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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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 events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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Find the domain and range of $f(x)=\frac{1}{1-2\cos x}.$
Vulch   1
N 9 minutes ago by aidan0626
Find the domain and range of $f(x)=\frac{1}{1-2\cos x}.$
1 reply
Vulch
24 minutes ago
aidan0626
9 minutes ago
J
H
Find the domain and range of $f(x)=\frac{4-x}{x-4}.$
Vulch   1
N 22 minutes ago by aidan0626
Find the domain and range of $f(x)=\frac{4-x}{x-4}.$
1 reply
Vulch
28 minutes ago
aidan0626
22 minutes ago
J
H
Find the domain and range of $f(x)=2-|x-5|.$
Vulch   0
23 minutes ago
Find the domain and range of $f(x)=2-|x-5|.$
0 replies
Vulch
23 minutes ago
0 replies
J
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Inequalities
sqing   5
N an hour ago by pooh123
Let $a,b,c> 0$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1.$ Prove that
$$ (1-abc) (1-a)(1-b)(1-c) \ge 208 $$$$ (1+abc) (1-a)(1-b)(1-c) \le -224 $$$$(1+a^2b^2c^2) (1-a)(1-b)(1-c) \le -5840 $$
5 replies
sqing
Jul 12, 2024
pooh123
an hour ago
J
No more topics!
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J
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sum of areas in hexagon independent of X (2011 Polish JMO R1 p4)
parmenides51   1
N Apr 2, 2021 by Vanew
A convex hexagon $ABCDEF$ is given. Point $X$ is inside this hexagon. The points $K, L, M, N, P, Q$ are the midpoints of the sides $AB, BC, CD, DE, EF, FA$ respectively, . Prove that the sum of the areas of the quadrilaterals $QAKX$, $LCMX$, $NEPX$ does not depend on the choice point $X$.
1 reply
parmenides51
Apr 1, 2021
Vanew
Apr 2, 2021
J
sum of areas in hexagon independent of X (2011 Polish JMO R1 p4)
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parmenides51
30650 posts
parmenides51
#1 h  Apr 1, 2021, 5:51 AM • 1 Y
Y by Mango247
A convex hexagon $ABCDEF$ is given. Point $X$ is inside this hexagon. The points $K, L, M, N, P, Q$ are the midpoints of the sides $AB, BC, CD, DE, EF, FA$ respectively, . Prove that the sum of the areas of the quadrilaterals $QAKX$, $LCMX$, $NEPX$ does not depend on the choice point $X$.
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Vanew
18 posts
Vanew
#2 h  Apr 2, 2021, 5:28 AM
Y by
It's obvious that the sum of the areas of the quadrilaterals $QAKX$, $LCMX$, $NEPX$ equals to half the area of $ABCDEF$
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