Sat hạch lan 3- Toan 11-A_B Le Xoay 2012

i+
rR{tOF{c
rHpr
r-,t
xoly
Og fru
rffAO
SAf
CffAf
LUqNG
_lAN
E
NAwt HQ9!{4lor2
MON
ioAN
ll Krrdi;B
Dd
chinh
thric
Thdi
gian:
180'phtit (khilng
kd thdi gian,giao
iti)
Ciu I.
GiAi c6c phuong
trinh
lugng
gi6c
1.
"or'[1"orr-!o)=,

\3
3
)
^
Ssina x-sin 4x-Zcos2x-2
'r_A
zcosx-JZ
Cffu II.
. lz*'+2xy-5x+y-2
1.
Giai h9
phuong
trinh
I :-'
-
2.
Chring minh
rdng
trong tam
gi6c
ABC,
n6u
-l
I
I
-
t
^#'#';F
theo thr?
ts l6P'h"1

^^22'2
cAp
s6 cQng thi
a,b,c citng
theo thri
qu
l6p thenh
c6p
sti cQng.
Trong d6
A, B,
C lAn
luqt
ld
ba
g6c
cira tam
gi6c
vi
a, b,
c
theo li
d0 dai
c6c
c4nh A6i
aien v6i
ba
g6c
A,
8,

C,
CAU III.
1.
Tinh t6ng
,S=Cl,
-C)^*C\, *(-I)'C;,
vdi
n
h
s6 nguyOn
duong
th6a
m6n
Ci
+Ci-t +Ci-z
=79
2.
Cho da
gi6c
l6i
c6 10
canh. L6y
ngdu nhi6n
ba clinh trong
st5
c6c
tlinh ctra
da
gi6c.
Tinh

x6c
sudt
d€ dugc mQt
tam
gi6c
kh6ng
c6 c4nh
ndo cga
tam
gi6c
li canh
ctra
da
giic.
Cflu IV.
Cho 3 s6 ducnrga,
b, cthoamdn
a<b<c vit
abc=1.
Chringminhrdng
,
l,
*rr-l
,
*-2-
=r.
a'+abc
b'+abc c+abc
Cffu V.
1. Cho hinh

ch6p S.,48
CD,
gqi
M
ld
m}t
di6m
thay
dOi tren
SC
kh6ng
tmng v6i
S
ve
C,
(P)
H
'
m{t
phing
di
qua
AM vit.song
song voi
BD. Xdc
ilinh tnitit
Oign ctra
hinh chtip cit
bdi mat
phang (P).

Chrmg minh ring
m{t
phing
(P)
lu6n di
qua
mgt
du}ng thing
cO
Ai,rh.
2. Cho
tu diQn ABCD.
Ggi M,.l/
theo
thf
t.u
lA
trung
di6m AB vd
CD. TrOn c4nh
BC
6y
di6m
.[sao cho IB
:
2IC,
Bi6t
mAt
phing (]IINI)
cht.nn@i

-{
Tinh ti rO
4.
JD
Ciu
VI.
Tr0n h9
tryc tga dQ
Oxy cho dudng
thing d: 2x
-
3y
-
5
:0
vithai
ili€m AGl;3.),
B(1;1).
Tim
trOn
duong
thing d di6m.M
sao cho
lzun-zuEl
nfrO nfrAt.
_____r*5t__
(Cdn
bQ coi thi khilng
gidi
th{ch

gi
thhm)
F{qvit6nthisinh:
SOUaodanh
Lop
N6i
d
"(n
8a)
.(r 8zr)
COs-
l
-cos
x_-
l=
I
€ slnl
_cOS.r__
l- 0
\3
3)
[3
3)
7t
8tt
c)
*cos.x
-
-?
=

kn
<+ cos.r
=
I
+3k,k
e Z.
JJ
Do -l<cosx<1
Suy ra cos.x
=
-1
.1
n€n
-1<8+3fr<1e
-3<k
3-:3
k=-3
3
<+.x- n+2ln,leZ.
2
(1.0d)
8sina x
-
sin 4x
-
ZcosLx
-
2
=
0

e Ssina x-sin
4x-2cas2x-2=0
<+
Ssina x-2sin Zxcos2x-4cost x
=
0
e Ssina x+8.sin3.xcos.x-4sinxcosx-4cos2
x
=
0
e 8sin3 x(sinx+cosx)-4cosr(sinx+cosx)
=
0
e
(z
sin3
x
-
cos r)(sin x + cos
x)
=
0
[sinx+cos.tr=0
(1)
<)t
[2sin'.r-cosx=0
(2)
(1)e
sinx+cosx
=

0 e x
=
-L
+
kn,k
eZ
(2)
e
2tan3
x-
(1
+ tun")
=
O <> tan r
=
1 <+ *
=
t
*
kn,k e
Z.
fiSt hqp vdi diAu
kiQn suy
ra
.r
=
x4
*
k\x,k
eZ.

1
(1.0iI)
EK
x+y>2
[2"'
+ty:
t.]
f2v=rJ*
+v-2
y-2
f(zx-t)(x+y-2)=0
AJ
+3
f2y=lJ*
+y-2+3
l[*=1
ll
2
1L**v
-2=0
t_
L2v
=
rJ*
+v
-2
+3
:_I:i ::=
Vflv hQ PT c6 nghiQm
suy

ra
"")"

(r.3
t
\2'2
31
22
. fl
r5T-"
"^lrt
+
)
I

A'
tan
-
1
,
.or{
"nr{ "or{
-+
lap thnnh
csc
<+
.+.:+=,
.+
tan- sm- sm- sm-
2222

(
t-r\
.
InT\/ |
B
sml
-l
n,

"^^^[
t
/
_"
tott
a .^:_
A
_,_c
B
o
-:ffi
=
t-:6
<)
zsm-srn-
=
stn-
sm sm-
sm-
?
222

^
,.
B
A-C
A+C
A-C
B
<D
Slll-:-
=
COS-
=
COS Sin-
2
2
2
2
-'-'2
0.25
B
A_C
B A_C
<>
ZSln
-:-
=
COS-
<+ Sin
B
=

COS:CO
2
2
2
2
1
<+
sin 3
=
a(sin
,4 +
sin
C)
.2'
.
A+C
A-C
-
sln
.,
,,
.L
0.25
Tir d6
suy ra
sinA+sinC
=
2sin,B
e a + c
=

Zb hay
a,b,c
l{p thinii
CSC.
0.25
m
1
(1.0iI)
Ci +Ci-t +C:-'
=79
e
"*ry=
78 e n' +n-156
=
, *l:=?r,
-Fvv
rs r.=!?.
0.5
Khi
d6
S
=
Clo
-
Clo
+
Ci^
+
Cii
|rlLt

T
=
CL
+
Ci
+
Ci, +
+
Cli
=
C)o +
Curo
+
Clu +
+
Cff
S,
=
cL +
cln
+
clo + +
cil;s,
=
c)o
+
ci
+
Cj,+ +
cji;

thitac6
S=Sr-Sz.
MFt
kh6c
r
=
cl+ + clo +

+
c:i
+
cll +
cii.
. . +
c',i
=
zs,
-
c)1
T
=clo+c'^+ +c;i+cif
+ ,1
cil
=2s,
Tir d6 suy ra 2St-C:1=
2Sz
<+
^9
=
S,

-
tr=i,rt
0.5
,,
(1.0d)
S0
c6ch
l6y ra ba dinh ld
Clo
=120
.
0.25
Khi lAy ra ba dinh la ludn
dugc
mQt
tam
gi6c.
C6
l
lopi
tam
gi6c
kh6c nhau:
LoSi 1: c6 2 c4nh
ld c4nh cria da
gi6c
c6 10 tam
gi6c.
Lo4i2: chi c6
1,cpnh ld cpnh

cria da
gi6c
c6
6*10
=
60 tam
gi6c.
Lo4i
3: Kh6ng c6 cpnh ndo ld cqnh
cria {la
gi6c
c6 120
-7Q
=
50 tam
gi6c.
0.5

50
5
VAv x5c suAt li P
:

=
-
.7J
'
'1,20
't'L
0.2s

IV
(1.0rD
tl2-
_
f

J
-
z'
',
a'+abc b'+abc c+abc
112cll2
A-!-a-A-J-a-
"
a,
+l'
b2
+l-
c+l-' a2 +l'
b2
+l-
ab+l
0.5
.l * .1
az +l
b?
+l-
ab+\
''
az

+1
ab+l'
b2
+l
ab+l-
"

I
-
I
-
I
-
I
.n
^t
-'
a'+l ab+l b2 +l ab+l-
-
e
@-4
(b-a)(!b-1).<
0 e
@-?)'("0.:t)
.
.o
-
(ob
+r)
(a'+

r)(a' * t)
=
"
*
(ou
+t)(a'+ r)(a'
* t)
-
"
Md theo
gin
thitit abc=l,a<b<c n€n c
>-!>ab=l=1
suy ra b6t
^.
c
cuol cung tuon oung. EEng thtc xAy ra khi
a: b
hoflc
c
:
1. Ta c6 diAu
minh.
dnng thfrc
ph6i
chimg
0.5
v
I
(1.0ir)

'/l\'
li\
f_[
/t\
JT-,
(Vc
hinh
dring*
m6i
cti6il
didD
-
\rur
I ra glao-qrem
AU
va trD.
J la
glao
dlem
AM
va
SI.
Tr€n
m{t
phdng
(sBD)
k6
duong
thang quu
J song

song
v6i
BD
cit
sB,
SD lin
Se$ip;e-1" $uy_r3"tlif
ig-ergilgsergtgeippjE_l4f,
0.5
Lauray
(r/ or
qua-drem
A
c0
drnh va
song
song
v6i
BD
c6
dinh
n6n
(p)
Iu6n
di
qua
mOt duong
thing
d c6
dinh

di
qua
a va
song
song
vdi
duone
tfrine
gn
-
0.5
2
(1.0d)
(V€
hinh
d,i4g*
m6i
ch6m
di6mj
Uor
"b
la
glao
di€m
cta MI
vd
AC thi
N, J
,
E th6ng

hdng
hay MI,
NJ, AC d&rg
quy
t4i
E.
a
Do IB=2IC
n6n
suy ra
CA=CE. (Do
CE
=
2MF=AC)
0.s
lu U Ke
ducrrrg
th6ng
song
song vdi
NJ c6t
AD tpi
K. Suy ra
KA:
KJ
MaNC:
ND
n€n JK
= JD.
1 f,t

y6,v
JD=!JA
6u,
t4
=2
3JD
0.s
VI
(r.0d)
o,{*=t:t.'
^
Gii sri
u(t+3t;-t+2t).
ly
=
-l+Zt
fu
=
(-z-zt;+
-zt);
uE
=
(-tt;z-a)
+ zffi-tffi
=
(tt
-
+;zt +z)
0.5
f

-
-11
lzMA-3MBl
=nf
-16t+20
Suy ra
lzue*zunl
nrto
"rt6t
8
e-t
13
suyra
-(#,*)
0.5
i
duyQt
Neudi
r;l
Ngud'i
du1
Td truong
gudi
b"(
'
t-4
t
45.
(
)=r

I /./ L "'
u
Nguy6n
ThiHpnh
Hodng
Drlc
Trudrng