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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.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]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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Number of real roots
girishpimoli   3
N 6 minutes ago by aidan0626
If $f(x)=x^2-2x$. Then number of real roots of $f(f(f(f(x))))=3$
3 replies
+1 w
girishpimoli
2 hours ago
aidan0626
6 minutes ago
J
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Proving that the line passes through the midpoint.
MTA_2024   2
N an hour ago by Royal_mhyasd
Let $ABC$ be a triangle of orthocenter $H$. The circle of diameter $AC$ and the circumcircle of triangle $AHB$ intersect a second time in $K$.
Prove that the line $(CK)$ passes through the midpoint of segment $HB$.
2 replies
MTA_2024
May 7, 2025
Royal_mhyasd
an hour ago
J
H
Square number
linkxink0603   4
N 3 hours ago by pooh123
Find m is positive interger such that m^4+3^m is square number
4 replies
1 viewing
linkxink0603
Yesterday at 11:20 AM
pooh123
3 hours ago
J
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Inequalities
sqing   7
N 4 hours ago by sqing
Let $ a,b>0, a^2+ab+b^2 \geq 6 $. Prove that
$$a^4+ab+b^4\geq 10$$Let $ a,b>0, a^2+ab+b^2 \leq \sqrt{10} $. Prove that
$$a^4+ab+b^4 \leq 10$$Let $ a,b>0, a^2+ab+b^2 \geq \frac{15}{2} $. Prove that
$$ a^4-ab+b^4\geq 10$$Let $ a,b>0, a^2+ab+b^2 \leq \sqrt{10} $. Prove that
$$-\frac{1}{8}\leq a^4-ab+b^4\leq 10$$
7 replies
sqing
Thursday at 2:42 PM
sqing
4 hours ago
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computational in a tetrahedron (2015 Euler Teachers' MO II p2)
parmenides51   0
Jul 25, 2020
In the $ABCD$ tetrahedron: $AB = 8, BC = 10, AC = 12, BD = 15$. It is known that four segments connecting the vertices of the tetrahedron with the centers of the circles inscribed in opposite faces intersect at one point. Find the lengths of edge $DA$ and $DC$
0 replies
parmenides51
Jul 25, 2020
0 replies
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computational in a tetrahedron (2015 Euler Teachers' MO II p2)
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parmenides51
#1 h  Jul 25, 2020, 4:49 PM
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In the $ABCD$ tetrahedron: $AB = 8, BC = 10, AC = 12, BD = 15$. It is known that four segments connecting the vertices of the tetrahedron with the centers of the circles inscribed in opposite faces intersect at one point. Find the lengths of edge $DA$ and $DC$
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