Stay ahead of learning milestones! Enroll in a class over the summer!

G
Topic
First Poster
Last Poster
k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/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.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

Prealgebra 1
Tuesday, May 13 - Aug 26
Thursday, May 29 - Sep 11
Sunday, Jun 15 - Oct 12
Monday, Jun 30 - Oct 20
Wednesday, Jul 16 - Oct 29

Prealgebra 2 Self-Paced

Prealgebra 2
Wednesday, May 7 - Aug 20
Monday, Jun 2 - Sep 22
Sunday, Jun 29 - Oct 26
Friday, Jul 25 - Nov 21

Introduction to Algebra A Self-Paced

Introduction to Algebra A
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
Tuesday, Jul 15 - Oct 28

Introduction to Counting & Probability Self-Paced

Introduction to Counting & Probability
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19

Introduction to Number Theory
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30

Introduction to Algebra B Self-Paced

Introduction to Algebra B
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14

Introduction to Geometry
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19

Paradoxes and Infinity
Mon, Tue, Wed, & Thurs, Jul 14 - Jul 16 (meets every day of the week!)

Intermediate: Grades 8-12

Intermediate Algebra
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22

Intermediate Counting & Probability
Wednesday, May 21 - Sep 17
Sunday, Jun 22 - Nov 2

Intermediate Number Theory
Sunday, Jun 1 - Aug 24
Wednesday, Jun 18 - Sep 3

Precalculus
Friday, May 16 - Oct 24
Sunday, Jun 1 - Nov 9
Monday, Jun 30 - Dec 8

Advanced: Grades 9-12

Olympiad Geometry
Tuesday, Jun 10 - Aug 26

Calculus
Tuesday, May 27 - Nov 11
Wednesday, Jun 25 - Dec 17

Group Theory
Thursday, Jun 12 - Sep 11

Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

MATHCOUNTS/AMC 8 Advanced
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21

AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22

AMC 12 Final Fives
Sunday, May 18 - Jun 15

AIME Problem Series A
Thursday, May 22 - Jul 31

AIME Problem Series B
Sunday, Jun 22 - Sep 21

F=ma Problem Series
Wednesday, Jun 11 - Aug 27

WOOT Programs
Visit the pages linked for full schedule details for each of these programs!


MathWOOT Level 1
MathWOOT Level 2
ChemWOOT
CodeWOOT
PhysicsWOOT

Programming

Introduction to Programming with Python
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22

Intermediate Programming with Python
Sunday, Jun 1 - Aug 24
Monday, Jun 30 - Sep 22

USACO Bronze Problem Series
Tuesday, May 13 - Jul 29
Sunday, Jun 22 - Sep 1

Physics

Introduction to Physics
Wednesday, May 21 - Aug 6
Sunday, Jun 15 - Sep 14
Monday, Jun 23 - Sep 15

Physics 1: Mechanics
Thursday, May 22 - Oct 30
Monday, Jun 23 - Dec 15

Relativity
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)
0 replies
jlacosta
May 1, 2025
0 replies
relay race!
A7456321   9
N 5 minutes ago by CJB19
Welcome to the math relay race! To participate, answer the problem in the latest post, then post one yourself! Please also mark the question number. E.x. if the one before you is question #35, then mark yours as question #36. Easy as pi!

Note: If you choose to help someone with a problem you don't have to make one yourself unless you want to. You are also welcome to ask a question without having to post a new problem. Please do not post a new problem until the previous one is solved. All topics are welcome except for anything >12th grade. Trig is fine. Calculus is not. :D

Question 1: If it takes 5 monkeys 5 days to eat 5 bananas, then how many days will it take for 4 monkeys to eat 4 bananas? (Hint: It's not 4)

Please upvote! :thumbup:

Goal: 100 questions!

Timeline
9 replies
A7456321
Today at 2:20 AM
CJB19
5 minutes ago
9 Prodigy AoPS or Khanacadamy
ZMB038   18
N 14 minutes ago by TalentedElephant41
Hey everyone just was wondering what everybody prefers? Try not to fight so this doesn't get locked!
18 replies
ZMB038
Yesterday at 1:15 PM
TalentedElephant41
14 minutes ago
Interesting Combinatorics Problem
Ro.Is.Te.   1
N 38 minutes ago by CJB19
Amanda has $1000$ red marbles, $2000$ yellow marbles, $3000$ green marbles, and $4000$ blue marbles. If Amanda takes the marbles one by one without replacing them until the $3999th$ marble. Then the probability that the $4000th$ marble is red is?
1 reply
Ro.Is.Te.
2 hours ago
CJB19
38 minutes ago
Summer math contest prep
Abby0618   7
N 2 hours ago by Konigsberg
School is almost out, so I have a lot of time in the summer. I want to be able to make DHR on AMC 8 in 7th grade

(current 6th grader) and hopefully get an average score in AMC 10. What should I do during the summer to achieve

these goals? For context, I have many books from AOPS, have already taken the Intro to Algebra A course, and took

AMC 8 for the first time as a 6th grader. If there are any challenging math problems you think would benefit learning,

please post them here. Thank you! :-D
7 replies
Abby0618
Yesterday at 8:52 PM
Konigsberg
2 hours ago
Metric space
wiseman   3
N May 21, 2025 by alinazarboland
Source: IMS 2014 - Day1 - Problem4
Let $(X,d)$ be a metric space and $f:X \to X$ be a function such that $\forall x,y\in X : d(f(x),f(y))=d(x,y)$.
$\text{a})$ Prove that for all $x \in X$, $\lim_{n \rightarrow +\infty} \frac{d(x,f^n(x))}{n}$ exists, where $f^n(x)$ is $\underbrace{f(f(\cdots f(x)}_{n \text{times}} \cdots ))$.
$\text{b})$ Prove that the amount of the limit does not depend on choosing $x$.
3 replies
wiseman
Oct 2, 2014
alinazarboland
May 21, 2025
Double integration
Tricky123   2
N May 21, 2025 by Mathzeus1024
Q)
\[\iint_{R} \sin(xy) \,dx\,dy, \quad R = \left[0, \frac{\pi}{2}\right] \times \left[0, \frac{\pi}{2}\right]\]
How to solve the problem like this I am using the substitution method but its seems like very complicated in the last
Please help me
2 replies
Tricky123
May 18, 2025
Mathzeus1024
May 21, 2025
Find solution of IVP
neerajbhauryal   2
N May 15, 2025 by Mathzeus1024
Show that the initial value problem \[y''+by'+cy=g(t)\] with $y(t_o)=0=y'(t_o)$, where $b,c$ are constants has the form \[y(t)=\int^{t}_{t_0}K(t-s)g(s)ds\,\]

What I did
2 replies
neerajbhauryal
Sep 23, 2014
Mathzeus1024
May 15, 2025
fourier series?
keroro902   2
N May 15, 2025 by Mathzeus1024
f(x)=$\sum _{n=0}^{\infty } \text{cos}(nx)/2^{n}$
f(x) = ?
thanks
2 replies
keroro902
May 14, 2010
Mathzeus1024
May 15, 2025
uniformly continuous of multivariable function
keroro902   1
N May 14, 2025 by Mathzeus1024
How can I determine which of the following functions are uniformly continuous on the given domain A?

$f \left( x, y \right) = \frac{x^3 + y^2}{x^2 + y}$ , $A = \left\{ \left( x, y
\right) \in \mathbb m{R}^2 \left|  \right.  \left| y \right| \leq \frac{x^2}{2}
%Error. "nocomma" is a bad command.
, x^2 + y^2 < 1 \right\}$

$g \left( x, y \right) = \frac{y^2 + 4 x^2}{y^2 - 4 x^2 - 1}$, $A = \left\{
\left( x, y \right) \in \mathbb m{R}^2 \left| 0 \leq x^2 - y^2 \leqslant 1
\right\} \right.$
1 reply
keroro902
Nov 2, 2012
Mathzeus1024
May 14, 2025
Miklos Schweitzer 1971_5
ehsan2004   2
N May 9, 2025 by pi_quadrat_sechstel
Let $ \lambda_1 \leq \lambda_2 \leq...$ be a positive sequence and let $ K$ be a constant such that \[  \sum_{k=1}^{n-1} \lambda^2_k < K \lambda^2_n \;(n=1,2,...).\] Prove that there exists a constant $ K'$ such that \[  \sum_{k=1}^{n-1} \lambda_k < K' \lambda_n \;(n=1,2,...).\]

L. Leindler
2 replies
ehsan2004
Oct 29, 2008
pi_quadrat_sechstel
May 9, 2025
Miklos Schweitzer 1968_9
ehsan2004   1
N May 8, 2025 by pi_quadrat_sechstel
Let $ f(x)$ be a real function such that
\[ \lim_{x \rightarrow +\infty} \frac{f(x)}{e^x}=1\]
and $ |f''(x)|\leq c|f'(x)|$ for all sufficiently large $ x$. Prove that \[ \lim_{x \rightarrow +\infty} \frac{f'(x)}{e^x}=1.\]

P. Erdos
1 reply
ehsan2004
Oct 8, 2008
pi_quadrat_sechstel
May 8, 2025
Range of 2 parameters and Convergency of Improper Integral
Kunihiko_Chikaya   3
N May 1, 2025 by Mathzeus1024
Source: 2012 Kyoto University Master Course in Mathematics
Let $\alpha,\ \beta$ be real numbers. Find the ranges of $\alpha,\ \beta$ such that the improper integral $\int_1^{\infty} \frac{x^{\alpha}\ln x}{(1+x)^{\beta}}$ converges.
3 replies
Kunihiko_Chikaya
Aug 21, 2012
Mathzeus1024
May 1, 2025
f'(1)>1 implies f has a fixed point in (0,1)
Sayan   13
N Apr 27, 2025 by Apple_maths60
Source: ISI(BS) 2010 #4
A real valued function $f$ is defined on the interval $(-1,2)$. A point $x_0$ is said to be a fixed point of $f$ if $f(x_0)=x_0$. Suppose that $f$ is a differentiable function such that $f(0)>0$ and $f(1)=1$. Show that if $f'(1)>1$, then $f$ has a fixed point in the interval $(0,1)$.
13 replies
Sayan
May 17, 2012
Apple_maths60
Apr 27, 2025
Maximum value of ∫_0^1 e^x logf(x) dx when ∫_0^1 f(x) dx =1
tom-nowy   2
N Apr 26, 2025 by Dattier
Source: 1982 Niigata University entrance exam
Let $\mathcal{F}$ be the set of continuous functions $f: [0,1] \to (0, \infty )$ such that $ \int_0^1 f(x) \, \mathrm dx =1 $. For $f \in \mathcal{F}$, let $$I(f)=\int_0^1 e^x \log f(x) \, \mathrm dx .$$Determine $\max_{f \in \mathcal{F}}I(f)$.
2 replies
tom-nowy
Jul 7, 2013
Dattier
Apr 26, 2025
Good resources for Mathcounts and AMCs
HoneyHap   5
N Apr 7, 2025 by HoneyHap
Hi people!
I have been and aops user for only a few months and not an active one either, just a user checking other posts and competitions. This is actually my first post. I am in 7th grade and only this year I have actually started locking in on competition math, before that, I didn’t really care about Mathcounts and AMCs. So, I hone my problem-solving skills by lightly doing some math problems. I have signed up for a lot of math competitions this month and am struggling to prepare properly with the resources I have. Do you guys have any resources you use to prepare for math competitions and that are actually helpful to use to prepare for competitions in a short amount of time. I am looking for resources that first teach you stuff and give you problems, like guided notes and handouts. I have few aops books like “Competition Math for Middle School” and “Intermediate Algebra”, but they’re not enough. I have learnt Algebra 1 and started doing high school geometry and a bit of Algebra 2 at home. Do let me know if you have any suggestions!
5 replies
HoneyHap
Apr 6, 2025
HoneyHap
Apr 7, 2025
Good resources for Mathcounts and AMCs
G H J
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
HoneyHap
9 posts
#1 • 2 Y
Y by PikaPika999, Sedro
Hi people!
I have been and aops user for only a few months and not an active one either, just a user checking other posts and competitions. This is actually my first post. I am in 7th grade and only this year I have actually started locking in on competition math, before that, I didn’t really care about Mathcounts and AMCs. So, I hone my problem-solving skills by lightly doing some math problems. I have signed up for a lot of math competitions this month and am struggling to prepare properly with the resources I have. Do you guys have any resources you use to prepare for math competitions and that are actually helpful to use to prepare for competitions in a short amount of time. I am looking for resources that first teach you stuff and give you problems, like guided notes and handouts. I have few aops books like “Competition Math for Middle School” and “Intermediate Algebra”, but they’re not enough. I have learnt Algebra 1 and started doing high school geometry and a bit of Algebra 2 at home. Do let me know if you have any suggestions!
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Inaaya
411 posts
#2 • 1 Y
Y by PikaPika999
Mathdash and AMCTrivial are great
start looking at Competition Math for Middle School, it's nicely condensed
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
RollingPanda4616
267 posts
#3 • 1 Y
Y by MathDolphin95
It doesn't teach you material, but mocking pasts tests with time is great. After, make sure to look at the solutions to any that you missed/didn't solve.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
sadas123
1319 posts
#4
Y by
Here are some resources:

AMC 8/10/12:https://math.llmlab.io/get_course?course_id=2

Mathcounts trainer on AOPS

Number Theory:https://sites.math.rutgers.edu/~zeilberg/DrZNumberTheoryhandouts.html

Counting and Probability: https://artofproblemsolving.com/videos/counting

I have more but I am a bit tired today.
This post has been edited 1 time. Last edited by sadas123, Apr 6, 2025, 11:53 PM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
MathDolphin95
2464 posts
#5
Y by
RollingPanda4616 wrote:
It doesn't teach you material, but mocking pasts tests with time is great.

yes, this kind of tells you the kinds of questions that will be on the test

it also can help you get faster and learn how best to pace yourself on different competitions
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
HoneyHap
9 posts
#6
Y by
Thank you so much! I checked out math dash and it seems pretty cool!
Z K Y
N Quick Reply
G
H
=
a