ka April Highlights and 2025 AoPS Online Class Information
jlacosta0
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)!
Prealgebra 1
Sunday, Apr 13 - Aug 10
Tuesday, May 13 - Aug 26
Thursday, May 29 - Sep 11
Sunday, Jun 15 - Oct 12
Monday, Jun 30 - Oct 20
Wednesday, Jul 16 - Oct 29
Introduction to Algebra A
Monday, Apr 7 - Jul 28
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
Wednesday, Apr 16 - Jul 2
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
Thursday, Apr 17 - Jul 3
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
Wednesday, Apr 16 - Jul 30
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14
Introduction to Geometry
Wednesday, Apr 23 - Oct 1
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
Intermediate: Grades 8-12
Intermediate Algebra
Monday, Apr 21 - Oct 13
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
Wednesday, Apr 16 - Jul 2
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
Friday, Apr 11 - Jun 27
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
Every day, I will try to post a new problem for you all to solve! If you want to post a daily problem, you can! :)
Please hide solutions and answers, hints are fine though! :)
Problems usually get harder throughout the week, so Sunday is the easiest and Saturday is the hardest!
Past Problems!
[quote=March 21st Problem]Alice flips a fair coin until she gets 2 heads in a row, or a tail and then a head. What is the probability that she stopped after 2 heads in a row? Express your answer as a common fraction.[/quote] Answer
[quote=March 22nd Problem]In a best out of 5 math tournament, 2 teams compete to solve math problems, with each of the teams having a 50% chance of winning each round. The tournament ends when one team wins 3 rounds. What is the probability that the tournament will end before the fifth round? Express your answer as a common fraction.[/quote] Answer
[quote=March 23rd Problem]The equations of and intersect at the point . What is the value of ?[/quote] Answer
[quote=March 24th Problem]Anthony rolls two fair six sided dice. What is the sum of all the different possible products of his rolls?[/quote] Answer
[quote=March 25th Problem]If , find the value of .[/quote] Answer
[quote=March 26th Problem]There is a group of 6 friends standing in line. However, 3 of them don't want to stand next to each other. In how many ways can they stand in line?[/quote] Answer
[quote=March 27th Problem]Two real numbers, and are chosen from 0 to 1. What is the probability that their positive difference is more than ?[/quote] Answer
[quote=March 28th Problem]What is the least possible value of the expression ?[/quote] Answer
[quote=March 29th Problem]How many integers from 1 to 2025, inclusive, contain the digit “1”?[/quote] Answer
[quote=April 3rd Problem]In families, there are children respectively. If a random child from any of the families is chosen, what is the probability that the child has siblings? Express your answer as a common fraction.[/quote] Answer
[quote=April 5th Problem]A circle with a radius of 3 units is centered at the point (0,0) on the coordinate plane. How many lattice points, points which both of the coordinates are integers, are strictly inside the circle?[/quote] Answer
[quote=April 6th Problem]If the probability that someone asks for a problem is , find the probability that out of people, exactly of them ask for a problem.[/quote] Answer
[quote=April 8th Problem]Find the value of such that .[/quote] Answer
[quote=April 9th Problem]In unit square , point lies on diagonal such that . Find the area of quadrilateral .[/quote] Answer
[quote=April 10th Problem]An function in the form has ,, and . Find the value of .[/quote] Answer
A store sells a strawberry flavoured candy for 1 dollar each. The store offers a promo where every 4 candy wrappers can be exchanged for one candy. If there is no limit to how many times you can exchange candy wrappers for candies, what is the maximum number of candies I can obtain with 100 dollars?
My favorite problems on the state test were target #6 and sprint #29. I loved the aha moment when I saw pascal's triangle on target #6, and even though I got sprint #29 wrong due to a long division error, it was so much fun to use the sum of the factors trick to find the right answer!
Also: My score was 29 with 12 on target and 17 (sad sillies) on sprint, so I didn't make CDR
This post has been edited 1 time. Last edited by Ljviolin11, Apr 1, 2025, 3:03 PM
let the legs of the triangle be and . Then we have Additionally, by the triangle inequality, we know the hypotenuse is less than , and because it is the longest side, it is greater than Also, because the question simply asks for the length of the hypotenuse without "simplest radical form" or "common fraction" at the end of the problem, we know the hypotenuse is an integer. Thus, the only numbers that can be the length of the hypotenuse are ,,,,, and . Plugging values into the equation in line yields
let the legs of the triangle be and . Then we have Additionally, by the triangle inequality, we know the hypotenuse is less than , and because it is the longest side, it is greater than Also, because the question simply asks for the length of the hypotenuse without "simplest radical form" or "common fraction" at the end of the problem, we know the hypotenuse is an integer. Thus, the only numbers that can be the length of the hypotenuse are ,,,,, and . Plugging values into the equation in line yields
bruh even worse sol, calc bash and guess based on answer form
; a^2+b^2=c^2 and a+b = 40-c. Square the second equation. a^2+b^2+2ab=1600+c^2-80c. Cancel out a^2+b^2 and c^2 from both sides since they are equivalent. 2ab = 1600-80c. In the problem we are given that ab/2 = 20 so 2ab=80. Now 1600-80c=80 or c=19.
I randomly added up all the squares from 1 to 2025 and divided that by the sum of all integers 1-2025 (I don't even know why) and somehow got the right answer.
I randomly added up all the squares from 1 to 2025 and divided that by the sum of all integers 1-2025 (I don't even know why) and somehow got the right answer.
I used a method kind of guessing but we can see the number of subsets that have 2025 as the greateset is (Not Blank)
2^2025-1
Then the number of subsets that have 2024 as the greatest is:
2^2024 -1
Then the numbers of subsets that have 2023 as the greatest is:
2^2023-1
We establish a pattern similar to an geometric sequence but not exact.... 1/2, 1/4, 1/8, 1/16, 1/32,1/64,1/128,1/256 So with this pattern we already know that the numbers that count the most are the first 3 numbers that I listed but if you look at it carefully you can see that when you subtract some integer n from n_1+n_2 we see what it is always 1/2^n so we can use this finding to see that is has to be somewhere between 2024>=x>=2023
but we again see that 1/4-1/8=1/8 so we are done and our final answer is
This post has been edited 1 time. Last edited by sadas123, Apr 5, 2025, 11:09 AM