De va da thi thu DHV lan 1 nam1

c
DAI Hec
vINH
Dt
o sAr cnAr tUqrrlc
t 6p tz LAN
r, NAwI zorr
T c
THPT CrrurEX
UOX: TOAX; Thdi
gian
I m
bii:
180
phrtt
r.
prrn
c
c cHo
rAr
cA
rff suvn
e,o
a$m')
7CiuI.(2,04i6m1
Chohdms6 v=
!*'-(2**l)x2+(m+2)t ,'+
cOd6th!
(C^),
m ldthams6.
'3

I . Khio
s6t sy bi6n
thi€n vi vE dd thi cua
ham s5 d[ cho l<hi
m
=
2 .
2. Gpi
A ld
grao
tti6m
crla
(C,)
vdi trUc
tung. T\m m sao cho ti6p tuy6n cua
(C.)
t1i A tAo vdi
hai
FUc
tga
itQ mQt tam
gi6c
c6 diQn tfch
Ui"g
1.
3
yCAu
trI"
(2,S
trfrenre)

1.
Giei
phuong
trinh
(x+
4)'
-6
=
13.
2.
Gifliphuong
tinh
(2cosx-
l)cotx
=
-l
*
srn.r,
Ciu
Itr.
(1,0
Ci6m)
Tfnh tfch
phin
/
=
dx.
Cf,u
IV.
(f,O

ai6m)
Cho
hinh hQp
ABCD.A'B'C'D'c6
ttQ Oai
dt ci cdc cenh <tdu Uang
a>0
vi
ZBAD=ZDAA'=LA'AB=600.
Ggi M,N 6n luqt ld trung
ttidm ctra AA',CD.
Chfmg
minh
MN ll(A'C'D)
vi tffi
cosin cta
g6c
t4o
bdi
hai tludng
rhing
MN vd B'C.
Clu
V.
(f,0
tli6m) Cho
c6c s5 ttrgc
E
a, h, c. Tlm
grd

fri l6n nh6t
cua bi6u th{rc
r
FCA
P_
a2
+
bz
+
c2
+l
(a'+
lxb + 1)(c +
l)
n.
G
Tht sinh cht ituqc tdm
mQt
trong hai
phdn
$hin
a, ho{c
b)
agn
Cf,u VIa.
(2,0
rf6n)
1. Trong
mflt
g

vdi hQ
W
Ory, cho tti6m MQ;I)
vi hai
ttudng
thing
dr:3x-y-5=0,d2:x+y-4=0.
Vi6tphuongtinht6ngqu6tcfia<firdng thing d ttiqua
M vdctt
dt, d2lin
t4t
A,
B saocho
2IuIA-3MB
=0.
2. Trong
kh6ng
gian
vdi
hg fiUc tga
tlQ
Oxyz,
cho c6c di6m A(2;0i;0),
H(l; l; l).
Vi6t
phuong
tinh
mflt
ph[ng
(P)

di
qt;n
A,.F/sao
cho
(P)
"ii(
q,
Oa
lhn hqt
Cr
B,
C
th6a mfln diQn tich cta tam
gi6c
ABC Uing
+G.
Clu VIIa.
(1,0
di6m) Cho
t$p A=10,1,2,3,4,5,,6,7).
H6i tU t$p ,qWp
tlugc bao
nhi€u
s5 tp
nhiOn
chin
gdm
4 cht s5
khdc nhau sao cho
m5i

s6
iffi ttAu l6n hon 2011.
b.
Theo chuolg
trlnh Nf,ng
cao
Ctu
VIb.
(2,0
di6n)
l. Trong m[t
phlng
vdi
hQ
W
Ory, cho c6c Adm ;0; 2), B(4;3). Ilm tAa d0 didm
\
M
soeho ZM4B= 1350
vdkhodnecdchtir
M dhnttu0nethEne AB hAns
JiO
.
gian
vdi hQ truc tqa d0 Oryz, cho
c6c tti6m
C(0; 0;
2),
K(6;-3; 0). Vi6t
phuong

tinh
di
qua
C,
K sao cho
(a)
cfit Ox,
q
4i
A, B
thlaman th6 tlch cria tf diQn OABC
[3t*'+3'
=
lo
'lt.
1.,
l;logr
x'
-logr
y
=
g
lz
I. Brc sd trd bdi vdo alc
ngdy 26, 27/03201I.
Dd nhdn
thrqc bdi thi, tht
sinh
phdi
nQp lqi

phiiiu
dtt
thi cho
BTC.
2. Kj
lrhdo sdt chiit ttrong
t,in 2 sd duqc t6 chftc
vdo chiiu ngdy 16 vd ngdy 17/04/2011. Ddng ki du
thi tqi
Vdn
phdng
Tr THPT ChuyAn
t* nSdy
26/03/201 I.
sent to www.laisac.page.tl
DAp
AN
of IsAo
sAr
cn,ir
LUqNG
nfip
pLAN
1, NAM
zorr
*fON:
TOAN;
Thiri
gian
lirm

bhiz
180
phrit
Ddn
dn
L;
(1,0
itiam)
-5x2+
+*+!.
a
J
0x+4.
f x
<ll2
<0<+ll2<x<2
vd'Y'>0€l
-
l*>2
khodng
(a;lll)
vil
(2;+o),
hAm
nghich
bi6n
t€n
(rtz;2).
i
C*

1,!:
Hilm
sd
dpt
clrc
tl4i
tpi
x
=
| I
2,
y"u
=
5 I
4
vi
tl4t
cgc
ti6u
t?i
x
=
2,
ltr
=
-t
.
c.
Ed
thi:

Ed
thi
cit
tryc
tung
tei
A(0;rl3)
I.
(2'0

I \
olem,
2.
fl,O
ttidm
Ta
c6
A(0;1/3)
vdy'=
4x2
-2(2m+
l)x
*
m
+2.
Suy
ra
y'(0)
-
m +2.

Ti6p
tuy6n
cria
tt6
thi
tai
A
l
d :
y
=
(m
+
z)x +
1.
Euhng
th[ng
d
cht
Oxtai
atfr
;
ol'
l.
(1,0
ili,
DiAu
kiQn: x3
+3x
2

0 e
x
>
0.
Kl
1
*:Te
:*
li
:9:::11*
i:l:l
f-:ff
I ?
:
Nhfln thdy
.r
=
0
kh6ng thda
min
n€n
(l)
tucmg duong
v&r
x +t *i-6trf,J
=
0
Dil
f+1,
=t,.t2ffi

t^dugc
t2
-6t+8=0<+t=2
holc
t=4
(tntlk)
0,5'
+)Vdi
t=2 tac6
x=l,r-3.
+)VOi
t=4
tac6
r 8+
Jdi,tr=8 fiT.
DiEu kiQn:
sin.r
*
O,cosr*l hay
x
*kn
.
vci
ailu
kign d6
phuang
trlnh
da cho
tuong
rhrongot

2cos2r-cos'r-3
smr
o
(2cosr-lXcosx+l)
-
2sinx-
<+
(2cosx-3)sin2x=
-2sin2
x
sinr cosr
-
I
0'5
AzcOsI-3=
-Zecos
x=l
O!= t!
+k\t.
23
0'5
Tac6 I
n
&
(2'
I
I
0
z',
Vdi

r= 0:+
t
=lrvdi
r=l=+
t
=2.
&=dt
hay
fo-gi2,
-".*?
3ln2'
3
0'5
=2'g,d,
:
I
'(
t
_
I
t
Khi
d6!=rnzlt''-zs
5rnzl\r-5
t+sl
#(,"F
-
sr
-
hr, .

rrl',,=#rn*
.
0'5
+)
Gqi
'f
l*ffing
di€m DC'.
Vl
NI//
CC'
vil
NI
*
I
Cc'n€n
NI
-
rhil'vil
NI
/l IV/4.'.
,2'
:
:
+)
vt
AI,B',C //A',D
nEn
flC)*./(A'I, A'D)
(r)

,"
-t\
,"
,r'
Dry a
0'5
0'5
t2
A' D2
+ A'.C',2
DC',z
5a2
oJi
Suyra
AI'=T-
,
=7+A't=7.
Trong
LA'"DI
ta
c6
cos
'/.DA'I
,
A' D2-+.A'12
r
DI,
=
-3,:
-<-i-

2A'D.A'I
2J5
*";:33.,5
Tt
(l)
ve
(2)suy
ra cps(IAf,
B'C)
=
|
cos /.DA'l
I
=
-::
=
-
_iN.__\___,
_,
r__
,
ZJS
l0
(2)
V.
(1'0
1
orem
,f e
Ap

uung;nrycosita c6
az +b' +cr
+r>|to+el'*
jtr+l)'>
Ir"*b+c+l)2,
(a
+lXb + l[c
*
g
<
['
*lftl']'
.
: , :
i
]
fr
Ps
2
-
54
Suy
ra
a+b+c+l
(a+b+c+3)3
DAt
t
-
a +
b + c +l,t >

I
.
Khi d6
ta
c6
P <? 54
=
t
(r+
2)t
0'5
Xdt him
f
(t)
=i
@
hen
(L
+
co).
Ta c6
f,
(t)
=
-3.#
=
0
<+ st
=
(t

+2)2 el"='.,
f,
(t)
>0
<+ I < t < 4
Suy ra
BBT
DWa
vdo BBT
suy ra
P
<l
.
n6u
ding thfc xiy
ra khi
vd
chl
khi
4
Vfly
gi6
tri ltu
nh6t cta
P le
1,
Uut
dugc
khi
a

-
fi
=c
=
I
.
4'
r
'
'
i
t'=4Qa=fi=c=l
_f'(t)
VIa.
(2,0
tti6m)
l,
(1,0
itifimr
-xr)'
r-
lzttu=3ffi
I
lzffi=-3ffi
3-xr)'
(1)
(2)
0'5
+)
(1)e

2(xr-1;
3xr-6)
-3(*r-l;3-
xr)O{*
=}
lx,
-z
(
suy
ra
^lit
;),
BQ;z)
.Suy ra
phucrns
nlnh d
: x
-
y-
0 .
*)
(2)<+
2(x,
-
1;
3*r-
6)
=
-3(x
,

-li3 -
xr)*
fi;
=1
Suy
ra
A(l;-Z), B(L;3).
Suy ra
phuongfitnh
d:x-l
=
0.
0'5
2.
(1,0
ilidrn)
Gid
su
Suy
ra
B(0;
b;
0),
C(0;
0; c)
trong
d6
bc
*
0

(vt
n6u
bc: 0
thi tam
(P)'*+
4*'
=l
.
vi
H
e(P)
non
1*1=
1
\
/
2
b
c
-\-,
-
b c 2
s,u"
=+lrzl,frll=;
(bc)z
+(2c)t +
(2b)'
-
4J6
e

b'c'
+4b
gi6c
ABC
suy
bi6n)
(l)
+4c2
=384
(2)
0'5
ii
OFI
b
+ c
=
u,
bc
=y
. Khi d6
tU
(1),
(2)
ta c6
ll
;i
-Zu)
=
384
b-c=4

[r=8,
y=16
<+l
.
L,
-
-6,p
=
-12'
suY ra
fi
=
-c
3
+
Jn
S=-c 3-
Jzl
Vpy
c6
3
m+t
phing (P)
thda
mdn li
(4)'*+
1*1=t
hay
2x+
y

244
+z-4-0,
c
1tS,|*-+.:h=t
hay 6x+(3
+Jn)y+(3-
^r7-t2=0"
e)';.#.;E=l
hay
6x+(3
-Jily+(3+
JnJ,-rZ=o.
VfIa.
(1'0
tli6m)
Gii srl s6
thda
mfln
bdi todn li
ab;A
. Theo
bdi
ra ta
c6 o.
{2,3,
4, 5, e,l\;
d
e
{0,2,4,61
.

Xdt hai tudrng hqrp:
TH I:
d
=
0 .
Khi cl6 a c6 6 cdch chgn, b c6 6 c6ch chgn, c c6
5 c6ch
chgn.
$qv rq
q6i
6x 6r |
=
t!9 tq6l
0'5
TIt 2:
d
.
Q,4,
61. Khi
d6 d c6
3
c6ch chgn, a c6 5 cdch
chgn,
D c6 6 c6ch chgn,
c c6 5
c6ch chgn.
Suy ra c6: 3
x
5
x

6
x
5
=
450
(s5).
Vfy s5 c6c s6
thda mdn h 180
+
450
=
630.
0'5
vIb.
(2,0
tli6m)
l.
(I,o
itidm)
Gii
su M(x;
y).
Ke
MH L AB
.
TU
giethi6t
suy
ra
MH=g

ve
LIyAH vu6ng c6n.
2
Suy
ra AA,I
=
MHJ,
=.,6.
l3 50
0'5
D[t u
-
x-1,
v
-
!
-2.
Khi
d6
ta
c6
(
-1,
v=-z
-zrv-1
0'5
2.
(1,0
iti6m)
(1)

fab=)
<+ sb
-9<*l
Lob
=
-i
Gi[ su
A(a;O;
0), 8(0;
b;0).
Vl Vonu"
>
0
n€n
ab *0.
Suyla
@):I+ 4*1=r.vi
Ke
(a)
n6n
9-l=r
'iiobzab
il
Oe,ACle
fii diqn
vudng
t4i
On€n
Vouur=
*

OA.OB.OC
=
*
I
ol.t b
I
-3
(2)
(3)
0'5
hw thi tn>
0,25
didm.
2x*2y+32-6=0
x+
4y'-32+6=0
0r5
VIIb.
(1'0

I \
otem)
EidukiQn:
x*0,y>0.
iu"o
|rcCr*'
-log,
y=
0 <+ log,
lx I

=
logr
y
elxl=
y
e
l:=:,
*
Vdi
x
=
y,
thay vio
phuong
hinh tht ntr6t ta
dugc
32*' +3'
=
10
c+
x
=
0
(ktm).
0'5
*
v6i
vay
n
=

10
0'5