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thi vo lp 10 mn Ton nm 2012 1

S GIO DC V O TO K THI TUYN SINH VO LP 10 THPT NM HC 2012NG NAI Kha ngy : 29 , 30 / 6 / 2012

Mn thi : TON HCThi gian lm bi : 120 pht( ny c 1 trang , 5 cu )

Cu 1 : ( 1,5 im )1 / Gii phng trnh : 7x2 8x 9 = 0 .

2 / Gii h phng trnh :3x+2y=1

4x+5y=6

Cu 2 : ( 2,0 im )

1 / Rt gn cc biu thc :12 +3 3 2 2

M ; N3 2 1

2 / Cho x1 ; x2 l hai nghim ca phng trnh : x2 x 1 = 0 .

Tnh :1 2

1 1+

x x.

Cu 3 : ( 1,5 im )Trong mt phng vi h trc ta Oxy cho cc hm s :

y = 3x2 c th ( P ) ; y = 2x3 c th l ( d ) ; y = kx + n c th l ( d1 ) vi k v n l nhng s thc .1 / V th ( P ) .2 / Tm k v n bit ( d1 ) i qua im T( 1 ; 2 ) v ( d1 ) // ( d ) .

Cu 4 : ( 1,5 im )Mt tha t hnh ch nht c chu vi bng 198 m , din tch bng 2430 m2 . Tnh chiu di v chiu

rng ca tha t hnh ch nht cho .

Cu 5 : ( 3,5 im )Cho hnh vung ABCD . Ly im E thuc cnh BC , vi E khng trng B v E khng trng C . V EF

vung gc vi AE , vi F thuc CD . ng thng AF ct ng thng BC ti G . V ng thng a i quaim A v vung gc vi AE , ng thng a ct ng thng DE ti im H .

1 / Chng minhAE CD

AF DE .

2 / Chng minh rng t gic AEGH l t gic ni tip c ng trn .3 / Gi b l tip tuyn ca ng trn ngoi tip tam gic AHE ti E , bit b ct ng trung trc ca

on thng EG ti im K . Chng minh rng KG l tip tuyn ca ng trn ngoi tip tam gic AHE .

CHNH THC

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thi vo lp 10 mn Ton nm 2012 2

HNG DN GII:

Cu 1 : ( 1,5 im )

1 / Gii phng trnh : 7x2 8x 9 = 0 ( x1,2 =4 79

7

)

2 / Gii h phng trnh : 3x+2y=14x+5y=6

( x ; y ) = (1 ; 2 )

Cu 2 : ( 2,0 im )

1 / Rt gn cc biu thc :12 +3 2 3 3

M 2 33 3

2

2 13 2 22 1

2 1 2 1

2 / Cho x1 ; x2 l hai nghim ca phng trnh : x2

x 1 = 0 .

S =b

1a

; P =c

1a

Nn : 1 2

1 2 1 2

11

1

x x1 1+

x x x x

Cu 3 : ( 1,5 im )1 / V th ( P ) .2 / ( d1 ) // ( d ) nn k = 2 ; n 3 v i qua im T( 1 ; 2 ) nn x = 1 ; y = 2 . Ta c phng trnh : 2 =

1.2 + n n = 0

Cu 4 : ( 1,5 im )Gi x ( m ) l chiu di tha t hnh ch nht ( 49,5 < x < 99 )Chiu rng ca tha t hnh ch nht l : 99 x ( m )Theo bi ta c phng trnh : x ( x 99 ) = 2430Gii c : x1 = 54 ( nhn ) ; x2 = 45 ( loi )Vy chiu di tha t hnh ch nht l 54 ( m )Chiu rng ca tha t hnh ch nht l : 99 54 = 45 ( m )

Cu 5 : ( 3,5 im )1 / Chng minh t gic AEFD ni tip

1 1

A D

AEF DCE ( g g )AE AF

=DC DEAE DC

=AF DE

2 / Ta c 2A ph vi

1A

Ta c 1E ph vi

1D

M 1 1A D

1

2

1

1

KI

b

a

GH

F

E

DC

BA

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thi vo lp 10 mn Ton nm 2012 3

2 1

A E Suy ra t gic AEFD ni tip ng trn ng knh HEGi I trung im ca HE I l tm ng trn ngoi tip t gic AEFD cng l ng trn ngoi tip

AHE I nm trn ng trung trc EG IE = IGV K nm trn ng trung trc EG KE = KGSuy ra IEK = IGK ( c-c-c )

0IGK IEK 90 KG IG ti G ca ng trn ngoi tip AHE

KG l tip tuyn ca ng trn ngoi tip AHE