2007 Cyprus MO/Lyceum/Problems

Problem 1

If ,then the value of the expression is

A.

B.

C.

D.

E.

Solution

Problem 2

Given the formula , then equals to

A.

B.

C. •

D.

E. •

Solution

Problem 3

A cyclist drives form town A to town B with velocity 40 and comes back with velocity 60. The mean valocity in for the total distance is

A. 45

B. 48

C. 50

D. 55

E. 100

Solution

Problem 4

We define the operation , .

The value of is

A. 2

B. 1

C. 0

D. \frac{1}{2}

E. \frac{5}{2}

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

See also

• 2007 Cyprus MO/Lyceum
• Cyprus Mathematical Olympiad
• Cyprus MO Problems and Solutions
• Mathematics competition resources