Đề kiểm tra học kì 1 môn Toán lớp 11 số 13

Đ KHẢO SÁT CHẤT LƯỢNG HỌC K I

Môn thi:Khối:
Thời gian làm bài: 90 phút ( không kể thời gian giao đề)
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Câu I (2,0 điểm) !"#$
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    
x
c c
π π
− − −
+%
, '& &
!( ) !( )*  !
    
x
c c
π π
− − −
Câu II: (1,0 điểm)-./0!1#23456
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n n
C C=
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x
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9":$
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'

n
x
x
 
+
 ÷
 
Câu III: (3,0 điểm) ;<%=->%=->/0 + 0?5@%/0#
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 !EN5FG(<=-)%
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S5"/KO+H,V
Câu 5. (2,0 điểm)S!1C(#
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)W"56$#
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
Y#

Z
*,%
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+%TU8"!1DAK#3%

Câu 7(1,0 điểm)5CC9T;E3+A[5C9"#BA;;'E3+
&"BE3+AWE0E3+E0%
"% T!1\#3"'E3+BA;;A8'50#&"BAWBE0%
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Hết
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^^
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Đ SỐ 13
HƯỚNG DẪN GIẢI
Câu NỘI DUNG Điểm
1a
 !"#$
 & '&
!( ) !( )*  !
    
x
c c
π π
− − −
1,0 đ
 & '&
!( ) !(  )*  !
    
x

c c
π π
− −
⇔
 & & '&
! ! !  ! *  !
    
x x
c c c− −
⇔
' '& '&
! !& ! ! * !
  
x
co c x−
⇔
'
! (!& ! )*

x
co x− −
⇔
'&
! 

 !( ) 

c
x
π


=



− =


+
'&
! 

c =
⇔

' '
k
x
π π
= +
+
 !( ) 

x
π
− =
⇔




x k
x k
π
π
π π

= +


= +

1b.
 !"#$
, '& &
!( ) !( )*  !
    
x
c c
π π
− − −
1,0 đ
, '& &
!( ) !(  )*  !
    
x
c c
π π
− −
⇔
, ,& '& ' &

! ! ! ! * !
    
x x
c c c− −
⇔
 & &
! !& ! ! *!
  
x
co c x−
⇔

! (!& ! )*

x
co x− −
⇔
&
! 

 !( ) 

c
x
π

=




− =


+
&
! 

c =
⇔

 
k
x
π π
= +
+
 !( ) 

x
π
− =
⇔



x k
x k
π
π
π π


= +


= +

2
-./0!1#23456
' 

n n
C C=
% 57!18"

x
9":$

'

n
x
x
 
+
 ÷
 
1,0đ
 5AL
,n
=

7!18"

x
MEN9*/0:
 ' 
,
% %'C

3 a  ;<%=->%=->/0 + 0?5@%/0#A:58"<B/05C
A:53D=-(9=E0-)%
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H(@)%
1,5đ
g
( ) ( )SAC SBD SO
∩ =
g@/0-8"
∆
<=3@hh<=
<#2"$
( ) ( ) h h
x
OMN SAB N SA∩ =
%
x
N
Q<-Di%cj2
{ }
( )SB OMN K∩ =
3b IBJ/K/L/0?58""5=>E0<>%M5HIJ! 

!EN5FG(<=-)%
1,5đ
";$
`J 
IJ h h
`< '
IE
SA
IA
= = ⇒
Mà
( ) IJ h h( )SA SAB SAB⊂ ⇒
4 O5C!P!Q?A1E0ARS/K%T&!#SA:U!1S5"/KO
+H,V
1,0 đ
";$
( ) Z%Z 'Zn Ω = =
=$kU!1S5"/KO+H,k
{ }
(lZ)B(Zl)B(l)B(l)B('l)B(l')A =
( ) Zn A⇒ =

( )
Z
P A⇒ =
5a S!1C(#

)W"56$#

X#

'
Y#
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*E0#
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Y#
Z
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1,0
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
)B";$
 ' 
 Z

,
u u u
u u
− + =


+ =

  
 
( ) (  ) (  ) 
(  ) ,
u d u d u d
u u d

+ − + + + =

⇔

+ + =

⇔


' 
  ,
u d
u d
+ =


+ =

⇔


'
u
d
=


=

5b. TU8"!1DAK#3 1,0 đ

";$
[ ]
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
%%%%  ( )

S u u u u d= + + + = + − =
[ ]

% ( )' m
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+ − =
6a 5CC9T;E3+A[5C9"#BA;;'E3+&"BE3+AW
E0E3+E0%
"% T!1\#3"'E3+BA;;A8'50#&"BAWB
E0%
0,5đ
:AL+"E3+;A8'50# "+&"B+AWE0+E0%
Suy ra số cách chọn là: 3.4.5 = 60 (cách)
6b T&!#SA:\#3]C"ZE3+A;9[;A8'50#% 0,5đ
<1Kn9["5\#$
Z

( ) mn CΩ = =
%
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$qS2ALZ+&"E0AW%;!1/S2/0$
Z
,
,C =

$qS2ALZ+&"E0E0%;!1/S2/0$
Z
r
rC =
'$qS2ALZ+AWE0E0%;!1/S2/0$
Z
m
rC =
<19.s##j/L+.1=$
( ) , r r mn A = + + =
t!#SK 5$
m ,
( )
m '
P A = =