User:Rowechen
Here's the AIME compilation I will be doing:
Contents
Problem 7
An angle is drawn on a set of equally spaced parallel lines as shown. The ratio of the area of shaded region to the area of shaded region
is 11/5. Find the ratio of shaded region
to the area of shaded region
Problem 2
A 100 foot long moving walkway moves at a constant rate of 6 feet per second. Al steps onto the start of the walkway and stands. Bob steps onto the start of the walkway two seconds later and strolls forward along the walkway at a constant rate of 2 feet per second. Two seconds after that, Cy reaches the start of the walkway and walks briskly forward beside the walkway at a constant rate of 4 feet per second. At a certain time, one of these three persons is exactly halfway between the other two. At that time, find the distance in feet between the start of the walkway and the middle person.
Problem 3
Let be the product of the first 100 positive odd integers. Find the largest integer
such that
is divisible by
.
Problem 9
The value of the sum
can be expressed in the form
, for some relatively prime positive integers
and
. Compute the value of
.
Problem 8
Determine the remainder obtained when the expression
is divided by
.
Problem 9
Let
where
and
. Determine the remainder obtained when
is divided by
.
Problem 11
A sequence is defined as follows and, for all positive integers
Given that
and
find the remainder when
is divided by 1000.
Problem 10
, and
are positive real numbers such that
Compute the value of
.
Problem 11
,
, and
are complex numbers such that
Let , where
. Determine the value of
.
Problem 12
is a scalene triangle. The circle with diameter
intersects
at
, and
is the foot of the altitude from
.
is the intersection of
and
. Given that
,
, and
, determine the circumradius of
.