DE THIDAP ANMA TRAN THI THU TN THPT 2011



 
!"#$%&
'!(" )*#+,-+%.$$&

+/!0$ 1
  
!"#$%& '%()*+ *+,- .+/0%
234)&- 
5#65&
%. 7 8.
94!"'4:'& $. ; ;.
- !<& $. % %.
+=#>& $. ; ;.
?)#& $. % %.
@*=A B=
)B&
$. % %.
-##C<& ;. % D.
$ 1 %D.
1 "
12"/
34562#78+
9:+;<)
2=
>/?#@A/@#B)+*C.>+
!"#$%&

D 
.+

/0%
 E/F >+/0) 1 B+
<C
1 B+
#
234
)&- 5#
65&
G)H$
%E
G)H%
.E
I
JKL
94!"'4:
'&
G)H;
$.
M
MKL
- !<&
G)H$
$.
M
MKL
+=#>&
G)H%
$.
M
MKL

?)#&
G)1H
NG)1HFG
$.
M
MKL
@*=A 
B=)B&
G)H$
.E
G)H%
.E
I
MKL
-##C
<&
G)1H&$
HG)1HF&$G
$.
G)1H&%
NG)1HF&%G
$.
I
IKL
IC
J
OKL
O
JKP
I

I
M
LKP
ML
ML
2"
Thi gian lm bi: 150 pht, không k thi gian giao đê
QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ
R5STUVWX3NYKL/0%Z
G)NJKL/0%Z?I)0
3
2
( ) 2 3
3
x
y f x x x= = - + -
MZ/F5J234
( )C
)&
IZK5# 5#65
( )C
LJ
( )C
BC
0
x
"
0
( ) 6f x
¢¢

=
&
G)NJKL/0%Z?
MZ 9# 0
2 2
log ( 3) log ( 1) 3x x- + - =
IZ+==#>0
0
(2 1)sinI x xdx
p
= -
ò
JZ+ 4!"'4:')0
3 2
2 3 12 2y x x x= + - +
J
[ 1;2]-
G)NMKL/0%Z?
I B#MS.ABCDBL6FNa?OP
%a
BQLFJR6FND.
.
&
MZ+=S*=A BBTS6!UVL5#6 B#&
IZ+==)B&
HR[NJKL/0%ZThí sinh chỉ được chọn một trong hai phần dưới đây
MH\#9]+)^
G)1NIKL/0%Z?+<OxyzUWdR#WHPG!X!(B#
 
3 2

: 1 ,( ) : 3 2 6 0
x t
d y t P x y z
z t
ì
ï
= - +
ï
ï
ï
= - + - + + =
í
ï
ï
= -
ï
ï
î
MZK5# R#WHQGAA3U<B"UWd.
IZK5# RX
( )S
>
(2;1;1)I
5#Y"#HPG&
G)1NMKL/0%Z?+=
1 2
x x+
F5
1 2
,x x

!*## >60
2
3 2 3 2 0x x- + =
IH\#9]+G+#
G)1ENIKL/0%Z?+<"*LCOxyz
(2;1; 1), ( 4; 1;3), (1; 2;3)A B C- - - -
MZK5# UWAB&
IZK5# RX
( )S
>C5#Y"UWAB&+ LC5#
UWAB"RX
( )S
&
G)1ENMKL/0%Z?9# >6J#)#0
2
4 8z z i+ =
QQQQQQQQQQFQQQQQQQQQQ
Thí sinh không được sử dụng tài liệu. Giám thị coi thi không giải thích gì thêm.
,J=0&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& ?)FS0&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
IQZ4$0&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& IQZ4%0&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
12@C@K+0%
G) 2@C@ 2/0%

,)0
3
2
( ) 2 3
3
x
y f x x x= = - + -

+#40
D = Ă
[L0
2
4 3y x x
Â
= - + -
I
2
1
0 4 3 0
3
x
y x x
x
ộ
=
ờ
Â
= - + - =
ờ
=
ờ
ở
0y
Â
>
JH$\;G

,)[OJH$\;G

0y
Â
<
JH]\$GH;\_G

^OJH]\$GH;\_G
,)L/LLP;

I[
0y =
L/LP$

CT
4
3
y =-
9"L0
; lim lim
x x
y y
đ- Ơ đ+Ơ
= +Ơ = - Ơ
OF5J
x
] $ ; _
y
Â
] L _ L ]
y
_ .

4
3
-
]
[)0
2
2 4 0 2
3
y x x y
ÂÂ
= - + = = ị = -
&
[)34!0
2
2;
3
I
ổ ử
ữ
ỗ
ữ
-
ỗ
ữ
ỗ
ố ứ
9"`0
0 0; 3y x x= = =
9"`0
0 0x y= ị =

O40x . $ % ; 7
y . ]7a; ]%a; . ]7a;
[34) 20

0 0 0 0
16
( ) 6 2 4 6 1
3
f x x x y
ÂÂ
= - + = = - ị =
LKIP
LKIP
LKIP
LKP
LKP
LKIP
LKP

2
0
( ) ( 1) ( 1) 4( 1) 3 8f x f
 Â
= - = - - + - - = -
- 5#65X !

16 8
8( 1) 8
3 3
y x y x- = - + =- -

LKIP
LKIP


2 2
log ( 3) log ( 1) 3x x- + - =
[M*0
3 0 3
3
1 0 1
x x
x
x x
ỡ ỡ
ù ù
- > >
ù ù
>
ớ ớ
ù ù
- > >
ù ù
ợ ợ
&B
2 2 2
log ( 3) log ( 1) 3 log ( 3)( 1) 3 ( 3)( 1) 8x x x x x x
ộ ự
- + - = - - = - - =
ở ỷ

2 2
1( )
3 3 8 4 5 0
5
x loai
x x x x x
x
ộ
= -
ờ
- - + = - - =
ờ
=
ờ
ở

K6# bB*S6'0xPE

0
(2 1)sinI x xdx
p
= -
ũ
[R
2 1 2.
sin cos
u x dx dx
dv xdx v x
ỡ ỡ
ù ù

= - =
ù ù
ị
ớ ớ
ù ù
= = -
ù ù
ợ ợ
&+6<=#>c#X
(0

0
0
0
(2 1)cos ( 2cos ) (2 1) 1 2sinI x x x dx x
p
p p
p= - - - - = - - +
ũ


(2 1) 1 2.0 2 2p p= - - + = -
+ 9+d^9+^^)
3 2
2 3 12 2y x x x= + - +
JL
[ 1;2]-
,)
3 2
2 3 12 2y x x x= + - +

!J`JL
[ 1;2]-

2
6 6 12y x x
Â
= + -
I
H!G

2
2 [ 1;2]
0 6 6 12 0
1 [ 1;2]
x
y x x
x
ộ
= - ẽ -
ờ
Â
= + - =
ờ
= ẻ -
ờ
ở
+B
3 2
(1) 2.1 3.1 12.1 2 5f = + - + = -
3 2

3 2
( 1) 2.( 1) 3.( 1) 12.( 1) 2 15
(2) 2.2 3.2 12.2 2 6
f
f
- = - + - - - + =
= + - + =
+)J)
5-
:')$E!"'&
K6
khi khi
[ 1;2] [ 1;2]
min 5 2, max 15 1y x y x
- -
= - = = = -
LKIP
LKP
LKIP
LKP
LKP
LKP
LKP

9O!> <ABCD&@S&ABCD! B# MJ
( )SO ABCD^
?6OB! 5<BSB!J#HABCDG
@B
ã
0

60SBO =
&5(#
2
2
a
r OB= =
60
LKIP
LKIP
0
2 6
.tan60 3
2 2
a a
h SO OB= = = × =
@*=A B0

2
2
. . 2
2
xq
a
S r l a ap p p= = × × =
HSG
+=)B0
2 3
2
1 1 6 6
. .

3 3 2 2 12
a a a
V r h
p
p p= = × × =
HG
LKIP
LKIP
1H

\#9]+)^
#HQGA
(1;1; 2)A -
<B"dJB#
(2;1; 1)
d
n u= = -
r r
K6-++e#HQG0
2( 1) 1( 1) 1( 2) 0x y z- + - - + =
2 5 0x y zÛ + - - =
fRX
( )S
B>!
(2;1;1)I
@
( )S
5#Y"#
( ) : 3 2 6 0P x y z- + + =
J

( )S
BF=
2 2 2
2 3.1 2.1 6 7 14
( ,( ))
2
14
1 ( 3) 2
R d I P
- + +
= = = =
+ - +
- RX
2 2 2
7
( ) :( 2) ( 1) ( 1)
2
S x y z- + - + - =
LKP
LKP
LKP
LKP
1H

2
3 2 3 2 0x x- + =
+B
2 2
( 2 3) 4.3.2 12 24 12 (2 3)iD = - - = - = - =
- bB%*#0

1,2
2 3 2 3 2 3 2 3 3 3
2.3 6 6 3 3
i
x i i
±
= = ± = ±
+cB
2 2 2 2
1 2
3 3 3 3 2 6
3 3 3 3 3
x x
æ ö æ ö æ ö æ ö
÷ ÷ ÷ ÷
ç ç ç ç
÷ ÷ ÷ ÷
ç ç ç ç
+ = + + + - =
÷ ÷ ÷ ÷
ç ç ç ç
÷ ÷ ÷ ÷
ç ç ç ç
è ø è ø è ø è ø
LKP
LKP
1HE
\#9]+G+#
[J UWAB0
(2;1; 1)A -

#UWAB0
( 6; 2;4)u AB= = - -
uuur
r
?6-++?UWAB0
2 6
1 2 ( )
1 4
x t
y t t
z t
ì
ï
= -
ï
ï
ï
= - Î
í
ï
ï
= - +
ï
ï
î
¡
fR#WHPGA0
(1; 2;3)C -
K 
( )P AB^

J0##HPG!0
( 6; 2;4)n AB= = - -
uuur
r
K6-++e#
( )P
0
0 0 0
( ) ( ) ( ) 0A x x B y y C z z- + - + - =
6( 1) 2( 2) 4( 3) 0
6 2 4 10 0
x y z
x y z
Û - - - + + - =
Û - - + - =
+6#AB-++e#HPG(0
LKP
LKP
6(2 6 ) 2(1 2 ) 4( 1 4 ) 10 0
1
56 26 0 0,5
2
t t t
t t
Û - - - - + - + - =
Û - = Û = =
+6tP.E# )AB(0
1; 0; 1x y z= - = =
K6LC 5X !
( 1;0;1)H -

K RXHSG>C5#Y"UWABJBAH
+>RX0
(1; 2;3)C -
O=RX0
2 2 2
(1 1) ( 2 0) (3 1) 2 3R CH= = + + - - + - =
K6# RX0
2 2 2
( 1) ( 2) ( 3) 12x y z- + + + - =
LKP
LKP
1HE

2
4 8z z i+ =
[R
2
2 2 2 2
z a bi z a b z a b= + Þ = + Þ = +
&+6# J
(0
2
2 2 2 2
2 2 2 2 2
4 8 4( ) 8 4 4 8
2
4 0 4 0 4 4 0
2
4 8 2 2
z z i a b a bi i a b a bi i

a
a b a a b a a a
b
b b b
+ = Û + + + = Û + + + =
ì ì ì
ì
ï ï ï
ï
= -
+ + = + + = + + =
ï ï ï
ï
ï ï ï
Û Û Û Û
í í í í
ï ï ï ï
=
= = =
ï ï ï ï
î
ï ï ï
î î î
K6zP]%_%i
LKP
LKP
1/0%`&/@E9a"
+9:/E/b,#&
2/c]
.94+)db%>

>+1eG%