đề kiểm tra toán lớp 11 học kì 2 đề số 15

Đề số 15
ĐỀ THI THỬ HỌC KÌ 2 – Năm học 2010 – 2011
Môn TOÁN Lớp 11

I. Phần chung:
Câu 1:

x
x
x x
2
3
3
lim
2 3
→−
+
+ −

x
x
x
2
2
5 3
lim
2
→−
+ −
+
Câu 2:!a"#$x%

x x
khi x
f x
x
a khi x
2
7 10
2
( )
2
4 2

− +

≠
=

−

− =

&
Câu 3:!'()"

y x x
2 3
( 1)( 2)= − +

x
y

x
4
2
2
2 1
3
 
+
=
 ÷
 ÷
−
 
Câu 4:*+(,-$./0+&/′0′+′12/0+34++/%a
+0%b5#//′0′034&6+78+9⊥/0′9:;;/′09∈/0′:∈//′&
+.-< 0+⊥+:/0′⊥+9:&
'1=5>//′0′03+9:&
'7(?6/@5>+9:&
II. Phần riêng:*Thí sinh chỉ được chọn một trong hai phần sau:
1. Theo chương trình Chuẩn
Câu 5a:!' 
n
n
2
2
1 2 2 2
lim
1 3 3 3
+ + + +
+ + + +

&
Câu 6a:
+("
y xsin(sin )=
&' 
y ( )
π
′′
&
+(+ 
y x x
3 2
3 2= − +
&A@BC-@2@)+()+3-$
(&
2. Theo chương trình Nâng cao
Câu 5b:!+.-<@"a, b, cDEF"E"x, y, zGD
EF"E3 
x a bc
2
= −

y b ca
2
= −

z c ab
2
= −
&

Câu 6b:
+("
y x x.sin=
&+.-< 
xy y x xy2( sin ) 0
′ ′′
− − + =
&
+(+ 
y x x
3 2
3 2= − +
&A@BC-@2@)+@@2@3413
B>H
y = x
1
1
3
− +
&
IIIIIIIIIIIIIIIIIIII9@IIIIIIIIIIIIIIIIIII
Họ và tên thí sinh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD . . . . . . . . . .
!
Đề số 15
ĐÁP ÁN ĐỀ THI THỬ HỌC KÌ 2 – Năm học 2010 – 2011
Môn TOÁN Lớp 11

Câu Ý Nội dung Điểm
1 
2

3 3
3 3
lim lim
( 3)( 1)
2 3
x x
x x
x x
x x
→− →−
+ +
=
+ −
+ −
&J
3
1 1
lim
1 4
x
x
→−
= −
−
&J

( )
→− →−
+ − − +
=

+
+ + +
x x
x x x
x
x x
2
2 2
2
5 3 ( 2)( 2)
lim lim
2
( 2) 5 3
&J
2 2
2 4 2
lim
6 3
5 36
x
x
x
→−
− −
= = = −
+ +
&J
2
x x
khi x

f x
x
a khi x
2
7 10
2
( )
2
4 2

− +

≠
=

−

− =

2
2 2 2 2
7 10 ( 2)( 5)
lim ( ) lim lim lim( 5) 3
2 2
x x x x
x x x x
f x x
x x
→ → → →
− + − −

= = = − = −
− −
J
f%KLa
 f x
#$x%⇔
2
lim ( ) (2) 4 3 7
x
f x f a a
→
= ⇔ − = − ⇔ =
:@D3a%"#$x%&
J
3 
2 3 5 3 2
( 1)( 2) 2 2y x x y x x x= − + ⇒ = − + −
J
4 2
' 5 3 4y x x x⇒ = − +
J

4 3
2 2
2 2 2 2
2 1 2 1 14
' 4
3 3 ( 3)
x x x
y y

x x x
   
+ + −
= ⇒ =
 ÷  ÷
 ÷  ÷
− − −
   
J
− +
⇒ =
−
x x
y
x
2 3
2 5
56 (2 1)
'
( 3)
J
4
J

+.-< 0+⊥+:/0′⊥+9:&
′ ′ ′
⊥ ⊥ ⇒ ⊥ ⇒ ⊥BC AC BC AA BC C C BC CK, (AA )
J
′ ′
⊥ ⇒ ⊥ ⊥ ⇒ ⊥AB A B KH A B KH AB CH AB AB CHK, ' ', ' ' ( )P

J

'1=5>//′0′03+9:&
+1
' ( ), ' ( ' ' ) ( ' ' ) ( )AB CHK AB AA B B AA B B CHK⊥ ⊂ ⇒ ⊥
J
0
(( ' ' ),( )) 90AA B B CHK =
J

 '7(?6/@5>+9:&
M1
' ( )( )AB CHK cmt⊥
9#
( ,( ))d A CHK AH=
J
( ), ' ( : ) ( ' ' ) 'AC BC gt CC AC gt lt AC CC B B AC CB⊥ ⊥ ⇒ ⊥ ⇒ ⊥
J
= + = + = = +
2 2 2 2 2 2
, ' 2 2 2AB AC BC a b AB AB a b
J
-(∆/+0N34+ 
′ ′
⊥ ⇒ =
2
.CH AB AC AH AB
2 2 2
2 2
'

2
2( )
AC a a
AH
AB
AB
a b
⇒ = = =
+
J
5a
1
2
2 1
2 1
1.
1 2 2 2
2 1
lim lim
1 3 3 3 3 1
1.
3 1
n
n
n n
+
+
−
+ + + +
−

= =
+ + + + −
−
J
1
1
1
1
1
2 2
2.
3
2.2 2
3
lim lim 0
1
3 1
1
3
n
n
n
n
n
+
+
+
+
+
 

−
 ÷
−
 
= =
−
−
J
6a 
+("
y xsin(sin )=
&' 
y ( )
π
′′
&
= ⇒ = − −y x x y x x x x x' cos .cos(sin ) " sin .cos(sin ) cos .cos sin(sin )
J
π
⇒ = − − ⇒ =y x x x x y
2
" sin .cos(sin ) cos .sin(sin ) "( ) 0
J

+(+ 
y x x
3 2
3 2= − +
&
′

= −y x x
2
3 6
&O()+3-$Px/!Q
( ) ( )
− +B C1 3;0 , 1 3;0
J
@2@/!Q1R"1k%L*#S 
= − +y x3 3
J
@2@
( )
−B 1 3;0
1R"1k%T#S 
6 6 6 3y x= − +
J
@2@
( )
+C 1 3;0
1R"1k%T#S 
= − −y x6 6 6 3
J
5b +UV@"a, b, cD+W+"x, y, zGD+W+
3 
x a bc
2
= −

y b ca
2

= −

z c ab
2
= −
&
a, b, c F"E#
+ =a c b2
12%
2 2 2
2 2 , ( )b ca x z a c b a c− + = + − +
J
⇒
2 2 2 2 2
( ) 2 2 4 2 2 2 2 2x z a c ac b b ac b b ac y+ = + − − = − − = − =

J
6b 
+("
y x x.sin=
&+.-< 
xy y x xy2( sin ) 0
′ ′′
− − + =
&
1
= + ⇒ = + − = −y x x x y x x x x x y' sin cos " cos cos sin 2cos
J
′ ′′
⇒ − − + = − + − + −xy y x xy xy x x x x x x y2( sin ) 2(sin cos sin ) (2cos )

J

= 0
J

+(+ 
y x x
3 2
3 2= − +
H
y = x
1
1
3
− +
&
A@2@3413H 
y = x
1
1
3
− +
#R"1)@2@k%*
J
OX
x y
0 0
( ; )
(E)@&
⇒

′
= ⇔ − − = ⇔ = − = +y x x x x x
2
0 0 0 0 0
( ) 3 3 6 3 0 1 2; 1 2
J
A
= − ⇒ = ⇒ = + −x y PTTT y x
0 0
1 2 2 : 3 4 2 3
J
A
= + ⇒ = − ⇒ = − −x y PTTT y x
0 0
1 2 2 : 3 4 2 3
J
*