Difference between revisions of "2006 Cyprus MO/Lyceum/Problems"
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== Problem 6 == | == Problem 6 == | ||
The value of the expression <math>K=\sqrt{19+7\sqrt{3}}-\sqrt{7+4\sqrt{3}}</math> is | The value of the expression <math>K=\sqrt{19+7\sqrt{3}}-\sqrt{7+4\sqrt{3}}</math> is | ||
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A. <math>4</math> | A. <math>4</math> |
Revision as of 11:19, 5 July 2007
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
Problem 12
If
then equals
A.
B.
C.
D.
E.