Đề kiểm tra học kì 1 môn Toán lớp 11 số 7

SỞ GD & ĐT THANH HÓA ĐỀ KIM TRA HỌC KÌ I NĂM 2014 – 2015 SỐ 7
ĐỀ 7 MÔN TOÁN – KHỐI 11
Ngày 13 tháng 12 năm 2014
Câu 1
 !" 

 #
      

    
− +
=
+

Câu 2$
% &'(!)**$*"*+*,*-*.*/0123# 45643$ 7  5
8#9:;<$75=:>5=?
#@ > AB85=4C+=D>=&EFG + =D  @
3A=DG9HG
EF;E!
   " +
+ + + + +
% % %  % %− + − + −
Câu 3
IJ=:K<G5>35LM.#N+O:;</5 LD4=:
.EF;
P J JJ JJJ 
= + + + +
n soá d
dd d
123

 3
n soá d
dd d
123
=:564Q75#NJ
Câu 4E<R@=S
2 2
x y
1
9 4
+ =
TUVC@ 
O@
u ( 3,4)= −
r
Câu 5$W
% 3PXY%3=:I8<XY%IZ[=: 4  L
PX  PZ!Z[![X
%MZ\\PY%
#I]=:5M<XT%MZ%]\\[Y
I1=: <R^Z]O_PY%%M1=:I8<
PY%
Câu 6.(1,0 điểm)En`4J2a
   $
 $ "    + 
n
n n n n n
C C C C n C n+ + + + + + = +
1bE
ĐÁP ÁN V8 BIU ĐIM ĐỀ 7 – HKI ( 2014−2015)

Câu 1: !" 

 Wcd9 e⇔
x k
4 2
x k

π π
≠ +



≠ π

⇔
2
sin2x cosx
4cos x
cos2x sinx
+ =
⇔
2
cosx
4cos x
sinx.cos2x
=
⇔ f"!
 !⇔
x k
2

π
= + π
&
sin4x 1 x k
8 2
π π
= ⇔ = +
&
#
     

    
− +
=
+
Wcd9 e⇔
2
x k2
3
x k

π
≠ ± + π



≠ π

⇔f f 


! ⇔  !
⇔
3x x 3x x
2cos cos 2sin cos 0
2 2 2 2
+ =
⇔ = + =
x 3x 3x
cos 0(i);sin cos 0 (ii)
2 2 2

x
cos 0 x k
2
= ⇔ = π+ π
= L⇔
3x
sin 0
2 4
 
π
+ =
 ÷
 
⇔
2
x k
6 3
π π
= − +

&
Câu 2: a,E1Y75c=?
−%I$75 +75=?<&(O:BM63
3
5
A
5L :
E1E #7535gO:5=?
−%I75g "75g3
2
4
C

−%I75=? +75=?3+
−PBM6$75'I3$h%i&`3
2
4
C .5.3!
5
jC=&3G=:
3 2 1
5 4 5
A C .C .3! 240 soá.+ =
#@ > AB85=4C+=D>
=&EFG +=D@ 3A=DG9HG
−%I +=D@ G9HG3
2
5
C


−(G<=D@ G9H>G=:
1
6
−(G<=D@ dKG9H>G=:
5
6
] 3GD=:
2 3
3
2
5
5
1 5 5 1250
C . 10.
6 6 7776
6
   
= =
 ÷  ÷
   
EF;E!
   " +
+ + + + +
% % %  % %− + − + −
E3
0 1 2 3 49 50
50 50 50 50 50 50
C C C C C C− + − + − +
!f
+

!Z:
0 50 1 49 24 26
50 50 50 50 50 50
C C , C C , ,C C= = =
P`
0 1 2 3 24 25
50 50 50 50 50 50
2C 2C 2C 2C 2C C 0− + − + + − =
⇒E
25
50
C
!⇒E!
25
50
C
2
−
Câu 3:IJ=:K<G5>35LM.#N+O:;<</5LD
4=:.EF;
{
 K J
P J JJ JJJ  JJJ= + + + +

E3
8
9
u 15
S 81


=


=


⇔
1
1
u 7d 15
9(2u 8d)
81
2

+ =


+
=


⇔
1
1
u 7d 15
u 4d 9

+ =



+ =


⇔
1
d 2
u 1

=


=


] 3
{
 K 
P     = + + + +
!
{
n so9
2
9 99 99 9
9
 
+ + +
 
 
 
P!

2 n
2
10 10 10 n
9
 
+ + + −
 
!
n
2 10
(10 1) n
9 9
 
− −
 
 
Câu 4: E<R@=S 
2 2
x y
1
9 4
+ =
 TUVC@ O@
u ( 3,4)= −
r
Z*`∈S⇔
2 2
x y
1
9 4

+ =

Zkk*`k=:<ZT
u
T
r
⇔
x' x 3
y' y 4

= −

= +

⇔
x x' 3
y y' 4

= +

= −


] 3⇔
2 2
(x' 3) (y' 4)
1
9 4
+ −
+ =

i&`<ST
u
T
r
=:Sk
2 2
(x 3) (y 4)
1
9 4
+ −
+ =
Câu 5:% 3PXY%3=:I8<XY%
IZ[=:4LPX  PZ!Z[![X
%MZ\\PY%
Ij=:<Y%3
KG 1 SM
KA 3 SA
= =
⇒Z\\Pj
:Pj⊂PY%O:Z⊄PY%⇒Z\\PY%
#I]=:5M<XT%MZ%]\\[Y
E3
1 1
KG AG GD
2 2
= =
4j=:<]
P`MY%]=:#:] 3Y\\%]
(UXZ]3[=:R#4[\\Z]
O:`Y[\\Z%]

I1=: <R^Z]O_PY%%M1=:I8<
PY%
E PXj
MD SK {H}∩ =
:Pj⊂PY%4
{H} MD (SBC)= ∩
HK DK 1
HK / /MG
MG DG 2
MG AG 2
MG / /SK
SK AK 3

⇒ = =




⇒ = =


HK 1
SK 3
⇒ =
] 31=:I8PY%
Câu 6(1,0 điểm) En`4J2a
   $
 $ "    + 
n
n n n n n

C C C C n C n+ + + + + + = +
(U
( )
( )
( ) ( ) ( )


  h
 h
 
h h
 h  
k k k k k k k
n n n n n n n
n n
k n
k C kC C C C nC C
k n k
k n k
−
−
−
+ = + = + = + = +
−
− − − −
 
 
i&`
   $       
   

 $ "         
n n n
n n n n n n n n n n n n n
C C C C n C n C C C C C C C C
−
− − − −
+ + + + + + = + + + + + + + + +
( )
 
   
n n n
n n
− −
= + = +
H
D
M
N
G
K
A
B
C
S
Z:
   $
 $ "    + 
n
n n n n n
C C C C n C n+ + + + + + = +

+ n⇔ +
( )
 
   
n n n
n n
− −
= + = +
n
⇔ =