Middle School Math
Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8
Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8
3
VNew Topic
kLocked
Middle School Math
Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8
Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8
3
VNew Topic
kLocked
G
Topic
First Poster
Last Poster
k a February Highlights and 2025 AoPS Online Class Information
jlacosta 0
We love to share what you can look forward to this month! The AIME I and AIME II competitions are happening on February 6th and 12th, respectively. Join our Math Jams the day after each competition where we will go over all the problems and the useful strategies to solve them!
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
0 replies
Really confusing question/topic
gbatkhuu1 2
Question: How many necklaces can be made using 5 identical red beads and 2 identical blue beads?
I got 21 by organizing them into a line and counting the ways they can be organized, but my book says the answer is 3 because there are 3 ways to divide the 5 red beads into the sum of two numbers. I don't get what this means, can someone please explain it?
I got 21 by organizing them into a line and counting the ways they can be organized, but my book says the answer is 3 because there are 3 ways to divide the 5 red beads into the sum of two numbers. I don't get what this means, can someone please explain it?
2 replies
[PMO25 Qualifying I.1] Number Counting
kae_3 1
How many four-digit numbers contain the digit
or
(or both)?

Answer Confirmation



Answer Confirmation

1 reply
Problems!
megahertz13 38
I don't think any of these problems are in alcumus, but I am not completely sure.
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 1
Let
, and
. Find all possible values of
.
Difficulty = 2-



Difficulty = 2-
Problem 2
In a school, the two classes are history and math. If
students take neither,
students take history,
take math, and
take both history and math, then find the number of students in the school.
Difficulty = 2




Difficulty = 2
Problem 3
I am thinking of a positive integer,
. When
is divided by
, it leaves a remainder of
. Find all possible values of the remainder when
is divided by
.
Difficulty = 2+






Difficulty = 2+
Problem 4
A positive factor of
is randomly selected. Find the probability it is not a multiple of
or
.
Difficulty = 3-



Difficulty = 3-
Problem 5
How many zereos does
end in when expressed in base
?
Difficulty = 3-


Difficulty = 3-
Problem 6
How many positive integers less than
are multiples are multiples of
or
but not
?
Difficulty = 3




Difficulty = 3
Problem 7
Find the sum of the squares of the last two digits of
.
Difficulty = 3

Difficulty = 3
Problem 8
Two random integers (not necessarily distinct) are chosen between
and
, inclusive. Find the probability their product has less than
positive factors. Calculators are allowed for this problem.
Difficulty = 3+



Difficulty = 3+
Problem 9
Let
be the area of the circle inscribed in a regular hexagon of side length
. Let
be the area of a circle inscribed in a equilateral triangle with altitude length
. Find
.
Difficulty = 4





Difficulty = 4
Problem 10
Let
and
be the roots of
. Find all possible values of
.
Difficulty = 4




Difficulty = 4
Problem 11
If
and
, then find
(Note:
).
Difficulty = 4+




Difficulty = 4+
38 replies
G
Topic
First Poster
Last Poster
k a February Highlights and 2025 AoPS Online Class Information
jlacosta 0
We love to share what you can look forward to this month! The AIME I and AIME II competitions are happening on February 6th and 12th, respectively. Join our Math Jams the day after each competition where we will go over all the problems and the useful strategies to solve them!
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
0 replies
Expected Value Involving Traffic Lights
Fall2021 0
There are 4 traffic lights placed uniformly at random on a 4-mile road. The traffic lights, all in sync, follow a 1-minute loop where they are red for 1 minute and then momentarily flash green so that only cars already stopped at the light can go on. A car arrives at one end of the road just as the lights are flashing green. If the car, when not stopped, always travels at 1 mile per minute, what is the expected number of minutes it takes for the car to traverse the road? Click to reveal hidden text
Answer confirmation: 

0 replies

Inequalities
sqing 4
Let
be real numbers such that
. Prove that
Let
be real numbers such that
. Prove that
Let
be real numbers such that
. Prove that
Let
be real numbers such that
. Prove that












4 replies
[PMO25 Qualifying I.8] Length of Diagonal
kae_3 0
The sides of a convex quadrilateral have lengths
cm,
cm,
cm, and
cm, and they are arranged so that there are no pairs of parallel sides. If one of the diagonals is
cm long, and the length of the other diagonal is a rational number, what is the length of the other diagonal?

Answer Confirmation






Answer Confirmation

0 replies
Contests & Programs
AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
3
VNew Topic
kLocked
Contests & Programs
AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
3
VNew Topic
kLocked
G
Topic
First Poster
Last Poster
k a February Highlights and 2025 AoPS Online Class Information
jlacosta 0
We love to share what you can look forward to this month! The AIME I and AIME II competitions are happening on February 6th and 12th, respectively. Join our Math Jams the day after each competition where we will go over all the problems and the useful strategies to solve them!
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
0 replies
How do student outside US take USAJMO
LemonMatcha 35
I'm a us citizen in Taiwan. I got 240/247.5 on amc10a+aimeii/amc10b+aimeii, so there is a big chance that I can get into jmo, but the office in charge of amc/aime isn't in charge of USA(j)MO. I've contacted them and they say that they don't know who should I find if I get into jmo. Who should I contact now?
35 replies
Geo is back??
GoodMorning 126
Source: 2023 USAJMO Problem 2/USAMO Problem 1
In an acute triangle
, let
be the midpoint of
. Let
be the foot of the perpendicular from
to
. Suppose that the circumcircle of triangle
intersects line
at two distinct points
and
. Let
be the midpoint of
. Prove that
.
Proposed by Holden Mui













Proposed by Holden Mui
126 replies

High School Olympiads
Regional, national, and international math olympiads
Regional, national, and international math olympiads
3
VNew Topic
kLocked
High School Olympiads
Regional, national, and international math olympiads
Regional, national, and international math olympiads
3
VNew Topic
kLocked
G
Topic
First Poster
Last Poster
k a February Highlights and 2025 AoPS Online Class Information
jlacosta 0
We love to share what you can look forward to this month! The AIME I and AIME II competitions are happening on February 6th and 12th, respectively. Join our Math Jams the day after each competition where we will go over all the problems and the useful strategies to solve them!
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
0 replies
Sequences Handout
M11100111001Y1R 3
Source: Own
Hi everyone, I wrote this handout about sequences in NT.
Hope you enjoy!
Hope you enjoy!
3 replies




[Handout] 50 non-traditional functional equations
gghx 2
Sup guys,
I'm retired. I love FEs. So here's 50 of them. Yea...
Functional equations have been one of the least enjoyed topics of math olympiads in recent times, mostly because so many techniques have been developed to just bulldoze through them. These chosen problems do not fall in that category - they require some combi-flavoured creativity to solve (to varying degrees).
For this reason, this handout is aimed at more advanced problem solvers who are bored of traditional FEs and are up for a little challenge!
In some sense, this is dedicated to the "covid FE community" on AoPS who got me addicted to FEs, people like EmilXM, hyay, IndoMathXdZ, Functional_equation, GorgonMathDota, BlazingMuddy, dangerousliri, Mr.C, TLP.39, among many others: thanks guys :). Lastly, thank you to rama1728 for suggestions and proofreading.
Anyways...
I'm retired. I love FEs. So here's 50 of them. Yea...
Functional equations have been one of the least enjoyed topics of math olympiads in recent times, mostly because so many techniques have been developed to just bulldoze through them. These chosen problems do not fall in that category - they require some combi-flavoured creativity to solve (to varying degrees).
For this reason, this handout is aimed at more advanced problem solvers who are bored of traditional FEs and are up for a little challenge!
In some sense, this is dedicated to the "covid FE community" on AoPS who got me addicted to FEs, people like EmilXM, hyay, IndoMathXdZ, Functional_equation, GorgonMathDota, BlazingMuddy, dangerousliri, Mr.C, TLP.39, among many others: thanks guys :). Lastly, thank you to rama1728 for suggestions and proofreading.
Anyways...
2 replies


concurrency in greek MO
parmenides51 1
Source: 2025 Greek MO p2 - Seniors
Let
be an acute triangle and
be a point of side
. Consider points
on line
such that
and
, and points
on line
such that
and
. Circumcircle of triangle
intersects for second time line
at point
(
) and circumcircle of triangle
intersects for second time line
at point
(
). Prove that lines
,
and
concur.






















1 reply
College Math
Topics in undergraduate and graduate studies
Topics in undergraduate and graduate studies
3
VNew Topic
kLocked
College Math
Topics in undergraduate and graduate studies
Topics in undergraduate and graduate studies
3
VNew Topic
kLocked
G
Topic
First Poster
Last Poster
k a February Highlights and 2025 AoPS Online Class Information
jlacosta 0
We love to share what you can look forward to this month! The AIME I and AIME II competitions are happening on February 6th and 12th, respectively. Join our Math Jams the day after each competition where we will go over all the problems and the useful strategies to solve them!
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
0 replies
subspace with dimension n-1
MrOreoJuice 4
Let
be a subspace of
, prove that
if and only if
for some non zero column vector
.





4 replies

D1004 : A general result on integral ?
Dattier 0
Source: les dattes à Dattier
Let
with
.
Is it true that
?
![$f,g \in C([0,1],[1,+\infty[)$](http://latex.artofproblemsolving.com/5/8/2/582e8c06fd3ba52aea1833f3d8b87c797ab1b8f0.png)

Is it true that

0 replies
Site Support
Tech support and questions about AoPS classes and materials
Tech support and questions about AoPS classes and materials
3
VNew Topic
kLocked
Site Support
Tech support and questions about AoPS classes and materials
Tech support and questions about AoPS classes and materials
3
VNew Topic
kLocked
G
Topic
First Poster
Last Poster
k a February Highlights and 2025 AoPS Online Class Information
jlacosta 0
We love to share what you can look forward to this month! The AIME I and AIME II competitions are happening on February 6th and 12th, respectively. Join our Math Jams the day after each competition where we will go over all the problems and the useful strategies to solve them!
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
Prealgebra 1 Self-Paced
Prealgebra 2
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10
Prealgebra 2 Self-Paced
Introduction to Algebra A
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28
Introduction to Algebra A Self-Paced
Introduction to Counting & Probability
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2
Introduction to Counting & Probability Self-Paced
Introduction to Number Theory
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3
Introduction to Algebra B
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30
Introduction to Algebra B Self-Paced
Introduction to Geometry
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1
Intermediate: Grades 8-12
Intermediate Algebra
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13
Intermediate Counting & Probability
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3
Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27
Precalculus
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3
Advanced: Grades 9-12
Olympiad Geometry
Wednesday, Mar 5 - May 21
Calculus
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2
MATHCOUNTS/AMC 8 Advanced
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27
AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
AMC 12 Problem Series
Sunday, Feb 23 - May 11
AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)
F=ma Problem Series
Wednesday, Feb 19 - May 7
Programming
Introduction to Programming with Python
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16
Intermediate Programming with Python
Tuesday, Feb 25 - May 13
USACO Bronze Problem Series
Thursday, Feb 6 - Apr 24
Physics
Introduction to Physics
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22
Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
0 replies
I cannot edit one of my posts.
AlienGirl05 63
Greetings, Site Support,
I have a post that I regularly update. I wanted to update it, but for some reason, I couldn't add anything to my post. It told me that I used a banned term. In fact, even if I don't change anything to my post, it still tells me that I used a banned term. I've tried reloading the page, but nothing happened. I literally updated my post only three hours ago. What is going on???
https://artofproblemsolving.com/community/c2788149h2988518p33892279.
I noticed the same problem occurring on another one of my posts.
https://artofproblemsolving.com/community/c2788149h3093533p27965363.
Thank you,
AlienGirl
I have a post that I regularly update. I wanted to update it, but for some reason, I couldn't add anything to my post. It told me that I used a banned term. In fact, even if I don't change anything to my post, it still tells me that I used a banned term. I've tried reloading the page, but nothing happened. I literally updated my post only three hours ago. What is going on???
https://artofproblemsolving.com/community/c2788149h2988518p33892279.
I noticed the same problem occurring on another one of my posts.
https://artofproblemsolving.com/community/c2788149h3093533p27965363.
Thank you,
AlienGirl

63 replies


How to make a poll
MusicalHorse18 4
Hi,
I am new to Aops and I don't really know how to make a poll and stuff, can someone help me?
Thanks!
MusicalHorse18
Click to reveal hidden text
Click to reveal hidden text
I am new to Aops and I don't really know how to make a poll and stuff, can someone help me?
Thanks!
MusicalHorse18
Click to reveal hidden text
Btw this is my first post
Click to reveal hidden text
Hide tags are confusingClick to reveal hidden text
4 replies
User not found error
math_men 3
Hi
I got user not found error. I have to reregister with same email . But lost my progress on alcumus. Is there a way to recover my progress?
Thanks
I got user not found error. I have to reregister with same email . But lost my progress on alcumus. Is there a way to recover my progress?
Thanks
3 replies
User number of posts status error
XAN4 5
Today I was browsing the forum High School Olympiads. There's a user whose username is the_universe6626, but then, when I flicked down to browse earlier answers today(note: I didn't 'search for this user's posts'), I found that one of them was labeled '23 posts'. I browsed his earlier answers today, and the number of posts increases, from 25 posts in the morning all the way to 36 posts right now. Is this a feature or a bug? If it is a feature, then certainly I haven't seen it elsewhere.
5 replies
Other Forums and Collections
?
AoPS Forums
Forums for AoPS books, courses, and other resources.
Forums for AoPS books, courses, and other resources.
3
VNew Topic
kLocked
AoPS Forums
Forums for AoPS books, courses, and other resources.
Forums for AoPS books, courses, and other resources.
3
VNew Topic
kLocked
Forums for AoPS books, courses, and other resources.
AoPS Online Classes
Questions and information about AoPS classes
Questions and information about AoPS classes
AoPS Books
Questions and information about AoPS books
Questions and information about AoPS books
Alcumus
The free AoPS online learning system
The free AoPS online learning system
For the Win! Problem Discussion
Discussion of problems found on For the Win!
Discussion of problems found on For the Win!
MATHCOUNTS Trainer
Discuss the AoPS MATHCOUNTS Trainer
Discuss the AoPS MATHCOUNTS Trainer
AoPS Videos
AoPS Videos from the AoPS Resources pages
AoPS Videos from the AoPS Resources pages
All Ten
Discussion of the All Ten game and its daily puzzles
Discussion of the All Ten game and its daily puzzles
Keep Learning
Resources for users at home during the COVID-19 crisis
Resources for users at home during the COVID-19 crisis
Graph Coloring
CrowdMath project forum
CrowdMath project forum
LaTeX and Asymptote
Mathematical typesetting with LaTeX and Asymptote
Mathematical typesetting with LaTeX and Asymptote
AoPS Blogs Discussions
Creating, using, and styling blogs on AoPS
Creating, using, and styling blogs on AoPS
AoPS Wiki Discussions
Content and operation of the AoPS Wiki
Content and operation of the AoPS Wiki
Test Forum
Test forum features here; all posts are temporary
Test forum features here; all posts are temporary
Contest Collections
Collections of competitions from around the world.
Collections of competitions from around the world.
3
VNew Topic
kLocked
Contest Collections
Collections of competitions from around the world.
Collections of competitions from around the world.
3
VNew Topic
kLocked
Collections of competitions from around the world.
International Contests
International competitions
International competitions
National and Regional Contests
National and regional competitions
National and regional competitions
Undergraduate Contests
Collegiate competitions
Collegiate competitions
National Olympiads
National math olympiads from around the world
National math olympiads from around the world
Team Selection Tests
IMO Team Selection Tests
IMO Team Selection Tests
Junior Olympiads
Junior olympiads from around the world
Junior olympiads from around the world
2025 Contests
Contests in the 2024-25 school year
Contests in the 2024-25 school year
2024 Contests
Contests in the 2023-24 school year
Contests in the 2023-24 school year
2023 Contests
Contests in the 2022-23 school year
Contests in the 2022-23 school year
2022 Contests
Contests in the 2021-22 school year
Contests in the 2021-22 school year
AoPS Yearly Contest Collections
2009 - 2025
2009 - 2025
New Post Collections
New contests and other new collections of posts
New contests and other new collections of posts
Contest Collections Discussion
For sets of contest problems to and requests for the Contest Collections
For sets of contest problems to and requests for the Contest Collections
Other Forums
Games, local and regional communities, and user-created forums.
Games, local and regional communities, and user-created forums.
3
VNew Topic
kLocked
M
Nothing matches your input.
Other Forums
Games, local and regional communities, and user-created forums.
Games, local and regional communities, and user-created forums.
3
VNew Topic
kLocked
M
Nothing matches your input.
Games, local and regional communities, and user-created forums.
Peer-to-Peer Programs
Schoolhouse.world, student-prepared handouts, and other peer-to-peer efforts
Schoolhouse.world, student-prepared handouts, and other peer-to-peer efforts
AoPS Mock Contests
A forum for posting, taking, and discussing contests created by AoPS users
A forum for posting, taking, and discussing contests created by AoPS users
USAMTS
The USA Mathematical Talent Search, a free math competition
The USA Mathematical Talent Search, a free math competition
ARML
The American Regions Mathematics League, a team math competition
The American Regions Mathematics League, a team math competition
HMMT
The Harvard-MIT Mathematics Tournament, a math meet in MA
The Harvard-MIT Mathematics Tournament, a math meet in MA
Physics
For topics in physics and discussion of physics competitions
For topics in physics and discussion of physics competitions
Princeton Math Competition
The Princeton Math Competition (PUMaC), a math meet in NJ
The Princeton Math Competition (PUMaC), a math meet in NJ
Math Prize for Girls
A math contest for girls in 11th grade or below (AMC 10/12 required to apply)
A math contest for girls in 11th grade or below (AMC 10/12 required to apply)
The Round Table
For serious discussions
For serious discussions
Purple Comet
A free online math meet for middle and high school students
A free online math meet for middle and high school students
Computer Science and Informatics
For topics in CS and informatics and discussion of CS competitions
For topics in CS and informatics and discussion of CS competitions
Chemistry
For topics in chemistry and discussion of chemistry competitions
For topics in chemistry and discussion of chemistry competitions
Biology
For topics in biology and discussion of biology competitions
For topics in biology and discussion of biology competitions
College
College admissions, preparing for college, etc.
College admissions, preparing for college, etc.
Ask the AoPS Community
General questions addressed to the community - for questions/comments that don't fit elsewhere.
General questions addressed to the community - for questions/comments that don't fit elsewhere.
Xarcade!⠀
Overload of games, and fun threads! Anyone can make threads! This forum is made for everyone! (Pronounced: Zar-Keid).
Overload of games, and fun threads! Anyone can make threads! This forum is made for everyone! (Pronounced: Zar-Keid).
The G@me of Life
Play, Chat, RP, and Explore!
Play, Chat, RP, and Explore!
Camp Half-Blood: the RPG
Here, you can roleplay a character in the setting of Camp Half-Blood!
Here, you can roleplay a character in the setting of Camp Half-Blood!
Boredom Buster!
Isn't it obvious? We bust your boredom!
Isn't it obvious? We bust your boredom!
The Eye of the Moonlark ©
This is just the calm before the storm~
This is just the calm before the storm~
Old High School Olympiads
Regional, National, and International Math Olympiads before 2001 mostly, recent years have been posted in order to make contest collections richer
Regional, National, and International Math Olympiads before 2001 mostly, recent years have been posted in order to make contest collections richer
The Clan Gathering
Live an adventurous wild cat life in The Clan Gathering!
Live an adventurous wild cat life in The Clan Gathering!
Ultim@te G@mes! ©
The greatest forum ever that now is dead. or is it really? come join to find out!
The greatest forum ever that now is dead. or is it really? come join to find out!
THE ULTIMATE GAME FORUM
Play games and have fun!
Play games and have fun!
The Unicorn-Burger F@ns!
Hi! i love burgers extra love for unicorns right in decripstion
Hi! i love burgers extra love for unicorns right in decripstion
The Mango Cult
A fun interactive forum with games, shops, chats, and more!
A fun interactive forum with games, shops, chats, and more!
The Hub!!!
Welcome to The Hub, your all-in-one community hub! We have games, an advertisement thread, and much more. Come join us!
Welcome to The Hub, your all-in-one community hub! We have games, an advertisement thread, and much more. Come join us!
The Problem Solving Warriors ©
Live the life of a warrior cat in a tropical rainforest sprinkled with magic!
Live the life of a warrior cat in a tropical rainforest sprinkled with magic!
Game Kingdom ©
Your forum for all games!
Your forum for all games!
Old Russian Math Olympiads
All Russian, Moscow, Tournament of Towns,...
All Russian, Moscow, Tournament of Towns,...
The Minecraft Forum 1832 SK
Calling all Minecraft Lovers! Please join this incredible forum! it is dying :(
Calling all Minecraft Lovers! Please join this incredible forum! it is dying :(
The Lost Cities!
Keeper of The Lost Cities roleplay and games!
Keeper of The Lost Cities roleplay and games!
Team Noodles and Fantastic Beasts forum!
Gaming, Harry Potter role-play, and discussion forum! Join the NOODLE community today!
Gaming, Harry Potter role-play, and discussion forum! Join the NOODLE community today!
The Cat Lovers Forum!
A forum for all cat lovers!
A forum for all cat lovers!
The Avatar Market ©
Making Your Avatars a Little Sweeter ✨
Making Your Avatars a Little Sweeter ✨
Starlight Haven Academy
Starlight Haven Academy is a RPG forum set in a prestigious high school high above the clouds, where exceptional students hone their talents and face unique challenges.
Starlight Haven Academy is a RPG forum set in a prestigious high school high above the clouds, where exceptional students hone their talents and face unique challenges.
✮⋆˙ Genesis Diary ᯓ★
Let your pen dance across the yellowed pages, the ebony ink splashing like waves...
Let your pen dance across the yellowed pages, the ebony ink splashing like waves...
⯎~Zodiax Academy~⯎
Greetings, since you have applied to our special Zodiax Academy, we will do our best to help you master your element!
Greetings, since you have applied to our special Zodiax Academy, we will do our best to help you master your element!
Music and Art
For discussions and questions related to music and other art
For discussions and questions related to music and other art
Swifter
This is for all Swifties! There will be Taylor Swift themed games, and more!!!
This is for all Swifties! There will be Taylor Swift themed games, and more!!!
The Animal Game Forum
The forum for all you animals!
The forum for all you animals!
Berkeley Math Tournament
The BMT, a math meet in CA for high school students and below
The BMT, a math meet in CA for high school students and below
。:+* K-POP WORLD *+:。
If you love K-Pop, come and join this fun forum! Create your own group, and idol!
If you love K-Pop, come and join this fun forum! Create your own group, and idol!
Demigod's Corner
This is a PJO fan forum. We have: A quest system, a storyline, RPGs, games, discussions, and you can RP as whoever youwant! A satyr, vampire, demigod, wheoever!
This is a PJO fan forum. We have: A quest system, a storyline, RPGs, games, discussions, and you can RP as whoever youwant! A satyr, vampire, demigod, wheoever!
India
For users from India and discussions related to India
For users from India and discussions related to India
RFR 2
Yup, RFR is back. This is a robot combat forum powered by AI battles.
Yup, RFR is back. This is a robot combat forum powered by AI battles.
How NOT to make a CHB forum*
*common mistakes i see everywhere
*common mistakes i see everywhere
versus
see for yourself ;)
see for yourself ;)
CMIMC
Forum for the Carnegie Mellon Informatics and Mathematics Competition, a math/CS contest held in Pittsburgh.
Forum for the Carnegie Mellon Informatics and Mathematics Competition, a math/CS contest held in Pittsburgh.
World of Cats ฅ ©
A place for everyone, like cat lovers and warriors roleplay!
A place for everyone, like cat lovers and warriors roleplay!
Special Collections
Collections of forums, tags, topics, and posts from the AoPS community.
Collections of forums, tags, topics, and posts from the AoPS community.
3
VNew Topic
kLocked
M
Nothing matches your input.
Special Collections
Collections of forums, tags, topics, and posts from the AoPS community.
Collections of forums, tags, topics, and posts from the AoPS community.
3
VNew Topic
kLocked
M
Nothing matches your input.
Collections of forums, tags, topics, and posts from the AoPS community.
Games Forums
FTW, Mafia, video games, etc.
FTW, Mafia, video games, etc.
Sciences
Chemistry, physics, biology, and other sciences.
Chemistry, physics, biology, and other sciences.
AoPS Olympiad & College Portal
Customized for Olympiad & College students
Customized for Olympiad & College students
Other Interests
Current events, music, arts, etc.
Current events, music, arts, etc.
Contest Forums
Forums for specific contests
Forums for specific contests
Summer Program Forums
Forums for specific summer programs
Forums for specific summer programs
Olympiad Classic View
High School Olympiads in the old AoPS style
High School Olympiads in the old AoPS style
College Classic View
College Math in the old AoPS style
College Math in the old AoPS style
Communities Around the World
Local and National Communities around the World
Local and National Communities around the World
New Forums
Public forums created in the last month
Public forums created in the last month
AoPS Blogroll
User-created blogs
User-created blogs
Other Collections
User-created collections.
User-created collections.
New Collections
New user-created collections.
New user-created collections.
After High School
Discussions about college and careers
Discussions about college and careers
Publications
Forums for specific books and journals
Forums for specific books and journals
Statistics:
Total posts: 24,453,571 | Total topics: 1,872,729 | Total members: 1,158,981