[/quote]
,
be a cyclic quadrilateral with 
and 
.
and 
are selected on segment 
such that 
.
and 
are selected on segment 
such that 
.
is a cyclic quadrilateral.
be an equilateral triangle with circumcenter 
.
and 
be two points on segments 
and 
,
.
is the reflection of 
,
and 
are parallel.
from the set of positive integers to the set of positive integers such that, for all positive integers 
and 
,![\[ a, f(b) \text{ and } f(b + f(a) - 1).\]](http://latex.artofproblemsolving.com/4/a/b/4ab97da27e05d0f9e7762f74d0d0bd2dc8b9842f.png)
be an acute-angled triangle with 
.
be the circumcircle of 
of 
.
meets 
at 
and meets 
.
at 
.
by 
.
.
.
be a cyclic pentagon inscribed in a circle of centre 
which has angles 
.
and 
meet at a point belonging to the diameter 
.
and the segment 
intersects the circumcircle of 
in a point 
.
be the midpoint of 
is parallel to 
.
be the set of all nonnegative integers. Find all the functions 
satisfying the relation![\[ f(f(f(n))) = f(n+1 ) +1 \]](http://latex.artofproblemsolving.com/8/b/9/8b953428105df2c2344963cbaf3eb81d8201e0df.png)
.
from the nonnegative integers to the integers satisfying 
and ![\[ f(mn) = f(m) + f(n) + f(m)f(n) \]](http://latex.artofproblemsolving.com/e/f/f/eff10a32cffaec742403ebfc46ff09bc8ef7b7c5.png)
for all nonnegative integers 
and 
.
,
,
![\[ \frac {f(x) + f(y)}{2} \ge f\left(\frac {x + y}{2}\right) + |x - y|
\]](http://latex.artofproblemsolving.com/3/b/a/3ba7733caf51cc70a090920ca21f8b47aad9b1ec.png)
and 
.
Y by
So I'm like a 8th grader so almost 9th over the summer and I suck at AMC 10. I got like a 75 for my first time but I can do like almost all the problems from AMC 8 with enough time which I find really weird because most other ppl who can do that get higher AMC 10 scores. I do like the first 11 problems a day from past years to try to at least get down the first 10 questions and move on from there. Does anyone have any good suggestions on how I can boost my AMC 10 scores?
+ something annoying that often happens is like I don't even know where to start when I see a problem.
+ something annoying that often happens is like I don't even know where to start when I see a problem.
