9 ĐỀ ÔN THI TUYỂN SINH ĐẠI HỌC MÔN TOÁN 2011 ppsx

Đ ÔN THI TUYN SINH ĐI HC, Môn TON - Đ 1
PHẦN CHUNG CHO TẤT CẢ THÍ SINH
Câu I
( )
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++++= xmmxxy
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  !"#$%&
 '()*"#+,-#!"./
01%&2,34
Câu II5+67)*()1%)189
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+
x
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x −
%
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

−
x
1
∈
:
Câu III'*)$;))<=>0?1-@6A)B)C
D


C



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

−
=
−
=
−
zyx
D

C



=−+−
=+−−
EFGG
EGGH
zyx
zyx
 I)*J)D
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D


K,
 5>L)#D
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D
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9
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Câu IV 'QQ+PL%
∫
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+
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x
xdx
5+67)*(

9
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π
−x

e
%)1
PHẦN RIÊNG Thí sinh chỉ được làm 1 trong 2 câu: V.a hoặc V.b
Câu V.a. Theo chương tr;nh KHÔNG phân ban
 R+O+S%
{ }
FH9E
TU/,V)!9W
$,6OR+XW#SY
 '*)Z+B)<=>0?1-)3M6A)$[
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3M
Câu V.b. Theo chương tr;nh phân ban
 5^+67)*()
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M%(,,;))/#_*Z+B)-3M*,)
S#3M_S%5>L`N6O*,)#S_4]
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d
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Q/<^
ĐP N – THANG ĐIM Đ 1
Câu N@i dung ĐiBm
I EE
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hM)C
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∞
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-  8
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





)E

≤
+
+
<⇔≤
+
+
<
x
x
x
x
EHE




E


E


E


E



−<⇔





−<



−>
−<
⇔







≤
+
>
+
+
⇔








≤−
+
+
>−
+
+
⇔ x
x
x
x
x
x
x
x
x
x
x
Đ ÔN THI TUYN SINH ĐI
HC, Môn TON - Đ 6
PHẦN CHUNG CHO TẤT CẢ THÍ SINH
Câu I () 
 
 y x x mx= − + + −

  !"#$%E
 '()*"#!)*$)E4
Câu II ()  5+67)*(




 
  9
tg x tgx
x
tg x
π
+
 
= +
 ÷
+
 
'(^)*"#+67)*(

9
 9 x x x m
+ + − + =
/{)0)=
Câu III () '*)$;))<=>0?1-@3H4H4E
6A)B)
  F
C 
  9
x y z
d
+ + −
= =

−
 '(>03
i
1I)<32,6A)B)D
 '(>0M,0D)3M,;).M
%
c

Câu IV () 'QQ+P


E
 
x
I x x e dx= + +
∫

5=+67)*(
 
 
 
G GE H E
G GE H E
G GE H E
x y x y
y z y z
z x z x

− + =


− + =


− + =

PHẦN RIÊNG. Thí sinh chỉ được làm 1 trong 2 câu: V.a hoặc V.b
Câu V.a Theo chương tr;nh KHÔNG phân ban ()
 /,)!9W$,zn,<7
HEE
 '*)Z+B)<=>0?1-(>0\#)3M
*J)6A)B)3M6A)$[X36A)*,),-$[XM
N6O/+67)*(189-g%E1g-8F%E18-gc%
E
Câu V.b Theo chương tr;nh phân ban ()
 5+67)*(
( ) ( )
H   H   
x x
x
+ + − =
 (/+_3M/-3M),;)P.\M3M%
_3%_3,;))/<Z+B)-]Z+B)2,3,;)
)/<_K_M_N6O.T'QdQ$ID=
_3T
ĐP N – THANG ĐIM Đ 6
Câu N@i dung ĐiBm
I EE
  !"#EE
%E*f
 

 y x x= − + −
• 'R+1"C
¡

• _C
w  w
 G 4 E Ey x x y x= − + = ⇔ =
Z
x
=

EH
• -
'
%-E%&-
j
%-%
EH
• M)C
 
EH
• j!"C
8
&
E

-


1

EH
 '()*"#kEE
'/

w 
 G y x x m= − + +
T!)*E4$\$
w
E E4y x≥ ∀ ∈

 G E4m x x x⇔ ≥ − ∀ ∈
EHE
vp

   Gg x x x= −
<1∈E4'/)
 
'X),-*)*"N(|E
EHE
II EE
 5+67)*(6O))EE
jn,$=C1≠E
o67)*(l67)67)<


 
 

tg x tgx
x x

tg x
+
= +
+
  
         x tg x tgx x x x x x x x⇔ + = + ⇔ + = +
    Ex x x
⇔ + − =
EHE
•
  E  
9
x x tgx x k
π
π
+ = ⇔ = − ⇔ = − +
•
 H
  E    
 G G
x x x k hay x k
π π
π π
− = ⇔ = ⇔ = + = +

j,<n,$=6O)=#+67)*(
( )
H
  
9 G G

x k x k x k k
π π π
π π π
= − + ∨ = + ∨ = + ∈
Z
EHE
 '(^)*"#kEE
jZ
 Et x
= + ≥
+67)*(l*f
9
9
 }t t m+ − =
'^-I)<z)=$;)P#+67)*(}/
{)0)=#+67)*(lD/+67)*(l
/{)0)=$\$+67)*(}/{)
0)=
EHE
vp
9
9
  f t t t= + −
<|E/
( )

~

9
9

   E

t
f t
t
= − <
+

]yE%
9


   E
x
f t
→+∞
=
•/)C
)
’
1
8
)1

'X),-*)*"N(#
9
E m< ≤

EHE
III

 '(>03
’
1I)<32,DkEE
j6A)B)D/d7\+67)
44 9u
= −
r
]Z+B)o
2,3,;))/<DR
u
r
d7++,-/+67)
*(
oC1gH8-gHg9@gE%E⇔18-g9@gH%E
EHE
5>T*,)#33
’
€)(,,))/#3
*D/T)#33
’
o/>01
"f=
  F
C
  9
  9 H E
x y z
d
x y z
+ + −


= =

−


+ − − =

5=*6OT4H4&,-*3
’
4H4&
EHE
 '(M,0DkEE
e(∈D3⊥D≡T4H4&(,,;))/#
3*D
EH
M∈DM&84&84Fg9
  

c  9  G m 9  c
9  E  
BC t t t
t t t t
= ⇔ − + − + − =
⇔ − + = ⇔ = ∨ =
t/M∈•44H4m4&H‚
EHE
,RC4H4&M∈•44H4m4&H‚
EH
IV

 'QQ+PEE
jZ


  
x
u x x
du x dx
dv e dx

= + +
⇒ = +

=

>
x
v e
=
 

E E

        
E
x x x
I x x e x e d x e x e dx
= + + − + = − − +
∫ ∫
EHE

'Q

E
  
x
J x e dx
= +
∫
jZ
 
 
x
u x
du dx
dv e dx
= +

⇒ =

=

>
x
v e
=

E

       
E

x x
J x e e dx e e e
= + − = − − + = +
∫
t/L%dg
EHE
 5=+67)*(
y
’

y
E
T=+67)*(l67)67)<






GE
G H
GE
G H
GE

G H
x
y
x
y

z
y
z
x
z

=

+


=

+


=

+

'X=,-*1-@$;)P
•R^-,1%E(-%@%E,-*E4E4E0)=#
=
EHE
•,1ƒE(-ƒE@ƒEvp


GE
   E
G H

t
f t t
t
= >
+
'/
( )
w


EEE
  E E
G H
t
f t t
t
= > ∀ >
+
t/y!)*$)
E48„T=6O.
 
 
 
y f x
z f y
x f z
=


=



=

'XQ!)#y,-*1%-%@5…1ƒ-
       f z f x z x f y f z y z
⇒ > ⇒ > ⇒ > ⇒ >
eR-1ƒ-ƒ@ƒ1C;†
'-=6O
H
G
x y z
= = =
'R+)=
H H H
E4E4E 4 4
G G G
 
 
 
 ÷
 
 

EHE
V.a EE
 /,kEE
5>Ul-,N,/D.)
abcd
•,ƒ/F>


c
A
>D/F

c
A
%
Hm>
abcd
EHE
•,%/H>

m
A
>D/H

m
A
%mE
>
abcd
eR-Ul-,N,Hm8mE%mEm
EHE
 '(>0\#)3MEE
'>0\3)=#=+67)*(
9  E
 4
  F E
x y

A
x y
+ − =

⇒ −

− + =

'>0\M)=#=+67)*(
9  E
G4 
  c E
x y
B
x y
+ − =

⇒ −

+ − =

EHE
j6A)B)M2,M,;))/<6A)$[X3
/+67)*(C1gG8-8%E⇔18-gG%E
'*,)3,06A)*,),-$[XM>0
EHE
)==+67)*(
  G E
4H
 

  c E
 
x y
C
x y
+ − =


⇒
 − +
+ − =



,RC3&4MG4&4H
V.b EE
 5+67)*(kEE
o67)*(l67)67)<
H  H 
  E
 
x x
   
+ −
+ − =
 ÷  ÷
 ÷  ÷
   

jZ

H  H  
E
 
x x
t
t
   
+ −
= > ⇒ =
 ÷  ÷
 ÷  ÷
   

o67)*(*f


 E   E  t t t t hay t
t
+ − = ⇔ − + = ⇔ = =
EHE
• e<%6O
H 
 E

x
x
 
+
= ⇔ =
 ÷

 ÷
 

• e<%6O
H 

H 
 ) 

x
x
+
 
+
= ⇔ =
 ÷
 ÷
 
'R+)=#+67)*(
H 

E) 
+
 
 
 
 
 
EHE
 'QdQ$ID=_3TkEE

e(_3⊥3M_3⊥M]3M⊥MD/M⊥_3M_,-*3T⊥M
]Z$3T⊥_3T⊥_M_,-*3T⊥_M3T⊥T
 
    }
 G
SAHK
V dt AHK SK AH HK SK
= =
'*))
_3M,;).3/Đ ÔN THI TUYN SINH ĐI HC, Môn TON - Đ 3
PHẦN CHUNG CHO TẤT CẢ THÍ SINH
Câu I
3 1
(1).
1
x
x
+
+
  !"#
 'QD=Q#).f*‡>0+,-<!"
.]&4H
Câu II5+67)*(
E99
99
=+++ xxxx
_
T
3


M

5^+67)*(181&


++−
xx
bg1&


Câu III'*)$;))<=>0?1-@Z+B)

α
C1g-8@8%E6A)B)DC





−
=
−
=
−
zyx
 '(>0)#D<
α
4Q#)/)WD
α


 e+67)*(ZN,/P,0D+1{<Z+B)
α

?1-
Câu IV'QQ+PL%

9

E


dx
x
x
xe
x
∫








−
−
1-UlE

π

≤≤
x
E

π
≤≤
y
I)*J)
18-
≤
81-
PHẦN RIÊNG Thí sinh chỉ được làm 1 trong 2 câu:V.a hoặcV.b
Câu V.a. Theo chương tr;nh KHÔNG phân ban
 I)B)I


E

8&
&


1
n
C
8k8

−
n
n

%
&
),-D67)
k
n
ˆO+R+$#
+N…
 '*)Z+B)<=>0?1-6A)*‰C1&9

8-

%9
S94'(>0]**‡,)X]$[6O+
,-]3]M6A)*‰<3M+6A)
B)3M2,S
Câu V.b. Theo chương tr;nh phân ban
 5^+67)*(
EG
9

≤−−
−−−− xxxx
 ID=3Mt]•oN6O,0.MMt3
M%9M]3%3oMt%M•]Z+B)]•oK3t.Š
'Q‹
AD
AQ
‹Q+N#$ID=3Mt6O+P
fZ+B)]•o
ĐP N – THANG ĐIM Đ 3

Câu N@i dung ĐiBm
I 2,00
1  !"#EE
'R+1"Ct%:Œ•&‚
_C
E



w
Dx
x
y ∈∀>
+
=
EH
'=RI)C1%&=R))C-% EH
M)C
1 &„&
8„
-i 88
- 8„ 
 &„
EH
j!"C
2 'QD=Q)EE
o67)*(+,-D#!".]C
-%-
i
&188H

⇔
-%18c EH
j6A)B)DK*‡.3






−
E4

c
K*‡,)
.ME4c
t=Q)?3M

9
m
c

c





=−==
OBOAS
OAB

EHE
II 2,00
1 5+67)*(6O))EE
o67)*(l67)67)<
( )( )
EH9EH9
E


9


=−+⇔=−−⇔
=+−+






−
xxxx
xxx
sin2 1 ,
4
x x k k Z
p
pÛ = - Û =- + Î
EHE
EHE

2 '(+67)*(/)=EE
jZ
E

≥++−=
xxt
//
( )( ) ( )
9



−=−−−=−+
txtxx
M^+67)*(*f
EH


& ?
-
1
( )
( )
( )
E
EE9


>++>⇔
>++−⇔>−+⇔−+<−

ttvit
tttttttt

'6O
E

+<<−⇔<−−⇔>++− xxxxx
•)=#^+67)*(
 +<<− x
EHE
III 2,00
1 '(>0)#D<qQ#)/k
EE
5>])#D<q'>0#])=
#=+67)*(C
44






E






−⇒






−
=
−
=
−
=++−
M
zyx
zyx
EHE
ed7++,-#q
( )
44
−=
n
d7\+67)
#D
( )
44
−=
u
5>•)/)WDq'/

c
9


9


 =
−−
==
un
un
ϕ
EHE
2 e+67)*(ZN,EE
5>L%8484&
∈
DP#ZN,_N(
t_+1{<qZ+B)?1-
( ) ( )
( ) ( )
2 1 1 2 4 1
1
, , 2 1 .
3 5
t t t
d I d I Oxy t t ta
+ - + - +
= Û = Û = - Ú =
EHE
e<%&(_/PLE4&4$Q:%_
/+67)*(
( ) ( )

9


=−+++
zyx
e<
H

=
t
(_/P






−
H

4
H
F
4
H
G
I
$Q:%
H



_/+67)*(

H
9
H

H
F
H
G

=






++






−+







−
zyx
EHE
IV 2,00
1 'QQ+PkEE
∫∫∫
−
−
+=








−
−=

E


E


E




99 x
xdx
dxxedx
x
x
xeI
xx
( )
[ ]








−===
∫∫ ∫

E


E


E


E





dxexeexddxxeK
xxxx

( )
[ ]
( )

9


9



E

+=−=
exe
x
[ ]
9
9


E

E


∫
−=−=
−
−
=
x
x
xdx
J
t/

9
F


−
+=+=
e
JKI
EHE
2 I)^B)IEE
t







∈

4E
π
yx


E
π
≤
+
≤≤
yx
xy
,-*


 xy
yx
≤
+
'/
xy
yxyxyx
yx 







≤
+
≤
−+
=+

EH
vp
( )
tttf 

−+=
<


4E






∈
π
t
'/

( )
( )

w
ttttf −=
•R^-yi%Ey%%&
•,Ebb(

bb

b

bD/y
iƒE
•,bb

π
(b

b

π


ƒ

ƒD/y
ibE
t//)
 E


π
yi 8E&
y
g
E
c


π
EHE
t
E
c


>
π

( )


4EE






∈∀≥

π
ttf
_,-*
( ) ( )
 xyxy
+≤
'X,-*n,+I)
0,25
V.a 2,00
1 I)B)IEE
vp$*
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
}

E

w


E
−−−−
−
−
−
++−+=+=⇒
++++=+=
n
n
n

n
nn
n
n
n
n
n
n
n
n
n
n
n
n
CxCnxCnxnxf
CxCxCxCxxf
EHE
'-1%}6O
( )

E
−−−
=++−+
nn
nn
n
n
n
nCCnCn
•R1pC/$*81


^-.1%
*!P
EHE
2 '(>0]EE
5>LP6A)*‰,-*L94Evp]E4,0
*‡,)X/$[6O+,-]3]M
6A)*‰5…
31

4-

4M1

4-

'/
( )
4

ayxMA
−=

( )

49 yxIA
−=

e(
MAIA

⊥

( ) ( ) ( ) ( )
E999E9





=−−++−⇔=−+−
ayxyxayyxx
e(3,0
E9

=−−
ayx
_,-*3,06A)
B)
91g-g%E
EHE
'67)M,06A)B)91g-g%Et/
+67)*(6A)B)3M91g-g%E
j6A)B)3M2,S94%9
jN(]E49
$C++,-.31

4-

/D.)
( )

1 1
4 ( 4) 4 0x x y y- - + - =
e(+,-2,]E4/
( )
1 1
4 ( 4) 4 0x ya- - + - =
'67)>0M1

4-

U
( )
2 2
4 ( 4) 4 0x y a- - + - =
_,-*+3M91g-g%E
EHE
V.b 2,00
1 5^+67)*(€EE
jZ%
E


>
−−
t
xx
M^+67)*(l*f


&

4
2 0
t
- £ Û


gg9ŽE
Û
&

88
Û
Ž
EHE
'/Eb



≤
−−
xx
Û
1

g1&ŽE
Û
 +≤≤− x
•)=#^+67)*(
 +≤≤− x
EHE

2 'Q‹kEE
5>S%]••t/Š%oS•3t5>•*,)
#M5*3t5~~oŠ•R
^-•t~~]•
'/

H









=+=+=+=+=+=
Α
MC
MF
EC
ED
PC
PG
AP
PG
AP
G
_,-*
H


==
AG
AP
AD
AQ
EHE
Đ ÔN THI TUYN SINH ĐI HC, Môn TON - Đ 2
PHẦN CHUNG CHO TẤT CẢ THÍ SINH
Câu I
Fm
9
+−= xxy

  !"#
 '()*"#6A)B)-%1gc+1{<!
"#
Câu II5+67)*(



9

9
 +







−=






−
ππ
xx
5^+67)*(








x
x
x
−
>+
−
Câu III'*)$;))<=>0?1-@Z+B)oC18-
g@8%E6A)B)

H

c

C
+
==
−
zyx
d
394E4M&4&4
44G
 e+67)*(ZN,_2,3M/P,0Z
+B)o
 e+67)*(Z+B)ŠI6A)B)DKZN,_d
06A)*‰/$Q<^
Câu IV'QQ+P

9


E
∫
−+
=
π
xx
xdx
I
I)*J)+67)*(
( )
99


=+
x
x
/{))=+P=
PHẦN RIÊNG Thí sinh chỉ được làm 1 trong 2 câu: V.a hoặc V.b
Câu V.a. Theo chương tr;nh KHÔNG phân ban
 '(=#.)I1
H
*)$*"I•,7#81


*J)
EE

=+
nn
AA
),-D67)
k
n
A
\O+R+$#
+N…
 '*)Z+B)<=>0?1-6A)*‰C


=+ yx
'(
)*"#*6A)B)-%!.{)Xz

/$[6O+,-<)/)W+,-/
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

Câu V.b. Theo chương tr;nh phân ban
1. 5+67)*(
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)
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





−=+
x
x
x
x
2. (/+_3MzZ0),;)_3%_M%_
%5>•]SN6O*,)#.3M3M4t
1I)#_2,S4L)#6A)B)3t<Z+B)
_]•I)*J)3t,;))/<_LQdQ#$
ID=]M_L
ĐP N – THANG ĐIM Đ 2

C
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N@i dung Đi
Bm
I 2,0
0
1  !"#
EE
'R+1"Ct%:
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4 16 4 4 , 0 0 2y x x x x y x hayx= - = - = Û = = ±
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1 &„&E
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B)kEE
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x
<
Rx
∈
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=++⇔= xxxf
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=++⇔ xx
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E
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)=+P=C
( )
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⇒=⇒=
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E
jn,$=
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c
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x
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( )
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x
xx
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E

3 4 2
6
3 9 3 2 0 1 2.x x x x x hayx
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Û = - Û - + = Û = ± = ±
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=
x
EH
E
2 'QQkEE
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⇒
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⊥
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⇒
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=+=
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Đ ÔN THI TUYN SINH ĐI HC, Môn TON - Đ 7
I. PHẦN CHUNG CHO TẤT CẢ THÍ SINH (7,0 điểm)
Câu I (2,0 điểm): 


x
y
x
+
=
+

  !"#l
 I)*J)<>sE6A)B)-%18,;K!".
+P=*)//0)/0U7&
Câu II (2,0 điểm): 1) 5+67)*(
( )

     

x x x
x
− + = − +
5^+67)*(


) 
) 

 H 9EE
+
+
<
x
x

Câu III (1,0 điểm):
( ) ( )
( )

 
x
f x x e
= + +

'QD=Q#(+B))<.f!"#y1*‡*‡,)
6A)B)1%
Câu IV (1,0 điểm):vp(/+_3Mt/_3%_M%_t%t3%3M%M%t%
MQ#$/+_3MtJ)


G
a
Q0D._d
Câu V (1,0 điểm):=#1
9
1
H
1

G
*)$*I#,I
81

dI/R+0^+0)'(),-D67)
II. PHẦN RIÊNG (3,0 điểm)
'Q\6O0*)+N+NZ+N
 'd67)*(,’
Câu VI.a (2,0 điểm):
 '*)Z+B)<=>0?1-6A)B)
D

C18-g%ED

C18-g9%ED

C1g-g%E
e+67)*(6A)*‰/P,0D

+1{!)A<D

D


 '*)$;))<=>0?1-@344&6A)B)D/
+67)*(C
 

 
x t

y t
z t
= − +


= −


= − +

e+67)*(#6A)B)
∆
2,3K,;))/<D
Câu VII.a (1,0 điểm):/HI)D0$(,-P#0;)-“
+N)6A6zI)E+)(D$Q*)z+)(/
0P,U$*+)($,)P,U$,4I)>
0+)(*)/1"P,U$*#(M*J)+)(/
(I))=,0EP,U$*DI)6,
l-Q1,^HP,UHI)>;0$,
 'd67)*(•P)
Câu VI.b (2,0 điểm):
 '*)Z+B)<=>0?1-)3M/6A)+P)$[X3
6A)*,),-$[XM6A)$[XN6O/+67)*(C
-%E91g-g%E18-%ETl-1">0#\3M
 '*)$;))<=>0?1-@6A)B)D/+67)*(C
  
  
x y z
− − +
= =

−
Z+B)C
oC18-g@8%EŠC1&-g@8%Ee+67)*(ZN,/P,0D
+1{!)A<Z+B)oŠ
Câu VII.b (1,0 điểm):'(+N+N#+I@

  z i= − +

ĐP N VÀ THANG ĐIM Đ 7
Câu Đáp án Điể
m
I (2,0
điểm)
 (1,25 điểm)
 'R+1"C
{ }
Œ 
= −
¡D

 _Cn,C
( )
~


E 

y x D
x
−

= < ∀ ∈
+
EHE
_,-*)"*z$)
( )
4 
−∞ −

( )
4− +∞

*"CT$;)/*"
5<.=RC
( ) ( )
 
  4    
x x
x x
y y y y
− +
→−∞ →+∞
→ − → −
= = = −∞ = +∞
_,-*!"#/0=R))6A)
B)-%0=RI)6A)B)1%&
EH
M)C
1 &„&8„
-i ””
- 8„

&„
EH
 j!"C EH
 (0,75 điểm)
T0)#6A)B)-%18!"
)=#+67)*(’1C
( )

 

x
mx m
x
+
= +
+
jZ%18s'X+67)*(/+67)*(’
C
( )
( ) ( )
 

t
m t
t
= +
−
'/C
( )
( )


E }


mt t m
t

− − =

⇔

≠


•R1pC%$;))=#
( )
}
/
UDn,$=
t
≠
EH
e<sE}+67)*(’R$;)R%
)=/Q%&%&

bE
_,-*+67)*(},;/)=+P=*D^,
$t/+67)*(,;/)=+P=*
D^,
EH

_,-*+67)*(,;/)=+P=*)
)=//0)=U7&'XP-/+
EH
-
1&

?