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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

Prealgebra 1 Self-Paced

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Thursday, Jun 12 - Sep 11

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Thursday, May 22 - Jul 31

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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

Bogus Proof Marathon

pifinity 7636

Hi!
I'd like to introduce the Bogus Proof Marathon.

In this marathon, simply post a bogus proof that is middle-school level and the next person will find the error. You don't have to post the real solution :P

Use classic Marathon format:

[hide=P#]a1b2c3[/hide]
[hide=S#]a1b2c3[/hide]

Example posts:

P(x)
-----
S(x)
P(x+1)
-----
Let's go!! Just don't make it too hard!

7636 replies

pifinity

Mar 12, 2018

TealFrog84

an hour ago

INTERSTING

teomihai 0

IF $1=3$
$2=3$

$3=4$
$4=5$
FIND $6=?$

0 replies

teomihai

3 hours ago

0 replies

Function Problem

Geometry285 2

The function $f(x)$ can be defined as a sequence such that $x=n$ , and $a_n = | a_{n-1} | + \left \lceil \frac{n!}{n^{100}} \right \rceil$ , such that $a_n = n$ . The function $g(x)$ is such that $g(x) = x!(x+1)!$ . How many numbers within the interval $0<n<101$ for the function $g(f(x))$ are perfect squares?

2 replies

Geometry285

Apr 11, 2021

Saucepan_man02

3 hours ago

9 Pythagorean Triples

ZMB038 47

Please put some of the ones you know, and try not to troll/start flame wars! Thank you :D

47 replies

ZMB038

Monday at 6:04 PM

pieMax2713

6 hours ago

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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120,674 topics

5 users

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

Got what it takes to disprove Euler?

4everwise 18

One of Euler's conjectures was disproved in then 1960s by three American mathematicians when they showed there was a positive integer $n$ such that $133^5 + 110^5 + 84^5 + 27^5 = n^5.$ Find the value of $n$ .

18 replies

4everwise

Feb 20, 2006

P162008

an hour ago

Inequalities

sqing 3

Let $a,b,c>0.$ Prove that $a^2+b^2+c^2+abc-k(a+b+c)\geq 3k+2-2(k+1)\sqrt{k+1}$ Where $7\geq k \in N^+.$
$a^2+b^2+c^2+abc-3(a+b+c)\geq-5$

3 replies

sqing

Yesterday at 2:23 PM

sqing

an hour ago

Inequalities

sqing 14

Let $a,b>0$ . Prove that
$\frac{a}{a^2+a +2b+1}+ \frac{b}{b^2+2a +b+1} \leq \frac{2}{5}$ $\frac{a}{a^2+2a +b+1}+ \frac{b}{b^2+a +2b+1} \leq \frac{2}{5}$

14 replies

sqing

May 13, 2025

sqing

2 hours ago

Maximum number of empty squares

Ecrin_eren 1

There are 16 kangaroos on a giant 4×4 chessboard, with exactly one kangaroo on each square. In each round, every kangaroo jumps to a neighboring square (up, down, left, or right — but not diagonally). All kangaroos stay on the board. More than one kangaroo can occupy the same square. What is the maximum number of empty squares that can exist after 100 rounds?

1 reply

Ecrin_eren

Yesterday at 6:35 PM

Ecrin_eren

3 hours 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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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

Two Sequences

worthawholebean 11

Source: AIME 2008II Problem 6

The sequence $\{a_n\}$ is defined by
$a_0 = 1,a_1 = 1, \text{ and } a_n = a_{n - 1} + \frac {a_{n - 1}^2}{a_{n - 2}}\text{ for }n\ge2.$ The sequence $\{b_n\}$ is defined by
$b_0 = 1,b_1 = 3, \text{ and } b_n = b_{n - 1} + \frac {b_{n - 1}^2}{b_{n - 2}}\text{ for }n\ge2.$ Find $\frac {b_{32}}{a_{32}}$ .

11 replies

worthawholebean

Apr 3, 2008

P162008

12 minutes ago

Goals for 2025-2026

Airbus320-214 160

Please write down your goal/goals for competitions here for 2025-2026.

160 replies

Airbus320-214

May 11, 2025

pieMax2713

3 hours ago

[TEST RELEASED] OMMC Year 5

DottedCaculator 98

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/
Our Discord (6000+ members): https://tinyurl.com/joinommc

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]

98 replies

DottedCaculator

Apr 26, 2025

AVY2024

3 hours ago

Essentially, how to get good at olympiad math?

gulab_jamun 10

Ok, so I'm posting this as an anynonymous user cuz I don't want to get flamed by anyone I know for my goals but I really do want to improve on my math skill.

Basically, I'm alright at computational math (10 AIME, dhr stanford math meet twice) and I hope I can get good enough at olympiad math over the summer to make MOP next year (I will be entering 10th as after next year, it becomes much harder :( )) Essentially, I just want to get good at olympiad math. If someone could, please tell me how to study, like what books (currently thinking of doing EGMO) but I don't know how to get better at the other topics. Also, how would I prepare? Like would I study both proof geometry and proof number theory concurrently or just study each topic one by one?? Would I do mock jmo/amo or js prioritize olympiad problems in each topic. I have the whole summer ahead of me, and intend to dedicate it to olympiad math, so any advice would be really appreciated. Thank you!

10 replies

gulab_jamun

May 18, 2025

gulab_jamun

Today at 2:23 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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313,009 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

Computing functions

BBNoDollar 0

Let $f : [0, \infty) \to [0, \infty)$ , $f(x) = \dfrac{ax + b}{cx + d}$ , with $a, d \in (0, \infty)$ , $b, c \in [0, \infty)$ . Prove that there exists $n \in \mathbb{N}^*$ such that for every $x \geq 0$
$f_n(x) = \frac{x}{1 + nx}, \quad \text{if and only if } f(x) = \frac{x}{1 + x}, \quad \forall x \geq 0.$ (For $n \in \mathbb{N}^*$ and $x \geq 0$ , the notation $f_n(x)$ represents $\underbrace{(f \circ f \circ \dots \circ f)}_{n \text{ times}}(x)$ . )

0 replies

BBNoDollar

15 minutes ago

0 replies

4 variables

Nguyenhuyen_AG 9

Let $a,\,b,\,c,\,d$ are non-negative real numbers and $0 \leqslant k \leqslant \frac{2}{\sqrt{3}}.$ Prove that
$a^2+b^2+c^2+d^2+kabcd \geqslant k+4+(k+2)(a+b+c+d-4).$ hide

9 replies

Nguyenhuyen_AG

Dec 21, 2020

arqady

15 minutes ago

3 var inequality

JARP091 3

Source: Own

Let $x, y, z \in \mathbb{R}^+$ . Prove that
$\sum_{\text{cyc}} \frac{x^3}{y^2 + z^2} \geq \frac{x + y + z}{2}$ without using the Rearrangement Inequality or Chebyshev's Inequality.

3 replies

JARP091

an hour ago

JARP091

19 minutes ago

Self-evident inequality trick

Lukaluce 11

Source: 2025 Junior Macedonian Mathematical Olympiad P4

Let $x, y$ , and $z$ be positive real numbers, such that $x^2 + y^2 + z^2 = 3$ . Prove the inequality
$\frac{x^3}{2 + x} + \frac{y^3}{2 + y} + \frac{z^3}{2 + z} \ge 1.$ When does the equality hold?

11 replies

Lukaluce

May 18, 2025

ytChen

21 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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114,310 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

Double integration

Tricky123 2

Q)
$\iint_{R} \sin(xy) \,dx\,dy, \quad R = \left[0, \frac{\pi}{2}\right] \times \left[0, \frac{\pi}{2}\right]$
How to solve the problem like this I am using the substitution method but its seems like very complicated in the last
Please help me

2 replies

Tricky123

May 18, 2025

Mathzeus1024

an hour ago

How can I know the sequences's convergence value?

Madunglecha 2

What is the convergence value of the sequence??
(n^2)*ln(n+1/n)-n

2 replies

1 viewing

Madunglecha

3 hours ago

Madunglecha

an hour ago

Unsolving differential equation

Madunglecha 3

For parameter t
I made a differential equation :
y"=y*(x')^2
for here, '&" is derivate and second order derivate for t
could anyone tell me what is equation between y&x?

3 replies

Madunglecha

May 18, 2025

solyaris

3 hours ago

Prove the statement

Butterfly 11

Given an infinite sequence $\{x_n\} \subseteq [0,1]$ , there exists some constant $C$ , for any $r>0$ , among the sequence $x_n$ and $x_m$ could be chosen to satisfy $|n-m|\ge r$ and $|x_n-x_m|<\frac{C}{|n-m|}$ .

11 replies

Butterfly

May 7, 2025

solyaris

3 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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18,666 topics

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

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jlacosta

May 1, 2025

0 replies

Introducing myself at AoPS, and what's your magic wand?

asuth_asuth 1256

Hi!

I'm Andrew Sutherland. I'm the new Chief Product Officer at AoPS. As you may have read, Richard is retiring and Ben Kornell and I are working together to lead the company now. I'm leading all the software and digital stuff at AoPS. I just wanted to say hello and introduce myself! I'm really excited to be part of the special community that is AoPS.

Previously, I founded Quizlet as a 15-year-old high school student. I did Course 6 at MIT and then left to lead Quizlet full-time for a total of 14 years. I took a few years off and now I'm doing AoPS! I wrote more about all that on my blog: https://asuth.com/im-joining-aops

I have a question for all of you. If you could wave a magic wand, and change anything about AoPS, what would it be? All suggestions welcome! Thank you.

1256 replies

asuth_asuth

Mar 30, 2025

GallopingUnicorn45

Today at 1:09 AM

All Topics Marked

alpha31415 9

Excuse me!
for I am a frashman in aops.I wonder how I could get back to mark all my read.All topics in the forum became as if they had been marked.Would someone please help me deal with it???

9 replies

alpha31415

May 16, 2025

peppermint_cat

Yesterday at 11:23 PM

k alcumus going crazy?

LittleSnake____ 61

all of a sudden, the alcumus forum has gotten completely exploded by gamebot's posts.

https://artofproblemsolving.com/community/c63h3570498_alcumus_going_crazy

61 replies

LittleSnake____

May 18, 2025

jlacosta

Monday at 4:40 PM

k New user not allowed to use LaTeX

Cats_on_a_computer 8

Do I seriously have to post everyday for 14 days for me not to be considered a “new user? I didn’t even upload any images, I just used LaTeX. How am I supposed to write anything without LaTeX?

8 replies