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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

Website to learn math

hawa 104

Hi, I'm kinda curious what website do yall use to learn math, like i dont find any website thats fun to learn math

104 replies

hawa

Apr 9, 2025

valenbb

3 minutes ago

AP calc?

Thayaden 0

How are we all feeling on AP calc guys?

0 replies

Thayaden

15 minutes ago

0 replies

Fun challange problem :)

TigerSenju 15

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. ;)

15 replies

TigerSenju

May 18, 2025

K1mchi_

36 minutes ago

The daily problem!

Leeoz 182

Every day, I will try to post a new problem for you all to solve! If you want to post a daily problem, you can! :)

Please hide solutions and answers, hints are fine though! :)

Problems usually get harder throughout the week, so Sunday is the easiest and Saturday is the hardest!

Past Problems!

182 replies

Leeoz

Mar 21, 2025

CJB19

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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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

Quite straightforward

steven_zhang123 1

Given that the sequence $\left \{ a_{n} \right \}$ is an arithmetic sequence, $a_{1}=1$ , $a_{2}+a_{3}+\dots+a_{10}=144$ . Let the general term $b_{n}$ of the sequence $\left \{ b_{n} \right \}$ be $\log_{a}{(1+\frac{1}{a_{n}} )} ( a > 0 \text{and} a \ne 1)$ , and let $S_{n}$ be the sum of the $n$ terms of the sequence $\left \{ b_{n} \right \}$ . Compare the size of $S_{n}$ with $\frac{1}{3} \log_{a}{(1+\frac{1}{a_{n}} )}$ .

1 reply

steven_zhang123

Jan 11, 2025

Mathzeus1024

an hour ago

THREE People Meet at the SAME. TIME.

LilKirb 6

Three people arrive at the same place independently, at a random between $8:00$ and $9:00.$ If each person remains there for $20$ minutes, what's the probability that all three people meet each other?

I'm already familiar with the variant where there are only two people, where you Click to reveal hidden text It was an AIME problem from the 90s I believe. However, I don't know how one could visualize this in a Click to reveal hidden text Help on what to do?

6 replies

LilKirb

Yesterday at 1:06 PM

LilKirb

an hour ago

Inequalities

sqing 12

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

12 replies

sqing

May 13, 2025

sqing

an hour ago

Inequalities

sqing 0

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 $7\geq k \in N^+.$
$a^2+b^2+c^2+abc-3(a+b+c)\geq-5$

0 replies

sqing

2 hours ago

0 replies

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

Essentially, how to get good at olympiad math?

gulab_jamun 6

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!

6 replies

gulab_jamun

May 18, 2025

RupertStream

a few seconds ago

Goals for 2025-2026

Airbus320-214 153

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

153 replies

Airbus320-214

May 11, 2025

pingpongmerrily

4 minutes ago

[TEST RELEASED] OMMC Year 5

DottedCaculator 85

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]

85 replies

+1 w

DottedCaculator

Apr 26, 2025

RupertStream

11 minutes ago

Random Math?

NASA1225 8

Does anybody here go to random math? If so, what was your experience like?

8 replies

NASA1225

Feb 6, 2022

aopslover08

16 minutes 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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312,997 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

Hard Inequality

danilorj 5

Let $a, b, c > 0$ with $a + b + c = 1$ . Prove that:
$\sqrt{a + (b - c)^2} + \sqrt{b + (c - a)^2} + \sqrt{c + (a - b)^2} \geq \sqrt{3},$ with equality if and only if $a = b = c = \frac{1}{3}$ .

5 replies

danilorj

Today at 5:17 AM

danilorj

28 minutes ago

easy geo

ErTeeEs06 5

Source: BxMO 2025 P3

Let $ABC$ be a triangle with incentre $I$ and circumcircle $\Omega$ . Let $D, E, F$ be the midpoints of the arcs $\stackrel{\frown}{BC}, \stackrel{\frown}{CA}, \stackrel{\frown}{AB}$ of $\Omega$ not containing $A, B, C$ respectively. Let $D'$ be the point of $\Omega$ diametrically opposite to $D$ . Show that $I, D'$ and the midpoint $M$ of $EF$ lie on a line.

5 replies

ErTeeEs06

Apr 26, 2025

Adywastaken

31 minutes ago

Inspired by SXJX (12)2022 Q1167

sqing 4

Source: Own

Let $a,b,c>0$ . Prove that $\frac{kabc-1} {abc(a+b+c+8(2k-1))}\leq \frac{1}{16 }$ Where $k>\frac{1}{2}.$

4 replies

1 viewing

sqing

Yesterday at 4:01 AM

sqing

33 minutes ago

Geometry hard problem.

noneofyou34 3

In a circle of radius R, three chords of length R are given. Their ends are joined with segments to
obtain a hexagon inscribed in the circle. Show that the midpoints of the new chords are the vertices of
an equilateral triang

3 replies

noneofyou34

Today at 9:50 AM

noneofyou34

37 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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114,307 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

Differential equations , Matrix theory

c00lb0y 3

Source: RUDN MATH OLYMP 2024 problem 4

Any idea?? Diff equational system combined with Matrix theory.
Consider the equation dX/dt=X^2, where X(t) is an n×n matrix satisfying the condition detX=0. It is known that there are no solutions of this equation defined on a bounded interval, but there exist non-continuable solutions defined on unbounded intervals of the form (t ,+∞) and (−∞,t). Find n.

3 replies

c00lb0y

Apr 17, 2025

loup blanc

4 hours ago

The matrix in some degree is a scalar

FFA21 4

Source: MSU algebra olympiad 2025 P2

$A\in M_{3\times 3}$ invertible, for an infinite number of $k$ :
$tr(A^k)=0$
Is it true that $\exists n$ such that $A^n$ is a scalar

4 replies

FFA21

Today at 12:11 AM

FFA21

4 hours ago

Prove the statement

Butterfly 10

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 $|x_n-x_m|<\frac{C}{|n-m|}$ .

10 replies

Butterfly

May 7, 2025

oty

6 hours ago

Definite integration

girishpimoli 1

If $\displaystyle g(t)=\int^{t^{2}}_{2t}\cot^{-1}\bigg|\frac{1+x}{(1+t)^2-x}\bigg|dx.$ Then $\displaystyle \frac{g(5)}{g(3)}$ is

1 reply

girishpimoli

Apr 6, 2025

Mathzeus1024

Today at 9:34 AM

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

0 replies

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

churumbel

41 minutes ago

All Topics Marked

alpha31415 3

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???

3 replies

alpha31415

May 16, 2025

jmr2010

3 hours ago

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

Yesterday 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