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

We have your learning goals covered with Spring and Summer courses available. Enroll today!
No tags match your search
M
G
Topic
First Poster
Last Poster
H
k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/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, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
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
Tuesday, Mar 25 - Jul 8
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
Sunday, Mar 23 - Jul 20
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
Sunday, Mar 16 - Jun 8
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
Monday, Mar 17 - Jun 9
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
Sunday, Mar 2 - Jun 22
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
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
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
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
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
Sunday, Mar 23 - Aug 3
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
Sunday, Mar 16 - Aug 24
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
Wednesday, Mar 5 - May 21
Tuesday, Jun 10 - Aug 26

Calculus
Sunday, Mar 30 - Oct 5
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
Sunday, Mar 23 - Jun 15
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
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23
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
Monday, Mar 24 - Jun 16
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
Sunday, Mar 30 - Jun 22
Wednesday, May 21 - Aug 6
Sunday, Jun 15 - Sep 14
Monday, Jun 23 - Sep 15

Physics 1: Mechanics
Tuesday, Mar 25 - Sep 2
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
Mar 2, 2025
0 replies
J
H
Amc10 prep question
Shadow6885   21
N 3 hours ago by Shadow6885
My question is how much of the geo and IA textbooks is relevant to AMC 10?
21 replies
Shadow6885
Mar 17, 2025
Shadow6885
3 hours ago
J
H
Water Watermelon
hwenterprise   9
N 3 hours ago by huajun78
A giant watermelon weighed 50 pounds and was 99 percent water. After sitting in the hot sun, some of the water evaporated so that the watermelon was only 98 percent water. What is the new weight of the watermelon?
9 replies
hwenterprise
Sep 18, 2005
huajun78
3 hours ago
J
H
Mathcounts STRATEGIES
Existing_Human1   28
N 3 hours ago by chesswillow
Hello commuinty!

I am wondering what your strategies are for mathcounts. Please note I do not mean tips. These can be for all rounds, but please specify. BTW, this is for state, but it can apply to any competition.

Ex:
Team - sit in a specific order
Target - do the easiest first
Sprint - go as fast as possible

I just made up the examples, and you will probably have better strategies, so if you want to help out, please do
28 replies
Existing_Human1
Mar 20, 2025
chesswillow
3 hours ago
J
H
MATHCOUNTS State Competition Thread
ilikemath247365   16
N 3 hours ago by jkim0656
I'll assume mathcounts state examination is over, but you can tell me to delete this post if I'm wrong:

$\begin{tabular}{c|c|c|c|c}Username & Grade & Score \\ \hline ilikemath247365 & 7 & 34 \\ \end{tabular}$
16 replies
ilikemath247365
5 hours ago
jkim0656
3 hours ago
J
H
USAMO question
bubby617   2
N 4 hours ago by Andyluo
if i had qualified for the usa(j)mo (i wish), would i have been flown out for free like mathcounts nationals or do you have to plan your own trip for going to the usamo
2 replies
bubby617
5 hours ago
Andyluo
4 hours ago
J
H
A hard inequality
JK1603JK   2
N 5 hours ago by sqing
Let a,b,c\ge 0: a+b+c=3. Prove \frac{1}{abc}+\frac{12}{a^2b+b^2c+c^2a}\ge 5.
2 replies
JK1603JK
6 hours ago
sqing
5 hours ago
J
H
Number theory question with many (confusing) variables
urfinalopp   2
N 5 hours ago by urfinalopp
Given m,n,p,q \in \mathbb{N+}, find all solutions to 2^{m}3^{n}+5^{p}=7^{q}$

One of the paths I've found is to boil it down to solving two non-simultaneous equations 2^{m_1}+5^{n_1}=7^{q_1} and
7^{m_1}+5^{n_1}=2^{q_1} but its too hard. Any other approaches/solutions or a continuation of this path?
2 replies
urfinalopp
Yesterday at 4:06 PM
urfinalopp
5 hours ago
J
H
Number theory national Olympiad
LoRD2022   2
N Today at 12:09 AM by alexheinis
Find all polynomials with integer coefficients such that, $a^2+b^2-c^2|P(a)+P(b)-P(c)$ for all $a,b,c \in mathbb{Z}$.
2 replies
LoRD2022
Yesterday at 8:54 PM
alexheinis
Today at 12:09 AM
J
H
Introduction & Intermediate C&P study guide!
HamstPan38825   25
N Yesterday at 11:47 PM by Andyluo
This took me quite a while to make, but enjoy!

Introduction to C&P (suitable for AMC 8, AMC 10/12)
Chapter 1 - This is like the "introduction", which is pretty easy and is not very important.
Chapter 2 - VERY important! Study this chapter closely, as it contains techniques that will be used again and again in harder problems.
Chapter 3 - Another quite important chapter, though not as important as chapter 2. This chapter covers some of the most confusing parts in C&P and even I can't distinguish that well in that chapter.
Chapter 4 - Interesting but very basic. Not that important, really.
Chapter 5 - Another interesting chapter, which should be studied in greater detail than Chapter 4. The distinguishability section is most important here.
Chapter 6 - Not much, but attempt the problems and read the examples since many of them are very interesting.
Chapter 7 - Pretty important chapter, make sure you read all the sections but not very interesting.
Chapter 8 - Another one of the VERY important sections - make sure read this section closely and do all the problems, since I still compare apples to oranges sometimes.
Chapter 9 - Interesting, but not very important. More important is the concept to "Think About It!"
Chapter 10 - The only topic in the entire C&P series that covers Geometric Probability, this chapter doesn't go into enough detail. Read it closely to get the basics, but I'd recommend doing more practice on Geometric Probability (I'll be making a handout!)
Chapter 11 - This chapter is not really important, reference the section in Intermediate C&P for a deeper understanding of Expected value.
Chapter 12 - Pretty important chapter, study it closely as it gives you the tools to prove combinatorial identities and Pascal's triangle is quite useful.
Chapter 13 - Just get the Hockey Stick Identity - not very useful chapter. Distributions will also be covered in Intermediate C&P.
Chapter 14 - A bit important, but not very - The binomial theorem is easy to master, but if you need more practice read the section in IA.
Chapter 15 - Similar to chapter 6, read all the examples and attempt all the problems here.

AMC 10/12 Chapters: 2, 3, 5, 6, 7, 8, 10, 12, 15

Intermediate C&P Suitable for late AMC 12, AIME + olympiads
Chapter 1 - Review this section thoroughly though there are no exercises here.
Chapter 2 - If you've learned set theory before, this chapter should be a review, but nonetheless skim over this chapter.
Chapter 3 - ANOTHER IMPORTANT CHAPTER! PIE is very important and might be a bit complicated, so study this chapter closely.
Chapter 4 - This chapter is also quite important - Make sure you master both parts of this chapter.
Chapter 5 - A good chapter, but it's a bit too short for my liking. Read extra handouts on the Pigeonhole Principle.
Chapter 6 - Another great chapter - attempt all the problems in this chapter!
Chapter 7 - Yet another very important chapter - distributions tend to pop up all over the place. Attempt all the problems here.
Chapter 8 - This isn't really a chapter - if you've mastered Mathematical Induction, you can just skip this but I recommend doing the problems.
Chapter 9 - This is really just the introduction to Chapter 10, but nonetheless do some of the problems to get a firm recursion basis.
Chapter 10 - Another VERY IMPORTANT CHAPTER! The recursion section is more important than the Catalan Number section unless you're preparing for olympiads.
Chapter 11 - Past this chapter, the concepts start to get quite advanced. This is an interesting chapter and is quite important, so do many of the problems here.
Chapter 12 - A great chapter! This chapter is quite general, but try to learn how to prove combinatorial identities on your own.
Chapter 13 - A quite complex chapter, not that important unless you're preparing for olympiads.
Chapter 14 - A hard but great chapter! GFs are hacks to many common counting problems.
Chapter 15 - Just skip this chapter unless you're doing the Putnam or olympiads, since it's basically nonexistent in the AMC/AIMEs.
Chapter 16 - Many of the problems here are very hard, but do as much as you can here! Try to attempt every single problem though they are very hard.

AMC 12 chapters: 1, 3, 4, 5, 6, 7, 9, 10
AIME chapters: 1, 3, 4, 5, 6, 7, 9, 10, 11
Olympiad chapters: 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15 [basically almost all of them rip]
25 replies
HamstPan38825
Dec 7, 2020
Andyluo
Yesterday at 11:47 PM
J
H
Number theory national Olympiad
LoRD2022   0
Yesterday at 9:09 PM
Find all polynomials with integer coefficients such that, $a^2+b^2-c^2|P(a)+P(b)-P(c)$ for all $a,b,c \in \mathbb{Z}$.
0 replies
LoRD2022
Yesterday at 9:09 PM
0 replies
J
H
area chasing, square, rhombus, symmetric (2018 Romanian NMO VII P2)
parmenides51   1
N Yesterday at 8:41 PM by vanstraelen
In the square $ABCD$ the point $E$ is located on the side $[AB]$, and $F$ is the foot of the perpendicular from $B$ on the line $DE$. The point $L$ belongs to the line $DE$, such that $F$ is between $E$ and $L$, and $FL = BF$. $N$ and $P$ are symmetric of the points $A , F$ with respect to the lines $DE, BL$, respectively. Prove that:

a) The quadrilateral $BFLP$ is square and the quadrilateral $ALND$ is rhombus.
b) The area of the rhombus $ALND$ is equal to the difference between the areas of the squares $ABCD$ and $BFLP$.
1 reply
parmenides51
Jun 3, 2020
vanstraelen
Yesterday at 8:41 PM
J
H
FB = BK , circumcircle and altitude related (In the World of Mathematics 516)
parmenides51   4
N Yesterday at 5:49 PM by Nioronean
Let $BT$ be the altitude and $H$ be the intersection point of the altitudes of triangle $ABC$. Point $N$ is symmetric to $H$ with respect to $BC$. The circumcircle of triangle $ATN$ intersects $BC$ at points $F$ and $K$. Prove that $FB = BK$.

(V. Starodub, Kyiv)
4 replies
parmenides51
Apr 19, 2020
Nioronean
Yesterday at 5:49 PM
J
H
Inequalities
sqing   3
N Yesterday at 4:13 PM by sqing
Let $ a,b> 0$ and $ a+b=1 . $ Prove that
$$ \frac{1}{a}+\frac{1}{b}\geq \frac{4+\frac{k}{4096}}{1+ ka^7b^7}$$Where $\frac{8192}{3}\geq k>0 .$
$$ \frac{1}{a}+\frac{1}{b}\geq \frac{\frac{14}{3}}{1+ \frac{8192}{3}a^7b^7}$$
3 replies
sqing
Yesterday at 3:14 PM
sqing
Yesterday at 4:13 PM
J
H
Inequalities from SXTX
sqing   11
N Yesterday at 3:47 PM by byron-aj-tom
T702. Let $ a,b,c>0 $ and $ a+2b+3c=\sqrt{13}. $ Prove that $$ \sqrt{a^2+1} +2\sqrt{b^2+1} +3\sqrt{c^2+1} \geq 7$$S
T703. Let $ a,b $ be real numbers such that $ a+b\neq 0. $. Find the minimum of $ a^2+b^2+(\frac{1-ab}{a+b} )^2.$
T704. Let $ a,b,c>0 $ and $ a+b+c=3. $ Prove that $$ \frac{a^2+7}{(c+a)(a+b)} + \frac{b^2+7}{(a+b)(b+c)} +\frac{c^2+7}{(b+c)(c+a)} \geq 6$$S
11 replies
sqing
Feb 18, 2025
byron-aj-tom
Yesterday at 3:47 PM
J
H
J
H
Good Mocks for STate
Existing_Human1   4
N 3 hours ago by huajun78
Hello Community!

I am wondering what are the best mocks for state, with solutions
4 replies
Existing_Human1
Friday at 11:52 PM
huajun78
3 hours ago
J
Good Mocks for STate
G H J
Reveal topic tags
L
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Existing_Human1
187 posts
Existing_Human1
#1 h  Friday at 11:52 PM
Y by
Hello Community!

I am wondering what are the best mocks for state, with solutions
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
giratina3
445 posts
giratina3
#2 h  Yesterday at 4:26 AM
Y by
Existing_Human1 wrote:
Hello Community!

I am wondering what are the best mocks for state, with solutions

There's always Math with Ms. Lin for past problems, and you can always go to the AoPS search bar and search up "Mathcounts State Mock Contests". You can also go to the AoPS Mock Contests forum to check out some Mathcounts mocks. In my opinion, I would say grinding past problems is better than doing mocks. But that's just me :play_ball:
This post has been edited 2 times. Last edited by giratina3, Yesterday at 4:26 AM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Leeoz
146 posts
Leeoz
#3 h  Yesterday at 4:51 PM
Y by
Existing_Human1 wrote:
Hello Community!

I am wondering what are the best mocks for state, with solutions

there are no "best" mocks, but if you want to find some mock contests, this is the forum: mock contests
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
ChaitraliKA
973 posts
ChaitraliKA
#4 h  Today at 1:01 AM
Y by
Try the Outside the Box mathcounts series trust
Sprint
Target

You can find many other mathcounts mocks on mathdash too
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
huajun78
30 posts
huajun78
#5 h  3 hours ago
Y by
Existing_Human1 wrote:
Hello Community!

I am wondering what are the best mocks for state, with solutions

If you google a year + mathcounts state sprint/target problems there will usually be a link to the pdf and you can download and print the questions.

Search up year + mathcounts state solutions to get the solutions pdf.
Z K Y
N Quick Reply
G
H
=
a