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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)!

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
Yesterday at 11:16 PM
0 replies
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pink mop through blue
vincentwant   4
N 39 minutes ago by vincentwant
does there exist a corresponding pink mop cutoff for blue? it exists for red and i think green as well but idk about blue

if it exists what was the cutoff thsi year
4 replies
vincentwant
Today at 3:48 AM
vincentwant
39 minutes ago
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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
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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
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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
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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
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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
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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
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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
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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
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SMT Online 2025 Certificates/Question Paper/Grading
techb   9
N Today at 5:18 AM by techb
It is May 1st. I have been anticipating the arrival of my results displayed in the awards ceremony in the form of a digital certificate. I have unfortunately not received anything. I have heard from other sources(AoPS, and the internet), that the certificates generally arrive at the end of the month. I would like to ask the organizers, or the coordinators of the tournament, to at least give us an ETA. I would like to further elaborate on the expedition of the release of the Question Papers and the grading. The question papers would be very helpful to the people who have taken the contest, and also to other people who would like to solve them. It would also help, as people can discuss the problems that were given in the test, and know different strategies to solve a problem they have solved. In regards to the grading, it would be a crucial piece of evidence to dispute the score shown in the awards ceremony, in case the contestant is not satisfied.
9 replies
techb
Yesterday at 7:21 PM
techb
Today at 5:18 AM
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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June contests?
abbominable_sn0wman   4
N Today at 3:57 AM by Sid-darth-vater
are there any good/fun math contests in june? obviously arml, but anything else?
4 replies
abbominable_sn0wman
Today at 1:46 AM
Sid-darth-vater
Today at 3:57 AM
J
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Question about AMC 10
MathNerdRabbit103   7
N Today at 3:49 AM by jb2015007
Hi,

Can anybody predict a good score that I can get on the AMC 10 this November by only being good at counting and probability, number theory, and algebra? I know some geometry because I took it in school though, but it isn’t competition math so it probably doesn’t count.

Thanks.
7 replies
MathNerdRabbit103
Today at 2:53 AM
jb2015007
Today at 3:49 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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Help with math problem
Cizt6464   0
Apr 18, 2025
Source: https://math.mosolymp.ru/upload/files/2018/khamovniki/7/2017-10-07_Kombinatorika.pdf
Given six distinct points on a plane, all pairwise distances between which are different. Prove that there exists a line segment connecting two of these points which is the longest side in one triangle formed by three of the points, and the shortest side in another triangle formed by three of the points.
0 replies
Cizt6464
Apr 18, 2025
0 replies
J
Help with math problem
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Cizt6464
#1 h  Apr 18, 2025, 1:59 PM
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Given six distinct points on a plane, all pairwise distances between which are different. Prove that there exists a line segment connecting two of these points which is the longest side in one triangle formed by three of the points, and the shortest side in another triangle formed by three of the points.
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