... integers such that the product
of the numbers of any pair plus the half of one of the numbers plus one
third of the other number is three times less than 15.
Q13. Let be given ∆ABC with area (∆ABC) = ... integers such that the product
of the numbers of any pair plus the half of one of the numbers plus one
third of the other number is 7 times less than 2009.
1.3. Hanoi Open Mathematical Olympiad 2008...
... Now that
16x + 1 = (x
2
− y
2
)
2
= (x −y)
2
(x + y)
2
≥ x
2
.
From this we obtain the inequality, x
2
− 16x − 1 < 0. Solving this inequality gives x ∈
{0, 1, ··· ,16}. In addition, 16x + 1 is ... y) = |x − y| + |x
3
− y
3
|
when x, y vary satisfying the restriction x
2
+ y
2
= 1.
Rewriting this as
f(x, y) = |x − y|(1 + x
2
+ xy + y
2
) = |x − y|(2 + xy).
from which we square to arrive ... xy
3
3
=
5
3
3
.
Hence,
f(x, y) ≤
5
3
.
5
3
.
Equality occurs when
xy = −
1
3
, x
2
+ y
2
= 1.
This simultaneous equations are equivalent to
xy = −
1
3
, x + y =
1
√
3
.
5
Hanoi Open Mathematical...
... BANG B * 2009-2010 * ĐỀ CT
SỞ GIÁO DỤC VÀ ĐÀO TẠO KỲ THI CHỌN HỌC SINH GIỎI CẤP TỈNH
KHÁNH HÒA NĂM HỌC 200-2010
Môn thi : TIẾNGANH – THPT (Bảng B)
Ngày thi : 06/04/2010
(Thời ... done nothing more exciting than work at home, read the 00 …….
………
newspaper and watch television. I had begun feeling bored with this 66. ………
and so, last weekend I thought I would do something ... will
_______________________________________________ Page 6 of 7 * HSG 12 BANG B * 2009-2010 * ĐỀ CT
(104) ………… our daily life we need to communicate with (105) ………… We need to
do this mostly by speaking to other people and listening...
... swimming
c) swim
d) to swim
6) There is nothing very ________ to do in that small
town.
a) enjoy
b) enjoyable
Đềthi trắc nghiệm tiếnganhbằng A-0047
1) ________ a letter here for...
... no
c) any
d) not
4) - What are you doing? - ________ .
a) No
b) None
c) Not
d) Nothing
8) Praja returned home as ________ as he could.
a) quick
b) quicker
c) quickly
d)...
... He
b) We
c) You
d) They
7) This book belongs to me, and this pen is ________,
too.
a) his
b) me
Đềthi trắc nghiệm tiếnganhbằng A-0043
1) - Is this your handbag? - ________?
a)...
... she ________ a bicycle.
a) can rode
b) can ride
c) could ride
d) could rode
Đềthi trắc nghiệm tiếnganhbằng A-0041
1) Have you read ________ paper?
a) today
b) today's
c) of ... enough for
a) each other
b) themselves
c) oneself
d) one another
8) Our people began this flight ________ 1973.
a) from
b) at
c) since
d) in
6) They went from one shop to ________....
... the art class were doing self-portraits
by looking at ________ in the mirror.
Đềthi trắc nghiệm tiếnganhbằng A-0040
1) Have you read ________ paper?
a) today
b) today's
c) of ...
d) in today
a) each other
b) themselves
c) oneself
d) one another
8) Our people began this flight ________ 1973.
a) from
b) at
c) since
d) in
a) is
b) are
c) has
d) have
5)...
... c) have
d) got
3) - I haven't got anything for you. - ________!
a) Never mind
b) It isn't the matter
c) Nothing
d) Not problem
4) I often spend two hours ________ ...
6) Give it to ________. It's my pencil.
a) I
b) me
c) my
d) mine
7) I don't think he ________ flowers very much.
a) like
b) liking
a) is
b) it
c) it's
d) is...
...
d) long
6) ________ your brother spend Christmas with you?
a) do
b) does
Đềthi trắc nghiệm tiếnganhbằng A-0038
1) There isn't ________ left.
a) enough sugar
b) sugar enough ... how's
d) when
9) Can you ________ on the light, please?
a) switch
b) switches
a) these
b) this
c) those
d) there
3) I'm tired ________ waiting for him.
a) from
b) for
c) of...
... every
d) The whole
9) We hire out bicycle ________.
a) by hours
b) by an hour
Đềthi trắc nghiệm tiếnganhbằng A-0037
1) I live about twenty km ________ here.
a) away of
b) away from
c)...
... Good-bye
c) Good evening
Đềthi trắc nghiệm tiếnganhbằng A-0036
1) You must ________ your work as soon as possible.
a) started
b) start
c) to start
d) to start to
2) This man has a ________....