[/quote]
,
be the set of all functions 
with the following properties:
the following equality holds: 
such that
,
.
such that:
,
bisects neither the angle 
nor the angle 
.
lies inside ![\[\angle PBC=\angle DBA\quad\text{and}\quad \angle PDC=\angle BDA.\]](http://latex.artofproblemsolving.com/c/2/0/c20761f3eadd054958f40259f3d1c05f26279783.png)
Prove that 
.
and 
meet at a point 
be the point of the line 
,
,
.
and 
.
lie on the same circle.
for at least one 
;
for every positive integers 
and 
;
there are infinitely many positive integers 
for all 
.
be positive real numbers such that 
.
knowing that the denominators are positive real numbers.
was chosen such that 
and 
.
.
balls to 
boxes as she wishes. After that, Aslı and Zehra make alternated moves which consists of taking a ball in any wanted box starting with Aslı. One who takes the last ball from any box takes that box to herself. What is the maximum number of boxes can Aslı guarantee to take herself regardless of Zehra's moves?
,
.
and the external angle bisector of 
and 
,
.
![\[f(xf(y) + x) = xy + f(x)\]](http://latex.artofproblemsolving.com/9/9/f/99f580ebc50846e6bc2c004667559922749a4dfa.png)
Y by Adventure10, Mango247, and 1 other user
Hello, I am new to these forums. I am currently a sophomore taking Precalculus that wants to get better at contest mathematics and hopefully qualify for USAMO next year. Last year, I did not qualify for the AIME, but this year, I scored a 117 on the AMC 10A, just enough to take the AIME, and the AIME was very hard for me. I have never had experience with any of the AoPS books and I was just wondering what you guys recommend that I should do in order to qualify for USAMO next year.
I'm thinking of working through AoPS vol 1 to bring up my fundamentals, and then maybe taking an AMC 12 or an AIME class over the summer along with doing the AoPS vol 2 to help on the AIME. I am unsure about the specific AoPS classes such as Precalculus and the Intermediate classes.
What do you suggest that I do? Thank you so much for your help.
I'm thinking of working through AoPS vol 1 to bring up my fundamentals, and then maybe taking an AMC 12 or an AIME class over the summer along with doing the AoPS vol 2 to help on the AIME. I am unsure about the specific AoPS classes such as Precalculus and the Intermediate classes.
What do you suggest that I do? Thank you so much for your help.
