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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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51,238 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

Wednesday at 11:40 PM

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 32

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

32 replies

1 viewing

Bummer12345

Today at 1:18 AM

s12d34

7 minutes ago

MathCounts National Sets

UberPiggy 2

Hi, does anyone happen to have MathCounts National round test problems from 2018-2024? I found 2000-2017 online but can't find anything past that year.

2 replies

UberPiggy

Today at 5:31 AM

Nioronean

11 minutes ago

interesting way to derive the quadratic formula

Soupboy0 2

If you have the quadratic $ax^2+bx+c$ , call the roots $r$ and $s$ with $r \ge s$ . Then by Vieta's, $r+s = \frac{-b}{a}$ and $rs = \frac{c}{a}$ . If we can find $r+s$ , we can find $r-s$ . Note that $(r-s)^2=r^2-2rs+s^2$ and $(r+s)^2=r^2+2rs+s^2$ . Therefore, $(r+s)^2-4rs=(r-s)^2$ , and $r-s=\sqrt{(r+s)^2-4rs} = \sqrt{\frac{-b}{a^2}^2-\frac{4c}{a}}=\sqrt{\frac{b^2-4ac}{a^2}}=\frac{\sqrt{b^2-4ac}}{a}$ . Now all we have to do is solve the following system:
$r+s=\frac{-b}{a}$ and $r-s=\frac{\sqrt{b^2-4ac}}{a}$ . Solving for $r$ by elimination, we get $2r = \frac{-b+\sqrt{b^2-4ac}}{a}$ , so ${r=\frac{-b+\sqrt{b^2-4ac}}{2a}}$ , which is the quadratic formula. Substituting this into our first equation, we get $\frac{-b+\sqrt{b^2-4ac}}{2a}+s=\frac{-b}{a}$ , and solving for $s$ yields $s=\frac{-b-\sqrt{b^2-4ac}}{2a}$ ,

2 replies

Soupboy0

an hour ago

Mathematicalprodigy37

44 minutes ago

The daily problem!

Leeoz 39

Every day, I will try to post a new problem for you all to solve! If you want to post a daily problem, you can! :)

Please hide solutions and answers, hints are fine though! :)

The first problem is:
[quote=March 21st Problem]Alice flips a fair coin until she gets 2 heads in a row, or a tail and then a head. What is the probability that she stopped after 2 heads in a row? Express your answer as a common fraction.[/quote]

Past Problems!

39 replies

Leeoz

Mar 21, 2025

HacheB2031

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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120,198 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

Wednesday at 11:40 PM

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

Inequalities

sqing 3

Let $a,b,c>0$ and $ab+bc+ca= abc.$ Prove that $ab^2+bc^2+ca^2-11(a+b+c)\geq -18$ $ab^2+bc^2+ca^2-\frac{52}{5} (a+b+c)\geq -\frac{63}{5}$

3 replies

sqing

Yesterday at 11:45 AM

sqing

an hour ago

functions false or true

Math2030 7

find all functions f: \mathbb{R} \to \mathbb{R} that satisfy the functional equation:

f(x^2 f(x) + f(y)) = (f(x))^3 + f(y), \quad \forall x, y \in \mathbb{R}

7 replies

Math2030

Mar 25, 2025

jasperE3

an hour ago

A tight inequality

jokehim 1

Let $a,b,c\ge 0: ab+bc+ca>0.$ Prove that $\frac{a+b}{2a^2+3ab+2b^2}+\frac{b+c}{2b^2+3bc+2c^2}+\frac{c+a}{2c^2+3ca+2a^2}\ge \frac{18}{7(a+b+c)}.$

1 reply

jokehim

Yesterday at 3:03 PM

liyufish

3 hours ago

Help me please

ntu0301 2

Determine all integers $n>1$ that satisfy the following condition: For every integer k such that $0\le k<n$ there always exists a positive integer $A$ that is divisible by n and $S(A)\equiv k (mod n)$ . $S(A)$ : sum of elements of $A$

2 replies

ntu0301

Mar 23, 2025

ntu0301

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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34,573 topics

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

rrusczyk

Mar 24, 2025

SmartGroot

Wednesday at 11:40 PM

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

PROM^2 for Girls 2025

mathisfun17 17

Hi everyone!

The Princeton International School of Math and Science (PRISMS) Math Team is delighted that $PROM^2$ for Girls, PRISMS Online Math Meet for Girls, is happening this spring! https://www.prismsus.org/events/prom/home/index

We warmly invite all middle school girls to join us! This is a fantastic opportunity for young girls to connect with others interested in math as well as prepare for future math contests.

This contest will take place online from 12:00 pm to 3:00 pm EST on Saturday, April 26th, 2025.

The competition will include a team and individual round as well as activities like origami. You can see a detailed schedule here. https://prismsus.org/events/prom/experience/schedule.

Registration is FREE, there are cash prizes for participants who place in the top 10 and cool gifts for all participants.

1st place individual: $500 cash
2nd place individual: $300 cash
3rd place individual: $100 cash
4th-10th place individual: $50 cash each

Some FAQs:
Q: How difficult are the questions?
A: The problem difficulty is around AMC 8 or Mathcounts level.

Q: Are there any example problems?
A: You can find some archived here: https://www.prismsus.org/events/prom/achieve/achieve

Registration is open now. https://www.prismsus.org/events/prom/register/register. Email us at prom2@prismsus.org with any questions.

The PRISMS Peregrines Math Team welcomes you!

17 replies

mathisfun17

Feb 22, 2025

exp-ipi-1

25 minutes ago

AMC 8 score thread

Squidget 224

$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline Squidget & 7 & 21 \\ \end{tabular}$

224 replies

+1 w

Squidget

Jan 30, 2025

Inaaya

32 minutes ago

Isosceles Triangulation

worthawholebean 69

Source: USAMO 2008 Problem 4

Let $\mathcal{P}$ be a convex polygon with $n$ sides, $n\ge3$ . Any set of $n - 3$ diagonals of $\mathcal{P}$ that do not intersect in the interior of the polygon determine a triangulation of $\mathcal{P}$ into $n - 2$ triangles. If $\mathcal{P}$ is regular and there is a triangulation of $\mathcal{P}$ consisting of only isosceles triangles, find all the possible values of $n$ .

69 replies

worthawholebean

May 1, 2008

gladIasked

an hour ago

Double dose of cyanide on day 2

brianzjk 29

Source: USAMO 2023/5

Let $n\geq3$ be an integer. We say that an arrangement of the numbers $1$ , $2$ , $\dots$ , $n^2$ in a $n \times n$ table is row-valid if the numbers in each row can be permuted to form an arithmetic progression, and column-valid if the numbers in each column can be permuted to form an arithmetic progression. For what values of $n$ is it possible to transform any row-valid arrangement into a column-valid arrangement by permuting the numbers in each row?

29 replies

brianzjk

Mar 23, 2023

gladIasked

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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311,267 topics

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

rrusczyk

Mar 24, 2025

SmartGroot

Wednesday at 11:40 PM

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

Polynomial and sequence

truongphatt2668 4

Let positive integer sequence $(a_n)$ has this identity: For all positive integer $m$ , the polynomial $P(x) = a_mx^m + a_{m-1}x^{m-1} + \cdots + a_1x + a_0$ has $m$ distinct roots. Prove that $a_n \ge n+1, \forall n \in \mathbb{N}$

4 replies

truongphatt2668

Dec 17, 2024

truongphatt2668

15 minutes ago

ez prolem

Noname23 1

Source: ..

Let $x,y>0$ and $x+y=\sqrt{10}$
Find min of Z(and prove): $Z=(x^4+1)(y^4+1)$

1 reply

+2 w

Noname23

29 minutes ago

truongphatt2668

19 minutes ago

inequalities

Jackson0423 7

if abc=1 what is the maximum value of a/(a^2+2)+b/(b^2+2)+c/(c^2+2)? please help

7 replies

Jackson0423

3 hours ago

Jackson0423

23 minutes ago

compare area of triangle with sides (a+b)/2, (b+c)/2, (c+a)/2

parmenides51 2

Source: 1998 Argentina IberoAmerican Training List p1

Let $a, b$ and $c$ be the lengths of the sides of a scalene triangle $\Delta$ and let $l =\frac{b + c}{2}$ , $m = \frac{c + a}{2}$ and $n =\frac{a + b}{2}$ . Prove that $l, m$ and $n$ are lengths of the sides of a scalene triangle whose area is greater than that of triangle $\Delta$ .

2 replies

parmenides51

Aug 22, 2021

AshAuktober

25 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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113,991 topics

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

rrusczyk

Mar 24, 2025

SmartGroot

Wednesday at 11:40 PM

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

Matrix problem

Marry123 4

If $A,B\in M_3(\mathbb{C})$ and $A^2+B^2=2AB$ , prove $det(A+B)^2=8det(A^2+B^2)$

4 replies

Marry123

Feb 22, 2019

Acridian9

19 minutes ago

Discuss the UC

easymath12345 1

Discuss the uniformly convergence of the series $\sum\limits_{n = 1}^\infty {{3^n}\sin \left( {\frac{1}{{{5^n}x}}} \right)}$ on $\left( {0, + \infty } \right)$

1 reply

easymath12345

an hour ago

jestrada

25 minutes ago

f"(x)>0, show that int(f(x)cosx dx) >0

Sayan 11

Source: ISI(BS) 2009 #2

Let $f(x)$ be a continuous function, whose first and second derivatives are continuous on $[0,2\pi]$ and $f''(x) \geq 0$ for all $x$ in $[0,2\pi]$ . Show that
$\int_{0}^{2\pi} f(x)\cos x dx \geq 0$

11 replies

Sayan

May 5, 2012

Mathzeus1024

30 minutes ago

Ahlfors 2.3.4.8

centslordm 1

Express $\arctan w$ in terms of the logarithm.

1 reply

centslordm

Jan 9, 2025

Mathzeus1024

4 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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18,563 topics

2 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

Wednesday at 11:40 PM

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

k Aops Glitching

jkim0656 26

Hi everyone!
I noticed that every time i try to answer a question and get it right/wrong the screen freezes and i can't scroll anymore...
100%
Chrome
PC
do u guys have the same issue?
I don't think it is like this for Alcumus but for normal class problems it does
*the challenge problems

EDIT: sry for the terrible title :blush:

26 replies

jkim0656

Yesterday at 2:22 AM

jlacosta

Yesterday at 5:03 PM

k New reaper game

Squidget 10

What does this mean?

Is this a glitch

10 replies

Squidget

Wednesday at 10:31 PM

Cerberusman

Yesterday at 2:31 PM

k Office Hours not starting yet?

GAMER100 5

Several posts have been made about this years before, but the office hours banner hasn't appeared yet even though I refreshed the page multiple times. It has been 50 minutes since when office hours should have started and no mods have responded to a question I posted 3 hours ago (relative to last edit). Can others confirm?

5 replies