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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 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

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:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies

jlacosta

Mar 2, 2025

0 replies

Some Important Problems in Mathematics

fossasor 10

1
2
3
4
5
6
7

10 replies

fossasor

an hour ago

jkim0656

19 minutes ago

9 Have you participated in the MATHCOUNTS competition?

aadimathgenius9 17

Have you participated in the MATHCOUNTS competition before?

17 replies

aadimathgenius9

Jan 1, 2025

jkim0656

39 minutes ago

exponents

Arvind_sn 40

What is the highest possible $e$ in $2^{e}<200$ ?

40 replies

Arvind_sn

Jul 12, 2006

jkim0656

44 minutes ago

How to see the light

Dream9 23

My subject is pretty weird but what I mean is the "light" at the end of the "tunnel" (the end of a very long post). For example, the Bogus Proof Marathon. It has like 7k replies and I really can't scroll down 7000 messages so, how do people reach the end of the reply chain? :yoda:

23 replies

Dream9

Mar 28, 2025

jkim0656

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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120,227 topics

3 users

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Last Poster

k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

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

Three 3-digit numbers

miiirz30 3

Leonard wrote three 3-digit numbers on the board whose sum is $1000$ . All of the nine digits are different. Determine which digit does not appear on the board.

Proposed by Giorgi Arabidze, Georgia

3 replies

miiirz30

Yesterday at 5:38 PM

henryli3333

44 minutes ago

what is tangent line at?

Miranda2829 3

I watched is video shows the tangent line is extended on the right side and cotangent is on the left side ,

as far as i know tangent line definition is
tangent line intersects a circle exactly one point

so in this diagram why on the right side is tangent, but on the left side is the cotangent?

thanks

3 replies

Miranda2829

Mar 28, 2025

ohiorizzler1434

an hour ago

An inequality

JK1603JK 2

Let a,b,c\ge 0: a+b+c>0 then prove \frac{a^{2}-bc}{3a+b+c}+\frac{b^{2}-ca}{3b+c+a}+\frac{c^{2}-ab}{3c+a+b}\ge 0

2 replies

JK1603JK

Yesterday at 1:47 PM

lbh_qys

2 hours ago

ordered primes (p,q)

SomeonecoolLovesMaths 5

Find all possible ordered pairs $(p,q)$ where $p$ and $q$ are primes such that $p^3 - q^3 = pq^3 - 1$ .

5 replies

SomeonecoolLovesMaths

Mar 7, 2024

mathprodigy2011

4 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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34,585 topics

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

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

[March 2025] MEX MAGAZINE

Possible 1

Hello AoPS!

MathEXplained MAGAZINE aims to be a monthly newsletter that publishes articles in a newspaper-style format about various math related subjects in a way which can appeal to a broader audience. Topics may range from trending news stories within the math community to in-depth dissections of niche and interesting mathematical topics for more advanced readers.

Our Goal

While many of us on this platform might feel as if math is something super familiar to us, the truth is that this isn't the case outside of our tightly-knit community. Math doesn't get much coverage in mainstream media due to it being wrongfully seen by the general population either as a nerd's hobby or extremely foreign to the average person. Our mission as an organization is to promote mathematics through recognizing top mathletes, covering interesting math topics, and painting mathematics as something which can be fun and easy to get into.

March 2025 Edition

Celebrate the month of $\pi$ with MEX MAGAZINE's new publication! Check out this google drive file to solve some $\pi$ related math problems! Make sure to also read about our other spreads which cover Buffon's needle problem, the mathematics behind chess, and the history of $\pi$ day!

Website

If you are interested in reading our past issues, you can check out our website at this link. Over there, you can find links to our discord community where problem discussions can happen.

Staff

Our program is currently looking for new staff members! Please fill out this form to be considered.

1 reply

Possible

7 minutes ago

Possible

6 minutes ago

Mop Qual stuff

HopefullyMcNats2025 65

How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard

65 replies

2 viewing

HopefullyMcNats2025

Sunday at 11:23 PM

DoughTruth

16 minutes ago

Nerfed 2023 JMO 1

brainfertilzer 29

Source: 2024 AIME II P11

Find the number of triples of nonnegative integers $(a,b,c)$ satisfying $a + b + c = 300$ and
$a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6{,}000{,}000.$

29 replies

2 viewing

brainfertilzer

Feb 8, 2024

Math-Lego

25 minutes ago

The 2nd geometry problem is #20

Frestho 59

Source: 2020 AMC 10A #20 / 2020 AMC 12A #18

Quadrilateral $ABCD$ satisfies $\angle ABC = \angle ACD = 90^{\circ}, AC = 20$ , and $CD = 30$ . Diagonals $\overline{AC}$ and $\overline{BD}$ intersect at point $E$ , and $AE = 5$ . What is the area of quadrilateral $ABCD$ ?

$\textbf{(A) } 330 \qquad\textbf{(B) } 340 \qquad\textbf{(C) } 350 \qquad\textbf{(D) } 360 \qquad\textbf{(E) } 370$

59 replies

Frestho

Jan 31, 2020

megahertz13

38 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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311,436 topics

14 users

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

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

On Solving G7s

HoRI_DA_GRe8 2

Source: Reunbarg

I'd like to point out that Dr Miroslav Schweinsteiger has published a 57 page long handout regarding the use of Cartesian Coordinates in solving a couple of G7's.

A pre insight to solving basic config geo is required along with an intuition for Cartesian co ordinates.Also the knowledge of calculus is necessary.He mailed me yesterday telling that he cannot open his aops account so I did the job for him.

Enjoy folks.

2 replies

+1 w

HoRI_DA_GRe8

3 minutes ago

ohiorizzler1434

a few seconds ago

NMO (Nepal) Problem 3

khan.academy 12

Let $ABC$ be an acute triangle and $H$ be its orthocenter. Let $E$ be the foot of the altitude from $C$ to $AB$ , $F$ be the foot of the altitude from $B$ to $AC$ . Let $G \neq H$ be the intersection of the circles $(AEF)$ and $(BHC)$ . Prove that $AG$ bisects $BC$ .

Proposed by Kang Taeyoung, South Korea

12 replies

khan.academy

Mar 17, 2024

Tony_stark0094

11 minutes ago

GEOMETRY GEOMETRY GEOMETRY

Kagebaka 71

Source: IMO 2021/3

Let $D$ be an interior point of the acute triangle $ABC$ with $AB > AC$ so that $\angle DAB = \angle CAD.$ The point $E$ on the segment $AC$ satisfies $\angle ADE =\angle BCD,$ the point $F$ on the segment $AB$ satisfies $\angle FDA =\angle DBC,$ and the point $X$ on the line $AC$ satisfies $CX = BX.$ Let $O_1$ and $O_2$ be the circumcenters of the triangles $ADC$ and $EXD,$ respectively. Prove that the lines $BC, EF,$ and $O_1O_2$ are concurrent.

71 replies

1 viewing

Kagebaka

Jul 20, 2021

jkim0656

27 minutes ago

Normal but good inequality

giangtruong13 1

Source: From a province

Let $a,b,c> 0$ satisfy that $a+b+c=3abc$ . Prove that: $\sum_{cyc} \frac{ab}{3c+ab+abc} \geq \frac{3}{5}$

1 reply

giangtruong13

Yesterday at 4:04 PM

arqady

38 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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114,026 topics

4 users

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Last Poster

k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

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

Putnam 2011 A2

Kent Merryfield 16

Let $a_1,a_2,\dots$ and $b_1,b_2,\dots$ be sequences of positive real numbers such that $a_1=b_1=1$ and $b_n=b_{n-1}a_n-2$ for $n=2,3,\dots.$ Assume that the sequence $(b_j)$ is bounded. Prove that $S=\sum_{n=1}^{\infty}\frac1{a_1\cdots a_n}$ converges, and evaluate $S.$

16 replies

Kent Merryfield

Dec 5, 2011

NicoN9

an hour ago

A property of Bernoulli numbers

Gauler 2

Define the Bernoulli numbers $B_n$ as
$\frac{x}{e^x-1}=\sum_{n\ge 0}B_n \frac{x^n}{n!}$ and the Bernoulli polynomials $B_n(t)$ as
$\frac{xe^{tx}}{e^x-1}=\sum_{n\ge 0} B_n(t)\frac{x^n}{n!}$ for $t\in \mathbb R$ .

From these definitions, prove that
$B_n\left(t\right)=\sum _{m=0}^n\binom{n}{m}B_{n-m}t^m$ and
$\int_a^x B_n(t) dt=\frac{B_{n+1}(x)-B_{n+1}(a)}{n+1}$ for all $n\ge 1$ .

2 replies

Gauler

Yesterday at 6:15 PM

Gauler

4 hours ago

Countable set

TurtleKing123 0

Let $f: (a,b) \to \mathbb{R}$ be a function having finite one-sided derivatives at all points in $(a,b)$ . Prove that $f$ is differentiable in $(a,b)$ except for a set that is at most countable.

0 replies

TurtleKing123

Yesterday at 8:55 PM

0 replies

Divergent sum of inverses

toto1234567890 7

Source: Miklós Schweitzer 2014, P5

Let $\alpha$ be a non-real algebraic integer of degree two, and let $\mathbb{P}$ be the set of irreducible elements of the ring $\mathbb{Z}[ \alpha]$ . Prove that
$\sum_{p\in \mathbb{P}}^{{}}\frac{1}{|p|^{2}}=\infty$

7 replies

toto1234567890

Dec 22, 2014

GreenKeeper

Yesterday at 8:04 PM

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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18,571 topics

5 users

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First Poster

Last Poster

k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

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

Happy April Fools!

jkim0656 6

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

6 replies

+1 w

jkim0656

17 minutes ago

At777

4 minutes ago

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

asuth_asuth 292

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.

292 replies

asuth_asuth

Sunday at 8:18 PM

yaxuan

16 minutes ago

How is this possible

Craftybutterfly 20

This is very wrong

20 replies

Craftybutterfly

Mar 26, 2025

Craftybutterfly

17 minutes ago

GIF avatars

FlamesOfHope 0

They should support GIF avatars of under 1GB in size (only applies if you input a GIF, does not support over 24KB if it's just an image.) Would be pretty cool!

0 replies