PHoNG GIAo DUC vA DAo rAo DrEN cnAu
Bn rnr voxc lr, cHeN Hec srNH crOr HUvEN Lop 9
NAvr Hec 2oL4 - 2ors M6n Todn - (hdi gian ldm bdi 150 philt)
Biri 1: (2 diem)
Tim sd tg nhi6n c6 5 cht sO
"tra, thoa m5nj^F"a" = ou Biri2 @ diem)
1, Tinh gi6 tri ctra bi6u thric: M = X * y,
Bi6t: lr" * Jr' + 201raJy *,,1 y' +2014)= 2914
z.Bi6ta-b: J2 + l,b-c: Ji -t
Timgi6trf criabi6uthric: A: f +b'+
"'-ab-bc- ca.
Bii 3: (6 diem)
Gi6i c6c phuong trinh vd hQ phucmg trinh sau:
I, ,lx'+ lox +2t - 3 ^l;$ + ZJii - 6
2, x (x+ 5) - 2t^[rt *5ta -2
3 'Lt'*!2=6 [v+x+y=2+3{2
a
Biri 4: (7 di€m)
1, Cho hinh vu6ng ABCD nQi ti6p trong ducrng trdn tdm O b6n kinh R M h
cli6m U6t tcy trdn dudrng trdn
" d, Chrmg minh: MAo+ MB4+ MC4+ MDokh6ng php thuQc vdo vi tri di6m M tr6n tlucmg trdn O
b, Chimg minh: MA.MB.MC.MD < 6R4
2, Cho tam gi6c ABC c6 tli6m D nim trong tam gi6c sao cho:
AD.BC : BD.AC vi ffi : ffi + 900 Tinh: AB'CD
AC.BD
Blri 5: (l diAm)
TrOn bdn cd 0 vu6ng kich thud c 2014x2015, trong m5i 0 c6 mQt vi€n bi Thuc hiQn di chuy6n cdc vi6n bi nhu sau: M5i lAn chgn Z 6Aatkj c6 bi vd di
X A ^
chuyOn 1 vi6n bi cria m6i O ndy sang O bOn canh (La O c6 chung cAnh)
H6i sau nhiAu lan di chuv6n c6 th6 dua t6t chcdcviOn bi vdo 1 0 duo. khdng ?
Trang 2
-ntit -prroNc GrAo DUc vA oAo rAo nrnx cnAu
Huol{c rAN cnAivr roAN 9 voNG rr
NAwI Hoc zor4 - zors
Bei I
(2 d)
Edt; ab = m;cde = n, Tir bdi ra ta c6; 1000m * n : m3 0,5
M{t kh6c vi: n ( 1000 = m' ( 1000m + 1000
+ m(m' - 1000) ( 1000,
0,5
N6u m ) 32 = m(m' - 1000) ) 1000 (VO lfl = m< 32; 121
Ti rtlvit Ql + m:32 = abcde :32768
0,5 Bai 2
(4 d)
I Tir di6u kiQn bdi ra ta c6:
t-\r-l
G - Jr\zotq )1, +,[7+zot+ly * ,[7 uo*l= 2uq1 - ^[.+zow7
0,5
Q)
Tuong tg ta cfing c6: x: - y - J7 +ni + (2) 0,5
Ti Ol vit 1z1suy ra x * y: 0 0,5
2 Tt diAu kiQn dd cho suy ra: a- c:ZJ-z;
= (a-b)' :3 + ZJi ;G-c)' :3 -2J, ;@-c)' :8 0,5
+ 2(at + b' + ct - ab- bc - ca) : 14 0,5
Bai 3
(6 d)
I DAt: G+3 =X;Jr+l =I' (X,Y
Phuong trinh dd cho trd thdnh:
>0), (X-2XY-3):0
0,5
NCu: X-2:0 <> x: 1: Ndu: Y- 3 :0 <+ x:2 0,5
Vdy phucrne trinh c6 nshidm ld: x: t vit x:2. 0,5
Phuong trinh dd cho trd thAnh: yt - 2y + 4 = 0
e ( y + 2)(y2 - 2y +2)= 0.<> y +2= 0 .e y = - 2
0,5
Thavy:- 2.taduoc: xt+5x - -6 €xt*5x+6:0 0,5
ex: -2 hoic:x: - 3 VOynghiQmPTld: x:- 2vitx- -3 0,5
a
J NhAn 2 vd pt thf nhat voi 2 r6i cQng vdo pt thv 2 ta dugc:
(x+y)2+2(x+y): I0+6J,
e(x*y* 1)': Q+ "12)tex*y* 1: t G+ Ji)
0,5
N6u x * y : 2 + J, vd xy : 2Ji gihirata dugc:
(x,y) : (2, D ) noAc: (x,y) : (J, ,2) 0,5
N6u x * y: - 4 - Jt vd xy: 6 + qJ, tlikh6ng c6 (x,y) th6a mdn
Vgy nghiQm cria hQ ld: (x,y) :{{z,Ji),{.11,4I
0,5
Trang 3Bei 4
(7 d)
1(a)
1,0
Ta c6:
MA4 +MCa : ( MA2 + MC2 )' -zME.MC2
: ACa -zr,lftf AC2 : 16Ra - gnf.vtt2 1,0 Tuong t-u: MBa + MDa : 16R4 - 8K-'.MK' 1,0
+ MAO + MB* + MC* + MD* : 32R* _ 8R' ( MH'+ MK')
:32Ra- 8FP'Ff :24R4
1,0
1(b) Ap dUtrg BAt deng thirc Cd si ta c6:
(MA4 +
1,0.
Vi: MA4 + IvBa > zJ u,q' -tila4 = 2MA2 MB2 MC4 + N{Da > zJ uct -ttoa = 2MC2 MDz
+(MAa+MBl )+(MC4+MD4) > zffi
= (MAa + NBa ) + ( MC4 + N,Da) > +vte.MB.MC.MD
1,0
+MA.MB.MC.MD < 6R4, Ddu ":" *Ay ta e MA: MB : MC : MD
Nhrme di6u niv kh6ne th6 xAv ra n6n: MA.MB.MC.MD 6R4
0,5
2
L6y di6m E sao cho tam gi6c BCE vu6ng cAn t4i C (Nhu hinh vQ Tir gi6thiOt = AADB - AACE
= AABE - AADC + AB.DC = BE.AD, md BE :BCJI
>AB.cD=BC.ADJ2:BD.AC Jz= 4t:Q2 : J,
AC.BD
0,5
Trang 4Bdi 5
(r d)
Ta t6 mdru c6c 0 vu6ng vbi2mdu den trdng xen nhau (Nhu ban cd vua) Ta th6y c6 1007x20I5 vi6n bi trong 0 d"n vd 1007x2015 vi6n
bi trong O Fetrg (I.a sO le) Sau mdi l6n di chuy6n: SiS vi6n bi den (Ho[c trdng) ho[c gifi
nsuyOn hodc thav ddi 2 vi6n (Ld sO
"han)
' !
0,5
Nhu vQy dir sau bao nhi6u ldn di chuydn thi sg thay tt6i s6 vi6n bi
den (Ho{c trdng) lu6n ld s6 chin + V6n cdn bi trong 0 *" vir trong
0 tr6ng, hay khdng th6 c6tdt chcdcviOn bi vdo trong 1 0.
0,5
Huong ddn chSm theo thang etiOm 20;
Bei 4 phdi c6 hinh vC tlung mdi chtim;
TrOn tldy ld eliOm ti5i ea cho m6i nQi dung, n6n khi chlim c6 th6 chi0t <ttin
0,25 dtrong trmg nQi dung d6;
CLc cichgiii khdc dfng ciing cho iti6m t0i tla theo timg phan co ban ndy;
T6ng tli6m todn bdi ld tdng <fjem ttmg phdn khdng tdm trdn
ddn ndy c6 3 trang)