GII THI MễN TON KHI A
K THI TUYN SINH H C NM 2009
I. Phn chung cho tt c thớ sinh
Cõu I: (2,0)
Cho hm s:
x 2
y (1)
2x 3
+
=
+
1. Kho sỏt s bin thiờn v v th ca hm s (1).
2. Vit phng trỡnh tip tuyn ca th hm s (1), bit tip tuyn ú ct trc
honh, trc tung ln lt ti hai im phõn bit A, B v tam giỏc OAB cõn ti gc
to O.
Bi gii
( )
3
x
2
x
2
3
1. TXé: \
2
S bi n thiờn
x 2 3
Tỡm ti m c n ng: lim th hm s (1) cú ti m c n ng x
2x 3 2
x 2 1 1

+
ữ ữ

ố ị ế ự ị.
Bng bin thiờn
th:
bng bin thiờn ph
V th:

-4 -3 -2 -1 1 2 3 4
-4
-2
2
4
x
y
Nhn xột: th nhn giao im ca 2 tim cn l im
3 1
I ,
2 2


ữ

lm tõm i xng.
( ) ( )
2. G i A a;0 Ox; B 0;b Oy theo gi thi t ta cú: |a| |b|
nh ng vỡ hm s lu n ngh ch bi n nờn ti p tuy n ch cú th cú d ng
y kx m v i k < 0 nờn a b 0.
x y

= +

+





=

+

= =


= + =

+ = =

=
ạ
ừ ươ
ậ ươ ế ế ủ
Cõu II: (2,0 )
1. Gii phng trỡnh:
( )
( ) ( )
1 2sinx cosx
3
1 2sinx 1 sinx

cos x 2sinxcos x 3 1 sinx 2sinx 2sin x
cosx 2sinxcosx 3 2sin x sinx +1
cos x 3 sin x 3 cos2x s
π

≠ − + π



+ ≠
≠ −

π
 
⇔ ⇔ ≠ + π
  
− ≠

 
≠

π

≠ + π


−
=
+ −
⇔ − = − + −

= − +


⇔ ⇔


π π π


− = − + π
= + π




¹

( )
( )
3
3
3
2
3
3 2
2
3
2
3 2
2

+ =
 


− + =
 ÷

 

 
− + =
 ÷
 
⇔ − + − =
⇔ − − + =
⇔ =
−
Æ
¶ ­¬
564v 624 0 VN
u 2
6 5x 16 x 2
+ =
= −
⇔ − = ⇒ = −
Câu III: (1,0 đ)

( )
( )
/2

5 3 15
π
π π
π π
π
π
= −
= − = −
= =
= −
= − +
π
 
= − +
 ÷
 
= − + =
∫
∫ ∫
∫ ∫
∫
∫
¶
( )
/2 /2
2
2
0 0
1 2
1