TU giethi6t suy ra MH=g ve LIyAH vu6ng c6n.
Trang 1c DAI Hec vINH Dt o sAr cnAr tUqrrlc t 6p tz LAN r, NAwI zorr
T c THPT CrrurEX UOX: TOAX; Thdi gian I m bii: 180 phrtt
r prrn c c cHo rAr cA rff suvn e,o a$m')
7CiuI.(2,04i6m1 Chohdms6 v= !*'-(2**l)x2+(m+2)t ,'+ cOd6th! (C^), m ldthams6.
'3
I Khio s6t sy bi6n thi€n vi vE dd thi cua ham s5 d[ cho l<hi m = 2
2 Gpi A ld grao tti6m crla (C,) vdi trUc tung T\m m sao cho ti6p tuy6n cua (C.) t1i A tAo vdi hai FUc tga itQ mQt tam gi6c c6 diQn tfch Ui"g 1.
3
yCAu trI" (2,S trfrenre) 1 Giei phuong trinh (x+ 4)' -6 = 13
2 Gifliphuong tinh (2cosx- l)cotx = -l *
srn.r,
Ciu Itr (1,0 Ci6m) Tfnh tfch phin / = dx
Cf,u IV (f,O ai6m) Cho hinh hQp ABCD.A'B'C'D'c6 ttQ Oai dt ci cdc cenh <tdu Uang a>0 vi
ZBAD=ZDAA'=LA'AB=600 Ggi M,N 6n luqt ld trung ttidm ctra AA',CD Chfmg minh
MN ll(A'C'D) vi tffi cosin cta g6c t4o bdi hai tludng rhing MN vd B'C.
Clu V (f,0 tli6m) Cho c6c s5 ttrgc E a, h, c Tlm grd fri l6n nh6t cua bi6u th{rc
r
FCA
P_
a2 + bz + c2 +l (a'+ lxb + 1)(c + l)
n G Tht sinh cht ituqc tdm mQt trong hai phdn $hin a, ho{c b)
agn
Cf,u VIa (2,0 rf6n) 1 Trong mflt g vdi hQ W Ory, cho tti6m MQ;I) vi hai ttudng thing
dr:3x-y-5=0,d2:x+y-4=0 Vi6tphuongtinht6ngqu6tcfia<firdng thing d ttiqua M vdctt
dt, d2lin t4t A, B saocho 2IuIA-3MB =0.
2 Trong kh6ng gian vdi hg fiUc tga tlQ Oxyz, cho c6c di6m A(2;0i;0), H(l; l; l) Vi6t phuong tinh
mflt ph[ng (P) di qt;n A,.F/sao cho (P)
"ii( q, Oa lhn hqt Cr B, C th6a mfln diQn tich cta tam
gi6c ABC Uing +G.
Clu VIIa (1,0 di6m) Cho t$p A=10,1,2,3,4,5,,6,7) H6i tU t$p ,qWp tlugc bao nhi€u s5 tp nhiOn
chin gdm 4 cht s5 khdc nhau sao cho m5i s6 iffi ttAu l6n hon 2011
b Theo chuolg trlnh Nf,ng cao
Ctu VIb (2,0 di6n) l Trong m[t phlng vdi hQ W Ory, cho c6c Adm ;0; 2), B(4;3) Ilm tAa d0 didm
\ M
soeho ZM4B= 1350 vdkhodnecdchtir M dhnttu0nethEne AB hAns JiO
.
gian vdi hQ truc tqa d0 Oryz, cho c6c tti6m C(0; 0; 2), K(6;-3; 0) Vi6t phuong tinh
di qua C, K sao cho (a) cfit Ox, q 4i A, B thlaman th6 tlch cria tf diQn OABC
[3t*'+3' = lo
'lt 1.,
l;logr x' -logr y = g
lz
I Brc sd trd bdi vdo alc ngdy 26, 27/03201I Dd nhdn thrqc bdi thi, tht sinh phdi nQp lqi phiiiu dtt
thi cho BTC
2 Kj lrhdo sdt chiit ttrong t,in 2 sd duqc t6 chftc vdo chiiu ngdy 16 vd ngdy 17/04/2011 Ddng ki du thi tqi
Vdn phdng Tr THPT ChuyAn t* nSdy 26/03/201 I.
trongxuanht@yahoo.com sent to www.laisac.page.tl
Trang 2DAp AN of IsAo sAr cn,ir LUqNG nfip pLAN 1, NAM zorr
*fON: TOAN; Thiri gian lirm bhiz 180 phrit
Ddn dn
L; (1,0 itiam)
-5x2+ +*+!.a
J
0x+4.
f x <ll2
<0<+ll2<x<2 vd'Y'>0€l
-l*>2
khodng (a;lll) vil (2;+o), hAm nghich bi6n t€n
(rtz;2).
i C* 1,!: Hilm sd dpt clrc tl4i tpi x = | I 2, y"u = 5 I 4 vi tl4t cgc ti6u t?i x = 2, ltr = -t .
c Ed thi: Ed thi cit tryc tung
tei A(0;rl3)
I.
(2'0
- I \
olem,
2 fl,O ttidm
Ta c6 A(0;1/3) vdy'= 4x2 -2(2m+ l)x * m +2 Suy ra y'(0) - m +2.
Ti6p tuy6n cria tt6 thi tai A l d : y = (m + z)x +
1 Euhng th[ng d cht Oxtai atfr ; ol'
l (1,0 ili,
DiAu kiQn: x3 +3x 2 0 e x > 0.
Kl
1 *:Te :* li :9:::11* i:l:l f-:ff I ? :
Trang 3Nhfln thdy .r = 0 kh6ng thda min n€n (l) tucmg duong v&r x +t *i-6trf,J = 0
Dil
f+1, =t,.t2ffi t^dugc t2 -6t+8=0<+t=2 holc t=4 (tntlk)
0,5'
+)Vdi t=2 tac6 x=l,r-3.
+)VOi t=4 tac6 r 8+ Jdi,tr=8-.fiT.
DiEu kiQn: sin.r * O,cosr*l hay x *kn .
vci ailu kign d6 phuang trlnh da cho tuong rhrongot 2cos2r-cos'r-3
smr
o (2cosr-lXcosx+l) - 2sinx- <+ (2cosx-3)sin2x= -2sin2 x
sinr cosr - I
0'5
Tac6 I n &
(2'
I
I
0
z',
Vdi r= 0:+ t =lrvdi r=l=+ t =2.
&=dt hay fo-gi2, 3ln2' -".*?
3
0'5
=2'g,d, : I '( t _ I t
Khi d6!=rnzlt''-zs
5rnzl\r-5 t+sl
#(,"F - sr - hr, rrl',,=#rn* . 0'5 +) Gqi 'f l*ffing di€m DC' Vl NI// CC'
vil NI * I Cc'n€n NI - rhil'vil NI /l IV/4.'.
,2'
:
+) vt AI,B',C //A',D
nEn flC)*./(A'I, A'D) (r)
,"
-t\ ,"
0'5
Trong LA'"DI ta c6 cos '/.DA'I , A' D2-+.A'12 r DI,
= -3,:
-<-i-2A'D.A'I 2J5
*";:33.,5
Tt (l) ve (2)suy ra cps(IAf, B'C) = | cos /.DA'l I =
-:: =
(2)
V
(1'0
-.1
orem
Ap uung;nrycosita c6
az +b' +cr +r>|to+el'* jtr+l)'>
Ir"*b+c+l)2,
(a +lXb + l[c * g < [' *lftl']'
.
-: -.- , : i ]
Trang 4Ps 2 - 54
Suy ra
a+b+c+l (a+b+c+3)3
DAt t - a + b + c +l,t > I Khi d6 ta c6 P <? 54 =
t (r+ 2)t
0'5
Xdt him f (t) =i @ hen (L + co) Ta c6
f, (t) = -3.# = 0 <+ st = (t +2)2 el"='., f, (t) >0 <+ I < t < 4
Suy ra BBT
DWa vdo BBT suy ra P <l n6u ding thfc xiy ra khi vd chl khi
4
Vfly gi6 tri ltu nh6t cta P le 1, Uut dugc khi a - fi =c = I .
t'=4Qa=fi=c=l
_f'(t)
VIa
(2,0
tti6m)
l, (1,0 itifimr
-xr)'
r-lzttu=3ffi
I
lzffi=-3ffi
3-xr)'
(1)
(2)
0'5
+) (1)e 2(xr-1; 3xr-6) -3(*r-l;3- xr)O{* =}
lx, -z (
suy ra
^lit ;), BQ;z) .Suy ra phucrns nlnh d : x - y- 0 .
*) (2)<+ 2(x,
- 1; 3*r- 6) = -3(x , -li3 - xr)*
fi; =1
Suy ra A(l;-Z), B(L;3) Suy ra phuongfitnh d:x-l = 0
0'5
2 (1,0 ilidrn)
Gid su
Suy ra
B(0; b; 0), C(0; 0; c) trong d6 bc * 0 (vt n6u bc: 0 thi tam
(P)'*+ 4*' =l vi H e(P) non 1*1= 1
b c 2 s,u" =+lrzl,frll=; (bc)z +(2c)t + (2b)' - 4J6 e b'c' +4b
gi6c ABC suy bi6n)
(l) +4c2 =384 (2)
0'5
ii
OFI b + c = u, bc =y Khi d6 tU (1), (2) ta c6
ll
-Zu) = 384 b-c=4
[r=8, y=16
L, - -6,p = -12'
suY ra fi = -c 3 + Jn
S=-c 3- Jzl
Vpy c6 3 m+t phing (P) thda mdn li (4)'*+ 1*1=t hay 2x+ y
Trang 51tS,|*-+.:h=t hay 6x+(3 +Jn)y+(3-
^r7-t2=0"
VfIa.
(1'0
tli6m)
Gii srl s6 thda mfln bdi todn li ab;A Theo bdi ra ta c6 o {2,3, 4, 5, e,l\; d e {0,2,4,61 .
Xdt hai tudrng hqrp:
TH I: d = 0 Khi cl6 a c6 6 cdch chgn, b c6 6 c6ch chgn, c c6 5 c6ch chgn
$qv rq q6i 6x 6r |
= t!9 tq6l
0'5
TIt 2: d Q,4, 61 Khi d6 d c6 3 c6ch chgn, a c6 5 cdch chgn, D c6 6 c6ch chgn, c c6 5
c6ch chgn
Suy ra c6: 3 x 5 x 6 x 5 = 450 (s5)
Vfy s5 c6c s6 thda mdn h 180 + 450 = 630
0'5
vIb.
(2,0
tli6m)
l (I,o itidm)
Gii su M(x; y) Ke MH L AB .
TU giethi6t suy ra MH=g ve LIyAH vu6ng c6n
2
Suy ra AA,I = MHJ, =.,6.
l3 50
0'5
D[t u - x-1, v - ! -2 Khi d6 ta c6
(
-1, v=-z
2 (1,0 iti6m)
(1)
fab=)
<+ sb -9<*l
Lob = -i
Gi[ su A(a;O; 0), 8(0; b;0) Vl Vonu" > 0 n€n ab *0.
Suyla @):I+ 4*1=r.vi Ke (a) n6n 9-l=r
'iiobzab
il
Oe,ACle fii diqn vudng t4i On€n Vouur=
* OA.OB.OC = * I ol.t b I -3
(2)
(3)
0'5
hw thi tn> 0,25 didm
2x*2y+32-6=0
VIIb.
(1'0
I \
otem)
EidukiQn: x*0,y>0.
iu"o
|rcCr*' -log, y= 0 <+ log, lx I = logr y elxl= y e
l:=:,
* Vdi x = y, thay vio phuong hinh tht ntr6t ta dugc 32*' +3' = 10 c+ x = 0 (ktm)
0'5
* v6i
vay n
= 10
0'5