Đề thi tuyển sinh vào lớp 10 THPT (2)

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9:;
(Đề thi có 01 trang)
9
+2$2 điểm
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!"#$%&'()*+,-
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!
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,
!
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+2%$ điểm
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!;

0<0 =
!

− =

+ =

x 2y 4
2x 3y 1
+2<$ điểm
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!
( )
= +A 32 3 18 : 2
!
− +
= −
− +
15 12 6 2 6
B
5 2 3 2
+2=$< điểm
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!"EF)J
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!A4FK1FL;>

1
!
=
R
OH
2
*U(4P.SV>1
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+2$2 điểm
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=YQY=
ZO'4N6'=Q,Q=
!ZO',0
!
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''
!
,
≠

!
⇔ − = − ≠ ⇔ = − ≠ −
1
1 2m vaø 2 n m vaø n 2
2
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!;

0<0 =';Q<Q 
∆ = − = − = > ⇒ ∆ = =
2 2
b 4ac 4 4.3.1 4 0 4 2
K9#24:%C4:/
− − ∆ − − − + ∆ − +
= = = − = = = −
1 2

b 4 2 b 4 2 1
x 1;x
2a 2.3 2a 2.3 3
@D@/'0;<0 =
K9#24:%C4:/
= − = − = −
1 2
c 1
x 1;x
a 3
!
   
− = − = − = = −
⇔ ⇔ ⇔
   
+ = + = + = =
   
x 2y 4 2x 4y 8 7y 7 y 1
2x 3y 1 2x 3y 1 2x 3y 1 x 2
\:%9#2(4:1"%4:
( )
{ }
= −
S 2; 1
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!
( ) ( )
= + = + = =A 32 3 18 : 2 4 2 9 2 : 2 13 2 : 2 13
!

( ) ( )
− +
− +
= − = − = −
− + − +
3 5 4 12 3 2
15 12 6 2 6
B 3
5 2 3 2 5 2 3 2
+2=$< điểm
 !FJHI%6IO')
·
⇒ =
o
ABO 90
ABO∆
,6MP4J)F)J
]
ABO∆
^''4@_6P)F
·
⇒ =
o
AOB 60
@D@/
ABO
∆
,6MP4J
· ·
= = = ⇒ =

o
OB R 1
cosAOB AOB 60
OA 2R 2
!'!.#643O'KL
⇒ ⊥OH PQ
P4.
"A4@).FJ
·
·
+ = + =
o o o
ABO AHO 90 90 180
]A4@).FJ(4HI%1
\<43)Q.QJQFT6((#B1
!`a
∆ABP
,
∆AQB

µ
A
6
·
·
»
= =
1
ABP AQB sñBP
2

Pb4H'HI%6I,C6,54
(4HI%TR(6
]
∆ ∆ −ABP AQB(g g)∽
⇒ = ⇒ =
2
AB AP
AP.AQ AB (1)
AQ AB
c$D@
ABO
∆
,6MP4J*VEK4W'W
"'
( )
= + ⇒ = − = − =
2
2 2 2 2 2 2 2 2
OA AB OB AB OA OB 2R R 3R (2)
"G ,
⇒ =
2
AP.AQ 3R
!
AHO
∆
,6MP4.*VEK4W'W
"'  
( )
 

= + ⇒ = − = − =
 ÷
 
2
2
2
2 2 2 2 2 2
R 15R
OA AH OH AH OA OH 2R
2 4
⇒ =
R 15
AH
2
`a
∆
AKC
,
∆
ACH
'/
µ
A
6
FJFUO'HI%6IR'6
⇒ ∆ABC
CP4F
·
·
⇒ =ACK ABC

c$D@
·
= ⇒
o
ACO 90
6(#BP4HI%A4@).FJ
·
·
»
⇒ = =
1
ABC AHC sñAC
2
(4HI%O'#BP4HI%A
4@).FJ
]
·
·
=ACK AHC
\
∆ ∆ −AKC ACH(g g)∽
⇒ = ⇒ = = = =
2 2
AK AC AC 3R 6R 6R 15
AK
AC AH AH 15
R 15 15
2
= − = − =
R 15 6R 15 R 15

HK AH AK
2 15 10

GHE
I#!J)!1!K#
9
 !"#%L%%
/F$
"44'/ =%?(không kể thời gian giao đề)
Z_= #'
MN(3,0 điểm)
'7484%9#2/
2
6 9 0x x
− + =

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4 3 6
3 4 10
x y
y x
− =


+ =

7484%9#2/
2
6 9 2011x x x
− + = −

MN%(2,5 điểm)
c('MP6M4BGFIJ#4PdBGJIFI
8<41"E,'MD45e$*4I#fN6+MFJ4;=
D,,B5<D!41
MN<(2,5 điểm)
"#e#B)'443c*g'c*)*gDM1.'4
HI%6IP4c*g,54#B)R'6P4F1"G)Dh,6M
,54)cRFgP4i1"GFDh,6M,54FcR)gP4j1A
4/
'i)iF
"'4@)jFC
MN=(2,0 điểm).
'"24:6eO'%9#2/

0

00;<=
'4@FJ,6MP4F17&4j4'43@%C4@
#1J4IFJk*jl1"EJ1

WWWWWWWWW.IWWWWWWW
OP)*QR)#!S T62UNV2U
/F$
W2QN)*
2U
MN(3,0 điểm)
4X2Y27!OZ)*1[\)!$
2
6 9 0x x
− + =

 T
Bài giải:"'
' 2
( 3) 9 0∆ = − − =

0,5
K9#24:/
6
3
2
x
−
=− =

0,5
6X2Y2!]7!OZ)*1[\)!$
4 3 6 (1)
3 4 10 (2)
x y
y x
− =


+ =

T
Bài giải:( ,'/<W;0;0< l
⇔
m l
⇔


0,5
"', /<1;l
⇔

2
3
1"%4:/
2
2
3
x
y
=



=


0,5
#X2Y27!OZ)*1[\)!$
2
6 9 2011x x x
− + = −
;
T
Bài giải:"'
( )
2

2
6 9 3 3x x x x
− + = − = −
0,5
c$D@/
2
6 9 0 2011 0 2011 3 3x x x x x x
− + ≥ ⇒ − ≥ ⇒ ≥ ⇒ − = −
\/;
3 2011 3 2011x x
⇔ − = − ⇔ − =
1K9#2,M4:
0,5
MN%(2,5 điểm )/W1#4)0#!^,_N02Q`)*1aEVb)[c2#!^,)*Od#Q`)*1aVb)
E!b11S1#Y=*23CJ)!ef)1g##4)0h!2)OP#,i)5j)*T62b1[k)*lNm)*n0)*EQ+2
<h e+ef)1g#Q`)*)OP#5+=h .*23C
%To
Bài giải: 7&4,O''MD45e$D!4Y< 0,5
\O''MD46M4B0<D!4*D4dBW<D!41
"44''M6M4BGFIJ
30
4x +
4*4dB
GJIF
30
4x −
41
0,5
"V4#''%9#2/
30 30

4
4 4x x
+ =
+ −
< 0,5
2
( 4) 30( 4) 30( 4) 4( 4)( 4) 15 16 0 1x x x x x x x
⇔ − + + = + − ⇔ − − = ⇔ =−
$
 l1g4:W n=eP4
0,5
\,O''MD45e$ lD!41 0,5
MN< (2,5 điểm) [i)VO3)*1[`)pX5S,!42V2U /Tn4'#!'/TTh!0)*
1!q)*!+)*C42rb71N,b)1^2/TeP2VO3)*1[`)pX#s1)!4N1^2ECaht
VO3)*eN0)**u#eP2/#s1E1^2CaEhtVO3)*eN0)**u#eP2E/#s11^2
C!K)* 2)!$4XvEC6X4 *2(#E#M)
A
S
O
N
M
I
0,5
4X!K)* 2)!$Ev
T
\2Fc*Fg@HI%6Ie/
·
¶
MAO SAO
=

 
0,5
\2cF!!i)e/
¶
¶
MAO SOA
=
V#
0,5
"G ,'/
¶
¶
SAO SOA
=

⇒
∆
iF)C
⇒
iFi)1%11
6X!K)* 2)!14 *2(#E#M)
T
\2Fc*Fg@HI%6Ie/
·
·
MOA NOA
=
;
0,5
\2c)!!Fje/

·
¶
MOA OAI
=
V#<
0,5
"G;,<'/
µ
µ
IOA IAO
=

⇒
∆
)jFC1%11
MN=(2,0 điểm).
4X\ )*!2] )*N,i)#w47!OZ)*1[\)!$_
%
x%,
%
x%_,x<,&=v 
T
5
x
6
D
B
A
C
I

E
Bài giải: 
⇔


00

0

0;<=
0,5

⇔


0

0W 0<=

⇔
W 0<W

0


\2W

0



≤
=,54&4*e/W 0<
≤
=
⇔
W<
≤

≤

0,5
\26ee
∈

{ }
4; 3; 2; 1; 0; 1− − − −
"'@4@#6eO','od@$%4:6eQO'K"
+/<QW<* QW;*kQW;*WQ=*W Q 1
4X !'14 *2(#EeN0)*1^2EC"25+*24'V2U #(#VO3)*7!M)*2(#1[')*C
2b1Evo# Tvy# CJ)!C
6X
#X
Bài giải:
7&4]24I6,6MO'
#eJj*p4'
43O'FJ,]1
∆
Jj 
·
DIC

    4  e/ 
·
DIC

¶
¶
$
µ
0 0
1
( ) 90 : 2 45
2
IBC ICB B C+ = + = =
⇒
DIC∆
,6MC
⇒
]l/
2
c$D@J]%C4@
,'e'4@Jp
7&4JJp1Y=1q%rsK4W'W,@'4@,6MFJ,Fp
'/F

J

FJ




k



Wk
p

F

0Fp



Wk0k



 =
 /
2




 =
O,5
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