đề thi thử toán-trường thpt minh khai

SỞ GD-ĐT HÀ TĨNH
TRƯỜNG THPT MINH KHAI

ĐỀ THI THỬ ĐẠI HỌC LẦN 1 - NĂM HỌC 2012 - 2013
MÔN THI: TOÁN
Thời gian: 180 phút(không kể thời gian giao đề)
I. PHẦN CHUNG CHO TẤT CẢ CÁC THÍ SINH (7,0 điểm)
Câu 1.(2,0 điểm)
 
 y x x= − + −

( )
C
a
b.  !"#$#%&'()*+,-.
( )
C
/ 0123)4,5
6572#809':
( )
C
/6/#;<=
Câu 2.(2,0 điểm)>0!?#;9&
a.
    @ ) ,  
A
 
x x x x
x
− − + − + +
=

+
b.
( )
B@A



+−=+ xxx
Câu 3.(1,0 điểm)7&
∫
+
dx
x
x

A

Câu 4.(1,0 điểm)80C368D369E#1/536(5

ABa
SB =
>F
>G;F#1D365C>
⊥
)36,7 7H80C36H#I 6
0)C3,
Câu 5.(1,0 điểm)55%!?#<J--(K#;L#&
  
  
A

  
a b c
a b b c c a
+ + ≥
+ + +
II. PHẦN RIÊNG (3,0 điểm): Thí sinh chọn một trong hai phần ( A hoặc B)
A. Theo chương trình chuẩn
Câu 6.a(1,0 điểm)
 
+ '
MG0)N,& A
AO @
+ =
  3)*@4*A,56)*A4A,PFQ
 R9Q)N,%27DR63G:=
Câu 7a.(1,0 điểm)>0!?#;&G#

)+

SB,-G#

)+-,

*G#

)+S,

(B
Câu 8.a(1,0 điểm)K#;L#&
,T),A)

UA

BB





∈∀+=++++
−
B. Theo chương trình nâng cao
Câu 6.b(1,0 điểm);#V0$#FQW+'59E#36X5 )4*, 
39Q!"#$#%&+-'*(Y>FRG;9# 65!"#$#XR0!?#
;&+S'S(Y PFQ 3565X
Câu 7.b(1,0 điểm)>0!?#;&
YZ,A+)G#,A+),A+)G#,A+O)




A
=−+−+++
Câu 8.b(1,0 điểm);#H; 
AB
B
,@) −
89/#G[9\
Hết
Cán bộ coi thi không giải thích gì thêm
]F7&C%

SỞ GD-ĐT HÀ TĨNH ĐÁP ÁN THI THỬ ĐẠI HỌC LẦN 1 - NĂM HỌC 2012 -
TRƯỜNG THPT MINH
KHAI

2013
MÔN TOÁN
CÂU Ý NỘI DUNG ĐIỂM
Câu 1 a. *P^&X(_
*C&->://E&
4
G G
x x
y y
→−∞ →+∞
= +∞ = −∞
-`9&


+ Y
'a + -O+4 'a Y 
+ 
=

= − = ⇔

=

]#;bH#)*c4Y,)4-c,5#
;)Y4,
]/ 9/+(Y4'


(*4///+(4'
^
(

*6#&

+ *cY-c
'd *Y-Y*
' -c

**c

Y5@
Y5@
Y5@
 ^&RQ 9Q&)A4Y,5)*A4,5)4*,

Y5@
b. e!?#;Q# %),&
*+

-+

*()*+,-)A,



=−−−=
=

⇔
,)Y++,+)f
+

Y5@
^!"#$#%.(C)/ 012
⇔
0)A,8#2
012
⇔
0),8#2012H





≠
−>
⇔



≠−
>+
⇔



≠
>∆

⇔
Y
B
g

Y
YgB
Y,)f
Y
Y5@
]Q 6G#20),
8&+
6
-+

(A+
6
+

(**
72#809':(C)/6G&
Y5@
'd)+
6
,'d)+

,()+
6



*O

+
6
,)+



*O+

,
(g)-A,

*gh*g
{ }
Yi,4
B
g
) +∞
−
∈∀
X=9j(j+k';H
(*Alm''d)+
6
,'d)+

,<=L#*g/!nH(*A
Y5@
CÂU Ý NỘI DUNG ĐIỂM
Câu 2 a.

^`9H2&


+ −≠

e!?#;J!?#!?#:&

Y++@++ =+−−−






=+
=
⇔=−+−⇔
=+−+−⇔
++

A
+
Y,++,)A+)
Y+@++++

Y5@
Y5@
π+
π
=⇔=

π
+⇔=+






π+
π
=
π+
π
=
⇔=
H
O
+A,

+)++
H
O
@
+
H
O
+

A
+

^9`9H2(o#20!?#;G
π+
π
= H
O
+

Y5@
Y5@
b.
e!?#;J!?#!?#:&
B++@A++
B
+−=++

,+)+B,+)+

+−=+⇔
^V


,+)+,+)+,+)+


=+⇒+=⇒+=
e!?#;;p



=

−=
⇔=−+⇔−=

B
YqB




Y5@
Y5@
+
+
Y+
Yq++
Y+
B,+)+B
B

−=⇔



=
<
⇔



=−+

<
⇔−=+⇒−=
A+
A+
Y+
Y++
Y+
,+)+

B

+−=⇔



+−=
>
⇔



=−+
>
⇔=+⇒=
Y5@
Y5@
Câu 3

∫ ∫∫
+

=
+
=
+
= %+
,+A)+
++
%+
,+A)+
+
%+
+A
+
r

^V(

x(o%(*xx%x

A A A A
) ,
 ) A,  A
dt
I dt
t t t t
= − = −
+ +
∫ ∫
A A A
)G s As G s s, G s s

 
t
t t c c
t
+
= + − + = +
Y5@
Y5@
Y5@


A A 
G) ,

x
c
cox x
+
= +
Y5@
CÂU Ý NỘI DUNG ĐIỂM
Câu 4
Câu 5
a. C
r6
3>*

>FrG;9# 36(o



r>


r ==>=
Dr>69E#/r(o>6

(r>

-r6

(

@

DC>69E#/>(oC>

(C6

*>6


(

(oC>(
B







A


A
C>

A
l

3636C
C ===
∆
t>uu6)∈3,⇒3⊥)C>,⇒C⊥3
D>9E#1/⇒>(>B@
Y
(



DC>9E#/>⇒

O
>C>C

=+=

D3r9E#/r⇒



rr33

=+=

C
DC3

B

3C

A

==



) 4) ,, 
S ABC
SAC
V
d B SAC a
S
∆
= =


g
B


g


,A)
g














 

O





−−=
++−≥
−=−≥

++
−=
+
!?#&


g
B

g




4
g
B

g








−−≥
+
−−≥

+
X8
Y5@
Y5@
Y5@
Y5@
Y5@
Y5@
Y5@

A

,)
g
B

Z
,)
g
B
,)
g

,)














=
++
−≥
++−++−++≥
++
+
+
Y5@
CÂU Ý NỘI DUNG ĐIỂM
Câu 6a e!?#;!"#$#36&+*'-(Y
36(
@
>vR)+

4'

,∈)N,⇒@+


-AO'




(qY
@
s'+s
YY
+−
= AB)d(M;
s'+s,364R)%36

A
YYR
−−==
∆
S
AB
8&
gs'+sg'+
O'+OOs'+s
O,'AO+@,)
B
A
@
A
),'B

A
+@
@
A
)
YYYY

YYYY

Y

Y

YY
≤+−⇒≤+−≤−⇔
≤−≤−⇔≤−⇒
=++≤−







−=
=
⇔



=−
−=
⇔








=+−
−
=
⇔=
∆

@
'

q
+
O'+
'q+@
g'+

A
'B
@
A
+@
g
Y
Y
YY
YY
YY
R

S
AB
lm' RwG&






−

@
4

q
R
Y5@
Y5@
Y5@
Y5@
Câu 7a ^`9H2+oV+x*
e!?#;J!?#!?#:&
G#

)+

SB,

-G#


)+-,

*G#

)+S,

(B

⇔ BG#

)+-,

(B
⇔G#

)+-,

(A⇔)+-,

(
⇔+

-B+-A(Y




−−=
+−=
⇔

+
+
^9:`9H2⇒#20!?#;G+(**

Y5@
Y5@
Y5@
Y5@
Câu 8a 8&
)A-+,

(


AA
A


A

Y

++++ +++++
−−
−
)A*+,

(



AA
A


A

Y

++++ +−−+−
−−
−

[ ]




Y


++,+A),+A) +++=−++⇒
Y5@
Y5@
+(!n&




Y


,)B,) −+=+++
 ⇒
,A)

B

A





Y

+=
+
=+++
−
Y5@
Y5@
CÂU Ý NỘI DUNG ĐIỂM
Câu
6b
3∈%⇒3)4*,
8&%)4XR,(

A
%)34XR,⇒sB*Bs(q⇔s*As(




−=
=
⇔
A

(⇒3)5*Z,)G/350H07XR,
(*A⇒3)*A5@,)<J,
>vX)4*,
,4@)X@
,A),),Z),A)
Y,A,)Z),,)A)
X3X
X3X

⇒=⇔



++−=−++
=+−+−+
⇒





=
⊥
>FrG19E#⇒rG;9# 3⇒r)A4A,

XrG;9# 6X⇒6)*4*A,
Y5@
Y5@
Y5@
Y5@
Câu
7b
^`9H2+o*A
e!?#;J!?#!?#:&




=++
−=+
⇔=−+−+++
Z,A+)G#,A+O)
A,A+)G#
YZ,A+)G#,O+O),A+)G#,A+O)







A
+

A

A+A,A+)G#

−=⇔=+⇔−=+
)<J`9H2,

Y
A+O
Z
,A+)G#Z,A+)G#,A+O)

=
+
−+⇔=++

Py
A+O
Z
,A+)G#,+)f

+
−+=
;)*A4-c,

a

A B A
) , Y ) A4 , i
) A,G  )O A, O
f x x
x x

 
= + > ∀ ∈ − +∞ −
 
+ +
 
]#;bH#
,
O
A
4A) −−

,4
O
A
) +∞−
⇒;bH#
,
O
A
4A) −−

,4
O
A
) +∞−
90!?#;f)+,(Y8
#28G#2%9'=
z/8f)A,(Y4f)*uB,(Y⇒+(Y+(*uBG#20!?#;
f)+,(Y
lm'0!?#;J8#2

A

x = −
4+(Y4+(*uB
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Y5@
Y5@
Y5@
Câu
8b
8&
AB
A A
AB
O
AB
B
 B  B
AB
Y
)  @,  @ ) A,   @
k k
k k
k
C
−
=
 
− = − = −
 ÷

 
∑
C/#K)H-A,G[9\
O

B
Y AB
k
N
k
N
k N
k

− ∈



∈
⇔


∈


≤ ≤


B
Y A

k i
i N
i
=


⇔ ∈


≤ ≤

⇒∈{Y4A4|4A}lm'8/#[9\
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