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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

Vol 1 enough?

Spacepandamath13 18

is aops vol 1 book enough for amc10 or is vol 2 required to be studied too?

18 replies

Spacepandamath13

Today at 1:07 AM

A7456321

5 minutes ago

INTERSTING

teomihai 24

IF $1=3$
$2=3$

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

24 replies

teomihai

Today at 7:34 AM

pieMax2713

5 minutes ago

cant understand so dumb

greenplanet2050 13

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

13 replies

greenplanet2050

May 18, 2025

CJB19

2 hours ago

Fun challange problem :)

TigerSenju 25

Scenario:

Master Alchemist Aurelius is renowned for his mastery of elemental fusion. He works with seven fundamental, yet mysterious, elements: Ignis (Fire), Aqua (Water), Terra (Earth), Aer (Air), Lux (Light), Umbra (Shadow), and Aether (Spirit). Each element possesses a unique 'potency' value, a positive integer crucial for his most complex fusions

Aurelius has lost his master log of these potencies. All he has left are seven cryptic scrolls, each containing a precise relationship between the potencies of various elements. He needs these values to complete his Grand Device. Can you help him deduce the exact potency of each element?

The Elements and Their Potencies:

Let I represent the potency of Ignis (Fire).
Let A represent the potency of Aqua (Water).
Let T represent the potency of Terra (Earth).
Let R represent the potency of Aer (Air).
Let L represent the potency of Lux (Light).
Let U represent the potency of Umbra (Shadow).
Let E represent the potency of Aether (Spirit).
The Cryptic Scrolls (System of Equations):

Aurelius's scrolls reveal the following relationships:

The combined potency of Ignis, Aqua, and Terra is equal to the potency of Aer plus Lux, plus a constant of two.

If you sum the potencies of Aqua and Umbra, it precisely equals the sum of Lux and Aether, minus one.

The sum of Terra and Aer potencies is the same as the sum of Ignis, Aqua, and Aether potencies, minus one.

Three times the potency of Ignis, plus the potency of Aer, is equal to the sum of Aqua, Terra, and Aether potencies, plus five.

The difference between Lux and Ignis potencies is identical to the difference between Umbra and Aqua potencies.

The sum of Umbra and Aether potencies, when decreased by the potency of Terra, results in twice the potency of Aqua.

The potency of Ignis added to Lux, minus the potency of Aer, is equivalent to the potency of Aether minus Umbra, plus one.

The Grand Challenge:

Using only the information from the cryptic scrolls, set up and solve the system of seven linear equations to determine the unique positive integer potency value for each of the seven elements: I,A,T,R,L,U,E.

good luck, and whoever finds the potencies first, gets a title of The SYSTEMS OF EQUATIONS MASTER

p.s. Yes, I did just come up with a whole story of words to make a ridiculously long problem, but hey, you're reading this, so you probably have nothing better to be doing. ;)

25 replies

TigerSenju

May 18, 2025

melloncandy

3 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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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

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jlacosta

May 1, 2025

0 replies

Vieta's Relations

P162008 7

If $\alpha,\beta$ and $\gamma$ are the roots of the cubic equation $x^3 - x^2 + 2x - 3 = 0.$
Evaluate $\sum_{cyc} \frac{\alpha^3 - 3}{\alpha^2 - 2}$
Is there any alternate approach except just bash

7 replies

P162008

an hour ago

alexheinis

15 minutes ago

Inequalities

sqing 4

Let $a,b,c\geq 0 ,a+b+c\leq 3.$ Prove that
$a^2+b^2+c^2+ab +2ca+2bc + abc \leq \frac{251}{27}$ $a^2+b^2+c^2+ab+2ca+2bc + \frac{2}{5}abc \leq \frac{4861}{540}$ $a^2+b^2+c^2+ab+2ca+2bc + \frac{7}{20}abc \leq \frac{2381411}{26460}$

4 replies

sqing

Today at 12:47 PM

ytChen

43 minutes ago

BMT Algebra #6 - Sum with Combinations

asbodke 2

Given that $\tbinom{n}{k}=\tfrac{n!}{k!(n-k)!}$ , the value of $\sum_{n=3}^{10}\frac{\binom{n}{2}}{\binom{n}{3}\binom{n+1}{3}}$ can be written in the form $\tfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Compute $m+n$ .

2 replies

1 viewing

asbodke

Oct 11, 2020

P162008

2 hours ago

the roots of ax^2+bx+c=0

zolfmark 2

the roots of ax^2+bx+c=0
3sinx+4cosy، 4cosx+3siny
find -b/a

2 replies

zolfmark

Oct 4, 2023

BlackOctopus23

2 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

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jlacosta

May 1, 2025

0 replies

Jane street swag package? USA(J)MO

arfekete 44

Hey! People are starting to get their swag packages from Jane Street for qualifying for USA(J)MO, and after some initial discussion on what we got, people are getting different things. Out of curiosity, I was wondering how they decide who gets what.
Please enter the following info:

- USAMO or USAJMO
- Grade
- Score
- Award/Medal/HM
- MOP (yes or no, if yes then color)
- List of items you got in your package

I will reply with my info as an example.

44 replies

arfekete

May 7, 2025

pieMax2713

4 minutes ago

for the contest high achievers, can you share your math path?

HCM2001 10

Hi all
Just wondering if any orz or high scorers on contests at young age (which are a lot of u guys lol) can share what your math path has been like?
- school math: you probably finish calculus in 5th grade or something lol then what do you do for the rest of the school? concurrent enrollment? college class? none (focus on math competitions)?
- what grade did you get honor roll or higher on AMC 8, AMC 10, AIME qual, USAJMO qual, etc?
- besides aops do you use another program to study? (like Mr Math, Alphastar, etc)?

You're all great inspirations and i appreciate the answers.. you all give me a lot of motivation for this math journey. Thanks

10 replies

HCM2001

3 hours ago

A7456321

5 minutes ago

9 Did I make the right choice?

Martin2001 41

If you were in 8th grade, would you rather go to MOP or mc nats? I chose to study the former more and got in so was wondering if that was valid given that I'll never make mc nats.

41 replies

Martin2001

Apr 29, 2025

GallopingUnicorn45

9 minutes ago

[TEST RELEASED] OMMC Year 5

DottedCaculator 102

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]

102 replies

1 viewing

DottedCaculator

Apr 26, 2025

Pengu14

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

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jlacosta

May 1, 2025

0 replies

points on sides of a triangle, intersections, extensions, ratio of areas wanted

parmenides51 2

Source: Mexican Mathematical Olympiad 1997 OMM P5

Let $P,Q,R$ be points on the sides $BC,CA,AB$ respectively of a triangle $ABC$ . Suppose that $BQ$ and $CR$ meet at $A', AP$ and $CR$ meet at $B'$ , and $AP$ and $BQ$ meet at $C'$ , such that $AB' = B'C', BC' =C'A'$ , and $CA'= A'B'$ . Compute the ratio of the area of $\triangle PQR$ to the area of $\triangle ABC$ .

2 replies

parmenides51

Jul 28, 2018

MathIQ.

12 minutes ago

integer functional equation

ABCDE 156

Source: 2015 IMO Shortlist A2

Determine all functions $f:\mathbb{Z}\rightarrow\mathbb{Z}$ with the property that $f(x-f(y))=f(f(x))-f(y)-1$ holds for all $x,y\in\mathbb{Z}$ .

156 replies

ABCDE

Jul 7, 2016

MathIQ.

26 minutes ago

Three numbers cannot be squares simultaneously

WakeUp 38

Source: APMO 2011

Let $a,b,c$ be positive integers. Prove that it is impossible to have all of the three numbers $a^2+b+c,b^2+c+a,c^2+a+b$ to be perfect squares.

38 replies

WakeUp

May 18, 2011

SomeonecoolLovesMaths

29 minutes ago

Primes and sets

mathisreaI 40

Source: IMO 2022 Problem 3

Let $k$ be a positive integer and let $S$ be a finite set of odd prime numbers. Prove that there is at most one way (up to rotation and reflection) to place the elements of $S$ around the circle such that the product of any two neighbors is of the form $x^2+x+k$ for some positive integer $x$ .

40 replies

mathisreaI

Jul 13, 2022

Tinoba-is-emotional

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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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

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jlacosta

May 1, 2025

0 replies

IMC 2018 P4

ThE-dArK-lOrD 18

Source: IMC 2018 P4

Find all differentiable functions $f:(0,\infty) \to \mathbb{R}$ such that
$f(b)-f(a)=(b-a)f’(\sqrt{ab}) \qquad \text{for all}\qquad a,b>0.$
Proposed by Orif Ibrogimov, National University of Uzbekistan

18 replies

ThE-dArK-lOrD

Jul 24, 2018

jonh_malkovich

2 hours ago

a^2=3a+2imatrix 2*2

zolfmark 3

A
matrix 2*2

A^2=3A+2i
A^3=mA+Li

i means identity matrix,

find constant m ، L

3 replies

zolfmark

Feb 23, 2019

Mathzeus1024

Today at 2:00 PM

polynomial having a simple root

FFA21 1

Source: MSU algebra olympiad 2025 P4

$f(x)\in R[x]$ show that $f(x)+i$ has at least one root of multiplicity one

1 reply

FFA21

Yesterday at 12:22 AM

Doru2718

Today at 1:59 PM

non-solvable group has subgroup that is not isomorphic to any normal subgroup

FFA21 1

Source: MSU algebra olympiad 2025 P7

Show that in every finite non-solvable group there is a subgroup that is not isomorphic to any normal subgroup

1 reply

FFA21

Yesterday at 12:29 AM

Doru2718

Today at 1:45 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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18,666 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

k Writing Problem is Grey

Anzzz 2

In the writing problem in a Self - Paced class, I submitted it, and got graded. However, the writing problem icon remains grey, like it wasn't graded yet. I tried refreshing it multiple times, but it doesn't change. This doesn't really change anything, but I keep feeling like I haven't done it when I review my progress.

PS: This has not happened before.

2 replies

Anzzz

May 18, 2025

jlacosta

3 hours ago

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

asuth_asuth 1251

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.

1251 replies

asuth_asuth

Mar 30, 2025

PikaPika999

Today at 12:34 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