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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)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/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.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

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Introduction to Algebra A
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0 replies
jlacosta
Apr 2, 2025
0 replies
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9 Did I make the right choice?
Martin2001   18
N an hour ago by steve4916
If you were in 8th grade, would you rather go to MOP or mc nats? I chose to study the former more and got in so was wondering if that was valid given that I'll never make mc nats.
18 replies
Martin2001
Yesterday at 1:42 PM
steve4916
an hour ago
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Inequalities
sqing   2
N 3 hours ago by sqing
Let $a,b,c> 0$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1.$ Prove that
$$ (1-abc) (1-a)(1-b)(1-c) \ge 208 $$$$ (1+abc) (1-a)(1-b)(1-c) \le -224 $$$$(1+a^2b^2c^2) (1-a)(1-b)(1-c) \le -5840 $$
2 replies
sqing
Jul 12, 2024
sqing
3 hours ago
J
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the circle problem
miquelmas   0
3 hours ago
Source: Olympiad of the city of Almaty (selection for the IZhO) 2010
The circle ω is centered at the quadrilateral ABCD. The lines AB and CD meet at point K, and the lines AD and BC meet at point L. A line passing through the center of ω and perpendicular to KL intersects KL, CD and AD at P, Q and R respectively. We need to prove that the lines QL, BP and KR all intersect at the same point.
0 replies
miquelmas
3 hours ago
0 replies
J
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How many approaches you got? (A lot)
IAmTheHazard   84
N 5 hours ago by User141208
Source: USAMO 2023/2
Let $\mathbb{R}^+$ be the set of positive real numbers. Find all functions $f \colon \mathbb{R}^+ \to \mathbb{R}^+$ such that, for all $x,y \in \mathbb{R}^+$,
$$f(xy+f(x))=xf(y)+2.$$
84 replies
IAmTheHazard
Mar 23, 2023
User141208
5 hours ago
J
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MasterScholar North Carolina Math Camp
Ruegerbyrd   5
N 6 hours ago by ohiorizzler1434
Is this legit? Worth the cost ($6500)? Program Fees Cover: Tuition, course materials, field trip costs, and housing and meals at Saint Mary's School.

"Themes:

1. From Number Theory and Special Relativity to Game Theory
2. Applications to Economics

Subjects Covered:

Number Theory - Group Theory - RSA Encryption - Game Theory - Estimating Pi - Complex Numbers - Quaternions - Topology of Surfaces - Introduction to Differential Geometry - Collective Decision Making - Survey of Calculus - Applications to Economics - Statistics and the Central Limit Theorem - Special Relativity"

website(?): https://www.teenlife.com/l/summer/masterscholar-north-carolina-math-camp/
5 replies
Ruegerbyrd
Today at 3:15 AM
ohiorizzler1434
6 hours ago
J
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Basic geometry
AlexCenteno2007   5
N Today at 7:02 AM by mathafou
Given an isosceles triangle ABC with AB=BC, the inner bisector of Angle BAC And cut next to it BC in D. A point E is such that AE=DC. The inner bisector of the AED angle cuts to the AB side at the point F. Prove that the angle AFE= angle DFE
5 replies
AlexCenteno2007
Feb 9, 2025
mathafou
Today at 7:02 AM
J
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Generating Functions
greenplanet2050   6
N Today at 6:56 AM by ohiorizzler1434
So im learning generating functions and i dont really understand why $1+2x+3x^2+4x^3+5x^4+…=\dfrac{1}{(1-x)^2}$

can someone help

thank you :)
6 replies
greenplanet2050
Yesterday at 10:42 PM
ohiorizzler1434
Today at 6:56 AM
J
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9 Physical or online
wimpykid   0
Today at 6:49 AM
Do you think the AoPS print books or the online books are better?

0 replies
wimpykid
Today at 6:49 AM
0 replies
J
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Three variables inequality
Headhunter   6
N Today at 6:08 AM by lbh_qys
$\forall a\in R$ ,$~\forall b\in R$ ,$~\forall c \in R$
Prove that at least one of $(a-b)^{2}$, $(b-c)^{2}$, $(c-a)^{2}$ is not greater than $\frac{a^{2}+b^{2}+c^{2}}{2}$.

I assume that all are greater than it, but can't go more.
6 replies
Headhunter
Apr 20, 2025
lbh_qys
Today at 6:08 AM
J
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Sequence
lgx57   8
N Today at 5:08 AM by Vivaandax
$a_1=1,a_{n+1}=a_n+\frac{1}{a_n}$. Find the general term of $\{a_n\}$.
8 replies
lgx57
Apr 27, 2025
Vivaandax
Today at 5:08 AM
J
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Geometric inequality
ReticulatedPython   3
N Today at 4:27 AM by ItalianZebra
Let $A$ and $B$ be points on a plane such that $AB=n$, where $n$ is a positive integer. Let $S$ be the set of all points $P$ such that $\frac{AP^2+BP^2}{(AP)(BP)}=c$, where $c$ is a real number. The path that $S$ traces is continuous, and the value of $c$ is minimized. Prove that $c$ is rational for all positive integers $n.$
3 replies
ReticulatedPython
Apr 22, 2025
ItalianZebra
Today at 4:27 AM
J
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Transformation of a cross product when multiplied by matrix A
Math-lover1   1
N Today at 1:02 AM by greenturtle3141
I was working through AoPS Volume 2 and this statement from Chapter 11: Cross Products/Determinants confused me.
[quote=AoPS Volume 2]A quick comparison of $|\underline{A}|$ to the cross product $(\underline{A}\vec{i}) \times (\underline{A}\vec{j})$ reveals that a negative determinant [of $\underline{A}$] corresponds to a matrix which reverses the direction of the cross product of two vectors.[/quote]
I understand that this is true for the unit vectors $\vec{i} = (1 \ 0)$ and $\vec{j} = (0 \ 1)$, but am confused on how to prove this statement for general vectors $\vec{v}$ and $\vec{w}$ although its supposed to be a quick comparison.

How do I prove this statement easily with any two 2D vectors?
1 reply
Math-lover1
Yesterday at 10:29 PM
greenturtle3141
Today at 1:02 AM
J
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Geometry books
T.Mousavidin   4
N Today at 12:10 AM by compoly2010
Hello, I wanted to ask if anybody knows some good books for geometry that has these topics in:
Desargues's Theorem, Projective geometry, 3D geometry,
4 replies
T.Mousavidin
Yesterday at 4:25 PM
compoly2010
Today at 12:10 AM
J
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trigonometric functions
VivaanKam   3
N Yesterday at 10:08 PM by aok
Hi could someone explain the basic trigonometric functions to me like sin, cos, tan etc.
Thank you!
3 replies
VivaanKam
Yesterday at 8:29 PM
aok
Yesterday at 10:08 PM
J
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J
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A Confused Canadian
sximoz   3
N Apr 3, 2025 by Gavin_Deng
I always wanted to apply for the AMC, and this year, I think I might have a chance. A friend did AMC 8, and she came back telling me I should do it too. I was really enthusiastic, and wanted to apply.

I do not have prior experience with the AMC, and I live in Alberta, Canada. Through my research, I learned that applications must be submitted via an International Group Leader. However, I am uncertain about who they are and what steps I need to take in order to apply. If you have any information about the application, I would greatly appreciate your help.

Additionally, I would be grateful for any advice on how to best prepare for the AMC, particularly the AMC 8, as this may be one of my last opportunities to participate before moving on to the AMC 10. Specifically, I am interested in understanding the scoring system, the format of the contest, and whether it is possible to participate online from my location.

If you have any further info or tips, I would sincerely appreciate your assistance.

Thanks you very much,
sximoz
3 replies
sximoz
Apr 3, 2025
Gavin_Deng
Apr 3, 2025
J
A Confused Canadian
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sximoz
497 posts
sximoz
#1 h  Apr 3, 2025, 10:42 PM
Y by
I always wanted to apply for the AMC, and this year, I think I might have a chance. A friend did AMC 8, and she came back telling me I should do it too. I was really enthusiastic, and wanted to apply.

I do not have prior experience with the AMC, and I live in Alberta, Canada. Through my research, I learned that applications must be submitted via an International Group Leader. However, I am uncertain about who they are and what steps I need to take in order to apply. If you have any information about the application, I would greatly appreciate your help.

Additionally, I would be grateful for any advice on how to best prepare for the AMC, particularly the AMC 8, as this may be one of my last opportunities to participate before moving on to the AMC 10. Specifically, I am interested in understanding the scoring system, the format of the contest, and whether it is possible to participate online from my location.

If you have any further info or tips, I would sincerely appreciate your assistance.

Thanks you very much,
sximoz
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BS2012
1025 posts
BS2012
#2 h  Apr 3, 2025, 10:50 PM
Y by
the AMC 8 is a 25 question 40 minute multiple choice (each question has 5 choices) contest where points are only given for correct answers, and each correct answer is 1 point.

also (dont quote me on this) i dont think you have to apply for the amc, but you register with a testing center near you. i believe canadians can partipate.
This post has been edited 2 times. Last edited by BS2012, Apr 3, 2025, 10:53 PM
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sximoz
497 posts
sximoz
#3 h  Apr 3, 2025, 10:53 PM
Y by
Thank you so much!

I'm wondering where I might find a testing center in my area, as I have not encountered any nearby.
This post has been edited 1 time. Last edited by sximoz, Apr 3, 2025, 10:55 PM
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Gavin_Deng
802 posts
Gavin_Deng
#4 h  Apr 3, 2025, 10:59 PM
Y by
You should simply keep searching for a testing location.
This post has been edited 1 time. Last edited by Gavin_Deng, Apr 3, 2025, 11:03 PM
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