tho ducrng tron tAm O b6n kinh R vd mQt.
Trang 1PHoNG GrAo DUC vA DAo rAo
THANH prro.rrAl DUONG
Cffu 1( 2,0 tli6m):
1) Giai c5c phucrng trinh sau:
a) Vx -3 =2
D GiAi hQ phuong trinh sau:
C6u 2( 2,0 tli6m):
l) Thgc hiQn phdp tinh:
I
a) J+s -Jts+)J+tz
J
on rrnvr rRA cuor HQC xt r NAvr HQC 2022 - 2023 Mdn: Tofn,lcrp 9
Thdi gian ldm bdi: 90 phft
DC bei gdm: 05 cAu, 01 trang
r^
b) V4x'+4x+l =3
lZ*-!=5
lsr*3-y=18
't ^lti l
hr : ''' :'
r/3 +l 2-.13
sJi +2
;vli x>0;x+4
x-4
CAu 3( 2,0 tli6m):
Cho hdm sO bac nhdt: y = (*-3)x+ 2m-5 (m ld tham s6, *+ 3) c6 d6 thi (d) a) Tim tli6u kien ctnmCC nam sO OOrg bi6n tr6n R.
b) Tim gi|tri oiam d6 ducrng thing (d) di qua tli6m A (-1; ).
c) Tim gi6 tri ci.r- m Oe nai duong thing (d) ve (d') : y = 2x + q cht nhau t4i cti6m c6
-;-J
noann oo Dans
-.4 Cflu 4( 3,0 tli6m):
tho ducrng tron tAm O b6n kinh R vd mQt <ti6m { nam ngoii ducrng tron Qua A kd ti6p tuy0n AB v6i cludng trdn (B ld ti€p tli0m) Tia Ax nim gifia AB vi AO c6t duong tron
(O; R) t4i hai <Ii€m C vd D (C n6m giira A vd D) Gqi M ld trung di6m cira ddy CO, ke gU
vu6ng g6c v6i AO tpi H
a) Tfnh OH.OA theo R.
^
b) Cho dAC =-ADB Chung minh AC.AD : AH.AO vd CFO *6O = 1800
c) Qua C k6 ti6p tuy6n thir hai vdi duong tron (O) cat ONzI tpi E .Chrmg minh ba cli6m E,H, B thdng hdng.
Cflu 5 (1,0 di6m):
Cho a, b, c duong th6a mdn 6a+ 3b * 2c: abc Tim gi|trilcrn nh6t cira bi0u thric:
r=_L*_L*_-'td t ^to' .i ,tc s
n6t -
2) Rft gon bi6uthric sau: P =*-g+
Ji+z 2-J;
M
Kf
\
i i
Trang 2PHONG GIAO DUC VA DAO TAO
THANH prrO.rrAr DUONG
HTIoNG nAx cnAnr
or rrBrvr rRA cu6t Hec rY I NAU Hec 2022 - 2023
M6n: To6n - Lcrp 9
Hu6ng d6n ch6m g6m 04 trang
-,.,=
,1;1 Cl'
iIt.lG G
'in 0A
,.\ -t
*g
i
I
la
]*i-z;DKXD: x23
<>x-3:4<>x-7(tlm).
VQy phucrng trinh c6 nghiCm x:7
0r25
0,25
1b
^[a; aayal =3
o,{12**tY =z olzx+ tl : :
0,25
l2x+l =-3 lx=-2
VQy nghiOm cua phucrng trinh ldr x: 1
( N€u thi€u I nghiQm tr* 0,25d)
hoflc x:-2
0,5
)
lZ*-!=5 lA*-3y=15
<e<
[5x + 3y =18 [5x + 3/ = l8
0,25
[l1r=33 [x=3
[5r+3Y=18 [r=,
0,25
Vfly he phucrng trinh c6 nghiQm (x; y) : (3;1) 0025
,
la
J48 - Jts *Il^,
J
=4Jj-s.,6 +ali
=3J1
0,25
0r25
1b
2
Jl+t
,-6 : zrJj -D _
2
J\<z-.,61
2-J,
0,25
2 V6ix)0,x +4 ,tac6.
Trang 3,i0 Bl](
i.iT40
/.t
-l'uU
g
-:-l-Ji*z 2-J; x-4
zJirJi -2) +(Ji * r)(J;
*2-SJi:2-2x - ali+.r + 3Ji + 2 - sJ; -2
zJirJi - zt 3J;
X6t hdm s6 bac rrhht: y : (* -3)x + 2m - 5 ( m *3)
DC hdm s6 eOng bitin tr0n R e m -3 > 0 e m>3
Vl AO-_ tt l t dm s6 di qua di6m A( - l; a)
nonta c6: (m-3).(-1) +2m-5=4
e-m+3+2m-5=4
€ nt=6 (t lm)
Vfly m: 6 thi thi hdm s6 di qua A(-1; a)
Xdt2iluongthang : (d): y -(m-3), +2m-5 ( m*3)
(d'): Y:2x+4
DK: Dudng thing (d) vd iluong thang (d) cat nhau
em-3+2em*5
Duong thing (d) vd (d') cat nhau t4i di6m c6 hodnh dQ bing -1
_?
=x: -i 4'2tnayvio (d') ta dugc Y: 5
0,25 '
-3s
Thav '42x - : vi v: a vdo (d) ta dugc:
(*.-t)t7)+2m-s =;
e -3m+9 +8m-20 =10 e * -\t t m)
5 Yav m =?)
)
Trang 4V6hinh dring ( n6u HS vE hinh d6n c6u a cfing cho cli6m t6i dal 0,25
a
X6t tam girlc ABO vu6ng tai B c6 BH
= OH.OA : OB2 ( hq thfc luqne)
I AO
0r5
Md OB: R+OH.OA: R2
b
X6t tam gi6c ABC vd tam gi6c ADB c6 :
ABC = ADB ; BAC chtng
= A ABC d6ng dpng A 4DB ( g-g)
AC AB
AB AD
0r25
X6t tam gi6c ABO vudng tpi B c6 BH I
AH AD ^
= = AC =1 AO md CAH chung
> LCAH d}ng dpng LOAD (c-g-c)
0r25
=fri=60
Md fra *Cfro= 18oo (kc bn)
= CHO + CDO = 1800 (dpcm)
0,25
c
X6t (O) c6 M ld trung di6m cira d6y CD
= oE LCD tai M (t/c)
X6t ACEO vu6ng taiC c6 CM f EO
Md OH.OA: OB2 vd OC : OB ( Brin kinh (O)
.QU OH
OA OE
= 5fu=ffi md 6dq=9oo > GE =9oo
= EH r OA md BH I OA > ba tli6m E;B; H thiirg hdng
Trang 5Hoc sinh gidi cdch khdc &ing vdn dqt di€m t6t da.
5
Dat x =a y=!, r=! thi x,.v, z>0 vd x+ y+z :xyz.
2'r Khi d6 taco r
=-L*J* l-JI +r' Jt *y' tlt+,'
0,25
Ta c6
-L_
2(x+y) 2(x+z)
Tuong tu,tac6.
l.x,Z1.,xy
0r25
x+y x+z v+z 3
Z(x+y) 4*+r) {y+r) 2
0,25
x=!:z= ,6= o=Ji, b=2.1i, c=3Ji.
Vpy gi6 tri lcrn nh6t ctra bi6u thirc T ld 1 khi vd chi khi
2
o=Ji, b=2Jj, r:3J1.
0,25