ĐỀ THI THỬ ĐẠI HỌC LẦN III KHỐI A NĂM 2009 Môn Toán




 !""#
$%&
'(()*+,*( "/01
234
Câu I (2 đim)5
-5 6&17*789:1;*+<=>?
@
A@?
!
BC
!5 D++9E/FG1HD
@ !
!
@ C )x x m− + =
IJ90@(K+5
Câu II (2 đim)5
-5 (6(,L1/FG1HD%
( ) ( )
C
!
M - M - ! "
x x
x+
− + + − ≤
!5 (6(/FG1HD%
!
N !O - !x x x x− + − = −


Câu III (2 đim)
-5 P(Q(RS%
- !
C
-
1N -O -
)(+
-
x
x
e x
x
−
→
+ − −
−
!5 DIJ/45TUIJ9&=)*D1(V
BAD
α
∠ =
5(+W1,XN4TO7*N4UOIY
7S$JI7Q(+W19&=V(+W1,XIZ)R([/7Q(9&=+\1JI
β
5R4>5P](K1PI
?S^S7*1E1PI_<(IJ/45TU5
Câu IV (1 đim).1+(&IT7Q(I&IIR)*V,VI5`+(Ha%

C C C ! ! ! ! ! !
C N O N O N Oa b c abc a b c b c a c a b+ + + ≥ + + + + +


b%Mỗi thí sinh chỉ chọn câu Va hoặc Vb
Câu Va (3 đimO5Chương trình cơ bản
-5 H+W1/c1d9\2?=I9F'1c
% ! C "x y∆ + − =
7*(9(E+N-e"OVTNCe@O5
f=1D+1HX9F'1c
∆
+\19(E+I
CMA MB+
uuur uuur
gL15
!5 H_$(7Q(K1d9\2?=hI(9F'1c%
-
-
% !
!
x t
d y t
z t
= −


=


= − +

7*
!
% - C

-
x t
d y t
z t
=


= +


= −

5i/
/FG1HD9F'1c9(^SN-e"e-O7*Ij1I6(9F'1c]
-
7*]
!
5
C5 D+</`Ih1g+f%
!
! "z z+ =
Câu Vb. (3 đim).Chương trình nâng cao
-5 H+W1/c1d9\I(9F'1HZN
-
O%?
!
B=
!
>-C7*N
!

O%N?kO
!
B=
!
>!MIj1S1R(
N!eCO5l(m1/FG1HD9F'1c9(^S7*Ij1N
-
OVN
!
O1n(]o=ISIJ9\]*(
,aS5
!5 H_$(7Q(K1d9\2?=hI(9F'1c%
-
-
% !
!
x t
d y t
z t
= −


=


= − +

7*
!
% - C

-
x t
d y t
z t
=


= +


= −

5i/
/FG1HD+W1IpSIJ9F'_P)*9R7S$JIISIq]
-
7*]
!
5
C5HI&I</`Ih1g+f9(rS_(K
- ! -z i+ + =
V1D+</`IhIJ+]SgL15
sm1s
N&,\I(1(_$(6(1PID1X+O
ttu
oS v \(]S (E+

!
- -
wU>
¡

(Q(R%
)(+
x
y
→±∞
= +∞
4x,(m1(X%=y>@?
C
.?
=y>"
"V !x x⇔ = = ±
T6,(m1(X
?
−∞

!−
"
!
+∞
=y "B""B
=
+∞
+∞
C
- -
*+<9:,(m1HXI&I_6
( ) ( )
!e" V !e− +∞
7*;I,(m1HXI&I_6
( ) ( )

e ! V "e !−∞ −
*+<9R1IxI9R(1R(?>"V=
U
>C5*+<9R1IxI1(ES1R(?>
!±
V=

>-
:1; =
C

C−
- 
C
-2 ?
"!M
"!M
"!M
"!M
! -
:1;*+<
@ !
@ Cy x x= − +
=
C =>)
!
+
-
?
2


C−

!−
--
!
C
4<(K+Iq/FG1HD
@ !
!
@ C )x x m− + =
,a<(9(E+Iq9:1;*+<
"!M
"!M
@ !
@ Cy x x= − +
7*9F'1c=>)
!
+5
li=/FG1HDIJ@(K+_(7*Iz_()
!
+>"WI
!
- ) + C< <

=+>-WI!{+{#
"!M
"!M
 !
- -

l(m1)R(,L1/FG1HD]FQ(]R
M - M -
! ! "
! !
x x
   
− +
+ − ≤
 ÷  ÷
 ÷  ÷
   
W11>
M -
V "5
!
x
t
 
+
>
 ÷
 ÷
 
_(9J
M - -
!
x
t
 
−

=
 ÷
 ÷
 
TL1/FG1HDIJ]R
1B
-
! ! "
t
− ≤

!
! ! - "t t⇔ − + ≤

! - ! -t⇔ − ≤ ≤ +

M - M -
! !
M -
! - ! -
!
) N ! -O ) N ! -O
x
x
+ +
 
+
⇔ − ≤ ≤ +
 ÷
 ÷

 
⇔ − ≤ ≤ +
"!M
"!M
"!M
"!M
! -
(rS_(K%
-x ≥
FG1HD1FG9FG7Q(
!
N - -O ! - !N -O "x x x x x− − − − − − − =
N|O
W1
-V "y x y= − ≥
5(9JN|OIJ]R%?
!
A?N=-OA!=A!=
!
>"

N ! ON -O "
! "N - "O
x y x y
x y do x y
⇔ − + + =
⇔ − = + + ≠


!

! -
@ @ "
!
x x
x x
x
⇒ = −
⇔ − + =
⇔ =

"!M
"!M
"M
 !
- -

- ! - !
C !
C
C
- -
- !
C ! C !
C C
!
- -
C ! C !
C C
- -
1N -O - - 1N -O

)(+ )(+ 5N -O
-
-
- 1N -O
)(+ 5N -O )(+ 5N -ON -O
- -
)(+N -O )(+N -ON -O #
x x
x x
x
x x
x x
e x e x
x x
x
x
e x
x x x x x
x x
x x x x x
− −
→ →
−
→ →
→ →
+ − − − + −
= + +
−
−
− −

= + + + + + +
− −
= + + + + + + =
"!M
"M
"!M
! -
}9F'I4Iq1+(&I4T5(9J
⊥
T
N;)PC9F'7S$JIO]9J
SIA
β
∠ =
4
>5I1
β
VT>U>
I1
(
a
β
α
V4>
(
a
β
! !
I1
5 5(

(
ABCD
a
S AB AD
β
α
α
= =

C !
5
I1
C(
S ABCD
a
V
β
α
=

4
?^
>4
4T
B4
4U
4
4T
B4
4U

T  
>
!
I1 -
5N- O
( (
a
β
α β
+
"!M
"!M
"!M
"!M
l -
IJ
C C C ! ! ! ! ! !
C N O N O N Oa b c abc a b c b c a c a b+ + + ≥ + + + + +

! ! ! ! ! ! ! ! !
C
! ! ! !
C
I I I
!
a b c b c a c a b
ab bc ca
A B C
+ − + − + −
⇔ + + ≤

⇔ + + ≤
W1_&I

! ! ! !
I I I NI I O5- NI I ( ( O
- - C
~NI I O - •B ~( B( T•I I
! ! !
A B C A B A B A B
A B A sB
+ + = + − −
≤ + + =
U9J
C
I I I
!
A B C+ + ≤
"!M
"!M
"M
l C
- -
d()*1HS9(E+IqTV€)*1HS9(E+IqT5(9JN-e!OV€N
M
e C
!
−
O
IJ%
C N O ! ! ! @MA MB MA MB MB MI MB MJ+ = + + = + =

uuur uuur uuur uuur uuur uuur uuur uuur
lD7i=
CMA MB+
uuur uuur
gL1_()*DI(mS7S$JIIq€1HX9F'1c
∆
F'1c€^S€7*7S$JI7Q(
∆
IJ/FG1HD%!?A=A.>"5
d9\9(E+)*(K+IqK
!
! C "
M
! . " -#
M
x
x y
x y
y
−

=

+ − =


⇔
 
− − =



=


7i=N
-# !
e
M M
−
O
"!M
"!M
"!M
"!M
! -
F'1c]
-
9(^SN-e"e!O7*IJ7nI1Iz/FG)*
-
N -e!e-Ou = −
ur
V9F'1c
]
!
9(^STN"e-e-O7*IJ7nI1Iz/FG)*
!
N-eCe -Ou = −
uur
5
d(

N OVN O
α β
)*I&I+W1/c9(^S7*)p)F[1I`]
-
7*]
!
5F'1cIp1D+
IP)*(1S=mIq(+W1/c
N O * N Ov
α β
IJ
N"e"e COV N -e-e"OMA MB= − = −
uuur uuur
- - ! !
-
e N!e-e"OV e N-e-e@O
C
n MA u n MB u
   
= = = − =
   
ur uuur ur uur uuur uur
)*I&I7nI1/&/1S=mIq
N O * N Ov
α β
F'(1S=mIq
N O * N Ov
α β
IJ7nI1GIz/FG
- !

e N@e .e-Ou n n
 
= = −
 
r ur uur
7*9(^S
N-e"e-OXIJ/FG1HD?>-B@1V=>.1Vh>-B1
"!M
"!M
"!M
"!M
C -
d(h>?B=5(5(9Jh
!
>?
!
A=
!
B!?=5(V
z x yi= −
! ! !
! !
! " ! !N -O "
! "
N -e COVN "e "OVN !e "O
!N -O "
z z x y x x yi
x y x
x y x y x y
x y

+ = ⇔ − + + − =

− + =
⇔ ⇔ = = ± = = = − =

− =

li=IJ@</`I1g+fh>"Vh>!7*h>-
Ci±
"!M
"!M
"!M
"!M
l, C
- -
d((9(E+1`(Iq9F'1cIp1D+7Q(N
-
O7*N
!
O)p)F[1)*7*
d(N?e=O
! !
-
N O -CC x y∈ ⇒ + =

N-O
lD)*1HS9(E+IqXN@A?ekA=O5
U
! !
!

N O N! O Nk O !MC x y∈ ⇒ + + − =

N!O
•N-O7*N!O1IJK
! !
! !
-C
N! O Nk O !M
x y
x y

+ =


+ + − =


(6(K19F[IN?>!e=>CON)R(O7*N?>
-‚
M
−
e=>
k
M
O5li=N
-‚
M
−
e
k

M
O
F'1cIp1D+9(^S7*IJ/FG1HD%?AC=B‚>"
"!M
"!M
"!M
"!M
! -
d(N-1e!1e!B1O
-
d∈
VN1ye-BC1y-1yO
!
d∈
F'1c]
-
IJ7nI1Iz/FG)*
-
N -e!e-Ou = −
ur
V9F'1c]
!
IJ7nI1Iz
/FG)*
!
N-eCe -Ou = −
uur
5
N ƒ -eC ƒ ! -e ƒ COMN t t t t t t= + − − + − − +
uuuur

)*9R7S$JIISIq]
-
7*]
!
_(7*Iz_(
-
!
5 "
! ƒ C C "
ƒ @ - "
5 "
MN u
t t
t t
MN u

=
− + =


⇔
 
− − =
=



uuuur ur
uuuur uur


C
ƒ
M
‚
M
t
t

=


⇔


=


"!M
"!M
U9JN
! -@ C
e e
M M M
− −
OVN
C -@ !
e e
M M M
O5
W1IpS9F'_PIJ,&_P>

!
! !
MN
=
7*1o+N
- -@ -
e e
-" M -"
−
OIJ
/FG1HD
! ! !
- -@ - -
N O N O N O
-" M -" !
x y z− + − + + =
"!M
"!M
C -
d(h>?B=(VN?e=O)*9(E+,(ES](„</`Ih5
! !
- ! - N -O N !O -z i x y+ + = ⇔ + + + =
F'1HZNO%
! !
N -O N !O -x y+ + + =
IJ1o+N-e!O 2
F'1c2IJ/FG1HD=>!?
4</`Ih1g+f9(rS_(K7*IJ+$]SgL1_(7*Iz_(9(E+
T(ES](„J1S\INO7*p<I1d9\2L1V9JIP)*+\11H(
(9(E+Iq9F'1c27*NO


(9J1d9\IqJ1g
+fK
! !
- -
- -
!
M M
V
! !
N -O N !O -
! !
M M
x x
y x
x y
y y
 
= − − = − +
 
=

 
⇔
  
+ + + =

 
= − − = − +
 

 
h>
- !
- N ! O
M M
i− + + − +
"!M
"!M
"!M
"!M

