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BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
ĐỀ 1
I.PHẦN CHUNG CHO TẤT CẢ THÍ SINH.(
Câu I
 

+

x
x

 !"!##$%&
' ()*!+,-! (. !%&/+&%&#0,1.!+
Câu II.
2()*!+,-!34+

5664+

56
78!9


:
 
π

x dx

;<!+ !#!+ !%&=5

65=


Câu III-!(>?@?@4&+#.A!+B!/@C
aAC
=
C>?
 ⊥ ABC
C++D&/!
"!>@#E!+F:
:
78!8%&G(
II. PHẦN RIÊNG
1.Theo chương trình chuẩn.
Câu IVa7,!+GA!++&!#0HI&JK5LCMNN:#O(P!+Q356RL6:
' ()*!+,-!OS.BM# (5T#0(Q
' ()*!+,-!)U!+P!+VW.&M##.A!++#0Q7-I&J+&
Câu Va.78!V"!8-!(P!++0/!X)U!+#
5

R5
2. Theo chương trình nâng cao.
Câu IVb7,!+GA!++&!#0HI&JK5LCM=NN#)U!+P!+V3
 
  
− +
= =

x y z

' ()*!+,-!OS.BM# (5T#0V
' ()*!+,-!O(P!+W.&M##.A!++#0V7-I&J+&
Câu Vb.78!VH!8-!(P!++0/!X)U!+



Y
x
#




− +x x
ĐỀ 2
I.PHẦN CHUNG CHO TÁT CẢ THÍ SINH
Câu I5

R5

6
 !"!##$%&
@H!4.Z![!+H%&()*!+,-!35

R5

R:
Câu II.
2()*!+,-!3
5
6
56
6
56

\
78!9

:
  +

x
x e dx
7-+,40!!#+,!]!^%&5
Y
R5

6,"!I&!_=N`
Câu III.78!8GaVH!b.>?@^/!b.E!+&
II. PHẦN RIÊNG
1.Theo chương trình chuẩn.
Câu IV a.7,!+GA!++&!#0HI&JK5LC?=NN:C@=N:NCNNCc:NN=

' ()*!+,-!O(P!+?@#()*!+,-!)U!+P!+?c
78!VH!8&+?@#8aVH!?@c
Câu V a78!8G,d!5&V-!(P!++0/!X)U!+&!5C:C5:C5
Y
π
W.&W.&!,1K5
2. Theo chương trình nâng cao
Câu IV b7,!+GA!++&!#0HI&JK5LC?=N:NC@:N:NCN:N=Cc\NN
=
' ()*!+,-!O(P!+QW.&&?C@C## ()*!+,-!)U!+P!+W.&c!+!+#0
?@
78!8%&GaVH!?@cC.,&JV)U!+&%&aVH!#$ef!c

Câu Vb78!8G,d!5&V-!(P!++0/!X)U!+



x
x e
C:C5:C5W.&
W.&!,1K5



BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
ĐỀ 3
I.PHẦN CHUNG CHO ẤT CẢ THÍ SINH. (
Câu I.=5

65=
  !"!##$%&
' ()*!+,-! (. !%&/.%&
Câu II.(
2()*!+,-!3

F4+  4+ = +
x
x
78!9


:
 Y 

π

x dx
7-+,40!!^#+,!]!^%&
4! x
x
,"!/!_N[

`
Câu III-!(&+b.>?@/!E!+&C/!"!b./#0J+F:
:

78!8%&G(
II. PHẦN RIÊNG.
1.Theo chương trình chuẩn.
Câu IV a.(7,!+GA!++&!#0HI&JK5LCO(P!+
Q356RLRF:#MC=N
' ()*!+,-!O(P!+gW.&M#!+!+#0(Q78!G]&!+eM !(Q
7-I&J! .%&M4"!(Q
Câu Va.2()*!+,-!35

R56\:,!+Z((a
2. Theo chương trình nâng cao.
Câu IV b7,!+GA!++&!#0HI&JK5LC&O(P!+
Q35R6LR\:Cg3Y56\RL6:
78!++D&&O(P!+## ()*!+-!&%&+&. !%&&O(P!+Q#g
' ()*!+,-!O(P!+hW.&+I&JK#.A!++#0Q#g
Câu Vb.((aL565C
∈ R
7-(S!#(S!%&(aL


RL6Y
ĐỀ 4
I.PHẦN CHUNG CHO TẤT CẢ THÍ SINH.
Câu I.

+
x
x

 !"!##$%&
' ()*!+,-! (. !%&/d&!J5=
Câu II
2()*!+,-!3
 
  :
+ −
+ =
x x

78!9
&!
Y

:

π

x
e

dx
x
7-+,40!!^#+,!]!^%&

− x

Câu III-!(a+b.>?@c/!E!+&C/!"!i(#0J+F:
:

78!8G(>?@c
7-B#8!!G8!OS.!+I& (-!(
II. PHẦN RIÊNG.
1. Theo chương trình chuẩn
Câu IV a.7,!+GA!++&!#0HI&JK5LCc=NN#O(P!+QW.&&?N
:NC@:NN:CNNj
' ()*!+,-!)U!+P!+?@#()*!+,-!O(P!+Q
' ()*!+,-!OS.BcC!G8!h\a!+!,E!+OS.!kO(P!+Q
Câu Va.78!VH!8-!(P!++0/!X)U!+4!5C:C5

e
C5[
2.Theo chương trình nâng cao
Câu IV b7,!+GA!++&!#0HI&JK5LCO(P!+Q3566L6\:#OS.>3
5

6

6L

R5RY6YL:

7-B#!G8!%&OS.>



BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
' ()*!+,-!O(P!+g!+!+#0Q# (5T#0>7-I&J%& (
Câu Vb7-)U!+P!+V356k3



+

x
x
/&(B!H
ĐỀ 5
I.PHẦN CHUNG CHO TẤT CẢ THÍ SINH
Câu I.=5
Y
65

6
 !"!##$%&
c&#C-+,%&()*!+,-!5
Y
R5

6:!!+H(B!H
Câu II.
2^()*!+,-!3

 Y
4+ 4+   − − =x x
78!9
Y
:
! 
  
π
+

x
dx
x



\
4+  +x
78!l
Câu III.-!(>?@?@4&+#.A!+/@C/!"!>?

?@C ?@&C@
a
C>?&
78!8G(>?@[&
2I94,.!+%&/!>C8!JV%&/!@9[&
II. PHẦN RIÊNG.
1.Theo chương trình chuẩn.
Câu IV a7,!+GA!++&!#0HI&JK5LC&?NYN:C@:NNCN:N=Y
7-I&Jc?@c4-!-!!#-I&JB%&-!-!!

' ()*!+,-!)U!+P!+VW.&,I!+B%&&+?@##.A!++#0(?@
Câu V a.78!8%&G,d!5&/!GW.&W.&!,1.!+-!(P!++0/!X
)U!+4!5C,1.!+#&)U!+P!+:C

2. Theo chương trình nâng cao
Câu IV b      7,!+  GA!+  +&!  #0  H  I&  J  K5LC    &  )U!+  P!+  V3 
  
  
− − −
= =
− −
x y z
C
Vl3
 \
 
=


= − −


= − −

x t
y t
z t
a!+!V#Vl<!&.
' ()*!+,-!O(P!+Qa&V#!+!+#0Vl78!G]&!++D&V#Vl
Câu V b.78!8G,d!5&/!GW.&W.&!,1d&!-!(P!++0/!X)U!+

4!5C:C5
ĐỀ 6
I.PHẦN CHUNG CHO TẤT CẢ THÍ SINH
Câu I55R


 !"!##$%&
' ()*!+,-!)U!+P!+W.&&,%&
Câu II
2^()*!+,-!3
 
 
4+ \ 4++ ≤x x

78!9


:
!  
π

x dx

7-+,40!!^#+,!]!^%&5

[
5
,"!!m&G!+=

N:`

Câu III-!(>?@?@4&+#.A!+/?@ ?@&C@&C>&#/!
"!>?#.A!++#078!8G(>?@[&
II. PHẦN RIÊNG.
1.Theo chương trình chuẩn.
Câu IV a.7,!+GA!++&!K5LC!?N=NC@N:N:C:NN:Cc:N:N
' ()*!+,-!O(P!+@c>.,&?@c4JaVH!
7-?l&(@c4O(P!+,.!+,%&I&!??l



BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
Câu V a.78!8G,d!5&/!GW.&W.&!,1d&!-!(P!++0/!X)U!+
!55C:C5:C5

π

2. Theo chương trình nâng cao.
Câu IV b7,!+GA!++&!#0HI&JK5LC)U!+P!+V3
 
  
− +
= =
x y z
#&O(P!+Q

35
6RL6\:CQ

35R6L6:
78!++D&(Q


#(Q

C++D&)U!+P!+V#(Q


' ()*!+,-!OS.B9.JV# (5T#0(Q

#(Q


Câu Vb.78!8G,d!5&/!GW.&W.&!,1.!+-!(P!++0/!X)U!+
5

#F=n5n
ĐỀ 7
I.PHẦN CHUNG CHO TẤT CẢ THÍ SINH.(
Câu I.
−
x
x
4
 !"!##$%&
7-)U!+P!+V3=56k/&(B!H
Câu II
2()*!+,-!3Y
5
6:
5
\

5

78!9
o

Y
 −

dx
x x
7-+,40!!^#+,!]!^%&
4!x x
,"!
I&!_N[`
Câu III-!(>?@c?@c4-!#.A!+/!&C/!"!>?&

##.A!++#0

78!8G(>?@c
a!+!,.!+9%&/!>4B%&OS.!+I& (-!(>?@c
II. PHẦN RIÊNG
1. Theo chương trình chuẩn.
Câu IV a7,!+GA!++&!#0HI&JK5LC&?NNC@N=N\
' ()*!+,-!OS.>)U!+G8!?@
7-M,"!)U!+P!+?@&&+MK?#.A!+/K
Câu V a. 2()*!+,-!&.,"!Z((a3L
Y
R:
2. Theo chương trình nâng cao
Câu IV b.7,!+GA!++&!#0HI&JK5LCOS.>35


6

6L

R5RYRFL:#&
MNNCpN=N\
7-B9#!G8!h%&OS.>' ()*!+,-!O(P!+QW.&-! .%&B9,"!
,1I&J
 a!+])U!+P!+MpkOS.>/&7-I&J+&
Câu V b@.Vq!(aLR

V)0V/!+4)i!++
ĐỀ 8
I.PHẦN CHUNG CHO TẤT CẢ THÍ SINH.
Câu I
Y 
 \

 
− +x x 4
 !"!##$%&
' ()*!+,-! (. !%&/MN:
Câu II.
2^()*!+,-!3

 
 Y
Y 


 

 ÷
 
x x
78!9


:

 !
π
+

x
dx
x

7-+,40!!^#+,!]!^%&!5R5,"!I&!
N
F 
π π

 
 
 

Câu III-!(>?@c?@c4-!#.A!+C/!"!
aSA
=

##.A!++#0C
++D&>#4Y\
:
78!8%&G(
II. PHẦN RIÊNG

Y
Y
BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
1.Theo chương trình chuẩn.
Câu IV a7,!+GA!++&!#0HI&JK5LC&?N:N=C@N=NY
' ()*!+,-!)U!+P!+?@#()*!+,-!O(P!+,.!+,%&I&!?@
' ()*!+,-!OS.B?#W.&@7-5a!+%&@W.&?
Câu V a78!8%&G,d!5&)i/!GW.&W.&!,1.!+-!(P!++0/!X
)U!+R5

#n5n
2. Theo chương trình nâng cao.
Câu IV b. 7,!+ GA!++&!#0HI&JK5LC&)U!+P!+V3 
  
  Y
− + −
= =
x y z
 # Vl3
 
 
Y Y
= − +



= +


= +

x t
y t
z t

a!+!V!+!+#0Vl78!G]&!++D&V#Vl
' ()*!+,-!O(P!+Qa&V#Vl
Câu V b

 F

+ +
+
x x
x
' ()*!+,-!)U!+P!+VW.&?N:#
H+4G'0+,!%&G-)U!+P!+V (5T#0%&
ĐỀ 9
I.PHẦN CUNG CHO TẤT CẢ THÍ SINH
Câu I.(=5

65

R
 !"!##$%&

' ()*!+,-! (. !#0  (. !H+G=o
Câu II.(
2()*!+,-!3

 
4+  4+   F
+
+ + =
x x

78!9

:
! 

 
π
+

x
dx
x
7-+,!]!^%&5R4!56
Câu III.-!(>?@>?C?@C@#.A!++#0!&.e!+AJ@ >?&C?@@&

78!8%&G(#-B%&OS.!+I& (-!(
II. PHẦN RIÊNG.
1. Theo chương trình chuẩn.
Câu IV a7,!+GA!++&!#0HI&JK5LC?N=NCO(P!+Q35==L6:#
)U!+P!+V3

 
  
− −
= =

x y z

7-I&J?l5a!+%&?W.&(Q
7-I&J%&M,"!)U!+P!+V&G]&!+eM !(QE!+
Câu V a2()*!+,-!&.,"!Z((a3L
Y
RL

RF:
2. Theo chương trình nâng cao.
Câu IV b7,!+GA!++&!#0HI&JK5LC?NNC(Q356RLR:#)U!+
P!+V3
 
  
− −
= =

x y z

7-?l5a!+%&?W.&V
' ()*!+,-!)U!+P!+W.&?C!+!+#0(Q#kV
Câu Vb.2H()*!+,-!3

 Y


 Y
\4+ 4+ j
\4+ 4+ o

− =


− =


x y
x y
ĐỀ 10
I.PHẦN CHUNG CHO TẤT CẢ THÍ SINH
Câu I5R

56


 !"!##$%&
7-)U!+P!+V3k/&(B!H
Câu II
2()*!+,-!34+5RR4+5

RY56

\
\
BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
78!9



 4! 

+

e
x
dx
x

5

R6564&7-,/5
Câu III-!4r!+,1?@?l@ll4&+b./!&C/!"!E!+&

#-! .%&
?l4"!(?@,s!+#0,.!+%&@78!8%&G4r!+,1
II. PHẦN CHUNG.
1. Theo chương trình chuẩn.
Câu IV a7,!+GA!++&!#0HI&JK5LC&?C@I&J5!XHa
 C Y Y
→ → → →
= − = − −
uuur uuur
OA i k OB j k
#O(P!+Q35R6FL6:
7-+&M%&)U!+P!+?@#0(Q
' ()*!+,-!-! .#.A!++%&?@,"!(Q
Câu V a78!8G,d!5&&!GW.&W.&!,1K5-!(P!++0/!X)U!+




+
x
x
C:C5=#5
2/ Theo chương trình nâng cao.
Câu IVb7,!+GA!++&!#0HI&JK5LC)U!+P!+V3
 

= +


=


=

x t
y t
z t
#O(P!+Q356RL
6:
' ()*!+,-!)U!+P!+W.&+I&JK#.A!++#0V#!+!+#0Q
' ()*!+,-!+OS.B.JVC (5TQ#!G8!E!+Y
Câu Vb78!
( )
j
 + i

ĐỀ 11
9tQS!V!^8!
B.9 
( )



+
=

x
y
x
4
 
 ' ()*!+,-! (. !%&  (. !W.&QN
B.99
 2^()*!+,-!3
o Y  
+ + >
x x
 78!8(B!3

\ 
:
= −

I x x dx
 7-+,40!!^#+,!]!^%&


+ +
=
x x
y
x
#0
:>x
B.999;!B#!G8!OS.!+/ (J-!4r!+,1&+b.o/!b.E!+&
99tQS!,"!+
 7[)*!+,-!.u!
B.9'&7,!+GA!++&!HI&JK5LC?N=N#&)U!+P!+V

#V

[a
()*!+,-!3
( ) ( )
 
  :
3   N 3
  :

=

− − + =


= − −
 
− + =



= −

x t
x y z
d y t d
x y
z t
a!+!,E!+V

CV

#?s!+.JJO(P!+
B.'&7-A.!%&(a
( )

 = + − −z i i
 7[)*!+!B!+&
B.9'7,!+GA!++&!HI&JK5LCO(P!+ 
( ) ( )
v
α β
v
4S!4)i()*!+,-!43
( ) ( )
3    :N 3 \ :
α β
− + + = + − + =x y z x y z
#MN:N\

 78!G!+eM !
( )
α
 ' ()*!+,-!O(P!+W.&+&. !V%&
( ) ( )
v
α β
v
!+U#.A!++#0O(P!+Q3
  :− + =x y
B.'' V/!+4)i!++%&(a
 = +z i

F
F
BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
ĐỀ 12
I. Phần chung cho tất cả thí sinh C:
B.9.( 3,0 điểm
 
 
 
= − − + +y x mx x m

( )
m
C
 !"!##$%&G:
7-!%&
( )

m
C

B.993,0 điểm
7-+,40!!^#!]!^%&
Y 
j F= − +y x x
,"!
/!_=N`
78!8(B!




:

=
+

x
I dx
x
2^()*!+,-!
:C\
 

\
4+
+


+
x
x
B.9991,0 điểm
aVH!>?@>?#.A!++#0O(P!+?@C>?&N?@?C
·
F:
°
=BAC
;!B#
!-!S.!+/ (aVH!>?@
II.Phần riêng(3,0 điểm
Thí sinh học chương trình nào thì chỉ được làm phần dành riêng cho chương trình đó.
1. Theo chương trình Chuẩn:
B.9'&2,0 điểm7,!+GA!++&!#0H/JK5L3
&wZ(()*!+,-!OS.B9=NN# (5T#0O(P!+
  \ :
+ − + =
x y z
78!G!++D&&O(P!+3
:Yj:Y
=−−−=+−−
zyxvàzyx

B.'&1,0 điểm2()*!+,-!3
Y 
 Y  :+ − =z z
,"!Z((a
2.Theo chương trình nâng cao.
B.9'(2,0 điểm

 7,!+GA!++&!#0H/JK5LC)U!+P!+V()*!+,-!3
 
  
− +
= =
x y z
#&O(P!+
:\3
=+−+
zyx
α
#
:3
=++−
zyx
β
wZ(()*!+,-!OS.B9.J)U!+P!+V# (5T
#0&O(P!+
( ) ( )
C
α β

B.'1 điểm)78!VH!8-!(P!++0/!X
C  C := = − =y x y x y
ĐỀ 13
I. Phần chung cho tất cả thí sinh C:
B.9.( 3,0 điểm
 !"!##$%&



+
=

x
y
x
7-,"!M&G!+eM !)U!+HZ!a!+E!+G!+eM !H
Z!!+&!+
B.993,0 điểm
2()*!+,-!
 
 \  Y\
− −
=
x x x
78!8(B!&

 4!+
=

e
x
I dx
x

B.9991,0 điểm
MJ-!,1 VH!W.&,14-!#.A!+CVH!85.!+W.&!4
Y
π


78!VH!8!(S!%&-!,1
78!8%&G,1
II.Phần riêng(3,0 điểm
Thí sinh học chương trình nào thì chỉ được làm phần dành riêng cho chương trình đó.
1. Theo chương trình Chuẩn:
B.9'&2,0 điểm7,!+GA!++&!#0H/JK5L3?N:N:C@NNC
  
N N
  
 
 ÷
 
C



BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
&' ()*!+,-!x!+W.%&O(P!+
( )
α
W.&K##.A!++#0K
' ()*!+,-!O(P!+
( )
β
a&?@##.A!++#0
( )
α
B.'&1,0 điểm 
7-!+H(a%&()*!+,-!
  Y+ = −z z i

ĐỀ 14
I. PHẦN CHUNG CHO TẤT CẢ CÁC THÍ SINH
Câu 1YC:3
 ##$%&
 
= −y x x
 c&#H!4.Z![!+H%&()*!+,-!
 
 :− + =x x m
 78!VH!8-!(P!++0/!X#,1!
Câu 2C:
 2()*!+,-!3

 \ F :
− + =
x x
 2()*!+,-!3

Y  :− + =x x
Câu 3C:
-!(>?@c?@c4-!#.A!+/!&C/!"!>@#.A!++#0C/!"!>E!+
a

 78!8%&G(>?@c
 a!+!,.!+%&/!>c4BOS.!+/ (-!(>?@c
II. PHẦN DÀNH CHO TỪNG THÍ SINH
A. Dành cho thí sinh Ban cơ bản:
Câu 4C:
78!8(B!3


:
 = +

x
I x e dx
7,!+GA!++&!#0HI&JK5L&?\N:NYC@\NNCNFNCcYN:NF
&' ()*!+,-!&%&)U!+P!+?@
' ()*!+,-!O(P!+
 
α
W.&c#!+!+#0O(P!+?@
B. Dành cho thí sinh Ban nâng cao
Câu 5C:
 78!8(B!3


 

= +

I x x dx
 7,!+GA!++&!#0HI&JK5LCMNN#O(P!+Q()*!+,-!35=6L6
:
& ' ()*!+,-!O(P!+gW.&M#!+!+#0O(P!+Q
 ' ()*!+,-!&%&)U!+P!+VW.&M##.A!++#0O(P!+Q7-I&J
+&y%&)U!+P!+V#0O(P!+Q
ĐỀ 15
9Qyzpy{p2yK7|7}7y~>9py
Câu 1  


Y

5 \
=5 6 
 

##$
' ()*!+,-! (. !/!J5
B.
78!8(B!
( )
+

1
3
2
0
I = 2x xdx
 7-+,40!!^#+,!]!^%&

 
 Y  
− + − +
x x x
,"!
_ N `


2()*!+,-!3
F Y F :− + =

x x
B.
G(>?@)U!+&>?&C&•:#4&+b.2+D&O"!>@#OVE!+
F:
:
78!8%&%&G(>?@[&
99Qyzph9€p2

j
j
BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
1. Theo chương trình Chuẩn:
B.Y&
7,!+GA!++&!#0H/JK5L?N:N:C@:NYN:#:N:NY
' ()*!+,-!OS.W.&Y•KC?C@C;!/JB9#8!!G8!h%&OS.
' ()*!+,-!O(P!+?@#)U!+P!+VW.&9#.A!++#0?@
B.Y7-(aL‚!
\=z
#(S!E!+4S!(S!%&!
Theo chương trình nâng cao:
B.Y&7,!+GA!++&!#0H/JK5LC)U!+P!+()*!+,-!



3 

= +


∆ = − −



=

x t
y t
z


 
3
  
− −
∆ = =

x y z
' ()*!+,-!O(P!+W.&)U!+P!+∆

#!+!+#0)U!+P!+∆


;!?,"!∆

#@,"!∆

&?@!+k!!^
B.Y2()*!+,-!,"!Z((a3L

6L6:
ĐỀ 16

9Qyzpy{p2yK7|7}7y~>9py
B.

Y 
5 665 6

##$G
7-,
B.
78!8(B!
( )
+

1
3
2
0
I = 4x .xdx
 7-+,40!!^#+,!]!^%&

 
 Y  − + +x x x
,"!
_ N`−

2()*!+,-!3
 
   F:
+ +
+ + =

x x x
B.
G(>?@4&+b./!&C&•:7&+>?B!/>+>?E!+F:
:
C>?⊥
?@78!8%&%&G(>?@[&
99Qyzph9€p2
2. Theo chương trình Chuẩn:
B.Y&
7,!+GA!++&!#0H/JK5L?NYN=C@NYN=CNYN#
cNN=
Mh?@⊥?C?⊥?cC?c⊥?@78!8%&aVH!?@c
' ()*!+,-!OS.W.&Y•?C@CCc;!/JB9#8!!G8!h%&OS.
B.Y
78!7
\ F
 Y

+
i
i
,"!Z((a
Theo chương trình nâng cao:
B.Y&
7,!+GA!++&!#0H/JK5L?YNNC@N:N:C:NN:#
c:N:N
' ()*!+,-!)U!+P!+W.&?#24,I!+B%&&+@c
' ()*!+,-!OS.B?# (5T@c
B.Y
(a

 
 
= − +z i
C8!L

6L6
ĐỀ 17
I . PHẦN CHUNG CHO TẤT CẢ THÍ SINH (7 điểm
Câu I.(3 điểm) 

 = − + −y x x

o
o
BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
 !"!##$‚
@H!4.Z![
m
!+H%&()*!+,-!

 
− + − =
x x m
Câu II.(3 điểm)
2()*!+,-!3

 F
  j: :

− − =

x x
78!!+."!3
4! −

x dx
7-+,40!!^#!]!^
 
   o = + − +f x x x x
,"!/!
[ ]
N−
Câu 3.(1 điểm)
aVH!>?@&/!>?C>@C>AJ#.A!++#>?&C>@C>y&MCp4S!4)i
.J/!?@C@&
 
C
 
= =AM AB BN BC
MO(P!+>Mp&GaVH!>?@!G&VH!
y#yl,!+y4G&VH!a&f!y‚8!8%&y#yl
II . PHẦN RIÊNG (3 điểm) : 
1. Theo chương trình chuẩn3
Câu IV.a(2 điểm) 7,!+GA!++&!#0HI&JK5LC?NYN#O(P!+Q()*!+,-!35
66LR:
 y‚-I&J%&-! .#.A!++%&?,"!O(P!+Q
 ' ()*!+,-!%&OS.B?C (5T#0Q
Câu V.a(1 điểm) 78!8G,d!5&)i/X(<(W.&W.&!,1K5-!(P!++0/!X)U!+

 C :C C := − + − = = =y x x y x x


2.Theo chương trình nâng cao :
Câu IV.b(2 điểm)
O(P!+Q356=L=:#)U!+P!+V3
 
  
+ +
= =

x y z
7-I&J+&M%&)U!+P!+V#O(P!+Q
' ()*!+,-!-! .%&)U!+P!+V,"!O(P!+Q
Câu Vb. (1 điểm)
;!I&J+&%&HZ!5"!%&

 

− +
=

x x
y
x
#0(&,&4Q3

 = − +y x x
ĐỀ 18
Câu I:3
1/ !"!##$%&



+

x
x
2/' ()*!+,-! (. !#0/+&%&#0,1.!+
Câu II3
78!9
( )

:
!

+

x
e x xdx
2^()*!+,-!4+

( )
+x

4+
o
( )
+x
78!/!%&-!D!Z.#!]!^,!+^!D!ZVH!8Yj

Câu III3
7,!+GA!++&!K5L?NNN@NN=YN#N=N=
' ()*!+,-!O(P!+?@

' ()*!+,-!OS.!+/ (aVH!K?@7B%&OS.,s!+#0,I!+B%&aVH!
GA!+ƒ
Câu IV3
-!(a+b.>?@c/!E!+&N+>?@E!+:
:
78!VH!85.!+W.&!%&
-!!!f!>C4-!,d!!+/ (a+?@c
Câu V:78!
 \
 

+
i
i
ĐỀ 19
9Qyzpy{p2yK7|7}7y~>9py
B.9C:

 
 = − + −xy x

 !"!##$

:
:
BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
 cs!+C5!G()*!+,-!
 
 :− + =xx k
T!+!+H(B!H

B.99C:
 2()*!+,-!3
Yo  F :  + − = ∈ ¡
x x x
x
 78!8(B!3



:

=
+

x
I dx
x

 7-+,40!!^C+,!]!^%&3

Y Y = + −y x
B.999C:
-!(S.ABCABC4&+#.A!+/AC
C C= =AB a AC a
O"!SBC 4&+b.#
#.A!++#0O(P!+78![&8%&G(S.ABC
99Qyzph9€p2
 7[)*!+,-!.u!3
B.9'&C:3
7,!+  GA!+  +&!  #0  H  I&  J Oxyz C    )U!+  P!+  V3 

 
  
+ +
= =

x y z
 #  O  (P!+Q3
  F :+ − + =x y z

' ()*!+,-!OS.B
N N −I
# (5T#0O(P!+Q
' ()*!+,-!O(P!+
 
α
a&)U!+P!+V##.A!++#0O(P!+Q
B.'&C:3
78!A.!%&(a

  

+
=

i
z
i

 7[)*!+,-!!B!+&3
B.9'C:37,!+GA!++&!#0HI&JOxyz C)U!+P!+V3

 
  
+ +
= =

x y z
#O(P!+
Q3
  F :
+ − + =
x y z

' ()*!+,-!OS.B
N N −I
# (5T#0O(P!+Q
' ()*!+,-!-! .#.A!++%&)U!+P!+V,"!O(P!+Q
B.'C:37-r!Z&%&(a
Y
= −
z i
ĐỀ 20
B.3

 = − +y x x

&##$
c&#H!4.Z![!+H()*!+,-!3

  :− + − =x x m
78!VH!8-!(P!++0/!X#,1K5

B.3
&78!/%&&.3
Y 
=5
+
=
x
y e c
N\
56!5

7-27wpC27pp%&
Y 

  
Y
= − +f x x x ,"!/!_=N:`
78!+,.a?
o 
 4+ Y  4+ 
  3 Y 
+ −
V2()*!+,-!C^()*!+,-!&.3
 Y F
4+ 4+ 4+ + + =x x x

[8!8(B!&.39




+

x x dx N„




 

π
π
π
 

 ÷
 

x dx

B.378!VH!85.!+W.&!#8G(a+b.JV/!"!+^(A/!#E!+&ƒ
B.Y?:NN#@=NN
&' ()*!+,-!OS.B?#W.&@
' ()*!+,-!&%&)U!+P!+VW.&@#!+!+#0K?
' ()*!+,-!O(P!+K?@
B.\&2()*!+,-!&.,!+Z(Z((a35

R56:
7-.!%&(a…R
ĐỀ 21
B.3&##$3


 

+
x
x

' ()*!+,-! (. !%&/!JE!+=
78!VH!8-!(P!++0/!XNH/!!+&!+N5:N5



BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
B. 3&7-27wpR27pp%&5RF

Y+x
,"!/!_:N`
7-3


x
=65

6Y56\!+ !,"!h
78!/&.3
&
( )

= −
x

y x e
5R4!

5
( )

4! +
=
x
y
x
V8!8(B!39
( )



4!+

e
x x xdx
N„


:
+ −

dx
x x
[2()*!+,-!3
&

 
4+  =64+  =x x

Y  Y :− − =
x x
B.37 VH!%&-!!!kXO(P!+W.&,1%&!4J&+b./!&
78!VH!85.!+W.&!N!(S!#8G!![&ƒ
B.Y37,!+GA!++&!K5L
&
Y = +
r r r
a i j
C
r
b
=NN78!


= −
r r r
c a b
?NNC@:NN:C:N:N
678!
uuur
AB

uuur
AC

6a!+!?C@CGA!+P!+!+' ()*!+,-!O(P!+?@

6' ()*!+,-!OS.B9=NN=# (5T?@
B.\3&2()*!+,-!3=56Y6\6
7-5N 35=6656R=\
ĐỀ 22
Câu1: Cho hàm s y = xố
3
- 3x
2
+ 2 (C)
a).Kh o sát s bi n thiên và v đ th hàm s .ả ự ế ẽ ồ ị ố
b).Tìm giá tr c a m đ ph ng trình : -xị ủ ể ươ
3
+ 3x
2
+ m = 0 có 3 nghi m phân bi t.ệ ệ
c) .Tính di n tích hình ph ng gi i h n b i (C); Ox ; Oy ; x=2. ệ ẳ ớ ạ ở
Câu 2: a)Tìm giá tr l n nh t, giá tr nh nh t c a hàm s : y = x+ị ớ ấ ị ỏ ấ ủ ố

− x
b)†!35

65

65&,
‡5
4! +
x
e
78!‡
l

4!
V2()*!+,-!C@^()*!+,-!3o
5
=Y
5
6ˆ:
[


:
 ! 
π
= +

E x x xdx
Câu 3 : Cho hình chóp t giác S.ABCD có đáy là hình vuông c nh a , c nh bên SA vuông góc v iứ ạ ạ ớ
đáy, c nh bên SC t o v i đáy m t góc 30ạ ạ ớ ộ
o
.
a) Tính di n tích xung quanh và th tích kh i chóp.ệ ể ố
b) Tìm tâm và bán kính m t c u ngo i ti p hình chóp.ặ ầ ạ ế
B.Y37,!+GA!++&!&)U!+P!+V

#V

()*!+,-!3V


 
 

 
= +


= + ∈


= −

x t
y t t R
z t




   

= +


= + ∈


= +

x m
y m m R
z m
&a!+]V


#V

k!&.
' ()*!+,-!O(P!+(a&V

#V


c. Vi t ph ng trình m t c u đ ng kính OH v i H là giao đi m c a hai đ ng th ng trênế ươ ặ ầ ườ ớ ể ủ ườ ẳ
Câu 5 : a. Tìm ngh ch đ o c a z = 1+2iị ả ủ
b. Gi i ph ng trình : (3+2i)z = z -1ả ươ
ĐỀ 23
?QS!.!+8!&&!
B.33
 
 Y= + −y x x
'04&
 ##$%&
 @H!4.Z![!+H%&()*!+,-!3
 
   :
+ + + =
x x m



BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
B.32H()*!+,-!&.3


  :
\ \ :

− + =


+ =

x y
x y
B.37-(S!#(S!%&(a&.3

 
   

+ −
= +
+
i i
z
i i
B.Y378!8%&G4r!+,1a!+4&+b./!&C++D&)U!+<O"!#4:J
@QS!,"!+8!e!+&!
Thí sinh ban khoa học tự nhiên làm câu 5a hoặc 5b
B.\&3
78!8(B!3

:
 !
π

= +

I x xdx
7-3

 Y

+ − −
=
+
x mx m
y
x
,!Es!+J(8&#0,1!
B.  \37,!+  H  /  J  K5L        ?:CCC  @CCC  CC=  wZ(  ()*!+  ,-!  O  (P!+    W.&
?C@Ca!+!,E!+K‰!+!E,"!O(P!+#K?@4-!D!Z78!8G(
>K?@ ,E!+>:C:C\
Thí sinh ban khoa họcxã hội làm câu 6a hoặc 6b
B.F&3
78!8(B!3


 4!= +

e
I x xdx
7-3
Y 
j \ ::j= − −y x mx
,

B.F37,!+H/JK5L3?:CCC@CCYC=C:Cy‚4Z(()*!+,-!O(P!+gW.&
?C@CwZ(()*!+,-!&%&)U!+P!+W.&@#M#0M4+&%&O(P!+g#0,1KL
ĐỀ 24
9Q ầ!.!+3 
B.935

R5
 "!"!##$%&
 c&#CH!4.Z![!+H%&()*!+,-!35

R56:
B.993
 2()*!+,-!34+

5R4+

56:
 78!8(B!39
 
:
5V5
π

x
e c
 ‡55

65

6' ()*!+,-! (. !%&W.&+I&J

B.9993-!(a+b.C^/!b.E!+&78!8-!(>?@c
99QS!,"!+ 3 
)*!+,-!.u! 3
B.9'&37,!+GA!++&!K5LY?N=N=C@NN:C:NNCc=NN
 ' ()*!+,-!O(P!+@c>.,&?@c4aVH!
 ' ()*!+,-!OS.B? (5T#0O(P!+@c
B.'&32()*!+,-!35

656:,"!B((a
)*!+,-!!B!+& 3
B.'93)U!+P!+V

3
Y

Y
= +


= −


=

x t
y t
z
CV

3


  Š
Š
=


= +


= −

x
y t
z t
 78!/!#.A!++.!+%&)U!+P!+V

#V

 ' ()*!+,-!OS.)U!+G8!4/!#.A!++.!+%&V

#V

B.'32()*!+,-!35

665RR:,"!B((a
ĐỀ 25
9Qyzpy{p23
B.93
 5R


YR5
 ##$%&' ()*!+,-! (. !%&/?N
 7-()*!+,-!35

RF5

6o5RYR:C&!+H(B!H



BỘ ĐỀ ÔN THI TỐT NGHIỆP TOÁN 12
B.993
 78!8(B!39

:
Y ! F 
π


x x x dx
2()*!+,-!3Y
5
RF
56
6:
 7-Z(5!%&3

 4+  − −x
B.9993
 -!(>?@c?@c4-!#.A!+/!&CO"!>?@4&+b.##.A!++#0

2Iy4,.!+?@a!+!,E!+3>y#.A!++O(P!+?@c78!8G(>?@c
[&
99Qyzph9€p23
7[)*!+,-!.u!3
B.9'&3
 7,!+GA!++&!K5LOS.>35

6

6L

R5RYRFL:
 ;!B#!G8!%&OS.>
 2I?N@N4S!4)i4+&G+/JK%&OS.>#0,1K5NKNKL7-/J
?N@N' ()*!+,-!O(P!+?@
B.'&3
 2()*!+,-!&.,"!Z((a3L

6YL

6::
7[)*!+,-!!B!+&3
B.9'3
 7,!+GA!++&!K5L)U!+P!+c3
  
  \
− + −
= =
x y z
#O(P!+Q3566LRj:

 a!+])U!+P!+cGA!+#.A!++(Q7-+&%&)U!+P!+c#O(P!+Q
 ' ()*!+,-!)U!+P!+cl4-! .#.A!++%&)U!+P!+c4"!O(P!+Q
B.'3
 2()*!+,-!&.,"!Z((a3L6

6L6R:
ĐỀ 26
Qyzpy{p2yK7|7}‹7y~>9py3
B.93
##$%&


+
=
+
x
y
x
Mh#0I+,%&C)U!+P!+V564.A!k/(B!H
2I?4+&%&#0,1K5' ()*!+,-! (. !%&/?
B.9932()*!+,-!3

 4+
 j

=
x
x
 7-+,40!!^#+,!]!^%&3!


56!5R
B.9993
aVH!>?@/!>?#.A!++#0O(P!+?@#>?&C?@C?#
·
:
o:=BAC

78!VH!8OS.#8GS.!+/ (aVH!>?@
Qyzph9€p23
7[)*!+,-!.u!3
B.9'&3
7,!+GA!++&!K5LM=NN#O(P!+Q()*!+,-!3566LR:
 y‚# ()*!+,-!)U!+P!+VW.&M##.A!++#0O(P+Q7-I&J+&y%&
)U!+P!+V#O(P!+Q
 y‚# ()*!+,-!OS.BM!G8!hYa!+]OS.!kO(P!+Q[+&
. !4)U!+,d!
B.'&3
78!VH!8-!(P!++0&
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!X)U!+Q3YR5

CV3=56
7[)*!+,-!pB!+&3
B.9'3
7,!+  GA!+  +&!  K5L    Y    ?=NNC  @:NYNC  \NN=\C  c=NjN=\  #  )U!+  P!+   V3
\  o
 \ Y
+ + −
= =


x y z

 ' ()*!+,-!OS.>!+/ (aVH!?@c
 7-I&J+&MCp%&V#0OS.>
 ' ()*!+,-!O(P!+ (5T#0OS.>/MCp
B.'378!VH!8-!(P!++0&!X)U!+Q35

6C (. !%&Q/MN\#,1K

Y
Y

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