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)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
Tuesday, Jul 15 - Oct 28
Introduction to Counting & Probability
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19
Introduction to Number Theory
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30
Introduction to Algebra B
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14
Introduction to Geometry
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19
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
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22
MATHCOUNTS/AMC 8 Basics
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
MATHCOUNTS/AMC 8 Advanced
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21
AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22
Introduction to Programming with Python
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22
Let be a random point on the smaller arc of the circumcircle of square , and let be the intersection point of segments and . The feet of the tangents from point to the circumcircle of the triangle are and , where is the center of the square. Prove that points ,, and lie on a single circle.
In 3D space , a cone has a vertex at , and its base is a circle lying on the plane . The angle at the cone's vertex is . Write the equation of a plane that contains the x-axis and divides the cone into two parts with a volume ratio of (the part containing vertex can have the smaller volume).
a) Given is a right cylinder of height and radius .
The sun shines on this solid at an angle of .
What is the area of the shadow that this solid casts on the plane of the botom base?
b) Given is a right cone of height and radius .
The sun shines on this solid at an angle of .
What is the area of the shadow that this solid casts on the plane of the base?
Given a pyramid where is a parallelogram.
The intersection of the diagonals of the base is point .
Point is connected to the midpoint of , point to the midpoint of ,
point to the midpoint of and point to the midpoint of .
a) Prove: the four lines are concurrent in a point .
b) Calulate .
One hemisphere is putting a truncated cone, with the base circles hemisphere. How height should have truncated cone as its lateral area to be minimal side?
Four balls of radius 1 are mutually tangent, three resting on the floor and the fourth resting on the others. A tetrahedron, each of whose edges have length , is circumscribed around the balls. Then equals
Given a regular tetrahedron with edges .
Construct at the apex three perpendiculars to the three lateral faces.
Take a point on each perpendicular at a distance from the apex such that these three points lie above the apex.
Calculate the lenghts of the sides of the triangle.
Given a tetrahedron and a plane , parallel with the edges and . .
a) Prove: the intersection of the tetrahedron with the plane is a parallelogram.
b) If and ,
calculates the lenghts of the sides of this parallelogram.
Given the points
a) Determine the point , above the xy-plane, such that the pyramid is a regular tetrahedron.
b) Calculate the volume.
c) Calculate the radius of the inscribed sphere and the radius of the circumscribed sphere.
volume 9f a pentagonal base pyramid circumscribed around a right circular cone
FOL1
NMay 6, 2025
by Mathzeus1024
A pentagonal base pyramid is circumscribed around a right circular cone, whose height is equal to the radius of the base. The total surface area of the pyramid is d times greater than that of the cone. Find the volume of the pyramid if the lateral surface area of the cone is equal to .
Let ,,. By the condition, , so . In addition, we solve out , so the desired inequality rewrites as or after plugging in and expansion, Let and be fixed such that , then it suffices to prove a linear inequality of . By the method, we may assume . In this case, (1) turns into So it suffices to show that The discrimination of is If , then and we are done. If , then is an increasing function. Since gives , then The proof is complete.
By the way, @mihaig, do you know whether this journal is still alive? And is "VL" an extremely abbreviated form of you and Vasile Cîrtoaje?
This post has been edited 1 time. Last edited by Quantum-Phantom, Apr 25, 2025, 9:40 AM