
-



32
y x 3x 3mx 1 (1)    

a) 


)

1 tanx 2 2sin x
4


  




4
4
22
1 1 2
2 ( 1) 6 1 0

     



     


x x y y
x x y y y
(x, y  R).
Tính tích phân
2
2
2
1
1
ln



x
I x dx
x

Cho 
0
ABC 30
,

S.ABC 
Câu    Cho các s          
2
(a c)(b c) 4c  
        

3 3 2 2
33
32a 32b a b
P
(b 3c) (a 3c) c

  


   Thí sinh chỉ được làm một trong hai phần (phần A
hoặc phần B)
A. 


2x y 5 0  
và
A( 4;8)

B qua C, N là hình 
-4).
              
x 6 y 1 z 2
:
3 2 1
  
  


và vuôn




sao cho AM =
2 30
.
 



              
:x y 0  

10



AB =
42


    Trong không gian        
(P):2x 3y z 11 0   
  
2 2 2
(S):x y z 2x 4y 2z 8 0      
 

Cho 
z 1 3i



5
w (1 i)z
.


Câu 1:
a) m= 0-x
3
+ 3x
2
-1
-3x
2
+  x = 0 hay x = 2; y(0) = -1; y(2) = 3

lim
x
y

 
và
lim
x
y

 


x

 0 2 +

 0 + 0 
y
+ 3
-1 

  
- 3
y" = -6x +  
 :









b. -3x
2
+ 6x+3m m=
2
2xx
=g(x)
 
 
0, 0;x   


 m
2
2xx

 
0;x  


 
 
2
0
min 2 , 0;
x
m x x x

    


 
11mg  

Câu 2 : 1+tanx=2(sinx+cosx)
 cosx+sinx = 2(sinx+cosx)cosx 
 sinx+cosx=0 hay cosx =
1
2
 tanx=-1 hay cosx =
1
2



2,
43
x k hay x k k


      

Câu 3 : 
1x

 
22
2 1 6 1 0     x y x y y
 
2
1 4 0    x y y
   
2
4 1 *   y x y


0y

4
4
1 1 2     x x y y



   
 
44
4
4
1 1 1 1 1 1 **        x x y y


4
11tt  
thì f )
Nên (**)  f(x) = f(y
4
+ 1)  x = y
4
+ 1
 4y = (y
4
+ y)
2
= y
8
+ 2y
5
+ y
2


74
01

24
yx
y y y
  


  


0
1
y
y





(vì g(y) = y
7
+ 2y
4
)
(x; y) = (1; 0) hay (x; y) = (2; 1).
Cách khác :
 
22
2 1 6 1 0     x y x y y
 x = -y + 1
2 y

vì x  1
 x = -y + 1
2 y

y
x
2
-1
3
0
 1  0 và v = y
4
 
44
22u u v v    


4
2tt
)  f(u) = f(v)  u = v  x  1 = y
4

Câu 4 :
2
2
2
1
1
ln
x

I xdx
x




t=lnx
 
, , (1) 0, 2 ln2
t
dx
dt x e t t
x
    

 
ln2
0
tt
I t e e dt

  


 u=t
,
tt
du dt dv e e

   


tt
v e e




I =
ln2
ln2
0
0
( ) ( )
t t t t
t e e e e dt


  


=
5ln2 3
2


Cách khác : 
u ln x

dx
du

x


dv =
2
22
x 1 1
dx (1 )dx
xx


1
vx
x
  
2
2
1
1
1 1 dx
I x ln x (x )
x x x

    




2
1

51
ln2 (1 )dx
2x

  

2
1
51
ln2 (x )
2x
  
51
ln2 (2 )
22
  
53
ln2
22


Câu 5.   (ABC) và SH =
3
2
a


BC=a,
3
,

22

aa
AC AB

3
1 1 3 3
3 2 2 2 2 16
a a a a
V




, 
HI=a/4,
3
2

a
SH

 SI thì HK  (SAB), ta có
22
2
1 1 1 3
52
3
4
2

a
HK
HK
a
a
   
   
   



= 2HK =
2 3 3
52 13

aa

Câu 6. G  
1 1 4
ab
cc
  
  
  
  


a
c
; y =

b
c
thì (x + 1)(y + 1) = 4  S + P = 3 P = 3  S
P =
3
3
22
32
33
xy
xy
yx



  










3
22
8
33

xy
xy
yx

  



=
3
2
32
8
39
2
S S P S
SP







=
3
2
3 2(3 )
8
3 (3 ) 9

2
S S S S
SS

  


  


S
A
B
C
H
I
=
3
3
2
5 6 1
88
2 12 2
22
S S S S S
S

  

  






=
3
( 1) , 2
2
S
SS  

 1)
2

1
2
> 0, S  2  P min = P (2) = 1 
2


Câu 7a. C(t;-2t-5)

4 2 3
;
22
   




tt
I

Ta có: IC
2
= IA
2
, suy ra t =1
-7)
-4;-7)
Câu 8a. Ptmp (P)   -3; -2; 1).
-3(x  1)  2(y  7) + z  3 = 0  3x + 2y  z  14 = 0
  M (6 -3t; -1  2t; -2 + t)
YCBT  (5  3t)
2
+ (-8  2t)
2
+ (-5 + t)
2
= 120
 14t
2
 8t  6 = 0  t = 1 hay t =
3
7


-3; -1) hay (
51
7

;
1
7

;
17
7

).
Câu 9a.   : 3.6.5=90




Câu 7b.
Cos(AIH) =
1
5
IH
IA

 IH =
2

 IH = 4
2
 Oy (0; y)
MI  AB  MI : x + y + c = 0 ; M (0;-c)
MH = d (M; ) =
2

c
= 4
2
 c = 8 hay c =-8
I (t; -t  8) hay (t; -t + 8)
d (I; ) =
8
2
2
tt
IH


 t = -3 hay t = -5
-3  I (-3; -5); t = -5  I (-5; -3)
 
2
+ (y + 5)
2
= 10 hay (x + 5)
2
+ (y + 3)
2
= 10.
Câu 8b. (S) có tâm là I (1; -2; 1) và R
2
= 14.

2(1) 3( 2) 1 11
14

   
=
14
= R

Pt (d) qua I và   :
1 2 1
2 3 1
x y z  

, T  (d)  T (1 + 2t; 3t  2; 1 + t)
T  (P)  
Câu 9b. r =
13
= 2; tg =
3
 =
3


 
2(cos sin )
33
i



M
A
B

I
H
 z
5
=
5 5 1 3
32(cos sin ) 32( )
3 3 2 2
ii

  

 w = 32(1 + i)
13
()
22
i
=
1 3 1 3
32( ) 32 ( )
2 2 2 2
i  


16 16 3

16 16 3
.



 TP.HCM)