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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

2000th Post!

PikaPika999 26

1. How many ways can you arrange the letters in the word ALGEBRA such that no two identical letters are adjacent?

2. Find the smallest positive integer n such that $n^2+n+41$ is not a prime number.

3. You have 4 red tiles, 3 blue tiles, and 2 green tiles. How many ways can you arrange them in a row such that no two tiles of the same color are adjacent?

4. You flip a fair coin repeatedly until you either get 3 tails or 4 heads. What is the expected number of flips before stopping?

5. Let $A(2,3)$ and $B(8,7)$ be two points in the coordinate plane. A circle is drawn such that $\overline{AB}$ is a diameter.

(a). Find the equation of the circle in the form $(x+a)^2+(y+b)^2=r^2$

(b). A line passes through the point P(6,2) and is tangent to the circle. Find the equation of this tangent line.

hopefully these problems weren't too easy lol

also,
Please tell me if any of these problems have any flaws! (also please put your answers in hide tags or quote tags)

26 replies

PikaPika999

Today at 1:53 AM

elizhang101412

2 minutes ago

Challenge: Make every number to 100 using 4 fours

CJB19 128

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

128 replies

CJB19

May 15, 2025

Shan3t

20 minutes ago

Mathcounts Nationals Written Score Hub

DhruvJha 77

Put in your estimated score on the written nats comp on Sunday after the comp so we can get a good idea of the cdr quals are

77 replies

DhruvJha

May 10, 2025

eyzMath

2 hours ago

Fun challange problem :)

TigerSenju 10

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. ;)

10 replies

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TigerSenju

Today at 1:04 AM

Pengu14

4 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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120,656 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

Ez comb proposed by ME

IEatProblemsForBreakfast 1

A and B play a game on two table:
1.At first one table got $n$ different coloured marbles on it and another one is empty
2.At each move player choose set of marbles that hadn't choose either players before and all chosen marbles from same table, and move all the marbles in that set to another table
3.Player who can not move lose
If A starts and they move alternatily who got the winning strategy?

1 reply

IEatProblemsForBreakfast

Today at 9:02 AM

n1g3r14n

34 minutes ago

geometry

luckvoltia.112 0

ChGiven an acute triangle ABC inscribed in circle $(O)$ The altitudes $BE, CF$ , intersect
each other at $H$ . The tangents at $B$ and $C$ of $(O)$ intersect at $S$ . Let $M$ be the midpoint of $BC$ . $EM$ intersects $SC$
at $I$ , $FM$ intersects $SB$ at $J.$
a) Prove that the points $I, S, M, J$ lie on the same circle.
b) The circle with diameter $AH$ intersects the circle $(O)$ at the second point $T.$ The line $AH$ intersects
$(O)$ at the second point $K$ . Prove that $S,K,T$ are collinear.

0 replies

luckvoltia.112

39 minutes ago

0 replies

Exponents of integer question

Dheckob 4

Find the smallest positive integer $m$ such that $5m$ is an exact 5th power, $6m$ is an exact 6th power, and $7m$ is an exact 7th power.

4 replies

Dheckob

Apr 12, 2017

LeYohan

an hour ago

ISI 2025

Zeroin 0

Let $\mathbb{N}$ denote the set of natural numbers and let $(a_i,b_i),1 \leq i \leq 9$ denote $9$ ordered pairs in $\mathbb{N} \times \mathbb{N}$ . Prove that there exist $3$ distinct elements in the set $2^{a_i}3^{b_i}$ for $1 \leq i \leq 9$ whose product is a perfect cube.

0 replies

Zeroin

an hour 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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34,713 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

No math to big math in 42 days

observer04 3

CAN IT BE DONE

usajmo

3 replies

observer04

Today at 1:08 AM

maxamc

2 hours ago

[TEST RELEASED] OMMC Year 5

DottedCaculator 73

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]

73 replies

+5 w

DottedCaculator

Apr 26, 2025

Ruegerbyrd

Today at 5:31 AM

Essentially, how to get good at olympiad math?

gulab_jamun 1

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!

1 reply

gulab_jamun

Today at 1:53 AM

Konigsberg

Today at 5:12 AM

9 best high school math competitions hosted by a college/university

ethan2011 16

I only included college-hosted comps since MAA comps are very differently formatted, and IMO would easily beat the rest on quality since mathematicians around the world give questions, and so many problems are shortlisted, so IMO does release the IMO shortlist for people to practice. I also did not include the not as prestigious ones(like BRUMO, CUBRMC, and others), since most comps with very high quality questions are more prestigious(I did include other if you really think those questions are really good).

16 replies

ethan2011

Apr 12, 2025

aarush.rachak11

Today at 4:23 AM

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

G, L, H are collinear

Ink68 4

Given an acute, non-isosceles triangle $ABC$ . $B, C$ lie on a moving circle $(K)$ . $(K)$ intersects $CA$ at $E$ and $BA$ at $F$ . $BE, CF$ intersect at $G$ . $KG, BC$ intersect at $D$ . $L$ is the perpendicular image of $D$ with respect to $EF$ . Prove that $G, L$ and the orthocenter $H$ are collinear.

4 replies

Ink68

Today at 2:44 AM

on_gale

5 minutes ago

A "side chase" for juniors

Lukaluce 0

Source: 2025 Junior Macedonian Mathematical Olympiad P5

Let $M$ be the midpoint of side $BC$ in $\triangle ABC$ , and $P \neq B$ is such that the quadrilateral $ABMP$ is cyclic and the circumcircle of $\triangle BPC$ is tangent to the line $AB$ . If $E$ is the second common point of the line $BP$ and the circumcircle of $\triangle ABC$ , determine the ratio $BE: BP$ .

0 replies

Lukaluce

6 minutes ago

0 replies

Self-evident inequality trick

Lukaluce 1

Source: 2025 Junior Macedonian Mathematical Olympiad P4

Let $x, y$ , and $z$ be positive real numbers, such that $x^2 + y^2 + z^2 = 3$ . Prove the inequality
$\frac{x^3}{2 + x} + \frac{y^3}{2 + y} + \frac{z^3}{2 + z} \ge 1.$ When does the equality hold?

1 reply

Lukaluce

9 minutes ago

Sadigly

6 minutes ago

Intersections and concyclic points

Lukaluce 1

Source: 2025 Junior Macedonian Mathematical Olympiad P2

Let $B_1$ be the foot of the altitude from the vertex $B$ in the acute-angled $\triangle ABC$ . Let $D$ be the midpoint of side $AB$ , and $O$ be the circumcentre of $\triangle ABC$ . Line $B_1D$ meets line $CO$ at $E$ . Prove that the points $B, C, B_1$ , and $E$ lie on a circle.

1 reply

Lukaluce

14 minutes ago

Ianis

7 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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114,294 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

Unsolving differential equation

Madunglecha 0

For parameter t
I made a differential equation :
y"=y*(x')^2
for here, '&" is derivate and second order derivate for t
could anyone tell me what is equation between y&x?

0 replies

Madunglecha

10 minutes ago

0 replies

hard number theory problem

danilorj 1

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

1 reply

danilorj

5 hours ago

Aiden-1089

2 hours ago

Expanding tan z?

ys-lg 1

How to expand $\tan z$ by residue theorem? Should by something like
$[z^n]\tan z\propto\oint _{|z|=N}\frac{\tan z}{z^{n+1}}\mathrm dz$ where $N$ tends to infty, but I'm not sure about details.

1 reply

ys-lg

Today at 6:46 AM

alexheinis

Today at 9:10 AM

2013 Japan MO Finals

parkjungmin 0

If there's anyone who's good at math

Please solve this problem

0 replies

parkjungmin

Today at 9:09 AM

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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18,663 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 5

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?

5 replies

Cats_on_a_computer

4 hours ago

MathDolphin95

14 minutes ago

My problem with AoPS account

BBNoDollar 2

Hello ! Sorry because this is not a math problem. I wanted to post an image with a math problem, but it says I can t add photos because my account is too new. I joined in 2 May 2025, so my account is more than 2 weeks old. How do I find a solution? Thanks!

2 replies

BBNoDollar

3 hours ago

SpeedCuber7

21 minutes ago

Writing Problem is Grey

Anzzz 1

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.

1 reply

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