Difference between revisions of "2007 Cyprus MO/Lyceum/Problems"
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== Problem 7 == | == Problem 7 == | ||
+ | If the angle of the diagonal d of a rectangle forms an angle <math>60^\circ</math> with one of its sides, then the area of the recangle is | ||
+ | |||
+ | A. <math>\frac{d^2 \sqrt{3}}{4}</math> | ||
+ | |||
+ | B. <math>\frac{d^2}{2}</math> | ||
+ | |||
+ | C. <math>2d^2</math> | ||
+ | |||
+ | D. <math>d^2 \sqrt{2}</math> | ||
+ | |||
+ | E. None of these | ||
[[2007 Cyprus MO/Lyceum/Problem 7|Solution]] | [[2007 Cyprus MO/Lyceum/Problem 7|Solution]] |
Revision as of 12:31, 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