ka February Highlights and 2025 AoPS Online Class Information
jlacosta0
Feb 2, 2025
We love to share what you can look forward to this month! The AIME I and AIME II competitions are happening on February 6th and 12th, respectively. Join our Math Jams the day after each competition where we will go over all the problems and the useful strategies to solve them!
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
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.
Introductory: Grades 5-10
Prealgebra 1
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
22 trees are arranged in a circle; on each tree, there is a crow.
Every minute, two crows each move to a neighboring tree.
Is it possible for all the crows, after a certain number of minutes, to gather on the same tree?
Let be a set of rational numbers satisfying contains at least one positive element If , then For all rational number , either or is in
Prove that contains all positive rational number.
is a chord of a circle such that and . Let be the centre of the circle. Join and extend to cut the circle at . (See diagram). Given , find the radius of the circle.
is a chord of a circle such that and . Let be the centre of the circle. Join and extend to cut the circle at . (See diagram). Given , find the radius of the circle.
This post has been edited 2 times. Last edited by djmathman, Aug 24, 2016, 3:57 PM
is a chord of a circle such that and . Let be the centre of the circle. Join and extend to cut the circle at . (See diagram). Given , find the radius of the circle.
Extend EC to a diameter so that the other side of C on the circle where the diameter intersects is A. So then if OE=x then OA=x+1 and AE=2x+1. So then and x=7, so the radius is
that is correct
the chord-chord power theorem states that in a circle with noncollinear chords AB and CD intersecting at E
then (AE)(EB)=(CE)(ED)
or 3*5=1*2x-1 (I use 2x-1 instead of 2x+1 because it elimiates adding 1 - yes I am that lazy (or efficient if you want to be nice about it))
in this case, one of the chords is the diameter so solving for the length of that diameter, (CE+OE+OF where F is the point on circle O diametrically opposite C)
this solves for x, the length of the radius