{a+2b}}+\frac{2(ab+bc+ca)}{9}\ge\frac{20}{3}$

17 replies

2 viewing

oldbeginner

Sep 22, 2016

sqing

11 minutes ago

Strictly monotone polynomial with an extra condition

Popescu 11

Source: IMSC 2024 Day 2 Problem 2

Let $\mathbb{R}_{>0}$ be the set of all positive real numbers. Find all strictly monotone (increasing or decreasing) functions $f:\mathbb{R}_{>0} \to \mathbb{R}$ such that there exists a two-variable polynomial $P(x, y)$ with real coefficients satisfying
$f(xy)=P(f(x), f(y))$ for all $x, y\in\mathbb{R}_{>0}$ .

Proposed by Navid Safaei, Iran

11 replies

Popescu

Jun 29, 2024

Iveela

19 minutes ago

College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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114,314 topics

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

Local extrema of a function

MrBridges 2

Calculate the local extrema of the function $f:\mathbb{R}^2 \rightarrow \mathbb{R}$ , $(x,y)\mapsto x^4+x^5+y^6$ . Are they isolated?

2 replies

MrBridges

Jun 28, 2020

Mathzeus1024

an hour ago

Integral

Martin.s 3

$\int_0^{\pi/6}\arcsin\Bigl(\sqrt{\cos(3\psi)\cos\psi}\Bigr)\,d\psi.$

3 replies

Martin.s

May 14, 2025

Figaro

2 hours ago

Reducing the exponents for good

RobertRogo 1

Source: The national Algebra contest (Romania), 2025, Problem 3/Abstract Algebra (a bit generalized)

Let $A$ be a ring with unity such that for every $x \in A$ there exist $t_x, n_x \in \mathbb{N}^*$ such that $x^{t_x+n_x}=x^{n_x}$ . Prove that
a) If $t_x \cdot 1 \in U(A), \forall x \in A$ then $x^{t_x+1}=x, \forall x \in A$
b) If there is an $x \in A$ such that $t_x \cdot 1 \notin U(A)$ then the result from a) may no longer hold.

Authors: Laurențiu Panaitopol, Dorel Miheț, Mihai Opincariu, me, Filip Munteanu

1 reply

RobertRogo

May 20, 2025

RobertRogo

3 hours ago

Sequence divisible by infinite primes - Brazil Undergrad MO

rodamaral 5

Source: Brazil Undergrad MO 2017 - Problem 2

Let $a$ and $b$ be fixed positive integers. Show that the set of primes that divide at least one of the terms of the sequence $a_n = a \cdot 2017^n + b \cdot 2016^n$ is infinite.

5 replies

rodamaral

Nov 1, 2017

cursed_tangent1434

5 hours ago

Site Support Tech support and questions about AoPS classes and materials

Tech support and questions about AoPS classes and materials

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Site Support Tech support and questions about AoPS classes and materials

Tech support and questions about AoPS classes and materials

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18,675 topics

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

Request for the access of private marathons

Vulch 2

To all AoPS users and admin,
Sometimes I came across the marathon(i .e number theory marathon, functional equation marathon etc) which allow access only after submitting log in request.There is no other way to access the question related to that marathons.It would be glad to open all private marathons publicly.Thank you!

2 replies

Vulch

Today at 6:06 AM

Dragon_Yang

5 hours ago

Who is Halp! ? (resolvedd)

A7456321 4

Is Halp! a bot? This user has been posting questions in nearly all of my AoPS classes when the user isn't a part of the class, and this user has 150k posts.

4 replies

A7456321

Yesterday at 9:22 PM

A7456321

Today at 2:53 AM

How to create a poll?

whwlqkd 23

How to create a poll in aops?

23 replies

whwlqkd

Yesterday at 12:24 PM

Craftybutterfly

Today at 2:18 AM

Stamina XP decreasing?

Craftybutterfly 18

Summary of the problem: Last night when I checked, alcumus said I had 4250 stamina XP which is more than other people. However, when I just checked, it said I only earned 3905 XP. What is wrong?
Page URL: Hall of Fame
Steps to reproduce:
1. Go to hall of fame
2. Scroll to stamina XP earned
Expected behavior: It should still say I earned 4250 XP
Frequency: 100%
Operating system(s): HP Elitebook
Browser(s), including version: Chrome
IMAGE

18 replies

Craftybutterfly

May 22, 2025

Craftybutterfly

Today at 2:02 AM

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