KÌ THI TUYỂN SINH LỚP 10 NĂM HỌC 2011-2012
KHÓA THI ngày 29-6-2011
MÔN : TOÁN
Thời gian làm bài: 120 phút (không kể thời gian giao đề)
Bài 1:  
2 9 3 16+

 !"
!#

$%#&'()%

*
4023
1
x y
x y
+ =


− =

 
Bài 2:  
+, -.)#

/0123456.)#&
!78369:;,<;=#.
*>?@.A,<;!,B!36
,:;,<;=#.,CDEFE>GCEG+GE+HCDI>I+
JK5

CLMN*"H
2
1
x x x
M
x x x
−
= +
− −
O
0; 1x x> ≠
Bài 3:P!*Q KR!"J!;!K#"K6ST*QDQ*Q>I<
*Q>U%M0V6ST*Q>WX*QDY;2C4Z[-B!!KJ
O.92\I*Q[-B!6SO2CJ]
Bài 4: C+,^!4S_=4JZD>`;+-1";,<5D=
+JRD+JR=a45b"!+"K/OD=c^!4S@,<d
9">d2e.`O`JR>`JRdQ".QB!^!4S@,<`c
45+d<fNg2!,B!D`+d
+H>+g`2HR;hQ4S
+Hf`)fg
CNi2_4S,<hQ!Rgd`+HdIiI>5ET/ ".!/D>i
/ -,JKYJ`!.Y9">d
Bài 5%+,j# 
( )
2
2 3 0x m x m− + + =
N#
 
#
 

2!B!
@,R1B!*"H
2 2
1 2
x x+

/R1ke


HẾT
HƯỚNG DẪN GIẢI ĐỀ CHÍNH THỨC
KÌ THI TUYỂN SINH LỚP 10 NĂM HỌC 2011-2012
MÔN : TOÁN
Bài 1:

2 2
2 9 3 16 2 3 3 4 2. 3 3. 4 2.3 3.4 6 12 18+ = + = + = + = + =
 !"
!
2
20 96 0x x− + =
2
' 10 1.96 100 96 4 0; ' 4 2∆ = + = − = > ∆ = =
3/_*
1
10 2
12
1
x
+

= =
E
2
10 2
8
1
x
−
= =
7[.[B!2
{ }
12;8S =

*
4023 2 4024 2012 2012
1 1 2012 1 2011
x y x x x
x y x y y y
+ = = = =
   
⇔ ⇔ ⇔
   
− = − = = − =
   
Bài 2: 1)
!78
( )
2
:P y x=
>R1l!#.

x -2 -1 0 1 2
y 4 1 0 1 4
78
( )
: 2d y x= +
6
4
2
-2
-4
-6
-10
-5
5
10
( )
( )
0 2: 0;2
0 2 : 2;0
x y A
y x B
= ⇒ =
= ⇒ = − −
*3,;!,B!362

( )
2 2
2 2 0 1x x x x= + ⇔ − − =
7
0a b c

− + =
9/!2
1 2
1; 2x x= − =
m7O
1 1
1 1x y= − ⇒ =
m7O
2 2
2 4x y= ⇒ =
7[.N!;!,B!362
( )
1;1−

( )
2;4
345D>/6<
( )
y ax b d= +
7
( )
2;4A

( )
3; 1B − −
";69!/
4 2 5 5 1
1 3 4 2 2
a b a a
a b a b b

= + = =
  
⇔ ⇔
  
− = − + = + =
  
7[.45D>2
2y x= +
!.
2; 1x y= − =
,45D>!/
1 2 2 1 0
= − + ⇔ =
K2Zn".!
( )
2;1C −
JK
";45D>!.*!
( ) ( ) ( )
2;4 ; 3; 1 ; 2;1A B C− − −
JK5
C
2
1
x x x
M
x x x
−
= +
− −

O
0; 1x x> ≠

( )
( )
( )
2
2 1 1
2 2 1 2 1
1
1 1 1 1 1 1
1
x x x
x x x x x x x x
M x
x x x x x x x x
x x
− −
− − − −
= + = + = − = = = −
− − − − − − −
−
7[.
1M x= −
O
0; 1x x> ≠

Bài 3: aY
1
20

3
ph h=
N[-B!!KJO.92\2#J]IJ#oC
7[-!K2M#"K6S2
( )
3 /x km h+
7[-!K2MV6S2
( )
3 /x km h−
4!!K#"K6STDQ>2
( )
15
3
h
x +
4!!KV6ST>XD2
( )
15
3
h
x −
74!!K#"K6SIV6SIJ!4!U2C4d,/!/
( )
15 15 1
3 1
3 3 3x x
+ + =
+ −
`+
( ) ( )

3 3 3x x+ −
p"00J^q"!V
( ) ( ) ( ) ( ) ( ) ( )
45 3 45 3 3 3 9 3 3x x x x x x− + + + − + = − +
2 2 2
45 135 45 135 9 9 81 8 90 72 0x x x x x x− + + + − = − ⇔ − − =
2
1 2
' 45 8.72 2061 ' 2601 51
45 51 45 51
12; 0,75
8 8
x x
∆ = + = ⇒ ∆ = =
+ −
= = = =
a-Q"OX"J#oC!e.U/#)k!@
7[.7[-B!!KJO.92\2J]
>F
GT
Nữa đường tròn (O) đường kính AB
C cố định và
C OA
∈
( )
M O∈
; ME là tiếp tuyến của (O)
CD OA⊥
I là tâm đường tròn ngoại tiếp
FDM∆

KL
a) BCFM là tứ giác nội tiếp đường tròn
b) EM = EF
c) D, I, B thẳng hàng; từ đó suy ra góc ABI có số đo không
đổi khi M thay đổi trên cung BD.
I
H
F
E
D
O
A
B
M
C
+H!!/
( )
M O∈
4JZD> ".!
·
0
90AMB =
/;hQcl!
4S!.
·
0
90FMB =
`\JR
·
0

90 ( )FCB GT=
d,/
·
·
0
180AMB FCB+ =
n".!>+g`
2HR;hQ4S
*!/>+g`2HR;hQ
·
·
( )
EFM 1CBM⇒ =
:*:O
·
CFM

`\JR
·
·
( )
EMF 2CBM =
/;hQ/<,*WhQ".Q6_.":c
¼
AM

( ) ( )
·
·
1 & 2 EFM EMF EFM⇒ = ⇒ ∆

_<f
EFEM⇒ =

N1P2"B!dgdre.
IH DF⊥

·
·
( )
IF
3
2
D
HID =

,4S
( )
I
!/
·
·
IF
2
D
DMF =
/;hQ/W_:c
»
DF
!.
·

·
( )
IF
4
2
D
DMA =
,4S
( )
O
!/
·
·
( )
5DMA DBA=
/;hQ:c
»
DA
s
( ) ( ) ( )
·
·
3 ; 4 ; 5 DIH DBA⇒ =
dre.
·
·
0
90CDB DBA= −

·

·
0
90HDI DIH= −
`
·
·
( )
DIK DBA cmt=
n".!
·
·
CDB HDI=
!.
·
·
; ;CDB CDI D I B= ⇒
5
!/D; I;B 5(cmt)
·
·
»
2
AD
ABI ABD sd⇒ = =
7+-19d-1
»
2
AD
sd⇒
JK

Y
d,//D>i/ -,JKYJ`!.Y9">d
Bài 5+,j#
( )
2
2 3 0x m x m− + + =
N
1
x

2
x
 
2!B!
@,R1B!*"H
2 2
1 2
x x+
/R1ke


3
( ) ( )
2
2 3 0 1x m x m− + + =
2*[!I/
( )
2
2 2 2 2
9 5

– 2m 3 4. 4 12 9 4 4 8 9 4 2 4 2 1
4 4
m m m m m m m m m m
   
 
∆ = + − = + + − = + + = + + = + + +
 ÷  ÷
 
   

( ) ( )
2 2
5
4 1 4 1 5 0
4
m m
 
∆ = + + = + + >
 
 
ONn".!
( )
1
2"K/!_
*/N
t6uH7vI!V
1 2
1 2
2 3
.

S x x m
P x x m
= + = +


= =

( ) ( )
2 2
2 2 2 2 2
1 2 1 2 1 2
2 2
2
5 9
2 2m 3 2 4 12 9 2 4 10 9 4
2 4
5 25 11 5 11 5 11 11
4 2. . 4 4
4 16 16 4 16 4 4 4
x x x x x x m m m m m m m m
m m m m
 
+ = + − = + − = + + − = + + = + +
 ÷
 
 
     
= + + + = + + = + + ≥
 
 ÷  ÷  ÷

     
 
 
de"w)x#.!J
5 5
0
4 4
m m+ = ⇔ = −
7[.R1keB!*"H2
2 2
1 2
x x+
2
11
4
J

5
4
m = −