Sat hạch T10-lần 1-Lê xoay-2012

\
Truong THPT
L€
Xoay
Nam hoc: 2Ol'1,
-
2012
DE THI KHAO
SAT CHUYEN
DE
LOP
lO I,AN
I
Mdn:Tor{n-KhdiA+AB
j'
Thdi
gian
lim
bii: 150
phrit
(kh6ng
kd thdi gian giao
dd)
^
-t2
CAu I
(2
ttidm):
Cho Parabol
(P)
c6

phuong
trinh:
y
=
-
'-vd
didm
MQ,-l).
Gqi d li duong
thing
qua
M
'4
vi
c6
hQ
sd
g6c
li k.
a.
Chfng
minh
rlng
vdi
moi
gLd
tri crla
k dudng rhing
d lu6n
cit

(P)
t+i hai
didrn A,
B
phan
biQt.
b. Xdc dinh
f*atictra
k
dd do4n
AB
ng6n
nhflr.
Cau II
(3.5
tlidm):
1.
Giii
phuong
trinh
sau: xt +rl
x' +I I
=3I.
.t
(z
2.
Giai he
phuong
trinh
sau:

lf^+
l'1+
3x
-
6v
=
0
lx'+xy-3
3.
Tim m dd
phtrong
trinh sau c6
3 nghiOm
phan
bi€t duong:
x3 +2(m-x)(mx-l)=mx'
CAu III
(2.5
tlidm): Cho tam
gi6c
ABC bidt
A(-2,3);
B(4,3;
vi
C(1,0);
Gqi
G
lii trgng
tam cfra
MBC

vd
I ld didm trOn canh
AB sao cho L{=2IB
a. Chrrng
minh r[ng:
MBC
lb
tam
g!6c
vuOng.
]
b.
X6c dinh tga
dQ ctra
didin D
tren dudng thioe
BC sao cho
dulng
thing
ID
song song vdi
dudng
thing
AG.
Cau
IV
(2
diim):
r r
sln2c

cos'a
'
1. Unung
intnn
rang:
I
-:- =
Sln d.cos
a
1+cota I+tana
(Vdi
gii
thi6t'cdc
bidu thrlc
dI cho ddu
c6
nghla)
2.
Cho
a,
b, c
ld c6c sdthuc
ducrng
th6a
mdn:
a+b+c
=J&
Clrring
nrinh rang:
ab +bc +

caZg(a
+
b + c)
zags -___-__
I{o v} fdn
thi
sinh:
.

Sd bdo danh:.
(
Cdn bQ coi thi
kh6ng
gitii
thich
gi
th€m)
oAp
AN *
THANG
udvr
Cdu
v
NOi
dung
Didm
I
a.
2
lho

Parabol
(P)
c6
phuong
trinh: y
=+vi
ttidm
M(0,-t).
Goi
a
li ttuong
thing
qua
M
rh
c6 h€
so
g6c
li k.
IMR: vdi
moi
gi6
tri cfia
k
tludng
thing
d
ludn cit
(P)
tai

hai diifn
A,
B
phan
bi6t.
1.0
-
Phuong
trinh
dudng thang
d li:
y
=
lu-|.
-
Phuong tdnh
hodnh
d0
giao
didm
cira
d vi
(P)
li:
2
-+
=/tx-
1
e
x2 +

4lu- 4=
0
(l)
4
C6: A'=4k2
+4>0,VftelR.
Do d6
phuong
trinh
(1)
luOn c6
hai
nghiQm
phAn
bi€t
x,,xrv6i
Vft
e
IR
-+Duong
thing
d lu6n
c6t
(P)
tai
hai
didm
A, B
phdn
biOr v6i

V&
e IR
0.25
a.2s
0.25
0.25
b.
Xdc
ttinh gi6
tri
cfia k
dddogn
AB
ngin
nhdt.
1.0
-
Gii srl
A(x,y,);B(x,yr)
trong
d6
x,,x, li hai
nghi0rn ph0n
biOt
ctra
ptr
(1)
t
=
.r;l"r-I;

/"
=
fuz-l
-
Ap dgng
dinh
lf
Vi-
et
ta c6:
x,*
x,
=
4k;x,x,
=
-4
-
Ta c6:
AB2,=
(*,
-
*r;' +
(r,
-
yr)'
=
(t
+
tc,)(x,
-

,r),
=
(t
+ k
)[(",
. *,,,)'
-
4*,*,]
=(t+k,)(an,+ro)>ro
-+
AB24
DAu"-"xiy
ra<+k=0
Vay vdi
k=O,thi
AB*,n
=
4.
0.2s
0.25
0.25
0.25
il
I
rt+ ,f,'+1i=31.
Giii
phuong
trinh
sau
1.5

Dk: VxeR
D+t
Jr'z+f
f
=
t, dk:
r
>
0
-+
xz
=tz
11
Khi
d6
phuong
rinh:d6
cho
tr6
rhlnh:
tz + t
-
42
=
0*
[;
=
U'
,1,,
,

^
v6it=6tac6:
J7.lI
=6+>
x2
=25*[t=t.
[x=-5
Vdy
phuong
trinh
dd cho
c6
hai
nghi€m
lh:
x=5; x= -5
0.25
0.5
0.5
0.25
Giei h0
phuong
trinh
sau;
Ta c6:
(r)
<+
{ff*+y)+
3x-6y=
o(l)

\
/
lx(x+
Y)=3(2)
-
Ta thdy
x
=
0 kh6ng
ld nghi€m
cira
hQ.
-XEt
x*
0. Khi
a6:
(z)
e x+
y
=1
(3)
The
(3)
vdo (i)
ra
dugc
prr:
U-
*Z*
-

6y
=
0 <+ 3y,
+3xz
-
6ry
=
0
,-,8)
o(t-
!)'=0<)x=!
Thay
x
-
y
vdo
(2)
ta
duoc:
2y'
=3
*> y'
3
E
=t*
Y:llt
r.r=*
V4y
hq
phuorng

trinh
d6
cho
c6
hai
nghiQrn
li:
(x,y)
=
[,E,1EJ,[
E
,rlz
I;
IJ
-
t_
,rlz
o.25
0.25
0.2s
4.25
m tli
phuong
trinh
sau c6
3
nghi€m
phfln
biQt d
Ta c6:

(t)
* x?(x-m)-2(x-m)(mx-t)
=
0
T- _
<t
(r- *)(*'
-2mx+2)=o
<+
l^;':
lx'-2mx+2=A Q)
Vdy phuong
trinh
(1)
c6
ba
nghidm phan
biQt
duong
*,
m
>
0
vd phuong
rrinh
(2)
c6
hai
nghi€m
phdn

biOt
duong
kh6c
m
l*>
o
lo'to
l.
e{sto
.'>
I
l"'o
l*'-zm2
+2*0
Vay gi6
tri cdn
tim
cira
mld:
m,
JZ
.
0.25
0.25
Cho t1m gi6c
ABC
bidt
,4(-2,3);
didm
trdn

canh
AB sao
cho
IA
=
ZIB
Ta c6:
trB
=
(6,0),
AC
=
(3,
-3),
gg
=
1-3,-3)
Khi
d6:
AC.BC
=
-9+9 =
0
*+
dC
t
gC
.
YQy
MBC vuOng

rai
C.
XD
tga
dQ
cria
diim
D t.Cn
f *^
_rn**u**,
_=2+4+l
_,
l^c .
^
1
'
r
-+G(1,2)
L,
-le*la*lc
=3*3*o
=2
fto
3
3
-
Vi
t ttrugc
cqnhAB
mi IA

=
2IB n€n
ra c6:
Vi
lZW
(
^/
.l*,
-xn=2(xu-x,)
t
1
ly,-yn=2(yu-y,)
-
Goi toa
dQ ctra
didm
D h:
D(x,y)
-
Vi
D tlruqc
dqdng
thing
BC non 3_D
ctrng
phucmg
vot
Ee
Mn BD=(x-
4;y-3);

Ee
=?3;-3)
-+
x-i
-+*"-y=l(l)
'-3-3
-
Theo
gt
h c6:
,ID cDng
phuong
vdi
AG
Md,,lD=
(.r
-
2; y
-
3), 7G
=(3;
-l)
-
+
=
+
-+,
+3,y=
I I
(2)

-
Ta
c6
tga dQ trgng
tdfn
G ctia tam gi6c
ABC lh:
Tu
(1)
vn
(2)
ta;c6
h€:
0.25
0.25
0.25
0.25
0.25
0.25
Chrrng
minh rnng:
,
sin2
4
cos'a
=
Slll 4:COS 4
l+cota
l+tana
.1

1
.
sln- 4
eos-a
laco:
vt
-t _+
_r,
sinl a +
cos3a_,
_
(sina+cosq)(sint
a +eosta-sina.cosa)
sina+cosa
sina+cosa
=
t-(l-sina.cosa)
=
sina.cos
a=VP
(dpcm)
Cho a,
b,
c Ii
€6c
sd
thr;c
duqng
th6a
m6n;

a +b
+ c
=
Jobt
Chung
minh
ringz
ob +bc +
ca)
9(a+b +
c)
Vdi
moi
sd
thuc
x,
y,
zta lu0n
c6:
x2
+ y'.+
z' 2 xy +
yz
+
zx
+(x+y+z)'
>3(xy+y+a)
.
Ap dqng
BDT tr0n v6i

x
=
ab;
y
=
bc;
z
=ea
ta duo. c:
"
(ob+be +c.a)i
23(,abzc+bcz
a,t,+ce2b1=3abc:(CI+b+c)
i
-+
(ab
+
b c + ca)
>
Ji.J
"b".J
a
+
b
+
c
=
Jj.@
+
b

+
clJi
a
a
111
:]
rl
l
. Ir , 13
Mrt
kh6c
ta
c6:
a +b
+
c
=
mZ'
lk,jjj,jf_
=
(a
+b
*
dW_
-+
Vc+b+p >3J3(2)
Tt
(1)
ve
(2)

ta
c6: ,ab
+
bc+
ca
>
g(a
+
b + c)
(dpcm)
Dau
"-r'
f6yrakhi
vichilthi:,a=
g=s-=
!.
:''
i'
0.25
0.25

(
Thf
qinh
lim
theo
c6eh
khdc
ddng
v6n

cho
didm rfii
da)
tdtr
g
Ra
ttd
virlipr66-
5o
1
L=
Nguydnfhi
Hdng
NgwydaThlEqnh
so
cD&
ur
viNn
pHUC
rnU$gc
rHpr
r,n
xoav
Ciu
I.
't
l.
3.
Cdu
II

ri
rnr.
sAr n4crr
LAN
r NAM
Hec
z0tt-2012
on
mu
nnON
roAlr
L'Op
ro-
icnot
o
Thli gian
ldm
bdi 150
phrit,
kh6ng
t<e tnOi gian
giao
d6
__-_;__ ______
-
2.
Tim
m
dd phuung
trinh

sau
v0
nghiQm
x-tit
.
x-3
I_
_.,
|
_L

x-l
x
cho phucrng
trinh:
zxz
+Z(m+r)x+
mz
+4nt+3=0
c6
2
nghiQm
",,x.
Tim
gi6
tri
ldrn
nh6t,
nh6
nh6t

cria
bi6u
rhric
A:2(
t
*
rl)_3*,*,.
Gi6i phucrng
trinh:
Js,i
+
Jut
=
4x
-9
+zr,\f
-
5,
*2
(t
i
ciai
he
phucmg
trinh:
{o,l._rtiiiul:_;o=0
2.
cho
h6 phucng
trinh:

{.:T;::r=|!,
rl_o*,
Tim
m
ae
ne
c6
nghiQm
duy
nh6t (
x,y)
th6a
mdn
r*t
=z
Cdu
III.
i.
cho
rarn
gi6c
a.BC,
,'€n
BC
l6y
di6m
D
sao
chorp
=1ae.

Gqi
E
Id
di€m
th6a
mdn
qEA+zEE
+rfr
:o
.
chrmg
minh
A,
E,
o
driig
rrang.
-

[
1+cosC
Za+b
.
2.
Nhfln
dang
tam
gi6c
biCr
I

ri"
c
=
G;-F
lo'@+c-a)=bo
+co
-ao
CSu
iV"
Cho
2
sti
thUc
a,b
th6a
mdn
a+b>2
Chring
rninh
rAng:
at
+b3
<
aa
+bo
H9
va tdn
thf
sinh:
S0

b6o,danh:
Cdn
b.6
coi
thi
khing.giirti
thfch
gi
th€m.
(s
Toa;tu
-
lfJ,lh'D
r/
BL:
f
zL
I
4
4
ltL+b
,Fr<4
@-*;
r.
*
qx'
i)
(r-a)
:
Jic

t
J)
t
tL
/rz.x-
+
lt 4t-+J
=
zzt-;,t_
_h1k
-LX_=
J
tL(n+z/
=
3
inl
NQj;
nt*e=a
qd
h=*2-
lRsn
/1t"a7r*1t/"V/V
NA ru
+-L
7tr
xts
a' lV
1>r
da-
ct*

riui
n
I
#,
:
L3
J
Dt
1n
t,t
I
J
K
d
2.
irt,
h,
le
{rnc,
tu+r-z=
-(na)
\
-
z :
taL+4tu
+3
2
A
:
a(trrrn

-
)x,)(L
=
J(\n
)
V
/\
=
*(kM)'-
fr-
{
<n
2h=
flvt"'+VVn+l+
L
4
=>
-
3,w'"'*
A-0
w,
(n\+n+))
-
f
au t{rru
-Jl
l*
*
tl
a

-,/
)ru
aH
ttl,
l8
,r,,
4{r=,
(rrt{
&=
b{
t4s
LJ,
=
-
t
t\'
-
Lorn-
47
'htt
LI,
-
4J
141
frr
*t
-r0I
^4
,/
+4

"/
;
(5
r
Y
.,t u:t-
.t/'
-la*
:
G't
LTUZA
=
"'6
.l
dzrlV/rl
LA:C
t:Ua'
{il,"
th**A,a
6rN{ll=o
tLhtor,'-,1
xL?.
L
l-
+
V
t-,1
l'
':;'''
I

=
)rt-t
{-L-4
-6-t
t.1
t
trq/
PTt t tt- r
/
t-
='t-*6
+
14
t'-t-(:0
Vo'
t=J
-t*
co,
,
,l/
T;P
f=
-
-(
ho,
t=
3
ll
Tr__L
+

ll r_a
$
re
+(
u
i-f
+,6
7ct
'!=)
L
*6
-Jl
x_+4x.>
;
2L=
2_
=a14
I
L L^4t(Le",\
,/
&di'tr
I
1
fd)
yt'
tr-
-;)44
+
[y'=
o

(,{
}
4n-+21!
ttr-
//=o
Q
b'-Aq
F=u
4
tL-o
)
(o,cr)
o
_
U,r.,:a';V€,
tUi-rf1l
C./*
ya
F*l,=
y
"3
Lo
l-
L
=4J
L
1=.j
XL
,, L-
'J

+'_
'4(xa,
tlVrr-,
*l[;;
=j
H,Gb
+
-tlffin,
=;!
ll
5r
s
tt+
z-
:
.{
*
LL-
'<)'
J
6-2_*_z"o
)
3*-_:fr._t,
=
qt
/*u,
-l
)
)(1__4qx_+
Eq

P1-
uj
l\,
,x
-,
)
oz{-
Etf
or3'-
q
zs-
CI)zi-
ry2f
Drt
,z \
t- rl
,ll
,
O
=
(144
-4[ra ,-f2
i),.
=
vt,(vt"-4)(
wwt1.)
{\
I)Y
=
t''

-l)
[v,,+r1
2
-*r'"
t
l\^
".t
tqL
rcI;
P)
I
LL=
&t-
4
luk=4
€r
f
l*
(O
Lq7r4
Le
{
tu'
+.Qf

vq't-,
/
?_
+
(tur.4

V=
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J
t"
+ ,,
I
I
I
I
I
I
I
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lq,r
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iVse
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i
iqi{
j
I
t
lo7,i'
d
'a?
.y,t+wGC*r"/\?-+1.'
t
tq
e
(ar+oo)
v;,7t
,
e,
€,)
td
.*))
\=/
,e At E/
t)
t/*-{*

o
'fii
/sT
I
cd
C,-
Xli,
C-'
4t
aflc
4
tuna
o
d
4
4n4
<-
i-a
-b
=
A+be
s
A)
Qa-{o
tl
qd'-b-
&:k-[')L
t-pa'4"
Ja+
b

+2a-(12
H4
2-
ze-b
J
A
-]a.e+o
q_
4{ttnc-
, #*
T
)1b,.e>
gj{rarte
t'
za+
L
-:-€-
+=J
{:,
A)
&\-
tr,
=-
trt
f't
=b
A
r+D
c-
,t.t:

0iLf
'r4-
vtI-
€
v
"7
r^

I
.[tt
t
tG
.h
I
I
l,,2)
n* I I
6\
+b
+bJtLr-:/
€
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2c
v,"
{,,
+b-L2/ 0
\
I
*)
frl

t,*,
rtt
tt0;
lr
:
).c
€
ill
(A-dl
r
l,)
(
b
-t)
r
a
<b-t
*
(a
^4)
* (b-a1>
o
\?
(.
rf(
6L{A{,{)
+tb-,r
)'(t\+
lr4l)
4

4i+-z7rD
U)
l)D
otrr,*,r=
q.L)i4)u
Va.
b'+
b+
*&l
L:I
w
*6
,hfu.u,
Pa
v?)
lp-4