Difference between revisions of "2007 Cyprus MO/Lyceum/Problems"
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== Problem 8 == | == Problem 8 == | ||
| + | If we substract from 2 the inverse number of <math>x-1</math>, we get the inverse of <math>x-1</math>. Then the number <math>x+1</math> equals to | ||
| + | |||
| + | A. <math>0</math> | ||
| + | |||
| + | B. <math>1</math> | ||
| + | |||
| + | C. <math>-1</math> | ||
| + | |||
| + | D. <math>3</math> | ||
| + | |||
| + | E. <math>\frac{1}{2}</math> | ||
[[2007 Cyprus MO/Lyceum/Problem 8|Solution]] | [[2007 Cyprus MO/Lyceum/Problem 8|Solution]] | ||
Revision as of 11:36, 6 May 2007
Contents
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 valocity 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
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
is a square of side 2 and 
is an arc of the circle with centre the midpoint 
os the side 
and radius 2. The length of the segments 
is
A. 
B. 
C. 
D. 
E. 
Problem 7
If the angle of the diagonal d of a rectangle forms an angle 
with one of its sides, then the area of the recangle is
A. 
B. 
C. 
D. 
E. None of these
Problem 8
If we substract from 2 the inverse number of 
, we get the inverse of . Then the number 
equals to
A.
B.
C.
D.
E.
