!"#$%&'())*)+
), ))
/012345%6(78
Thời gian làm bài : 150 phút (không kể thời gian giao đề)
9:6(2,0 điểm)
( ) ( )
x y x y
x x y y
+ = + +
− − =
9:6)(2,0 điểm)
u, v
(
)
(
)
u u v v v
+ + − + − + =
!"
u v uv
+ + =
9:6+(2,0 điểm)
#$%&'()&'*(+,-.)/#-0''1+
#$0./ 2$0 3 456)7#$%&'(-8456)7
#$%&'1(-9):;.#4#$03<7:
;/#4#$03 2$0=,.)7#$03+
#$%&'(>"#?"@)+#$%&'*(>"#?"A B@+A9
- 2$0@A+/)9/<C<D-E)
(!"!/9F4#D#$%
G(!""E<"H
9:6,(2,0 điểm)
(B",>I<Jx, y, zK"L#M$#N,:,
xOyOz)
x y z
+ + =
G(!"PM-Q,>I
8
8
8RR8
Q
O
O
ORRO
Q
)
Q Q
+ + + + + =
9:6;((2,0 điểm)
(!"PISTU!#VP"W>
"F#$%G:SX<,YKWGPX
G(5)<I#Z5[\
B"]K^T
5
x y
T
y x y
+
=
−
______E4_______
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
E`)>SRRRRRRRRRRRRaGIRRRRRRRRRRRRR
U:bT"]RRRRRRRRRR U:bT"]RRRRRRRR
<
!" 24/6/2012
/01 234(78
=>?2
Bài 1
(2đ)
6@6%AB%CD4E5FG4%(
( ) ( )
x y x y
x x y y
+ = + +
− − =
E#L#)7
( ) ( )
& ( & (
x x y y
x x y y
− + − =
− − =
Q8cQ
2W,\5
_58)\
_
d
d
u
v
u v
uv
u
v
=
=
+ =
⇔
=
=
=
Q8cQ
e7,\df)\
d
x
x
x x
y
y y
y
= −
=
− =
⇔
= −
− =
=
B$Dg"&_f_(8&_f(8&f_(8&f(
Q8cQ
e7,\f)\d
d
x
x
x x
y
y y
y
= −
=
− =
⇔
= −
− =
=
B$Dg"&_f_(8&_f(8&f_(8&f(
E#L"&_f_(8&_f(8&f_(8&f(8&_f_(8&_f(8&f_(8&f(
Q8cQ
Bài 2
(2đ)
%H'I'JK5%L'MNOJPH'%H(
(
)
(
)
u u v v v+ + − + − + =
%Q4E$64%(
u v uv
+ + =
B;4
(
)
(
)
& ( & ( u u v v u u v v
+ + − + − + = ⇒ + + = − + − +
Q8cQ
(
)
(
)
& ( & ( u u v v u u v v
+ + − + − + = ⇒ + − = − + + −
Q8cQ
a,
& ( 8 & ( u v u v u v u v
+ − = + − − + + − = − + + − +
Q8cQ
9#,[)\
a,
& ( & ( u v uv u v u v uv uv
+ + = + − + + =
Q8cQ
Bài 3
Câu a
(1 đ)
%Q4E$64%9R:5QE6I'4S656TBUCV'5FH4EUCW4E5FX4Y
Q8c
`h<#?"T./)9
B
∠
/h\
∠
@.&9.@/F4#$%&'((
i
∠
@.\
∠
9&99jj@A(>
∠
/h\
∠
9
Q8c
B
∠
9/h\
∠
9 Q8c
B;#
∠
/9[
∠
9\
∠
/h[
∠
9/h[
∠
9
\
∠
9[
∠
9[
∠
9\Q
9#/9<!F4#D"F#$%
Q8c
Bài 3
Câu b
(1đ)
%Q4E$64%FZ4E5P$E6I'R:5P$E6I''[4Y
B
∠
9\
∠
@.\
∠
.9 B
∠
9\
∠
.9
9#39\3.9 a,\.89\9. #?"89P">
,. B;#9
⊥
.
Q8c
9Ejj9>k.
⊥
E&( Q8c
9
∠
.h\
∠
/h>3.hl3/h a,h
\h. h/
Bh9
\h. h/ 9#h\h9 Q8c
99jjE>
h
.E
\
/h
/.
\
h9
.
ih\h9>.E\. &(
B;&()&(,"EH-
Q8c
Bài 4
Câu a
(1 đ)
G$'I'JK4EM\]4^CD4ER_`N\Na5%bP$c4Ud4E5%W6'I'U6eMf6A4JPM(
`g\gaO:
x y z
+ + =
B
x
O
O
x
>mn5n 95<J>5\oW5\c Q8c
p4,5\o
y
[
z
\
g
qgr\&[r(q&g_(&gr_(\
o
9<J8oOOr>oOg_Ogr_ p4,gs\m:Y,>
B$D:Y8rKG
Q8c
p4,5\c
y
[
z
\
c
qr\c&[r(q&_c(&r_c(\
c
9<J8cOOr>_cV?<8c8m
etV$D5\c8\m8r\gcK>,C,TG
Q8cQ
Bài 4
Câu b
(1đ)
%Q4E$64%FZ4E5d45h6)+JK4EM\]4^CD4EP
NP
)
NP
+
NiiNP
)+
JPH'%H(
P
gP
)
gP
+
giigP
)+
O:
Q Q
+ + + + + =
B\
[
[
d
Q8c
u-
c
[
m
[
gc
\
q
n
\
cn
[
mn
[
gcn
)7"`,>I Q8c
9#\
[
c m gc
+ +
÷
[
d
\
[
c
[
d
[
m
[
gc
gc
\
c
\
c c
[
c m
[
c gc
f\
[
c
[
d
[
m
[
oc
[
c
[
( )
c
Q8c
B=,>>"QQ<C8IL,>I
8
8
8 8
Q
K"L>,C,TG
Q8c
Bài 5
Câu a
(1đ)
%Q4E$64%FZ4E^6A45j'%'kP4%l4E5QE6I''m'I'Un4%4Z$5FH4E%Ho'
5F]4$S5UCW4E5FX4pI4fj4%qRM344%b%D4%Ho'pZ4E)q
)
Y
`./9<!P"%&'8X( '.vX8'/vX8'vX8'9vX
p4,'P"&W>(!./9a
./9
\a
'./
[a
'/
[a
'9
[a
'9.
p4,'P"!./9a
./9
Oa
'./
[a
'/
[a
'9
[a
'9.
9#<,Ya
./9
va
'./
[a
'/
[a
'9
[a
'9.
Q8c
Ba
'./
\
'. /Ev
'. '/v
X
&/E<N,T3'./( Q8c
Ba
'/
v
X
8a
'9
v
X
8a
'9.
v
X
Q8c
e)ta
./9
v
X
[
X
[
X
[
X
\X
Q8c
Bài 5
Câu b
(1đ)
%H`O:\R:'I'JK5%L'^CD4E5%P\Ur6JPH'%H`s\t)Y
G$E6I5Fu4%b4%v5'kP
5
x y
T
y x y
+
=
−
Y
B
5 & (
x y
T
xy
+
=
−
Q & ( Q
x y
xy xy xy xy
+
≤ = ⇒ < ≤ ⇒ − >
Q8c
& ( g
& ( & ( & (
xy y x y
x y xy T
xy xy xy xy xy xy
+ +
+ ≥ ⇒ ≥ = =
− − −
Q8c
& & ((
Q & ( g
g
xy xy
xy xy T
+ −
< − ≤ = ⇒ ≥
Q8c
9^,#0!5:)V:5\\
w\E6I5Fu4%b4%v5'kPR:,
Q8c