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To All Interested Mathematics Students
Topic Started: Oct 17 2011, 09:55 AM (67 Views)
Daltizio
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Randolph High School is looking for eight talented mathematics students to represent our school for the Princeton University Mathematics Competition. Students who are interested should be able to solve the problems from previous PUMaCs, AMC10/12s and AIMEs. Please copy the following text into
this link.

Let $X$ and $Y$ be defined such that

\[X=10+12+14+...+102\]
\[Y=12+14+16+...+104\]

What is $Y-X$? (SOURCE: 2011 AMC 10A Problem 4)

Let $a_1,a_2,...$ be a geometric sequence with first term $a$ and common ratio $r$. If $\log_6 a_1+\log_6 a_2+\cdots+\log_6 a_{12}=2006$, then find the number of possible ordered pairs $(a,r)$. (SOURCE: 2006 AIME I Problem 9)

Let $P$ be a polynomial of minimal degree such that \[P\left(\sqrt{3+\sqrt{3+\sqrt{3+\cdots}}}\right)=0\]. Find $P(5)$. (SOURCE: 2010 PUMaC Algebra A)

Let $A_n=\dfrac{n(n-1)}{2}\cos \dfrac{n(n-1)\pi}{2}$. Find $|A_{19}+A_{20}+\cdots+A_{98}|$. (SOURCE: 1998 AIME Problem 5)

Anybody interested should contact Mrs. Franklin during our Science Olympiad meeting on Thursday. (I got consent from her to post this)
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