ĐỀ ĐÁP ÁN THI KI 2-TOÁN-12

TRƯỜNG THPT LAO BẢO Đ KIÊM TRA HC K II- MÔN TON - 12
TRƯỜNG THPT LAO BẢO Đ KIÊM TRA HC K II- MÔN TON - 12
TỔ TON
TỔ TON
……………………………… …………………………………………………
……………………………… …………………………………………………
Đ RA:
I:PHẦN CHUNG (7 điểm)
Câu 1;.
3 2
1
2 3 1
3
y x x x= − + −
 C
 !"#$"%&'(()* +C,-('(
0, 2, 3y x x= = =

Câu 2.:.
 / 0&,1(%
2 2 2 2
3  4 . .5− − ≥
 !""&67I8
1
2
ln(1 x )dx
0
+
∫
Câu 3:.95!%:;&<z =>(
( )

1 2 (4 5 ) 1 3i z i i− + − = +

II:PHẦN TỰ CHN: (3điểm) (Thí sinh chọn 1 trong 2 câu sau)
Câu 4 a:(3 điểm)!(?:((Oxyz,-('(
1 2
: 1
x t
d y t
z t

= +

= +


=

@&'(PA&,1(
%
2 2 3 0x y z+ − + =

9B/CMD(,-('(d@&'(PECFM
.BGH&&,1(%@I;SA6;Fd=&2J@&'(PA ?"R89
Câu 4b:( 3,0 điểm )7
%F&KHLMN
9 9 9 9
A B C D
A*
9
LL a=

LM8LN8./C
OPDID,QD;(*LMLN
9
LL
9B!"R?(S
9
C
=@&'(OP
.B!"R"<#$
9
C MNK

. . . . . . . .Hết . . . . . . .


ĐP N VÀ BIỂU ĐIỂM
Câu Nội dung bài làm cơ bản T
Câu1

.
U!ET7
¡
U
2
' 4 3y x x= − +
2
1
' 0 4 3 0
3
x

y x x
x

=
= ⇔ − + = ⇔

=

U/)*
lim
x
y
→+∞
= +∞

lim
x
y
→−∞
= −∞
UM( =
V W( =?(
( )
;1−∞

( )
3;+∞

V W( =
( )

1;3

V TX*
1
1;
3
 
 ÷
 
V TX;
( )
3; 1−
UT
TYZ*&6 $
OF;F
x 5 9 .  4
y
1−
1
3
1
3
−
1−
1
3
5.
5
5.
5

5.
5.
5.
5.

95
!R6;#$"%&'(()* +C,-('(
0, 2, 3y x x= = =
D
3
3 2
2
1
2 3 1
3
S x x x dx= − + −
∫

3
3 2
2
1
2 3 1
3
x x x dx
 
= − − + −
 ÷
 
∫

5.
5.
 
3
4 3
2
1 2 3
12 3 2
x x x x
 
= − − + −
 ÷
 

3
4
=
#

5
6;.
9
 [
 .
.2 2 2 . 2 2 2 2 2
&  \  . ]    .     9 5
 
⇔ ≥ + ⇔ ≥ + ⇔ + − ≤
(1)
+T@^28

 .
9
 
x
x
 
 
+ −
 ÷
 ÷
 ÷
 
 
8_

  5f x x R≤ ∀ ∈
`%
5 2
0 , 1
3 3
< <


 f x
( =
¡
[O@?7^.85 &9
⇔
^2
≤

^.
⇔
2
≥
.
5.
5
5.

9
b) 9) + Đặt
2xdx
2
du
u ln(1 x )
2
1 x
dv dx
v x


=
 
= +
⇒
 
+
=




=

+ Ta có :
= + − = − −
+ +
= − + − +
+
∫ ∫
∫
1 1
2
1
x 1
2
I xln(1 x ) 2 dx ln2 2 (1 )dx
2 2
0
1 x 1 x
0 0
1
1
1
ln2 [2x] dx = ln2 2 2I
1
0
2
1 x
0
+Với

=
+
∫
1
1
I dx
1
2
1 x
0
. Đặt
x tant=
, ",Q
9
I
=
4
π

+Do đó :
I ln2 2
2
π
= − +

5.
5.
5.
5
5.

Câu3
9
( )
( )
( )
( ) ( )
( ) ( )
2
2 2
1 2 (4 5 ) 1 3
1 2 1 3 (4 5 )
1 2 3 8
3 8 1 2
3 8
1 2
1 2 1 2
3 6 8 16
1 2
19 2 19 2
5 5 5
i z i i
i z i i
i z i
i i
i
z
i
i i
i i i
z

i
z i
− + − = +
⇔ − = + − −
⇔ − = − +
− + +
− +
⇔ = =
−
− +
− − + +
⇔ =
+
− + −
⇔ = = +
NA
2 2
19 2 19 2 73 365
5 5 5 5 5 5
z i
   
− −
= + = + = =
 ÷  ÷
   

5.
5.
5.
5.

6;4
99
9
( )
1 2 ;1 ;M d M t t t∈ ⇔ + +
5.
( ) ( ) ( )
2 1 2 1 2 3 0
2
M P t t t
t
∈ ⇔ + + + − + =
⇔ = −
a;bCFMD
( )
3; 1; 2M − − −
5
5.
2) .
./CID6@I;S
( )
1 2 ;1 ;I d I t t t∈ ⇔ + +
S=&2J)P
( )
,( )d I P R⇔ =
( ) ( )
+ + + − +
⇔ =
+ +
= −


⇔ + = ⇔

= −

2 2 2
2 1 2 1 2 3
1
2 1 2
1
3 6 3
3
t t t
t
t
t
U
( ) ( ) ( )
2 2
2
1 1;0; 1 ( ): 1 1 1t I S x y z= − ⇒ − − ⇒ + + + + =

U
( ) ( ) ( ) ( )
2 2 2
3 5; 2; 3 ( ): 5 2 3 1t I S x y z= − ⇒ − − − ⇒ + + + + + =
5.
5
5
5.

5.
Câu 4b
9. 
9[C$ZCFc2bdA(ce()LZc2cbcd
f;MN
9
A
,%

[A7L5B5B5M.B5B5N5B.B5
9
A
5B5B
9
C
.B.BOB5B5
P5BB55B5B
a
2

[A7
(MNK):x y 2z a 0+ + − =

[a;b7
=
5a 6
d(C ;(MNK))
1
6


5
5
5
5
2) 9
2) Ta có :
+ với
2 2
a a
2
[MN,MK] ( ; ;a )
2 2
=
uuuur uuuur
+
= =
uuuur uuuur uuuuur
1
3
1 5a
V [MN,MK].MC
C MNK 1
6 12
5
5
 HẾT