Đề thi tuyển sinh vào lớp 10 THPT (6)

SỞ GIÁO DỤC VÀ ĐÀO TẠO KỲ THI TUYỂN SINH LỚP 10 THPT
TP. Hà Nội MÔN : TOÁN - Năm h'c : 2011 – 2012
22 tháng 6 năm 2011
Thời gian làm bài: 120 phút
Bài I(2,5 điểm)

x 10 x 5
A
x 25
x 5 x 5
= − −
−
− +

x 0, x 25≥ ≠


 !"#$%&
'()$*
1
A
3
<

Bài II (2,5 điểm)Giải bài toán sau bằng cách lập phương trình hoặc hệ phương trình:
+,*,$--#./0.123),456* 7
)8*,*90:;<)=3>*,*?#./4)@A"
6* :0>)*;<23BC-#./*,$-0."
>D
Bài III (1,0 điểm)E""FGE
2

y x=
:*;AHGI
2
y 2x m 9= − +

()/*,"*)!"E""FGE:*;AHGI#)%
())**;AHGIJE""FGE/"*)K):L"M"!"N
Bài IV (3,5 điểm)
*;AOP)QR*;A#S%TI

:I

F"U.M.!"*;A
OGQ/"*):STVF*)!"Q:WF*),*;AOGQ
GW#XY::SZ;AHI*6"*)W::X9:WVJ"
*;AHI

:I

F[F;</+R
)+WVF,U.M
)
ENI EBI∠ = ∠
:
0
MIN 90∠ =

')+S%VSV
1T\F*)]"!"S#X"W!"*;AOGQB?
^I_^!"")+V-#"*)WRVR\H

Bài V (0,5 điểm)   $  `  2R  a)      C  3  !"    
2
1
M 4x 3x 2011
4x
= − + +

HƯỚNG DẪN GIẢI
Bài 1:
bZc
x 0, x 25≥ ≠
( ) ( )
( ) ( ) ( ) ( )
x. x +5 -10 x -5. x -5
x 10 x 5 x+5 x -10 x -5 x +25
A= - - = =
x-25
x -5 x +5
x -5 x+5 x -5 x +5
( ) ( )
( )
( ) ( )
2
x -5
x-10 x +25 x -5
= = = ( x 0; x 25)
x +5
x -5 x +5 x -5 x +5
≥ ≠
b$%&C")?

x 0, x 25≥ ≠
R>$* *;<R"9
3
=
x
d
4
1
8
2
53
53
−=
−
=
+
−
=
A
'b"9Zc
x 0, x 25≥ ≠

( )
( )
1 x - 5 1 3 x - 15 - x - 5
A - 0 0
3 3
x + 5
3 x +5
2 x - 20 0 (Vì 3 x +5 0) 2 x < 20 x < 10 x < 100

< ⇔ < ⇔ <
⇔ < > ⇔ ⇔ ⇔
c.<M:
x 0, x 25≥ ≠
d:2e$f22:$g=(fb'
Bài 2
TA"*,$-0.-#./F$GGZc$`
(A"h.*,$-*90.F$iG
+8-#./*,$-*9Mj0*;<
140
x
G3
h.*,*9*?0*;<12k2%=2G3>)8*,*90*;<
150
1x −
G3
(h.)8*,*90:;<)=3R>"9M
150 140
5
1x x
− =
−
⇒=2$i12$k12%=$

l=$⇔=$

l=$i2$l12%2⇔=$

l=$l12
%2

⇔$

l'$lm%2Tj"$%nGb+:$%l1GF/
dA"*,$-*90.-#./Fn
Bài 3:
b)%"9GI%$km
E;@(*,*)!"GE:GIF
$

%$kmf%`$

i$im%2
Tj"$%1%`%o
$%l%`%1
"*,"*)!"GE:GIFG1po:Glp1
bE;@(*,*)!"GI:GEF$

i$k)

i&%2G
ZGIJGE/"*)MP_K):L"M"!"N(M;@(G
9"_)I3
⇒"f2⇒)

i&f2⇒G)i'G)k'f2
Tj"9i'f)f'
Bài 4
bqrVW+9
9+V%9+WV%&2



%`9+Vk9+WV%m2


+90: *5I_
%`VW+,U.M
bqrSVW9
9VW%9VS%&2


 9VWk9VS%m2


 VSW,U.M
 9WV%9WSV%s4*VWGt
 7+WV,U.M
%`9W+V%9WV%s4*WSGtt
uGt:Gtt4"
9W+Vk9WV%s4*S%&2


'bqr"):X+V:"):XSV9
9V+%9SVGY,:9VS%&2


 ∆+Vv∆SVGl

BN
AI
BI

AM
=
 +S%VSV
1bcVRWR\H"9(:w
7+WV,U.M
>9+V%9W\%1=


>")+V:XP/
);@h"9")SV:XP/S
 +%VRSV%S
xMINE"^*;<
2
23
;
2
2 R
IN
R
MI
==
d
4
3

2
1
2
R
INIMS

MIN
==
G*:I
Bài 5:

2 2 2
1 1 1
4 3 2011 4 4 1 2010 (2 1) ( ) 2010
4 4 4
M x x x x x x x
x x x
= − + + = − + + + + = − + + +
(
2
(2 1) 0x − ≥
:$`2
1
0
4x
⇒ >
RxMINI445I;@"9$k
1
4x
1 1
2 . 2. 1
4 2
x
x
≥ = =
 +%

2
1
(2 1) ( ) 2010
4
x x
x
− + + +
≥2kk22%2
 +≥2p73y%z$j"
2
1
2
1
2 1 0
2
1 1
1
4 4
2
0
0
1
2
0
x
x
x
x x
x
x

x
x
x
x

=



=

− =





  

= ⇔ = ⇔
=
  

  

>
>
  



= −
 




>


⇔$%
1
2
d+
)
%2*/*;<#$%
1
2
Bài 5: 
2 2 2
2
2
1 1 1 1 1
4 3 2011 3 2010
4 4 8 8 4
1 1 1 1
3 2010
2 8 8 4
M x x x x x
x x x
M x x

x x
 
= − + + = − + + + + + +
 ÷
 
 
= − + + + + +
 ÷
 
xMINX4"45
xx
x
8
1
,
8
1
,
2
"9
4
3
8
1
.
8
1
.3
8
1

8
1
3
22
=≥++
xx
x
xx
x
73{%|$}"#$%b
)
0
2
1
≥






−
x
73{%|$}"#$%b
d
20112010
4
1
4
3

0
=+++≥
M
d C3!"+K2#+%
1
2