Difference between revisions of "2007 Cyprus MO/Lyceum/Problems"

(Problem 4)
(Problem 4)
Line 49: Line 49:
 
The value of <math>(2*0)*1</math> is
 
The value of <math>(2*0)*1</math> is
  
A. 2
+
A. <math>2</math>
  
B. 1
+
B. <math>1</math>
  
C. 0
+
C. <math>0</math>
  
D. \frac{1}{2}
+
D. <math>\frac{1}{2}</math>
  
E. \frac{5}{2}
+
E. <math>\frac{5}{2}</math>
  
  

Revision as of 12:11, 6 May 2007

Problem 1

If $x-y=1$,then the value of the expression $K=x^2+x-2xy+y^2-y$ is

A. $2$

B. $-2$

C. $1$

D. $-1$

E. $0$

Solution

Problem 2

Given the formula $f(x) = 4^x$, then $f(x+1)-f(x)$ equals to

A. $4$

B. $4^x$

C. $2$$4^x$

D. $4^{x+1}$

E. $3$$4^x$

Solution

Problem 3

A cyclist drives form town A to town B with velocity 40$\frac{km}{h}$ and comes back with velocity 60$\frac{km}{h}$. The mean valocity in $\frac{km}{h}$ for the total distance is

A. 45

B. 48

C. 50

D. 55

E. 100

Solution

Problem 4

We define the operation $a*b = \frac{1+a}{1+b^2}$, $\forall a,b \in \real$.

The value of $(2*0)*1$ 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