tống hợp đề cương ôn thi đại học môn toán

Trung Tâm Luyện Thi Vĩnh Viễn
Lưu Nam Phát

Câu I (2 

2x 4
x1


(C)
1. 
2.  
ang c
Câu II (2 
1. 
2sin4x 3 3sin2x 3cos2x  

2. 
 
22
3 3 2
x y 1
x 6y 2x y 3y xy 1




   



Câu III (1 
Tính tích phân I =
e
2
1
x1
( )ln xdx
x



Câu IV (1 
 
 SC, SD sao cho:
SM SP 2
SB SD 3

,
SN 3
SC 4



Câu V (1 

 
 
x 4 y
ln x y
y 4 x





Câu VI. ( 2 
1. 
67 4
;
99





2. 
x 1 y 6 z 4
1 3 2
  


, mp(): x + 2y  3z  
 qua I = d
Câu VII. (1 

 
2
2
z z 4

ÑEÀ SOÁ 1

Trung Tâm Luyện Thi Vĩnh Viễn

Lưu Nam Phát
Câu I (2 

32
x 3x mx 2  

1. 
2. Tìm 
 1.
Câu II (2 
1. 
 
 
2
2 sinx 1 sin 2x 3sinx 1 sin4x.cosx   

2. 
22
2
2xy
x y 1
xy
x y x y

  





  


Câu III (1 
Tính tích phân I =
 
2
3
0
sin xdx
sin x 3cosx




Câu IV (1 

tích 
Câu V (1 

        
3 3 3
x y z
1 y 1 z 1 z 1 x 1 x 1 y

     

Câu VI. (2 

1. 3 ;  y  1 = 0. Tìm
Md sao cho:
AM 2BM

2.  z 
 

Câu VII. (1 

1
, z
2

 
2
z 8 1 i z 63 16i 0    
. Tính A =
22
12
11
zz






ÑEÀ SOÁ 2

Trung Tâm Luyện Thi Vĩnh Viễn

Nguyễn Văn Hòa
Câu I: 
 (1)
1. -2
2. Tìm 

2
.
Câu II: 
1. 


2


) + cotx + 4cos2
()
4
x


= 0
Câu III: (1  Tính tích phân:

Câu IV:(1 

6
2
a

1. 
2 

Câu V: (1  Cho
a
,
b
 
0abc  

3 4 3 4 3 4 6
a b c
     


Câu VI: 
1. -2, 0 ), B( -2, 1, 3 ), C( 4, -2, - 2z + 3 = 0.

 


-  3y + 1 = 0.


Câu VII: (1 


5
12

33
1 sin cos , ( 3 )
55
z i z i

    

  =
12
zz


ÑEÀ SOÁ 3

Trung Tâm Luyện Thi Vĩnh Viễn

Nguyễn Văn Hòa

Câu I: 

1. 
1
4


2. 
32
2
.

Câu II: 
1. 

- 
2 x + 4 x = 3sinx
Câu III: 
Tính tích phân:


Câu IV: (1 
 
AB=BC=BD=AC=a, AD=a
2

1. 
2. 

Câu V: (1  Cho
a
,
b

3
4
abc  

3 3 3
3 3 3 3a b b c c a     

Câu VI: 

1. 

3
6
4
4
2
2






 zyx
và MN =
29

-
 C là 2x-y-

Câu VII: (1  
5
12
33
1 sin cos , ( 3 )
55
z i z i


    

 =
1
2
z
z


ÑEÀ SOÁ 4

Trung Tâm Luyện Thi Vĩnh Viễn
Phạm Hồng Danh

 
 
113
23
 xmmxxy

1. -1.
2. -i qua


 tanx = cotx + 4cos2x.

12 x
+
x23

=
2
)12(
2
x
(x

R).
) =



3
2
1
3
.
22x
xdx

)



MC

=

(


<90
0

,



.
) Cho
a
,
b
 
33
2ab

4 4 4 4
3( ) 2 8a b a b  

Câu V
1. 
d
1
:
1
3
2
3
2
3 




 zyx
và d
2
:





.0766
013665
zyx
zyx


1
và d
2
. 
1
, d
2


42
41
.

,
-

2

.

Câu VII (1)

=
 
.7,5,4,3,2,1,0

 ?






ÑEÀ SOÁ 5

Trung Tâm Luyện Thi Vĩnh Viễn
Phạm Hồng Danh
)
78
24
 xxy
(1).
1. (1).

2. = mx (1).
)
1
.
2
2
4
sin
4
2sin 















xx


.
1

3
1
1
1
2
2
x
x
x




Câu III (1) 
.
2cossin43
2sin
2
0




xx
xdx
I

Câu IV (1)
, SA = SB = SC = a



.
)
Cho
a
,
b

22
1 1 1
1
(1 ) (1 )
ab
ab
+³
+
++

Câu VI)

1. (P) : 2x + 3y  3z + 1 =
1
5
92
3
:


 zyx
d

(4 ; 0 ; 3), B( - 1 ; - 1 ; 3), C(3 ; 2 ; 6).
(S) (P).

.
(C):
1
22
 yx


60
o
.
Câu VII (1)

.
6
9log
log
1
3
3







x

x
x
x





ÑEÀ SOÁ 6

Trung Tâm Luyện Thi Vĩnh Viễn

Trần Văn Tòan

Câu I : 
y = x
4
 2mx
2
+ m + m 
m = 1.

1
, x
2
, x
3
, x
4


mãn
4444
1 2 3 4
x x x x 20   
.
Câu II : 

  
2
4sin3x.sin x 4cos 3x .cos x cos 2x 2 2 0
4 4 4
     
      
     
     
.

 
 
3
3
x 21y 20 1
x y 20 21








.
Câu III : (1 
Tính tích phân
4
2
0
sin4x
I dx
1 cos x




.
Câu IV : (1
) , cho tam giác cân AOB có OA = OB = 2a ,
0
AOB 120



Câu V : (1 

3
23
x 1 x x 2   
.
Câu VI : 
1. 3 ; 



2. Tron 
3 ; 
Câu VII: (1 
 

23z
.
ÑEÀ SOÁ 7

Trung Tâm Luyện Thi Vĩnh Viễn
Trần Văn Tòan
Câu I : 

x2
y
x1



. (1)

 
Câu II : (2 

 



    



32
2
3 1 sin x
x
3tan x tanx 8cos 0
42
cos x
.

 
3
4
x 8 x 1 y (1)
x 1 y (2)

   






Câu III : (1 
Tính tích phân
3
1
0
2

x
I dx
x x 1



.
Câu IV : (1

  

Câu V : (1 
 trình :
 
22
x 1 x 2 x x 2    
.
Câu VI : (2 
1. 
ng tròn

2. 
1
và d
2


1
x 2 y 3 z 4
d:

2 3 5
  


,
2
x 1 y 4 z 4
d:
3 2 1
  


.

1
, d
2

1
và
d
2

1
và d
2
.
Câu VII: (1 
 2i)
3

= 9 + 14i.

ÑEÀ SOÁ 8

Trung Tâm Luyện Thi Vĩnh Viễn
Lê Ngô Thiện


Cho hàm s
1
2
x
y
x
-
=
+


-


1. 
8 8 2
2
8(sin cos ) cos 2 1
(sin cos )
sin2 1
x x x
xx

x
+ + -
=+
-
.

22
4( 1) (2 10)(1 3 2 )x x x+ < + - +
.


Tính tích phân
4
2
0
tan
cos 3 2cos
x
I dx
xx
p
=
-
ò
.







1 2 1 10x y z- + - + = -
. Tìm 

xy
A
z
+
=


1.     
3 5 1 0xy- - =

4 21 0xy+ - =


2.             
1
:
12
1 2 1
x y z++
==
và d
2
:
2 1 1
2 1 1
x y z- - -

==
   
2 5 0x y z+ - + =
      

1
, d
2



2zi
z
+

ÑEÀ SOÁ 9

Trung Tâm Luyện Thi Vĩnh Viễn

Lê Ngô Thiện
Câu I (2 )

32
(2 1) (3 1) 1y x m x m x m= - + + + - +

1. 
2. 
3yx=-



Câu II (2 
ình
88
1
sin cos cos4 0
8
x x x+ + =
.

22
2 8 6 1 2 2x x x x+ + + - = +
.

Câu III (1 
Tính tích phân
ln 8
ln 3
1
x
dx
I
e
=
+
ò









6a b c+ + ³

3 3 3
6
a b c
b c c a a b
+ + ³
+ + +


Câu VI (2 
1. 
22
6 2 2 0x y x y+ - - + =


góc nhau.
2. Trong không gian 
2 3 0xy+ + =


Câu VII (1 

9 3 3 9 3
log (log ) log (log ) 2 log 36 ( )x x x R+ + = Î

ÑEÀ SOÁ 10

Trung Tâm Luyện Thi Vĩnh Viễn

Trần Minh Thịnh
Câu I. (m)

32
2 3(2 1) 6 ( 1) 1y x m x m m x     

m
).


 
;2


Câu II. (2 m)

1)12cos2(3cos2 xx

2. 
2log9)2log3(
22
 xxx


Câu III. (1 m) Tính tích phân
1

2
0
ln( 1)x x x dx



Câu IV. (1 m)
S.ABCD SA G 
SACABG) SC MSD NMNABCD 
SA=AB=a AN và mp(ABCD) 
0
30
.

Câu V. (1 m) 
2
+ y
2
+ z
2
= 2.
 P = x
3
+ y
3
+ z
3
 3xyz.

Câu VI m)

1. 
 2y + 2 = 0,
AB = 

1
( ):
1 1 2
x y z
d 
và
2
11
( ):
2 1 1
x y z
d



.
M 
1
()d

2
()d
MN 
(P):x  MN 
2
.

Câu VII (1 m)

10)2)(3)((
2
 zzzz
,
z
C.



ÑEÀ SOÁ 11

Trung Tâm Luyện Thi Vĩnh Viễn
Trần Minh Thịnh
Câu I. (m) Ch
24
1
x
x




 
C

dAk. Tìm k sao cho (dC M,
N và

3 10MN 
.
Câu II. (2 m)
in3x  3sin 2x  cos2x + 3sinx + 3cosx  2 = 0.

22
22
14
( ) 2 7 2
x y xy y
y x y x y

   

   

.
Câu III. (1 m) Tính tích phân:
2
3
0
3sin 2cos
(sin cos )
xx
I dx
xx








Câu IV. (1 m)
 

 .Tìm sin 

Câu V. (1 m) Cho tam giác nhn ABC,tìm GTNN ca S = cos3A + 2cosA + cos2B + cos2C

Câu VI. m)
1. 
)5;2(,)1;1( BA


04 x

0632  yx

giác ABC.

2
:
1 1 1
x y z
d




/
2 3 5
:
2 1 1
x y z
d
  


;
        
)(

 


Câu VII 
Tì
n
 ãnh
log
4
(n  3) + log
4
(n + 9) = 3

ÑEÀ SOÁ 12

Trung Tâm Luyện Thi Vĩnh Viễn

Trương Quang Ngọc

Câu I (2 ):
Cho hàm 
   
3
(2 1)y x m x

1
2

CâuII (2  ):

   
88
2(cos sin ) 1 cos4 0x x x



     
22
2 1 1
log (2 3 1) log (4 4 1) 4
xx
x x x x


Câu III ( ) : Tính
 
xx

ln5
ln2
dx
I
10e 1 e 1






Câu IV ( 1  ) :


B

C



0
60BAD
a



Câu V ( 1  ) : Cho
a
,
b


22
2 2 2 2 4
1 1 4 32( )
()
ab
a b a b a b

  


Câu VI ( 1  ):
-
CM: x+y-
-


()


Câu VII (  ):

3
1
.0
1
32
log
2










x
x

ÑEÀ SOÁ 13

Trung Tâm Luyện Thi Vĩnh Viễn

Trần Minh Quang

CâuI (2  ): 
   
32
31y x x

1.  
2.  
1

CâuII  ):

    
42

(2sin 1)(2cos 2sin 3) 4cos 3x x x x


Câu III  ) : Tính




2
6
3
sin cos
dx
I
xx


Câu IV  
1abc =

2 2 2
3
1 1 1 2
a b c
b c a
+ + ³
+ + +


Câu V  ): 

/ / /
.ABC A B C
có tam giác
ABC

C
,
2 , 6BC a AC a

H

 

/
, BC B H ABC
và
 

/o
, 45BB ABC
.


 
//
ABB A
và
 
//
CBB C

Câu VI 
1.--
tâm

72
( ; )
33
G
 
2. Trong không gian Oxyz cho
   ( ) : 3 0P x y z
và
   ( ) : 1 0Q x y z

)(



()P
và
()Q

)(



Câu VII  
1. 

2. 
ÑEÀ SOÁ 14

Trung Tâm Luyện Thi Vĩnh Viễn

Hà Văn Chương
CâuI  ): 


2
1
x
y
x

1. 
2. 
 
1; 2x

( 2) 0m x m  
.
CâuII  ):

2cos3 (2cos2 1) 1xx


2 

     


2
( 1)( 2) ( 1) 2 0
1
x
x x x
x


Câu III  ) : Tính
8
8
cos cos8 cos7
1 2cos5
x x x x
I dx
x









Câu IV  ) : 
/
B
/

C
/
D
/

/

và N sao cho BM = DN = x
(0 )xa

/
và

Câu V  
5
1
4
a  
. 

5 4 1
5 4 2 1 6
aa
P
aa
  

   

Câu VI 
           -1; 0), B(2; 0; -    


14
.
            
22
( 1) ( 2) 9xy   
 
-


Câu VII Tính
2011
()
1
i
i



ÑEÀ SOÁ 15

Trung Tâm Luyện Thi Vĩnh Viễn

Hà Văn Chương

CâuI  Cho
   

32
3 1 (1)y x x mx

1 (C) khi
0m 
.
2. Tìm m :
1y
 A(0; 1), B, C sao cho 
.
Câu II ( 2  ):


   sin 4 cos4 4 2 sin( ) 1
4
x x x
= 0



  





8
5
x x y x y y
xy

Câu III  Tính I =



2
4
0
tan
cos 1 cos
x
dx
xx

Câu IV ) :  chóp S.ABCD D là hình vuông 

0
60


Câu V  
3ab bc ca+ + =
. C
3 3 3
2 2 2
3
4
3 3 3
a b c
b c a

+ + ³
+ + +

CâuVI 
1. 

0
60
.

-
Câu VII 



ÑEÀ SOÁ 16

Trung Tâm Luyện Thi Vĩnh Viễn

Hòang Hữu Vinh
CâuI (  ):

   
3 2 3
34y x mx m


1
M
và

2
M
sao cho tam giác
12
OM M
vuông cân

O
.
ên khi
1m
.

Câu II ( 2 ):
1. 
   
2
3sin2 2sin 4cos 7 0x x x

2. 





2
1
1
11
log ( 1)

log ( 1)
x
x
x
x


Câu III ( ) : 

( ): , : 2C y x d y x  


Câu IV ( 1  ) :

(ABC), DM=
2a
.
1. 


Câu V (  ): Cho
a
,
b

22
9 8 7 6a ab b  

7 5 12 9a b ab  

Câu VI ( 2  ):
1. 




=
6
5

2. Trong  ABCD có B(-2; 0), D( 4; 4 ). 


Câu VII (  ): 
0 1 2 2 2011 2011
2011 2011 2011 2011
C C i C i C i   

ÑEÀ SOÁ 17

Trung Tâm Luyện Thi Vĩnh Viễn

Hòang Hữu Vinh

CâuI ( 2 i ): 
   
32
31y x x mx

1

3m
.
2
  
3
3 ( 1)x x x k

Câu II ( 2  ):




46
cos cos2 2sin
0
1 cos
x x x
x


2. 
  
32
5 1 2 4xx

Câu III  ) :
Tính tích :
( ): ln , :C y x d x e
.

Câu IV ( 1  )

0
45SAB SAC
, SA=
2a





Câu V ( 1  ): 
22
24
cos cos
3(1 ) 3(1 )
xx
y
xx





Câu VI ( 2  ):
1. 
: 0 : (1 ) 0x mz m m x my

     

T
,


.

(0; 3)A

cho
0
30BAC 

Câu VII ( 1  ):  

2 10
2 20
3 (1 ) 30
x iy t
x y it
ix iy it
  


  


   


ÑEÀ SOÁ 18

Trung Tâm Luyện Thi Vĩnh Viễn

Hòang Hữu Vinh

CâuI (2  ): 
x3
x1



1. 
2. Tìm M  (C) sao cho 

CâuII (2  ):

  
2
cot tan 4sin2
sin2
x x x
x






  



2
22
(1 ) 6
1 ( 5) 0
x xy y
xy

Câu III  ) : Tính I =




1
0
1
x
x
dx
xe


Câu IV  ) 
( , )OR
và
/
( , )OR


( , )OR

và M
/
( , )OR


Câu V ( 1  ):  :
2 4 2
x 3x 1 x x 1 0     
.

Câu VI 
1. 
2 2 2 2
( ): 2 4 13 0S x y z my z m      
và
15
:2
34
xt
yt
zt



  


  



/

là hình chi

trên 
/


2.
22
( ): 1
43
xy
E 
. Tìm trên
()E
i
là tam giác vuông câu 
()E

Câu VII 

0 1 2 1
4 5 6 3
1.2 2.3 3.4 .( 1) 64

11
n
n

nn
C C C C



    

ÑEÀ SOÁ 19

Trung Tâm Luyện Thi Vĩnh Viễn

Hòang Hữu Vinh

CâuI (2  ): 
    
4 2 2
22y x mx m m

1có ba  
2
2m
.
CâuII (2  ):


   
44
2sin( )(cos 3 sin 3 ) sin2 1
4
x x x x

2ng trình :
22
log (2 4) log (2 12) 3
xx
x    

Câu III ( 1  ): Tính 
(C)
2
ln( 1) ; 3y x x x   
; 
Câu IV  ): 

.

và


Câu V ( 1  ):
Cho
22
2 1.x y xy  
 
22
M x y

Câu VI 
1. 
:2 1 0 ; : 1 0kx y z x ky z


       


2. 
(0;5), ( 2; 1), (4;2)A B C

M
l
BC
sao cho

ABM

ACM

AM BC


Câu VII  àng 
 


ÑEÀ SOÁ 20