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
For a given positive integer , determine the smallest integer , such that it is possible to place numbers around a circle so that the sum of every consecutive numbers takes one of at most values.
Suppose that a,b < or = 2010 are positive integers with b * Lcm(a,b) < or = a * gcd(a,b). Let N be the smallest positive integer value of n such that either nb/a and na/b are integers. What, over all a,b, is the greatest possible value of N?
In school we had this beginners like middle school contest, but we had to right down our solution kind of like usajmo except no proofs. It was also graded out of 7 but I got 4 Points docked for this question. what was my problem??? But I kind of had to rush the solution on this question because there was another problem before this that was like 1000x times harder.
Question:The solutions to the equation x^3-13x^2+ax−48=0 are all positive whole numbers. What is ?
Solution: We can see that we can use Vieta's formulas to find that the product of the roots is , and the sum of the roots is . So we need to find a combination of integers that multiply to and add up to . Let's call the roots of the equation p, q, and r. From Vieta's, we get that and . Looking at the factors of , which is , we try to split the numbers in a way that gives us the correct sum and product. Trying 3, -2, and -8, we see that they add up to and multiply to , so they work. That means the roots of the polynomial are -3, -2, and -8, and the factorization is . Multiplying it out, we get , so we find that a = 46.
Can someone help me understand Vieta's Formula? I am currently learning it for my class. I learned that for a polynomial of degree , all the roots added will give . I also learned that if every single root, multiplies every single root, it will give . I also learned that if all the roots are multiplied, it will give . Is this right? And is there any purpose for these equations?
ChGiven an acute triangle ABC inscribed in circle The altitudes , intersect
each other at . The tangents at and of intersect at . Let be the midpoint of . intersects
at , intersects at
a) Prove that the points lie on the same circle.
b) The circle with diameter intersects the circle at the second point The line intersects at the second point . Prove that are collinear.
I personally probably would have waited until the paper was finished being written before posting the problems online.
To fill in the details for the other response, we note that is a sum of two squares, and so the only possible primes factors are , prime factors of , and primes that are congruent to modulo . If were one of the prime factors, then would be even. But then we would have that , and so it would not be a square. Thus every prime factor of is congruent to modulo . (Since is itself congruent to modulo .) Since is a factor of , this implies that every prime factor of is congruent to modulo , and so . But then , and so would have a prime factor congruent to modulo , a contradiction.
Motivation (USATST p4 trick:
Notice that :
So :
And :
By Fermat's Chrismats theoreme :
Hence :
Which is impossible because quadratique residus mod 4 are 0,1