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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.

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[*]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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a,b,c irrational, f(x)=ax^2+bx+c : [-1,1] to [-1,1] surjective
tom-nowy   1
N 6 minutes ago by alexheinis
Consider a quadratic function $f(x) = ax^2 + bx + c$, where the coefficients $a, b,$ and $c$ are all irrational numbers.
Is it possible for this function to have a maximum value of $1$ and a minimum value of $-1$ over the interval $[-1, 1]$?
1 reply
tom-nowy
Yesterday at 11:03 PM
alexheinis
6 minutes ago
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Inequalities
sqing   3
N an hour ago by DAVROS
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
$$-\frac{1}{8}\leq a^4-ab+b^4\leq 10$$
3 replies
sqing
Yesterday at 2:42 PM
DAVROS
an hour ago
J
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Inequalities
sqing   0
2 hours ago
Let $ 0\leq x,y,z\leq 2. $ Prove that
$$-48\leq (x-yz)( 3y-zx)(z-xy)\leq 9$$$$-144\leq (3x-yz)(y-zx)(3z-xy)\leq\frac{81}{64}$$$$-144\leq (3x-yz)(2y-zx)(3z-xy)\leq\frac{81}{16}$$
0 replies
sqing
2 hours ago
0 replies
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How inflated are current aime/amc problems
derekli   2
N 4 hours ago by Mathgloggers
So I've been working on a math grinding tool in Stellar Learning (https://stellarlearning.app/competitive) and I was wondering how to make an algorithm that can calculate the difficulty of a problem. Specifically I want to know how difficult past AIMEs and AMC 10s and other contests are, compared to our current contests. I'm planning to make a problem ELO system similar to mathdash or something like that. Any help would be appreciated! Again if you would like to support me you may consider joining our developer team! :D
2 replies
derekli
Today at 1:30 AM
Mathgloggers
4 hours ago
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2023 Official Mock NAIME #15 f(f(f(x))) = f(f(x))
parmenides51   1
N 6 hours ago by jasperE3
How many non-bijective functions $f$ exist that satisfy $f(f(f(x))) = f(f(x))$ for all real $x$ and the domain of f is strictly within the set of $\{1,2,3,5,6,7,9\}$, the range being $\{1,2,4,6,7,8,9\}$?

Even though this is an AIME problem, a proof is mandatory for full credit. Constants must be ignored as we dont want an infinite number of solutions.
1 reply
parmenides51
Dec 4, 2023
jasperE3
6 hours ago
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Inequalities
sqing   3
N Today at 3:29 AM by sqing
Let $ a,b>0 $ and $\frac{a}{a^2+3}+ \frac{b}{b^2+ 3} \geq \frac{1}{2} . $ Prove that
$$a^2+ab+b^2\geq 3$$$$a^2-ab+b^2 \geq 1 $$Let $ a,b>0 $ and $\frac{a}{a^3+3}+ \frac{b}{b^3+ 3}\geq \frac{1}{2} . $ Prove that
$$a^3+ab+b^3 \geq 3$$$$ a^3-ab+b^3\geq 1 $$
3 replies
sqing
Wednesday at 12:59 PM
sqing
Today at 3:29 AM
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exist solutions?
teomihai   6
N Today at 12:05 AM by iwastedmyusername
Find how many perfect squares of five different digits there are, with elements from the set ${0,1,4,6,9}$.
6 replies
teomihai
Yesterday at 5:04 PM
iwastedmyusername
Today at 12:05 AM
J
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A pentagon inscribed in a circle of radius √2
tom-nowy   6
N Yesterday at 11:55 PM by anticodon
Can a pentagon with all rational side lengths be inscribed in a circle of radius $\sqrt{2}$ ?
6 replies
tom-nowy
May 6, 2025
anticodon
Yesterday at 11:55 PM
J
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Menelau's theorem
noneofyou34   6
N Yesterday at 11:10 PM by Shan3t
Please can someone help me prove that orthocenter of a triangle exists by using Menelau's Theorem!
6 replies
noneofyou34
Yesterday at 5:52 PM
Shan3t
Yesterday at 11:10 PM
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Math analytical geometry
JDog22   2
N Yesterday at 8:37 PM by Alex-131
Could you please tell me if this is correct:
If you take the position vector of an arbitrary point P, which is known to lie on the plane E, then the dot product of P and the normal vector n always results in the same number, regardless of the coordinates of point P. As long as the point lies on the plane, this calculation always gives the same number. Is that true?
2 replies
JDog22
Yesterday at 8:24 PM
Alex-131
Yesterday at 8:37 PM
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Hard Inequality
William_Mai   14
N Yesterday at 5:34 PM by hi2024IMOp14
Given $a, b, c \in \mathbb{R}$ such that $a^2 + b^2 + c^2 = 1$.
Find the minimum value of $P = ab + 2bc + 3ca$.

Source: Pham Le Van
14 replies
William_Mai
May 3, 2025
hi2024IMOp14
Yesterday at 5:34 PM
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Geometry
MTA_2024   7
N Yesterday at 4:56 PM by hi2024IMOp14
Let $ABC$ be a triangle such that $AB=3$,$BC=5$ and $AC=6$.Let $D$ be a point on side $AC$ and $E$ one on side $BC$ so that the line $DE$ is tangent to the incircle of $\triangle ABC$ .
Evaluate the perimeter of triangle $\triangle CDE$.
7 replies
MTA_2024
Wednesday at 6:52 PM
hi2024IMOp14
Yesterday at 4:56 PM
J
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four point lie on circle
Kizaruno   0
Yesterday at 3:29 PM
Let triangle ABC be inscribed in a circle with center O. A line d intersects sides AB and AC at points E and D, respectively. Let M, N, and P be the midpoints of segments BD, CE, and DE, respectively. Let Q be the foot of the perpendicular from O to line DE. Prove that the points M, N, P, and Q lie on a circle.
0 replies
Kizaruno
Yesterday at 3:29 PM
0 replies
J
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Range if \omega for No Inscribed Right Triangle y = \sin(\omega x)
ThisIsJoe   0
Yesterday at 2:02 PM
For a positive number \omega , determine the range of \omega for which the curve y = \sin(\omega x) has no inscribed right triangle.
Could someone help me figure out how to approach this?
0 replies
ThisIsJoe
Yesterday at 2:02 PM
0 replies
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Complex Numbers
luiz   2
N Mar 31, 2025 by MathIsFun286
Considere the set A:$|2z+3i|$=$|zˆ2|$
What are the maximun and the minimum value of $|z|$ wich belongs to set A ?
2 replies
luiz
Mar 30, 2025
MathIsFun286
Mar 31, 2025
J
Complex Numbers
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Reveal topic tags
complex numbers
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luiz
87 posts
luiz
#1 h  Mar 30, 2025, 10:16 PM
Y by
Considere the set A:$|2z+3i|$=$|zˆ2|$
What are the maximun and the minimum value of $|z|$ wich belongs to set A ?
This post has been edited 12 times. Last edited by luiz, Mar 30, 2025, 10:44 PM
Reason: Yyyyy
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Inaaya
349 posts
Inaaya
#2 h  Mar 30, 2025, 10:17 PM
Y by
fix ur latex plss
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MathIsFun286
145 posts
MathIsFun286
#3 h  Mar 31, 2025, 2:29 AM
Y by
Solution
This post has been edited 1 time. Last edited by MathIsFun286, Mar 31, 2025, 2:30 AM
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