30 đề thi thử THPT môn toán

 

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

012345( 7,0 điểm 6
7+893,0 điểm6
 
 y x x
= − + −
 !"# $
%&'   () !""" *+,()&
 
 -x x m
− + − =
.(/ *0/$
7+:93,0 điểm6#
1'*+,()&
( ) ( )

 
2( 3  42( 3  5 -
+ − + + >
%66 *0

-
 
x x
I x e e dx
= +
∫

%&'   () !"7
= − + −
3 2 2
y x 2mx m x 2
8  798
3 
=
$
7+;91,0 điểm6#
& .*:$;<= .>;<=2& ?@A  B:;<:;=
9C((. D>A:;E;<E"A(. 
·
-
:=; -
=
$%676 F .*:$;<=$
01<(3,0 điểm ):
Thí sinh chỉ được chọn một trong 2 phần ( phần 1 hoặc phần 2 )
Phần 1. Theo chương trình Chuẩn:
7+=>92,0 điểm6%)(FC(("D/8GH3>I 7;JJA+K(L(
∆
 .*+,()&
 

x t
y t
z t
= +



= − +


= −

B*L(
α
 .*+,()&3M>MIE-$
N*+,()&B*L(OP9";9C((. D+K(L(
∆
$
N*+,(B Q9:0RS)+K(L(
∆
A*3T DB*L(
α
 .F6S($
7+?>91,0 điểm6#%&*U 2V* !"*U 
 
 
i
z
i
−
=
+
$
Phần 2.Theo chương trình Nâng cao:
7+=@92,0 điểm6#%)(FC(("D/8GH3>I 7WJJ+K(
L(X .*+,()&
3  >  I 

  
− + −
= =

N*+,()&B*L(
α
P9"7W U")Y H3$
N*+,()&+K(L(P9"WA Z9C((. D+K(L(X$
7+?@91,0 điểm6#%&   3A>["#

      x i y i i
+ + − = +

\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 01
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EF"GH6
7+8#9;F"GH6
  !"
 
 4y x + x –= −
$
 %&7*+,()&
 

 - x x m –  –+ =
 .6'"(/$
7+:#9;F"GH6
1*+,()&
x x
1
3
log 3=
%66 *0
I x dx
2
2
0
4= −
∫
%&1%]^A1%^^ !"
x
y
x
2 3
3 2
+
=
−
)8_J`$
7+;#98F"GH6WGF)Y .F6) a9 "
h r3=
$%6X/6 39(P9"
76  !"F)Y$
01<9;F"GH6

I0!J&)!KL, *M!)!+N
7+=>9:F"GH6%)(FC(("H3>IA "7;bJJA<-JJAJ-J$
U("( ;<9C($N*+,()&" !" 8<$
N*+,()&B Q9P9"7;A<AH$
7+?>98F"GH6%&*U I["#
z i z
z i z
2
1

− =

− = −

0!J&)!KL, *M!7,)>&
7+=@#9:F"GH6%)(FC((" "7;bJJA<J-Jb4JbJ$
%&c"G& 9\ !";)+K(L(<$
N*+,()&B Q9 .0;*3T D<$
7+?@#98F"GH61*+,()&"9)@*V**U 

( ) ( )

  
      -z z z z z z–+ + + + + =
\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 02
 C:D8=


 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EF"GH6
7+89;ODF"GH6
x xy
3 2
3 4+ −=
 .$
$
c+K(L(
m
d y mx m( ): 2 16= − +
D2"$U()S(
m
d( )
29C Z8G7 R$
7+:9;ODF"GH6
1'*+,()&
x
x
x
1
1
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( 2 1) ( 2 1)
−
−
+
+ ≥ −


f x dx
1
0
( ) 2=
∫
Dd22e$\#>66 *0RE
f x dx
0
1
( )
−
∫
$
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x
x
y
2
4 1
2
+
=
$
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\& 99C((.  !";g39(B*L(;<2)9(7 !";<$WB
;;gg8D>G(. S(
45
o
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I0!J&)!KL, *M!)!+N
7+=>9:ODF"GH6#%)(FC(("D/c"GH3>I$N*+,()&B*L(O
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x y z 0+ + =
  7WJJ
1−
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2
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i
z
i
1
1
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x t
y t
z
1 2

2
1

= +

=
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
= −
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B*L(O
x y z2 2 1 0+ − − =
$
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 N*+,()&+K(L(
∆
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+K(L(X$
7+?@98ODF"GH6#%)@**U A&<7*+,()&@ "
z Bz i
2
0+ + =
 .i(
&*+,("(/S(
i4−

\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 03

 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, khơng kể thời gian giao đề.
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 !"
="A/29@j(/ !"*+,()&
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x x
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∫
x
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x x
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∆
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∆
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 N*+,()&B*L(<=$%o.9>)";<=2GUX/
 N*+,()&B Q9: .0;*3T DB*L(<=
7+@Tính thể tìch các hình tròn xoay do các hình phẳng giới hạn bởi các đường sau đây quay
quanh trục Ox : y = cosx , y = 0, x = 0, x =

π

\

AB S# 04
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.
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− + =
x x
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7+0>
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>MI4E-
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7+0>1/O%
5 $ 
5 $ 

− =


=
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N*+,()&B*L(OP9"^9C((. D8W^$
7+0@ 1/O%

2( 5   
2( 5   
+ =



+ =


x
y
x y
y x

\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 05
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+89;ODF"GH6
xy x
3 2
3 1= − + −
 .
$

=t(A3 k7*+,()&"9 .T((/*0/

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3 0− + =
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1*+,()&
x
x
x
x
cos
3
log 2log cos 1
log 1
3
3 2
π
π
− +
−
=
%66 *0 RE
+
∫
x
x x e dx
1
0

( )
%&()2D'()[' !"
y x x x
3 2
2 3 12 2= + − +
)
[ 1;2]
−
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%676  !"&2f()YX/6  !"B Q9(8*&2f()Yja$
01<9;F"GH6
I0!J&)!KL, *M!)!+N#
7+=>9:ODF"GH6#%)(FC(("D/c"GH3>IA "+K(L(
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x t
d y
z t
1
2 2
( ): 3
 
x y z
d

2
2 1
( ):
1 1 2
− −
= =
−
 U()S("+K(L(
d d
1 2
( ),( )
9C((. "9+(FC( Z"9$
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z i i
3
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α
"+K(
L((d
1
), (d
2

) .*+,()&
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x y z( ):2 2 3 0
α
− + − =
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1
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d
1
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z z
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=
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z
2*U 2V* !"
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Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 06
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.
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7+89;F6>E3

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\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 07
 C:D8=
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 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.
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AB S# 08
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
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Thời gian bài làm: 150 phút, không kể thời gian giao đề.
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AB S# 09
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
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Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 10
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Thời gian bài làm: 150 phút, không kể thời gian giao đề.
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2x
=
|7 .7  )
7+9;0DF"GH6#
1'*+,()&


 
2( -

x
x
−
≥
+

%66 *0

π
+
∫
2
2
0
2 sin
1 sin
xdx

x


1
ln( )
1
y
x
=
+
$Ws
. ' 1
y
x y e
+ =
7+980DF"GH6#
&.)k3"> .n2:A+K()k> .0HAGX+K(
l a
=
A 
(. V*l+K(B*L( U"+K()k>2
4
π
$%6X/6 39(P9"
X/6 *Q !"&.j
a
$
01<9;0DF"GH6
Thí sinh học chương trình nào thì chỉ được làm phần dành riêng cho chương trình đó
86!J&)!KL, *M!)!+N#

7+0>9:0DF"GH6
%)(FC(("D/c"GH3>I$B*L(O
3 2 3 7 0x y z
− − − =
A;JJ$
%&c"G7;g2& 9 !";)O$
N*+,()&B Q9 .0;*3T DO$
7+0>980DF"GH6
*U 
 
 
z i= − +
$\#>6

z z
+ +
:6!J&)!KL, *M!7,)>&#
7+0@9:0DF"GH6
%)(FC(("D/c"GH3>I$B*L(O
  4 -x y z
− + + =
  7
;-J-JA<J-J-
N*+,()&B*L( U";<9C((. DB*L(O$
N*+,()&B Q9P9"HA;A<*3T DB*L(O$
7+0@980DF"GH6
%&
Ax y
" 


   x i x yi
+ = − +

\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 11
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+9;ODF"GH6#
2
(1 ) (4 )y x x= - -
86
( )C
 !"# $
:6N*+,()&*9> !"
( )C
8("7 !"
( )C
D)Y $
;6%&m 7*+,()&"90> .(/*0/
3 2
6 9 4 0x x x m- + - + =
7+9;ODF"GH6#
861*+,()&
2 1

2 3.2 2 0
x x+
- - =
:6%66 *0
1
0
(1 )
x
I x e dx= +
ò
;6%&()2D'[' !"
2
( 1)
x
y e x x= - -
)8_-J`$
7+98ODF"GH6#
& .*a9S.ABCD . 8>aA(. (?" 8B>S(5-
-
$%67
6  !"& .*$
01<9;ODF"GH6Thí sinh chỉ được chọn một trong hai phần dưới đây
80!J&)!KL, *M!)!+N
7+>9:ODF"GH6#%)(FC(("D/8GOxyzA 
(2;0; 1), (1; 2;3), (0;1;2)A B C- -
$
86U(7AABAC FC(L(($ N*+,()&B*L(
( )ABC
$
:6%&8G& 99C((.  !"( 8GO2B*L(

( )ABC
$
7+>98ODF"GH6#%&*U 2V* !"*U z)S(
2 6 2z z i+ = +
$
:0!J&)!KL, *M!7,)>&
7+@9:ODF"GH6#%)(FC(("D/8GOxyz 
(2;0; 1), (1; 2;3), (0;1;2)A B C- -
86U(7AABAC FC(L(($ N*+,()&B*L(
( )ABC
$
:6N*+,()&B Q90BA*3T D+K(L(AC$
7+@98ODF"GH6#%6C9 !"*U zE
2014
( 3 )i-
$
\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 12
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+8#9;ODF"GH6
>E3

M3


M .$
$  !"$
$%&7*+,()&
 
-
 
x x
m− + =
 .(/*0/$
7+:9;ODF"GH6
"x$%6  6 *0"9


-
I x x dx
= +
∫
x$1*+,()&
4

4$4$

=−
−− xx
x$%&1%]^1%^^ !"

 
x
y x e

−
= +
)8_J`
7+;#98ODF"GH6& .*:$;<= .>2&9C( 8"

A(. (?"B
>S(5-
-
$1c12)c(0"( :;$%676 F .*1$;<=j"$
01<9;ODF"GH6
Thí sinh chỉ được chọn một trong hai phần sau( phấn 1 hoặc phần 2)
80!J&)!KL, *M!)!+N#
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Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 13
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Thời gian bài làm: 150 phút, không kể thời gian giao đề.
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Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 14
 C:D8=
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7+?@98ODF"GH6%&*Q *Q !"*U IE
( )
4
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


i
i
i
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+ −
 ÷
−
 
\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 15
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+8#9;ODF"GH6
 

x
y
x
−
=
+
A }2
"$$
$N*+,()&*9> !"87 .9(GS($
7+:#9;ODF"GH6
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2(  5 2( 2( 4x x+ = −
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B>S(
-
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01<9;ODF"GH6
Thí sinh chỉ được chọn một trong hai phần sau( phấn 1 hoặc phần 2)
80!J&)!KL, *M!)!+N#
7+=>#9:ODF"GH6
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*+,()&3b>MIzE-$
$N*+,()&" !"+K(L(XP9";9C((. DB

*L(O$%&8G("7 !"+K(L(XDB*L(O$
 $N*+,()&B Q90;*3T DB*L(O
7+?>#9:ODF"GH61*+,()&3

b3ME-)@**U $%6
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 
 

   J    
  
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x t
x y z
y t
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= −

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B*L(O>MIE-$
$%&7^2&9C( 9(.  !"7W2+K(L(∆
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7+?@98ODF"GH6%& 7*U IE

bM29Q$
\

AB S# 16
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+8#9;ODF"GH6


+−= xxy


$ f $
$ %&7*+,()&
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7+:#9;ODF"GH6
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∫
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
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7+;#98ODF"GH6F .*:$;< .>2"( a9 8"A"( :; 0
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01<9;ODF"GH6
Thí sinh chỉ được chọn một trong hai phần sau( phấn 1 hoặc phần 2)
80!J&)!KL, *M!)!+N#
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( )
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$N*+,()&B*L(
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N*+,()&B Q90<*3T D+K(L(;
7+?@98ODF"GH6%6

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 y
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\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 17
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+8#9;ODF"GH6
>E3

M3

M3M
$# $
$N*+,()&*9>D87 .G2(/ !"*+,(
)&d•3E-$
7+:#9;ODF"GH6
$1*+,()&
2
logx logx log9x+ =
$%66 *0



-
 
 
π
=
−
∫
x
I dx
x
$C
( )

  2  f x x x= + + +
$1'*+,()&
€
  -f x ≥

7+;#98ODF"GH6& .*:$;<= .;<=2&9C( 8"A:;9C((.
D>$1cWA^2Q2+V2)9(7 !"<=A(. (?":W^;<=S(
-
-
$%676 F .*:$;<=
01<9;ODF"GH6
Thí sinh chỉ được chọn một trong hai phần sau( phấn 1 hoặc phần 2)
80!J&)!KL, *M!)!+N#
7+=>#9:ODF"GH6%)(FC(("D/c"GH3>I "7;J-JJ<JJJ
-JJ-$1c12)c(0 !""( ;<
$N*+,()&+K(L(H1
$N*+,()&B Q9:P9"7HA;A<A$

7+?>#98ODF"GH6%&"*U i( !" T(S(6  !" T(S(
:0!J&)!KL, *M!7,)>&#
7+=@#9:ODF"GH6%)(FC(("H3>IA WJJh3b>MIME-
$N*+,()&+K(L(P9"W9C((. Dh$
$%&Wg3U(WP9"h$
7+?@#98ODF"GH6%&C9 !"*U I
 z z i+ = +
\

AB S# 18
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+8#9;ODF"GH6

 
y x x= − +
$ !"$
$%&7*+,()&
 
 -x x m− + =
 .(/*0/$
7+:#9;ODF"GH6
$1*+,()&
  
2( 2(   2(  -x x+ + − =

$%66 *0RE



x x dx+
∫
$%&1%]^1%^^ !"
3 2
3 9 35y x x x= − − +
)_J`
7+;#98ODF"GH6& .*:$;<= .>;<=2& ?@;<E"$;=E"$
8:;9C((. D>A(. (?":<B>24
-
$
"$ %676 F .*:$;<=
$ 1c\A2Q2+V2)9(7 !":<:$%676 F .*:$;\=
01<9;ODF"GH6
Thí sinh chỉ được chọn một trong hai phần sau( phấn 1 hoặc phần 2)
80!J&)!KL, *M!)!+N#
7+=>#9:ODF"GH6
B Q9: .*+,()&
-5

=−−−++ zyxzyx
" %&c"G0B Q9F6B Q9
 WB Q9: Z")Y c"G-3A->A-I2Q2+V8;A<AF ( H$N
*+,()&B*L(;<
7+?>#98ODF"GH6U()S(M

bM


E-
:0!J&)!KL, *M!7,)>&#
7+=@#98ODF"GH6
"+K(L(
∆

x
∆
2Q2+V .*+,()&+"9

x
  €
    €
   €
x t x t
y t y t
z z t
= + = − +
 
 
∆ = − + ∆ =
 
 
= = +
 
" um)6+,((?""+K(L()
 N*+,()&B*L(O U"
∆
O((D

∆
g
+?@#98ODF"GH6%& f@ " !"*U "9IEM5
4

\

AB S# 19
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+8#9;ODF"GH6



++−= xxy
 .
$ $
$ %&7*+,()&
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=+−
m
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 .(/*0/
7+:#9;ODF"GH6
$1*+,()&
5z2(5$2(
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xx
$%66 *0
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x
x
xI
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

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


+=
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$%&()2D'A()[' !"
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x
y
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-
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Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.

AB S# 20
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Thời gian bài làm: 150 phút, không kể thời gian giao đề.
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 
 
-
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01<9;ODF"GH6
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80!J&)!KL, *M!)!+N#
7+=>#9:ODF"GH6
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AB S# 21
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
 C:D8=


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Thời gian bài làm: 150 phút, không kể thời gian giao đề.
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7+?>#98ODF"GH6
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3

:0!J&)!KL, *M!,)>&#
7+=@#9:ODF"GH6
%)((H3>I "+K(L(X


 
  
x y z− −
= =
−
X


 

x t
y
z t
= −


=


=

$U(X


X

 m"9$
$%&8G  7;9G X

<9G X

" ;< .GX(Z'$
7+?@#98ODF"GH6%6()79U 
( ) ( )
4 4
   P i i= + + −

AB S# 22
\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+8#9;ODF"GH6
 
> 3 3 = − + −
 .
$$
$=t(A3 F7*+,()&"9 .T((/*0/


 
 
3 3 F -
5 
− + =
$
7+:#9;ODF"GH6
"$1*+,()&
 



2( 3 2( 3  -− − =
$%66 *0





I x dx
x
= + −
∫
$%&()2D'[' !"

y x x x= − + +
)8

J


 
−
 
 
7+;#98ODF"GH6
& .*:$;< .>;<2"( 9C( 08<D<;E<E"
:;9C((. D>:V*D:;<G(. -
-
$%676 F .*:$;<
01<9;ODF"GH6
Thí sinh chỉ được chọn một trong hai phần sau( phấn 1 hoặc phần 2)
80!J&)!KL, *M!)!+N#
7+  =># 9:ODF"GH6 %)(  FC(  ("  D  /  c"  G  H3>I  A    +K(  L(  X  
x 2 y z 3
1 2 2
+ +
= =
−
B*L(O
d
2
( )

"$U()S(X ZO8;$%&c"G7;$
$N*+,()&+K(L(
∆
2& 9 !"X2O$
7+?>#98ODF"GH61*+,()&I

bI


bE-$
:0!J&)!KL, *M!7,)>&#
7+=@# 9:ODF"GH6 %)(FC(("D /c"GH3>IA  +K(L(X
x 2 4t
y 3 2t
z 3 t

= +

= +


= − +

B*L(O
x y 2z 5 0− + + + =

"$U()S(XS)B*L(O$
$N*+,()&+K(L(
∆
S)(OA((DX  XG
F(2
14
$
7+?@#98ODF"GH6%&7*U 
 
   z m m m i= − + + −
29Q$

AB S# 23
\
Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+8#9;ODF"GH6
3 
>
3 
+
=
−
 .
"$$
$U()S(+K(L(>E3M29C ZDc()
$
7+:#9;ODF"GH6
$1*+,()&
 z q
4
2( 2(  2(

x x x+ + =
$%66 *0RE
+ +
∫

1
dx
x 1 x
0
$%&()2D'[' !"
 zy x x= − + −
)@*3  !"
.$
7+;#98ODF"GH6
UX/;<= .;<2"( a9A<=2"( 9C( 08=S
)(B*L(9C((. D>;<$<;=V*D<=G(. 5-
-
$%67
6 UX/;<=$
01<9;ODF"GH6
Thí sinh chỉ được chọn một trong hai phần sau( phấn 1 hoặc phần 2)
80!J&)!KL, *M!)!+N#
7+=>#9:ODF"GH6
%)(FC(("D/c"GH3>IA 7WJ-J4"B*L(
 O
2x y 3z 1 0
− + + =
h
− + + =2x y 3z 5 0
$
"$N*+,()&+K(L(XP9"W9C((. h
 $N*+,()&B Q90W*3T DOh$
7+?>#98ODF"GH61*+,()&
2
x 4x 7 0− + =

)@**U $%6
   
x x x x+ +
ƒ
:0!J&)!KL, *M!7,)>&#
7+=@# 9:ODF"GH6 %)(FC(("D /c"GH3>IA  +K(L(X
x 3 y 1 z 3
2 1 1
+ + −
= =
B*L(O
x 2y z 5 0+ − + =
$
 "$%&c"G("7 !"+K(L(XB*L(O$
 $N*+,()&+K(L(
∆
2& 9 !"+K(L(X2O$
7+?@#98ODF"GH6 

x mx
y
x m
+ +
=
+
2"$%&78 
883E$
\

AB S# 24

Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
 C:D8=

 !"#$"%&'() *+,!-).!/ !,
Thời gian bài làm: 150 phút, không kể thời gian giao đề.

0123459EODF"GH6
7+8#9;ODF"GH6
 3
>
3 
−
=
−
 .
"$$
$%&7+K(L(>EM3 Z8"7*0/$
7+:#9;ODF"GH6
"$1*+,()&
5 
  -
x x
e e− + =
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−
+
∫
1
x
x(x e )dx

0
$%&()2D'()[' !" 

y x x= + −
 )8
J 
 
−
 
$
7+;#98ODF"GH6
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
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01<9;ODF"GH6
Thí sinh chỉ được chọn một trong hai phần sau( phấn 1 hoặc phần 2)
80!J&)!KL, *M!)!+N#
7+=>#9:ODF"GH6
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−
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−
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 $N*+,()&B Q9P9"7;A<AA=$
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2 2
P (1 2 i) (1 2 i)= − + +
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−
JA"+K(L(

x 1 y z
( ):
1
1 1 4
−
∆ = =
−
A
x 2 t
( ): y 4 2t
2
z 1

= −

∆ = +


=

B*L(O

y 2z 0+ =
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2
∆
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$N*+,()&+K(L( Z "+K(L( 
( ) ,( )
1 2
∆ ∆
S)(
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
  4   -z i z i+ + − + =
$%6C9 !"*U
 
Z z z= +

AB S# 25