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k a July Highlights and 2025 AoPS Online Class Information
jwelsh   0
Jul 1, 2025
We are halfway through summer, so be sure to carve out some time to keep your skills sharp and explore challenging topics at AoPS Online and our AoPS Academies (including the Virtual Campus)!

[list][*]Over 60 summer classes are starting at the Virtual Campus on July 7th - check out the math and language arts options for middle through high school levels.
[*]At AoPS Online, we have accelerated sections where you can complete a course in half the time by meeting twice/week instead of once/week, starting on July 8th:
[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC Problem Series[/list]
[*]Plus, AoPS Online has a special seminar July 14 - 17 that is outside the standard fare: Paradoxes and Infinity
[*]We are expanding our in-person AoPS Academy locations - are you looking for a strong community of problem solvers, exemplary instruction, and math and language arts options? Look to see if we have a location near you and enroll in summer camps or academic year classes today! New locations include campuses in California, Georgia, New York, Illinois, and Oregon and more coming soon![/list]

MOP (Math Olympiad Summer Program) just ended and the IMO (International Mathematical Olympiad) is right around the corner! This year’s IMO will be held in Australia, July 10th - 20th. Congratulations to all the MOP students for reaching this incredible level and best of luck to all selected to represent their countries at this year’s IMO! Did you know that, in the last 10 years, 59 USA International Math Olympiad team members have medaled and have taken over 360 AoPS Online courses. Take advantage of our Worldwide Online Olympiad Training (WOOT) courses
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0 replies
jwelsh
Jul 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
Combinatorics
jawadkaleem   2
N 20 minutes ago by Alphabeta123
Michel starts with the string HMMT.
An operation consists of either replacing an occurrence of H with HM, replacing an
occurrence of MM with MOM, or replacing an occurrence of T with MT. For example,
the two strings that can be reached after one operation are HMMMT and HMOMT.
Compute the number of distinct strings Michel can obtain after exactly 10 operation
2 replies
jawadkaleem
Jul 2, 2025
Alphabeta123
20 minutes ago
Find the value of angle C
markosa   10
N 23 minutes ago by wisewigglyjaguar
Given a triangle ABC with base BC

angle B = 3x
angle C = x
AP is the bisector of base BC (i.e.) BP = PC
angle APB = 45 degrees

Find x

I know there are multiple methods to solve this problem using cosine law, coord geo
But is there any pure geometrical solution?
10 replies
markosa
2 hours ago
wisewigglyjaguar
23 minutes ago
An easy geometry in Taiwan TST
Li4   8
N 25 minutes ago by Aiden-1089
Source: 2022 Taiwan TST Round 3 Independent Study 1-G
Let $ABC$ be an acute triangle with orthocenter $H$ and circumcircle $\Omega$. Let $M$ be the midpoint of side $BC$. Point $D$ is chosen from the minor arc $BC$ on $\Gamma$ such that $\angle BAD = \angle MAC$. Let $E$ be a point on $\Gamma$ such that $DE$ is perpendicular to $AM$, and $F$ be a point on line $BC$ such that $DF$ is perpendicular to $BC$. Lines $HF$ and $AM$ intersect at point $N$, and point $R$ is the reflection point of $H$ with respect to $N$.

Prove that $\angle AER + \angle DFR = 180^\circ$.

Proposed by Li4.
8 replies
Li4
Apr 27, 2022
Aiden-1089
25 minutes ago
combinatorics
kjhgyuio   1
N 28 minutes ago by Alphabeta123
........
1 reply
kjhgyuio
Jun 25, 2025
Alphabeta123
28 minutes ago
Inspired by old results
sqing   1
N 29 minutes ago by sqing
Source: Own
Let $ a,b> 0, a^2+b^2+ab=3 .$ Prove that
$$ 3\sqrt 3 \geq(a+b)^2(\frac {a} {b^2+b+1}+\frac {b} {a^2+a+1}) \geq   \frac {8} {3}$$$$ \frac {8} {3} \geq(a+b)^2(\frac {a} {b^2+a+1}+\frac {b} {a^2+b+1}) \geq  \frac {3(3-\sqrt 3)} {2} $$
1 reply
sqing
39 minutes ago
sqing
29 minutes ago
6 points concyclic wanted, touchpoints of incircle related
parmenides51   1
N 32 minutes ago by SuperBarsh
Source: Mexican Geometry Olympiad 2014 (OMG) - La Geometrense p1 https://artofproblemsolving.com/community/c2664039_2014_mexican_geometr
The incircle of triangle $ABC$ touches sides $BC$, $CA$, and $AB$ at $A'$, $B'$, and $C'$ respectively. $G$ is the intersection point of $AA '$, $BB'$ and $CC '$. The circumcircle of $GA'B'$ again touches $AC$ and $BC$ at points $C_A$ and $C_B$ respectively. Similarly are defined points $B_A$, $B_C$, $A_B$ and $A_C$ . Show that the points $C_A$, $C_B$, $B_A$, $B_C$, $A_B$ and $A_C$ all lie on the same circle.
1 reply
parmenides51
Nov 28, 2021
SuperBarsh
32 minutes ago
Interesting geometrical configuration
SeboS   1
N 42 minutes ago by Lil_flip38
Let $ABC$ be a triangle with orthocentre $H$, and altitudes $D,E,F$ on sides $(BC), (AC), (AB)$
If $$ (HBC) \cap (HEF)=X $$$$(AHC) \cap (DHF)=Y $$$$(ABH) \cap (DEH)=Z $$Prove that the points $ H, X, Y, Z $ are cyclic
1 reply
SeboS
an hour ago
Lil_flip38
42 minutes ago
4 var inequality
ehuseyinyigit   2
N an hour ago by ehuseyinyigit
Source: Own
Let $a,b,c,d$ be positive real numbers. Prove
$$\sum{a^2}+3\sum{a^2b^2c^2}+\sum{ab^2c}+12abcd$$$$\geq 2abcd[(a+c)(b+d)-ac-bd]+3\sum{a^2bc}+\sum{abc^2}$$
2 replies
1 viewing
ehuseyinyigit
Yesterday at 2:53 PM
ehuseyinyigit
an hour ago
Interesting functional equation
TheUltimate123   14
N an hour ago by math-olympiad-clown
Source: ELMO Shortlist 2023 A2
Let \(\mathbb R_{>0}\) denote the set of positive real numbers. Find all functions \(f:\mathbb R_{>0}\to\mathbb R_{>0}\) such that for all positive real numbers \(x\) and \(y\), \[f(xy+1)=f(x)f\left(\frac1x+f\left(\frac1y\right)\right).\]
Proposed by Luke Robitaille
14 replies
TheUltimate123
Jun 29, 2023
math-olympiad-clown
an hour ago
Inequalities
sqing   9
N an hour ago by sqing
Let $ a,b> 0 $ and $2a+2b+ab=5. $ Prove that
$$ \frac{a^4}{b^4}+\frac{1}{a^4}+42ab-a^4\geq  43$$$$ \frac{a^5}{b^5}+\frac{1}{a^5}+64ab-a^5\geq  65$$$$ \frac{a^6}{b^6}+\frac{1}{a^6}+90ab-a^6\geq  91$$$$ \frac{a^7}{b^7}+\frac{1}{a^7}+121ab-a^7\geq  122$$
9 replies
sqing
May 28, 2025
sqing
an hour ago
Inequalities
sqing   4
N an hour ago by sqing
Let $ a,b> 0, a^2+b^2+ab=3 .$ Prove that
$$ (a+b+1)^2(\frac {a} {b^2+1}+\frac {b} {a^2+1})\geq 9$$Let $ a,b> 0, a+b+ab=3 .$ Prove that
$$(a+b+1)^2(\frac {a+1} {b^2+1}+\frac {b+1} {a^2+1})\geq 18$$Let $ a,b> 0, a+b+2ab=4.$ Prove that
$$(a+b+1)^2(\frac {a} {b^2+1}+\frac {b} {a^2+1})\geq 9$$$$ (a+b+1)^2(\frac {a+1} {b^2+1}+\frac {b+1} {a^2+1}) \geq 18$$
4 replies
sqing
Today at 2:57 AM
sqing
an hour ago
A specific case of my previous conjecture
Rhapsodies_pro   1
N an hour ago by nexu
Source: n=4
Prove that \(3\) is the largest value of the constant \(k\) such that \[{ab+ac+ad+bc+bd+cd-6}\leqslant{k{\left(a+b+c+d-1\right)}{\left(a+b+c+d-4\right)}}\]holds for any nonnegative real numbers \(a, b, c, d\) satisfying \({a^2+b^2+c^2+d^2+5abcd}\geqslant9\).
1 reply
Rhapsodies_pro
Wednesday at 4:38 PM
nexu
an hour ago
3 var inequality
ehuseyinyigit   9
N an hour ago by nexu
Source: Own
Let $x,y,z$ be positive real numbers. Prove that

$$\dfrac{x^3+72xy^2}{z^3+x^2y}+\dfrac{y^3+72yz^2}{x^3+y^2z}+\dfrac{z^3+72zx^2}{y^3+z^2x}\geq \dfrac{15}{2}+\dfrac{102xyz(x+y+z)}{x^3y+y^3z+z^3x}$$
9 replies
ehuseyinyigit
Jul 21, 2025
nexu
an hour ago
Four variables
Nguyenhuyen_AG   3
N an hour ago by nexu
Let $a,\,b,\,c,\,d$ non-negative real numbers. Prove that
\[\frac{abc}{(a+b+c)^3}+\frac{bcd}{(b+c+d)^3}+\frac{cda}{(c+d+a)^3}+\frac{dab}{(d+a+b)^3} \leqslant \frac{(a+b+c+d)^2}{27(a^2+b^2+c^2+d^2)}.\]
3 replies
Nguyenhuyen_AG
Jul 23, 2025
nexu
an hour ago
AP calc?
Thayaden   31
N May 29, 2025 by Mathzeus1024
How are we all feeling on AP calc guys?
31 replies
Thayaden
May 20, 2025
Mathzeus1024
May 29, 2025
AP calc?
G H J
G H BBookmark kLocked kLocked NReply
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Thayaden
1366 posts
#1
Y by
How are we all feeling on AP calc guys?
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Math-lover1
470 posts
#2
Y by
Thayaden wrote:
How are we all feeling on AP calc guys?

wrong forum
consider moving to hsm or something
This post has been edited 1 time. Last edited by Math-lover1, May 20, 2025, 6:20 PM
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freefall222
5 posts
#3
Y by
good frfr
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K1mchi_
189 posts
#4
Y by
Thayaden wrote:
How are we all feeling on AP calc guys?

prob move to HSM but may be targeted to middle school calc people

imo lobotomy kaisen calc saga is w learning strat
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CJB19
178 posts
#5
Y by
Do your schools let you take Calc in middle school?!
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K1mchi_
189 posts
#6 • 1 Y
Y by valenbb
CJB19 wrote:
Do your schools let you take Calc in middle school?!

well aops and rms allow it…

the highest u can take in 8th grade at my school is algebra 2 in 8th grade
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valenbb
825 posts
#7
Y by
K1mchi_ wrote:
CJB19 wrote:
Do your schools let you take Calc in middle school?!

well aops and rms allow it…

the highest u can take in 8th grade at my school is algebra 2 in 8th grade

for my school it's geometry... our school has some really bad fluency percents lol
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CJB19
178 posts
#8
Y by
K1mchi_ wrote:
CJB19 wrote:
Do your schools let you take Calc in middle school?!

well aops and rms allow it…

the highest u can take in 8th grade at my school is algebra 2 in 8th grade

Yeah in my district I don't think they let you be any more than three grades ahead
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HungryCalculator
547 posts
#9 • 1 Y
Y by valenbb
valenbb wrote:
K1mchi_ wrote:
CJB19 wrote:
Do your schools let you take Calc in middle school?!

well aops and rms allow it…

the highest u can take in 8th grade at my school is algebra 2 in 8th grade

for my school it's geometry... our school has some really bad fluency percents lol

same

whats actually kinda sad is how so many parents are concerned with the fact that some kids are 2-3 grade levels ahead instead of focusing on their child. It's more of a crab mentality rather than being focused about their child's future. in my middle school they were about to remove geometry because plenty of parents whose 8th graders were taking algebra were concerned.
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Aopsauser9999
734 posts
#10
Y by
Quote:
whats actually kinda sad is how so many parents are concerned with the fact that some kids are 2-3 grade levels ahead instead of focusing on their child. It's more of a crab mentality rather than being focused about their child's future. in my middle school they were about to remove geometry because plenty of parents whose 8th graders were taking algebra were concerned.

huh, there's no need to drag down kids who are excelling
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Inaaya
506 posts
#11
Y by
in my school it shouldnt physically be possible to take it before 9th grade, but a certain tryharding someone broke the rule
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sangriabeaver5
21 posts
#12
Y by
Inaaya wrote:
in my school it shouldnt physically be possible to take it before 9th grade, but a certain tryharding someone broke the rule

In my school there's nothing against it, so a couple of people have taken AP Calc in 8th and there are more people taking AP Calc in 9th.
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Aopsauser9999
734 posts
#13
Y by
in my school kids dont take ap calc ab untill 11th luckily i took a placement test
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RandomMathGuy500
69 posts
#14
Y by
CJB19 wrote:
Do your schools let you take Calc in middle school?!

sadly, no. But I self studied it so I'm good for the exam
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K1mchi_
189 posts
#15
Y by
standards based grading is a grading system that uses standards and no letter grades.

no percents are implemented so its considered low stress.

imo tho

IT IS AN ABOMINATION.

like it gives me no motivation and the grades are terrible and easy

i understand that some parents want this but this just isnt the motivation and stress i want
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maxamc
594 posts
#16
Y by
K1mchi_ wrote:
standards based grading is a grading system that uses standards and no letter grades.

no percents are implemented so its considered low stress.

imo tho

IT IS AN ABOMINATION.

like it gives me no motivation and the grades are terrible and easy

i understand that some parents want this but this just isnt the motivation and stress i want

china japan or korea has way better education system ()
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K1mchi_
189 posts
#17
Y by
maxamc wrote:
K1mchi_ wrote:
standards based grading is a grading system that uses standards and no letter grades.

no percents are implemented so its considered low stress.

imo tho

IT IS AN ABOMINATION.

like it gives me no motivation and the grades are terrible and easy

i understand that some parents want this but this just isnt the motivation and stress i want

china japan or korea has way better education system ()

Korea just has traditions of children going to tutoring (학원) and afterschool the kids just go to these tutoring for a rlly long time as almost a second school
This post has been edited 1 time. Last edited by K1mchi_, May 21, 2025, 6:54 PM
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icepeach107
21 posts
#18
Y by
Yeah and in Korea some of the academies(학원) almost ends in 11PM....
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sangriabeaver5
21 posts
#19
Y by
K1mchi_ wrote:
standards based grading is a grading system that uses standards and no letter grades.

no percents are implemented so its considered low stress.

imo tho

IT IS AN ABOMINATION.

like it gives me no motivation and the grades are terrible and easy

i understand that some parents want this but this just isnt the motivation and stress i want
My school system: there are letter grades, but there are decimals that correspond to letter grades with lower cutoffs (C = 1.6+, B = 2.7+, A = 3.4+)
This is an abomination as well...such low standards for grades.
In our district they emphasize A LOT how 'most students don't skip' and 'it's okay and recommended to not skip' etc
That doesn't help anyone...
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Evanlovemath
230 posts
#20
Y by
Quote:
whats actually kinda sad is how so many parents are concerned with the fact that some kids are 2-3 grade levels ahead instead of focusing on their child. It's more of a crab mentality rather than being focused about their child's future. in my middle school they were about to remove geometry because plenty of parents whose 8th graders were taking algebra were concerned.

Bruhhh that's like saying "Oh my child is doing bad lets make all the other kids that are doing good also be bad"
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Pengu14
652 posts
#21
Y by
Pretty good!

I got the easier sets for both MCQ and FRQ :P
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sanaops9
864 posts
#22
Y by
Inaaya wrote:
in my school it shouldnt physically be possible to take it before 9th grade, but a certain tryharding someone broke the rule

i assume ur talking abt me

but i didn't break any rules

i just like math
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Inaaya
506 posts
#23
Y by
sanaops9 wrote:
Inaaya wrote:
in my school it shouldnt physically be possible to take it before 9th grade, but a certain tryharding someone broke the rule

i assume ur talking abt me

but i didn't break any rules

i just like math

how the hell do you even get approved to start champ in 6th that shouldn't be possible
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SpeedCuber7
1904 posts
#24
Y by
Thayaden wrote:
How are we all feeling on AP calc guys?

it's not terrible but it's kinda free ngl i hate integral ):
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K1mchi_
189 posts
#25
Y by
SpeedCuber7 wrote:
Thayaden wrote:
How are we all feeling on AP calc guys?

it's not terrible but it's kinda free ngl i hate integral ):

aura
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K1mchi_
189 posts
#26
Y by
Evanlovemath wrote:
Quote:
whats actually kinda sad is how so many parents are concerned with the fact that some kids are 2-3 grade levels ahead instead of focusing on their child. It's more of a crab mentality rather than being focused about their child's future. in my middle school they were about to remove geometry because plenty of parents whose 8th graders were taking algebra were concerned.

Bruhhh that's like saying "Oh my child is doing bad lets make all the other kids that are doing good also be bad"

tbf tho middle school isn’t important

still, if i can, i want to be 3 tracks ahead in prior to high school yk
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Inaaya
506 posts
#27 • 1 Y
Y by MathPerson12321
skipping middle school grades/courses is like 10x easier than skipping high school grades/courses
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K1mchi_
189 posts
#28
Y by
Inaaya wrote:
skipping middle school grades/courses is like 10x easier than skipping high school grades/courses

https://www.khanacademy.org/college-careers-more/talks-and-interviews/talks-and-interviews-unit/conversations-with-sal/v/lets-teach-for-mastery-not-test-scores-sal-khan

sal talked abt this
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jmr2010
1262 posts
#29
Y by
I did AP calc last week. Think I nailed it.

In the description it says grades 5-8. I am in 8th grade so it fits
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BS2012
1072 posts
#30
Y by
Pengu14 wrote:
Pretty good!

I got the easier sets for both MCQ and FRQ :P

did u get the one with the parametrics
meanwhile form 1 ppl with polar + 2x series (it still wasnt too bad though)
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Pengu14
652 posts
#31
Y by
BS2012 wrote:
Pengu14 wrote:
Pretty good!

I got the easier sets for both MCQ and FRQ :P

did u get the one with the parametrics
meanwhile form 1 ppl with polar + 2x series (it still wasnt too bad though)

yeah the one with the particle
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Mathzeus1024
1073 posts
#32
Y by
Good luck on the AP Calculus Examinations this May......hope to see some of you in Purdue's Engineering program! :)
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