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!
No tags match your search
M
G
Topic
First Poster
Last Poster
H
k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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 events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/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
Sunday, Apr 13 - Aug 10
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
Sunday, Apr 13 - Aug 10
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
Monday, Apr 7 - Jul 28
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
Wednesday, Apr 16 - Jul 2
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
Thursday, Apr 17 - Jul 3
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
Wednesday, Apr 16 - Jul 30
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14

Introduction to Geometry
Wednesday, Apr 23 - Oct 1
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

Intermediate: Grades 8-12

Intermediate Algebra
Monday, Apr 21 - Oct 13
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
Friday, Apr 11 - Jun 27
Sunday, Jun 1 - Aug 24
Wednesday, Jun 18 - Sep 3

Precalculus
Wednesday, Apr 9 - Sep 3
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
Wednesday, Apr 16 - Jul 2
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
Friday, Apr 11 - Jun 27
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

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
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)
0 replies
jlacosta
Apr 2, 2025
0 replies
J
H
max n with n times n square are black
NicoN9   1
N 10 minutes ago by WallyWalrus
Source: Japan Junior MO Preliminary 2022 P5
Find the maximum positive integer $n$ such that for $45\times 45$ grid, no matter how you paint $2022$ unit squares black, there exists $n\times n$ square with all unit square painted black.
1 reply
NicoN9
Today at 9:19 AM
WallyWalrus
10 minutes ago
J
H
Find triple
kalandar   2
N 15 minutes ago by mathlover1231
Find all triple ( x, y, z ) of natural numbers satisfying the equation $1+4^x+4^y=z^2$.
2 replies
kalandar
Apr 26, 2019
mathlover1231
15 minutes ago
J
H
[SEIF Q1] FE on x^3+xy...( ͡° ͜ʖ ͡°)
EmilXM   17
N 16 minutes ago by jasperE3
Source: SEIF 2022
Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that any real numbers $x$ and $y$ satisfy
$$x^3+f(x)f(y)=f(f(x^3)+f(xy)).$$Proposed by EmilXM
17 replies
EmilXM
Mar 12, 2022
jasperE3
16 minutes ago
J
H
IMO 2018 Problem 4
orthocentre   54
N 18 minutes ago by zuat.e
Source: IMO 2018
A site is any point $(x, y)$ in the plane such that $x$ and $y$ are both positive integers less than or equal to 20.

Initially, each of the 400 sites is unoccupied. Amy and Ben take turns placing stones with Amy going first. On her turn, Amy places a new red stone on an unoccupied site such that the distance between any two sites occupied by red stones is not equal to $\sqrt{5}$. On his turn, Ben places a new blue stone on any unoccupied site. (A site occupied by a blue stone is allowed to be at any distance from any other occupied site.) They stop as soon as a player cannot place a stone.

Find the greatest $K$ such that Amy can ensure that she places at least $K$ red stones, no matter how Ben places his blue stones.

Proposed by Gurgen Asatryan, Armenia
54 replies
orthocentre
Jul 10, 2018
zuat.e
18 minutes ago
J
No more topics!
H
J
H
An easy Geo
Math-wiz   7
N Jun 26, 2023 by rajiscrazy
Source: PRMO 2019 Leg 2 P6
Let $ABC$ be a triangle such that $AB=AC$. Suppose the tangent to the circumcircle of ABC at B is perpendicular to AC. Find angle ABC measured in degrees
7 replies
Math-wiz
Aug 25, 2019
rajiscrazy
Jun 26, 2023
J
An easy Geo
G H J
Reveal topic tags
geometry
Triangle
L
G H BBookmark kLocked kLocked NReply
Source: PRMO 2019 Leg 2 P6
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Math-wiz
6107 posts
Math-wiz
#1 h  Aug 25, 2019, 4:45 PM • 1 Y
Y by Adventure10
Let $ABC$ be a triangle such that $AB=AC$. Suppose the tangent to the circumcircle of ABC at B is perpendicular to AC. Find angle ABC measured in degrees
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
amar_04
1915 posts
amar_04
#2 h  Aug 25, 2019, 5:06 PM • 2 Y
Y by mathingbingo, Adventure10
Was really easy. :o

Let the intersection of the tangent at $B$ and $AC$ be $K$. Hence, $\angle KBA=\angle ACB=\theta(say)$, also $\angle KAB=2\theta$. Hence $\theta=\angle ABC=30^\circ$.
This post has been edited 1 time. Last edited by amar_04, Aug 25, 2019, 5:07 PM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Math-wiz
6107 posts
Math-wiz
#3 h  Aug 25, 2019, 5:12 PM • 2 Y
Y by Adventure10, Mango247
amar_04 wrote:
Was really easy. :o

Let the intersection of the tangent at $B$ and $AC$ be $K$. Hence, $\angle KBA=\angle ACB=\theta(say)$, also $\angle KAB=2\theta$. Hence $\theta=\angle ABC=30^\circ$.

Nice. Afterall, it was an actual 2 marker. Not to mention P1 :D
This post has been edited 1 time. Last edited by Math-wiz, Aug 25, 2019, 5:12 PM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Hexagrammum16
1774 posts
Hexagrammum16
#4 h  Aug 26, 2019, 5:06 AM • 1 Y
Y by Adventure10
In other words, $OB || AC$. Which again gives a 120-30-30 triangle.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
RamK
47 posts
RamK
#6 h  Aug 31, 2019, 6:30 PM • 2 Y
Y by Ha_ha_ha, Adventure10
Is the tangent perpendicular to line segment AC or line containing AC?

And how is angle KBA = angle ACB?

Thank you.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
AK-EINSTEIN
6 posts
AK-EINSTEIN
#7 h  Nov 16, 2020, 3:06 PM • 4 Y
Y by Ha_ha_ha, Mango247, Mango247, Mango247
30 is the answer
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
franzliszt
23531 posts
franzliszt
#8 h  Nov 16, 2020, 11:25 PM • 1 Y
Y by Ha_ha_ha
Let the tangent at $B$ meet the extension of $CA$ at $X$. Notice that $\measuredangle XBA =\measuredangle BCA =\measuredangle ACB$. Considering $\triangle BXC$, it is evident that the answer is $30^\circ$.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
rajiscrazy
10 posts
rajiscrazy
#9 h  Jun 26, 2023, 8:05 AM
Y by
will somebody show me a diagram for these question I am not getting it
This post has been edited 1 time. Last edited by rajiscrazy, Jun 26, 2023, 8:05 AM
Z K Y
N Quick Reply
G
H
=
a