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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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51,240 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

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

is 8 divisible by 3

Soupboy0 9

Is 8 divisible by 3?

9 replies

Soupboy0

Mar 25, 2025

cheltstudent

15 minutes ago

real math problems

Soupboy0 17

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 $3$ ?

17 replies

Soupboy0

Mar 25, 2025

cheltstudent

28 minutes ago

Mathcounts chapter target q8

LXC007 45

Did anyone solve question 8 of target for chapter. The question was find the area of the equilateral triangle with one vertex on (20,25) and the other two on the positive part of the x and y axis. This question was basically impossible in the roughly six minutes you had. nobody at my chapter solved it.

45 replies

LXC007

Mar 3, 2025

chenhan29

35 minutes ago

Base Problem

Yummo 3

For any number N, prove that n in base (n-1) = 11.
For example, 3 in base 2 is 11.

3 replies

Yummo

Mar 24, 2025

ilikejam

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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120,203 topics

6 users

TOPICS

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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

I need help!

nonofuukl 2

I need some help with a math problem I’ve been working on. I’m really struggling to understand how to apply Schur’s inequality to solve inequalities, and I feel a bit lost about when and how to use it.

2 replies

nonofuukl

an hour ago

NamelyOrange

2 minutes ago

Rubik's cube problem

ilikejam 15

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)

15 replies

ilikejam

Yesterday at 12:58 AM

mpcnotnpc

12 minutes ago

dumb and bad

fruitmonster97 4

source: some old mathdash monday, mine
Let $f(n)=\frac{n^3}{3}+\frac{n^2}{2}+\frac{n}{6}.$ Compute $\sum_{i=0}^{2023}(f(2024)-f(i))\pmod{1000}.$

4 replies

fruitmonster97

Yesterday at 6:21 PM

maxamc

17 minutes ago

what is tangent line at?

Miranda2829 1

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

1 reply

Miranda2829

4 hours ago

ilikejam

an hour 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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34,573 topics

11 users

TOPICS

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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

AMC 10/AIME Study Forum

PatTheKing806 54

[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!

54 replies

PatTheKing806

Thursday at 11:34 PM

Andyluo

35 minutes ago

2025 INTEGIRLS NYC/NJ Math Competition

sargamsujit 2

NYC/NJ INTEGIRLS will be hosting our second annual math competition on May 3rd, 2025 from 9:30 AM to 4:30 PM EST at Rutgers University. Last year, we proudly organized the largest math competition for girls globally, welcoming over 500 participants from across the tristate area. Join other female-identifying and non-binary "STEMinists" in solving problems, socializing, playing games, and more! If you are interested in competing, please register at https://forms.gle/jqwEiq5PgqefetLj7

Find our website at https://nyc.nj.integirls.org/

[center]Important Information[/center]

Eligibility: This competition is open to all female-identifying and non-binary students in 8th grade or under. The competition is also completely free, including registration and lunch.

System: We will have two divisions: a middle school division and an elementary school division. There will be an individual round and team 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 elementary school problems will range from introductory to AMC 8 level, while the middle school problems will be for more advanced problem-solvers. Team round problems will cover various difficulty levels.

Platform: This contest will be held in person at Rutgers University. Competitors will all receive free merchandise, raffle tickets, and the chance to win exclusive gift prizes!

[center]Prizes

Over $2,000 in awards, including plaques, medals, plushies, gift cards, toys, books, swag, and more for top competitors and teams

[center]Help Us Out[/center]

[center]Please help us in sharing our competition and spreading the word! 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!
Format credits go to Indy INTEGIRLS!

2 replies

sargamsujit

Jan 28, 2025

sargamsujit

an hour ago

A lot of integer lengths: JMO #6 or USAMO Problem 4

BarbieRocks 80

Let $ABC$ be a triangle with $\angle A = 90^{\circ}$ . Points $D$ and $E$ lie on sides $AC$ and $AB$ , respectively, such that $\angle ABD = \angle DBC$ and $\angle ACE = \angle ECB$ . Segments $BD$ and $CE$ meet at $I$ . Determine whether or not it is possible for segments $AB$ , $AC$ , $BI$ , $ID$ , $CI$ , $IE$ to all have integer lengths.

80 replies

2 viewing

BarbieRocks

Apr 29, 2010

Maximilian113

3 hours ago

2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!

audio-on 13

Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary

Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!

13 replies

audio-on

Jan 26, 2025

mkwhe

3 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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311,326 topics

17 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

Maximizing the Area

steven_zhang123 0

Source: China TST 2025 P21

Given a circle $\omega$ and two points $A$ and $B$ outside $\omega$ , a quadrilateral $PQRS$ is defined as "good" if $P, Q, R, S$ are four distinct points on $\omega$ in order, and lines $PQ$ and $RS$ intersect at $A$ and lines $PS$ and $QR$ intersect at $B$ .

For a quadrilateral $T$ , let $S_T$ denote its area. If there exists a good quadrilateral, prove that there exists good quadrilateral $T$ such that for any good quadrilateral $T_1 (T_1 \neq T)$ , $S_{T_1} < S_T$ .

0 replies

+1 w

steven_zhang123

27 minutes ago

0 replies

Modular Matching Pairs

steven_zhang123 0

Source: China TST 2025 P20

Let $n$ be an odd integer, $m = \frac{n+1}{2}$ . Consider $2m$ integers $a_1, a_2, \ldots, a_m, b_1, b_2, \ldots, b_m$ such that for any $1 \leq i < j \leq m$ , $a_i \not\equiv a_j \pmod{n}$ and $b_i \not\equiv b_j \pmod{n}$ . Prove that the number of $k \in \{0, 1, \ldots, n-1\}$ for which satisfy $a_i + b_j \equiv k \pmod{n}$ for some $i \neq j$ , $i, j \in \left \{ 1,2,\cdots,m \right \}$ is greater than $n - \sqrt{n} - \frac{1}{2}$ .

0 replies

1 viewing

steven_zhang123

29 minutes ago

0 replies

An almost identity polynomial

nAalniaOMliO 3

Source: Belarusian National Olympiad 2025

Let $n$ be a positive integer and $P(x)$ be a polynomial with integer coefficients such that $P(1)=1,P(2)=2,\ldots,P(n)=n$ .
Prove that $P(0)$ is divisible $2 \cdot 3 \cdot \ldots \cdot n$ .

3 replies

nAalniaOMliO

5 hours ago

jasperE3

30 minutes ago

Harmonic Series and Infinite Sequences

steven_zhang123 0

Source: China TST 2025 P19

Let $\left \{ x_n \right \} _{n\ge 1}$ and $\left \{ y_n \right \} _{n\ge 1}$ be two infinite sequences of integers. Prove that there exists an infinite sequence of integers $\left \{ z_n \right \} _{n\ge 1}$ such that for any positive integer $n$ , the following holds:

$\sum_{k|n} k \cdot z_k^{\frac{n}{k}} = \left( \sum_{k|n} k \cdot x_k^{\frac{n}{k}} \right) \cdot \left( \sum_{k|n} k \cdot y_k^{\frac{n}{k}} \right).$

0 replies

steven_zhang123

31 minutes ago

0 replies

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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114,004 topics

6 users

TOPICS

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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

Time Scale Calculus- Dynamical inequalities

ehuseyinyigit 3

Does Maclaurin's Inequality have a dynamic version in time scale calculus, especially for diamond alpha calculus?

3 replies

ehuseyinyigit

Mar 23, 2025

paxtonw

2 minutes ago

Matrix problem

hef4875 7

The matrix $A = (a_{ij}) \in Mat_p(\mathbb{C})$ is defined by the conditions
$a_{12} = a_{23} = \dots = a_{(p-1)p} = 1$ and $a_{ij} = 0$ for a set of indices $(i,j)$ .
Prove that there do not exist nonzero matrices $B, C \in Mat_p(\mathbb{C})$ satisfying the equation
$(I_p + A)^n = B^n + C^n.$ $\forall$ $n$ is a postive integer.

7 replies

hef4875

Mar 26, 2025

Etkan

10 minutes ago

Gheorghe Țițeica 2025 Grade 11 P3

AndreiVila 1

Source: Gheorghe Țițeica 2025

Let $(a_n)_{n\geq 0}$ be a sequence defined by $a_0\geq 0$ and the recurrence relation $a_{n+1}=\frac{a_n^2-1}{n+1},$ for all $n\geq 0$ . Prove that here exists a real number $a> 0$ such that:
[list]
[*] if $a_0\geq a,$ $\lim_{n\rightarrow\infty}a_n = \infty$ ;
[*] if $a_0\in [0,a),$ $\lim_{n\rightarrow\infty}a_n = 0$ .

1 reply

AndreiVila

3 hours ago

paxtonw

20 minutes ago

Definite integral

PolyaPal 1

If $n$ is a nonnegative integer, evaluate $\int_0^1 \frac{x^n}{1 + x^2}\,dx$ .

1 reply

PolyaPal

an hour ago

alexheinis

an hour 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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18,564 topics

1 user

TOPICS

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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

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

2 hours ago

k They added something new on community!!!!

jb2015007 7

They added something new on community!!!!

7 replies

jb2015007

4 hours ago

eg4334

3 hours ago

Python exit() module decriptions appear as "undefined"

SoaringHigh 11

Summary of the problem: When using exit() (or quit()) in the Python windows on AoPS the "Description" and "To fix" options show up as "undefined"
sample program

exit("Goodbye world")

Page URL: N/A
Steps to reproduce:
1. Use the AoPS Python module to execute the exit() or quit() functions in a program. (try running the sample program)
Expected behavior: The "Description" and "To fix" sections give a description of SystemExit
Frequency: Always
Operating system(s): Windows 11 Home
Browser(s), including version: Microsoft Edge 130.0.2849.46
Additional information: N/A

11 replies