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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

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

2025 MATHCOUNTS State Hub

SirAppel 53

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)
[*] NY: 42 (43 42 42 42 41 40)
[*] TX: 42 (43 43 43 42 42 40 40 38 38 38)
[*] 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 (41 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)
[*] 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]

Note

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.

53 replies

+4 w

SirAppel

4 hours ago

jb2015007

a few seconds ago

April Fools! (math edition)

Dream9 1

What are some good sillies I can do on my friends? :yoda:

1 reply

Dream9

3 minutes ago

fossasor

a few seconds ago

The daily problem!

Leeoz 49

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!

49 replies

Leeoz

Mar 21, 2025

HacheB2031

44 minutes ago

mathcounts state discussion

Soupboy0 31

les goo its finally april

31 replies

Soupboy0

Today at 5:00 AM

Soupboy0

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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120,243 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

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

a minute 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

7 minutes ago

Inequalities (Please help me!!!)

yt12 6

Let $a,b,c$ be reals with $a+b+c=1$ and $a,b,c \ge \frac{-3}{ 4}$ . Prove that
$\frac{a}{a^2+1}+\frac{b}{b^2+1}+\frac{c}{ c^2+1} \le \frac{9}{ 10}$

6 replies

yt12

Mar 4, 2023

lamhihi1234

21 minutes ago

geometry incentre config

Tony_stark0094 0

In a triangle $\Delta ABC$ $I$ is the incentre and point $F$ is defined such that $F \in AC$ and $F \in \odot BIC$
prove that $AI$ is the perpendicular bisector of $BF$

0 replies

Tony_stark0094

28 minutes ago

0 replies

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

11 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

Berkeley mini Math Tournament Solutions Released

BerkeleyMathTournament 0

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

0 replies

BerkeleyMathTournament

8 minutes ago

0 replies

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

2 hours ago

2012 AIME II Problem 12

xHypotenuse 4

Hello guys, I want to know what was wrong with my PIE approach.

First here's the problem:

For a positive integer $p$ , define the positive integer $n$ to be $p$ -safe if $n$ differs in absolute value by more than $2$ from all multiples of $p$ . For example, the set of $10$ -safe numbers is $\{ 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 23, \ldots\}$ . Find the number of positive integers less than or equal to $10,000$ which are simultaneously $7$ -safe, $11$ -safe, and $13$ -safe.

My approach was finding the number of 7-unsafe numbers, 11-unsafe, and 13-unsafe, then finding 77-unsafe, 91-unsafe, 143-unsafe, and finally 1001-unsafe numbers and using PIE for a complementary counting approach. But somehow I got a number over than 10,000 for the total number of unsafe numbers. Is my approach valid and have I made arithmetic errors or does the PIE approach just not work?

4 replies

xHypotenuse

Yesterday at 11:40 PM

Soupboy0

2 hours ago

k confusion about homework

aidan0626 8

I was doing my calculus homework, and when I turned it in, my teacher said that "my parents failed me", "the only place you will be hired is at McDonald's", and "I will personally send you to hell." Can someone help explain why? I checked with my friends, and I got the same answers as them, yet they got a perfect score.

8 replies

+1 w

aidan0626

Today at 7:04 AM

aidan0626

2 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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311,458 topics

18 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

FE over R

IAmTheHazard 19

Source: ELMO Shortlist 2024/A3

Find all functions $f : \mathbb{R}\to\mathbb{R}$ such that for all real numbers $x$ and $y$ ,
$f(x+f(y))+xy=f(x)f(y)+f(x)+y.$
Andrew Carratu

19 replies

+1 w

IAmTheHazard

Jun 22, 2024

Bardia7003

5 minutes ago

Find values of $a b+a c+b c$

NJAX 11

Source: 2nd Al-Khwarizmi International Junior Mathematical Olympiad 2024, Day2, Problem6

Let $a, b, c$ be distinct real numbers such that $a+b+c=0$ and $a^{2}-b=b^{2}-c=c^{2}-a.$ Evaluate all the possible values of $a b+a c+b c$ .

Proposed by Nguyen Anh Vu, Vietnam

11 replies

NJAX

May 31, 2024

Baimukh

17 minutes ago

Final fool geometry

giangtruong13 0

Let $ABC$ be a pointed triangle and altitudes $AD, BE, CF$ . Prove that: $S_{DEF}=(sin^2A*sin^2B+sin^2C-2)S_{ABC}$

0 replies

giangtruong13

28 minutes ago

0 replies

Interesting config

TheUltimate123 37

Source: ELMO 2023/4

Let $ABC$ be an acute scalene triangle with orthocenter $H$ . Line $BH$ intersects $\overline{AC}$ at $E$ and line $CH$ intersects $\overline{AB}$ at $F$ . Let $X$ be the foot of the perpendicular from $H$ to the line through $A$ parallel to $\overline{EF}$ . Point $B_1$ lies on line $XF$ such that $\overline{BB_1}$ is parallel to $\overline{AC}$ , and point $C_1$ lies on line $XE$ such that $\overline{CC_1}$ is parallel to $\overline{AB}$ . Prove that points $B$ , $C$ , $B_1$ , $C_1$ are concyclic.

Proposed by Luke Robitaille

37 replies

TheUltimate123

Jun 26, 2023

E50

32 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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114,030 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

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

4 minutes 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

1 viewing

Alidq

an hour ago

Alidq

25 minutes ago

ecuation real numbers

MihaiT 2

Let $f,g:R->R$ be continuous, and $f$ is increasing and $g$ is decreasing. If $f,g$ have the same horizontal asymptote at $+\infty$ ,which is the number of solutions of the equation $f(x)=g(x)$ ?(Or can this number not be specified?)

2 replies

MihaiT

Yesterday at 6:52 PM

MihaiT

3 hours ago

$f$ an endomorphism of a vector space V with dimension $n$ satisfy $f^2=f$

al3abijo 1

If $f$ an endomorphism of a vector space V with dimension $n$ satisfy $f^2=f$ with $r=r(f)=dim(Im f)$
Prove that there exists a basis of V $(v_1,\ldots ,v_n)$ such that
$f(v_i)=v_i , i\leq r$ and $f(v_i)=0 , i>r$
And find the matrix of $f$ in the basis $(v_1,\ldots ,v_n)$

1 reply

al3abijo

5 hours ago

al3abijo

5 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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18,573 topics

16 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

Reaper bug

AmberTiger79 4

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?

4 replies

AmberTiger79

3 hours ago

Major_Monogram

a few seconds ago

Happy April Fools!

jkim0656 40

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

40 replies

jkim0656

Today at 4:32 AM

Major_Monogram

4 minutes ago

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

asuth_asuth 324

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.

324 replies

2 viewing

asuth_asuth

Sunday at 8:18 PM

PrayingCowboy

17 minutes ago

GIF avatars

FlamesOfHope 1

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!

1 reply