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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
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)!

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[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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KSEA NMSC Mock Contest Group B (Last Problem)
Shiyul   5
N an hour ago by Shiyul
Let $a_n$ be a sequence defined by $a_n = a^2 + 1$. Then the product of four consecutive terms in $a_n$ can be written as the product of two terms in $a_n$. Find $p + q$ if $(a_(11))(a_(12))(a_(13))(a_(14)) = (a_p)(a_q)$.
5 replies
Shiyul
Yesterday at 3:09 PM
Shiyul
an hour ago
J
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Distance vs time swimming problem
smalkaram_3549   0
an hour ago
How should I approach a problem where we deal with velocities becoming negative and stuff. I know that they both travel 3 Lengths of the pool before meeting a second time.
0 replies
smalkaram_3549
an hour ago
0 replies
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Regarding IMO prepartion
omega2007   1
N an hour ago by omega2007
<Hey Everyone'>
I'm 10 grader student and Im starting prepration for maths olympiad..>>> From scratch (not 2+2=4 )

Do you haves compilled resources of Handouts,
PDF,
Links,
List of books topic wise
which are shared on AOPS (and from your prespective) for maths olympiad and any useful thing, which will help me in boosting Maths olympiad prepration.
1 reply
omega2007
Yesterday at 3:14 PM
omega2007
an hour ago
J
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School Math Problem
math_cool123   6
N 2 hours ago by anduran
Find all ordered pairs of nonzero integers $(a, b)$ that satisfy $$(a^2+b)(a+b^2)=(a-b)^3.$$
6 replies
math_cool123
Apr 2, 2025
anduran
2 hours ago
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2013 preRMO p4, X,Y,Z collinear XY = 10, XZ = 3, YZ=?
parmenides51   1
N Aug 9, 2019 by GeoMetrix
Three points $X, Y,Z$ are on a striaght line such that $XY = 10$ and $XZ = 3$. What is the product of all possible values of $YZ$?
1 reply
parmenides51
Aug 8, 2019
GeoMetrix
Aug 9, 2019
J
2013 preRMO p4, X,Y,Z collinear XY = 10, XZ = 3, YZ=?
G H J
Reveal topic tags
geometry
algebra
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parmenides51
30629 posts
parmenides51
#1 h  Aug 8, 2019, 6:43 PM • 2 Y
Y by Adventure10, Mango247
Three points $X, Y,Z$ are on a striaght line such that $XY = 10$ and $XZ = 3$. What is the product of all possible values of $YZ$?
Z K Y
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GeoMetrix
924 posts
GeoMetrix
#2 h  Aug 9, 2019, 12:24 AM • 1 Y
Y by Adventure10
pretty easy
case1: $X$ lies b/w $Y$ and $Z$.
in this case $YZ$=$10+3=13$

case2:$Y$ lies b/w $X$ and $Z$
this case is not possible

case3:$Z$ lies b/w $X$ and $Y$
in this case $YZ=XY-YZ=10-3=7$

Product=$13 \times 7=\fbox{91}$
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