2007 Cyprus MO/Lyceum/Problems
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 Problem 26
- 27 Problem 27
- 28 Problem 28
- 29 Problem 29
- 30 Problem 30
- 31 See also
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 length 2 and
is an arc of the circle with centre the midpoint
of the side
and radius 2. The length of the segments
is
A.
B.
C.
D.
E.
Problem 7
If a diagonal of a rectangle forms a
angle with one of its sides, then the area of the rectangle is
A.
B.
C.
D.
E. None of these
Problem 8
If we subtract 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.
Problem 10
The volume of an orthogonal parallelepiped is and its dimensions are integers. The minimum sum of the dimensions is
A.
B.
C.
D.
E. None of these
Problem 11
If and
, which of the following is correct?
A.
B.
C.
D.
E.
Problem 12
The function has the properties
and
, where
is a constant. The value of
is
A.
B.
C.
D.
E.
Problem 13
If are the roots of the equation
and
are the roots of the equation
, then the expression
equals to
A.
B.
C.
D.
E.
Problem 14
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In the square ABCD the segment KB equals to the side of the square. The ratio of areas is
A.
B.
C.
D.
E.
Problem 15
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Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
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Problem 22
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Problem 23
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Problem 24
Problem 25
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Problem 26
Problem 27
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Problem 28
Problem 29
Problem 30
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