ka May Highlights and 2025 AoPS Online Class Information
jlacosta0
Thursday at 11:16 PM
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.
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
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
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
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
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
I have seen many posts talking about commonly asked questions, such as finding the value of ,,,, why or even expressions of those terms combined as if that would make them defined. I have made this post to answer these questions once and for all, and I politely ask everyone to link this post to threads that are talking about this issue.
[list]
[*]Firstly, the case of . It is usually regarded that , not because this works numerically but because it is convenient to define it this way. You will see the convenience of defining other undefined things later on in this post.
[*]What about ? The issue here is that isn't even rigorously defined in this expression. What exactly do we mean by ? Unless the example in question is put in context in a formal manner, then we say that is meaningless.
[*]What about ? Suppose that . Then we would have , absurd. A more rigorous treatment of the idea is that does not exist in the first place, although you will see why in a calculus course. So the point is that is undefined.
[*]What about if ? An article from brilliant has a good explanation. Alternatively, you can just use a geometric series. Notice that
[*]What about ? Usually this is considered to be an indeterminate form, but I would also wager that this is also undefined.
[/list]
Hopefully all of these issues and their corollaries are finally put to rest. Cheers.
2nd EDIT (6/14/22): Since I originally posted this, it has since blown up so I will try to add additional information per the request of users in the thread below.
INDETERMINATE VS UNDEFINED
What makes something indeterminate? As you can see above, there are many things that are indeterminate. While definitions might vary slightly, it is the consensus that the following definition holds: A mathematical expression is be said to be indeterminate if it is not definitively or precisely determined. So how does this make, say, something like indeterminate? In analysis (the theory behind calculus and beyond), limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits. However, if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then the expression is called an indeterminate form. For example, we could say that is an indeterminate form.
But we need to more specific, this is still ambiguous. An indeterminate form is a mathematical expression involving at most two of , or , obtained by applying the algebraic limit theorem (a theorem in analysis, look this up for details) in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity, and thus does not determine the limit being calculated. This is why it is called indeterminate. Some examples of indeterminate forms are etc etc. So what makes something undefined? In the broader scope, something being undefined refers to an expression which is not assigned an interpretation or a value. A function is said to be undefined for points outside its domain. For example, the function given by the mapping is undefined for . On the other hand, is undefined because dividing by is not defined in arithmetic by definition. In other words, something is undefined when it is not defined in some mathematical context.
WHEN THE WATERS GET MUDDIED
So with this notion of indeterminate and undefined, things get convoluted. First of all, just because something is indeterminate does not mean it is not undefined. For example is considered both indeterminate and undefined (but in the context of a limit then it is considered in indeterminate form). Additionally, this notion of something being undefined also means that we can define it in some way. To rephrase, this means that technically, we can make something that is undefined to something that is defined as long as we define it. I'll show you what I mean.
One example of making something undefined into something defined is the extended real number line, which we define as So instead of treating infinity as an idea, we define infinity (positively and negatively, mind you) as actual numbers in the reals. The advantage of doing this is for two reasons. The first is because we can turn this thing into a totally ordered set. Specifically, we can let for each which means that via this order topology each subset has an infimum and supremum and is therefore compact. While this is nice from an analytic standpoint, extending the reals in this way can allow for interesting arithmetic! In it is perfectly OK to say that, So addition, multiplication, and division are all defined nicely. However, notice that we have some indeterminate forms here which are also undefined, So while we define certain things, we also left others undefined/indeterminate in the process! However, in the context of measure theory it is common to define as greenturtle3141 noted below. I encourage to reread what he wrote, it's great stuff! As you may notice, though, dividing by is undefined still! Is there a place where it isn't? Kind of. To do this, we can extend the complex numbers! More formally, we can define this extension as which we call the Riemann Sphere (it actually forms a sphere, pretty cool right?). As a note, means complex infinity, since we are in the complex plane now. Here's the catch: division by is allowed here! In fact, we have where and are left undefined. We also have Furthermore, we actually have some nice properties with multiplication that we didn't have before. In it holds that but and are left as undefined (unless there is an explicit need to change that somehow). One could define the projectively extended reals as we did with , by defining them as They behave in a similar way to the Riemann Sphere, with division by also being allowed with the same indeterminate forms (in addition to some other ones).
Due to excessive spam and inappropriate posts, we have locked the Prealgebra and Beginning Algebra threads.
We will either unlock these threads once we've cleaned them up or start new ones, but for now, do not start new marathon threads for these subjects. Any new marathon threads started while this announcement is up will be immediately deleted.
ki Basic Forum Rules and Info (Read before posting)
jellymoop368
NMay 16, 2018
by harry1234
f(Reminder: Do not post Alcumus or class homework questions on this forum. Instructions below.)f
Welcome to the Middle School Math Forum! Please take a moment to familiarize yourself with the rules.
Overview:
[list]
[*] When you're posting a new topic with a math problem, give the topic a detailed title that includes the subject of the problem (not just "easy problem" or "nice problem")
[*] Stay on topic and be courteous.
[*] Hide solutions!
[*] If you see an inappropriate post in this forum, simply report the post and a moderator will deal with it. Don't make your own post telling people they're not following the rules - that usually just makes the issue worse.
[*] When you post a question that you need help solving, post what you've attempted so far and not just the question. We are here to learn from each other, not to do your homework. :P
[*] Avoid making posts just to thank someone - you can use the upvote function instead
[*] Don't make a new reply just to repeat yourself or comment on the quality of others' posts; instead, post when you have a new insight or question. You can also edit your post if it's the most recent and you want to add more information.
[*] Avoid bumping old posts.
[*] Use GameBot to post alcumus questions.
[*] If you need general MATHCOUNTS/math competition advice, check out the threads below.
[*] Don't post other users' real names.
[*] Advertisements are not allowed. You can advertise your forum on your profile with a link, on your blog, and on user-created forums that permit forum advertisements.
[/list]
As always, if you have any questions, you can PM me or any of the other Middle School Moderators. Once again, if you see spam, it would help a lot if you filed a report instead of responding :)
Marathons!
Relays might be a better way to describe it, but these threads definitely go the distance! One person starts off by posting a problem, and the next person comes up with a solution and a new problem for another user to solve. Here's some of the frequently active marathons running in this forum:
[list][*]Algebra
[*]Prealgebra
[*]Proofs
[*]Factoring
[*]Geometry
[*]Counting & Probability
[*]Number Theory[/list]
Some of these haven't received attention in a while, but these are the main ones for their respective subjects. Rather than starting a new marathon, please give the existing ones a shot first.
Hey AoPS,
Wow.
It's aready my 1000th post :)
Time flies...
Anw as usualllllll
Math Story!:
Kindergarden:
Me No remember :skull:
First grade:
My mom started making me do math worksheets. There was a bit of ... anger ... in the family if i messed up on them lol :)
Second grade:
Nothing rlly... Covid started at the end of my school year :(
Third grade:
Ohh the covid years
:sob:
Online classes were like POV: lemme turn video off and do whatevs the rest of the day
It was like teachers gotta teach -- nope!
I think I really got into math classes around here on online math.
Forth grade:
Back at school!
I don't mean to brag but a lot of people at school thought I was really smart :blush: but on AoPS... *cough* *cough*
Fifth grade:
NOW things get funnnnn
I took my first AMC8 -> 17 :)
I was happy...
yayyaya!
I made HR btw :)
6th grade:
I took the amc8 at my school on a digital computer...
I wanna cry -> Click to reveal hidden text
13 :sob: :sob: :sob:
7th grade (now):
AMC 8 -> I sold a 20 :(
AMC10 ->
IMPORTANT: RULE OF AOPS
EVERYONE HAS A 140 ON THE 10 AND 12 BESIDES YOU
-> *HIDES IN SHAME* Click to reveal hidden text
69 and 73.5
Mathcounts chapter -> 34 ...
...
lets not talk abt it :)
Ok that's it for me :)
Sry for not using hide tags...:)
~jkim
A store sells a strawberry flavoured candy for 1 dollar each. The store offers a promo where every 4 candy wrappers can be exchanged for one candy. If there is no limit to how many times you can exchange candy wrappers for candies, what is the maximum number of candies I can obtain with 100 dollars?
What's the chance that two AoPS accounts generate with the same icon?
Math-lover15
N2 hours ago
by Math-lover1
So I've been wondering how many possible "icons" can be generated when you first create an account. By "icon" I mean the stack of cubes as the first profile picture before changing it.
I don't know a lot about how AoPS icons generate, so I have a few questions:
- Do the colors on AoPS icons generate through a preset of colors or the RGB (red, green, blue in hexadecimal form) scale? If it generates through the RGB scale, then there may be greater than different icons.
- Do the arrangements of the stacks of blocks in the icon change with each account? If so, I think we can calculate this through considering each stack of blocks independently.
Math Problem I cant figure out how to do without bashing
equalsmc25
N2 hours ago
by nmlikesmath
Hi,
I cant figure out how to do these 2 problems without bashing. Do you guys have any ideas for an elegant solution? Thank you!
Prob 1.
An RSM sports field has a square shape. Poles with letters M, A, T, H are located at the corners of the square (see the diagram). During warm up, a student starts at any pole, runs to another pole along a side of the square or across the field along diagonal MT (only in the direction from M to T), then runs to another pole along a side of the square or along diagonal MT, and so on. The student cannot repeat a run along the same side/diagonal of the square in the same direction. For instance, she cannot run from M to A twice, but she can run from M to A and at some point from A to M. How many different ways are there to complete the warm up that includes all nine possible runs (see the diagram)? One possible way is M-A-T-H-M-H-T-A-M-T (picture attached)
Prob 2.
In the expression 5@5@5@5@5 you replace each of the four @ symbols with either +, or, or x, or . You can insert one or more pairs of parentheses to control the order of operations. Find the second least whole number that CANNOT be the value of the resulting expression. For example, each of the numbers 25=5+5+5+5+5 and 605+(5+5)×5+5 can be the value of the resulting expression.
Prob 3. (This isnt bashing I don't understand how to do it though)
Suppose BC = 3AB in rectangle ABCD. Points E and F are on side BC such that BE = EF = FC. Compute the sum of the degree measures of the four angles EAB, EAF, EAC, EAD.
P.S. These are from an RSM olympiad. The answers are
Note that this is in no way trying to slander people who qualified through states with lower cutoffs. It is to compare cutoffs from 2022-2025. Qualifying nationals in any state is an exceptional achievement.
All credit goes to @peace09 for compiling previous years.
Additionally, thanks to @ethan2011/@mathkiddus for the template.
Tier colors have been removed as per the nationals' server requests.
For those asking about the removal of the tiers, I'd like to quote Jason himself:
[quote=peace09]
learn from my mistakes
[/quote]
I'm in 7th grade and thought it would be good to start preparing for the AMC 10. I'm not extremely good at math though.
I feel that I am better at Mathcounts than AMC 8. I got a 41 on chapter and did not take state (I was sick), and a 20 on the AMC 8 this year. Are there any parts to AMC 8 and 10 that are special, or any strategies? What are some important topics I should study? Please comment below. Thanks! :D
I can sense that \frac{\sqrt{13}}{6} = \sqrt{(\frac{1}{2})^2+(\frac{1}{3})^2}.
For example, by setting the unit square into 2 by 3 (6 rectangles), if any of the two points are lying in the same smaller rectangle, we are done.
Sadly, pigeon principle does gives anything here so there should be a better way to count. Click to reveal hidden text
Why I STILL cannot pose LaTeX.
Well an archive here said that n = 6 was proved by Graham, but it is not a simple one at least in 1991.
https://archive.org/details/unsolvedproblems0000crof/page/108/mode/2up Click to reveal hidden text
New users cannot post link too.
This post has been edited 1 time. Last edited by Fishheadtailbody, Apr 18, 2025, 4:09 PM Reason: Added the archive.