de thi ts lop 10 tinh phu tho 20122013

7/29/2019 De Thi TS Lop 10 Tinh Phu Tho 20122013

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Nguyn Thanh Tun Ton hc + ng dng TP Quy Nhn Tnh B

Cu1 (2)a) Gii phng trnh 2x-5=1b) Gii bt phng trnh 3x-1>5

Cu2 (2)

a) Gii h phng trnh

72

33

yx

yx

b) Chng minh rng 7

6

23

1

23

1

Cu 3 (2)Cho phng trnh x2 -2(m-3)x 1 =0

a) Gii phng trnh khi m=1b)Tm m phng trnh c nghim x1 ; x2 m biu thc

A=x12 x1x2 + x2

2 t gi tr nh nht? Tmgi tr nh nht .

Cu 4 (3)

Cho tam gic ABC vung ti A. Ly B lm tmv ng trn tm B bnknh AB.Ly C lm tmv ng trn tm C bn knh AC, hai ng trnny ct nhau ti im th 2 l D.V AM, AN ln lt l cc dy cungcang trn (B) v (C) sao cho AM vung gc vi AN v D nm gia M; N.

a) CMR: ABC=DBCb)CMR: ABDC l t gic ni tip.c) CMR:ba im M, D, N thng hngd)Xc nhv tr ca cc dy AM; AN ca ng trn (B) v (C) sao

cho on MN c di ln nht.

Cu 5 (1) Gii H PT

yxyxyxyx

yyx

2)324(12)142(

385 22

---------------------------Ht--------------------------

S GIO DC V O TOPH TH

KTHI TUY N SINHVO LP 10 TRUNG HC PHTHNG

NM HC 2012-2013Mn ton

Thi gian lm bi: 120 pht, khng k thi gian giao thi c 01 trang

-------------------------------------------


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Cu1 (2) a) Gii phng trnh 2x-5=1b) Gii bt phng trnh 3x-1>5

p n a) x=3 ; b) x>2

Cu2 (2) a) Gii h phng trnh

72

33

yx

yx

b) Chng minh rng76

23

1

23

1

p n a) x=2 ; y= -3

b) VT =76

22323

=VP (pcm)

Cu 3 (2) Cho phng trnh x2 -2(m-3)x 1 =0c) Gii phng trnh khi m=1d)Tm m phng trnh c nghimx1 ; x2 m biu thc

A=x12 x1x2 + x2

2 t gi tr nh nht? Tmgi tr nh nht .p n a) x1 = 52 ; x2 = 52

e)Thy h s ca pt : a=1 ; c=-1 =>pt lun c 2 nghimTheo vi-t ta c x1 + x2 =2(m-3) ; x1x2 = -1M A=x1

2 x1x2 + x22 = (x1 + x2 )

2 - 3x1x2 = 4(m-3)2 + 3 3

=> GTNN ca A = 3m=3Cu 4 (3) Cho tam gic ABC vung ti A. Ly B lm tmv ng trntm B bn knh AB.Ly C lm tmv ng trn tm C bn knh AC, hai

ng trn ny ct nhau ti im th 2 l D.V AM, AN ln lt l cc dycung ca ng trn (B) v (C) sao cho AM vung gc vi AN v D nmgia M; N.

e) CMR: ABC=DBCf) CMR: ABDC l t gic ni tip.g)CMR:ba im M, D, N thng hngh)Xc nhv tr ca cc dy AM; AN ca ng trn (B) v (C) sao

cho on MN c di ln nht.Hng dn

a)C AB=DB; AC=DC; BC chung =>

ABC=

DBC (c-c-c)b)ABC=DBC => gc BAC=BDC =90 => ABDC l t gic ni tip


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2

1

43

21

21

4

32

1

2

1M

DN

CB

A

c) C gcA1 = gcM1 ( ABM cn ti B)gcA4 = gcN2 ( ACN cn ti C)gcA1 = gcA4 ( cngph A2;3 )gcA1= gcM1=gcA4= gcN2gcA2 = gcN1 ( cng chn cung AD ca (C) )

Li c A1+A2+A3=900 => M1+N1+A3 = 900MAMN vung ti A => M1+N1+M2 = 90

0=> A3=M2 => A3 = D1

CDN cn ti C => N1;2= D4D2;3+ D1 + D4 =D2;3+D1 +N1;2 =D2;3+ M2 + N1 + N2

= 900 + M2 + N1 + M1( M1 =N2)=900 +900 =1800

M; D; N thng hng.d) AMN ngdngABC (g-g)

Ta c NM2

= AN2

+AM2

NM ln nht th AN ; AM ln nhtM AM; AN ln nht khi AM; AN ln lt lng knhca (B) v (C)Vy khi AM; AN ln lt lng knhca (B) v (C) th NM ln nht.


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Cu 5 (1) Gii H PT

yxyxyxyx

yyx

2)324(12)142(

385 22

Hng dn

yxyxyxyx

yyx

2)324(12)142(

385 22

)2(2)1122(12)122(

)1(385 22

yxyxyxyx

yyx

T (2) t x+2y=a ; 2x-y-1 = b (a:b 0)Ta dc (2a-1) b=(2b-1) a ( ba )(2 )1ab =0 a=b

x=3y+1 thay vo (1) ta dc2y2 y 1=0 => y1 =1 ; y2 =-1/2

=> x1 =4 ; x2 = -1/2

Thy x2 + 2y2 =-1

de thi ts lop 10 tinh phu tho 20122013

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