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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

aops ids

Bummer12345 61

Make your argument here on why your AoPS user ID is the coolest!!!!! :pilot: :pilot: :pilot: :pilot: :pilot:

For instance, my ID, $573803$ , can be written as $547 \cdot 1049$ , both which are prime.

$547$ is a cuban prime, prime index prime

$1049$ is a Sophie Germain prime

I think my ID is pretty cool, but theres probably better IDs out there.

stuff

61 replies

Bummer12345

Mar 28, 2025

yaxuan

18 minutes ago

MathLeague Middle School States Makeup

kamuii 10

Is anyone doing the states makeup for Mathleague middle school?
And also, how does qualification to nats work from there? Is it a by state or by grade thing

10 replies

kamuii

5 hours ago

DreamineYT

2 hours ago

Math Problem(s)

greenhuman23 3

Fill in the blanks to make the equation true.
( __−__ ) ⋅ __ ÷ __ + __ = 59/7

With the digit(s) below make the equation true-

$1$ , $3$ , $5$ , $7$ , $9$ .

3 replies

greenhuman23

Today at 3:45 AM

yaxuan

2 hours ago

real math problems

Soupboy0 29

Ill be posting questions once in a while. Here's the first question:

What fraction of numbers from $1$ to $1000$ have the digit $7$ and are divisible by $3$ ?

29 replies

Soupboy0

Mar 25, 2025

swaga

2 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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120,221 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

Inequalities

sqing 15

Let $a,b,c\geq 0$ and $a+b+c=1$ . Prove that
$a^2+b^2+ ab +21abc\leq\frac{512}{441}$ Equality holds when $a=b=\frac{38}{21},c=\frac{5}{214}.$
$a^2+b^2+ ab +19abc\leq\frac{10648}{9747}$ Equality holds when $a=b=\frac{22}{57},c=\frac{13}{57}.$
$a^2+b^2+ ab +22abc\leq\frac{15625}{13068}$ Equality holds when $a=b=\frac{25}{66},c=\frac{8}{33}.$

15 replies

sqing

Mar 26, 2025

aidan0626

2 hours ago

Rubik's cube problem

ilikejam 20

If I have a solved Rubik's cube, and I make a finite sequence of (legal) moves repeatedly, prove that I will eventually resolve the puzzle.

(this wording is kinda goofy but i hope its sorta intuitive)

20 replies

ilikejam

Mar 28, 2025

jasperE3

2 hours ago

line AO passes through the midpoint of segment EF

toanrathay 1

Given a triangle $ABC$ with $AB < AC$ and the angle bisector $AD$ .
The line passing through $A$ and perpendicular to $AC$ intersects the line passing through $B$ and parallel to $AD$ at point $E$ .
The line passing through $A$ and perpendicular to $AB$ intersects the line passing through $C$ and parallel to $AD$ at point $F$ .
Let $O$ be the intersection of the three perpendicular bisectors of triangle $ABC$ .
Prove that line $AO$ passes through the midpoint of segment $EF$ .

1 reply

toanrathay

Today at 5:08 AM

joeym2011

5 hours ago

inequality

sunshine_12 2

|a| + |b| + |c| − |a + b| − |b + c| − |c + a| + |a + b + c| ≥ 0
hey everyone, so I came across this inequality, and I did make some progress:
Let (a+b), (b+c), (c+a) be three sums T1, T2 and T3. As there are 3 sums, but they can be of only 2 signs, by pigeon hole principle, atleast 2 of the 3 sums must be of the same sign.
But I'm getting stuck on the case work. Can anyone help?
Thnx a lot

2 replies

sunshine_12

Today at 1:53 PM

sunshine_12

5 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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34,579 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

Fixed point as P varies

tenniskidperson3 86

Source: 2016 USAJMO 1

The isosceles triangle $\triangle ABC$ , with $AB=AC$ , is inscribed in the circle $\omega$ . Let $P$ be a variable point on the arc $\stackrel{\frown}{BC}$ that does not contain $A$ , and let $I_B$ and $I_C$ denote the incenters of triangles $\triangle ABP$ and $\triangle ACP$ , respectively.

Prove that as $P$ varies, the circumcircle of triangle $\triangle PI_BI_C$ passes through a fixed point.

86 replies

tenniskidperson3

Apr 19, 2016

ErTeeEs06

15 minutes ago

Colored Pencils for Math Competitions

Owinner 14

I've heard using colored pencils is really useful for geometry problems. Is this only for very hard problems, or can it be used in MATHCOUNTS/AMC 8/10? An example problem would be much appreciated.

14 replies

Owinner

Yesterday at 5:56 PM

BS2012

25 minutes ago

9 Which math contest is your favorite?

mdk2013 4

links for details on each comp

i think thats all the major ones, comment if you have any more that i forgot to include
upvote if you're like me and you think MATHCOUNTS is obv better!

EDIT: i forgot ARML and JBMO, comment if you like those

4 replies

mdk2013

43 minutes ago

Andyluo

28 minutes ago

AMC 10/AIME Study Forum

PatTheKing806 93

[center]

Me (PatTheKing806) and EaZ_Shadow have created a AMC 10/AIME Study Forum! Hopefully, this forum wont die quickly. To signup, do /join or \join.

Click here to join! (or do some pushups) :P

People should join this forum if they are wanting to do well on the AMC 10 next year, trying get into AIME, or loves math!

93 replies

PatTheKing806

Mar 27, 2025

forestcaller2010

an hour 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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311,402 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

Finding big a_i a_i+1

nAalniaOMliO 1

Source: Belarusian National Olympiad 2025

Positive real numbers $a_1>a_2>\ldots>a_n$ with sum $s$ are such that the equation $nx^2-sx+1=0$ has a positive root $a_{n+1}$ smaller than $a_n$ .
Prove that there exists a positive integer $r \leq n$ such that the inequality $a_ra_{r+1} \geq \frac{1}{r}$ holds.

1 reply

nAalniaOMliO

Friday at 8:36 PM

RagvaloD

a minute ago

nice problem

hanzo.ei 2

Source: I forgot

Let triangle $ABC$ be inscribed in the circumcircle $(O)$ and circumscribed about the incircle $(I)$ , with $AB < AC$ . The incircle $(I)$ touches the sides $BC$ , $CA$ , and $AB$ at $D$ , $E$ , and $F$ , respectively. A line through $I$ , perpendicular to $AI$ , intersects $BC$ , $CA$ , and $AB$ at $X$ , $Y$ , and $Z$ , respectively. The line $AI$ meets $(O)$ at $M$ (distinct from $A$ ). The circumcircle of triangle $AYZ$ intersects $(O)$ at $N$ (distinct from $A$ ). Let $P$ be the midpoint of the arc $BAC$ of $(O)$ . The line $AI$ cuts segments $DF$ and $DE$ at $K$ and $L$ , respectively, and the tangents to the circle $(DKL)$ at $K$ and $L$ intersect at $T$ . Prove that $AT \perp BC$ .

2 replies

hanzo.ei

Yesterday at 5:58 PM

Lil_flip38

6 minutes ago

Fixed point config on external similar isosceles triangles

Assassino9931 2

Source: Bulgaria Spring Mathematical Competition 2025 10.2

Let $AB$ be an acute scalene triangle. A point $D$ varies on its side $BC$ . The points $P$ and $Q$ are the midpoints of the arcs $\widehat{AB}$ and $\widehat{AC}$ (not containing $D$ ) of the circumcircles of triangles $ABD$ and $ACD$ , respectively. Prove that the circumcircle of triangle $PQD$ passes through a fixed point, independent of the choice of $D$ on $BC$ .

2 replies

Assassino9931

Today at 12:41 PM

bin_sherlo

8 minutes ago

VERY HARD MATH PROBLEM!

slimshadyyy.3.60 17

Let a ≥b ≥c ≥0 be real numbers such that a^2 +b^2 +c^2 +abc = 4. Prove that
a+b+c+(√a−√c)^2 ≥3.

17 replies

slimshadyyy.3.60

Yesterday at 10:49 PM

GreekIdiot

15 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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114,019 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

nice integral

Martin.s 3

$\int_0^\infty \frac{\tanh x}{4x (1+\cosh(2x))} dx$

3 replies

Martin.s

Friday at 8:09 PM

Martin.s

3 minutes ago

determinant of matrix

jokerjoestar 4

Calculate the determinant of the matrix below: $A = \begin{bmatrix} 1 & 2 & 3 & \cdots & n-1 & n \\ 2 & 3 & 4 & \cdots & n & 1 \\ 3 & 4 & 5 & \cdots & 1 & 2 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ n-1 & n & 1 & \cdots & n-3 & n-2 \\ n & 1 & 2 & \cdots & n-2 & n-1 \end{bmatrix}$

4 replies

jokerjoestar

4 hours ago

vanstraelen

7 minutes ago

The ratio between two integral

Butterfly 4

Prove $\frac{I_1}{I_2}=\sqrt{2}$ where $I_1=\int_{0}^{\frac{\sqrt{3}-1}{\sqrt{2}}} \frac{1-x^2}{\sqrt{x^8-14x^4+1}}dx$ and $I_2=\int_{0}^{\sqrt{2}-1} \frac{1+x^2}{\sqrt{x^8+14x^4+1}}dx.$

4 replies

Butterfly

Mar 28, 2025

paxtonw

3 hours ago

A complex integral

Gauler 1

For $s=c+it$ with $|t|\le T$ , prove that
$\frac{1}{2\pi i}\int _{c-iT}^{c+iT}\frac{e^{su}}{s}ds=\frac{1}{2}+\frac{Tu}{\pi }+O\left(T^2u^2+\frac{c}{T}\right)$ for $T|u|\le 1$ .

1 reply

Gauler

4 hours ago

paxtonw

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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18,565 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

Blog error (resolved)

Beaniebo4 9

I was making my blog and trying to add contributors, but after pressing the checkmark, the site kept on refreshing, deleting all my blog info and not adding contributors. This happened several times.

9 replies

Beaniebo4

Yesterday at 3:07 AM

jkim0656

2 hours ago

How is this possible

Craftybutterfly 18

This is very wrong

18 replies

Craftybutterfly

Mar 26, 2025

sultanine

4 hours ago

Pressing 'go down button' always creates a gray box on the last post

Craftybutterfly 21

Summary of the problem: Pressing go down to last post button always creates a gray box overlapping last post
Page URL: any forum
Steps to reproduce:
1. Go to any topic in a forum
2. The gray box at the bottom overlaps part of the first post
Expected behavior: Should not show a gray box
Frequency: 100% of the time
Operating system(s): Linux HP EliteBook 835 G8 Notebook PC
Browser(s), including version: Chrome 133.0.6943.142 (Official Build) (64-bit) (cohort: Stable)
Additional information: It works on any other device, on my iPhone XR, a MacOS, and my iPad. Took the screenshot a month ago. The gray box still appears

21 replies

Craftybutterfly

Mar 12, 2025

jlacosta

Friday at 11:05 PM

k They added something new on community!!!!

jb2015007 7

They added something new on community!!!!

7 replies