' 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.. trOn duong
Trang 1i+ rR{tOF{c rHpr r-,t xoly Og fru rffAO
SAf CffAf LUqNG _lAN E
Dd chinh thric Thdi gian: 180'phtit (khilng kd thdi gian,giao iti)
1
"or'[1"orr-!o)=, \3 3 )
'r_A
zcosx-JZ
lz*'+2xy-5x+y-2
-l
I I
-
t
^#'#';F
^^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
x6c sudt d€ dugc mQt tam gi6c kh6ng c6 c4nh ndo cga tam gi6c li canh ctra da giic.
Chringminhrdng a'+abc b'+abc , l, *rr-l , *-2- c+abc =r.
' 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
.[sao cho IB : 2IC, Bi6t mAt phing (]IINI) cht.nn@i -{ Tinh ti rO 4.
JD
Ciu VI.
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
Trang 2N6i d
"(n 8a) .(r 8zr)
COs- l -cos x_- l= I € slnl _cOS.r l- 0
c) *cos.x - -? = kn <+ cos.r = I +3k,k e Z
JJ
Do -l<cosx<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
<+ Ssina x-2sin Zxcos2x-4cost x = 0
e 8sin3 x(sinx+cosx)-4cosr(sinx+cosx) = 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.
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 t_ -2=0
L2v = rJ* +v -2 +3
:_I:i ::=
suy ra
"")" -
(r.3
t-.-\2'2
31 22
"^lrt + )
I
A'
tan -1
, .or{ "nr{ "or{
-+ tan- lap thnnh csc <+ sm- sm- +.:+=, sm- +
2222
Trang 3( t-r\
sml
-l
n,
.- "^^^[ t / _" tott a .^:_ A _,_c B
o -:ffi = t-:6 <) zsm-srn- =
222
<D Slll-:- = COS- =
0.25
<> ZSln -:- = COS- <+ Sin B = COS:CO
1
<+ sin .2' 3 = a(sin ,4 + sin C)
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
S, = cL + cln + clo + + cil;s, = c)o + ci + Cj,+ + cji;
thitac6 S=Sr-Sz.
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)
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
Lo4i 3: Kh6ng c6 cpnh ndo ld cqnh cria {la gi6c c6 120 -7Q = 50 tam gi6c
0.5
50 5
VAv x5c .7J ' - suAt li P : =
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 - -' ^t I - I - I n
a'+l ab+l b2 +l ab+l-
-e - (ob @-4 +r) (a'+ (b-a)(!b-1).< r)(a' * t) = 0 " e * @-?)'("0.:t) o
(ou +t)(a'+ r)(a' * t) - "
Md theo gin thitit abc=l,a<b<c n€n c >-!>ab=l=1 suy ra b6t
cuol cung tuon oung EEng thtc xAy ra khi a: b hoflc c : 1 Ta c6 diAu
minh
dnng thfrc ph6i chimg
0.5
Trang 4I
(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
0.s
MaNC: ND n€n JK = JD
y6,v JD=!JA 6u, t4 =2
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
lzMA-3MBl =nf -16t+20
Suy ra lzue*zunl nrto "rt6t e-t 8
13
Ngud'i du1
Td truong
gudi
b"(
'
t-4 t 45
( )=r
I /./ L-.-"'
u