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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
Yesterday at 11:16 PM
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)!

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[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
Yesterday at 11:16 PM
0 replies
J
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Maximum value of n
Ecrin_eren   0
33 minutes ago


"Let M be the set {1, 2, 3, ..., 2025}. Jack selects n different subsets of M. If the union of any two subsets Jack selects is never equal to M, what is the maximum possible value of n?"

0 replies
Ecrin_eren
33 minutes ago
0 replies
J
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How many integer pairs
Ecrin_eren   0
38 minutes ago

"Let m and n be integers. How many different integer pairs (m, n) satisfy the equation m^3 - 3m^2n + 4n^3 = 44?"

0 replies
Ecrin_eren
38 minutes ago
0 replies
J
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How many triangles
Ecrin_eren   0
an hour ago


"Inside a triangle, 2025 points are placed, and each point is connected to the vertices of the smallest triangle that contains it. In the final state, how many small triangles are formed?"


0 replies
Ecrin_eren
an hour ago
0 replies
J
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Find the functions
Ecrin_eren   2
N 2 hours ago by Ecrin_eren
"Find all differentiable functions f that satisfy the condition f(x) + f(y) = f((x + y) / (1 - xy)) for all x, y ∈ R, where xy ≠ 1."
2 replies
Ecrin_eren
Yesterday at 8:58 PM
Ecrin_eren
2 hours ago
J
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All possible values of k
Ecrin_eren   1
N 2 hours ago by Ecrin_eren


The roots of the polynomial
x³ - 2x² - 11x + k
are r₁, r₂, and r₃.

Given that
r₁ + 2r₂ + 3r₃ = 0,
what is the product of all possible values of k?

1 reply
Ecrin_eren
4 hours ago
Ecrin_eren
2 hours ago
J
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Angle AEB
Ecrin_eren   1
N 2 hours ago by Ecrin_eren
In triangle ABC, the lengths |AB|, |BC|, and |CA| are proportional to 4, 5, and 6, respectively. Points D and E lie on segment [BC] such that the angles ∠BAD, ∠DAE, and ∠EAC are all equal. What is the measure of angle ∠AEB in degrees?

1 reply
Ecrin_eren
3 hours ago
Ecrin_eren
2 hours ago
J
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20 fair coins are flipped, N of them land heads 2024 TMC AIME Mock #6
parmenides51   6
N 3 hours ago by MelonGirl
$20$ fair coins are flipped. If $N$ of them land heads, find the expected value of $N^2$.
6 replies
parmenides51
Apr 26, 2025
MelonGirl
3 hours ago
J
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China MO 1996 p1
math_gold_medalist28   0
3 hours ago
Let ABC be a triangle with orthocentre H. The tangent lines from A to the circle with diameter BC touch this circle at P and Q. Prove that H, P and Q are collinear.
0 replies
math_gold_medalist28
3 hours ago
0 replies
J
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A problem with a rectangle
Raul_S_Baz   14
N 4 hours ago by george_54
On the sides AB and AD of the rectangle ABCD, points M and N are taken such that MB = ND. Let P be the intersection of BN and CD, and Q be the intersection of DM and CB. How can we prove that PQ || MN?
IMAGE
14 replies
Raul_S_Baz
Apr 26, 2025
george_54
4 hours ago
J
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Inequalities
sqing   16
N 4 hours ago by sqing
Let $ a,b>0 $ and $ a+ b^2=\frac{3}{4} $.Prove that
$$ \frac{1}{a^3(a+b)} + \frac{2}{b^3(2b+1)} + \frac{16}{2a+1} \geq 24$$Let $ a,b>0 $ and $a^2+b^2=\frac{1}{2} $.Prove that
$$ \frac{1}{a^3(a+b)} + \frac{2}{b^3(2b+1)} + \frac{16}{2a+1} \geq 24$$
16 replies
sqing
Nov 29, 2024
sqing
4 hours ago
J
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Sum of solutions
Ecrin_eren   1
N 4 hours ago by Mathzeus1024

"[(x - 2)^2 + 4] * (x + (1/x)) = 10. What is the sum of the elements in the solution set of this equation?

1 reply
Ecrin_eren
5 hours ago
Mathzeus1024
4 hours ago
J
H
Value of expression
Ecrin_eren   0
5 hours ago
Let a be a root of the equation x^3-x-1=0 , with a>1
What is the value of the expression:
∛(3a^2 - 4a) + ∛(3a^2 + 4a + 2)?
0 replies
Ecrin_eren
5 hours ago
0 replies
J
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Inequalities
sqing   5
N Today at 4:55 AM by sqing
Let $ a,b,c>0 . $ Prove that
$$ \left(1 +\frac{a}{b}\right)\left(1+\frac{b}{c}\right)\left(1+\frac{c}{a}\right )\geq 4\left(\frac{a+b}{b+c}+ \frac{b+c}{a+b}\right)$$$$ \left(1 +\frac{a}{b}\right)\left(1+\frac{b}{c}\right)\left(1+\frac{c}{a}\right )\geq \frac{32}{9}\left(\frac{a+b}{b+c}+ \frac{c+a}{a+b}\right)$$$$ \left(1 +\frac{a}{b}\right)\left(1+\frac{b}{c}\right)\left(1+\frac{c}{a}\right )\geq \frac{8}{3}\left( \frac{a+b}{b+c}+ \frac{b+c}{c+a}+ \frac{c+a}{a+b}\right)$$$$ \left(1 +\frac{a^2}{b^2}\right)\left(1+\frac{b^2}{c^2}\right)\left(1+\frac{c^2}{a^2}\right )\geq \frac{8}{3}\left( \frac{a^2+bc}{b^2+ca}+\frac{b^2+ca}{c^2+ab}+\frac{c^2+ab}{a^2+bc}\right)$$https://artofproblemsolving.com/community/c6h107534p608181:
$$\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\geq 1+\frac{a+b}{b+c}+\frac{b+c}{a+b}$$
5 replies
sqing
Yesterday at 12:20 AM
sqing
Today at 4:55 AM
J
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Inequality
Ecrin_eren   1
N Today at 1:17 AM by sqing


Let a, b, c be positive real numbers. Prove the inequality:

sqrt(a² - ab + b²) + sqrt(b² - bc + c²) ≥ sqrt(a² + ac + c²)



1 reply
Ecrin_eren
Yesterday at 8:47 PM
sqing
Today at 1:17 AM
J
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J
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2014 preRMO p15, computational with right triangle and midpoints
parmenides51   1
N Aug 9, 2019 by NikoIsLife
Let $XOY$ be a triangle with $\angle XOY = 90^o$. Let $M$ and $N$ be the midpoints of legs $OX$ and $OY$, respectively. Suppose that $XN = 19$ and $YM =22$. What is $XY$?
1 reply
parmenides51
Aug 9, 2019
NikoIsLife
Aug 9, 2019
J
2014 preRMO p15, computational with right triangle and midpoints
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Reveal topic tags
geometry
midpoint
right triangle
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parmenides51
30650 posts
parmenides51
#1 h  Aug 9, 2019, 12:35 AM • 2 Y
Y by Adventure10, Mango247
Let $XOY$ be a triangle with $\angle XOY = 90^o$. Let $M$ and $N$ be the midpoints of legs $OX$ and $OY$, respectively. Suppose that $XN = 19$ and $YM =22$. What is $XY$?
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NikoIsLife
9657 posts
NikoIsLife
#2 h  Aug 9, 2019, 12:39 AM • 2 Y
Y by Adventure10, Mango247
Solution
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