TRI'ONG
TIIPT
DAo
DUY TTI
-
IIA
NoI
of
rrn rrnlDAr
Hgc
r,Arv
r
(2010 2011)
nndx,
roAN
rn6r a
Thdi gian:
180
phtu (kh6ng
*6 nm
g*n
giaa
di)
CAu
I.
Cho
him
s5
y:
x3
-

AO
tni
hdm
sd
(1),
rim
di€rn
lvi
nim
trOn cung OA
crha dd thihAm
sO
(t)
sao
cho khodng
c6ch
tu
M cli5n
OA ld
ld.n
nh6t,
Cffu II.
1/ Cho
b6t
phuong
trinh:
JT3x+2)
7n-rt7
1x+4
l,

Cffu III.
V
ttTrCn
m{t
phdne
tqa d0
Oxy, tim
phuong
trinh
tludrng
thingr
di
qua
di6rn
M(l; 3) sao cho dudng theng
d6 ctrng
v6i2
dudrng
thang
(d1):
3x-{-
4y
+
5
:
{j
vi
(d2):
4x
+

AC
:
?,a;
RC
-
2a
c6c m{t
bon ctrng tao vdi ttax,m0t
g6c
600.
Hinh
chitiu
H
cia dinh
s xu6ng
(ABC)
nam
O trong tam
gi6cABC.
'/
at
cntng
minh t6ng H h tem
dulng
trdn
nQi
ti6p cria
tam
gi6c
ABC.

cria
A.
Tim
k e
{1,2,3, ,n}
sao cho
si5
tfp
con
g6m
k
phAn
trl cria A ln lcrn nhdt.
Cf,uY,
Cho 3 sO
kh6ng
6m
a,b,c. Chung minh
ring:
a3 +bt +c'> a'Jbc
+b'Ji
+t'^[on
.
www.laisac.page.tl
_x
oAp
An
vA
rHANc
orru

R
Gioih4n:
L im1x3-3x;=
to
r+
t@
Strbitinthi6n:
y'=3*-3.
Tac6y'=0<=>x=
t I
Bnng bi6n thi6n:
HAm
sii
tt6ng biiSn
tr0n
(-co;
-l)
vi
(l;
+o);
Nghlch
biiSn
ffin
Gl;
t)
Hnm
si5 d4t
cyc d?r
t?r
(-l;2),cgc

y"
= 6x =
0
<:>
x
=
0
. Ei6m
u6nU(0;
0)
Ve hinh
a2
Tim m ttti
phuong
fiinh x3
-3x
=
+
c6 3 nghiQm
phdn
biQt.
m" +l
1.00
Sưu tầm: Nguyễn Minh Hải
SO nghigm
cua
phuong
trinh
x3
-3,c

<
0
<
m'
-m
+
I
(Lu0n
dung
voi mgi m)
V{y voi mgi m
phuong trinh
ludn s[ ]nghiQm
phan
bipt.
0.25
43.
1.00
Gpi
M(xo;
yo)
voi
0
<
xo <
zlb,mOt
diem
bat
kj' n[m tr0n
cung

M.
Phuong
tinh duong
thdng OA li
y
=
x
=>
Tiiip tuy6n
t4i M
song
song voi OA
c6 hQ sd
g6c
f
(x6):
I
<=>
3xo2-
3
=
I
=)
Xo
=
#
r**(hrfl
,!
S 4*a2,
a

+.*.*
0
Khi
d6
hai
vii cua BPT
di cho
ludn
duong, binh
phuong
hai vi6 ta c6:
BPT
<=>
x'
-3x+2r-16-sJ*
1r+4 +x2
-3x+4
[*.
u-s,
a=2
4"{y,
-{J
)-9
<=> x,
-*-!.
o
.=r
l
^
-

.fir' 3r *
4
>
m
A
xet nam so
f
(x)
='[x'
1x
+, +'[77)c
+ 4
(**)
=>
/(x)
=
2x-3
2x-3
D6 th6y
f
'(x)>0
Vx
>
3
n€n
(x)
<l6ng
biiSn ffin
(3;
+o1

''
cos cos.r
2
xx
cosr.cos-+sm slnI
(=)
tflox*
cosx
-cost
x
=
sinx(4)
x
cos cosr
(n)
,O'I
(=>
tanx*cosr-cos'x
=
sinx
2
.orI ort
2
<=>cosx-cos2x-0<->cosx=
I
<->x:k2
r
$e
Z)
Nghr€m

(q
t4o voi
(dr);
(dz)
mQt tam
gi6c
cdn
tai
dinh
ld
giao
cua
(dr);
(dz)
<=>
t(d
;
d,)
=
t(d
;
d
)
,
I
3 A
!
4 B
!
-

ttuong
thlttg
(d)
c6 d4ng:
x
+
y
-
4= 0
ho{c
x
-
y
-
2
:
0-
Go. i
MN,
P lan
luqt
h
hinh chi6u
cria
H l€n
c6c
c4nh
BC,
AC,
AB

=;SH.SABc
li ducrng
cao, dudng
trung
tuy6n
cria tam
gi6c
Sesc=
%ANI.vc=
|Jst
-+A.za=a2Ji
Ta l+i
c6 Sesc
:
pr:
P.
HN
=) HN
:
ry
=
=>sH=HN.tan60o
=$.a:+
4
j4
=)
vsnsc=:+tJ3=f"
<=>
(n
-

{0;1;2; ;18}.
Ta
c6 T
:
-*
=
.\*t=<
I
<=>
/r <
8,5
1=)
k= 0;l;2 ;g
ciJ'
18-k
'v
v'r''"''e
Tuongt.uT>
|
4=)k=9;
l0; ;18
Tt d6 ta nh{n
duo. c
c,!
Ma,r
k{ri
k
=
8 ho{c
9. so

a2
(b
+ c)
+
b2
(a
+
c) +
c,
1a
+
< ab(a
+
b) +
bc(b +
c)
+
ca(a +
c)
(l)
Lai c6
dE dang chimg
minh
ttugc
a3
+b3
>-ab(a+b)
cq(Do
a3+
b3

Ddu
":'xiy
ra khi
a
=
b
=c.
r7
Sưu tầm: Nguyễn Minh Hải