2006 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
A diary industry, in a quantity of milk with $4%$ (Error compiling LaTeX. Unknown error_msg) fat adds a quantity of milk with $1%$ (Error compiling LaTeX. Unknown error_msg) fat and produces kg of milk with $2%$ (Error compiling LaTeX. Unknown error_msg) fat.
The quantity of milk with $1%$ (Error compiling LaTeX. Unknown error_msg) fat, that was added is (in kg)
A.
B.
C.
D.
E.
Problem 2
The operation is defined by
.
The value of the expression
is
A.
B.
C.
D.
E.
Problem 3
The domain of the function is
A.
B.
C.
D.
E.
Problem 4
Given the function ,
Which of the following is correct, about the graph of
?
A. intersects x-axis
B. touches y-axis
C. touches x-axis
D. has minimum point
E. has maximum point
Problem 5
If both integers are bigger than 1 and satisfy
, then the minimum value of
is
A.
B.
C.
D.
E.
Problem 6
The value of the expression is
A.
B.
C.
D.
E.
Problem 7
In the figure, is an equilateral triangle and
,
,
. If
, then the length of the side os the triangle ABC is
A.
B.
C.
D.
E.
Problem 8
In the figure is a regular 5-sided polygon and
,
,
,
,
are the points of intersections of the extensions of the sides.
If the area of the "star"
is 1, then the area of the shaded quadrilateral
is
A.
B.
C.
D.
E. None of these
Problem 9
If and
, then which of the following is correct
A.
B.
C.
D.
E. None of these
Problem 10
If and
, then the product
equals
A.
B.
C.
D.
E.
Problem 11
The lines and
intersect at the point
. If the line
intersects the axes
and
to the points
and
respectively, then the ratio of the area of the triangle
to the area of the triangle
equals
A.
B.
C.
D.
E.
Problem 12
If
then equals
A.
B.
C.
D.
E.
Problem 13
The sum of the digits of the number is
A.
B.
C.
D.
E. None of these
Problem 14
The rectangle is a small garden divided to the rectangle
and to the square
, so that
and the shaded area of the triangle
is
. The area of the whole garden is
A.
B.
C.
D.
E.
Problem 15
The expression : equals
A.
B.
C.
D.
E.