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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

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0 replies
jlacosta
Apr 2, 2025
0 replies
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1234th Post!
PikaPika999   194
N 3 minutes ago by PikaPika999
I hit my 1234th post! (I think I missed it, I'm kinda late, :oops_sign:)

But here's a puzzle for you all! Try to create the numbers 1 through 25 using the numbers 1, 2, 3, and 4! You are only allowed to use addition, subtraction, multiplication, division, and parenthesis. If you're post #1, try to make 1. If you're post #2, try to make 2. If you're post #3, try to make 3, and so on. If you're a post after 25, then I guess you can try to make numbers greater than 25 but you can use factorials, square roots, and that stuff. Have fun!

1: $(4-3)\cdot(2-1)$
194 replies
PikaPika999
Apr 21, 2025
PikaPika999
3 minutes ago
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Basic, Part B
CarSa   0
6 minutes ago
For each four--digit number $\overline {abcd}$, that is, with $a$ nonzero, let $P(\overline {abcd})$ be the product $(a+b)(a+c)(a+d)(b+c)(b+d)(c+d)$.
For example, $P(2022) = (2+0)(2+2)(2+2)(0+2)(0+2)(2+2) = 512$ and $P(1234) = (1+2)(1+3)(1+4)(2+3)(2+4)(3+4)$.
How many numbers $\overline {abcd}$ with at least one $0$ amoung their digits satisfy that $P(\overline {abcd})$ is a power of 2?
0 replies
CarSa
6 minutes ago
0 replies
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Area of Polygon
AIME15   53
N 19 minutes ago by ReticulatedPython
The area of polygon $ ABCDEF$, in square units, is

IMAGE

\[ \textbf{(A)}\ 24 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 46 \qquad \textbf{(D)}\ 66 \qquad \textbf{(E)}\ 74 \]
53 replies
1 viewing
AIME15
Jan 12, 2009
ReticulatedPython
19 minutes ago
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9 What is the most important topic in maths competition?
AVIKRIS   40
N an hour ago by K1mchi_
I think arithmetic is the most the most important topic in math competitions.
40 replies
AVIKRIS
Apr 19, 2025
K1mchi_
an hour ago
J
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A Ball-Drawing problem
Vivacious_Owl   2
N 5 hours ago by Vivacious_Owl
Source: Inspired by a certain daily routine of mine
There are N identical black balls in a bag. I randomly take one ball out of the bag. If it is a black ball, I throw it away and put a white ball back into the bag instead. If it is a white ball, I simply throw it away and do not put anything back into the bag. The probability of getting any ball is the same.
Questions:
1. How many times will I need to reach into the bag to empty it?
2. What is the ratio of the expected maximum number of white balls in the bag to N in the limit as N goes to infinity?
2 replies
Vivacious_Owl
Today at 2:58 AM
Vivacious_Owl
5 hours ago
J
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Infinite sum
Thanhdoan1   0
5 hours ago
Calculate the sum
τ(1):1-τ(2):2+τ(3):3-....+(-1)^(n-1)*τ(n):n, with τ(n) is the number of divisors of n.
0 replies
Thanhdoan1
5 hours ago
0 replies
J
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Learning 3D Geometry
KAME06   2
N Today at 1:52 PM by KAME06
Could you help me with some 3D geometry books? Or any book with 3D geometry information, specially if it's focuses on math olympiads (like Putnam).
2 replies
KAME06
Apr 19, 2025
KAME06
Today at 1:52 PM
J
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Matrices and Determinants
Saucepan_man02   6
N Today at 9:10 AM by kiyoras_2001
Hello

Can anyone kindly share some problems/handouts on matrices & determinants (problems like Putnam 2004 A3, which are simple to state and doesnt involve heavy theory)?

Thank you..
6 replies
Saucepan_man02
Apr 4, 2025
kiyoras_2001
Today at 9:10 AM
J
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Two times derivable real function
Valentin Vornicu   13
N Today at 6:54 AM by solyaris
Source: RMO 2008, 11th Grade, Problem 3
Let $ f: \mathbb R \to \mathbb R$ be a function, two times derivable on $ \mathbb R$ for which there exist $ c\in\mathbb R$ such that
\[ \frac { f(b)-f(a) }{b-a} \neq f'(c) ,\] for all $ a\neq b \in \mathbb R$.

Prove that $ f''(c)=0$.
13 replies
Valentin Vornicu
Apr 30, 2008
solyaris
Today at 6:54 AM
J
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Problem with lcm
snowhite   4
N Today at 6:36 AM by ddot1
Prove that $\underset{n\to \infty }{\mathop{\lim }}\,\sqrt[n]{lcm(1,2,3,...,n)}=e$
Please help me! Thank you!
4 replies
snowhite
Yesterday at 5:19 AM
ddot1
Today at 6:36 AM
J
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I.S.I. B.Math.(Hons.) Admission test : 2010 Problem 5
mynamearzo   17
N Today at 4:46 AM by P162008
Let $a_1>a_2>.....>a_r$ be positive real numbers .
Compute $\lim_{n\to \infty} (a_1^n+a_2^n+.....+a_r^n)^{\frac{1}{n}}$
17 replies
mynamearzo
Apr 10, 2012
P162008
Today at 4:46 AM
J
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x^{2s}+x^{2s-1}+...+x+1 irreducible over $F_2$?
khanh20   2
N Yesterday at 7:26 PM by GreenKeeper
With $s\in \mathbb{Z}^+; s\ge 2$, whether or not the polynomial $P(x)=x^{2s}+x^{2s-1}+...+x+1$ irreducible over $F_2$?
2 replies
khanh20
Apr 21, 2025
GreenKeeper
Yesterday at 7:26 PM
J
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Equation over a finite field
loup blanc   2
N Yesterday at 6:16 PM by loup blanc
Find the set of $x\in\mathbb{F}_{5^5}$ such that the equation in the unknown $y\in \mathbb{F}_{5^5}$:
$x^3y+y^3+x=0$ admits $3$ roots: $a,a,b$ s.t. $a\not=b$.
2 replies
loup blanc
Apr 22, 2025
loup blanc
Yesterday at 6:16 PM
J
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Can a 0-1 matrix square to the matrix with all ones?
Tintarn   4
N Yesterday at 5:47 PM by loup blanc
Source: IMC 2024, Problem 3
For which positive integers $n$ does there exist an $n \times n$ matrix $A$ whose entries are all in $\{0,1\}$, such that $A^2$ is the matrix of all ones?
4 replies
Tintarn
Aug 7, 2024
loup blanc
Yesterday at 5:47 PM
J
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J
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k Algebra 1 Final
Robo_J   37
N Aug 23, 2016 by reaganchoi
What is the best way to study for a common core algebra 1 final? Resources would be awesome :blush:
37 replies
Robo_J
Aug 16, 2016
reaganchoi
Aug 23, 2016
J
Algebra 1 Final
G H J
Reveal topic tags
L
G H BBookmark kLocked kLocked NReply
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Robo_J
157 posts
Robo_J
#1 h  Aug 16, 2016, 9:24 PM • 1 Y
Y by Adventure10
What is the best way to study for a common core algebra 1 final? Resources would be awesome :blush:
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fazsal1986
196 posts
fazsal1986
#2 h  Aug 16, 2016, 9:30 PM • 2 Y
Y by Adventure10, Mango247
well go over everthing youve done over the course :-D have someone make some problems up and do them
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m1234567
1107 posts
m1234567
#3 h  Aug 16, 2016, 9:31 PM • 2 Y
Y by Adventure10, Mango247
https://www.khanacademy.org

Or if your feeling practical
http://www.artofproblemsolving.com/community

Or even creative!

http://www.artofproblemsolving.com/alcumus
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claserken
1772 posts
claserken
#4 h  Aug 16, 2016, 9:31 PM • 2 Y
Y by Adventure10, Mango247
Practice problems: http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_04/pdfs/Alg1NC_EOG.pdf and http://ecfmath.weebly.com/math-1-eoc-prep.html. Although these are for NC's Math 1 EOC's, it should still be the same concepts.

@above He/She meant common core(except khanacademy is useful for Math 1)
This post has been edited 2 times. Last edited by claserken, Aug 16, 2016, 9:32 PM
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Robo_J
157 posts
Robo_J
#5 h  Aug 16, 2016, 9:32 PM • 1 Y
Y by Adventure10
Thanks everyone!!! :-D
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fazsal1986
196 posts
fazsal1986
#6 h  Aug 16, 2016, 9:34 PM • 2 Y
Y by Adventure10, Mango247
hope you pass :blush:
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reaganchoi
5289 posts
reaganchoi
#7 h  Aug 16, 2016, 10:48 PM • 2 Y
Y by Adventure10, Mango247
m1234567 wrote:
https://www.khanacademy.org

Or if your feeling practical
http://www.artofproblemsolving.com/community

Or even creative!

http://www.artofproblemsolving.com/alcumus

@1 Khan academy is nice, but it takes too much time (especially when you're reviewing)
@2 Could be good but I don't think there will be a thread for each topic, and it would be hard to look through
@3 Best option out of the three IMO (cuz aops >>>>>>>> everything else)
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GeneralCobra19
1535 posts
GeneralCobra19
#9 h  Aug 16, 2016, 11:10 PM • 2 Y
Y by Adventure10, Mango247
Intro to Algebra 1-11 chapter reviews. Challenge is too much.
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pi-3.14
131 posts
pi-3.14
#10 h  Aug 17, 2016, 1:34 AM • 1 Y
Y by Adventure10
As long as you listened in class and did your homework, you should be fine. Just relax and review your notes before the test, it's what I do before any test(including Mathcounts and AMCs).
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zxcv1337
1631 posts
zxcv1337
#11 h  Aug 17, 2016, 1:51 AM • 2 Y
Y by Adventure10, Mango247
In my Algebra 1 final, like what the above said, I went over all the homework and tests/quizzes. Also, I reviewed notes and did a bunch of problems on Khan Academy and did a bit in Alcumus! Anything that you are kinda shaky or feel like you need a good review, you could just go over an Algebra 1 textbook or use Intro to Algebra (if you have any of these) or just look it up.
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jack74
2319 posts
jack74
#12 h  Aug 18, 2016, 5:31 PM • 2 Y
Y by Adventure10, Mango247
Learn to use a graphing calculator. That would help a lot! :-D
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B-mode
2270 posts
B-mode
#13 h  Aug 18, 2016, 5:40 PM • 2 Y
Y by Adventure10, Mango247
Try to memorize everything u learned in statistics(conditional row probability, standard deviation, etc.)
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william2001
110 posts
william2001
#14 h  Aug 18, 2016, 6:13 PM • 2 Y
Y by Adventure10, Mango247
I would recommend that before you look at other sources, you first review all your past tests, homework, and classwork. Those are the priorities.
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pi-3.14
131 posts
pi-3.14
#15 h  Aug 18, 2016, 6:25 PM • 1 Y
Y by Adventure10
jack74 wrote:
Learn to use a graphing calculator. That would help a lot! :-D

When I took it, there was a non calculator portion and a calculator portion.
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reaganchoi
5289 posts
reaganchoi
#16 h  Aug 18, 2016, 9:35 PM • 2 Y
Y by Adventure10, Mango247
Try a few practice IMOs, they might help.

Yeah the topics in your school vs here would be different, so checking over school courses and stuff should be enough.
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blitzkrieg21
996 posts
blitzkrieg21
#17 h  Aug 19, 2016, 6:57 PM • 1 Y
Y by Adventure10
Robo_J wrote:
What is the best way to study for a common core algebra 1 final? Resources would be awesome :blush:

The Algebra 1 final contains many applications related to graphs so I would suggest understanding and learning how to use a graphing calculator well
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blitzkrieg21
996 posts
blitzkrieg21
#18 h  Aug 19, 2016, 6:58 PM • 1 Y
Y by Adventure10
If you do MC or other math competitions, the calculations/manipulations (factoring, determining solutions, etc) should be a piece of cake
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Littlelachy
934 posts
Littlelachy
#19 h  Aug 20, 2016, 1:36 PM • 2 Y
Y by Adventure10, Mango247
Robo_J wrote:
What is the best way to study for a common core algebra 1 final? Resources would be awesome :blush:

Woah what?

Isn't algebra non-final? Aren't finals for high school only?
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HL226
32 posts
HL226
#20 h  Aug 20, 2016, 2:08 PM • 2 Y
Y by Adventure10, Mango247
For what
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zxcv1337
1631 posts
zxcv1337
#21 h  Aug 20, 2016, 3:22 PM • 2 Y
Y by Adventure10, Mango247
@LittleLachy I think his school offers it in Middle School. (My school does, you can take Algebra 1 in 7th grade, even in 6th grade)
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reaganchoi
5289 posts
reaganchoi
#22 h  Aug 21, 2016, 5:29 AM • 1 Y
Y by Adventure10
Littlelachy wrote:
Robo_J wrote:
What is the best way to study for a common core algebra 1 final? Resources would be awesome :blush:

Woah what?

Isn't algebra non-final? Aren't finals for high school only?

Technically, for us, Algebra 1 is a high school course.
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SPG2500
856 posts
SPG2500
#23 h  Aug 21, 2016, 7:17 AM • 1 Y
Y by Adventure10
Yeah. Algebra I and up are all high school courses (at least in NJ)
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Littlelachy
934 posts
Littlelachy
#24 h  Aug 21, 2016, 12:22 PM • 2 Y
Y by Adventure10, Mango247
ramarnath2 wrote:
@LittleLachy I think his school offers it in Middle School. (My school does, you can take Algebra 1 in 7th grade, even in 6th grade)

Lucky our school is cheap and won't let people take Algebra Geo ect. in 6th meanwhile 5 years ago my friend took Algebra II in 6th grade.
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reaganchoi
5289 posts
reaganchoi
#25 h  Aug 21, 2016, 1:27 PM • 1 Y
Y by Adventure10
Alg 2 in 6th? Darn our school only lets us skip 1 a year (so 6th in 5th, 8th in 6th, 10th in 7th, etc.)
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NorwegianStar
120 posts
NorwegianStar
#26 h  Aug 21, 2016, 3:17 PM • 2 Y
Y by Adventure10, Mango247
I am going to 9th grade, taking algebra 2. How hard is it
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fishy15
2219 posts
fishy15
#27 h  Aug 21, 2016, 4:36 PM • 2 Y
Y by Adventure10, Mango247
it depends on your ability as an algebra student
can you manipulate equations well?
can you understand variables like a second language?
if the answer is yes, then algebra 2 will be easy for you
if the answer is no, you will have to put in a little work but it is still doable

also next time when you have a new question please post it in another topic (unless it is relevant)
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HenryZhang
225 posts
HenryZhang
#28 h  Aug 21, 2016, 10:08 PM • 2 Y
Y by Adventure10, Mango247
just read your textbook
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math129
700 posts
math129
#29 h  Aug 21, 2016, 11:10 PM • 1 Y
Y by Adventure10
HenryZhang wrote:
just read your textbook

Sometimes teachers don't use textbooks much in class. If your teacher used the textbook on a daily basis, then maybe you could do the above.
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blitzkrieg21
996 posts
blitzkrieg21
#30 h  Aug 22, 2016, 2:44 AM • 2 Y
Y by Adventure10, Mango247
Im taking Precalc in 8th grade :D
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blitzkrieg21
996 posts
blitzkrieg21
#31 h  Aug 22, 2016, 2:44 AM • 2 Y
Y by Adventure10, Mango247
Which begins in 5 days for me :O
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Flash12
2837 posts
Flash12
#32 h  Aug 22, 2016, 4:45 AM • 1 Y
Y by Adventure10
wow such a beast
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Temp456
994 posts
Temp456
#33 h  Aug 22, 2016, 12:54 PM • 4 Y
Y by TopNotchMath, blitzkrieg21, Adventure10, Mango247
blitzkrieg21 wrote:
Which begins in 5 days for me :O

Hello, this is incorrect, as Wake county school system starts on the 29th. Unless you have changed schools without my knowing...
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blitzkrieg21
996 posts
blitzkrieg21
#34 h  Aug 22, 2016, 4:50 PM • 2 Y
Y by Adventure10, Mango247
oh no I meant that that was the date of my orientation yah school starts on the 29th...
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blitzkrieg21
996 posts
blitzkrieg21
#35 h  Aug 22, 2016, 4:52 PM • 2 Y
Y by Adventure10, Mango247
Flash12 wrote:
wow such a beast

ugh why are you following me?

No wonder you were banned from the URC forum :diablo:
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Flash12
2837 posts
Flash12
#36 h  Aug 22, 2016, 5:15 PM • 1 Y
Y by Adventure10
blitzkrieg21 wrote:
Flash12 wrote:
wow such a beast

ugh why are you following me?

No wonder you were banned from the URC forum :diablo:


Hi your logic makes no sense since I posted in the rubik's cube forum after.
Besides, I occasionally scroll through MSM, which is not banned by the AoPS TOS, so I am allowed to do so. Also, please learn to edit your post and not double post.
At least when I was posting in URC I never double posted ;)
This post has been edited 1 time. Last edited by Flash12, Aug 22, 2016, 5:16 PM
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blitzkrieg21
996 posts
blitzkrieg21
#37 h  Aug 22, 2016, 8:38 PM • 1 Y
Y by Adventure10
@Flash12 why u so savage? Like why does it bother you if I double post?

Also you are so smart since you just now found out that I don't use logic :/
This post has been edited 2 times. Last edited by blitzkrieg21, Aug 22, 2016, 8:49 PM
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NorwegianStar
120 posts
NorwegianStar
#38 h  Aug 22, 2016, 11:49 PM • 2 Y
Y by Adventure10, Mango247
Wow blitzkrieg you are smart I'm in algebra 2 in 9th grade!
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reaganchoi
5289 posts
reaganchoi
#39 h  Aug 23, 2016, 12:58 AM • 1 Y
Y by Adventure10
wait darn im algebra 2 in 7th
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