ka May Highlights and 2025 AoPS Online Class Information
jlacosta0
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]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.
Introduction to Algebra A
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
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Thursday, May 15 - Jul 31
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Introduction to Number Theory
Friday, May 9 - Aug 1
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Introduction to Algebra B
Tuesday, May 6 - Aug 19
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Introduction to Geometry
Sunday, May 11 - Nov 9
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Paradoxes and Infinity
Mon, Tue, Wed, & Thurs, Jul 14 - Jul 16 (meets every day of the week!)
Intermediate: Grades 8-12
Intermediate Algebra
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
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MATHCOUNTS/AMC 8 Basics
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
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MATHCOUNTS/AMC 8 Advanced
Sunday, May 11 - Aug 10
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AMC 10 Problem Series
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Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Final Fives
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Tuesday, May 27 - Aug 12
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Introduction to Programming with Python
Thursday, May 22 - Aug 7
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Tuesday, Jun 17 - Sep 2
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Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:
To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.
More specifically:
For new threads:
a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.
Examples: Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿) Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"
b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.
Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".
c) Good problem statement:
Some recent really bad post was:
[quote][/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.
For answers to already existing threads:
d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve , do not answer with " is a solution" only. Either you post any kind of proof or at least something unexpected (like " is the smallest solution). Someone that does not see that is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.
e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.
To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!
Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).
The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
Source: Serbian selection contest for the IMO 2025
Determine the smallest positive real number such that there exists a sequence of positive real numbers ,, with the property that for every it holds that: Proposed by Pavle Martinović
centroid wanted, point that minimizes sum of squares of distances from sides
parmenides511
N23 minutes ago
by SuperBarsh
Source: Oliforum Contest V 2017 p9 https://artofproblemsolving.com/community/c2487525_oliforum_contes
Given a triangle , let be the point which minimizes the sum of squares of distances from the sides of the triangle. Let the projections of on the sides of the triangle . Show that is the barycenter of .
Strictly monotone polynomial with an extra condition
Popescu11
N33 minutes ago
by Iveela
Source: IMSC 2024 Day 2 Problem 2
Let be the set of all positive real numbers. Find all strictly monotone (increasing or decreasing) functions such that there exists a two-variable polynomial with real coefficients satisfying for all .
Given triangle ABC, any line d intersects AB at D, intersects AC at E, intersects BC at F. Let O1,O2,O3 be the centers of the circles circumscribing triangles ADE, BDF, CFE. Prove that the orthocenter of triangle O1O2O3 lies on line d.
Try to avoid Directed angles
Let ABC be an acute triangle inscribed in circle . Let be the midpoint of the arc not containing and define similarly. Show that the orthocenter of is the incenter of .
Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2013
It is given polygon with sides . His vertices are marked with numbers such that sum of numbers marked by any consecutive vertices is constant and its value is . If we know that is marked with and is marked with , determine with which number is marked
Triangle has two isogonal conjugate points and . The circle intersects circle at , and the circle intersects circle at . Prove that and are isogonal conjugates in triangle .
Note: Circle is the circle with diameter , Circle is the circle with diameter .
right triangle, midpoints, two circles, find angle
star-1ord0
an hour ago
Source: Estonia Final Round 2025 8-3
In the right triangle , is the midpoint of the hypotenuse . Point is chosen on the leg so that the line segment meets again at (). Let be the reflection of in . The circles and meet again at (). Find the measure of .
is a diameter of a circle with center . Let and be two different points on the circle on the same side of , and the lines tangent to the circle at points and meet at . Segments and meet at . Lines and meet at . Prove that and are concyclic.
is a diameter of a circle with center . Let and be two different points on the circle on the same side of , and the lines tangent to the circle at points and meet at . Segments and meet at . Lines and meet at . Prove that and are concyclic.
This problem is famous , it is from Russia , in that problem , you have to prove is perpendicular to and this is just the key step to solve this CWMO problem.
Let and meet at point , easy to get : , , Notice that , hence is the circumcentre of triangle .because ,hence is collinear , Obviously is the orthocentre of triangle ,hence is perpendicular to .
Join , ; are both concyclic , , Hence are concyclic .
QED.
Solution 1
Note that and
Note that since , lies on the perpendicular bisector of .
Also,
Thus is the circumcenter of , so and thus . Thus is cyclic, similarly is cyclic, so is cyclic.
In fact, here is a more interesting and quicker solution: Solution 2
Rotate about until coincides with , let rotate to . Note that we have and . Also, . Next, and . Thus, . It follows that , so is cyclic, similarly is cyclic, so is cyclic.
I actually went to this year's CWMO, and to be honest, almost the entire Hong Kong team used coordinate geometry to solve both geometry problems - i guess that's our style.
I actually went to this year's CWMO, and to be honest, almost the entire Hong Kong team used coordinate geometry to solve both geometry problems - i guess that's our style.
Wow, that's quite amazing. I also used Pascal to solve this. This is my friend's solution:
and . Thus , therefore lie on a circle centered at , which gives . So , thus . So , which implies that are cyclic.
Dear mathlinkers,
yes, the idea of using Pascal is good in order to have a synthetic proof.
After, we can can show thet this circle goes through the midpoint of AB...
Sincerely
Jean-Louis
Let cut at , cut at . is , the polar of is , the polar of . As is on , must be on , the polar of . Thus are all on , they are collinear and .
It follows that are concyclic.
There's another simple solution. Suppose and meet at (still using the figure above), we easliy get is the orthocenter of . Let be the midpoint of , then we have , hence , which means is tangent to circle at . Similarly, we have is tangent to circle at , so is , thus . Finally, we have are on the nine-point-circle of .
Extend to meet at .Note that is the polar of and it passes through .So the polar of must pass through .Also it is well known that the polar of passes through .So is the polar of which means that .Now the rest is easy:Note that concyclic(why?) which means and everything is oK.
Just a question, do u still need to deal with the config issue where F could be inside or outside the semicircle, or it's ok to just deal with the inside case?
Let and . Then by Brocard's theorem is the polar of , and hence . Now is the polar of lies on the polar of . By La hire's theorem the polar of which is passes through . So collinear. Hence . So is concyclic.
We claim that is the circumcenter of triangle , indeed which is true as is the diameter of the circle with center . So, we now prove that quadrilateral is cyclic, Then, we show that quadrilateral is cyclic, Therefore, since quadrilaterals and are cyclic, we have quadrilateral is cyclic.