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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