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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.

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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)!

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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
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Mathcounts Countdown Round Hub
DhruvJha   27
N 7 minutes ago by MathPerson12321
We will post cdr updates for those who are blocked at school! Also put your current rankings and predictions.
27 replies
+2 w
DhruvJha
4 hours ago
MathPerson12321
7 minutes ago
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Favorite Memory at MATHCOUNTS
MathRook7817   15
N 8 minutes ago by xiaoya.peng
Hey guys, what is everyone's favorite memory at any Mathcounts competition?

Mine was arriving at the hotel for the 2024 nats comp.
15 replies
+1 w
MathRook7817
3 hours ago
xiaoya.peng
8 minutes ago
J
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system linear equation with substitution
Miranda2829   2
N 18 minutes ago by Miranda2829
5x-3y=-22
6x+4y=-34

whats the steps by using substitution in this question?

many thanks
2 replies
Miranda2829
2 hours ago
Miranda2829
18 minutes ago
J
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2025 MATHCOUNTS State Hub
SirAppel   833
N 31 minutes ago by MathPerson12321
Previous Years' "Hubs": (2022) (2023) (2024)Please Read

Now that it's April and we're allowed to discuss ...
[list=disc]
[*] CA: 43 (45 44 43 43 43 42 42 41 41 41)
[*] NJ: 43 (45 44 44 43 39 42 40 40 39 38) *
[*] NY: 42 (43 42 42 42 41 40 38 38 38 38 38 38)
[*] TX: 42 (43 43 43 42 42 40 40 38 38 38)
[*] MA: 41 (45 43 42 41)
[*] WA: 41 (41 45 42 41 41 41 41 41 41 40) *
[*]VA: 40 (41 40 40 40)
[*] FL: 39 (42 41 40 39 38 37 37)
[*] IN: 39 (41 40 40 39 36 35 35 35 34 34)
[*] NC: 39 (42 42 41 39)
[*] IL: 38 (41 40 39 38 38 38)
[*] OR: 38 (44 39 38 38)
[*] PA: 38 (41 40 40 38 38 37 36 36 34 34) *
[*] MD: 37 (43 39 39 37 37 37)
[*] AZ: 36 (40? 39? 39 36)
[*] CT: 36 (44 38 38 36 35 35 34 34 34 33 33 32 32 32 32)
[*] MI: 36 (39 41 41 36 37 37 36 36 36 36) *
[*] MN: 36 (40 36 36 36 35 35 35 34)
[*] CO: 35 (41 37 37 35 35 35 ?? 31 31 30) *
[*] GA: 35 (38 37 36 35 34 34 34 34 34 33)
[*] OH: 35 (41 37 36 35)
[*] AR: 34 (46 45 35 34 33 31 31 31 29 29)
[*] NV: 34 (41 38 ?? 34)
[*] TN: 34 (38 ?? ?? 34)
[*] WI: 34 (40 37 37 34 35 30 28 29 29 29) *
[*] HI: 32 (35 34 32 32)
[*] NH: 31 (42 35 33 31 30)
[*] DE: 30 (34 33 32 30 30 29 28 27 26? 24)
[*] SC: 30 (33 33 31 30)
[*] IA: 29 (33 30 31 29 29 29 29 29 29 29 29 29) *
[*] NE: 28 (34 30 28 28 27 27 26 26 25 25)
[*] SD: 22 (30 29 24 22 22 22 21 21 20 20)
[/list]
Cutoffs Unknown

* means that CDR is official in that state.

Notes

For those asking about the removal of the tiers, I'd like to quote Jason himself:
[quote=peace09]
learn from my mistakes
[/quote]

Help contribute by sharing your state's cutoffs!
833 replies
+1 w
SirAppel
Apr 1, 2025
MathPerson12321
31 minutes ago
J
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Logarithmic function
jonny   2
N 4 hours ago by KSH31415
If $\log_{6}(15) = a$ and $\log_{12}(18)=b,$ Then $\log_{25}(24)$ in terms of $a$ and $b$
2 replies
jonny
Jul 15, 2016
KSH31415
4 hours ago
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book/resource recommendations
walterboro   0
Yesterday at 8:57 PM
hi guys, does anyone have book recs (or other resources) for like aime+ level alg, nt, geo, comb? i want to learn a lot of theory in depth
also does anyone know how otis or woot is like from experience?
0 replies
walterboro
Yesterday at 8:57 PM
0 replies
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Engineers Induction FTW
RP3.1415   11
N Yesterday at 6:53 PM by Markas
Define a sequence as $a_1=x$ for some real number $x$ and \[ a_n=na_{n-1}+(n-1)(n!(n-1)!-1) \]for integers $n \geq 2$. Given that $a_{2021} =(2021!+1)^2 +2020!$, and given that $x=\dfrac{p}{q}$, where $p$ and $q$ are positive integers whose greatest common divisor is $1$, compute $p+q.$
11 replies
RP3.1415
Apr 26, 2021
Markas
Yesterday at 6:53 PM
J
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Incircle concurrency
niwobin   0
Yesterday at 4:28 PM
Triangle ABC with incenter I, incircle is tangent to BC, AC, and AB at D, E and F respectively.
DT is a diameter for the incircle, and AT meets the incircle again at point H.
Let DH and EF intersect at point J. Prove: AJ//BC.
0 replies
niwobin
Yesterday at 4:28 PM
0 replies
J
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Weird locus problem
Sedro   1
N Yesterday at 4:20 PM by sami1618
Points $A$ and $B$ are in the coordinate plane such that $AB=2$. Let $\mathcal{H}$ denote the locus of all points $P$ in the coordinate plane satisfying $PA\cdot PB=2$, and let $M$ be the midpoint of $AB$. Points $X$ and $Y$ are on $\mathcal{H}$ such that $\angle XMY = 45^\circ$ and $MX\cdot MY=\sqrt{2}$. The value of $MX^4 + MY^4$ can be expressed in the form $\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
1 reply
Sedro
Yesterday at 3:12 AM
sami1618
Yesterday at 4:20 PM
J
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Inequalities
sqing   4
N Yesterday at 3:35 PM by sqing
Let $ a,b,c\geq 0 , (a+8)(b+c)=9.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{38}{23}$$Let $ a,b,c\geq 0 , (a+2)(b+c)=3.$ Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}\geq \frac{2(2\sqrt{3}+1)}{5}$$
4 replies
sqing
Saturday at 12:50 PM
sqing
Yesterday at 3:35 PM
J
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Find the range of 'f'
agirlhasnoname   1
N Yesterday at 2:46 PM by Mathzeus1024
Consider the triangle with vertices (1,2), (-5,-1) and (3,-2). Let Δ denote the region enclosed by the above triangle. Consider the function f:Δ-->R defined by f(x,y)= |10x - 3y|. Then the range of f is in the interval:
A)[0,36]
B)[0,47]
C)[4,47]
D)36,47]
1 reply
agirlhasnoname
May 14, 2021
Mathzeus1024
Yesterday at 2:46 PM
J
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Function equation
hoangdinhnhatlqdqt   1
N Yesterday at 1:52 PM by Mathzeus1024
Find all functions $f:\mathbb{R}\geq 0\rightarrow \mathbb{R}\geq 0$ satisfying:
$f(f(x)-x)=2x\forall x\geq 0$
1 reply
hoangdinhnhatlqdqt
Dec 17, 2017
Mathzeus1024
Yesterday at 1:52 PM
J
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Inequality with function.
vickyricky   3
N Yesterday at 1:51 PM by SpeedCuber7
If x satisfies the inequalit$ |x - 1| + |x - 2| + |x - 3| \ge 6$, then
$(a) 0 \le x \le 4. (b) x \le 0 or x \ge 4. (c) x \le -2 or x \ge 4$. (d) None of these.
3 replies
vickyricky
May 28, 2018
SpeedCuber7
Yesterday at 1:51 PM
J
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Writing/Evaluating Exponential Functions
Samarthsshah   1
N Yesterday at 1:47 PM by Mathzeus1024
Rewrite the function and determine if the function represents exponential growth or decay. Identify the percent rate of change.

y=2(9)^-x/2
1 reply
Samarthsshah
Jan 30, 2018
Mathzeus1024
Yesterday at 1:47 PM
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J
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Can someone explain this one
hawa   10
N Apr 29, 2025 by VivaanKam
Suppose n is the largest integer obtained by solving the following inequality:

3+9+18+30+...+n
n < 2021.
10 replies
hawa
Apr 29, 2025
VivaanKam
Apr 29, 2025
J
Can someone explain this one
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Reveal topic tags
inequalities
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G H BBookmark kLocked kLocked NReply
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hawa
2 posts
hawa
#1 h  Apr 29, 2025, 1:36 AM
Y by
Suppose n is the largest integer obtained by solving the following inequality:

3+9+18+30+...+n
n < 2021.
Z K Y
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FredyCrooger
62 posts
FredyCrooger
#2 h  Apr 29, 2025, 1:45 AM
Y by
So first you find the change in the difference between the numbers and assuming the question is asking to find the largest $n$, you can add them up and continue from there.
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johnnie.walker
2 posts
johnnie.walker
#3 h  Apr 29, 2025, 1:38 PM
Y by
Hint
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fossasor
603 posts
fossasor
#4 h  Apr 29, 2025, 1:48 PM
Y by
Hint #2
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snake2020
4510 posts
snake2020
#5 h  Apr 29, 2025, 1:51 PM
Y by
Hint #3
This post has been edited 1 time. Last edited by snake2020, Apr 29, 2025, 1:51 PM
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snake2020
4510 posts
snake2020
#6 h  Apr 29, 2025, 2:08 PM
Y by
Solution
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Andrew2019
2312 posts
Andrew2019
#7 h  Apr 29, 2025, 5:32 PM
Y by
snake2020 wrote:
Solution

believe this is incorrect, it says $n$ is less that $2021$, not the sum
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VivaanKam
160 posts
VivaanKam
#8 h  Apr 29, 2025, 8:01 PM
Y by
The general term of the sequence is $a_n=\dfrac{3n(n-1))}{2}$
This post has been edited 1 time. Last edited by VivaanKam, Apr 29, 2025, 8:10 PM
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VivaanKam
160 posts
VivaanKam
#9 h  Apr 29, 2025, 8:04 PM
Y by
But I don't get the problem. Are you saying that $3+9+18+30+\dots +n<2021$ and $n<2021$?
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VivaanKam
160 posts
VivaanKam
#10 h  Apr 29, 2025, 8:05 PM
Y by
nvm I figured it out.
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VivaanKam
160 posts
VivaanKam
#11 h  Apr 29, 2025, 8:23 PM
Y by
Solution
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