Art of Problem Solving
AoPS Online AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy AoPS Academy
Small live classes for advanced math
and language arts learners in grades 1-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Stay ahead of learning milestones! Enroll in a class over the summer!
Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
3 M G
BBookmark  VNew Topic kLocked
Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
3 M G
BBookmark  VNew Topic kLocked
t 
34,691 topics
w
5 users
TOPICS
No tags match your search
M
AMC
AIME
AMC 10
geometry
USA(J)MO
AMC 12
USAMO
AIME I
AMC 10 A
USAJMO
AMC 8
poll
MATHCOUNTS
AMC 10 B
number theory
probability
summer program
trigonometry
algebra
AIME II
AMC 12 A
function
AMC 12 B
email
calculus
inequalities
ARML
analytic geometry
3D geometry
ratio
polynomial
AwesomeMath
search
AoPS Books
college
HMMT
USAMTS
Alcumus
quadratics
PROMYS
geometric transformation
Mathcamp
LaTeX
rectangle
logarithms
modular arithmetic
complex numbers
Ross Mathematics Program
contests
AMC10
Math Kangaroo
No tags match your search
M
G
Topic
First Poster
Last Poster
H
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
J
H
purple comet discussion
ConfidentKoala4   59
N an hour ago by hzbrl
when can we discuss purple comet
59 replies
ConfidentKoala4
May 2, 2025
hzbrl
an hour ago
J
H
A Collection of Good Problems from my end
SomeonecoolLovesMaths   6
N an hour ago by SomeonecoolLovesMaths
This is a collection of good problems and my respective attempts to solve them. I would like to encourage everyone to post their solutions to these problems, if any. This will not only help others verify theirs but also perhaps bring forward a different approach to the problem. I will constantly try to update the pool of questions.

The difficulty level of these questions vary from AMC 10 to AIME. (Although the main pool of questions were prepared as a mock test for IOQM over the years)

Problem 1

Problem 2

Problem 3
6 replies
SomeonecoolLovesMaths
Yesterday at 8:16 AM
SomeonecoolLovesMaths
an hour ago
J
H
parallelogram in a tetrahedron
vanstraelen   0
4 hours ago
Given a tetrahedron $ABCD$ and a plane $\mu$, parallel with the edges $AC$ and $BD$.
$AB \cap \mu=P$.
a) Prove: the intersection of the tetrahedron with the plane is a parallelogram.
b) If $\left|AC\right|=14,\left|BD\right|=7$ and $\frac{\left|PA\right|}{\left|PB\right|}=\frac{3}{4}$,
calculates the lenghts of the sides of this parallelogram.
0 replies
vanstraelen
4 hours ago
0 replies
J
H
USAJMO problem 3: Inequality
BOGTRO   104
N Today at 4:00 AM by justaguy_69
Let $a,b,c$ be positive real numbers. Prove that $\frac{a^3+3b^3}{5a+b}+\frac{b^3+3c^3}{5b+c}+\frac{c^3+3a^3}{5c+a} \geq \frac{2}{3}(a^2+b^2+c^2)$.
104 replies
BOGTRO
Apr 24, 2012
justaguy_69
Today at 4:00 AM
J
H
Polynomial
kellyelliee   0
Today at 3:57 AM
Let the polynomial $f(x)=x^2+ax+b$, where $a,b$ integers and $k$ is a positive integer. Suppose that the integers
$m,n,p$ satisfy: $f(m), f(n), f(p)$ are divisible by k. Prove that:
$(m-n)(n-p)(p-m)$ is divisible by k
0 replies
kellyelliee
Today at 3:57 AM
0 replies
J
H
2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
audio-on   68
N Today at 3:51 AM by RainbowSquirrel53B
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!


68 replies
audio-on
Jan 26, 2025
RainbowSquirrel53B
Today at 3:51 AM
J
H
Question about AMC 10
MathNerdRabbit103   15
N Today at 3:02 AM by GallopingUnicorn45
Hi,

Can anybody predict a good score that I can get on the AMC 10 this November by only being good at counting and probability, number theory, and algebra? I know some geometry because I took it in school though, but it isn’t competition math so it probably doesn’t count.

Thanks.
15 replies
MathNerdRabbit103
May 2, 2025
GallopingUnicorn45
Today at 3:02 AM
J
H
Arithmetic Series and Common Differences
4everwise   6
N Today at 2:12 AM by epl1
For each positive integer $k$, let $S_k$ denote the increasing arithmetic sequence of integers whose first term is $1$ and whose common difference is $k$. For example, $S_3$ is the sequence $1,4,7,10,...$. For how many values of $k$ does $S_k$ contain the term $2005$?
6 replies
4everwise
Nov 10, 2005
epl1
Today at 2:12 AM
J
H
find number of elements in H
Darealzolt   0
Today at 1:50 AM
If \( H \) is the set of positive real solutions to the system
\[ x^3 + y^3 + z^3 = x + y + z \]\[ x^2 + y^2 + z^2 = xyz \]then find the number of elements in \( H \).
0 replies
Darealzolt
Today at 1:50 AM
0 replies
J
H
old problem from an open contest
Darealzolt   0
Today at 1:41 AM
Given that $a, b \in \mathbb{R}$ satisfy
\[ a + \frac{1}{a + 2015} = b - 4030 + \frac{1}{b - 2015} \]and $|a - b| > 5000$. Determine the value of
\[ \frac{ab}{2015} - a + b. \]
0 replies
Darealzolt
Today at 1:41 AM
0 replies
J
H
f_n(x)=\sum sin(nx)/n
Urumqi   6
N Today at 1:04 AM by Urumqi
$F_n(x)=\sum_{k=1}^{n}\frac{\sin (kx)}{k}$, prove that for all $x \in (0,\pi), F_n(x)>0$.

Thanks.
6 replies
Urumqi
Yesterday at 2:13 AM
Urumqi
Today at 1:04 AM
J
H
Looking for users and developers
derekli   9
N Today at 12:57 AM by musicalpenguin
Guys I've been working on a web app that lets you grind high school lvl math. There's AMCs, AIME, BMT, HMMT, SMT etc. Also, it's infinite practice so you can keep grinding without worrying about finding new problems. Please consider helping me out by testing and also consider joining our developer team! :P :blush:

Link: https://stellarlearning.app/competitive
9 replies
derekli
Yesterday at 12:57 AM
musicalpenguin
Today at 12:57 AM
J
H
Regular tetrahedron
vanstraelen   6
N Yesterday at 11:36 PM by Math-lover1
Given the points $O(0,0,0),A(1,0,0),B(\frac{1}{2},\frac{\sqrt{3}}{2},0)$
a) Determine the point $C$, above the xy-plane, such that the pyramid $OABC$ is a regular tetrahedron.
b) Calculate the volume.
c) Calculate the radius of the inscribed sphere and the radius of the circumscribed sphere.
6 replies
vanstraelen
Yesterday at 3:23 PM
Math-lover1
Yesterday at 11:36 PM
J
H
How many pairs
Ecrin_eren   5
N Yesterday at 10:19 PM by imbadatmath1233


Let n be a natural number and p be a prime number. How many different pairs (n, p) satisfy the equation:

p + 2^p + 3 = n^2 ?



5 replies
Ecrin_eren
May 2, 2025
imbadatmath1233
Yesterday at 10:19 PM
J
H
J
H
Help with a 2022 Math Kangaroo Grade 7 Problem
Cornelson   2
N Apr 18, 2025 by maxamc
A frog jumps in a straight line every 3 meters. If the frog starts at 0 and jumps 5 times, how many different positions could it land on if it could also jump backwards?
2 replies
Cornelson
Apr 18, 2025
maxamc
Apr 18, 2025
J
Help with a 2022 Math Kangaroo Grade 7 Problem
G H J
Reveal topic tags
Math Kangaroo
L
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Cornelson
1 post
Cornelson
#1 h  Apr 18, 2025, 2:26 AM
Y by
A frog jumps in a straight line every 3 meters. If the frog starts at 0 and jumps 5 times, how many different positions could it land on if it could also jump backwards?
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
math_on_top
24 posts
math_on_top
#2 h  Apr 18, 2025, 3:23 AM
Y by
There's 0, 5 to the right, 5 to the left, so 11 possibilities
This post has been edited 1 time. Last edited by math_on_top, Apr 18, 2025, 3:23 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
maxamc
567 posts
maxamc
#3 h  Apr 18, 2025, 3:37 AM
Y by
math_on_top wrote:
There's 0, 5 to the right, 5 to the left, so 11 possibilities

0, 6, 12, -6, -12 are not possible.
Z K Y
N Quick Reply
G
H
=
a