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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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Prealgebra 1 Self-Paced

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0 replies

jlacosta

May 1, 2025

0 replies

Challenge: Make every number to 100 using 4 fours

CJB19 175

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:
$(4-4)*4*4=0$ $4-4+4/4=1$ $4/4+4/4=2$ $(4+4+4)/4=3$ $4+(4-4)*4=4$ $4+4^{4-4}=5$ $4!/4+4-4=6$ $4+4-4/4=7$ $4+4+4-4=8$

175 replies

CJB19

May 15, 2025

JARP091

a minute ago

9 zeroes!.

ericheathclifffry 22

i personally have no idea

22 replies

ericheathclifffry

May 5, 2025

Yihangzh

3 hours ago

Find digits

MihaiT 9

Find digits $a,b,c$ s.t. $\frac{a}{a+b+c}=\overline{0,abc }$

9 replies

MihaiT

Yesterday at 4:56 PM

MihaiT

3 hours ago

cant understand so dumb

greenplanet2050 8

am i stupid or smth

2001 AMC 10

Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible?

umm why isnt it 3^4

8 replies

greenplanet2050

Yesterday at 6:02 PM

tikachaudhuri

5 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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120,659 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 14

Let $a,b,c >2$ and $ab+bc+ca \leq 75.$ Show that
$\frac{1}{a-2}+\frac{1}{b-2}+\frac{1}{c-2}\geq 1$ Let $a,b,c >2$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{6}{7}.$ Show that
$\frac{1}{a-2}+\frac{1}{b-2}+\frac{1}{c-2}\geq 2$

14 replies

sqing

May 13, 2025

sqing

2 hours ago

Pertenacious Polynomial Problem

BadAtCompetitionMath21420 6

Let the polynomial $P(x) = x^3-x^2+px-q$ have real roots and real coefficients with $q>0$ . What is the maximum value of $p+q$ ?

This is a problem I made for my math competition, and I wanted to see if someone would double-check my work (No Mike allowed):

solution
Is this solution good?

6 replies

BadAtCompetitionMath21420

May 17, 2025

lbh_qys

3 hours ago

Vieta's Formula.

BlackOctopus23 4

Can someone help me understand Vieta's Formula? I am currently learning it for my class. I learned that for a polynomial of degree $n$ , all the roots added will give $-\frac{a_{n-1}}{a_n}$ . I also learned that if every single root, multiplies every single root, it will give $\frac{a_{n-2}}{a_n}$ . I also learned that if all the roots are multiplied, it will give $-\frac{a_0}{a_n}$ . Is this right? And is there any purpose for these equations?

4 replies

BlackOctopus23

Yesterday at 11:10 PM

compoly2010

4 hours ago

The sum of 335 distinct positive integers

Streit31415 1

The sum of 335 distinct positive integers is equal to 100000
a) what is the minimum number of odd numbers among them ?
b) what is the maximum number of odd numbers among them ?

1 reply

Streit31415

Yesterday at 11:38 PM

Bocabulary142857

Today at 12:36 AM

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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34,719 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

[TEST RELEASED] OMMC Year 5

DottedCaculator 81

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]

81 replies

DottedCaculator

Apr 26, 2025

fuzimiao2013

5 minutes ago

EGMO help

mathprodigy2011 25

If we have a quadrilateral with 1 pair of parallel sides but the parallel sides are also equal, is that sufficient to stating the quadrilateral is a parallelogram. if it's not, please give a counter-example.

25 replies

mathprodigy2011

Yesterday at 10:30 PM

Schintalpati

20 minutes ago

MathILy 2025 Decisions Thread

mysterynotfound 42

Discuss your decisions here!
also share any relevant details about your decisions if you want

42 replies

mysterynotfound

Apr 21, 2025

quavante

an hour ago

[CASH PRIZES] IndyINTEGIRLS Spring Math Competition

Indy_Integirls 22

[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: Follow us on Instagram @indy.integirls, join our Discord, follow us on TikTok @indy.integirls, and 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!

22 replies

Indy_Integirls

May 11, 2025

Ruegerbyrd

2 hours 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

Distance between any two points is irrational

orl 21

Source: IMO 1987, Day 2, Problem 5

Let $n\ge3$ be an integer. Prove that there is a set of $n$ points in the plane such that the distance between any two points is irrational and each set of three points determines a non-degenerate triangle with rational area.

21 replies

+1 w

orl

Nov 11, 2005

cursed_tangent1434

19 minutes ago

Symmetric inequality

mrrobotbcmc 5

Let a,b,c,d belong to positive real numbers such that a+b+c+d=1. Prove that a^3/(b+c)+b^3/(c+d)+c^3/(d+a)+d^3/(a+b)>=1/8

5 replies

mrrobotbcmc

2 hours ago

youochange

25 minutes ago

Two perpendiculars

jayme 0

Source: Own?

Dear Mathlinkers,

1. ABC a triangle
2. 0 the circumcircle
3. D the pole of BC wrt 0
4. B', C' the symmetrics of B, C wrt AC, AB
5. 1b, 1c the circumcircles of the triangles BB'D, CC'D
6. J the center of 1b
7. V the second point of intersection of DJ and 1c.

Prove : CV is perpendicular to BC.

Sincerely
Jean-Louis

0 replies

jayme

35 minutes ago

0 replies

Probably a good lemma

Zavyk09 4

Source: found when solving exercises

Let $ABC$ be a triangle with circumcircle $\omega$ . Arbitrary points $E, F$ on $AC, AB$ respectively. Circumcircle $\Omega$ of triangle $AEF$ intersects $\omega$ at $P \ne A$ . $BE$ intersects $CF$ at $I$ . $PI$ cuts $\Omega$ and $\omega$ at $K, L$ respectively. Construct parallelogram $KFRE$ . Prove that $A, R, L$ are collinear.

4 replies

Zavyk09

Yesterday at 12:50 PM

Zavyk09

2 hours 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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114,296 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

Calculus

youochange 3

Find the area enclosed by the curves $e^x,e^{-x},x^2+y^2=1$

3 replies

youochange

May 10, 2025

c00lb0y

a minute ago

D1034 : Super TVI

Dattier 1

Source: les dattes à Dattier

Let $f \in C([0,1])$ . Is it true that $\exists a \in \left[0;\dfrac 12\right], |f(a)| \leq 8 |f(1-a)|$ ?

1 reply

Dattier

Yesterday at 10:21 PM

c00lb0y

10 minutes ago

Convergence of complex sequence

Rohit-2006 1

Suppose $z_1, z_2,\cdots,z_k$ are complex numbers with absolute value $1$ . For $n=1,2,\cdots$ define $w_n=z_1^n+z_2^n+\cdots+z_k^n$ . Given that the sequence $(w_n)_{n\geq1}$ converges. Show that,
$z_1=z_2=\cdots=z_k=1$ .

1 reply

Rohit-2006

Saturday at 7:56 PM

ohiorizzler1434

4 hours ago

hard number theory problem

danilorj 3

Let $a$ and $b$ be positive integers. Prove that
$a^2 + \left\lceil \frac{4a^2}{b} \right\rceil$ is not a perfect square.

3 replies

danilorj

Yesterday at 10:51 AM

ohiorizzler1434

4 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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18,668 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

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

Cats_on_a_computer

Yesterday at 11:43 AM

Cats_on_a_computer

an hour ago

Time travel

centslordm 19

IMAGE

19 replies

centslordm

Yesterday at 10:59 PM

Yihangzh

3 hours ago

Duplicate Gamebot

cz1917 3

The same problem of Alcumus is posted twice by Gamebot. They even have different links:
First Link
Second Link

3 replies

cz1917

5 hours ago

aiops

3 hours ago

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

asuth_asuth 1196

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.

1196 replies