S GIO DC V O TOK THI TUYN SINH VO LP 10 THPT
TNH B RA VNG TU
Nm hc 2009 2010
-------------------
----------------------- CHNH THC
Mn thi: TON
Ngy thi 02 thng 07 nm 2009
Thi gian lm bi thi: 120 phtBi 1: ( 2 im)
a\ Gii phng trnh : 2x2 3x 2 = 0
b\ Gii h phng trnh:
Bi 2: ( 2 im)
Cho hm s y=x2 c th l parabol (P) v hm s y= x+m c th l ng thng
(d)
a\ V parabol (P)
b\ Tm gi tr ca m (d) ct (P) ti hai im phn bit.
Bi 3: (2,5 im)
a\ Rt gn biu thc : M=
b\ Tm gi tr ca k phng trnh : x2 (5 +k)x +k = 0 c hai nghim x1;
x2 tha mn iu kin: x12 +x22 = 18Bi 4: (3 im):
Cho na ng trn tm O c ng knh AB = 2R. Ax; By l cc tia vung gc vi
AB( Ax, By v na ng trn cng thuc na mt phng c b l ng thng AB). Qua
im M thay i trn na ng trn ( M khc A v B), k tip tuyn vi na ng trn
ln lt ct Ax, By ti C v D.
a\ Chng minh t gic ACMO ni tip.
b\ Chng minh v
c\ Xc nh v tr ca M : AC + BD t gi tr nh nhtBi 5: (0,5 im)
Cho a+b, 2a v x l cc s nguyn. Chng minh y = ax2+bx +2009 nhn gi
tr nguyn.-----------Ht------------S GIO DC V O TOK THI TUYN SINH VO
LP 10 THPT
TNH B RA VNG TU
Nm hc 2010 2011
-------------------
----------------------- CHNH THC
Mn thi: TON
Ngy thi 02 thng 07 nm 2010
Thi gian lm bi thi: 120 phtCu I: ( 3 im)
1) Gii phng trnh : 2x2 + 3x 5 =0
2) Gii h phng trnh:
3) Rt gn: M =
Cu II: ( 1,5 im)
Cho phng trnh x2 mx 2 =0
1) Chng minh phng trnh c hai nghim phn bit vi mi gi tr ca m.
2) Gi x1; x2 l nghim ca phng trnh.
Tm cc gi tr ca m sao cho x12 +x22 3x1x2 =14
Cu III: ( 1,5 im)
Mt ca n chy vi vn tc khng i trn mt khc song di 30 km, c i v v ht
4 gi. Tnh vn tc ca ca n khi nc yn lng, bit vn tc ca dng nc l 4
km/h.
Cu VI: ( 3,5 im)
Cho tam gic ABC vung ti A ( AB>AC) Trn cnh AC ly im M (khc A
v C). ng trn ng knh MC ct BC ti E v ct ng thng BM ti D ( E khc C ;
D khc M).
1) Chng minh t gic ABCD ni tip.
2) Chng minh
3) ng thng AD ct ng trn ng knh MC ti N ( N khc D). ng thng MD ct
CN ti K, MN ct CD ti H. Chng minh KH song song vi NE.
Cu V: ( 0,5 im)
Tm gi tr nh nht ca : y=
---------------------HT-------------------S GIO DC V O TO
K THI TUYN SINH VO LP 10 THPT
TNH B RA VNG TU
Nm hc 2011 2012
-------------------
-----------------------
CHNH THC
Mn thi: TON
Ngy thi 08 thng 07 nm 2011
Thi gian lm bi : 120 pht ( khng k thi gian giao )
Bi 1: ( 3,0 im)
a) Rt gn: A =
b) Gii phng trnh : x2 - 4x + 3 =0
c) Gii h phng trnh:
Bi 2: ( 1,5 im)
Cho Parabol (P): y = x2 v ng thng (d) : y = 2x + a
a\ V Parabol (P)
b\ Tm tt c cc gi tr ca a ng thng (d) v parabol (P) khng c im
chung
Bi 3: ( 1,5 im):
Hai t cng lc khi hnh t thnh ph A n thnh ph B cch nhau 100 km vi
vn tc khng i.Vn tc t th hai ln hn vn tc t th nht 10km/h nn t th hai
n B trc t th nht 30 pht.Tnh vn tc ca mi t trn.
Bi 4: ( 3,5 im)
Trn ng trn (O,R) cho trc,v dy cung AB c nh khng di qua O.im M bt
k trn tia BA sao cho M nm ngoi ng trn (O,R).t M k hai tip tuyn MC v
MD vi ng trn (O,R) (C,D l hai tip im)
a\ Chng minh t gic OCMD ni tip.
b\ Chng minh MC2 = MA.MB
c\ Gi H l trung dim on AB , F l giao im ca CD v OH.
Chng minh F l im c nh khi M thay i
Bi 5: ( 0,5 im)
Cho a v b l hai s tha mn ng thc: a2 + b2 + 3ab -8a - 8b - 2+19 =
0 Lp phng trnh bc hai c hai nghim a v
b---------------------HT-------------------S GIO DC V O TO
K THI TUYN SINH VO LP 10 THPT
TNH B RA VNG TU
Nm hc 2012 2013
CHNH THC
MN THI: TON
Ngy thi: 05 thng 7 nm 2012
Thi gian lm bi : 120 phtBi 1: ( 3 im)
a/ Rt gn biu thc:A=
b/ Gii phng trnh
x2 +8x 9 = 0
c/ Gii h phng trnh
Bi 2: (1,5 im)
Cho parabol (P): y=x2 v ng thng (d): y=
a/ V (P) v (d) trn cng mt h trc ta .
b/ Tm ta giao im ca (P) v (d) bng php tnh.
Bi 3: (1,5 im)
Hai i cng nhn lm mt cng vic. Nu hai i cng lm chung th hon thnh
cng vic sau 12 ngy. Nu mi i lm ring th i mt s hon thnh cng vic
nhanh hn i 2 l 7 ngy. Hi nu lm ring th mi i phi lm trong bao nhiu
ngy hon thnh cng vic ?
Bi 4: (3,5 im)
Cho ng trn (O) ng knh AB. V tip tuyn Ax vi ng trn (O). Trn Ax ly
im M sao cho AM>AB, MB ct (O) ti N ( N khc B). Qua trung im P ca
on AM dng ng thng vung gc vi AM ct BM ti Q.
a/ Chng minh t gic APQN ni tip ng trn.
b/ Gi C l im trn cung ln ca ng trn (O) ( C khc N v B)
Chng minh
c/ Chng minh PN l tip tuyn ca ng trn (O)
d/ Gi s ng trn ni tip c di ng knh bng di on OA.
Tnh gi tr ca
Bi 5: ( 0,5 im)
Cho phng trnh x2 -2(m-1)x +m2 m 1 =0 ( m l tham s). Khi phng
trnh trn c nghim x1; x2 . Hy tm gi tr nh nht ca biu thc M= (x1 1 )2
+ (x2 -1)2 +m.
----------Ht--------S GIO DC V O TO
K THI TUYN SINH VO LP 10 THPT
TNH B RA VNG TU
Nm hc 2013 2014
MN THI: TON
Ngy thi: 29 thng 6 nm 2013
Thi gian lm bi : 120 pht
Bi 1: ( 3.0 im)
1\ Gii phng trnh v h phng trnh sau:
a\ x2 6x + 8 = 0
b\
2\ Cho biu thc: A= (Vi x 0)
a\ Rt gn biu thc A
b\ Tnh gi tr ca biu thc A khi x = 9.Bi 2: ( 1.5 im) Cho parabol
(P): y=x2 v ng thng (d): y= x + m (vi m l tham s)
1\ V parabol (P)
2\ Tm tt c cc gi tr ca m (d) ct (P) ti hai im phn bit.
Bi 3: (1.5 im):
Mt mnh t hnh ch nht c din tch bng 600m2. Do thc hin quy hoch
chung, ngi ta ct gim chiu di mnh t 10m nn phn cn li ca mnh t tr
thnh hnh vung. Tnh chiu rng v chiu di ca mnh t hnh ch nht ban u.Bi
4: (3.5 im): Cho tam gic ABC c ba gc nhn, ni tip ng trn (O), cc ng
cao AM, BN, CP ca tam gic ABC ng quy ti H (.
1\ Chng minh t gic MHNC ni tip ng trn.
2\ Ko di AH ct (O) ti im th hai l D. Chng minh:
3\ Tip tuyn ti C ca ng trn ngoi tip t gic MHNC ct ng thng AD ti
K. Chng minh: KM.KH + HC2 = KH2 .
4\ Ko di BH v CH ln lt ct (O) ti cc im th hai l Q v E.
Tnh gi tr ca tng:.
Bi 5: (0,5 im) Cho ba s a, b, c tha mn a2 + b2 + c2 18. Tm gi tr
nh nht ca biu thc:
P = 3ab + bc + ca
------------HT-----------Bi 5
Mt khc :
Cng tng v (1) v (2) ta c P = 3ab+bc+ca khi
Bi 4:
a\ T gic MHNC ni tip ng trn ng knh CH ( v chng l hai gc i
nhau)
b\ T gic MBAN ni tip ng trn ng knh AB ( v c hai nh lin tip M, N
cng nhn AB di gc 900) ( cng chn cung )
hay
Trong ng trn (O) : ( cng chn cung )
c\ Trong tam gic vung KCH c CM l ng cao nn ta c : KM.KH = KC2;
HK2 = KC2 +HC2 KM.KH + HC2 = KH2d\ T cu b v suy ra tam gic DBH cn
ti B MD =MH
Tng t tam gic AHE cn ti APE=PH
Tam gic AQH cn ti A NQ=NH
Ta c:
=
-------Ht-------
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