Tim m sao cho dudrng thing d cet Parabol P tai mQt diem duy nh6t vd tim tga dQ giao cti€m d6.. Chring minh r6ng khi m thay... Gini phuong trinh z.,m=lx-ll+a.
Trang 1TRIJONG THPT rr, xoay
pe rHI sAr HACH rAN r
UON: roAN - Lop to - BAN D Thli gian: 150 phft
Ciu I( 3 tli6m ) Cho Parabol (P): y = x2 +2x vd dudrng thang (d); y = -2x* m.
1 Tim m sao cho dudrng thing (d) cet Parabol (P) tai mQt diem duy nh6t vd tim tga dQ giao cti€m d6.
2 Tim m sao cho duong theng (d) cat parabol (p) tai hai di€m ph6n biet A, B Chring minh r6ng khi m thay <t6i trung cti0m I cria AB lu$n nim tr€n m6t dudng thing cO e6ft
Ciu II( 2,5 tli0m ).
1 Giei phuong trinh: 2(t- *).,17 +zr-t = x2 -zx-1
2 Giaiphuong trinh: zJx*=lr-{+al
CAu III( 1,5 tli6m ) ciei hg phuong t infr {'1' +2)(2x+ v)=s t
lx" +4x=6-!
C6u IV( 2 tti€m ).
1 Trong mst phing ory chole;\ vd r(0;r) .xircdinh tqa d0 diem M sao cho
ffi cingphucrng vhi-7 vd c6 dq ddi bing 6.
2 Cho tam gi6c ABC Chung minh r6ng
A=6o0<> I * I = 3
cf,u v( 1 di6m ) cho c6c sd thgc duon g x;y th6a m6n x+ y <l Tim gi6 tri nh6 nh6t cta bi6u thric p =- I I
Gi6m thi coi thi khOng giii thich gi th6m
ndt
Hg vd t€n thf sinh SBD
http://www.violet.vn/haimathlx
Trang 2TRT'dNG THPT r,8 xoay
EAP AN on THI KSCL vTON ToAN LoP 10 BAN D
NAvr Hgc 2afi - 2011
Ciu I
3,0 di6m
1 Tim m dG dulng ttring 1ay cit
o Hodnh dQ giao ctidm cria(d)va(p) lan@
x2 +Zx=-Zx+me x2 +4x-m=0 (l)
Eulng thdng (d) cft parabol (pi
PT(1) c6 nghiQm duy nh6t € A = m+4 =0 e m = _4
Vdi z=-4, (d) cat 1f; tai di6m Ouy nt6t@
2 Chring minh trung di6m I
.-o Dubng thEurg (d) cit parabol,t,
PT(l) c6 hai nghiQm phAn biQt e A,= m+4 > 0 e m > _4
o Gi6 s'h A(x,;y,) vd B(x,; yr) v6i x,;x,
ly vidt ta c6 {x' + x' = 4
lxrx, = -m
ld nghiQm cria PT(t) Theo ctinh
r rrung di6m cria AB c6 tsa aO ,(21) f ( ,) ,,r4.j
V4y khi m thay d6i, trung cti€m I luO
c6 phuong trinh ;r = -2
Cf,u II
2,5 tti6m
l Giei phucrng trinh z1t-r1J7Tz*_t=x2 _2x_r <f l
a
o
TXD: o = (-.o;-r-r$]r[-r+€r.")
D4t r ='li$;>o:+ t, =x, +2x-1.
Thay vdo pT (1) ta dugc
z(t- x)t = f - 4x € t, -z(t- x)t - 4x =0 o f, = 2_
It = -Zx
Vdi r =Z+,17 2.-t =2 e" = -1iJ
vdi r = -2x + J;i;zx-r = -2xo {" .'
o
l3'r2 -2x+l = o (HQ v6 nghiQm )'
VAy nghiQm cta phuong trinh ld: x = _r tG.
Trang 32 Gini phuong trinh z.,m=lx-ll+a (1) l15
o THl.Ntiu x>l thiPT(l) 62 [,srt=x*3o[x=-3(/)
[-r=l t
0,5
TH2.N6u -:<x<1 thi pr(r) ezJ*+s=5-x*[;=13 troail
0r5
o Vay phuong trinh dd cho c6 nghiQm duy nh6t x = t 0,5
Cffu III
. .7
Ir5 dtem
Giei he phuong trinh {,j,* z)(zx+ y)=o (r)
lx" +4x=6-l
1'5
a Der ' Ir(r +2)=1a
ly*2x=v He (I) trO thanh
luv =9 lu =3
ie{
fu=3 ly+2x=3
l{; =l
L{;=;
ghiQm
3
(t;t) vd (-:;q).
Vfly hQ phucrng trinh c6 n
1'0
C0u IV
2,0 tli6m
1 Trong mit phinE ory cho i(z;r) n
sao cho Ifr cingphuong vdi i vir c6 dO dni Uing 6.
1r0
o Gi6 sri M(*o;yo)+Vfr(xo;.yr-t)
7fr cirng phucrng vdi i tctri vd chi khi: & =
Khi d6 M (*o;yo)+ .eU (Zyo-Z;yo -t). I 0,25
o
2 Cho tam gi6c ABC Chri'ng minh ring A=6o0ol*l=3
1'0
o Tac6: -!*I= l-el+ c +t+ b
=3
a+b a+c a+b+c ' a+b c+a
0,25
Trang 4a <+ cb
-+- a+b c+a
o 9 qz =b2 +c'-bc b2 +cz -bc I
2bc 2
0,25
I <+cosl=1o A=600
2
4,25
Ciu V
1,0 tli6m
' Cho c6c s6 thgc duon E x;y th6a min x+ y <1 Tim gi6 ir.i nho n
cria bi6u thric .p =-i- +L+q*y
x'+y' ry
I Theo bdt cl6ng thrlc AM-GM ta c6:
Y6i va,b> o thi (,.r)(;.;)= - *:.i.# 0,25
Ap dpng:
a = ; x'+y' ry - x'+y' Z- l T -ay =-n-7 , T:-T t'- Zxy 4xy 4xy-r4xy
,', o "r*-]- +z>=J ^* L ^ +z=7
(** y)' 4xY (r* y)' (r* y)'
0,5
Chf f: N6u thi sinh kh6ng tim theo cich itfp 6n n6u nhung vin tlfng thi tlu-nc
tli6m tirng phffn theo dfp 6n quy d!nh