Thi Thử ngày 6/3/2011


TRƯỜNG THPT LÊ VĂN THNH
Đ KIM TRA CHT LƯNG LP 12 NĂM HỌC 2010- 2011
Môn: TOÁN ;Kh&i A
Thời gian làm bài: 180 phút,không k thời gian pht đê
I. PHẦN CHUNG CHO TT CẢ CÁC THÍ SINH(7,0điểm)
Câu I(2,0 điểm) 
x m
y
x m
+
=
−

 !"#$%&$'&(()*+,-.$/
0*1*23&45&4678/9:;*+,-<$$*$1=>&#$?@@/


Câu II (2,0 điểm)
 $!$=2A&4B0&
( )
C 
    $&  D

x
x x x− + + − =
.
$!$?=2A&4B0&
( ) ( )
( )
C

   
 
C

EF D  G H 
x x y x x y
x y x x

− + = −



− + = +


Câu III (1,0 điểm) I&

C
C 

D D
$&

  G$&
x
I x x dx dx
x x
π
= + +
+

∫ ∫

Câu IV(1,0 điểm)0&J=@J*"8@0&&4>&<&#'&@//@/
C
/4J@/FD
D
$%K=5&4@(LM&44J(N$K=5&4@4J4$OK=5&4
@(N$K=5&4@#P&4GQ
D
I&6$?&I0&&4@(1I.$J=@
Câu V(1,0 điểm) #"62A&4R&4$&BP&47

( )
( )
( )
( )
( )
( )
  
  
  
  
H
  
a b c b c a c a b
a b c b c a c a b
+ + + + + +
+ + ≤
+ + + + + +
PHẦN RIÊNG(3 điểm) Thí sinh chỉ chọn một trong hai phần (phần A hoặc phần B)

A. Theo chương trình chuẩn
Câu VI.a (2,0 điểm)
 B&4K=5&4S*TOxy0&O&U@J=2A&4B0&*23&45&4@79:8V/D*$1
VCWLT
IB ID= −
uur uur
0S*T@#$%*$1J&*T62A&4(@/@
 B&4.M&44$&S*TX98YU==2A&4B0&KZLJ>LTK=5&4[79:C8VY:/D
(4$-K=5&4\79V8VY:F/D(N$KZL*23&4B]&J>VWWC(#"&.I&
Hr =

Câu VII.a (1,0 điểm) 0=RY^_&
( )
( )
 z z i− +
(
 Qz − =

B. Theo chương trình nâng cao
Câu VI.b (2,0 điểm)
B&4K=5&4<*TX98$*23&45&4

7 C Dd x y− =
(

7 Dd x =
`U==2A&4B0&*23&4
B]&#$%$%=9a(N$6

<$@(;6


<$$*$1
ABC
∆
(LM&4<$@(JL($
#P&4
C C+

B&4.M&44$&S*TX98Y$*23&45&4

  
7
  
x y z
d
− − −
= =
(

C  
7
 C 
x y z
d
− − −
= =

`U==2A&4B0&*23&45&46(LM&44J(N$K=5&4\79V8VY:/D*+&43$6;!6

(6



Câu VII.b (1,0 điểm $!$?=2A&4B0&
( )
 
 G
4 4 C

F
x y
x y R
x y
+ =

∈

+ =

bbbbbbbHếtbbbbbbb
Thí sinh không được sử dụng tài liệu. Cán bộ coi thi không giải thích gì thêm
S('&I$&W#"6&
ĐÁP ÁN MÔN TOÁN Đ KIM TRA CHT LƯNG LP 12 NĂM HỌC 2010 – 2011
Câu ý Nội dung $1
I
1
c7/defg

$ W
x
y

−
→
= −∞


$
x
y
+
→
= +∞

⇒
9/$?U&*R&4
W$ =
−∞→
y
x

$ =
+∞→x
y

⇒
8/$?U&&4&4
DQ
8h/

C
DW 

 
x
x
−
< ∀ ≠
−
⇒
&4,#$%&B'&".!&4
( )
W−∞
(
( )
W+∞
W
.M&4*<B,
DQ
`U=*a&4*Z8*- DQ
i)*+, DQ
2
\2A&4B0&&*T4$*$1-6(7

( )
( )

   D 

 
x m x m
x m
x

x m
x m

− + − =
+

= + ⇔

−
≠



DQ
6;<$$*$1=>&#$?
⇔
J$&4$?=>&#$?

⇔
J$&4$?=>&#$?9

W9
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 

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W Q  F Q  FW e D j
 D
m m
m
m m m m

+ + >

⇔ ⇔ ∈ −∞ − − ∪ − − +∞

− − − ≠


DQ
$*J
( ) ( ) ( ) ( )
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         
W  W W    GA x x B x x AB x x x x x x
 
+ + ⇒ = − = + −
 
k?R($k
( )

 D AB m m⇒ = + +
*J
( )


D
 D  
D 
m L
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=
⇒ = ⇔ + + = ⇔

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
DQ
DQ
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 
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x
x x x

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
⇔

+ + − =


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 
 G W G
C C
x k x k k Z
π π
π π
⇔ = + = − + ∈
DQ
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x x x
x x x x x
⇔ + + − =

⇔ − + + − =
DQ
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 W 

x k x k k Z
π
π π
= + = ∈
DQ
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G W G W G W G
C C 
x k x k x k x k k Z
π π π
π π π π
= + = − + = + = ∈
DQ
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
x y≥
DQ
2
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⇔
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 Dx x y x x y− + − − =
⇔
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(
)
   
 Dx x x y x y x x y
 
− − + − − − =
 

(
)
(
)
( )
  
  
 Dx x y x x x y x y
x x y y x x
 
⇔ − − + − + − =
 
 
⇔ = − ⇔ = −
DQ
$*J=
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( ) ( )


C

C
nF D  G H 
H 
H 
C

H  G H 
 C
x x x x
x
x
x x x
⇒ − + = +
+
+ +
⇔ − + = +
DQ
o6p&4M$Cbb0*2l&4$?6L8&q-=2A&4B0&

H
x =
 DQ
III
cr

C 


D
I x x dx= +
∫
K

x u+ =
b
( )

 


I u u du⇒ = −
∫

Q C

  
Q C Q
u u
 
+
= − =
 ÷
 
DQ
DQ
cr
C C


  
D D
$& $& 
  G$&   G$&
x x x
I dx dx
x x x x
π π
= =
+ +
∫ ∫
K

 G$& x u+ =
bbbbI&*2l

 E C Q
&

 Q
I
+
=
DQ
IV
I&*2l

C C
G
ABCD

S a=
DQ
s
SH AD⊥
( ) ( )
( ) ( )
( )
 SH AD H AD
SAD ABCD AD SH ABCD
SAD ABCD

⊥ ∈

⇒ ∩ = ⇒ ⊥


⊥

s
( ) ( )
HK AB K AB SHK AB SK AB⊥ ∈ ⇒ ⊥ ⇒ ⊥
·
D
 GQSKH⇒ ⇒ =
DQ
K/9
D

W
$& FD

C
HK x
HK x AH⇒ = = =
cr4$"(LM&4@J7

    
G C
C
C
E
x a
SA AH SK a x x= + ⇔ = + ⇔ =
DQ
$*J7
C

 

C D
S ABCD ABCD
a
V SH S= =
DQ
K
 W
a b c
x y z
a b c a b c a b c
= = =
+ + + + + +

.$*JJx+y+z=1(98Y62A&4
( )
( )
( )
( )
( )
( )
  
  
  
  
  
x y z y z x z x y
P
x y z y z x z z y
+ + + + + +
⇒ = + +
+ + + + + +
DQ
V

VI.a
1
  
  
     
C   C   C  
x x y y z z
P
x x y y z z

+ + + + + +
⇒ = + +
− + − + − +
J


  G
G
C   C
x x
x
x x
+ +
≤ +
− +

( ) ( )
( )
 
C   C    Gx x x x x⇔ + + ≤ − + +

( ) ( )

 C  G  Dx x⇔ ⇔ − + ≥
`LM&*a&4(N$S$962A&4
*J
( )
G G HP x y z≤ + + + =
qL#P&49!8B.$/#/
DQ

DQ
J
( )
( )
W
Q Q @/@
I AD
d ID Do= ⇒ =
( ) ( ) ( )
 
7 C  QD C x y⇒ ∈ + + − =
DQ
*JS*T&4$?-?7
( ) ( )
 
W 
C  Q
CW E
  D
x y
x y
x y
x y

= = −

+ + − =

⇔
 

= − =
+ − =





( )
W D⇒ −
i0J&6T62A&4
DQ
( )
 WHIB ID B= − ⇒ −
uur uur
\2A&4B0&@79V8:E/DW@VQW DQ
( )
QW GAB DC D= ⇒ − −
uuur uuur
DQ
2
$!oKZLJ>#"&.I&d
\2A&4B0&7


C
x t
y t
z t
= − +



= −


= −

i0*$tL((LM&44J(N$\
DQ
*J
( )
I IH Q= ∩ ⇒
S*TDWW DQ

 
C FEIH R r IH= ⇒ = + =
\2A&4B0&KL7
( ) ( )
 

  FEx y z+ − + − =
DQ
VII.a
KY/:#$#
( )
( )
( )
 
    z z i a b a b a b i− + = + − − + + −

( )

  D a b⇒ + − =
DQ
7
( ) ( )


 Q  Q z a b− = ⇔ − + =
DQ
u(JW#/DWWWV DQ
iU8Y/$WY/V$
DQ
VI.b
1
$!oJ>(#"&.I&d
J6

(6

4$&L<$X(4J@X/CD
D
DQ

( ) ( )
C C C C C C 
ABC
C AB BC CA R R R
∆
= + + = + ⇒ + = + ⇒ =
DQ
X/d/

( ) ( )
WD W WDI I⇒ −
DQ
⇒
=2A&4B0&*23&4B]&77
( )


 x y− + =
W
( )


 x y+ + =
DQ
$!o
 
Wd d A d d B∩ = ∩ =
( ) ( ) ( )
 W  W W C W C W  W C  WA a a a B b b b AB b a b a b a+ + + + + + ⇒ + − + − + −
uuur
DQ
6(LM&44J(N$\
WAB n⇔
uuur r
v&4=2A&4
AB k n⇔ =
uuur r
DQ
2

 Q
 C    GWQWC
 DQ
b a k a
b a k b B
b a k k
+ − = =
 
 
⇔ + − = − ⇔ = ⇒
 
 
+ − = − =
 
VËy ph¬ng tr×nh d:
G Q C
  
x y z− − −
= =
− −

DQ
VII.
b
.79wDW8wD
?=2A&4B0&



 G

 G
4 C
H
F
F
xy
xy
x y
x y


=
=
 
⇔ ⇔
 
+ =
+ =




DQ
$!$=*2l
 
 
x
y

=


⇔

=


DQ