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TUYỂN TẬP ĐỀ THI MÔN TOÁN TỪ BỘ GIÁO DỤC VÀ ĐÀO TẠO ( có đáp án)

Ngân hàng đề thi đại học Môn Toán năm 2014 Blog: www.caotu28.blogspot.com


Page 1

ST: Cao Văn Tú
Email: caotua5lg3@gmail.com

B 


*** THI 

A-A1-B-D 101
k


(7,0 điểm)
(2 điểm)
1. 
21

1
x
y
x




2. 
2
.
(2 điểm)
1) 
2
17
sin(2 ) 16 2 3.sin cos 20sin ( )
2 2 12
x
x x x

    

2) 
4 3 2 2
32
1
1
x x y x y
x y x xy

  


   



(1 điểm): 
4
0


tan .ln(cos )
cos
xx
dx
x



(1 điểm):


0


(1 điểm) 

3
a b b c c a
ab c bc a ca b
  
  
  

(3 điểm) Thí sinh chỉ được làm một trong hai phần (phần A hoặc B)
A. 
(1 điểm)


: 2x + 3y + 4 = 0.







0
.
(1 điểm): -1;1)

1
( ):
1 2 3
x y z
d




14
( '):
1 2 5
x y z
d



.
(1 điểm)
:
22
2
(24 1)
(24 1) (24 1)
log log



x
x x x x
log x x x


Ngân hàng đề thi đại học Môn Toán năm 2014 Blog: www.caotu28.blogspot.com


Page 2

ST: Cao Văn Tú
Email: caotua5lg3@gmail.com
(1 điểm)

22
( ): 1C x y

( ): 0d x y m  



m

()C

()d

(1 điểm)

(P): 2x  y + z + 1 = 0, (Q): x  y + 2z + 3 = 0, (R): x + 2y  3z + 1 = 0

1

:
2
2

x
=
1
1y
=
3
z

2



1

,
2

.
(1 điểm) 
x
( log
3
( 9
x
 72 ))

1



 
 
\1D 

2
1
' 0
( 1)
y x D
x

   



( ;1)

(1; )



1x
Limy


 

1x
Limy


 

2
x
Lim y



2
x
Lim y







00
( ; ( )) ( )M x f x C

0 0 0
'( )( ) ( )y f x x x f x  
Hay
22
0 0 0
( 1) 2 2 1 0x x y x x     
(*)

2

0
4
0
22
2
1 ( 1)
x
x





0
0x 

0
2x 

10xy  

50xy  

 
os2 3sin2 10 os( ) 6 0
6
c x x c x

    

os(2 ) 5 os( ) 3 0
36
c x c x

     

2
2 os ( ) 5 os( ) 2 0
66
c x c x

     

1
os( )
62
cx

  

os( ) 2
6
cx

  


1
os( )
62
cx

  

2
2
xk




5
2
6
xk


  

 
2 2 3
32
( ) 1
( ) 1
x xy x y
x y x xy

  


   




2
3
x xy u
x y v








2
1
1
uv
vu



  

-2;-
-1;0)
 -
4
x



1
2
t 

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
1
1
2
22
1
1
2
ln lntt
I dt dt
tt
  


2
1
ln ;u t dv dt
t


11
;du dt v
tt
   

Suy ra
1
2
1
2
11
1 1 2 1
ln ln2
11
2
22
I t dt
t t t
     


2
2 1 ln2
2
I   


*
()SH ABC


0
60SEH SFH


HK SB

HKA
.

2
2
a
HA 
,
0
3
tan60
2
a
SH HF


2 2 2
1 1 1 3
10
KH a
HK HS HB
   


2
20
2
tan
3
3
10
a
AH
AKH
KH
a
  

3
cos
23
AKH


11
1 (1 )(1 )
a b c c
ab c ab b a a b
  

     


1 1 1
(1 )(1 ) (1 )(1 ) (1 )(1 )
c b a
VT
a b c a c b
  
  
     

-a,1-b,1-


3
1 1 1
3. . .
(1 )(1 ) (1 )(1 ) (1 )(1 )
c b a
VT
a b c a c b
  

     


1
3
a b c

 *


13
22
xt
yt



  


( 3;2)u 




(1 3 ; 2 2 )A t t   


)=45
0

1
os( ; )
2
c AB u

.
1
2
.
AB u
AB u



2
15 3
169 156 45 0
13 13
t t t t        

12
32 4 22 32
( ; ), ( ; )
13 13 13 13
AA


1
(0; 1;0)M 

1
(1; 2; 3)u   


2
(0;1;4)M

2
(1;2;5)u 


12
; ( 4; 8;4)u u O

   

,
12
(0;2;4)MM 

1 2 1 2
; . 16 14 0u u M M

   


 
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
(1;2; 1)n 

1

2 2 0x y z   
-
 


1x 


1 2 1
1 2log (24 1) 2 log (24 1) log (24 1)
x x x
x x x

    


log ( 1)
x
xt

1 2 1
1 2 2t t t


-2/3

log ( 1) 1
x
x  

-2/3
2
log ( 1)
3
x
x   

23
.(24 1) 1xx  
(*)

1
8
x 

1
8
x 


1
8
x 

1
8
x 


1
8
x 


( ; ) 1d O d


1 1 1
. .sin .sin
2 2 2
OAB
S OAOB AOB AOB  


0
90AOB 
1
( ; )
2
d I d

1m  

 *
1


22
1
3
xt
yt
zt



  




*
2


2
53
xs
ys
zs










12
;d A d B   

(2 2 ; 1 ;3 ) B(2+s;5+3s;s)A t t t   

*
( 2 ;3 6; 3 )AB s t s t s t    

(1;2; 3)n 

*
( ) &d R AB n

2 3 6 3
1 2 3
s t s t s t   
  

23
24
t


1 1 23
( ; ; )
12 12 8
A

(1;2; 3)n 

23
11
8
12 12
1 2 3
z
xy





 :
3
0
log (9 72) 0
9 72 0
x
x
x 








9
log 73x 


9
log 73x 

3
log (9 72)
x
x

9 72 3
xx
  


38
39
x
x









2x

9
(log 72;2]T 



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
*** 

-A1-B-D 102


 ( 7 điểm )
 ) 
3
 (m + 1)x + 5  m
2
.
1) 
2) 

 
3
27
log 1 x log x
.








24
cos2sin
2
cossin
2
sin1
22
x
x
x
x
x


  
2 2 2
8 15 4 18 18 2 15x x x x x x       

( I=


4
2
3
121 xx
dx


1
B
1
C
1


0

1
B
1
C
1

B
1
C
1
. 
1

1
C
1
theo a.
 
A/ 
 
1. -1)
2
+ (y+2)
2
= 9


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Page 6

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Email: caotua5lg3@gmail.com
2.-1) 








tz
ty
tx
31
21

 

n 1 n 2 n 3 2n 1 2n 8
2n 1 2n 1 2n 1 2n 1 2n 1
C C C C C 2 1
.

10
tro
n
34
1 x x x
.
B/ 

1 -1)
2
+ (y+2)
2
= 9


2.-








tz
ty
tx
31
21


  
32
4
)32()32(
1212
22


 xxxx





102
 : 1, 
3
 (m + 1)x + 5  m
2
.
 
3
 3x + 1

R


 
lim
x
fx

 
:
 


xf
x
lim


2
 3 ,
' 0 1yx   


x --
 0 - 0 +



-- 1

 
 
1;

 
;1

 
1;1


1; 3
CD
xy  

1; 1
CT
xy  
,

'' 6yx

 
0;1U
:
 
0;1U




2
-1
1
2
x
1
3
-1
-2
y
O
Ngân hàng đề thi đại học Môn Toán năm 2014 Blog: www.caotu28.blogspot.com


Page 7

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Email: caotua5lg3@gmail.com





 
 
2
  
 3(m + 1) > 0  m > 1 (*)

2
2
( 1) 5
3
y m x m   


2
5 4 1mm    

:
3
27
log 1 x log x
.

t
7
t log x x 7
.

tt
t t t t
33
t
3 3 3 3
2
17
pt log 1 7 t 1 7 2 1 7 8 1
88
(*).


:







24
cos2sin
2
cossin
2
sin1
22
x
x
x
x
x


)1(
24
cos2sin
2
cossin
2
sin1
22







x
x
x
x
x


 
xsin1x
2
cos1xsin
2
x
cosxsin
2
x
sin11
2












01
2
x
cos
2
x
sin2.
2
x
cos
2
x
sinxsin01xsin
2
x
cos
2
x
sinxsin 
















01
2
x
sin2
2
x
sin21
2
x
sinxsin
2
















2
sin 0,sin 1,2sin 2sin 1 0
2 2 2
x x x
x     


,2
4
22
xk
x
x k k x k
xk


  



      





2 2 2
8 15 4 18 18 2 15x x x x x x       
(1)

5, 5, 3x x x  


TH2
5x 

17
5 5 4 6
3
x x x x       

17
5
3
x

TH3
5x 

17
5 5 6 4
3
x x x x        

5x 


 
17
( ; 5) 3 (5; )
3
S     

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Page 8

ST: Cao Văn Tú
Email: caotua5lg3@gmail.com
: I=


4
2
3
121 xx
dx

+I=


4
2
3
121 xx
dx
 t=
12 x

12
2
 xt

tdt=dx 
2
3

t = 2
x=4

t = 3
 I=



3
2
2
1
2
1
t
t
tdt
=


3
2
2
)1(
2
t
tdt

dt
t
t



3
2
2
)1(
11
=




3
2
2
3
2
)1(
2
)1(
1
2
t
dt
dt
t

=
3
2
3
2
1
2
1ln2


t
t
I= 2ln2+1
: Cho l
1
B
1
C
1


0

1
B
1
C
1

1
C
1


1

1
C
1
theo a.
Do
)(
111
CBAAH 

1
AA H

1

1
B
1
C
1

1
AA H

30
0
. 
1

1

1
AA H
=30
0

2
3
1
a
HA 
.

1
B
1
C
1
 
1
C
1

2
3
1
a
HA 

1

B
1
C
1

11
CBAH 

)(
111
HAACB 












1

1

1
C
1


1
.HK = A
1
H.AH
4
3
.
1
1
a
AA
AHHA
HK 


-1)
2
+ (y+2)
2
= 9

 
-
ACAB 

23 IA


5
1
3 2 1 6
7
2
m
m
m
m



     




A1
1111
1111
1

A
B
C
C
1
B
1
K
H
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ST: Cao Văn Tú
Email: caotua5lg3@gmail.com
-









tz
ty
tx
31
21




HIAH 

IA 

 
AH

)31;;21( tttHdH 

)3;1;2((0.  uuAHdAH


)5;1;7()4;1;3(  AHH
 10) + (y  2)  5(z + 1) = 0
 7x + y -5z -77 = 0

n 1 n 2 n 3 2n 1 2n 8
2n 1 2n 1 2n 1 2n 1 2n 1
C C C C C 2 1
.

10

n
34
1 x x x
.
n 1 n 2 n 3 2n 1 2n
2n 1 2n 1 2n 1 2n 1 2n 1
S C C C C C

2n 1 0 1 2 n 1 n n 1 n 2 2n 2n 1
2n 1 2n 1 2n 1 2n 1 2n 1 2n 1 2n 1 2n 1 2n 1
(1 1) C C C C C C C C C

2n 1 0 2n 1 2n 2n 1 n 2 n 1 n 1 n 2 2n 1 2n
2n 1 2n 1 2n 1 2n 1 2n 1 2n 1 2n 1 2n 1 2n 1 2n 1
2 C C C C C C C C C C
2n 1 2n 2n 8
2 2 2S 2 1 S 2 2 n 4
.

n4
4
4
3 4 3 3
1 x x x (1 x) x (1 x) 1 x 1 x

0 1 2 2 3 3 4 4 0 1 3 2 6 3 9 4 12
4 4 4 4 4 4 4 4 4 4
C C x C x C x C x C C x C x C x C x
.

10

1 3 4 2
4 4 4 4
C .C C .C 10
.

 
32
4
)32()32(
1212
22


 xxxx

Bpt
   
43232
22
22

 xxxx

 
)0(32
2
2


tt
xx

4
1

t
t

014
2
 tt
3232  t
(tm)

 
323232
2
2

 xx
121
2
 xx



2121012
2
 xxx

KL:









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Page 10

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Email: caotua5lg3@gmail.com























*** THI 

 A-A1-B-D 103
k




43
23
 xxy

C
d A mm d C
A, M, N CM N 







yyxx
yyxyx
)2)(1(
4)(1
2
2
(x, y

)

8
1
3
tan
6
tan
3coscos3sin.sin
33

















xx
xxxx




1
0
2
)1ln( dxxxxI

ABC.ABCa
AABCO ABCng (PBC 
Ngân hàng đề thi đại học Môn Toán năm 2014 Blog: www.caotu28.blogspot.com


Page 11

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Email: caotua5lg3@gmail.com
AA
8
3
2
a

ABC.ABC
V (1  Cho a, b, c abc = 1
32
1
32
1
32
1
222222






accbba
P

)
.C 
         Oxy cho parabol (P):
xxy 2
2

     E):
1
9
2
2
 y
x
P) giao (E

         Oxyz    S   
011642
222
 zyxzyx
   

    x + 2y  z     




S
6.
x
2

n
x
x









4
2
1
,
n 
1
6560
1
2
3
2
2
2
2
1
2
3
1
2
0





n
C
n
CCC
n
n
n
nnn

(
k
n
C

k n 
 
Oxy d
1
: x + y + 5 = 0, d
2
: x + 2y - 
ABC AGB d
1


C d
2

ABC.
Oxyz ABC A(1; 2; 5), B(1; 4; 3), C(5;
2P): x  y  z  M P

222
MCMBMA 









1
)1(2
yxe
xee
yx
yxyx
(x, y

)


103
Câu 1: 1, Khảo sát hàm số
43
23
 xxy

1. Tập xác định: R
2. Sự biến thiên:



)4x3x(limylim,)4x3x(limylim
23
xx
23
xx


2
- 6x, y' = 0

x = 0, x = 2

x
-

0 2 +


y'
+ 0 - 0 +
y
4 +




-

0
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- -




- x = 0, y


CT
= 0.
3. Đồ thị-













Câu1 : 2,Tìm m để hai tiếp tuyến vuông góc
h y = m(x  3) + 4.







0mx
3x
0)mx)(3x(4)3x(m4x3x
2
223


1)m('y).m('y 

9
35318
m01m36m91)m6m3)(m6m3(
2



Câu 2: 1, Giải hệ phương trình đại số

     











1)2yx(
y
1x
22yx
y
1x
2
2

2yxv,
y
1x
u
2



  
1vu
1uv
2vu






Suy ra








12yx
1
y
1x
2
.
-2; 5)
Câu 2: 2,Giải phương trình lương giác

0
3
xcos
6
xcos
3
xsin
6
xsin 


































1x
6
cot
6
xtan
3
xtan
6
xtan 


































8
1
x3cosxcosx3sin.xsin
33


1 cos2x cos2x cos4x 1 cos2x cos2x cos4x 1
2 2 2 2 8
   
    

x
y
-1
2
O
4
2
1
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2
1
x2cos
8
1
x2cos
2
1
)x4cosx2cosx2(cos2
3















k
6
x
(lo¹i) k
6
x
,
(k )



 k
6
x
,
(k )

Câu 3:Tính tích phân 















2/xv
dx
1xx
1x2
du
xdxdv
)1xxln(u
2
2
2

1
1
2 3 2
2
2
0
0
x 1 2x x
I ln(x x 1) dx
2 2 x x 1

   









1
0
2
1
0
2
1
0
1xx
dx
4
3
dx
1xx
1x2
4
1
dx)1x2(
2
1
3ln
2
1

 
11
1
0
2
1
0
2
I
4
3
3ln
4
3
I
4
3
)1xxln(
4
1
xx
2
1
3ln
2
1



1
:


















1
0
2
2
1
2
3
2
1
x
dx
I









2
,
2
t,ttan
2
3
2
1
x

Suy ra
9
3
t
3
32
ttan1
dt)ttan1(
3
32
I
3/
6/
3/
6/
2
2
1











12
3
3ln
4
3
I







A' AM


3
3a
AM
3
2
AO,
2
3a
AM 


4
3a
HM
8
3a
BC.HM
2
1
8
3a
S
22
BCH


4
a3
16
a3
4
a3
HMAMAH
22
22



AH
HM
AO
O'A


suy ra
3
a
a3
4
4
3a
3
3a
AH
HM.AO
O'A 


12
3a
a
2
3a
3
a
2
1
BC.AM.O'A
2
1
S.O'AV
3
ABC


Câu 5 : Tìm giá trị lớn nhất

2
+b
2
 2ab, b
2

+ 1  2b 
1bab
1
2
1
21bba
1
3b2a
1
22222







1aca
1
2
1
3a2c
1
,
1cbc
1
2
1
3c2b
1
2222







2
1
bab1
b
ab1b
ab
1bab
1
2
1
1aca
1
1cbc
1
1bab
1
2
1
P 

























A
B
C


A
H
O
M
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2
1
P 
khi a = b 
2
1
khi a = b = c = 1.
Câu 6a: 1,Viết phương trình đường tròn đi qua giao điểm của(E) và (P)

09x37x36x91)x2x(
9
x
23422
2

(*)

9x37x36x9)x(f
234

-1)f(0) < 0,


 







1y
9
x
x2xy
2
2
2

09y8x16y9x9
9y9x
y8x16x8
22
22
2







(**)








9
4
;
9
8
I

9
161


Câu 6a: 2,Viết phương trình mặt phẳng (

)
Do () // ( z + D = 0 (D

17)
- . 

435rR
2222











(lo¹i) 17D
7D
12D54
)1(22
D3)2(21.2
222

 z - 7 = 0
Câu 7a : Tìm hệ số của x
2

 


2
0
nn
n
22
n
1
n
0
n
2
0
n
dxxCxCxCCdx)x1(I 

2
0
1nn
n
32
n
21
n
0
n
xC
1n
1
xC
3
1
xC
2
1
xC










suy ra I
n
n
1n
2
n
3
1
n
2
0
n
C
1n
2
C
3
2
C
2
2
C2




(1)

1n
13
)x1(
1n
1
I
1n
2
0
1n







(2)
 
n
n
1n
2
n
3
1
n
2
0
n
C
1n
2
C
3
2
C
2
2
C2




1n
13
1n






7n65613
1n
6560
1n
13
1n
1n









 






















7
0
4
k314
k
7
k
k
7
0
4
k7
k
7
7
4
xC
2
1
x2
1
xC
x2
1
x


2

2k2
4
k314



4
21
C
2
1
2
7
2


Câu b:1, Viết phương trình đường tròn
Do B  d
1
- m  5), C  d
2
 2n; n)
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





0.3n5m3
2.3n27m2













1n
1m
2nm
3n2m

Suy ra B = (-1; -4), C= (5; 1)

0cby2ax2yx
22

. Do A, B, C  

















27/338c
18/17b
54/83a
0cb2a10125
0cb8a2161
0cb6a494


0
27
338
y
9
17
x
27
83
yx
22


Câu 6b :2, Tìm giá trị nhỏ nhất 






3;
3
8
;
3
7

Ta 
     
222
222
GCMGGBMGGAMGMCMBMAF 

22222222
GCGBGAMG3)GCGBGA(MG2GCGBGAMG3 

 MG
2
 

33
19
111
333/83/7
))P(,G(dMG 




3
64
9
104
9
32
9
56
GCGBGA
222



9
553
3
64
33
19
.3
2










Câu 7b: Giải hệ phương trình mũ















1yxe
1yxe
1yxe
)1x(2ee
yx
yx
yx
yxyx

- 











)2(uvee
)1(1ue
1ve
1ue
vu
v
u
v

- 
- 
vu 


u

u
- u- 1 , f'(u) = e
u
- 1

u
-

0 +


f'(u)
- 0 +
f(u)




0

0u 
.













0y
0x
0yx
0yx
0v







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 
-A1-B-D 104




43
23
 xxy

C
d Amm d C
A, M, N CM N 







yyxx
yyxyx
)2)(1(
4)(1
2
2
(x, y

)
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
8
1
3
tan
6
tan
3coscos3sin.sin
33

















xx
xxxx




1
0
2
)1ln( dxxxxI

ABC.ABCa
AABCO ABCPBC 
AA
8
3
2
a

ABC.ABC
V (1  Cho a, b, c abc = 1
32
1
32
1
32
1
222222






accbba
P

)
.C 
         Oxy cho parabol (P):
xxy 2
2

     E):
1
9
2
2
 y
x
P) giao (E

         Oxyz    S   
011642
222
 zyxzyx
   

    x + 2y  z     




S
6.
x
2

n
x
x









4
2
1
,
n 
1
6560
1
2
3
2
2
2
2
1
2
3
1
2
0





n
C
n
CCC
n
n
n
nnn

(
k
n
C

k n 
 
Oxy d
1
: x + y + 5 = 0, d
2
: x + 2y - 
ABC AGB d
1


C d
2

ABC.
Oxyz ABC A(1; 2; 5), B(1; 4; 3), C(5;
P): x  y  z  M P

222
MCMBMA 









1
)1(2
yxe
xee
yx
yxyx
(x, y

)






Câu 1: 1, Khảo sát hàm số
43
23
 xxy

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Page 18

ST: Cao Văn Tú
Email: caotua5lg3@gmail.com
1. Tập xác định: R
2. Sự biến thiên:



)4x3x(limylim,)4x3x(limylim
23
xx
23
xx


2
- 6x, y' = 0

x = 0, x = 2

x
-

0 2 +


y'
+ 0 - 0 +
y
4 +




-

0
- -




- 


CT
= 0.
3. Đồ thị-













Câu1 : 2,Tìm m để hai tiếp tuyến vuông góc
 3) + 4.







0mx
3x
0)mx)(3x(4)3x(m4x3x
2
223


1)m('y).m('y 

9
35318
m01m36m91)m6m3)(m6m3(
2


(
Câu 2: 1, Giải hệ phương trình đại số

     











1)2yx(
y
1x
22yx
y
1x
2
2

2yxv,
y
1x
u
2



  
1vu
1uv
2vu






Suy ra








12yx
1
y
1x
2
.
-2; 5)
x
y
-1
2
O
4
2
1
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Page 19

ST: Cao Văn Tú
Email: caotua5lg3@gmail.com
Câu 2: 2,Giải phương trình lương giác

0
3
xcos
6
xcos
3
xsin
6
xsin 


































1x
6
cot
6
xtan
3
xtan
6
xtan 


































8
1
x3cosxcosx3sin.xsin
33


1 cos2x cos2x cos4x 1 cos2x cos2x cos4x 1
2 2 2 2 8
   
    

2
1
x2cos
8
1
x2cos
2
1
)x4cosx2cosx2(cos2
3















k
6
x
(lo¹i) k
6
x
,
(k )



 k
6
x
,
(k )

Câu 3:Tính tích phân 















2/xv
dx
1xx
1x2
du
xdxdv
)1xxln(u
2
2
2

1
1
2 3 2
2
2
0
0
x 1 2x x
I ln(x x 1) dx
2 2 x x 1

   









1
0
2
1
0
2
1
0
1xx
dx
4
3
dx
1xx
1x2
4
1
dx)1x2(
2
1
3ln
2
1

 
11
1
0
2
1
0
2
I
4
3
3ln
4
3
I
4
3
)1xxln(
4
1
xx
2
1
3ln
2
1



1
:


















1
0
2
2
1
2
3
2
1
x
dx
I









2
,
2
t,ttan
2
3
2
1
x

Suy ra
9
3
t
3
32
ttan1
dt)ttan1(
3
32
I
3/
6/
3/
6/
2
2
1











12
3
3ln
4
3
I







A' AM


3
3a
AM
3
2
AO,
2
3a
AM 


4
3a
HM
8
3a
BC.HM
2
1
8
3a
S
22
BCH


4
a3
16
a3
4
a3
HMAMAH
22
22



AH
HM
AO
O'A


suy ra
3
a
a3
4
4
3a
3
3a
AH
HM.AO
O'A 

A
B
C


A
H
O
M
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
12
3a
a
2
3a
3
a
2
1
BC.AM.O'A
2
1
S.O'AV
3
ABC


Câu 5 : Tìm giá trị lớn nhất

2
+b
2
 2ab, b
2

+ 1  2b 
1bab
1
2
1
21bba
1
3b2a
1
22222







1aca
1
2
1
3a2c
1
,
1cbc
1
2
1
3c2b
1
2222







2
1
bab1
b
ab1b
ab
1bab
1
2
1
1aca
1
1cbc
1
1bab
1
2
1
P 

























2
1
P 

2
1
khi a = b = c = 1.
Câu 6a: 1,Viết phương trình đường tròn đi qua giao điểm của(E) và (P)

09x37x36x91)x2x(
9
x
23422
2

(*)

9x37x36x9)x(f
234

-1)f(0) < 0,


  







1y
9
x
x2xy
2
2
2

09y8x16y9x9
9y9x
y8x16x8
22
22
2







(**)








9
4
;
9
8
I

9
161

 
Câu 6a: 2,Viết phương trình mặt phẳng (

)
Do () // ( z + D = 0 (D

17)
- . 

435rR
2222











(lo¹i) 17D
7D
12D54
)1(22
D3)2(21.2
222

 z - 7 = 0
Câu 7a : Tìm hệ số của x
2

 


2
0
nn
n
22
n
1
n
0
n
2
0
n
dxxCxCxCCdx)x1(I 

2
0
1nn
n
32
n
21
n
0
n
xC
1n
1
xC
3
1
xC
2
1
xC










suy ra I
n
n
1n
2
n
3
1
n
2
0
n
C
1n
2
C
3
2
C
2
2
C2




(1)

1n
13
)x1(
1n
1
I
1n
2
0
1n







(2)
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
n
n
1n
2
n
3
1
n
2
0
n
C
1n
2
C
3
2
C
2
2
C2




1n
13
1n






7n65613
1n
6560
1n
13
1n
1n









 






















7
0
4
k314
k
7
k
k
7
0
4
k7
k
7
7
4
xC
2
1
x2
1
xC
x2
1
x


2

2k2
4
k314



4
21
C
2
1
2
7
2


Câu b:1, Viết phương trình đường tròn
Do B  d
1
- m  5), C  d
2
 2n; n)






0.3n5m3
2.3n27m2













1n
1m
2nm
3n2m

Suy ra B = (-1; -4), C= (5; 1)

0cby2ax2yx
22

. Do A, B, C  

















27/338c
18/17b
54/83a
0cb2a10125
0cb8a2161
0cb6a494


0
27
338
y
9
17
x
27
83
yx
22


Câu 6b :2, Tìm giá trị nhỏ nhất 






3;
3
8
;
3
7


     
222
222
GCMGGBMGGAMGMCMBMAF 

22222222
GCGBGAMG3)GCGBGA(MG2GCGBGAMG3 

 MG
2
 

33
19
111
333/83/7
))P(,G(dMG 




3
64
9
104
9
32
9
56
GCGBGA
222



9
553
3
64
33
19
.3
2










Câu 7b: Giải hệ phương trình mũ















1yxe
1yxe
1yxe
)1x(2ee
yx
yx
yx
yxyx

- 











)2(uvee
)1(1ue
1ve
1ue
vu
v
u
v

- 
- 
vu 


u

u
- u- 1 , f'(u) = e
u
- 1

u
-

0 +


f'(u)
- 0 +
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f(u)




0

0u 
.













0y
0x
0yx
0yx
0v






































 
-A1-B-D 105


PHẦN CHUNG CHO TẤT CẢ THÍ SINH (7,0 điểm)
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Page 23

ST: Cao Văn Tú
Email: caotua5lg3@gmail.com

 = x
3
 3x
2
+2 (1)

-



cos2x 2sinx 1 2sinxcos2x 0   

 
 
2
4x 3 x 3x 4 8x 6    


3
6
cotx
I dx
sinx.sin x
4














0
.

2
+b
2
+c
2

3 3 3
2 2 2
3 3 3
a b c
P
b c a
  
  

PHẦN RIÊNG (3 điểm)(Học sinh chỉ làm một trong hai phần sau)


             
22
x y 2x 8y 8 0    
 
-





z 2 i 2  

 

1. 
2 4 6 100
100 100 100 100
4 8 12 200A C C C C    
.
2. 
1
23
:1
32
xz
dy

  

2
3
: 7 2
1
xt
d y t
zt










1

2



2
+3(1+i)z-6-13i=0







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Page 24

ST: Cao Văn Tú
Email: caotua5lg3@gmail.com

 

   
3 2 3 2
lim 3 2 lim 3 2
xx
x x x x
 
       
x
2
-6x=0
0
2
x
x








x - 0 2 + 
- 0 +
2 + 
y
- -2
-)

f

=f(0)=2; f
CT
=f(2)=-2
-6=0<=>x=1
khi x=1=>y=0 x=3=>y=2 x=-1=>y=-2

-2)
-y-2
--2)=>P=6>0
-
-2x+2

4
32
5
2 2 2
5
x
yx
yx
y








  





=>
42
;
55
M





cos2x 2sinx 1 2sinxcos2x 0   
(1)

        
1 os2 1 2sin 1 2sin 0 os2 1 1 2sin 0c x x x c x x        

Khi cos2x=1<=>
xk


,
kZ

Khi
1
sinx
2


2
6
xk




5
2
6
xk



,
kZ


2, 
 
2
4x 3 x 3x 4 8x 6    
(1)(1)
 


2
4 3 3 4 2 0x x x     

-3=0<=>x=3/4
2
3 4 2xx  
=0<=>x=0;x=3

x - 
4x-3 - - 0 + +
2
3 4 2xx  
+ 0 - - 0 +
i - 0 + 0 - 0 +



3
0; 3;
4
x

  



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Page 25

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Email: caotua5lg3@gmail.com
 
   
3 3 3
2
6 6 6
cot cot cot
22
sinx sinx cos sin x 1 cot
sinxsin
4
x x x
I dx dx dx
xx
x
  
  

  





  

 
2
1
sin
dx dt
x
  
Khi
31
1 3;
63
3
x t x t


      


 
31
31
31
3
31
3
12
2 2 ln 2 ln 3
3
t
I dt t t
t






    




 

0
3
cos30
2
a
AH SA


3
2
a
AH 

  BC => BC(SAH)
 

0
3
AHsin30
24
AH a
HK   


3
4
a

 
3 3 2 6 2
3
22
33
3
16 64 4
2 3 2 3
a a b a a
bb

   

(1)

3 3 2 6 2
3
22
33
3
16 64 4
2 3 2 3
b b c c c
cc

   

(2)
3 3 2 6 2
3
22
33
3
16 64 4
2 3 2 3
c c a c c
aa

   

(3)

 
2 2 2
2 2 2
93
16 4
abc
P a b c
  
   
(4)

2
+b
2
+c
2

3
2
P

3
2
P 
khi a=b=c=1.
-
,
=>  -2=0)
 
22
5 3 4

 
2
4 10 1
34
,4
31
4 10 1
c
c
dI
c


  
    


  




3 4 10 1 0xy   

3 4 10 1 0xy   
.

 
1; 4; 3AB    

1
54
43
xt
yt
zt









H
A
C
B
S
K

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