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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.

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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]
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0 replies
jlacosta
Mar 2, 2025
0 replies
J
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k i A Letter to MSM
Arr0w   23
N Sep 19, 2022 by scannose
Greetings.

I have seen many posts talking about commonly asked questions, such as finding the value of $0^0$, $\frac{1}{0}$,$\frac{0}{0}$, $\frac{\infty}{\infty}$, why $0.999...=1$ 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 $0^0$. It is usually regarded that $0^0=1$, 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 $\frac{\infty}{\infty}$? The issue here is that $\infty$ isn't even rigorously defined in this expression. What exactly do we mean by $\infty$? Unless the example in question is put in context in a formal manner, then we say that $\frac{\infty}{\infty}$ is meaningless.

[*]What about $\frac{1}{0}$? Suppose that $x=\frac{1}{0}$. Then we would have $x\cdot 0=0=1$, absurd. A more rigorous treatment of the idea is that $\lim_{x\to0}\frac{1}{x}$ does not exist in the first place, although you will see why in a calculus course. So the point is that $\frac{1}{0}$ is undefined.

[*]What about if $0.99999...=1$? An article from brilliant has a good explanation. Alternatively, you can just use a geometric series. Notice that
\begin{align*} \sum_{n=1}^{\infty} \frac{9}{10^n}&=9\sum_{n=1}^{\infty}\frac{1}{10^n}=9\sum_{n=1}^{\infty}\biggr(\frac{1}{10}\biggr)^n=9\biggr(\frac{\frac{1}{10}}{1-\frac{1}{10}}\biggr)=9\biggr(\frac{\frac{1}{10}}{\frac{9}{10}}\biggr)=9\biggr(\frac{1}{9}\biggr)=\boxed{1} \end{align*}
[*]What about $\frac{0}{0}$? 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 $0/0$ 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 $0/0$ 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 $0$, $1$ or $\infty$, 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
\[0/0, \infty/\infty, \infty-\infty, \infty \times 0\]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 $f:\mathbb{R}^{+}\cup\{0\}\rightarrow\mathbb{R}$ given by the mapping $x\mapsto \sqrt{x}$ is undefined for $x<0$. On the other hand, $1/0$ is undefined because dividing by $0$ 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 $0/0$ 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
\[\overline{\mathbb{R}}=\mathbb{R}\cup \{-\infty,+\infty\}.\]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 $-\infty\le a\le \infty$ for each $a\in\overline{\mathbb{R}}$ which means that via this order topology each subset has an infimum and supremum and $\overline{\mathbb{R}}$ is therefore compact. While this is nice from an analytic standpoint, extending the reals in this way can allow for interesting arithmetic! In $\overline{\mathbb{R}}$ it is perfectly OK to say that,
\begin{align*} a + \infty = \infty + a & = \infty, & a & \neq -\infty \\ a - \infty = -\infty + a & = -\infty, & a & \neq \infty \\ a \cdot (\pm\infty) = \pm\infty \cdot a & = \pm\infty, & a & \in (0, +\infty] \\ a \cdot (\pm\infty) = \pm\infty \cdot a & = \mp\infty, & a & \in [-\infty, 0) \\ \frac{a}{\pm\infty} & = 0, & a & \in \mathbb{R} \\ \frac{\pm\infty}{a} & = \pm\infty, & a & \in (0, +\infty) \\ \frac{\pm\infty}{a} & = \mp\infty, & a & \in (-\infty, 0). \end{align*}So addition, multiplication, and division are all defined nicely. However, notice that we have some indeterminate forms here which are also undefined,
\[\infty-\infty,\frac{\pm\infty}{\pm\infty},\frac{\pm\infty}{0},0\cdot \pm\infty.\]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 $\infty \times 0=0$ as greenturtle3141 noted below. I encourage to reread what he wrote, it's great stuff! As you may notice, though, dividing by $0$ 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
\[\mathbb{C}^*=\mathbb{C}\cup\{\tilde{\infty}\}\]which we call the Riemann Sphere (it actually forms a sphere, pretty cool right?). As a note, $\tilde{\infty}$ means complex infinity, since we are in the complex plane now. Here's the catch: division by $0$ is allowed here! In fact, we have
\[\frac{z}{0}=\tilde{\infty},\frac{z}{\tilde{\infty}}=0.\]where $\tilde{\infty}/\tilde{\infty}$ and $0/0$ are left undefined. We also have
\begin{align*} z+\tilde{\infty}=\tilde{\infty}, \forall z\ne -\infty\\ z\times \tilde{\infty}=\tilde{\infty}, \forall z\ne 0 \end{align*}Furthermore, we actually have some nice properties with multiplication that we didn't have before. In $\mathbb{C}^*$ it holds that
\[\tilde{\infty}\times \tilde{\infty}=\tilde{\infty}\]but $\tilde{\infty}-\tilde{\infty}$ and $0\times \tilde{\infty}$ 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 $\mathbb{C}^*$, by defining them as
\[{\widehat {\mathbb {R} }}=\mathbb {R} \cup \{\infty \}.\]They behave in a similar way to the Riemann Sphere, with division by $0$ also being allowed with the same indeterminate forms (in addition to some other ones).
23 replies
Arr0w
Feb 11, 2022
scannose
Sep 19, 2022
J
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k i Marathon Threads
LauraZed   0
Jul 2, 2019
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.
0 replies
LauraZed
Jul 2, 2019
0 replies
J
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k i Basic Forum Rules and Info (Read before posting)
jellymoop   368
N May 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]

Here are links to more detailed versions of the rules. These are from the older forums, so you can overlook "Classroom math/Competition math only" instructions.
Posting Guidelines
Update on Basic Forum Rules
What belongs on this forum?
How do I write a thorough solution?
How do I get a problem on the contest page?
How do I study for mathcounts?
Mathcounts FAQ and resources
Mathcounts and how to learn

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.

You can also view marathons via the Marathon tag.

Think this list is incomplete or needs changes? Let the mods know and we'll take a look.
368 replies
jellymoop
May 8, 2015
harry1234
May 16, 2018
J
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Mathcounts STRATEGIES
Existing_Human1   10
N 9 minutes ago by jb2015007
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
10 replies
+1 w
Existing_Human1
Yesterday at 7:27 PM
jb2015007
9 minutes ago
J
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Factoring Marathon
pican   1430
N an hour ago by Cerberusman
Hello guys,
I think we should start a factoring marathon. Post your solutions like this SWhatever, and your problems like this PWhatever. Please make your own problems, and I'll start off simple: P1
1430 replies
pican
Aug 4, 2015
Cerberusman
an hour ago
J
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How important is math "intuition"
Dream9   14
N an hour ago by BananaBall00
When I see problems now, they usually fall under 3 categories: easy, annoying, and cannot solve. Over time, more problems become easy, but I don't think I'm learning anything "new" so is higher level math like AMC 10 more about practice, so you know what to do when you see a problem? Of course, there's formulas for some problems but when reading a lot of solutions I didn't see many weird formulas being used and it was just the way to solve the problem was "odd".
14 replies
Dream9
Wednesday at 2:16 PM
BananaBall00
an hour ago
J
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a problem
Bummer12345   6
N 3 hours ago by Bummer12345
Alice and Bob play a game where Alice starts with $3$ MathJuice bottles and Bob starts with $2$ MathJuice bottles. An unfair coin is then flipped, with probability $\frac{2}{3}$ of landing heads. If the coin lands heads, Alice gives Bob a bottle; otherwise, Bob gives Alice a bottle. This process repeats until someone runs out of bottles.

(a): What is the probability that Bob will lose all of his bottles before Alice does?
(b): What is the expected number of times the coin has been flipped by the time the game ends?

Source: Own
6 replies
Bummer12345
Wednesday at 8:00 PM
Bummer12345
3 hours ago
J
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Does Beast Academy Fully Cover Common Core?
markonthird   3
N 4 hours ago by Andyluo
I was thinking about switching my son to the Beast Academy books but there aren't many reviews of this book series and it is relatively new. Do you happen to know if there are any reviews of the Beast Academy books from highly reputable sources? I am going to use the Beast Academy books as a supplemental but I was thinking about using them as the primary math books.

About how well does Beast Academy cover common core? Does it cover it very thoroughly?

Background: My son is an advanced math learner. I want him to do AMC 8. I am teaching him with Into Math by HMH--he will be done with its 4th grade book at the end of this summer, I estimate. He is currently in 1st grade. At his school, he is in their 2nd/3rd grade math class. Into Math by HMH follows common core closely and he is doing well with it, so I'm hesitant to change. Into Math is also a well-reviewed book series.


3 replies
+1 w
markonthird
4 hours ago
Andyluo
4 hours ago
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MATHCOUNTS on ESPN
rrusczyk   21
N 5 hours ago by MathRook7817
ESPN noon EST - the Countdown round of Nationals.

(Disclaimer: yours truly is an 'analyst' for the broadcast.)
21 replies
rrusczyk
May 27, 2003
MathRook7817
5 hours ago
J
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Angle problem
FlyingDragon21   24
N 5 hours ago by FlyingDragon21
In Isosceles triangle ABC where AB equals AC and point D lies on line AB, line CD splits line AB so that AD equals BC. If angle BAC is 20 degrees, what is the measure of angle DCA?
24 replies
FlyingDragon21
Mar 18, 2025
FlyingDragon21
5 hours ago
J
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Combi counting
Caasi_Gnow   1
N Yesterday at 7:27 PM by franklin2013
Find the number of different ways to arrange seven people around a circular meeting table if A and B must sit together and C and D cannot sit next to each other. (Note: the order for A and B might be A,B or B,A)
1 reply
Caasi_Gnow
Yesterday at 7:39 AM
franklin2013
Yesterday at 7:27 PM
J
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Mathcounts Challenge: Area and Perimeter
Syntax Error   20
N Yesterday at 6:25 PM by mathelvin
If the perimeter of an isosceles triangle is 36cm and the altitude to its base is 12cm, what is the area, in square centimeters, of the triangle?


this was a countdown round, so do it fast
20 replies
Syntax Error
Sep 9, 2003
mathelvin
Yesterday at 6:25 PM
J
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Tangent Spheres in a plane
ReticulatedPython   13
N Yesterday at 6:02 PM by ChaitraliKA
Three mutually tangent spheres with radius $6$ rest on a plane. A sphere with radius $10$ is tangent to all of them, but does not intersect nor lie on the plane. A sphere with radius $r$ lies on the plane, and is tangent to all three spheres with radius $6.$ Compute the shortest distance between the sphere with radius $r$ and the sphere with radius $10.$

Source: Own
13 replies
ReticulatedPython
Wednesday at 9:44 PM
ChaitraliKA
Yesterday at 6:02 PM
J
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state mathcounts colorado
aoh11   55
N Yesterday at 2:35 PM by Nioronean
I have state mathcounts tomorrow. What should I do to get prepared btw, and what are some tips for doing sprint and cdr?
55 replies
aoh11
Mar 15, 2025
Nioronean
Yesterday at 2:35 PM
J
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Why was this poll blocked
jkim0656   10
N Yesterday at 2:16 PM by iwastedmyusername
Hey AoPS ppl!
I made a poll about Pi vs Tau over here:
https://artofproblemsolving.com/community/c3h3527460
But after a few days it got blocked but i don't get why?
how is this harmful or different from other polls?
It really wasn't that harmful or popular i got to say tho... :noo:
10 replies
jkim0656
Mar 18, 2025
iwastedmyusername
Yesterday at 2:16 PM
J
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Amc10 prep question
Shadow6885   20
N Yesterday at 1:57 PM by hashbrown2009
My question is how much of the geo and IA textbooks is relevant to AMC 10?
20 replies
Shadow6885
Mar 17, 2025
hashbrown2009
Yesterday at 1:57 PM
J
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quadratics
luciazhu1105   17
N Yesterday at 1:55 PM by Charizard_637
I really need help on quadratics and I don't know why I also kinda need a bit of help on graphing functions and finding the domain and range of them.
17 replies
luciazhu1105
Feb 14, 2025
Charizard_637
Yesterday at 1:55 PM
J
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J
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Amc10 prep question
Shadow6885   20
N Yesterday at 1:57 PM by hashbrown2009
My question is how much of the geo and IA textbooks is relevant to AMC 10?
20 replies
Shadow6885
Mar 17, 2025
hashbrown2009
Yesterday at 1:57 PM
J
Amc10 prep question
G H J
Reveal topic tags
AMC 10
AMC
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G H BBookmark kLocked kLocked NReply
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Shadow6885
2402 posts
Shadow6885
#1 h  Mar 17, 2025, 6:20 AM
Y by
My question is how much of the geo and IA textbooks is relevant to AMC 10?
Z K Y
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sadas123
1063 posts
sadas123
#2 h  Mar 17, 2025, 3:24 PM
Y by
Shadow6885 wrote:
My question is how much of the geo and IA textbooks is relevant to AMC 10?

Those are the book I already bought lol. Geo is perfect for AMC 10 and IA is also pretty good.
This post has been edited 1 time. Last edited by sadas123, Mar 17, 2025, 3:35 PM
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krish6_9
18 posts
krish6_9
#3 h  Mar 17, 2025, 3:32 PM
Y by
i finished these books at 2 months old (jk ofc, i am still working on chapter 4 of geo and just started int alg). however, i think most of the int alg is too hard for amc 8 but will probably be helpful for amc 10
This post has been edited 1 time. Last edited by krish6_9, Mar 17, 2025, 3:32 PM
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sadas123
1063 posts
sadas123
#4 h  Mar 17, 2025, 3:40 PM
Y by
I would say to skip Algebra and Number Theory and just straight dive into Geo and C and P, after that go to Inter Alg and Inter c and P then move onto to pre calc and if you want calc
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Shadow6885
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#5 h  Mar 17, 2025, 11:52 PM
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Sorry I phrased the question wrong, up to what chapter is the content relevant
This post has been edited 1 time. Last edited by Shadow6885, Mar 17, 2025, 11:53 PM
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sadas123
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sadas123
#6 h  Mar 17, 2025, 11:58 PM
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Shadow6885 wrote:
Sorry I phrased the question wrong, up to what chapter is the content relevant

oh lol.... I think honestly just the whole book because each chapter matters except the boring introductions skip those :)
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#7 h  Mar 18, 2025, 12:00 AM
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sadas123 wrote:
Shadow6885 wrote:
Sorry I phrased the question wrong, up to what chapter is the content relevant

oh lol.... I think honestly just the whole book because each chapter matters except the boring introductions skip those :)

Geo or IA?
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sadas123
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sadas123
#8 h  Mar 18, 2025, 12:01 AM
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Shadow6885 wrote:
sadas123 wrote:
Shadow6885 wrote:
Sorry I phrased the question wrong, up to what chapter is the content relevant

oh lol.... I think honestly just the whole book because each chapter matters except the boring introductions skip those :)

Geo or IA?

I am not sure
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Shadow6885
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#9 h  Mar 18, 2025, 12:04 AM
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Srry lemme rephrase this: should I do all of geo, all of IA, or all of both (if I don’t do all of one book, what chapter should I go to?)
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EaZ_Shadow
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EaZ_Shadow
#10 h  Mar 18, 2025, 12:05 AM
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Shadow6885 wrote:
Srry lemme rephrase this: should I do all of geo, all of IA, or all of both (if I don’t do all of one book, what chapter should I go to?)

All of both
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Shadow6885
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#11 h  Mar 18, 2025, 12:06 AM
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EaZ_Shadow wrote:
Shadow6885 wrote:
Srry lemme rephrase this: should I do all of geo, all of IA, or all of both (if I don’t do all of one book, what chapter should I go to?)

All of both

Ok thx
Edit: wait I’ve never seen complex numbers on amc 10, why would I do that
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sadas123
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sadas123
#12 h  Mar 18, 2025, 12:08 AM
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Shadow6885 wrote:
EaZ_Shadow wrote:
Shadow6885 wrote:
Srry lemme rephrase this: should I do all of geo, all of IA, or all of both (if I don’t do all of one book, what chapter should I go to?)

All of both

Ok thx
Edit: wait I’ve never seen complex numbers on amc 10, why would I do that

I mean if you want to make AIME then I guess you have to study complex numbers because it is on there all the time for AIME but it might be on AMC 10 it depends I would recommend to do what you are weak at first then move up to the easier topics you know already.
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#13 h  Mar 18, 2025, 12:09 AM
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@bove k that makes more sense
I wanna qual for AIME but 0% chance I jmo qual
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RandomMathGuy500
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RandomMathGuy500
#14 h  Mar 18, 2025, 12:09 AM
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For AIME you should def know IA including complex numbers
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EaZ_Shadow
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#15 h  Mar 18, 2025, 10:43 PM
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Shadow6885 wrote:
EaZ_Shadow wrote:
Shadow6885 wrote:
Srry lemme rephrase this: should I do all of geo, all of IA, or all of both (if I don’t do all of one book, what chapter should I go to?)

All of both

Ok thx
Edit: wait I’ve never seen complex numbers on amc 10, why would I do that

Bc its on aime+ you use it (might) on amc 10 to make solving a problem easier
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Shadow6885
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#16 h  Mar 18, 2025, 11:52 PM
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@bove k I see
I'm prob not going to try on AIME, I just started IA so I prob won't be ready by then
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iwastedmyusername
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iwastedmyusername
#17 h  Mar 18, 2025, 11:54 PM
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why not
aime is in a year you have more than enough time to prepare
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Shadow6885
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#18 h  Mar 18, 2025, 11:58 PM
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iwastedmyusername wrote:
why not
aime is in a year you have more than enough time to prepare

IA is fairly long, and I'll need to do most of precalc, Inter CP and probably Inter NT
I'll take it, but I won't worry about it much
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yegorovm
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yegorovm
#19 h  Mar 19, 2025, 12:02 AM
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Personally I recommend taking Inter CP and NT later. And no matter what it doesn't stop you form actually taking the competition.
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Shadow6885
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#20 h  Mar 19, 2025, 12:05 AM
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yegorovm wrote:
Personally I recommend taking Inter CP and NT later. And no matter what it doesn't stop you form actually taking the competition.

Ye I'll take it but not put 100% effort into it
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hashbrown2009
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hashbrown2009
#21 h  Yesterday at 1:57 PM
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Introduction to Geometry is actually pretty hard, but it provides a solid fundamental in geometry up to AMC10-AMC12.
Introduction to Algebra is good also, can help you get to like 105-110 on AMC10 or 90-95 AMC12 but Intermediate Algebra is necessary to get higher like 125+.
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