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
Inequalities
sqing   10
N 3 hours ago by sqing
Let $a,b,c >2 $ and $ ab+bc+ca \leq 75.$ Show that
$$\frac{1}{a-2}+\frac{1}{b-2}+\frac{1}{c-2}\geq 1$$Let $a,b,c >2 $ and $ \frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{6}{7}.$ Show that
$$\frac{1}{a-2}+\frac{1}{b-2}+\frac{1}{c-2}\geq 2$$
10 replies
sqing
May 13, 2025
sqing
3 hours ago
9 How many squares do you have memorized
LXC007   27
N 4 hours ago by whwlqkd
How many squares have you memorized. I have 1-20
27 replies
LXC007
Yesterday at 3:44 PM
whwlqkd
4 hours ago
2000th Post!
PikaPika999   7
N 4 hours ago by elizhang101412
1. How many ways can you arrange the letters in the word ALGEBRA such that no two identical letters are adjacent?

2. Find the smallest positive integer n such that $n^2+n+41$ is not a prime number.

3. You have 4 red tiles, 3 blue tiles, and 2 green tiles. How many ways can you arrange them in a row such that no two tiles of the same color are adjacent?

4. You flip a fair coin repeatedly until you either get 3 tails or 4 heads. What is the expected number of flips before stopping?

5. Let $A(2,3)$ and $B(8,7)$ be two points in the coordinate plane. A circle is drawn such that $\overline{AB}$ is a diameter.

(a). Find the equation of the circle in the form $(x+a)^2+(y+b)^2=r^2$

(b). A line passes through the point P(6,2) and is tangent to the circle. Find the equation of this tangent line.

hopefully these problems weren't too easy lol

also,
Please tell me if any of these problems have any flaws! (also please put your answers in hide tags or quote tags)
7 replies
PikaPika999
Today at 1:53 AM
elizhang101412
4 hours ago
Challenge: Make every number to 100 using 4 fours
CJB19   126
N 4 hours ago by e_is_2.7182818
I've seen this attempted a lot but I want to see if the AoPS community can actually do it. Using ONLY 4 fours and math operations, make as many numbers as you can. Try to go in order. I'll start:
$$(4-4)*4*4=0$$$$4-4+4/4=1$$$$4/4+4/4=2$$$$(4+4+4)/4=3$$$$4+(4-4)*4=4$$$$4+4^{4-4}=5$$$$4!/4+4-4=6$$$$4+4-4/4=7$$$$4+4+4-4=8$$
126 replies
CJB19
May 15, 2025
e_is_2.7182818
4 hours ago
9 Am I going insane?
PenguFish   26
N 5 hours ago by nmlikesmath
I feel stupid honestly, and fyi, I did go over every question. Focus is counting with symmetry
26 replies
PenguFish
Mar 26, 2025
nmlikesmath
5 hours ago
Concurrent in a pyramid
vanstraelen   1
N Yesterday at 7:53 PM by vanstraelen

Given a pyramid $(T,ABCD)$ where $ABCD$ is a parallelogram.
The intersection of the diagonals of the base is point $S$.
Point $A$ is connected to the midpoint of $[CT]$, point $B$ to the midpoint of $[DT]$,
point $C$ to the midpoint of $[AT]$ and point $D$ to the midpoint of $[BT]$.
a) Prove: the four lines are concurrent in a point $P$.
b) Calulate $\frac{TS}{TP}$.
1 reply
vanstraelen
May 10, 2025
vanstraelen
Yesterday at 7:53 PM
bisector of <BAC _|_AD, trapezium, AB = BE, AC = DE NZMO 2021 R1 p2
parmenides51   3
N Yesterday at 7:49 PM by LeYohan
Let $ABCD$ be a trapezium such that $AB\parallel CD$. Let $E$ be the intersection of diagonals $AC$ and $BD$. Suppose that $AB = BE$ and $AC = DE$. Prove that the internal angle bisector of $\angle BAC$ is perpendicular to $AD$.
3 replies
parmenides51
Sep 20, 2021
LeYohan
Yesterday at 7:49 PM
Pertenacious Polynomial Problem
BadAtCompetitionMath21420   4
N Yesterday at 7:40 PM by soryn
Let the polynomial $P(x) = x^3-x^2+px-q$ have real roots and real coefficients with $q>0$. What is the maximum value of $p+q$?

This is a problem I made for my math competition, and I wanted to see if someone would double-check my work (No Mike allowed):

solution
Is this solution good?
4 replies
BadAtCompetitionMath21420
Yesterday at 3:13 AM
soryn
Yesterday at 7:40 PM
shadow of a cylinder, shadow of a cone
vanstraelen   3
N Yesterday at 7:35 PM by vanstraelen

a) Given is a right cylinder of height $2R$ and radius $R$.
The sun shines on this solid at an angle of $45^{\circ}$.
What is the area of the shadow that this solid casts on the plane of the botom base?

b) Given is a right cone of height $2R$ and radius $R$.
The sun shines on this solid at an angle of $45^{\circ}$.
What is the area of the shadow that this solid casts on the plane of the base?
3 replies
vanstraelen
May 9, 2025
vanstraelen
Yesterday at 7:35 PM
Challenge Problem: triangle inequality
Bottema   7
N Yesterday at 6:02 PM by Speedysolver1
Prove that in any triangle we have:

a^{2}+b^{2}+c^{2} \geq 4sqrt{3}S
7 replies
Bottema
May 12, 2004
Speedysolver1
Yesterday at 6:02 PM
2022 MARBLE - Mock ARML I -8 \frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=32
parmenides51   2
N Yesterday at 4:33 PM by Kempu33334
Let $a,b,c$ complex numbers with $ab+ +bc+ca = 61$ such that
$$\frac{1}{b+c}+\frac{1}{c+a}+\frac{1}{a+b}= 5$$$$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=32.$$Find the value of $abc$.
2 replies
parmenides51
Jan 14, 2024
Kempu33334
Yesterday at 4:33 PM
Geomettry ez
AnhIsGod   1
N Yesterday at 1:17 PM by Soupboy0
Let two circles (O) and (O') intersect at two points (one of which is called A). The common tangent CD (with C belonging to (O) and D belonging to (O')) lies on the same side as A with respect to the line OO', intersecting OO' at S. The line segment SA intersects circle (O) at E (different from A). Prove that EC is parallel to AD.
1 reply
AnhIsGod
Yesterday at 12:43 PM
Soupboy0
Yesterday at 1:17 PM
Minimum and Maximum of Complex Numbers
pythagorazz   1
N Yesterday at 8:39 AM by alexheinis
Let $a,b,$ and $c$ be complex numbers. For a complex number $z=p+qi$ where $i=\sqrt(-1)$, define the norm $|z|$ to be the distance of $z$ from the origin, or $|z|=\sqrt(p^2+q^2 )$. Let $m$ be the minimum value and $M$ be the maximum value of $\frac{(|a+b|+|b+c|+|c+a|)}{(|a|+|b|+|c| )}$ for all complex numbers $a,b,c$ where $|a|+|b|+|c|\ne 0$. Find $M+m$.
1 reply
pythagorazz
Apr 14, 2025
alexheinis
Yesterday at 8:39 AM
Folklore
Osim_09   2
N Yesterday at 8:36 AM by pigeon123
Let ABCD be a circumscribed quadrilateral, which is also cyclic. Let I be the incenter, O the circumcenter, and E the intersection point of the diagonals of the quadrilateral. Prove that the points O, I, and E are collinear.
2 replies
Osim_09
Jan 21, 2025
pigeon123
Yesterday at 8:36 AM
stat moment pt 2
fruitmonster97   1
N Apr 17, 2025 by iwastedmyusername
There exists a list of $n$ positive integers with mean, median, mode, and range equal to positive real $x.$ Compute the minimum possible value of $n.$
1 reply
fruitmonster97
Apr 17, 2025
iwastedmyusername
Apr 17, 2025
stat moment pt 2
G H J
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.
fruitmonster97
2498 posts
#1 • 1 Y
Y by Exponent11
There exists a list of $n$ positive integers with mean, median, mode, and range equal to positive real $x.$ Compute the minimum possible value of $n.$
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
iwastedmyusername
164 posts
#3 • 2 Y
Y by Exponent11, Soupboy0
Click to reveal hidden text
This post has been edited 1 time. Last edited by iwastedmyusername, Apr 17, 2025, 4:50 PM
Reason: i frogor positive integers
Z K Y
N Quick Reply
G
H
=
a