Đề thi tuyển sinh lớp 10 môn toán năm 2014 2015 THPT chuyên bến tre

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