THI TOÁN L1-2011(CHUYÊN NGUYỄN HUỆ HN)

TRUC'NG THPT
CHUY6N
NGUYEN
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roAN
xmox
a,n
Thoi
gian
liun
bdi:
180 phrit,
khdng
te
thO'i
gian
giao
d€

Cf;u
tr:
(2,8
di€,m)
Cho hdm
s6
!
:
x3
-
3(n +7)x2
+
9x
*
m
,
v\i nt Id
tham
sO
thuc.
l. Kh6o s6t su bi6n thi6n
vd
ve
AO
tni cria hlm sO
Aa cho irng
voi nt:7.
2.
Xic
dinh nt dd

hem
sO
Oa
cho dat'cuc tri tqi rr,)r? sao c.iro
lx,
-
rrl=2.
C6u
X{:
(.2,8
dihwe)
1.
,
Giai
phuo'ng
trinh:
2.
Giai
he
phuong
trinh:
'.'
I
+
3
cosr;
+ cos
2x
-2cos3x
=

4sin
x.sin 2x
f:-ra
].'t
*
t). +
Y-
* 1
:J:-r-l'
l.xy
+:r
+zv
=1
(x'
Ye
R)
Csu
EEE:
(f,8
di\m)
T\tn
f :f ox
sinx.sinl
"
-t
'.
I
\
4,/
C6u

EV:
(1,8
di6mc)
Cho lang
tru
tain
gi6c
ABC.ATBTCT c6 tdt
ch cdc
canh bAng a.
g5c
tao bdi
canh
bon
rzd
md'r
phing
d6y'oang
300. Flinh chieu H
cira
didin
A tron
mat
ph&ng
(ArBrCi)
rhuOc
dubng thing
8,C,. Tinh thd tich
khdi 16ng tru ABC.ATB'C, vd
tfnh

khoang c6ch
gir-r'a
hai dubng
thing AA,
vlL
B,C,
theo
a.
C6u V:
(I,ff
dihree) ){et circ
sd thqc <lucrng
a, b,
c
th6a
mdn
didu kiOn
a + b +c
=
1 . Tim
gi6
tri
nho nh6t eri.a
:
r=
Ciiu VI
y2,t)
*i6rte'S
1. Trong mat
phing

v6i h0
toa
dd
Oxy
cho hai duo'ng
trdn
:
,
(lC1):
x2
+
f
.:13
vi
(C2): (x
:
6)t
+
y2
:25
cit trirau
tai A(Z:3).
Vi€t
phuong
trinh duo'ng
th6ng di
qua
A va
ldn luryt
c5t

(C'), (Cz)
theo irai
dAy cung
phAn
bi6t
c6 dQ ddi
bdrrg
nhau.
2. Trong kh6ng
gian
vo'i hQ toa dQ Oxyz cho tam
giac
i,uong
cdn ABC
c6
A(5
;
3
;
- 1),
C
(2
;3 ;
-
ilvd
B
ld
ditim nirn tr6n rndt
phing
co

phucng
trinh
:
.
-^ ;.
lrm toa do cllern u.
CAU VII
Q,A
diAwt)
Giii
phuong
trinh :
A
(z-tog i-)iogn.3-;
:-
=l
l-
iog,
x
F{Ct
Thf sinh
kltong
duqc
sw dung
tdi !f.€u.
Cd"n
bc
coi tlti
kltong
giai

thich
gi
thenr
{r+-{+-)r:-l
BA
:
tsC. Bi6t
.x+y-z-6=4.
TR.IIONG
TT{PT
CI{UYEN
NGUYEN
HUE
IITI$NG
NAX
CTTANN
rrU
rgtl
DAI
HqC
LAN
g'rr{I
ror{Ar
NAM
FIQC
2010
-
20r
1
pg

rril nnoN:
ToAN
KHoI
A,
ts
t
-6"t
+9x_1.
-12"r'f9:3(;r
-4x+3)
<0<=l<x<3.
=JX
Y6im=l
tac6
y=a
*
T4p
xiic dinh:
D
=
R
*
Su bidn thiOn
n
Chidu'bidn
thi6n: y',
^
["r3
laco v'>(l€l
'

| , 1
L.^
-
-uo
do:
+
Him
sd ddng
bidn trOn
m6i
khoing
( ,1)
+
FIdm
sd nghich
bidn
tre-1
khoring-
(1,
3),
*
Cuc
tri:
H)m
sd dat
cuc
dai tai
x:1 r,b
va
(3,

+
*).
.''''' ''.'''''''''.''.'''''''''' ''''
lcn:
Y(1)
=
3;
dat
ti0u
4"25
n ){
n ?5
4,25
o ?5
n ?(
n-1
{1di6m)
(Idrem)
)cr:YG):-1-
e
Gi6i han:
lirn
;r
-
-co,
'P
:
+oo.
"
BAng

bidn thiOn:
Ta c6 yl;
3x2
*
6(y+
l)x
+- 9,
Him
sd dat
cuc
dai,
cuc
fid;
di
;;, ;;;
d,,*""g
tii"r,
t.=
0;
i;";;hie*
;t
ra
",
,
",
e
Ft
xt
-21nt+1)x+3:0
c6

hai
nghi€m phin
biOt
ld
x1,
x2.
l-'uT
.2
1\,= (m+
l)t
-
3
>
o
+>
|
r/?
>
-r
-f
{r
(l)
1,,
<
-l
-",,5
V,
-
*rl
=

2
e
(x, +x,
)'
-
4r,r,
-
4
e 4(m
+t)'
-12
=
+
T
a(nt+l)2:
,ol'n=-'
lm
=l
(2)
q2s
0 ?5
0,25
o)s
0 )s
0.25
n ?s
4,25
4,25
0.2
5

o ?i
4.25
o ?5
"
)
<> 1 +
3cosx+
cos 2x
*2cos(2r+
x)
=
4sinx.sin2x
1
+
3cosx+ cos
2x
-
Z(cos
x.cos 2r
-
sin x.sin 2x)
=4sinx.sin
2x
|
+
3 co_s:r r,
9os2x
_
2cpS,r
:

0.<+^
]
+ c,os x +
c_os 2::
=
-0
fcos":
o
2costr+cos.t-0e
I I
I
cosx
=

l2
P'f
[-_, ,
{-t-1-l/-l
Suv ra
I
-
[-r
*.v 4
VO'i
., i y
-t
thay
vdo
t2)
duqc

-
r
l-
2),
=A
Tiry
dusc
(x;;r)
:
(1;0);
(x,y-)
:
(
1;7)
Vcvi
:r * y
=
-{
thay
vdo
(2)
duo'c
-),2
*3),-
Irhuong
trinh
ver nghi0m
H€
c6 2 nghiim
(x;y)

:
(1;0);
(x,),)
:
(-1,2)
f
l/T
lx:-*Kn
lr
|
'to
I
"r':
+
+
K2tr
L3
(t^)^t
lt''
+2x +J'-+
f
=J-
")tl
lr,'-+)'l'rJ'
+2.rt.v
=3
(l)
1 €<
["ry+x+2y:l
l-\.y+.\'*21,:l

(2)
CQng
(1)
vd
(2)
theo
vC
duoc
(;,:
+
-1,12
+ 3("r
r 1')
-
4
:
0
II-1
(1
tli6m)
{H
(1
eli6m)
f
cot-r
l
I / ci^'
:
Jt
I

.l 7T\
srnxsrnl"*,
J
cot
-x
___d
_
s
inx
(s
inx +
cos x)
dx
:
Jt[
cot x
sin2x(1+cotx)
r:rCotx+l-l
:-42lt4a(cotr)
J
cot-r+1
gifra
AA,
r')r
(A,B,C,),
theo giA
thiet
thi gdc
AB
J7

(-
"ot
:r + ln
lcot
x + rl)
+C
Do AH
L(A.B.C,)
nOn
g5c
A,4,H
llgdc
AA.H bang
30('.
EI-?
{n
diem}
IV
{1
di6m}
n')<
X6t
tam
gi6c
vuOng
AHArc6
AA,
=
a, g6c
AA.H

=30"
=
v :lor,
-L.L.u'Jt-u'Jt
'ABL,l,B,cr-3tttt"uA,Br,
-tt
4
-
U
AH:!
2
0 ?5
Xdt
tam
gi6c
vuOng
AHAr cd
AA,
=
a,
g6c
AA,H=300
->
AtH
:+
Do tam
gi6c
ArBrCr l) tam
gir4c
ddu

canh
a,
H
thu6c B,C,
r'd
Matkh6c
AH J B,C,
nen
B{'t J
(,4Afi)
I^'
AtI{
:$
nen
A,H
vudng g6c
v6i
8,C,.
,)
K6 du'dng cao HK- cfra tam g-1;l-c_
AA,H
thi
FIK
cliinli
ld
khoing cdch gifr'a
AA,
rlh
ts,C,
A, H.AH orll

Ta
c6 AAI.HK
=
ATH.AH
-)
HK
-
"''
:
1A,
4
nhdn
c6 :
(t +a)](t
+ c)
-
ab)(r
-
bc)(t
_(r
'.;
cQn
-i)f 1)
)\ca
)
;il;g
bi"h
.(
a-p)
-l

'i.
At afig B
1-ab>7-
(abc)2
trung binh
[(t
+ a)+
-
ro)
015
0 ?5
gva
{z+a+u)(z*o*h}
TuongtU
c6: 1-bc>@
2.
(1
di6ma)
n
,
('1")J(!:Xl:b)
Suy
ra
H,ra:
[i.;)[t*-;Xt.:)-
?'.#-)'
,
o' Do
d6 minp:
B

dardusckhi
a:b: c
Goi
giao
di€m
thri'hai cira
duong thing
tirn
vdi
(Cr)
vd
(Cz)
16n luot
id M vd
N
Ggi I\{(x:
V)e
(C,)
=
"'*-y2
:l
j
(1)
vi A le
truns di6*
;d ffi;d N(4:;; 6
:
tj
DoN e
(Cr)+(2+

x)2
+(6-),)2:25
(2)
(
z 2 ,^
lx +V
:lJ
Tn(l)ra(2)tacohd
I
"
'ftz*x)2+(6-1'l:=25
11
6
_17
Giai heladuoc(x:l:y:3)(loai vi
trungA)va(x= ;
,V:]
f
Val
M1
-
555
oucms
thilg.in
rir"
oi
q;;
A
id
M io

pn".ig rrinrr
: i
-
iy
I
i-: a
0 ?5
0 ?5
0?5
vr-
1
(1
tli6m)
6
^:)
5
AC
:
3J2
suy ra BA:
BC:
3
n ?q
a)5
0 75
0 ?5
o ?5
o ?{
4,25
+(2*

x)2
tqidoBi['gt'i6 iiinepii,,*'eiiilil'
[{"-s)'
+
(y
-3)2
+(z+l)2
=
9
lfr
-r>'
+
(.y
-3\2
+
(z
+ 4)2
=
e
f"*,
-z-6:0
[r"-sl;i6_i;l;
ir,i
i;
=s
'[r"
-s;;;a;-;;;'
o]"
*z-1=0
olr=l-x

l,.l
["*y-z-6:0
l:t=7-2x
':, .
::"
VII.
(1
tli6m)