ĐÁP ÁN VÀ ĐỀ THI THỬ ĐẠI HỌC - TRƯỜNG THPT NGUYỄN HUỆ - ĐẮK LẮK - ĐỀ SỐ 20 doc


TRƯỜNG THPT NGUYỄN HUỆ
ĐỀ THI THỬ ĐẠI HỌC
MÔN TOÁN NĂM 2012 - 2013
Thời gian làm bài: 180 phút.
PHẦN CHUNG CHO TẤT CẢ CÁC THÍ SINH ( 07 điểm )
Câu I  
!  !
! "
 
y x mx m= − +
1. #$%&'()%*)++,-%. /0"
2. 
1
-%. 2342&252&2%6 78)9:64;<)9%=)9>07?
Câu II?
"?#@;A)9%BC)D
! !
"E
F  )  G2 !  2 H 2

"F
2
x x x x
x
π
+ + −
=
+I
J
 K 

 
x
π π
∈
?4LMN@;A)9%BC):





=−++
=+−+−

OFH

H
yxyx
yyxx
Câu III"?@;A)9%BC)
7 7 7 !
E ! J 4E ! J 
+
+ + − =
4#@;A)9%BC)/40E
'C4@;A)9%BC)2P23Q%)9R
Câu IV"?/ ST)9%BUVW?VXWXX23$>VWS%49$2+6Y)92Z)25)6>[)VW0

?
\]%@=)9VVXW+6Y)9932+I]%@=)9VWVVX0
!

?32
·
^A AB
S932)N)+]%@=)9
VXV%5+I]%@=)9VWQ%932F

?_)%%_2/ ST)9%BUVW?VXWXX
Câu V"?
x y
`S2$2 %&2a;A)9+%#b)[6/R)
"x y z+ + =
?cb>%C9$%B.)d
)e%2f4
" " "
" " " M
x y z
= + + +
?
PHẦN RIÊNG CHO TỪNG CHƯƠNG TRÌNH ( 03 điểm )
(Thí sinh chỉ chọn một trong hai chương trình Chuẩn hoặc Nâng cao để làm bài.)
A/ Phần đề bài theo chương trình chuẩn
Câu VI.a:?
1,B)9]%@=)9+IR%5QOxyb>+(%@;A)9%BC)2$225)2f4%49$2ABC'(%%B&2%Z
"KH
2Z);<)9245%gP)BS
K K
%B6)925)ABS
!K"M
?
2,CR 2f4 5)9284

F
x
%B)9/4%B)
"

n
x
x
 
+
 ÷
 
'(%Bh)9
 "
"
H F
n
n n
A C n
−
+
− = +
?
Câu VII.a:"? #@;A)9%BC)D
( ) ( )
 !
G

H
S9 "  S9 H S9 Hx x x

+ + = − + +
B/ Phần đề bài theo chương trình nâng cao
Câu VI.b: ?1, B)9]%@=)9%5Q7>24;<)9%=)9a
"
DH7i!>i"0+a

DH7j
!>i"0?C%5Q%Z+'$)/_);<)9%Bk))Q%(@%49$223!25))h%B*)a
"
a

%BU2>?
2,MS@lD
 
7 >
"
"F O
+ =
+;<)9%=)9a
!
D

!7jH>0
a)8)9)Bh)9;<)9%=)9a
!
2m%MS@l%54@Z)'R%V+W?C%5Q43
+Ik4)Q2f4V)dA))Q2f42f4W?
b)C\7K>%6Q2l42%49$2\VW23aR)%_2'h)9"?
Câu VII.b:"?#R@;A)9%BC)D


S9   G F
G  ?! ?!
x x y x y
y x
+
− + =



+ =


 Hết iiiiiiiiiiiiiiiiiii

HƯỚNG DẪN
Z6"D"0"%423
! 
! "
 
y x x= − +
.
Tập xác định:
¡

Sự biến thiên
iI5)%5+Y2&2D
S
x
y
→−∞

= −∞

S
x
y
→+∞
= +∞
i[6'()%*)D423

^ ! !y x x= −
K

^ 
"
x
y
x
=

= ⇔

=

W#)9'()%*)
7
−∞
"
+∞
>X jij
>


"


+∞


−∞
c -)9'()%B*)/#)9
( )
K−∞
+
( )
"K+∞
c )9.2'()%B*)/#)9
( )
K"

i&2%B.Dc 5%2&25%570
"


CÐ
y y= =
c 5%2&2%6%570"
( )
" 
CT
y y= =
!?

Đồ thị:-%.2m%%BU2)%5
"
K

 
−
 ÷
 
K
( )
"K
+2m%%BU2%6)9%5
"
K

 
 ÷
 
?-%.)n)6 )
" "
K
 H
U
 
 ÷
 
S%Z 78)9?
Câu 1: 2
1
-%. 2342&252&2%6 78)9:64;<)9%=)9>07?

423>X0

! !x mx−


^ 
x
y
x m
=

= ⇔

=

-%. 232&252&2%6%
1

^ y =
234)9R@Z)'R%
m
⇔ ≠
?39#o2$22&252&2%6SD
!
K

m
A
 
 ÷

 
+
( )
K B m
423D
!
K

m
AB m
 
−
 ÷
 
uuur
K%B6)92f4VWSD
!
K
 H
m m
I
 
 ÷
 
M>*62p6'%$)V+W 78)9+I)46:64;<)9%=)9>07%
1
;<)9%=)9VW+6Y)9932+I
D y x∆ =
+%B6)92f4VW%6Q2;<)9%=)9
? AB u

I
∆

=

⇔

∈∆


uuur uur
!
!




H 
m
m
m
m
m m

− =

=


⇔ ⇔



= ±


=


 2(6[6/R)%423
m = ±
Câu 2: 1,423D
2 

x x k
π
π
≠ ⇔ ≠ +
I/@%"
⇔

( )
!  
G2 F  )  )  2  "F2x x x x x+ + =


!
H2 !  )  G2x x x⇔ + =

2 !  ) H x x
⇔ + − =


) !  )  x x⇔ − + =
( )
!
  
H H
x k x k k
π π
π π
⇔ = + = + ∈¢
n>@;A)9%BC)T223)9R
J
 K 
 
x
π π
∈
S
! O
K
H H
x x
π π
= =
Câu 2: 2
⇔






=−++
=−+−

H!


xyx
yx
⇔





=−−++−+−
=−+−
!!H
H!


xyx
yx





=−−++−+−
=−+−

!!H
H!


xyx
yx
Đặt



=−
=−
vy
ux
!


* 4>+%423R@%



=++
=+
GH?
H

vuvu
vu

#PR%4;q2




=
=


v
u
c]2



=
=


v
u
4>+9#%423



=
=
!

y
x
;




=
−=
!

y
x
;



=
=
J

y
x
;



=
−=
J

y
x


Câu 3 :
E ! J
 

x
t
+
=
%r%423@%

G t t a− + =
"
I40E%423

G t t a− + =

% "% E⇔ = =
s;A)9%BC)234)9RS
E ! J

7 7 S9 E
+
= =
 )9R2f4@%"S )9R%r2f4@;A)9%BC)

Ga t t= − +
S 26)92f4;<)9%=)9>0
4+-%.

Gy t t= − +

+I%r
Sn@'#)9'()%*)2f43

Gy t t= − +
+I%r/(%S6n)@%2P23Q%)9R/40"F]2
a
≤

Câu 4DN?\SC)2(62f4VX%B*)VW+V
23D
⊥ ⇒ ⊥( ' ) ( ) ' ( )AA B ABC A K ABC
? 423VX\
⊥
V+\
⊥
V
·
=
0
' 60A MK


='A K x
?%423
= − = −
2 2 2
' ' 3AK A A A K x
 \0
·
= −

2
2
sin 3 .
2
AK KAM x
\]%/$2
= =
0
' cot 60
3
x
MK A K
+n>%423@%
− = ⇔ =
2
2 3
3 .
2
3 5
x
x x

Λ
= = =
. ' ' '
1 3 5
. ' . . '
2 10
ABC A B C ABC
V S A K AC BC A K

Câu 5D
" " "  " " "
" " " 
x y z
M
x y x xyz
+ + +
= + + + =
?

H

H

H
" H
" H
" H
x x x y z x yz
y y x y z xy z
z z x y z xyz
+ = + + + ≥
+ = + + + ≥
+ = + + + ≥
H H H
H
 " " "
FH
x y z
x y z

M
xyz xyz
+ + +
= ≥
?e607#>B4/70>0`0"t!
Câu 6aD"j;<)9%=)9AC +6Y)9932+IHK )*))n)
 "K HK = −
uuur
S+%@%+AC:64K)*)
  D  H ?AC x y− + =
42u)9av23D
  D   BK x y+ − =
?
j
A AC B BK∈ ∈
)*)9#o
 HK   K   ?A a a B b b− −
\]%/$2
!K"M
S
%B6)92f4AB)*)%423RD
 H F  " H
?
     
a b a b a
a b a b b
− + = + = =
  
⇔ ⇔
  

+ − = − = =
  
6>B4D
HK H K ?A B −
j6>B4D
 K FAB = − −
uuur
6>B4D
  D! G AB x y− − =
?
j;<)9%=)9BC:64B++6Y)9932+IAH)*))n)
!K HHA =
uuur
6>B4D
  D! H  ?BC x y+ + =
Dn>D
  D  H − + =AC x y
  D! G − − =AB x y

  D! H  ?+ + =BC x y
Câu 6a:#@;A)9%BC)
 "
"
H F
n
n n
A C n
−
+
− = +

KĐiều kiệnD)wK)∈x?
s;A)9%BC)%;A)9;A)9+I
 "y
 " H F
y "y
n
n n n
n
+
− − = +
−
⇔
 "
 " H F

n n
n n n
+
− − = +
⇔)

z"")z"0⇔)0i"5]2)0"?
I)0"%423).%82x6%A)D
( )
"
H !
" "
"
"
 

" "
" "
"
  ? ? ?
k k
k
k k k
k k
x C x x C x
x
−
−
−
−
= =
 
+ = =
 ÷
 
∑ ∑
 5)9)>284
F
x
/
  "
H
H ! "
k N k
k
k

∈ ≤ ≤

⇔ =

− =

?n>R 2f4 5)9284
F
x
SD
H G
"
C
Câu 7aD
( ) ( )
 !
H G

S9 "  S9 H S9 Hx x x+ + = − + +
[6/R)D
" 
H H
H 
"
H 
x
x
x
x
x

+ ≠

− < <


− > ⇔
 
≠ −


+ >

( ) ( )
( )
( )

    
 
 
 S9 "  S9 H S9 H S9 "  S9 "F
S9 H " S9 "F H " "F
x x x x x
x x x x
⇔ + + = − + + ⇔ + + = −
⇔ + = − ⇔ + = −
jI
" Hx
− < <
%423@;A)9%BC)


H "  !x x+ − =
K
( )
 Fx x⇔ = = − lo¹i
I
H "x
− < < −
%423@;A)9%BC)

H  x x− − =
HK
( )
 H  Hx x⇔ = − = + lo¹i
n>@;A)9%BC)32234)9RS
x
=
]2
( )
 " Fx = −

Câu 6bD"NVS94a
"
+a

%42{V!K
NWS94a
"
+I%BU2>%423WKiHNS94a

+I>%423KH

NWS;<)9@Z)9$2%B)9932W+I%6Q2V/3%423Ht!K|0Ht!6>B4@%;<)9%Bk)
5QVWS)9R2f4RD
 
7 >
"
"F O
3x 4y

+ =



+ =

n>a
!
2m%l%5@Z)'R%
! 
V  K

 
−
 ÷
 

! 
W  K

 
−

 ÷
 
423\7K>
∈
l
⇔
70H2%+>0!)%+I%
∈
}K
π
~
{•DVW0
J 
23"0
∆
\VW
0
"

J 
a\VW0
0
"

J 
"2 % ") %
J
+
0"
2% 

H
π
−

⇒

2% 
H
π
−
0"
⇒
%0
π
tHK%0J
π
tH
n>23\%#b)SD
"
! 
\  K

 
 ÷
 
+

! 
\  K


 
− −
 ÷
 
Câu 7bDs%p6
⇔
>z7jG0
( )
F

y x⇔ =
%(+@%%84%4;q2D
 !
G  ?! ?!
x x x x
+ =
G "G ?E
x x x
⇔ + =
G "G

E E
x x
   
⇔ + =
 ÷  ÷
   
!
 


! !
x x
   
⇔ + =
 ÷  ÷
   
]%D%0

!
x
 
 ÷
 
/%r
%423@%D
( )
( )
! 
  "  t t t t t+ − = ⇔ − + + =

"

x
t
y
=

⇔ = ⇒

=


