so crAo DUC vA DAo rAo
BEN TRE
Bn cniNn rntlc
CAu 1: (4,0 di6m)
1/ Cho bi6u thric A -
UN TTTT TUYEN SINH LOP 10
TRUNG HQC PHO THONG CHUYIN BEN TRE
NAtu Hoc 2ou4-2ots
M6n: TOAN (chuy6n)
Thdi gian: 150 phrit (kh6ng kC ph6t de)
-
Jtq+J+o +Jso * .,fi40
Ji*Ji*Ji
Kh6ng dung m5y tinh cAm tay hfly tinh giStri cira A.
2t chobi6u thric , _zJi(Ji + Ju - Jta)+ Jx(zJi - Jx)-z^Jz
uJi +J3rb
a/ Tim cti6u kiQn c'ia avd b c16 B x6c clinh vd rut gon B.
blHdy titth gii,tr! cira B khi a = 1* lJi;b : 10 * t tt6
,3
CAu 2: (6,0 cli6m)
ChophuongtrinhbQchai x' - 2(^- 1)" + 2m' - 3m + 1 = 0 (1), voi m ldtham sd.
Il Chungminh ring (1) c6 nghiQm khai vd chi khi 0 < m < 1
2l Goi Xri Xz Id nghiOm cira phucrng trinh (1)
a/ Chimgminh lx, + x, * *,*, | < 2
b/ Tim m sao cho (1) c6 hai nghiQm ph6n biet tr6i d6u thoa mdn lx, - *,1= 1
Cdu 3: (4,0 cli6m)
1/Cho x'-x-1=0. Tinh giS,tricriabiiSuthric Q- xu -3x'+-3xo -x'+2014
\ xu -x'-3xt -3x + 2ol4
2l Cho x,y, Z ld crlc sO ducrng.
t"
l_
!v*,
CAu 4: (6 di6m)
Cho dycrng trdn (O), dudng thAng d clt (O) tpi hai di6m C vd D. Tir iliem M tty y
tr6n d, kd tii5p tuy6n MA vd MB v6i (O), A vd B Id circ ti6p cli6m, Ggi I ld trung di6m
cria CD.
l/ Chring minh tu giirc MAIB n6i ti6p.
2/ Cdc duong th6ng MO vd AB c8t nhau t4i H. Chfng minh H thu6c dudng trdn
ngoai ti6p tam gi6c COD.
3/ Chring minh ducrng thang AB 1u6n di qua m6t <litim cO Airn khi M thay d6i.
4t Chimsminh ry =E{
MC HC,
Chring minh b6t ilang thirc
f" f,
.{;;*{,.- "
SO CT.IO DUC VA DAO TAO
BEN TRE on rnr ruytN srNH Lop 10
TRUNG Hec pHo rHONc cnuytN BEN TRE
xAwr Hoc zot4-zots
MOn: TOAN (chung)
Thli gian: 120 ph:iot (kh6ng kC ph6t dC)
, v6i x+0.
ON CTTINH THIIC
CAu 1: (2,5 cli0m)
Rrit gon cdc bi6u thric
(T
b/cho bi6uthirc n=[-If- Ji ='l(.*Ji), v6i x> 0 vd x +r
Ix+2Vx+1 x-] )
i/ Rirt gon bi6u thfc B.
iil Tim circ gi6,tri nguy6n ctra x OC e nfrpn gi6tringuy6n.
Cdu 2: (2,5 di6m)
cho hQ phucrng trinh {: * ." = -'. - v6i m ld tham s6.
[3x + (m + l)y: -1
I/ Giei h6 phucmg trinh v6i m : 3
2l Giei vd biQn lupn h6 phucrng trinh theo m.
3/ Tim circ giittrf nguyOn ctra m de hg phucrng trinh c6 nghiCm ld s6 nguy6n.
CAu 3: (2 di6m)
1/ cho phucrng trinh bdc hai x' - mx + m - 1= 0 (1) , v6i m ld tham s6
il Giaiphucrng trinh (1) khi m:4.
iil Tim cdc giirtri cria m d6 phucrng trinh (l) c6 hai nghiCm ld x1; x2thlamdn hQ
thilc I 1 _x,+x,
xl x2 2014 x'-2x+2014
2lTim gi|trinho nh6t cua bi6u thric C =
CAu 4: (3 di6m)
Cho tam gi6c d,5u ABC n6i ti6p ducrng trdn dudng kinh AD. Goi M le m6t ditlm di
clQng tr6n cung nho AB. (M kh6ng trung vdi c6c cli6m A vd B).
1/ Chimg minh ring MD ld ph6n gi6c ciag6c BMC.
2l Cho AD : 2R. Tinh di6n tfch cira tu giSc ABDC theo R.
3/ Gqi O ld t6m duong trdn dudng kinh AD. Hdy tinh di6n tich hinh vi6n phAn
gi6i h4n boi cung AMB vd ddy AB theo R.
4l Gqi K ld giao di6m cria AB vd MD, H ld giao di6m cira AD vd MC. Chirng
minh ring ba ducrng thing AM, DB, HK d6ng quy.
2
x