[/quote]
,
and 
are independently and uniformly randomly chosen subsets of 
.
be the conditional probability that the intersection of 
,
have?
be a cyclic quadrilateral with circumcircle 
.
and 
intersect at point 
,
,
.
is tangent to segments 
at points 
respectively,and intersects with circle 
.
intersect line 
at 
respectively.Show that 
are concyclic.
with 
.![$P(x,y) \in \mathbb Q[x,y]$](http://latex.artofproblemsolving.com/b/3/7/b37942b05292a493c8e350322adc122205bc778d.png)
?
such that
for all 
.
satisfies 
.
,
at 
,
be the midpoint of 
intersect 
at 
,
meet 
,
meet 
at 
.
are concurrent.
be its circumcenter and 
its incenter.
be the isogonal conjugate of 
be the Gergonne point of the triangle 
is parallel with line 
.
such that the value of the
is a square of an integer.
for which the following statement holds: there exists at least one triple 
of integers such that
and all triples 
are integers.
be a rational function with complex coefficients whose denominator does not have multiple roots. Let 
be the complex roots of 
and 
be the roots of 
.
is a simple root of ![\[ \sum_{k=1}^m \frac{1}{w_k - u_0} = 2\sum_{k = 1}^n\frac{1}{u_k - u_0}.\]](http://latex.artofproblemsolving.com/6/f/3/6f36b138d97a24d1941d21f7ffbc11530ca2adde.png)
and 
are interior points of the edges 
and 
and 
,
and 
,
then 
Y by RadioActive, nosaj, MathLearner01, flamefoxx99, football017, Benq, mathsolver101, chessderek, kj2002, greenchicken, C-bass, Adventure10, Mango247, and 9 other users
I recently (as in in the shower yesterday) had the idea of making a mock MATHCOUNTS competition. Unlike most mock competitions, I was thinking of releasing multiple tests (School, Chapter, State, and possibly National Mock Tests) over the course of the whole mock Mathocunts "season".
The competition will go as follows: I will release each level of the competition every month or so. You will have a 1-2 week window to officially submit your test answers, through PM. For the PM, please refrain yourself to use LaTex! Write fractions in the form A/B,
as pi, and square roots in the form sqrtx. Every test will have a raw maximum of 46, and the raw score is calculated by 
. Taking the raw scores, your official score will be calculated by ![$2\cdot\text{[School Raw Score]} + 3\cdot\text{[Chapter Raw Score]} + 4\cdot\text{[State Raw Score]} + 5\cdot\text{[National Raw Score]} = \text{Final Score}$](//latex.artofproblemsolving.com/8/9/7/8973b84c52be08db279270a1cd0f74fdb1505dac.png)
. After doing some math, you will find that the maximum score is a score of 
. If you submit your answers after the window is over, I will only grade it and send it back to you, deeming it useless contributing to your mock season score.
Each test packet contains a traditional 30 questions for sprint, and a traditional 8 questions for the Target Round. Every question in the sprint is designed such that calculators are unnecessary in solving the problem, so calculators are strcitly prhibited for the Sprint Round of the portion, with a time limit of 40 minutes. On the contrary, the Target Round is designed to have the assistance of a non-computer calculator, so follow accordingly. Instructions are thoroughly explained in each test packet. Feel free to print out the packet to solve or keep!
When submitting your answers, submit them to Th3Numb3rThr33 (dur). Do NOT include labels (such as "1337 Leets"), and please number your answers. While breaking the above two recommendations will not result in a penalty, it will make it extremely easy for me to grade the tests (using diffchecker.com).
By the way, this was inspired by the Mock AMC 6, and iNomOnCountdown's Mock MATHCOUNTS test. Check them both out!
=======================================================================
EDIT: The Chapter Competition is up and running! Deadline for submissions is February 28, 2015, at 11:59 PM. Do the test while you can!
ERRATA LIST FOR CHAPTER COMPETITION:
The competition will go as follows: I will release each level of the competition every month or so. You will have a 1-2 week window to officially submit your test answers, through PM. For the PM, please refrain yourself to use LaTex! Write fractions in the form A/B,
as pi, and square roots in the form sqrtx. Every test will have a raw maximum of 46, and the raw score is calculated by 
. Taking the raw scores, your official score will be calculated by ![$2\cdot\text{[School Raw Score]} + 3\cdot\text{[Chapter Raw Score]} + 4\cdot\text{[State Raw Score]} + 5\cdot\text{[National Raw Score]} = \text{Final Score}$](http://latex.artofproblemsolving.com/8/9/7/8973b84c52be08db279270a1cd0f74fdb1505dac.png)
. After doing some math, you will find that the maximum score is a score of 
. If you submit your answers after the window is over, I will only grade it and send it back to you, deeming it useless contributing to your mock season score.Each test packet contains a traditional 30 questions for sprint, and a traditional 8 questions for the Target Round. Every question in the sprint is designed such that calculators are unnecessary in solving the problem, so calculators are strcitly prhibited for the Sprint Round of the portion, with a time limit of 40 minutes. On the contrary, the Target Round is designed to have the assistance of a non-computer calculator, so follow accordingly. Instructions are thoroughly explained in each test packet. Feel free to print out the packet to solve or keep!
When submitting your answers, submit them to Th3Numb3rThr33 (dur). Do NOT include labels (such as "1337 Leets"), and please number your answers. While breaking the above two recommendations will not result in a penalty, it will make it extremely easy for me to grade the tests (using diffchecker.com).
By the way, this was inspired by the Mock AMC 6, and iNomOnCountdown's Mock MATHCOUNTS test. Check them both out!
=======================================================================
EDIT: The Chapter Competition is up and running! Deadline for submissions is February 28, 2015, at 11:59 PM. Do the test while you can!
ERRATA LIST FOR CHAPTER COMPETITION:
This post has been edited 15 times. Last edited by Th3Numb3rThr33, Feb 21, 2015, 11:54 PM
