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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.

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0 replies

jlacosta

May 1, 2025

0 replies

Challenge: Make every number to 100 using 4 fours

CJB19 229

I've seen this attempted a lot but I want to see if the AoPS community can actually do it. Using ONLY 4 fours and math operations, make as many numbers as you can. Try to go in order. I'll start:
$(4-4)*4*4=0$ $4-4+4/4=1$ $4/4+4/4=2$ $(4+4+4)/4=3$ $4+(4-4)*4=4$ $4+4^{4-4}=5$ $4!/4+4-4=6$ $4+4-4/4=7$ $4+4+4-4=8$

229 replies

CJB19

May 15, 2025

Moon_settler

23 minutes ago

Tricky problem

VivaanKam 5

$\text{Mrs. Lee announced that any student who scored }90\text{ or higher on the final test would receive an }A\text{ for the class.}$
$\text{Consider the following statements:}$

$\text{Lauren scored an }80\text{ on the final and received an }A\text{ for the class.}$
$\text{Lauren scored a }90\text{ on the final and received an }A\text{ for the class.}$
$\text{Lauren scored an }80\text{ on the final and did not receive an }A\text{ for the class.}$
$\text{Lauren scored a }90\text{ on the final and did not receive an }A\text{ for the class.}$

$\text{How many of the statements above are possibly true?}$

I got this problem wrong when I first tried it. :(

5 replies

VivaanKam

Yesterday at 6:36 PM

Craftybutterfly

25 minutes ago

Estimation Problems

slightly_irrational 1

Is there a general strategy for problems like this where you find the first nonzero digit of some number?

Mathcounts 2025 Chapter Sprint 28
What is the first non-zero digit of $\sqrt{75^2 + 1}$ that appears after the decimal point?

1 reply

slightly_irrational

an hour ago

aidan0626

an hour ago

prime numbers

wpdnjs 125

does anyone know how to quickly identify prime numbers?

thanks.

125 replies

wpdnjs

Oct 2, 2024

MMA2024

an hour 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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120,715 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

Inequalities

sqing 20

Let $a,b,c>0 , a+b+c +abc=4$ . Prove that
$\frac {a}{a^2+2}+\frac {b}{b^2+2}+\frac {c}{c^2+2} \leq 1$ Let $a,b,c>0 , ab+bc+ca+abc=4$ . Prove that
$\frac {a}{a^2+2}+\frac {b}{b^2+2}+\frac {c}{c^2+2} \leq 1$

20 replies

sqing

May 15, 2025

ytChen

2 hours ago

a tst 2013 test

Math2030 5

Given the sequence $(a_n): a_1=1, a_2=11$ and $a_{n+2}=a_{n+1}+5a_{n}, n \geq 1$
. Prove that $a_n$ not is a perfect square for all $n > 3$ .

5 replies

Math2030

Today at 5:26 AM

Shan3t

3 hours ago

[Sipnayan SHS] Written Round, Average, #4.6

LilKirb 4

Define the function
$f(n) = \sum_{k=0}^{n} \binom{n}{k} a_k, \quad n = 1, 2, 3, \ldots$ where
$a_k = \begin{cases} 3^k, & \text{if } k \text{ is even}, \\ 0, & \text{if } k \text{ is odd}. \end{cases}$ Find the remainder when $f(10^9 + 2)$ is divided by $2^{20} + 1$

4 replies

LilKirb

Today at 2:25 PM

Shan3t

4 hours ago

Remaining balls

pacoga 4

A bag contains $20$ white balls, $30$ red balls and $40$ black balls. We extract balls at random without replacement until the bag becomes empty. What is the probability that there are still black and red balls in the bag when the last white ball is drawn?

4 replies

pacoga

Feb 3, 2021

mafj

4 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

How Math WOOT Level 2 prepare you for olympiad contest

AMC10JA 0

I know how you do on Olympiad is based on your effort and your thinking skill, but I am just curious is WOOT level 2 is generally for practicing the beginner olympiad contest (like USAJMO or lower), or also good to learn for hard olympiad contest (like USAMO and IMO).
Please share your thought and experience. Thank you!

0 replies

AMC10JA

8 minutes ago

0 replies

[CASH PRIZES] IndyINTEGIRLS Spring Math Competition

Indy_Integirls 50

[center]IMAGE

Greetings, AoPS! IndyINTEGIRLS will be hosting a virtual math competition on May 25,
2024 from 12 PM to 3 PM EST. Join other woman-identifying and/or non-binary "STEMinists" in solving problems, socializing, playing games, winning prizes, and more! If you are interested in competing, please register here![/center]

----------

[center]Important Information[/center]

Eligibility: This competition is open to all woman-identifying and non-binary students in middle and high school. Non-Indiana residents and international students are welcome as well!

Format: There will be a middle school and high school division. In each separate division, there will be an individual round and a team round, where students are grouped into teams of 3-4 and collaboratively solve a set of difficult problems. There will also be a buzzer/countdown/Kahoot-style round, where students from both divisions are grouped together to compete in a MATHCOUNTS-style countdown round! There will be prizes for the top competitors in each division.

Problem Difficulty: Our amazing team of problem writers is working hard to ensure that there will be problems for problem-solvers of all levels! The middle school problems will range from MATHCOUNTS school round to AMC 10 level, while the high school problems will be for more advanced problem-solvers. The team round problems will cover various difficulty levels and are meant to be more difficult, while the countdown/buzzer/Kahoot round questions will be similar to MATHCOUNTS state to MATHCOUNTS Nationals countdown round in difficulty.

Platform: This contest will be held virtually through Zoom. All competitors are required to have their cameras turned on at all times unless they have a reason for otherwise. Proctors and volunteers will be monitoring students at all times to prevent cheating and to create a fair environment for all students.

Prizes: At this moment, prizes are TBD, and more information will be provided and attached to this post as the competition date approaches. Rest assured, IndyINTEGIRLS has historically given out very generous cash prizes, and we intend on maintaining this generosity into our Spring Competition.

Contact & Connect With Us: Email us at indy@integirls.org.

---------
[center]Help Us Out

Please help us in sharing the news of this competition! Our amazing team of officers has worked very hard to provide this educational opportunity to as many students as possible, and we would appreciate it if you could help us spread the word!

50 replies

+1 w

Indy_Integirls

May 11, 2025

ChaitraliKA

27 minutes ago

Equilateral triangle $ABC$, $DEF$ has twice the area

v_Enhance 122

Source: JMO 2017 Problem 3, Titu, Luis, Cosmin

Let $ABC$ be an equilateral triangle, and point $P$ on its circumcircle. Let $PA$ and $BC$ intersect at $D$ , $PB$ and $AC$ intersect at $E$ , and $PC$ and $AB$ intersect at $F$ . Prove that the area of $\triangle DEF$ is twice the area of $\triangle ABC$ .

Proposed by Titu Andreescu, Luis Gonzales, Cosmin Pohoata

122 replies

v_Enhance

Apr 19, 2017

lpieleanu

an hour ago

[TEST RELEASED] OMMC Year 5

DottedCaculator 124

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]

124 replies

DottedCaculator

Apr 26, 2025

vincentwant

an hour ago

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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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

USA GEO 2003

dreammath 21

Source: TST USA 2003

Let $ABC$ be a triangle and let $P$ be a point in its interior. Lines $PA$ , $PB$ , $PC$ intersect sides $BC$ , $CA$ , $AB$ at $D$ , $E$ , $F$ , respectively. Prove that
$[PAF]+[PBD]+[PCE]=\frac{1}{2}[ABC]$
if and only if $P$ lies on at least one of the medians of triangle $ABC$ . (Here $[XYZ]$ denotes the area of triangle $XYZ$ .)

21 replies

dreammath

Feb 16, 2004

lpieleanu

8 minutes ago

Balkan Mathematical Olympiad

ABCD1728 0

Can anyone provide the PDF version of the book "Balkan Mathematical Olympiads" by Mircea Becheanu and Bogdan Enescu (published by XYZ press in 2014), thanks!

0 replies

ABCD1728

17 minutes ago

0 replies

An amazing functional equation over positive reals

ariopro1387 0

Source: Iran Team selection test 2025 - P6

Find all functions $f:\mathbb{R}^+ \rightarrow \mathbb{R}^+$ , such that:
$f(f(f(xy))+x^2)=f(y)(f(x)-f(x+y))$
for all $x, y>0$ .

0 replies

1 viewing

ariopro1387

an hour ago

0 replies

Nice "if and only if" function problem

ICE_CNME_4 10

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 $\underbrace{(f \circ f \circ \dots \circ f)}_{n \text{ times}}(x)$ . )

Please do it at 9th grade level. Thank you!

10 replies

ICE_CNME_4

Yesterday at 7:23 PM

maromex

an hour 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

Different Paths Probability

Qebehsenuef 4

Source: OBM

A mouse initially occupies cage A and is trained to change cages by going through a tunnel whenever an alarm sounds. Each time the alarm sounds, the mouse chooses any of the tunnels adjacent to its cage with equal probability and without being affected by previous choices. What is the probability that after the alarm sounds 23 times the mouse occupies cage B?

4 replies

Qebehsenuef

Apr 28, 2025

Qebehsenuef

19 minutes ago

Primes and automorphisms

CatalinBordea 2

Source: Romanian District Olympiad 2016, Grade XII, Problem 3

Let be a group $G$ of order $1+p,$ where $p$ is and odd prime. Show that if $p$ divides the number of automorphisms of $G,$ then $p\equiv 3\pmod 4.$

2 replies

CatalinBordea

Oct 5, 2018

a_0a

Today at 5:07 PM

Japanese Olympiad

parkjungmin 7

It's about the Japanese Olympiad

I can't solve it no matter how much I think about it.

If there are people who are good at math

Please help me.

7 replies

parkjungmin

May 10, 2025

Gauler

Today at 4:16 PM

Find the expected END time for the given process

superpi 2

This problem suddenly popped up in my head. But I don't know how to deal with it.

There are N bulbs. All the bulbs' available time follows same exponential distribution with parameter lambda(Or any arbitrary distribution with mean $\mu$ ). We do following operations
1. First, turn on the all $N$ bulbs
2. For each $k >= 2$ bulbs goes out, append ONE NEW BULB and turn on (This step starts and finishes immediately when kth bulb goes out)
3. Repeat 2 until all the bulbs goes out

What is the expected terminate time for the above process for given $N, k, \lambda$ ?

Or, is there any more conditions to complete the problem?

2 replies

superpi

Yesterday at 4:33 PM

Hello_Kitty

Today at 1:32 PM

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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18,674 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

Stamina XP decreasing?

Craftybutterfly 16

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

16 replies

Craftybutterfly

May 22, 2025

Craftybutterfly

an hour ago

banned myself from own blog

Spacepandamath13 7

I got curious and decided to see if I can ban myself from my own blog.
can site admins give it back? it says site admins are the administrators of this blog

I honestly don't know where I come up with stuff like this

7 replies

1 viewing

Spacepandamath13

Today at 3:02 AM

Spacepandamath13

2 hours ago

Who is Halp! ?

A7456321 3

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.

3 replies