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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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51,257 topics

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

I write today to announce my retirement as CEO from Art of Problem Solving. When I founded AoPS 22 years ago, I never imagined that we would reach so many students and families, or that we would find so many channels through which we discover, inspire, and train the great problem solvers of the next generation. I am very proud of all we have accomplished and I’m thankful for the many supporters who provided inspiration and encouragement along the way. I'm particularly grateful to all of the wonderful members of the AoPS Community!

I’m delighted to introduce our new leaders - Ben Kornell and Andrew Sutherland. Ben has extensive experience in education and edtech prior to joining AoPS as my successor as CEO, including starting like I did as a classroom teacher. He has a deep understanding of the value of our work because he’s an AoPS parent! Meanwhile, Andrew and I have common roots as founders of education companies; he launched Quizlet at age 15! His journey from founder to MIT to technology and product leader as our Chief Product Officer traces a pathway many of our students will follow in the years to come.

Thank you again for your support for Art of Problem Solving and we look forward to working with millions more wonderful problem solvers in the years to come.

And special thanks to all of the amazing AoPS team members who have helped build AoPS. We’ve come a long way from here:IMAGE

1571 replies

1 viewing

rrusczyk

Mar 24, 2025

SmartGroot

Mar 26, 2025

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
Our full course list for upcoming classes is below:
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0 replies

jlacosta

Mar 2, 2025

0 replies

mathcounts state score thread

Soupboy0 18

\begin{table}[]
$\begin{tabular}{llllll} Username & Score & Sprint & Target & Nats? & Sillies \\ Soupboy0 & 40 & 24 & 16 & yes & 6 \\ & & & & & \\ & & & & & \end{tabular}$ \end{table}

18 replies

Soupboy0

4 hours ago

snc_2022

a few seconds ago

2025 MATHCOUNTS State Hub

SirAppel 73

Previous Years' ``Hubs": (2022) (2023) (2024)

Now that it's April and we're allowed to discuss, and no one else has made this yet ...
[list=disc]
[*] CA: 43 (45 44 43 43)
[*] NJ: 43 (45 44 44 43 39 42 40 40 39 38)
[*] NY: 42 (43 42 42 42 41 40)
[*] TX: 42 (43 43 43 42 42 40 40 38 38 38)
[*] MA: 41 (45 43 42 41)
[*] WA: 41 (41 45 42 41 41 41 41 41 41 40)
[*] FL: 39 (42 41 40 39 38 37 37)
[*] IN: 39 (41 40 40 39 ?? 35)
[*] NC: 39 (42 42 41 39)
[*] PA: 38 (41 40 40 38 38 37 36 36 34 34)
[*] MD: 37 (43 39 39 37 37 37)
[*] CT: 36 (44 39 ?? 36)
[*] MN: 36 (40 36 36 36 35 35 35 34)
[*] CO: 35 (41 37 37 35 35 35 ?? 31 31 30)
[*] OH: 35 (41 37 36 35)
[*] AR: 34 (46 45 35 34 33 31 31 31 29 29)
[*] DE: 30 (34 33 32 30 30 29 28 27 26? 24)
[*] RI*
Cutoff estimated to be 29
: ?? (36 ?? ?? ??)
[*] NE: 28 (34 30 28 28 27 27 26 26 25 25)
[*] SD: 22 (30 29 24 22 22 22 21 21 20 20)
[/list]

Notes
Potential tier changes (opinions)

Help contribute by sharing your state's cutoffs!
As per last year's guidelines, refrain from problem discussion until their official release on the MATHCOUNTS website.

73 replies

+2 w

SirAppel

Today at 12:22 PM

BS2012

5 minutes ago

MATHCOUNTS Chapter Score Thread

apex304 111

$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline apex304 & 8 & 46 \\ \end{tabular}$

111 replies

apex304

Mar 1, 2025

nmlikesmath

6 minutes ago

9 Have you taken the AMC 10 test before?

aadimathgenius9 98

Have you taken the AMC 10 test before?

98 replies

aadimathgenius9

Jan 5, 2025

nmlikesmath

11 minutes 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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120,242 topics

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

1 viewing

rrusczyk

Mar 24, 2025

SmartGroot

Mar 26, 2025

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

Geo Mock #3

Bluesoul 1

Consider square $ABCD$ with side length of $5$ . The point $P$ is selected on the diagonal $AC$ such that $\angle{BPD}=135^{\circ}$ . Denote the circumcenters of $\triangle{BPA}, \triangle{APD}$ as $O_1,O_2$ . Find the length of $O_1O_2$

1 reply

Bluesoul

Today at 7:02 AM

Sedro

2 hours ago

Complex + Radical Evaluation

Saucepan_man02 3

Evaluate: (without calculators)
$(\sqrt{6 - 2 \sqrt{5}} + i \sqrt{2 \sqrt{5} + 10})^5 + (\sqrt{6 - 2 \sqrt{5}} - i \sqrt{2 \sqrt{5} + 10})^5$

3 replies

Saucepan_man02

Mar 17, 2025

SmartHusky

3 hours ago

Geo Mock #2

Bluesoul 1

Consider convex quadrilateral $ABCD$ such that $AB=6, BC=10, \angle{ABC}=90^{\circ}$ . Denote the midpoints of $AD,CD$ as $M,N$ respectively, compute the area of $\triangle{BMN}$ given the area of $ABCD$ is $50$ .

1 reply

Bluesoul

Today at 6:59 AM

Sedro

3 hours ago

Geo Mock #1

Bluesoul 1

Consider the rectangle $ABCD$ with $AB=4$ . Point $E$ lies inside the rectangle such that $\triangle{ABE}$ is equilateral. Given that $C,E$ and the midpoint of $AD$ are on the same line, compute the length of $BC$ .

1 reply

Bluesoul

Today at 6:58 AM

Sedro

3 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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34,588 topics

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

1 viewing

rrusczyk

Mar 24, 2025

SmartGroot

Mar 26, 2025

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

USAMO Scores Release Date

CrunchyCucumber 0

Does anyone know when individual scores, and medal+MOP cutoffs on the USAMO will be officially released? The website says 2-3 weeks, but I’ve heard it takes much longer in previous year.

0 replies

CrunchyCucumber

an hour ago

0 replies

Berkeley mini Math Tournament Solutions Released

BerkeleyMathTournament 5

BmMT Solutions Leaked :oops_sign: https://berkeley.mt/relaysolutions

5 replies

BerkeleyMathTournament

3 hours ago

fake123

an hour ago

CMIMC 2025

Allen31415 4

Hi everyone,

CMIMC's annual math competition will take place on March 15, 2025. Registration is now open, and there is no registration fee, so make sure to sign up! Please see the flyer below for details. Email us at cmimc.info@gmail.com, or put any questions in this thread.

4 replies

Allen31415

Nov 21, 2024

vincentwant

an hour ago

Square Root Equality

djmathman 67

Source: 2013 USAJMO #6/USAMO #4

Find all real numbers $x,y,z\geq 1$ satisfying $\min(\sqrt{x+xyz},\sqrt{y+xyz},\sqrt{z+xyz})=\sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}.$

67 replies

djmathman

May 1, 2013

vincentwant

4 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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311,457 topics

14 users

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

1 viewing

rrusczyk

Mar 24, 2025

SmartGroot

Mar 26, 2025

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

Is this FE solvable?

Mathdreams 0

Find all $f:\mathbb{R} \rightarrow \mathbb{R}$ such that $f(2x+y) + f(x+f(2y)) = f(x)f(y) - xy$ for all reals $x$ and $y$ .

0 replies

Mathdreams

19 minutes ago

0 replies

OFM2021 Senior P1

medhimdi 0

Let $a_1, a_2, a_3, \dots$ and $b_1, b_2, b_3, \dots$ be two sequences of integers such that $a_{n+2}=a_{n+1}+a_n$ and $b_{n+2}=b_{n+1}+b_n$ for all $n\geq1$ . Suppose that $a_n$ divides $b_n$ for an infinity of integers $n\geq1$ . Prove that there exist an integer $c$ such that $b_n=ca_n$ for all $n\geq1$

0 replies

medhimdi

26 minutes ago

0 replies

Hard NT problem

tiendat004 2

Given two odd positive integers $a,b$ are coprime. Consider the sequence $(x_n)$ given by $x_0=2,x_1=a,x_{n+2}=ax_{n+1}+bx_n,$ $\forall n\geq 0$ . Suppose that there exist positive integers $m,n,p$ such that $mnp$ is even and $\dfrac{x_m}{x_nx_p}$ is an integer. Prove that the numerator in its simplest form of $\dfrac{m}{np}$ is an odd integer greater than $1$ .

2 replies

tiendat004

Aug 15, 2024

avinashp

40 minutes ago

disjoint subsets

nayel 2

Source: Taiwan 2001

Let $n\ge 3$ be an integer and let $A_{1}, A_{2},\dots, A_{n}$ be $n$ distinct subsets of $S=\{1, 2,\dots, n\}$ . Show that there exists $x\in S$ such that the n subsets $A_{i}-\{x\}, i=1,2,\dots n$ are also disjoint.

what i have is this

2 replies

nayel

Apr 18, 2007

alexanderhamilton124

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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114,030 topics

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

1 viewing

rrusczyk

Mar 24, 2025

SmartGroot

Mar 26, 2025

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

Range of solutions to the log equation

obihs 0

Source: Own

Let $n$ be a positive integer, and consider the equation:
$(\log x)^n - x + 1 = 0\quad\cdots(\heartsuit)$ Answer the following questions. You may assume that $2.7<e<2.72$ is known.

$(1)\quad$ Determine the number of real solutions of equation $(\heartsuit)$ for each $n$ .

$(2)\quad$ For $n\ge 3$ , let $r_n$ be the segond largest real solution of $(\heartsuit)$ .

$(\i)\quad$ Find $\alpha$ such that $\lim_{n\to\infty} r_n =\alpha.$

$(\i\i)\quad$ Find $\lfloor\beta\rfloor$ , where $\beta$ is defined as

$\lim_{n\to\infty}n(r_n-\alpha)=\beta.$

0 replies

obihs

an hour ago

0 replies

Strange limit

Snoop76 4

Find: $\lim_{n \to \infty} n\cdot\sum_{k=1}^n \frac 1 {k(n-k)!}$

4 replies

Snoop76

Mar 29, 2025

Svyatoslav

3 hours ago

Improper integrahl manipulation

MetaphysicalWukong 1

Given the image, find out with justification if the following integrals converge or are uncertain to converge:
$\int _1^{\infty }\:\frac{h\left(x\right)}{x}dx,\:\int _1^{\infty \:}\:\sqrt{h\left(x\right)}dx,\:\int _1^{\infty \:}\:h\left(x^2\right)dx$

1 reply

MetaphysicalWukong

Today at 7:09 AM

HacheB2031

3 hours ago

n->inf, f(n)->0

Alidq 2

I have a sequence $a_n=\sqrt[n]{f(n)} , n \geq 2$ where $f$ is a bijection from $\{0,1,2,….,n\}$ to itself.I need to find the limit of this sequence when $n$ tends to infinity , in the solution my friend gave to me he said that it’s trivial that the limit is greater or equal than 1 can someone tell me why?

2 replies

Alidq

4 hours ago

Alidq

3 hours ago

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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18,574 topics

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

1 viewing

rrusczyk

Mar 24, 2025

SmartGroot

Mar 26, 2025

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

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

asuth_asuth 341

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.

341 replies

asuth_asuth

Sunday at 8:18 PM

RedChameleon

3 minutes ago

9 Math Jam

RedChameleon 1

[quote=MrMustache]Voting yes means that you want Mr. Rusczyk, in celebration of his retirement, to run one last Math Jam.[/quote]

1 reply

RedChameleon

2 hours ago

MrMustache

2 hours ago

Reaper bug

AmberTiger79 8

So, i went to the reaper page, and it is saying that i was the least person to reap, but i never reaped. Is this supposed to happen?

8 replies

AmberTiger79

6 hours ago

RedChameleon

2 hours ago

Happy April Fools!

jkim0656 41

Happy April Fools day everyone!
U can post below what tricks u guys are gonna play one each other :)
*grins mischevious grin

41 replies

jkim0656

Today at 4:32 AM

RedChameleon

2 hours ago

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General questions addressed to the community - for questions/comments that don't fit elsewhere.

LLG CA- OMG SILLY VANIl- THE RABBIT WILL FIND YOU
Here, you can roleplay a character in the setting of Camp Half-Blood! April fools, you actually can’t. Do not roble play here, it’s illegal unless you’re an admin. #adminabuse

Old High School Olympiads
Regional, National, and International Math Olympiads before 2001 mostly, recent years have been posted in order to make contest collections richer

The Campfire
Where you can hang with others, play games, advertise, and more!

Boredom Buster‎!
Isn't it obvious? We bust your boredom!

Demigod's Corner
This is a PJO fan forum. We have: A quest system, a storyline, RPGs, games, discussions, and you can RP as whoever youwant! A satyr, vampire, demigod, wheoever!

Swim Hub
For Swimmers Out There

The Fox Forum
Forum about foxes!

CMIMC
Forum for the Carnegie Mellon Informatics and Mathematics Competition, a math/CS contest held in Pittsburgh.

Old Russian Math Olympiads
All Russian, Moscow, Tournament of Towns,...

The Mango Cult
A fun interactive forum with games, shops, chats, and more!

Harker Math Invitational
The official AoPS forum for the Diana Nichols Harker Math Invitational

The Dog Lovers Forum!
Hi! Ever had a dog, wanted one, or wanted to experience the life of a puppy? You came to the right place! Here, you can express your love for dogs...FREELY! We have games, RPGs, and talks from expert dog owners who have lots of experience!

The Clan Gathering
Live an adventurous wild cat life in The Clan Gathering!

The Hub!!!
Welcome to The Hub, your all-in-one community hub! We have games, an advertisement thread, and much more. Come join us!

Kids just wanna have fun
We mostly RP, but there are a lot of other fun games.

Doggy Forum
Come play doggy games :)

The Cat Lovers Forum!
A forum for all cat lovers!

THE ALTERNATE BLAME MORON
Play games and have fun!

。:+* K-POP WORLD *+:。
If you love K-Pop, come and join this fun forum! Create your own group, and idol!

The Incredible Forum
Welcome to the game forum!

The Cooking & Baking Forum
Like cooking and/or baking? This forum is the right place for you! Join us for a tasty treat!

Cobble's Wolf Pack
This is Cobble918's RPG game. Live a life of a wild wolf!

India
For users from India and discussions related to India

FTW/Reaper/GC General Discussion
Use this forum for general discussion, tournament creation, etc.

Team Noodles and Fantastic Beasts forum!
Gaming, Harry Potter role-play, and discussion forum! Join the NOODLE community today!

Epic fun forum
Epic games and fun here join today!

The Lost Cities!
Keeper of The Lost Cities roleplay and games!

A Galaxy Far Far away
Epic games and RPG from the Star Wars galaxy

Special Collections Collections of forums, tags, topics, and posts from the AoPS community.

Collections of forums, tags, topics, and posts from the AoPS community.

VNew Topic kLocked

Nothing matches your input.

Special Collections Collections of forums, tags, topics, and posts from the AoPS community.

Collections of forums, tags, topics, and posts from the AoPS community.

VNew Topic kLocked

Nothing matches your input.

Collections of forums, tags, topics, and posts from the AoPS community.

Games Forums
FTW, Mafia, video games, etc.

Sciences
Chemistry, physics, biology, and other sciences.

AoPS Olympiad & College Portal
Customized for Olympiad & College students

Other Interests
Current events, music, arts, etc.

Contest Forums
Forums for specific contests

Summer Program Forums
Forums for specific summer programs

Olympiad Classic View
High School Olympiads in the old AoPS style

College Classic View
College Math in the old AoPS style

Communities Around the World
Local and National Communities around the World

New Forums
Public forums created in the last month

Other Collections
User-created collections.

New Collections
New user-created collections.

After High School
Discussions about college and careers

Publications
Forums for specific books and journals

Statistics:

Total posts: 24,685,503 | Total topics: 1,888,043 | Total members: 1,168,749