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S GIO DC V O TOTHNH PH CN TH

K THI TUYN SINH LP 10 THPTNM HC 2012-2013Kha ngy:21/6/2012

MN: TONThi gian lm bi: 120 pht(khng k thi gian pht )

Cu 1: (2,0 im)Gii h phng trnh , ccphng trnh sau y:

1.

43

3 2 19

x y

x y

2. 5 2 18x x

3.2 12 36 0x x

4. 2011 4 8044 3x x Cu 2: (1,5 im)

Cho biu thc:2

1 1 12 :

1

aK

a aa a

(vi 0, 1a a )

1. Rt gn biu thcK.

2. Tm a 2012K .

Cu 3: (1,5 im)Cho phng trnh (n sx): 2 24 3 0 *x x m .1. Chng minh phng trnh (*) lun c hai nghim phn bit vi mi m.2. Tm gi tr ca m phng trnh (*) c hai nghim 1 2,x x tha 2 15x x .

Cu 4: (1,5 im)Mt t d nh i tAnBcch nhau 120 km trong mt thi gian quy nh. Sau khi i c 1

gi th t b chn bi xe cu ha 10 pht. Do n Bng hn xe phi tng vn tc thm 6km/h. Tnh vn tc lc u ca t.

Cu 5: (3,5 im)Cho ng trn O , t im A ngoi ng trn v hai tip tuyn AB vAC( ,B Cl cc tipim). OActBCti E.1. Chng minh t gic ABOCni tip.2. Chng minh BCvung gc vi OA v . .BA BE AE BO .3. GiI l trung im ca BE, ng thng quaI v vung gc OI ct cc tia ,AB ACtheo th

t ti D v F. Chng minh IDO BCO v DOF cn ti O .4. Chng minh Fl trung im caAC.

GI GII:Cu 1: (2,0 im)

Gii h phng trnh , cc phng trnh sau y:

1.43 2 2 86 5 105 21

3 2 19 3 2 19 43 22

x y x y x x

x y x y x y y

2. 5 2 18 ; : 9x x K x

23( )

5 2 18 135 2 18 ( )

3

x TMK

x xx x x KTMK

3.2 2

12 36 0 ( 6) 0 6x x x x

CHNH THC

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4.2011 4 8044 3; : 2011

3 2011 3 2012( )

x x K x

x x TMK

Cu 2: (1,5 im)

Cho biu thc:2

1 1 12 :

1

aK

a aa a

(vi 0, 1a a )

2

1 1 1 1 1

2 : 2 : ( 1)1 ( 1)

1 1 12 : 2 : ( 1) 2

( 1) ( 1) ( 1)

a a a a

K a a a aa a a a

a a aa a a a a a

2012K 2 a = 2012 a = 503 (TMK)

Cu 3: (1,5 im)Cho phng trnh (n sx):.

1.

2 2

2 2

4 3 0 *

16 4 12 4 4 4 0;

x x m

m m m

y (*) lun c hai nghim phn bit vi mi m.2. Tm gi tr ca m phng trnh (*) c hai nghim 1 2,x x tha 2 15x x .

Theo h thc I-ET c :x1.x2 = - m2 + 3 ;x1+ x2 = 4 m 2 15x x => x1 = - 1 ; x2 = 5

Thay x1 = - 1 ; x2 = 5 vo x1.x2 = - m2 + 3 => m = 2 2

Cu 4: (1,5 im)

Gi x (km/h) l vt d nh x 0 = Thi gian d nh :120

( )hx

Sau 1 h t i c x km = qung ng cn li 120 x ( km)t lc sau: x + 6 ( km/h)

Pt1 120 120

16 6

x

x x

= x = 48 (TMK) = KL

HD C3

Tam gic OC cn ti O = gc OC = gc OCT gic OID c gc OID = gc OD = 00 nn OID ni tip = gc ODI = gc OI

Do IDO BCO Li c FIOC ni tip nn gc IFO = gc ICOSuy ra gc OPF = gc OFP vy DOF cn ti O .

HD C4

t t gic PFE c I = IE IP = IF ( Tam gic OPF cn c OI l ng cao= ) Nn PEF l Hnh bnh hnh = P // FETam gic C c E = EC // FE nn EF l T ca tam gic C = F = FC