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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.
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[*]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]
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0 replies
jlacosta
May 1, 2025
0 replies
k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
Challenge: Make every number to 100 using 4 fours
CJB19   127
N 9 minutes ago by Shan3t
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:
$$(4-4)*4*4=0$$$$4-4+4/4=1$$$$4/4+4/4=2$$$$(4+4+4)/4=3$$$$4+(4-4)*4=4$$$$4+4^{4-4}=5$$$$4!/4+4-4=6$$$$4+4-4/4=7$$$$4+4+4-4=8$$
127 replies
CJB19
May 15, 2025
Shan3t
9 minutes ago
2000th Post!
PikaPika999   16
N 15 minutes ago by BlackOctopus23
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 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)
16 replies
PikaPika999
Today at 1:53 AM
BlackOctopus23
15 minutes ago
d1-d2 divides n for all divisors d1, d2
a_507_bc   6
N 24 minutes ago by Assassino9931
Source: Romania 3rd JBMO TST 2023 P1
Determine all natural numbers $n \geq 2$ with at most four natural divisors, which have the property that for any two distinct proper divisors $d_1$ and $d_2$ of $n$, the positive integer $d_1-d_2$ divides $n$.
6 replies
a_507_bc
May 20, 2023
Assassino9931
24 minutes ago
Good divisors and special numbers.
Nuran2010   4
N 25 minutes ago by Assassino9931
Source: Azerbaijan Al-Khwarizmi IJMO TST 2024
$N$ is a positive integer. Call all positive divisors of $N$ which are different from $1$ and $N$ beautiful divisors.We call $N$ a special number when it has at least $2$ beautiful divisors and difference of any $2$ beautiful divisors divides $N$ as well. Find all special numbers.
4 replies
Nuran2010
Apr 29, 2025
Assassino9931
25 minutes ago
Mathcounts Nationals Written Score Hub
DhruvJha   77
N 26 minutes ago by eyzMath
Put in your estimated score on the written nats comp on Sunday after the comp so we can get a good idea of the cdr quals are
77 replies
DhruvJha
May 10, 2025
eyzMath
26 minutes ago
Hard math inequality
noneofyou34   0
26 minutes ago
If a,b,c are positive real numbers, such that a+b+c=1. Prove that:
(b+c)(a+c)/(a+b)+ (b+a)(a+c)/(c+b)+(b+c)(a+b)/(a+c)>= Sqrt.(6(a(a+c)+b(a+b)+c(b+c)) +3
0 replies
noneofyou34
26 minutes ago
0 replies
JBMO Shortlist 2023 N2
Orestis_Lignos   5
N 33 minutes ago by Just1
Source: JBMO Shortlist 2023, N2
A positive integer is called Tiranian if it can be written as $x^2+6xy+y^2$, where $x$ and $y$ are (not necessarily distinct) positive integers. The integer $36^{2023}$ is written as the sum of $k$ Tiranian integers. What is the smallest possible value of $k$?

Proposed by Miroslav Marinov, Bulgaria
5 replies
Orestis_Lignos
Jun 28, 2024
Just1
33 minutes ago
Inequality on non-nagative numbers
TUAN2k8   3
N 36 minutes ago by sqing
Source: My book
Let $a,b,c$ be non-nagative real numbers such that $a+b+c=3$.
Prove that $ab+bc+ca-abc \leq \frac{9}{4}$.
3 replies
TUAN2k8
2 hours ago
sqing
36 minutes ago
2-var inequality
sqing   2
N an hour ago by sqing
Source: Own
Let $ a,b>0,  ab^2+a+2b\geq4  $. Prove that$$  \frac{a}{2a+b^2}+\frac{2}{a+2}\leq 1$$
2 replies
sqing
Today at 6:16 AM
sqing
an hour ago
Inspired by 2022 MARBLE - Mock ARML
sqing   0
an hour ago
Source: Own
Let $ a,b,c\geq 0 , \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}= 5 $ and $ \frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=32. $ Prove that $$\frac{1}{2}>ab+bc+ca \geq  \frac{49}{34}$$Let $ a,b,c\geq 0 ,ab+bc+ca = \frac{49}{34} $ and $ \frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=32. $ Prove that $$\frac{51}{10}>\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}\geq5$$Let $ a,b,c\geq 0 ,ab+bc+ca = \frac{49}{34} $ and $ \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}=5. $ Prove that $$\frac{63}{2}<\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\leq32$$
0 replies
sqing
an hour ago
0 replies
Inequality
Sappat   8
N an hour ago by skellyrah
Let $a,b,c$ be real numbers such that $a^2+b^2+c^2=1$. Prove that
$\frac{a^2}{1+2bc}+\frac{b^2}{1+2ca}+\frac{c^2}{1+2ab}\geq\frac{3}{5}$
8 replies
Sappat
Feb 7, 2018
skellyrah
an hour ago
Symmedian line
April   92
N an hour ago by zuat.e
Source: All Russian Olympiad - Problem 9.2, 10.2
Let be given a triangle $ ABC$ and its internal angle bisector $ BD$ $ (D\in BC)$. The line $ BD$ intersects the circumcircle $ \Omega$ of triangle $ ABC$ at $ B$ and $ E$. Circle $ \omega$ with diameter $ DE$ cuts $ \Omega$ again at $ F$. Prove that $ BF$ is the symmedian line of triangle $ ABC$.
92 replies
April
May 10, 2009
zuat.e
an hour ago
Probably a good lemma
Zavyk09   0
2 hours ago
Source: found when solving exercises
Let $ABC$ be a triangle with circumcircle $\omega$. Arbitrary points $E, F$ on $AC, AB$ respectively. Circumcircle $\Omega$ of triangle $AEF$ intersects $\omega$ at $P \ne A$. $BE$ intersects $CF$ at $I$. $PI$ cuts $\Omega$ and $\omega$ at $K, L$ respectively. Construct parallelogram $QFRE$. Prove that $A, R, P$ are collinear.
0 replies
Zavyk09
2 hours ago
0 replies
Fun challange problem :)
TigerSenju   10
N 3 hours ago by Pengu14
Scenario:

Master Alchemist Aurelius is renowned for his mastery of elemental fusion. He works with seven fundamental, yet mysterious, elements: Ignis (Fire), Aqua (Water), Terra (Earth), Aer (Air), Lux (Light), Umbra (Shadow), and Aether (Spirit). Each element possesses a unique 'potency' value, a positive integer crucial for his most complex fusions

Aurelius has lost his master log of these potencies. All he has left are seven cryptic scrolls, each containing a precise relationship between the potencies of various elements. He needs these values to complete his Grand Device. Can you help him deduce the exact potency of each element?

The Elements and Their Potencies:

Let I represent the potency of Ignis (Fire).
Let A represent the potency of Aqua (Water).
Let T represent the potency of Terra (Earth).
Let R represent the potency of Aer (Air).
Let L represent the potency of Lux (Light).
Let U represent the potency of Umbra (Shadow).
Let E represent the potency of Aether (Spirit).
The Cryptic Scrolls (System of Equations):

Aurelius's scrolls reveal the following relationships:

The combined potency of Ignis, Aqua, and Terra is equal to the potency of Aer plus Lux, plus a constant of two.

If you sum the potencies of Aqua and Umbra, it precisely equals the sum of Lux and Aether, minus one.

The sum of Terra and Aer potencies is the same as the sum of Ignis, Aqua, and Aether potencies, minus one.

Three times the potency of Ignis, plus the potency of Aer, is equal to the sum of Aqua, Terra, and Aether potencies, plus five.

The difference between Lux and Ignis potencies is identical to the difference between Umbra and Aqua potencies.

The sum of Umbra and Aether potencies, when decreased by the potency of Terra, results in twice the potency of Aqua.

The potency of Ignis added to Lux, minus the potency of Aer, is equivalent to the potency of Aether minus Umbra, plus one.

The Grand Challenge:

Using only the information from the cryptic scrolls, set up and solve the system of seven linear equations to determine the unique positive integer potency value for each of the seven elements: I,A,T,R,L,U,E.

good luck, and whoever finds the potencies first, gets a title of The SYSTEMS OF EQUATIONS MASTER

p.s. Yes, I did just come up with a whole story of words to make a ridiculously long problem, but hey, you're reading this, so you probably have nothing better to be doing. ;)
10 replies
TigerSenju
Today at 1:04 AM
Pengu14
3 hours ago
amc10 chances?
aoh11   29
N Apr 5, 2025 by avyaank
if i got a 55.5 on amc10, what are my chances of making aime???
29 replies
aoh11
Apr 4, 2025
avyaank
Apr 5, 2025
amc10 chances?
G H J
G H BBookmark kLocked kLocked NReply
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aoh11
209 posts
#1 • 2 Y
Y by PikaPika999, Exponent11
if i got a 55.5 on amc10, what are my chances of making aime???
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giratina3
547 posts
#2 • 1 Y
Y by PikaPika999
It really depends on how devoted you are to math… I would recommend editing your original post and include how long you can study, some other scores from other test, and books and tests you’ve done, so we have a better idea how to answer your question.
This post has been edited 3 times. Last edited by giratina3, Apr 4, 2025, 4:08 AM
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jkim0656
1032 posts
#3 • 1 Y
Y by PikaPika999
also we need ur age too
a 55 isn't too good but if ur young enough u could pull it off
andyluo had like a 90 point jump over a year i think
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jb2015007
1963 posts
#4 • 1 Y
Y by PikaPika999
super possible i got around that score this year but im mocking 130's on older tests
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Andyluo
981 posts
#5 • 1 Y
Y by PikaPika999
jb2015007 wrote:
super possible i got around that score this year but im mocking 130's on older tests

130 on old tests is like equivalent to a 100 on 2022 test
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Dream9
84 posts
#6 • 1 Y
Y by PikaPika999
how do people make these jumps. like I got a 70 first time for 8th grade and all i need is like 25 more pts but I can't up my score
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jb2015007
1963 posts
#7 • 1 Y
Y by PikaPika999
Andyluo wrote:
jb2015007 wrote:
super possible i got around that score this year but im mocking 130's on older tests

130 on old tests is like equivalent to a 100 on 2022 test

bro u js gotta put the work in
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anticodon
164 posts
#8
Y by
a raw score of 55.5 will not make aime.
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jb2015007
1963 posts
#9 • 1 Y
Y by Exponent11
no hes talking about next year :skull:
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Dream9
84 posts
#10
Y by
jb2015007 wrote:
no hes talking about next year :skull:

I thought he was talking about in general like all the remaining years he has.
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sadas123
1309 posts
#11
Y by
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?
This post has been edited 1 time. Last edited by sadas123, Apr 4, 2025, 10:21 PM
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BrocSoc
22 posts
#12
Y by
146.5 is not a possible score
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jb2015007
1963 posts
#13
Y by
bruh i sold on 2021 AMC 10A
so hard
i only got 100.5
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sadas123
1309 posts
#14
Y by
jb2015007 wrote:
bruh i sold on 2021 AMC 10A
so hard
i only got 100.5

that's pretty good.
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Catcumber
162 posts
#15
Y by
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

i guess for you it really just comes down to how much you silly on the test
if you dont silly much, you'll probably get hr, but if you do silly a lot, you wont.
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Bigtree
205 posts
#16
Y by
I got 228.5 index my first yr it really just depends on the person
This post has been edited 1 time. Last edited by Bigtree, Apr 4, 2025, 11:00 PM
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mathprodigy2011
335 posts
#17
Y by
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

if your saying rn, then not very high especially since 2023 amc 10a was a very considerably easy test compared to any past test(other than 2024 amc 10b). Also how did u do worse on amc 10a 2023 than 2022(p=one of the hardest past amcs). anyways if you spend enough time on math then you could probably get in, also pls pm me if u have discord

EDIT: i thought u said DHR lol, u probably have a good chance at hr
This post has been edited 1 time. Last edited by mathprodigy2011, Apr 4, 2025, 11:44 PM
Reason: .
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aoh11
209 posts
#18
Y by
i am in 8th grade right now btw so am I cooked??
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elizhang101412
1239 posts
#19
Y by
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

didnt you make dhr already
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jb2015007
1963 posts
#20
Y by
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

bruh whyd u edit the 96 on AMC 10A 2021 to a 105 this is such cap bro
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sadas123
1309 posts
#21
Y by
elizhang101412 wrote:
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

didnt you make dhr already

Nope I missed it on A by 4 points :(
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elizhang101412
1239 posts
#22
Y by
sadas123 wrote:
elizhang101412 wrote:
sadas123 wrote:
If I mocked:

150 on AMC 10 A 2002
146.5 on AMC 10 A 2003
136.5 on AMC 10 A 2004
105 on AMC 10 A 2021
118.5 on AMC 10 A 2022
109.5 on AMC 10 A 2023

What are my chanches for AMC 10 HR next year?

didnt you make dhr already

Nope I missed it on A by 4 points :(

ok then why are you worried about it when you almost made dhr
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jb2015007
1963 posts
#23
Y by
no i think he thinks u said hr not dhr
but sadas why change the 96 to a 105 on 2021 AMC 10A Fall
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Dream9
84 posts
#24 • 1 Y
Y by PikaPika999
aoh11 wrote:
if i got a 55.5 on amc10, what are my chances of making aime???

Is this amc 10a or b or highest out of both? Also, 8th grade rn means 2 more years of amc10 and 4 more of amc 12 so I mean it can really go either way. Most people can't turn that score around very well but idrk what you'll do so like personally, maybe 8%?
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cheltstudent
625 posts
#25 • 1 Y
Y by PikaPika999
If ur going rly serious about AMC 10, go on HSM, there are some good problems there, but the community is way worse.
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c_double_sharp
319 posts
#26 • 2 Y
Y by PikaPika999, MathPerson12321
cheltstudent wrote:
If ur going rly serious about AMC 10, go on HSM, there are some good problems there, but the community is way worse.

*loud incorrect buzzer*
no one trolls about divisibility by 3 and half the problems are sqing’s inequalities

also because this is aops hsm problems are way too hard if you got a 55.5
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MathPerson12321
3787 posts
#27
Y by
c_double_sharp wrote:
cheltstudent wrote:
If ur going rly serious about AMC 10, go on HSM, there are some good problems there, but the community is way worse.

*loud incorrect buzzer*
no one trolls about divisibility by 3 and half the problems are sqing’s inequalities

also because this is aops hsm problems are way too hard if you got a 55.5

if you can get the first 15 then hsm is good
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MathPerson12321
3787 posts
#28
Y by
Dream9 wrote:
aoh11 wrote:
if i got a 55.5 on amc10, what are my chances of making aime???

Is this amc 10a or b or highest out of both? Also, 8th grade rn means 2 more years of amc10 and 4 more of amc 12 so I mean it can really go either way. Most people can't turn that score around very well but idrk what you'll do so like personally, maybe 8%?

you are so wrong
i got a low 60 in 6th grade and was close to aime in 8th, not everyone can, but with effort you can and you cannot put a percentage on this @op
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cheltstudent
625 posts
#29 • 1 Y
Y by MathPerson12321
c_double_sharp wrote:
cheltstudent wrote:
If ur going rly serious about AMC 10, go on HSM, there are some good problems there, but the community is way worse.

*loud incorrect buzzer*
no one trolls about divisibility by 3 and half the problems are sqing’s inequalities

also because this is aops hsm problems are way too hard if you got a 55.5

i forgot about the stupid div 3 though lol, also MSM is more active
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avyaank
53 posts
#30
Y by
aoh11 wrote:
i am in 8th grade right now btw so am I cooked??

uh if you put in effort then ya sure
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