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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

2000th Post!

PikaPika999 33

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 value of the 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)

33 replies

PikaPika999

Today at 1:53 AM

BlackOctopus23

24 minutes ago

Mathcounts Nationals Written Score Hub

DhruvJha 78

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

78 replies

DhruvJha

May 10, 2025

ZMB038

44 minutes ago

How to fix careless mistakes

hellohi321 0

I feel like every time I go to a contest like mathcounts or amc8 i always make stupid mistakes on very easy problems whioch makes me do bad. I don't have this problem on tests like the aime tho probably cuz i have more time. Do you all have any tips

0 replies

hellohi321

44 minutes ago

0 replies

MAP Goals

Antoinette14 28

What's yall's MAP goals for this spring?
Mine's a 300 (trying to beat my brother's record) but since I'm at a 285 rn, 290+ is more reasonable.

28 replies

Antoinette14

May 8, 2025

GallopingUnicorn45

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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120,656 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

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

2 hours 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

2 hours 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

2 hours 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

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

Docked 4 points Help

sadas123 3

In school we had this beginners like middle school contest, but we had to right down our solution kind of like usajmo except no proofs. It was also graded out of 7 but I got 4 Points docked for this question. what was my problem??? But I kind of had to rush the solution on this question because there was another problem before this that was like 1000x times harder.

Question:The solutions to the equation x^3-13x^2+ax−48=0 are all positive whole numbers. What is $a$ ?

Solution: We can see that we can use Vieta's formulas to find that the product of the roots is $48$ , and the sum of the roots is $13$ . So we need to find a combination of integers that multiply to $48$ and add up to $13$ . Let's call the roots of the equation p, q, and r. From Vieta's, we get that $p+q+r=-13$ and $pqr = -48$ . Looking at the factors of $48$ , which is $2^4*3$ , we try to split the numbers in a way that gives us the correct sum and product. Trying 3, -2, and -8, we see that they add up to $-13$ and multiply to $-48$ , so they work. That means the roots of the polynomial are -3, -2, and -8, and the factorization is $(x-3)(x-2)(x-8)$ . Multiplying it out, we get $x^3-13x^2+46x-48$ , so we find that a = 46.

3 replies

+1 w

sadas123

34 minutes ago

clarkculus

a minute ago

[CASH PRIZES] IndyINTEGIRLS Spring Math Competition

Indy_Integirls 17

[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!

17 replies

Indy_Integirls

May 11, 2025

Indy_Integirls

33 minutes ago

No math to big math in 42 days

observer04 3

CAN IT BE DONE

usajmo

3 replies

observer04

Today at 1:08 AM

maxamc

3 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

+2 w

DottedCaculator

Apr 26, 2025

Ruegerbyrd

Today at 5:31 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

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jlacosta

May 1, 2025

0 replies

Coloring is hard

liekkas 3

Source: 2019 China TST Test 3 P6

Given positive integers $d \ge 3$ , $r>2$ and $l$ , with $2d \le l <rd$ . Every vertice of the graph $G(V,E)$ is assigned to a positive integer in $\{1,2,\cdots,l\}$ , such that for any two consecutive vertices in the graph, the integers they are assigned to, respectively, have difference no less than $d$ , and no more than $l-d$ .
A proper coloring of the graph is a coloring of the vertices, such that any two consecutive vertices are not the same color. It's given that there exist a proper subset $A$ of $V$ , such that for $G$ 's any proper coloring with $r-1$ colors, and for an arbitrary color $C$ , either all numbers in color $C$ appear in $A$ , or none of the numbers in color $C$ appear in $A$ .
Show that $G$ has a proper coloring within $r-1$ colors.

3 replies

liekkas

Mar 29, 2019

sttsmet

3 minutes ago

thanks u!

Ruji2018252 0

Find all functions $f: \mathbb{R}\to \mathbb{R},f$ that are continuous on $\mathbb{R}$ satisfying
$f(x+9f(y))=4y+f(x), \forall x,y \in \mathbb{R}$

0 replies

Ruji2018252

15 minutes ago

0 replies

Hard Number Theory Problem

ZeltaQN2008 3

Source: VIMONI Test 2025

Let $n$ be a positive integer. Define $N_1$ as the number of integer pairs $(x,y)$ satisfying $x^{2}+3y^{2}=8n+4$ with $x$ odd. Define $N_2$ as the number of integer pairs $(x,y)$ satisfying $x^{2}+3y^{2}=8n+4.$
Prove that $N_{1}= \frac23\,N_{2}.$

3 replies

ZeltaQN2008

2 hours ago

ZeltaQN2008

21 minutes ago

Monic Polynomial

IstekOlympiadTeam 23

Source: Romanian Masters 2017 D1 P2

Determine all positive integers $n$ satisfying the following condition: for every monic polynomial $P$ of degree at most $n$ with integer coefficients, there exists a positive integer $k\le n$ and $k+1$ distinct integers $x_1,x_2,\cdots ,x_{k+1}$ such that $P(x_1)+P(x_2)+\cdots +P(x_k)=P(x_{k+1})$ .

Note. A polynomial is monic if the coefficient of the highest power is one.

23 replies

IstekOlympiadTeam

Feb 25, 2017

blueprimes

26 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

an hour 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

6 hours ago

Aiden-1089

3 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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18,664 topics

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jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

alcumus going crazy?

LittleSnake____ 19

all of a sudden, the alcumus forum has gotten completely exploded by gamebot's posts.

https://artofproblemsolving.com/community/c63h3570498_alcumus_going_crazy

19 replies

+2 w

LittleSnake____

Today at 5:22 AM

SpeedCuber7

4 minutes ago

Gamebot Problem

zhenghua 4

Summary of the problem: Multiple topics of the same problem are on the feed.
Page URL: Global Feed
Steps to reproduce:
1. Open the global feed
2. There are a lot of topics of the same problem.
Expected behavior: Should only be one topic.
Frequency: 100%
Operating system(s): Windows 10
Browser(s), including version: Google (don't know which version)
Additional information: None

4 replies

zhenghua

19 minutes ago

MathPerson12321

5 minutes ago

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

asuth_asuth 1184

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.

1184 replies

asuth_asuth

Mar 30, 2025

awesometriangles

22 minutes ago

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