TiR UN{;'rertry {,.T"f,}.F[ g* m*,&,jq*
sd +q' - Hq;ri zq}4 F-fr'F'F{ANF{ HGHI
ilT : G,$,22,453 3 3{t - {},# "2:2# t E F 2#
a-#E TEXE TFEti *)AE ffiSC (*qt 2)
na$ru T*€I: T$AN
Ky thi rcgdy:27183I201i T'hbi giarc ldm !;di : 180 pk*t
-:i
pnAru emur*G fHa rAr cA eAc rmisrnr-i
(lau I (Z,fi diArn) Cho y=xr-2(m+i )x2+mr+nr+3 (l;, l) Khao sdi & vC d0 thi lrirnr:,0 khi nr=O
2) ain sir dd thi (1) cit ox rtri + diem c6 hoirnh dQ x,, x2, xr, xo chfng minh rang:
xljrl + irr-t1 +.r1.\:.1 +.r).tr +,y,_rr 1 r ,-r., { $ Cau II {2,t} diAm)
II Ciai phLr,rrlg llinh : sirr' l.r.uti5g.v+sinr3-u= lrin''t.rin 9"
222
2) Girii he iren iP,:
ti _r .,ll
l1l 1-.1 '.=
-{lnu ttl {l.S didrn}
Cdu IV (1,0 diilmr
Lang tlu ABC.A'B'C' cd cirirrr cil-Ldng cao FI ke tr.lr A' 1) trung didm BC 6i = 600, AB=a
AC=2a A.'A=2a, tfnh khoring c{ch gifra A'A & BC
Cau V {1,0 di6m) Gidi phrrong ri'inh: r,f,+qI \' | ^[x1
pniix nrEuo ( rhi sinh chi duoc lirm phdn A hoac phdn B )
Ciu Vila (2,0 diiim) i)Trong h0 rOy cho hinh binh hlnh ABCD c6 C(-4,-5) duong cao (AH): x+Zy-2=A.dudng
ch6o (BD): 8x-y-3=0, tim toii clo A, B, D 2)Trong h0 Oxyz viet phuong trinh mat phing (Q) song song mht phing (F): x+y-22+3=0 sao
cho (Q) cat hai dudng thlng 1ct,): ! =':t = 1e(d,): {-,1 = v :}-= i theo doan AB=9
2 I I 2 t"-"
(A ed,,13
= d, )
Cflu VIIa (1,0 didrn) Girii phuong trinh: logi -r + (.r - l2)log,x + I I -.r = 0
Cau VIb (2,0.tiem)
1) Trong he xOy cho hinh binli hanh ABCD c6 B(1,5), dudng cao (AH): x+2y-2=0 phAn
gi6c i-n lii x-y- l=0 'fim roir do A, C, D
I
r - .1,' /a \ .lJx 7r\
srnl - |
tj \ ! a]t/
4,r
) I J
{)
rffi
{r&
4q$
€
ft,, w,i
u
rty#
{
-s
rS
,, tR.
T$
& -'*+
N
S"C
&
{EF
*S
o.ip
€b
,f ,rflt
*'*J
d\
(o z\
srnl -+ - I
l? al
2)Trong h0 Oxyz ,, iet phrLcruu rrlnh mat phang (Q) r @,+ =
cdu (s): x2+y2+22 -2;<+4y-62- I l=0 theo dudng rrbn (c) c6 b6n kfnh bang 3
CAu VIIb (1,0 di0m)
Cho s0 phuc z thod mln : l.i- :' = 3(- I +2i), rtm jzl +lrl' +lrl'
0'Cdn bO r:oi rhi khilng gitii rhich gi th\m
-Thi thft,lrtt I nsi,r iQn4l20l I drt rudi nphv I6/06l?0l I
Trang 2-t e
EEBIqFII€G lEbAFg V& ffiARS ,&ro EqFAH
g'E{F TE{[i *]&g E{{}C S#T {X
r
_;_ _ _
i;:
r
025
1i
,r
\A. 0+ 0 0 -f
- +41
\ '\
"'
- -
4 t"
0.5
I
;i't = i) ,,i,, : i'i 2x) y 2 ((1; 'l){D: It
SR'l': * -y'= 4lt 4-r =.-l.ti-.,;] -i): Ct+,).i
I
L
) i,
-
t-)r
-
I
I no riii (C') n Oy = {0,2);
(C)nOx-Q
U.i)
0.7lt
a.25
n ti
di6m phdn biOt khi phuong trinh
c6 2 nghiQrn duong phin biQt
rfr^ (r), kLt dilr, J-."
-J+ =0
N,tx3 + xtx4 + x)x3 + l,x4 + x.,xa) = ri + 4 + xi +-"ut ) 0
Edt t =xt >0 thi do thi (1) c'at ox b 4,
f -2(m+ 1)/ + m' + nt +2 = 0 (2) Phai t
lL':*-l>0
I
€ l,S =2(nt+ l) > 0 <> in > 1
I
lP = rt2 + m+2> 0
G" rr,/, h, ttghf*;"""g Pha" btcJ;
trinh xl =1, vi xt =tz + xr +.f,' r.Y, *
Ta l4i c6: (x, + \ +x, + xu)t -2(xtx, + t
=0-ZT>A=T 3A
2
i
I
I
I
I
I
iiI
I
0.5
Pt e (L -cos4x)cos6x+ I -cos6x = rin* rinI
22
<> 1-
f,korzr+ cosl0x) = jt.otr-cos10,r) <> cos2x+cosx-2
D+
IL
2cos2
'-.
lr'
- l_-,
L-x+cosx-3
1 y'+9
xz+{v=.y2
COSx=1
-7 ,IJJ
t^ - y
It^
l-6x'+
-g
12x =3
k2
) v'
lf)
+
k
3
e
v = nt - 6xt +l2x -B = y3 +3y2 +3y +l 0.5
Trang 3L:-, r - l
ilAL t -= ]+ I rhi i - f:ln rr 2tlr =ZJt+rl,r; t- i)dt:J{ tcos2 t -')\dr
I -' rgeli6m cua ACthitirgidthi€tsuy ra BC:a-/i,Znc:900=*, HK,llC.l{A'dli
r r uol K la irtu
m6t vu6ng g6c nhau n€n xem I!(CI,0,0),AFI ='[AE + THt
L?!/ _, ,,,,0trJ -, L- \ : , ru), 0) e {}x
2, ?_
t:
KQ.;,a) eo1,; o(+
lrrc1L!!,o,as L I " N,f
Xem ilaa'c'r'1 = (0, 3,2) =>
11
-tL 1 - /L
-')
.L
72
(t.25
*Tu ,4 B * B'(0,
tl
4.7 5
1.t
3y +22 = 0 =+ d:(AA", BC) = d(A, BB C C') : -:*
vti
EK: x >2.Taco pt€>
r : Vx,+91-10=Vx- Z-r+x= -g€-#- =-Q ,+(-r-3)(x+ j)
"lxt +91 +i0 tJx-2+l
0.5
zd
oiu aa (-2, i) = BC
, -5) vir vu6ng gbc v
+4)-t-(y+5)=0=
l-zr+y-3=0
l+
\-L8t-y-i=0
ltc diqua di€m C(-4
c6 phuorng trinh -2(x
I toa dQ B la nghiCm hQ
I
B(1,5)
Trang 4Al2 -,) tt,{t}.; Il_ , - o,!tf)e 8x - t' - ] = i-)
.Ek: x > 0 DAi / = log, x, phuorrg trinh tro thirnh:
t(I
l rt * (x-12)t+11-r=0, a+b+c=0 suy ra hodc log, -r=1hcdc log,x=11-x
|* log,r=i=x='l(nhan)
t-| * l"g, -r - I I -x=)x =S lirnghi0m duy nh6t vi VT d,3ngbi6n VP nghich bidn
vib I2d
I eC ai qua ciiem B(1,5) vA vuong goc v6'i tt.-,,(-2,1.=+ BC
, {, A'^ *
I
toa a0 c ld righi€m n*
trl, i, = u " -> C(-4,-5|
I Cqi ,a la diim dOixrmg cuaB quaphAn giitc x-3t-l=O(d),BA n d = K (KB) rii qua B vi
I {"-'-:=^o=0= xf1,trl= A(6,0) Do A=C.4 r-t AH ndn toadol tanghiQm hQ
lf"-y-I=0 '2'2'
ll'-zv' 6=o=o
=A(4.-t)
Ll"?41-o
I n=ID=D(-1,-ll)
0.5
0.25
Q.25
0.5
(,S) c6 tltm I(7,-2,3), fi = 5
(Q) co dang 2x -2y + z + m = 0, d{l,Q) = 4 0,5
12+1+3+n',1
-J
m+9 =12 _-r,
m+9 = -1'2
m=3
-i m=-2I
(Q):2x*2y+z+3=A (Q):2x -2y + z -21= A
0.5
VIIb 1d
i
Gi6 sit z = x* yi
regt=.p.t _1- - -i _ - l ll" rlx" +y-.
lY=3
(x,veR)'
I Er;.]
-2(* - !i) = -3+6i <3' i v^' )/
lzv=s
A4 t1 t1:
lx/-r:l "l-l ) €>1 2
f"' +9 = 12x-3)2 L:r' -l2r = 0
=l'l+ltl' +lrl' =5+25+125 =155
0.5
- Thi thfi dot 3 nsdy 3010412011
- Thi thit rlrtr ntdi nadv I6106120l I