Stay ahead of learning milestones! Enroll in a class over the summer!

G
Topic
First Poster
Last Poster
k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

Prealgebra 1
Tuesday, May 13 - Aug 26
Thursday, May 29 - Sep 11
Sunday, Jun 15 - Oct 12
Monday, Jun 30 - Oct 20
Wednesday, Jul 16 - Oct 29

Prealgebra 2 Self-Paced

Prealgebra 2
Wednesday, May 7 - Aug 20
Monday, Jun 2 - Sep 22
Sunday, Jun 29 - Oct 26
Friday, Jul 25 - Nov 21

Introduction to Algebra A Self-Paced

Introduction to Algebra A
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
Tuesday, Jul 15 - Oct 28

Introduction to Counting & Probability Self-Paced

Introduction to Counting & Probability
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19

Introduction to Number Theory
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30

Introduction to Algebra B Self-Paced

Introduction to Algebra B
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14

Introduction to Geometry
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19

Paradoxes and Infinity
Mon, Tue, Wed, & Thurs, Jul 14 - Jul 16 (meets every day of the week!)

Intermediate: Grades 8-12

Intermediate Algebra
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22

Intermediate Counting & Probability
Wednesday, May 21 - Sep 17
Sunday, Jun 22 - Nov 2

Intermediate Number Theory
Sunday, Jun 1 - Aug 24
Wednesday, Jun 18 - Sep 3

Precalculus
Friday, May 16 - Oct 24
Sunday, Jun 1 - Nov 9
Monday, Jun 30 - Dec 8

Advanced: Grades 9-12

Olympiad Geometry
Tuesday, Jun 10 - Aug 26

Calculus
Tuesday, May 27 - Nov 11
Wednesday, Jun 25 - Dec 17

Group Theory
Thursday, Jun 12 - Sep 11

Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

MATHCOUNTS/AMC 8 Advanced
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21

AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22

AMC 12 Final Fives
Sunday, May 18 - Jun 15

AIME Problem Series A
Thursday, May 22 - Jul 31

AIME Problem Series B
Sunday, Jun 22 - Sep 21

F=ma Problem Series
Wednesday, Jun 11 - Aug 27

WOOT Programs
Visit the pages linked for full schedule details for each of these programs!


MathWOOT Level 1
MathWOOT Level 2
ChemWOOT
CodeWOOT
PhysicsWOOT

Programming

Introduction to Programming with Python
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22

Intermediate Programming with Python
Sunday, Jun 1 - Aug 24
Monday, Jun 30 - Sep 22

USACO Bronze Problem Series
Tuesday, May 13 - Jul 29
Sunday, Jun 22 - Sep 1

Physics

Introduction to Physics
Wednesday, May 21 - Aug 6
Sunday, Jun 15 - Sep 14
Monday, Jun 23 - Sep 15

Physics 1: Mechanics
Thursday, May 22 - Oct 30
Monday, Jun 23 - Dec 15

Relativity
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)
0 replies
jlacosta
May 1, 2025
0 replies
k i Peer-to-Peer Programs Forum
jwelsh   157
N Dec 11, 2023 by cw357
Many of our AoPS Community members share their knowledge with their peers in a variety of ways, ranging from creating mock contests to creating real contests to writing handouts to hosting sessions as part of our partnership with schoolhouse.world.

To facilitate students in these efforts, we have created a new Peer-to-Peer Programs forum. With the creation of this forum, we are starting a new process for those of you who want to advertise your efforts. These advertisements and ensuing discussions have been cluttering up some of the forums that were meant for other purposes, so we’re gathering these topics in one place. This also allows students to find new peer-to-peer learning opportunities without having to poke around all the other forums.

To announce your program, or to invite others to work with you on it, here’s what to do:

1) Post a new topic in the Peer-to-Peer Programs forum. This will be the discussion thread for your program.

2) Post a single brief post in this thread that links the discussion thread of your program in the Peer-to-Peer Programs forum.

Please note that we’ll move or delete any future advertisement posts that are outside the Peer-to-Peer Programs forum, as well as any posts in this topic that are not brief announcements of new opportunities. In particular, this topic should not be used to discuss specific programs; those discussions should occur in topics in the Peer-to-Peer Programs forum.

Your post in this thread should have what you're sharing (class, session, tutoring, handout, math or coding game/other program) and a link to the thread in the Peer-to-Peer Programs forum, which should have more information (like where to find what you're sharing).
157 replies
jwelsh
Mar 15, 2021
cw357
Dec 11, 2023
k i C&P posting recs by mods
v_Enhance   0
Jun 12, 2020
The purpose of this post is to lay out a few suggestions about what kind of posts work well for the C&P forum. Except in a few cases these are mostly meant to be "suggestions based on historical trends" rather than firm hard rules; we may eventually replace this with an actual list of firm rules but that requires admin approval :) That said, if you post something in the "discouraged" category, you should not be totally surprised if it gets locked; they are discouraged exactly because past experience shows they tend to go badly.
-----------------------------
1. Program discussion: Allowed
If you have questions about specific camps or programs (e.g. which classes are good at X camp?), these questions fit well here. Many camps/programs have specific sub-forums too but we understand a lot of them are not active.
-----------------------------
2. Results discussion: Allowed
You can make threads about e.g. how you did on contests (including AMC), though on AMC day when there is a lot of discussion. Moderators and administrators may do a lot of thread-merging / forum-wrangling to keep things in one place.
-----------------------------
3. Reposting solutions or questions to past AMC/AIME/USAMO problems: Allowed
This forum contains a post for nearly every problem from AMC8, AMC10, AMC12, AIME, USAJMO, USAMO (and these links give you an index of all these posts). It is always permitted to post a full solution to any problem in its own thread (linked above), regardless of how old the problem is, and even if this solution is similar to one that has already been posted. We encourage this type of posting because it is helpful for the user to explain their solution in full to an audience, and for future users who want to see multiple approaches to a problem or even just the frequency distribution of common approaches. We do ask for some explanation; if you just post "the answer is (B); ez" then you are not adding anything useful.

You are also encouraged to post questions about a specific problem in the specific thread for that problem, or about previous user's solutions. It's almost always better to use the existing thread than to start a new one, to keep all the discussion in one place easily searchable for future visitors.
-----------------------------
4. Advice posts: Allowed, but read below first
You can use this forum to ask for advice about how to prepare for math competitions in general. But you should be aware that this question has been asked many many times. Before making a post, you are encouraged to look at the following:
[list]
[*] Stop looking for the right training: A generic post about advice that keeps getting stickied :)
[*] There is an enormous list of links on the Wiki of books / problems / etc for all levels.
[/list]
When you do post, we really encourage you to be as specific as possible in your question. Tell us about your background, what you've tried already, etc.

Actually, the absolute best way to get a helpful response is to take a few examples of problems that you tried to solve but couldn't, and explain what you tried on them / why you couldn't solve them. Here is a great example of a specific question.
-----------------------------
5. Publicity: use P2P forum instead
See https://artofproblemsolving.com/community/c5h2489297_peertopeer_programs_forum.
Some exceptions have been allowed in the past, but these require approval from administrators. (I am not totally sure what the criteria is. I am not an administrator.)
-----------------------------
6. Mock contests: use Mock Contests forum instead
Mock contests should be posted in the dedicated forum instead:
https://artofproblemsolving.com/community/c594864_aops_mock_contests
-----------------------------
7. AMC procedural questions: suggest to contact the AMC HQ instead
If you have a question like "how do I submit a change of venue form for the AIME" or "why is my name not on the qualifiers list even though I have a 300 index", you would be better off calling or emailing the AMC program to ask, they are the ones who can help you :)
-----------------------------
8. Discussion of random math problems: suggest to use MSM/HSM/HSO instead
If you are discussing a specific math problem that isn't from the AMC/AIME/USAMO, it's better to post these in Middle School Math, High School Math, High School Olympiads instead.
-----------------------------
9. Politics: suggest to use Round Table instead
There are important conversations to be had about things like gender diversity in math contests, etc., for sure. However, from experience we think that C&P is historically not a good place to have these conversations, as they go off the rails very quickly. We encourage you to use the Round Table instead, where it is much more clear that all posts need to be serious.
-----------------------------
10. MAA complaints: discouraged
We don't want to pretend that the MAA is perfect or that we agree with everything they do. However, we chose to discourage this sort of behavior because in practice most of the comments we see are not useful and some are frankly offensive.
[list] [*] If you just want to blow off steam, do it on your blog instead.
[*] When you have criticism, it should be reasoned, well-thought and constructive. What we mean by this is, for example, when the AOIME was announced, there was great outrage about potential cheating. Well, do you really think that this is something the organizers didn't think about too? Simply posting that "people will cheat and steal my USAMOO qualification, the MAA are idiots!" is not helpful as it is not bringing any new information to the table.
[*] Even if you do have reasoned, well-thought, constructive criticism, we think it is actually better to email it the MAA instead, rather than post it here. Experience shows that even polite, well-meaning suggestions posted in C&P are often derailed by less mature users who insist on complaining about everything.
[/list]
-----------------------------
11. Memes and joke posts: discouraged
It's fine to make jokes or lighthearted posts every so often. But it should be done with discretion. Ideally, jokes should be done within a longer post that has other content. For example, in my response to one user's question about olympiad combinatorics, I used a silly picture of Sogiita Gunha, but it was done within a context of a much longer post where it was meant to actually make a point.

On the other hand, there are many threads which consist largely of posts whose only content is an attached meme with the word "MAA" in it. When done in excess like this, the jokes reflect poorly on the community, so we explicitly discourage them.
-----------------------------
12. Questions that no one can answer: discouraged
Examples of this: "will MIT ask for AOIME scores?", "what will the AIME 2021 cutoffs be (asked in 2020)", etc. Basically, if you ask a question on this forum, it's better if the question is something that a user can plausibly answer :)
-----------------------------
13. Blind speculation: discouraged
Along these lines, if you do see a question that you don't have an answer to, we discourage "blindly guessing" as it leads to spreading of baseless rumors. For example, if you see some user posting "why are there fewer qualifiers than usual this year?", you should not reply "the MAA must have been worried about online cheating so they took fewer people!!". Was sich überhaupt sagen lässt, lässt sich klar sagen; und wovon man nicht reden kann, darüber muss man schweigen.
-----------------------------
14. Discussion of cheating: strongly discouraged
If you have evidence or reasonable suspicion of cheating, please report this to your Competition Manager or to the AMC HQ; these forums cannot help you.
Otherwise, please avoid public discussion of cheating. That is: no discussion of methods of cheating, no speculation about how cheating affects cutoffs, and so on --- it is not helpful to anyone, and it creates a sour atmosphere. A longer explanation is given in Seriously, please stop discussing how to cheat.
-----------------------------
15. Cutoff jokes: never allowed
Whenever the cutoffs for any major contest are released, it is very obvious when they are official. In the past, this has been achieved by the numbers being posted on the official AMC website (here) or through a post from the AMCDirector account.

You must never post fake cutoffs, even as a joke. You should also refrain from posting cutoffs that you've heard of via email, etc., because it is better to wait for the obvious official announcement. A longer explanation is given in A Treatise on Cutoff Trolling.
-----------------------------
16. Meanness: never allowed
Being mean is worse than being immature and unproductive. If another user does something which you think is inappropriate, use the Report button to bring the post to moderator attention, or if you really must reply, do so in a way that is tactful and constructive rather than inflammatory.
-----------------------------

Finally, we remind you all to sit back and enjoy the problems. :D

-----------------------------
(EDIT 2024-09-13: AoPS has asked to me to add the following item.)

Advertising paid program or service: never allowed

Per the AoPS Terms of Service (rule 5h), general advertisements are not allowed.

While we do allow advertisements of official contests (at the MAA and MATHCOUNTS level) and those run by college students with at least one successful year, any and all advertisements of a paid service or program is not allowed and will be deleted.
0 replies
v_Enhance
Jun 12, 2020
0 replies
k i Stop looking for the "right" training
v_Enhance   50
N Oct 16, 2017 by blawho12
Source: Contest advice
EDIT 2019-02-01: https://blog.evanchen.cc/2019/01/31/math-contest-platitudes-v3/ is the updated version of this.

EDIT 2021-06-09: see also https://web.evanchen.cc/faq-contest.html.

Original 2013 post
50 replies
v_Enhance
Feb 15, 2013
blawho12
Oct 16, 2017
Challenge: Make every number to 100 using 4 fours
CJB19   197
N 6 minutes ago by JohannIsBach
I've seen this attempted a lot but I want to see if the AoPS community can actually do it. Using ONLY 4 fours and math operations, make as many numbers as you can. Try to go in order. I'll start:
$$(4-4)*4*4=0$$$$4-4+4/4=1$$$$4/4+4/4=2$$$$(4+4+4)/4=3$$$$4+(4-4)*4=4$$$$4+4^{4-4}=5$$$$4!/4+4-4=6$$$$4+4-4/4=7$$$$4+4+4-4=8$$
197 replies
CJB19
May 15, 2025
JohannIsBach
6 minutes ago
9 Pythagorean Triples
ZMB038   4
N 30 minutes ago by sadas123
Please put some of the ones you know, and try not to troll/start flame wars! Thank you :D
4 replies
ZMB038
an hour ago
sadas123
30 minutes ago
Probability problem
CJB19   2
N 33 minutes ago by Yiyj
Me and my math teacher got different answers for this so I'm asking you all:

Clare has a spinner split into fourths and labeled A, B, C, and D so that there is a $\frac{1}{4}$ chance of it landing on each section. She plays a game where if you spin it and it lands on A, you win. However, if you don't land on A the first time, you can try again. What are the odds of winning? (You don't spin again if you land on A the first time)
2 replies
CJB19
an hour ago
Yiyj
33 minutes ago
2000th Post!
PikaPika999   47
N an hour ago by PikaPika999
1. How many ways can you arrange the letters in the word ALGEBRA such that no two identical letters are adjacent?

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

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

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

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

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

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

hopefully these problems weren't too easy lol

also,
Please tell me if any of these problems have any flaws! (also please put your answers in hide tags or quote tags)
47 replies
PikaPika999
Yesterday at 1:53 AM
PikaPika999
an hour ago
How you study effectively
FuturePanda   8
N May 4, 2025 by Konigsberg
Discuss how you study math below!

For example, for me, my goal is to make JMO and get at least 25+ on it (aka bronze/silver), and so far I am doing:
- 50% computational (ARML, HMMT, AMC 10 mocks, occasionally AIME problems(since I’ve done most of them already))
-50% Olympiad (OTIS)
8 replies
FuturePanda
May 3, 2025
Konigsberg
May 4, 2025
Olympiad Problems Correlation with Computational?
FuturePanda   8
N Apr 30, 2025 by deduck
Hi everyone,

Recently I;ve started doing a lot of nice combo/algebra Olympiad problems(JMO, PAGMO, CMO, etc.) and I’ve got to say, it’s been pretty fun(I’m enjoying it!). I was wondering if doing Olympiad problems also helps increase computational abilities slightly. Currently I am doing 75% computational, 25% oly but if anyone has any expreience I want to switch it to 25% computational and 75% Olympiad, though I still want to have computational skills for ARML, AIME, SMT, BMT, HMMT, etc.

If anyone has any experience, please let me know!

Thank you so much in advance!
8 replies
FuturePanda
Apr 26, 2025
deduck
Apr 30, 2025
Questions
FuturePanda   4
N Apr 16, 2025 by mathprodigy2011
Hi everyone,
I have 2 questions. Could anyone help me with them?
1. How do I get good at computational? I'm pretty good with AMC/AIME/BmMT, but I'm really bad at the subject tests in college competitions. (Last year 24th place general BMT). For example, I can solve around 8-12 AIME problems, but mocking a HMMT or SMT past test from 2024 gives me 3(which is probably top lik2 25% only). How do I improve my computational skills? I have OTIS, past tests, and lots of textbooks to use. What is the most efficient way to place top 50 at these competitions?

2. What is the ranking of college comps in terms of difficulty. My personal is:
BmMT < BMT< HMMT Nov < PUMAC < SMT < HMMT Feb

I just wanna know so I know which ones to mock first.

Thanks in advance!
4 replies
FuturePanda
Apr 14, 2025
mathprodigy2011
Apr 16, 2025
Unofficial HMMT feburary discussion thread
lovematch13   24
N Feb 22, 2025 by lovematch13
Idk, post your score distribution or something here, made this since I didn't see any such thread on AoPS yet.

Official results have not come out yet, but I got hold of a copy of the text file somehow.

Algebra: 11001 00000 (234th) - double silly
Geometry: 11100 00000 (358th) - bro really did not cook here :skull: spent way too long in p5 and missed the angle chase and config, and sillied #4 by multiplying the wrong lengths somehow.
Combo: 11110 11000 (18th) - wild rng. "C = A + G" - my friends

Team: hahaha i will not dox myself
24 replies
lovematch13
Feb 21, 2025
lovematch13
Feb 22, 2025
HMMT February 2025
maxamc   4
N Jan 30, 2025 by maxamc
Hi guys, for next month's HMMT competition, does any team in the Greater Boston Area need another team member? Please private message me. I moved from Washington state to the Boston area last December so I did not get a chance to join any team yet. Appreciate your help!
4 replies
maxamc
Jan 28, 2025
maxamc
Jan 30, 2025
Advice for after AIME (and possibly oly)
416554   14
N Dec 24, 2024 by MathRook7817
My index was a 191.5 through 10A+I, so 2.5 points away from the cutoff. 10B was pretty bad but I was sick that day.

I'd say I did fairly well on the 10A (121.5 with only 1 silly), but I did completely horrible on the AIME I.

TL;DR I have competition taking issues but my skill set in reach; should I continue practice with short-answer questions or olympiad training, given my goal next year is USAMO qual/USAJMO winner (depends on which one I qualify for).

I got stuck on P5 and P8, and I'd say I probably spent an hour on both total just because I let my ego get ahead of me (I wouldn't let myself "get defeated by a problem 8"). In the last 30 minutes I came up with a 2 minute solution for P5, and I spent like 45 minutes wondering why my logic for P8 was wrong; turns out, I got it right.

I sillied P7 because while going through the different cases I came up with possibilities modulo 60 but then forgot to include the modulo 6 and that it had to be distinct also.
I sillied P9, because I forgot that the polynomial could also be in the form $(x-2)^2(x-k)$. However, I remembered that $k \neq 2$.

I was halfway through P10 and then I just stopped doing it for some reason; I think it was because the numbers looked kinda big (1349 times 2023 iirc) and so I stopped, thinking it might get sorta bashy.
I saw P11 and immediately knew it was recursion, but at that point I had 5 minutes left in the test so made up a BS answer and went back to try to check P8.

Ended up only getting 1,2,3,4,5,6 and 8. However, after the contest, I was able to solve the first 12. This is pretty disappointing because I think my skill set is definitely within reach, even if my test-taking abilities are not (for reference, a similar experience of stress and sillies happened two years ago for me).

What are my next steps? Should I just continue practicing AIME qustions and choose harder ones closer to the end of the test (in practice I can usually solve P15 algebra though, but it's mostly geometry that screws me over), and mix that
with problems from HMMT, CMIMC, and PUMaC? Or is it better to just start studying for Olympiads, even if the questions are drastically different from short-answer contests? (I'd say I'm definitely ready for Olympiad level, and I'm in OTIS right now; but I'm not sure if this is the best way to go). My goal is USAMO qualification next year at the bare minimum, but I also want to be a USAJMO winner (which is pretty doable, considering that on a mock olympiad for OTIS I was able to solve all three problems). I probably will be able to spend ~10 hours a week, because I have other things to do too.

Additionally, how should I feel about not being able to qualify for JMO even as a freshmen? I felt like I was easily capable of doing so, but now I just don't really have anything that impressive; pretty much everyone who does competition math competitively enough from my school end up qualifying for JMO sophomore year, and now that's my only bet.
14 replies
416554
Mar 9, 2023
MathRook7817
Dec 24, 2024
HMMT top 50 November
CatDog76   7
N Dec 19, 2024 by KevinChen_Yay
For people who made HMMT top 50, or people who knew others that made top 50 in November, how good do you have to be?
7 replies
CatDog76
Dec 19, 2024
KevinChen_Yay
Dec 19, 2024
Question?
FuturePanda   4
N Dec 17, 2024 by lpieleanu
What other prestigious math competitions are there other than the AMCS’s? I would like redemption. I plan to go to:
HMMT Nov + Feb
PUMAC
SMT
BmMT
BMT
A bunch of random online contests

What other ones are there?

Thanks in advance! Here is my background:
Recently, in 7th grade, I got an 81 on 12A and 102 on 10B(missing AIME by 3). During the summer, I read the intro books and vol1/2 thoroughly and sped through the intermediate series(read thoroughly first few chapters, then sped through chapters 11-20, skipped linear algebra in precalc). After the test, I started reading Awesomemath Books and am planning to take Awesomemath Academy 3 in the spring. What should I do during winter break to get better and make JMO next year?

Should I reread the intermediate books’ again, revisiting the last chapters to improve my AMC score, or should I continue reading Awesomemath Books? Or is there something better for me to do?
4 replies
FuturePanda
Dec 14, 2024
lpieleanu
Dec 17, 2024
How do I prep for AIME?
williamxiao   16
N Nov 23, 2024 by xTimmyG
So, this year I really want to qualify for JMO (and my parents will be really mad if I don't). My AMC 10 scores were not that good (124.5 A, 133.5 B), so I'm probably going to need around an 11 on AIME to qualify. Problem is, I'm not sure how I should prep for the AIME right now. I want to save my mocks for later closer to the actual AIME date. Last year I mocked 9-11s but only got a 6 on the actual AIME because all the problems were bad geo (and some very specific poorly worded problems), which was my main weakness. Right now, I feel like my geo has improved a lot, and apart from that there aren't really any specific subjects I feel like I need to focus on. How should I practice? Should I try finding a subject to focus on, work on problems from other comps like HMMT, or smth else? Any help would be appreciated.
16 replies
williamxiao
Nov 20, 2024
xTimmyG
Nov 23, 2024
Competitions other than AMC PUMAC and HMMT?
ranand2009   6
N Nov 23, 2024 by exp-ipi-1
Missed reg dates for 2 and sold on AMC (only took A) and im in 10th. I'm actually cooked for math if I can't find other math comps to do.
6 replies
ranand2009
Nov 22, 2024
exp-ipi-1
Nov 23, 2024
easy olympiad problem
kjhgyuio   7
N Apr 23, 2025 by Charizard_637
Find all positive integer values of \( x \) such that
\[
\sqrt{x - 2011} + \sqrt{2011 - x} + 10
\]is an integer.
7 replies
kjhgyuio
Apr 17, 2025
Charizard_637
Apr 23, 2025
easy olympiad problem
G H J
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
kjhgyuio
69 posts
#1
Y by
Find all positive integer values of \( x \) such that
\[
\sqrt{x - 2011} + \sqrt{2011 - x} + 10
\]is an integer.
This post has been edited 2 times. Last edited by kjhgyuio, Apr 17, 2025, 2:01 PM
Reason: nil
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Mathdreams
1472 posts
#2
Y by
Solution
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Charizard_637
118 posts
#3
Y by
$x-2011$ and $2011-x$ are each other's negatives, and you can't take the square root of a negative number while having an integer solution. Therefore the only solution that would work is if they were both non-negative, and based on this they must be zero because one positive number will lead to one negative number. Since 0 is neither negative or positive it's what's under both square roots. Therefore, $\sqrt{x-2011} = 0$. Squaring both sides gives $x-2011 = 0$, hence $x = 2011$. This is the only solution.

Edit: I know it's verbose but it's an "olympiad problem"
This post has been edited 2 times. Last edited by Charizard_637, Apr 21, 2025, 5:44 PM
Reason: e
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
vincentwant
1426 posts
#4
Y by
Charizard_637 wrote:
$x-2011$ and $2011-x$ are each other's negatives, and you can't take the square root of a negative number while having an integer solution. Therefore the only solution that would work is if they were both non-negative, and based on this they must be zero because one positive number will lead to one negative number. Since 0 is neither negative or positive it's what's under both square roots. Therefore, $\sqrt{x-2011} = 0$. Squaring both sides gives $x-2011 = 0$, hence $x = 2011$. This is the only solution.

Edit: I know it's verbose but it's an olympiad problem

you dont have to do this, this is enough

Notice that for the expression to be real, $x-2011\geq0$ and $2011-x\geq 0$, otherwise the imaginary part of the expression would be positive. Thus no solutions other than $x=2011$ exist, and inspection gives that $x=2011$ works. Thus the answer is $x=2011$.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
deduck
238 posts
#5
Y by
this is a past amc8 problem
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Roger.Moore
5 posts
#6
Y by
The both the roots there are reals only if x=2011
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Maxklark
6 posts
#7
Y by
Click to reveal hidden text
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Charizard_637
118 posts
#8
Y by
deduck wrote:
this is a past amc8 problem

oh
my
:rotfl:
Z K Y
N Quick Reply
G
H
=
a