2007 Cyprus MO/Lyceum/Problems
Contents
Problem 1
If ,then the value of the expression
is
A.
B.
C.
D.
E.
Problem 2
Given the formula , then
equals to
A.
B.
C.
D.
E.
Problem 3
A cyclist drives form town A to town B with velocity and comes back with velocity
. The mean velocity in
for the total distance is
A.
B.
C.
D.
E.
Problem 4
We define the operation ,
.
The value of is
A.
B.
C.
D.
E.
Problem 5
If the remainder of the division of with
is
, then the remainder of the division of
with
is
A.
B.
C.
D.
E.
Problem 6
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is a square of side 2 and
is an arc of the circle with centre the midpoint
os the side
and radius 2. The length of the segments
is
A.
B.
C.
D.
E.
Problem 7
If the angle of the diagonal d of a rectangle forms an angle with one of its sides, then the area of the recangle is
A.
B.
C.
D.
E. None of these
Problem 8
If we substract from 2 the inverse number of , we get the inverse of
. Then the number
equals to
A.
B.
C.
D.
E.
Problem 9
We consider the sequence of real numbers such that
,
and
,
. The value of the term
is
A.
B.
C.
D.
E.