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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

Fun challange problem :)

TigerSenju 21

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. ;)

21 replies

TigerSenju

May 18, 2025

LXC007

34 minutes ago

Vol 1 enough?

Spacepandamath13 6

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

6 replies

Spacepandamath13

an hour ago

GallopingUnicorn45

40 minutes ago

AP calc?

Thayaden 13

How are we all feeling on AP calc guys?

13 replies

Thayaden

Yesterday at 3:48 PM

RandomMathGuy500

an hour ago

Bogus Proof Marathon

pifinity 7633

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!

7633 replies

pifinity

Mar 12, 2018

Cerberusman

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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120,674 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

Polynomial Minimization

ReticulatedPython 4

Consider the polynomial $p(x)=x^{n+1}-x^{n}$ , where $x, n \in \mathbb{R+}.$

(a) Prove that the minimum value of $p(x)$ always occurs at $x=\frac{n}{n+1}.$

4 replies

ReticulatedPython

May 6, 2025

jasperE3

44 minutes ago

Trig Identity

gauss202 2

Simplify $\dfrac{1-\cos \theta + \sin \theta}{\sqrt{1 - \cos \theta + \sin \theta - \sin \theta \cos \theta}}$

2 replies

gauss202

May 14, 2025

MathIQ.

an hour ago

2018 Mock ARML I --7 2^n | \prod^{2048}_{k=0} C(2k , k)

parmenides51 3

Find the largest integer $n$ such that $2^n$ divides $\prod^{2048}_{k=0} {2k \choose k}$ .

3 replies

parmenides51

Jan 17, 2024

MathIQ.

an hour ago

f(2x+y)=f(x+2y)

jasperE3 3

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

3 replies

jasperE3

5 hours ago

MathIQ.

an hour 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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34,722 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

OTIS or MathWOOT 2

math_on_top 12

Hey AoPS community I took MathWOOT 1 this year and scored an 8 on AIME (last year I got a 6). My goal is to make it to MOP next year through USAMO. It's gonna be a lot of work, but do you think that I should do MathWOOT 2 or OTIS? Personally, I felt that MathWOOT 1 taught me a lot but was more focused on computational - not sure how to split computation vs olympiad prep. So, for those who can address this question:

(1) How much compuational vs olympiad
(2) OTIS or MathWOOT 2 and why

12 replies

+1 w

math_on_top

May 18, 2025

N3bula

33 minutes ago

Essentially, how to get good at olympiad math?

gulab_jamun 9

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!

9 replies

gulab_jamun

May 18, 2025

N3bula

35 minutes ago

[TEST RELEASED] OMMC Year 5

DottedCaculator 96

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]

96 replies

1 viewing

DottedCaculator

Apr 26, 2025

mickeymouse7133

2 hours ago

looks like roots of unity filter!

math31415926535 37

Source: 2022 AIME II Problem 13

There is a polynomial $P(x)$ with integer coefficients such that $P(x)=\frac{(x^{2310}-1)^6}{(x^{105}-1)(x^{70}-1)(x^{42}-1)(x^{30}-1)}$ holds for every $0<x<1.$ Find the coefficient of $x^{2022}$ in $P(x)$

37 replies

math31415926535

Feb 17, 2022

xHypotenuse

5 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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313,004 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

An important lemma of isogonal conjugate points

buratinogigle 6

Source: Own

Let $P$ and $Q$ be two isogonal conjugate with respect to triangle $ABC$ . Let $S$ and $T$ be two points lying on the circle $(PBC)$ such that $PS$ and $PT$ are perpendicular and parallel to bisector of $\angle BAC$ , respectively. Prove that $QS$ and $QT$ bisect two arcs $BC$ containing $A$ and not containing $A$ , respectively, of $(ABC)$ .

6 replies

buratinogigle

Mar 23, 2025

buratinogigle

an hour ago

A difficult problem [tangent circles in right triangles]

ThAzN1 48

Source: IMO ShortList 1998, geometry problem 8; Yugoslav TST 1999

Let $ABC$ be a triangle such that $\angle A=90^{\circ }$ and $\angle B<\angle C$ . The tangent at $A$ to the circumcircle $\omega$ of triangle $ABC$ meets the line $BC$ at $D$ . Let $E$ be the reflection of $A$ in the line $BC$ , let $X$ be the foot of the perpendicular from $A$ to $BE$ , and let $Y$ be the midpoint of the segment $AX$ . Let the line $BY$ intersect the circle $\omega$ again at $Z$ .

Prove that the line $BD$ is tangent to the circumcircle of triangle $ADZ$ .

comment

48 replies

ThAzN1

Oct 17, 2004

Autistic_Turk

an hour ago

IMO 2008, Question 2

delegat 63

Source: IMO Shortlist 2008, A2

(a) Prove that
$\frac {x^{2}}{\left(x - 1\right)^{2}} + \frac {y^{2}}{\left(y - 1\right)^{2}} + \frac {z^{2}}{\left(z - 1\right)^{2}} \geq 1$ for all real numbers $x$ , $y$ , $z$ , each different from $1$ , and satisfying $xyz=1$ .

(b) Prove that equality holds above for infinitely many triples of rational numbers $x$ , $y$ , $z$ , each different from $1$ , and satisfying $xyz=1$ .

Author: Walther Janous, Austria

63 replies

+1 w

delegat

Jul 16, 2008

ezpotd

an hour ago

USAMO 2003 Problem 1

MithsApprentice 69

Prove that for every positive integer $n$ there exists an $n$ -digit number divisible by $5^n$ all of whose digits are odd.

69 replies

MithsApprentice

Sep 27, 2005

de-Kirschbaum

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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114,308 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

Definite integration

girishpimoli 2

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

2 replies

girishpimoli

Apr 6, 2025

Amkan2022

2 hours ago

Putnam 1968 A6

sqrtX 11

Source: Putnam 1968

Find all polynomials whose coefficients are all $\pm1$ and whose roots are all real.

11 replies

sqrtX

Feb 19, 2022

ohiorizzler1434

2 hours ago

Affine variety

YamoSky 1

Let $A=\left\{z\in\mathbb{C}|Im(z)\geq0\right\}$ . Is it possible to equip $A$ with a finitely generated k-algebra with one generator such that make $A$ be an affine variety?

1 reply

YamoSky

Jan 9, 2020

amplreneo

5 hours ago

Reducing the exponents for good

RobertRogo 0

Source: The national Algebra contest (Romania), 2025, Problem 3/Abstract Algebra (a bit generalized)

Let $A$ be a ring with unity such that for every $x \in A$ there exist $t_x, n_x \in \mathbb{N}^*$ such that $x^{t_x+n_x}=x^{n_x}$ . Prove that
a) If $t_x \cdot 1 \in U(A), \forall x \in A$ then $x^{t_x+1}=x, \forall x \in A$
b) If there is an $x \in A$ such that $t_x \cdot 1 \notin U(A)$ then the result from a) may no longer hold.

Authors: Laurențiu Panaitopol, Dorel Miheț, Mihai Opincariu, me, Filip Munteanu

0 replies

RobertRogo

Yesterday at 6:38 PM

0 replies

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

GallopingUnicorn45

an hour ago

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

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

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