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k a June Highlights and 2025 AoPS Online Class Information
jlacosta   0
Today at 3:57 PM
Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC 10 Problem Series[/list]
For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this 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 a transformative 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][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/list]
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0 replies
1 viewing
jlacosta
Today at 3:57 PM
0 replies
J
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Original Problem on Logarithms
yes45   1
N 3 hours ago by vanstraelen
What is the value of $\log _{xyz}{n}$ if
$\log _{xy}{n} = 48$,
$\log _{yz}{n} = 64$, and
$\log _{z}{n} = 96$?

Answer

Solution
1 reply
yes45
Today at 3:09 PM
vanstraelen
3 hours ago
J
H
Find the value of pq+rs/ps+qr
Darealzolt   1
N 3 hours ago by vanstraelen
Let \(p,q,r,s\) be real numbers that satisfy
\[ p^2+q^2=r^2+s^2 \]\[ p^2+s^2-ps=q^2+r^2+qr \]Hence find the value of \(\frac{pq+rs}{ps+qr}\)

Click to reveal hidden text
1 reply
Darealzolt
Yesterday at 3:40 AM
vanstraelen
3 hours ago
J
H
Original Problem (Complex Numbers)
qrxz17   1
N 4 hours ago by sultanine
Problem: Given that for a complex number \(z\), the value of \(z \cdot \overline{z} +(z+\overline{z})\) is \(19\). Find all complex numbers \(z\).

Answer: Click to reveal hidden text

Solution: Writing the given equation in standard form, we get
\begin{align*} (a+bi)\cdot(a-bi) +[(a+bi)+(a-bi)] =a^2+b^2+2a. \end{align*}
Then we have
\begin{align*} a^2+b^2+2a &= 19 \\ (a+1)^2+b^2 &=20 \end{align*}
This is the standard equation of a circle. So, \(r^2=20\) and \(r=2\sqrt{5}\).

Therefore, the combined value of the sum and product of a complex number and its conjugate is \(19\) when the complex numbers lie on the circle centered at \((-1,0)\) with radius \(2\sqrt{5}\).
1 reply
qrxz17
Today at 3:18 PM
sultanine
4 hours ago
J
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Daily Problem Writing Practice
KSH31415   2
N 4 hours ago by sultanine
I'm trying to get better at writing problems so I decided to challenge myself to write one problem for every day this month (June 2025). I will post them in this thread as well as edit this post with all of them in hide tags. If I can, I'll include a difficulty level in the form of AIME placement. If anybody wants to solve them and give feedback on the problem and/or my difficulty rating, please do!

June 1 (AIME P4)

June 1 (AIME P4)
A bag contains $6$ red balls and $6$ blue balls. A draw consists of randomly selecting $2$ of the remaining balls from bag without replacement, and then setting them aside. A draw is called a match if the two balls have the same color. Compute the expected number of draws until either a match occurs or the bag is empty.
2 replies
KSH31415
Today at 3:13 PM
sultanine
4 hours ago
J
No more topics!
H
J
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Preparation for AMC 10?
LiBoy   3
N Oct 3, 2010 by AlphaMath1
Hi all. I'm in 8th grade and this year I plan to take the AMC 10. I currently have AOPS volume 1 & 2. Can anyone tell me what parts I need to read to do well on AMC10?
Thanks
3 replies
LiBoy
Oct 3, 2010
AlphaMath1
Oct 3, 2010
J
Preparation for AMC 10?
G H J
Reveal topic tags
AMC
AMC 10
geometry
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trigonometry
logarithms
complementary counting
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LiBoy
695 posts
LiBoy
#1 h  Oct 3, 2010, 5:31 PM • 2 Y
Y by Adventure10, Mango247
Hi all. I'm in 8th grade and this year I plan to take the AMC 10. I currently have AOPS volume 1 & 2. Can anyone tell me what parts I need to read to do well on AMC10?
Thanks
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AlphaMath1
1457 posts
AlphaMath1
#2 h  Oct 3, 2010, 5:40 PM • 2 Y
Y by Adventure10, Mango247
Well from what I heard, AoPS Volume 1+Introduction series is more than well enough to ace the AMC 10. Volume 2 is more AMC 12 and AIME.
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dft
821 posts
dft
#3 h  Oct 3, 2010, 5:54 PM • 1 Y
Y by Adventure10
I agree with AlphaMath. To answer your question, read ALL of Volume 1(except for maybe logs, cause that isn't covered in AMC 10, but nice to know) and DO THE PROBLEMS. Have fun!
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AlphaMath1
1457 posts
AlphaMath1
#4 h  Oct 3, 2010, 6:00 PM • 1 Y
Y by Adventure10
So basically you need to know Algebra I, Geometry, Counting/Probability fundamentals (counting, binomial probability, correcting over counting, complementary counting, etc...) and some Number Theory (ex: Modular Arithmetic). You do not need to know stuff like Trigonometry, Complex Numbers, logarithms on the AMC 10 but sometimes they can be helpful.
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