Đề thi toán 11 - sưu tầm đề kiểm tra, thi học kỳ, thi học sinh giỏi tham khảo bồi dưỡng (50)

ĐỀ 1
A.ĐẠI SỐ (7 điểm):
Câu 1:3điểm




  

  
x
x x
x x
→−
− + +
+ +







  
x
x x
x x
→−
+ +
+ −



 

 
x
x
x
π
→
−

Câu 2: ! "2điểm

 #
   y x x= − −

 
  
x
y
x
−
=
+
Câu 3:1điểm
$ "
 

x
y

x
+
=
−
$%&'()*'+'&(',&-$&''&(',&-).
'/
 0 #x y+ − =
Câu 4:1điểm
$ "
y x x=
$1+2
  
 3  33x y x y x− + + =
B.HÌNH HỌC (3điểm):$4(567$84,67$8 -9 56
 ABCD⊥

56:
Câu 1:$1+2
BD SC
⊥
(
 SAD ⊥
(
 SCD
Câu 2:4;57- (56$
Câu 3:<=> '+?58@A;).'/78- $>
ĐỀ 2
I. Đại số và giải tích: (7đ)
1. ( 2đ)
a.




  

 
x
x x
x x
→
− +
− +
b.


 


x
x
x x
→−
+ −
+ −
2.( 2đ) ! "
a.



x

y
x
+
=
+
 b.

  '  y x x= − +
3. ( 1đ)$>B&
 y x c x=
'
  3    33 #x y y c x x y− − + =

4.( 2đ)$ "

 
 
x
y f x
x
−
= =
−
4C'D
( )
C
EF(()*'+'&(',&
( )
∆
-

( )
C

&'
( )
∆
-
( )
  #d x y+ − =

II. Hình học: (3đ)
$4(567$84
( )
56 67$8
⊥
G,67$8 '-9'6- 8-
SA a
=
G
68:8$: :

AB
a
<=H '+?!67
1. 1đ)$1+2
( ) ( )
SDI SAC⊥

2. ( 1đ)ID- '4'JK'(/67$8- 5$8
3. ( 1đ)@A;).'/L67- 5$

ĐỀ 3
A. Giải tích:
! "G#




 


x
x x
x
→
+ −
−


 

  
x
x
x x x
→−∞
−
− + −
 ! "G#



 x
y
x
=
 
 
 = −y x x

EF(()*'+'&(',&!C'D "

     

C y f x x
x
= = − +
−
-).
'/
 y x= − +
G#
$>B&
'y x x=
'
  
33    #x y x y y− + + =
G#
B. Hình học: G#$4(567$84,67$8 '-9'6- 8
 SA ABCD⊥
   


AB
AD DC a SA a= = = =
H '+?67
1. $1
 BC SCA⊥
2. ID- '4;57$- 67$8
3. @A;8H- 57
ĐỀ 4
Câu 1: 




  


x
x x
x
→
− +
−


2
3
4 21
lim
3
x

x x
x
→
+ −
−
Câu 2:IL''M'N! "






≤+
>
−
−−
=
G
G

#

xmx
x
x
x
xf
G?O5E'P:

 

  
 

QPR  
x
khi x
f x
x
khi x

− −

≠
=

−

=

'
#
x
=
Câu 3:  ! "

x x
y
x
2
2

2 1
+ −
=
+


 y x x
= −



 
y
x
=
+
S
y x
2
(1 cot )
= +
T
y x
2 3
(2 sin 2 )
= +
U
y x xsin 2
= +


y x
2
cos 1 2= −
Câu 4:$ "

   y f x x x= = − +
4C'D $%&'()*'+'&(',&!$&''&(
',&-).'/
 y x
= +

Câu 5$ ",:P

QP

Q$
 P?,VW#
 %&'()*'+'&(',&-C'D$&'X"42
Câu 6:$ "
y x x.cos
=
$1+2
x y x y y2(cos ) ( ) 0
′ ′′
− + + =

 %&'()*'+'&(',&!C'D$! "
y f x x x
3
( ) 2 3 1

= = − +
'?
!$-'+N'
$1()*'+
x x
3
3 1 0
− + =
4X(YX'
Câu 7:$4(567$84,67$8 ''YZGM56-94-,67$8
 $1578
⊥
56$
 [\6O
⊥
7$'O$15O
⊥
7$
 7&'
AB a
=
G
SA a=
G
·
#
]#ABC
=
4;K'(/57$- 67$8
S @A;).'/7$- 58

ĐỀ 5
Câu 1:




 


x
x x
x
→
− −
−




  


x
x x
x
→
− +
−
 
x

x
x x
2
3
3
lim
2 15
→
−
+ −
S
x
x
x
1
3 2
lim
1
→
+ −
−
Câu 2: M'N! "

^ 
  

 
  
]
x

khi x
x
f x
x
khi x

+ −
≠


−
=


=


'
#
x =


x x
khi x
f x
x
a khi x
2
2
1

( )
1
1 1

− −

≠ −
=

+

+ =

a? 
"M'N'P:
Câu 3:  ! "

 

x
y
x
+
=
−


 y x x
=




 
y
x
−
=
+
S
y x1 2tan
= +
Câu 4:$ "

  ] y f x x x= = − + +
4C'D $%&'()*'+'&(',&!$&''&(
',&-94-).'/



y x
= − +

Câu 5:$ "
y x x x
3 2
2 5 7
= − + + −
4C'D$
<A_'()*'+ 
2 6 0y

′
+ >

%&'()*'+'&(',&!C'D$'?4 `
x
0
1= −

Câu 6:$ "
x
y
x
3
4
−
=
+
$1+2
y y y
2
2 ( 1)
′ ′′
= −

$ "
y xcot2
=
$1+2
y y
2

2 2 0
′
+ + =

Câu 7:$4(567$84,67$8 -9'YZ2a-
56⊥67$856:
a 6
3
<=OG[a)b' &-94!6M57G58
 $178⊥5$G5Z⊥78G
 $1567⊥57$G5$⊥6O[
4;5$- K'(/67$8G5HG67$8-H '+?5Z
@ 'c6&57$
ĐỀ 6
Câu 1G#?

x
x x
x
3 2
1
2 3 1
lim
1
→−
+ −
+

( )
x

x x x
2
lim 1
→+∞
+ + −
Câu 2G#?IL''M'N! "'?
x
0
2=

x
khi x
f x
x x
khi x
2( 2)
2
( )
² 3 2
2 2

−

≠
=

− +

=


Câu 3G#? ! "

x
y
x
2
2 1
2
−
=
−
 
y x
2
cos 1 2= −
Câu 4G#?$1+2()*'+
x x
5
3 1− =
4'_'`'X'`(
Q)
Câu 5G#?
$ "
y xcot2=
$1+2
y y
2
2 2 0
′
+ + =


$ "
x
y
x
3 1
1
+
=
−
4C'D$%&'()*'+'&(',&!$'?6d
Câu 6#?$4(567$84,67$8 -9G56⊥67$8- 56:
$1
⊥CD SAD( )

$1
SCD SAD( ) ( )⊥

4;57- 56$
ĐỀ 7
Câu 1G#?

x
x x
x x
2
2
2 1
lim
3 2

→+∞
+ −
+

x
x
x
2
2
2 2
lim
4
→
+ −
−
Câu 2G#?IL''M'N! "'?
x
0
1=

x khi x
f x
khi x
x x
1 1
( )
1
1
² 3


+ ≤

=

>

−

Câu 3G#? ! "

y xsin(cos )
=

x x
y
x
2
2 3
2 1
− +
=
+
Câu 4G#?$1+2()*'+4'_'X
x x x
5 4 3
5 3 4 5 0− + − =
Câu 5G#?
$ "
f x x x x
5 3

( ) 2 3= + − −
$1+2
f f f(1) ( 1) 6. (0)
′ ′
+ − = −
$ "
x x
y
x
2
2
1
− +
=
−
4C'D$%&'()*'+'&(',&!$'?>
Câu 6G#?$4(567$84, -967$8aG'YZ$56:a- 56
⊥
67$8<=eGfa)b' &-94!6M57- 58
$17$
⊥
567G$8
⊥
568
$16ef
⊥
56$
'ϕ-ϕ 4;5$-67$8
ĐỀ 8
Câu 1 ( 1.0 điểm)


 

   
x
x x
x
→−∞
− + + −

 

 
x
x
x
→+∞
−
−

Câu 2 (1.0 điểm)IL''M'N! "'+M'F(PD!4


  
 
]


x x
f x

x x
x
x

+ − ≥

=

+ −
<

−

Câu 3 (3.0 điểm) !g "
 ,:
 

 x x
x
− + + −
,:PR'

P
 
 
x
y
x
−
=

−


y x x
= +


Câu 4(2.0 điểm)$ "UP:P

dP

R4C'D$%&'()*'+'&(',&!$G&'
&(?4'`,
#

:
&(',&-).'/S,:QPR
Câu 5 (3.0 điểm)$4(567$84,67$8 -9$M56-94
-,G56:
]

a
<=>Gha)b' '+?!8$- 7$
 $15>h-94-56$
 4;578- 67$8G;6$- 57$
 ID-94- '@A;).'/68- 5$
ĐỀ 9
A-ĐẠI SỐ : (6,5 điểm)
Câu I(2điểm): ! "


  
 

x
x
x
→
+ −
−

(
)
 
   
x
x x x
→+∞
+ − +
Câu II (1điểm): ? "M'N

  


 

 R 

x
v i x
x

f x
x v i x

+ −
>


−
=


≤


í
í
'P:
Câu III (1,5 điểm):   "
 ,:P

dPP

RP

d




x x

y
x x
−
=
+ +


  y x=

Câu IV (1 điểm): <=$ C'D "
 
 y x x= − +
%&'('+'&(',&!$
7&''&(',&-).'/PR,d:#
7&''&(',&-94-).'/Pd,d:#
Câu V (1 điểm):$ "
= −
2
y 2x x
$1+2
+ =
3
y y" 1 0
B-HÌNH HỌC : (3,5 điểm) $4(567$84,67$8 -9G
SA (ABCD)⊥
- 
SA a 2=

$>B$K'M!4( '-9
$>B(56$

⊥
(578
4
α
;5$- (67$8G4
β
;5$- (567
S@A'c?6&K'(/57$G@A'c?6&(5$8

ĐỀ 10
A-ĐẠI SỐ : (6,5 điểm)
Câu I(2điểm): ! "

→
−
+ −
2
2
lim
7 3
x
x
x

(
)

  
x
x x x

→−∞
− +
Câu II (1điểm): ? "M'N

 
#
 
P
# #

+ −

≠
=


− =

x
v i x
f x
a v i x
í
í
'?P:#
Câu III (1,5 điểm):   "

− +
=
+

2
2 6 5
2 4
x x
y
x
  
+
=
−
sin cos
sin cos
x x
y
x x
,:P
Câu IV (1 điểm): . %&'i!C'D "
= − +
3 2
3 2y x x

&''&(',&'?>QQ
&''&(',&-94-'
= − +
1
2
9
y x

Câu V (1 điểm):$ "

+ +
=
2
2 2
2
x x
y
$1+2,,VVd:,V

B-HÌNH HỌC : (3,5 điểm)
Câu VI (3,5 điểm) $4(567$8467$8 '-9'6G67:7$:- 68:
OK'M567G568j-94-K',- 56:
2

$>B7$
⊥
(567
$>B$8
SC⊥

4
α
;5$- 67$8G4
β
;5$- 567G4
γ
;58- 56$
S'!4
ϕ
;(57$- (67$8

T@A;56- 78
U@A'c6&578
ĐỀ 11
Câu I?
1. 

 

  
      

x x
x
a b x x x
x
→ →+∞
+ −
+ − +
−

Câu II?? "

 
G 
 

G 
x
khi x
f x

x
a khi x

+ −
≠

=

−

− =

M'N'?
x =

Câu IIIG? ! "

 


     '

x x
a y b y x x c y x
x x
−
= = + + = +
+ +
Câu IV?%&'()*'+'&(',&!C'D
 C

! "

 

x
y f x
x
+
= =
−
&''&(',&
-94-).'/

   

d y x= +
Câu V?
$

  f x x= −
<A()*'+

3  y y x= −
Câu VIG?
$4(567$4,67$ '-9Y'756⊥67$- 56:G6$:
 $1+257$⊥567
 @A'c?6&(57$
 4;57$- 67$
S 8k- '`S -94!56- 7$
ĐỀ 12

Câu I?

 
#


0 
x
x
x
→
+ −


     
x
x x
→−∞
+ +

Câu II?? "UP:

  

 



x x
khi x

x
mx khi x

− +
≠


−


− =


M'N'?P

:
Câu IIIG? ! "

 
 
      ' 

x
a y b y x x x c y x
x
+
= = + + =
−
Câu IV?%&'()*'+'&(',&!C'D
 C

! "
 
    y f x x x x
= = − + −
&'
'&(',&-94-).'/
   d y x= − +
Câu V?$ "
 
    f x x x= +
-

    

g x x
=
$>B
3  3  f x g x x
= ∀ ∈
¡


CâuVIG?$4(567$4,67$ 'lG56-94-K'
(/67$- 56:OG[a)b' '+?!67- 7$
 $1+2$O⊥567
 $1+257$⊥56[
 4;).'/5$-K'(/67$
 @A'c?6&K'(/57$