UBND TP THAI
NGUYEN
KIEM TRAKHA9
sA1' HQC SINH LoP 9pHoNG_q4q luc_yADAo rao Nim
hsc 202t _ 2022MON: TOAN
Thdi gian ldm bdi: 120 philt, kh6ng ke thdt gion giao
di pO
memtra
gdm c6 01 trang, L0 cffu, m6i ceu 1,0 tli6m)on
gA.rCflu
1. Kh6ng dirng mdytinh cdmtay,rut
ggn bi6u thric:o:(# 4Jr*fi) Jr-Ji
Ciu2.Khdng dirng
mdy tinhcAmtay,
hdy giinhQ phuongtrinh: {'*-^'= .'
lx+3Y = 4 Cffu 3. Cho phucmg
trinh
2x2-6x+2m-5
=0
(1)v6i
m ld tham s6.a) Gi6i phuong
trinh
(1)v6i m:2.
b)
Tim gi|tactra
m dO phucmg trinh (1) c6 hai nghiQm phan biQt x,,xr thohmdn t1 '
+j-
= 6xt
x2t- r-
Ciu
4. Chobi6uthirc:
p= 2^l*;9 -+! *2tU
+1'voi x)
0,x*4,x+9
x-54x +6 tlx -2
...lx-3
a) Rirt ggn bi6u
thirc P.
b) Tim t?rt citgi|tri oia x
dC p >f
.C6u 5.
Cho ducmgthSng(d):y =(r-2k)x+3. Tim ei6tri cirak
ACducrngthing (d)
cAt tryc hodnh tpi mQt di6m c6 hodnh dQbing
- 2.C6u 6. Hdng ngey bpn Lan di hgc bdng xe dap, queng ducrng tu nha d6n trudng ddi 4 km.
H6m nay, khi dA di du-o.
c
1 km thi xe dap bi h6ng, ngaylfp
tuc Lan di nhd d6n truong bdttg xe m6y v6i van t6c lon hon van t6c khi di xe dpp ld24 krnlh,vi
th6 Lan ddd5n trudng s6m hcvn 10 phirt. Tinh vQn t6c cria bpn Lan khi <Ii hgcbing
xe dpp.Ciu
7. Cho tam gi6cABC
vu6ngtai A dulng
caoAH,
c6AB : 9
cm,AC :
12 cm.Tinh dO dai cludng cao
AH,
dopn HC vd s,5 do g6cB
(ldm trdn d6n d0).,
Cffu 8. Cho tam gi6cABC
ngopititip
tlucrng trdn (O;r),
GqiI
ld ti6p cli6mcta
cpnh BCv6i
duong trdn (O).Ve
dudngkinh IN, tiiip
tuy6n cria dudrngtrdn
(O) taiN cit AB
vdAC
lAn luqt tpi D vd E. Chimg minhring: DN
.BI :
12.Cffu 9. Cho hai ducrng tron (O) vd
(O')
c8t nhau taiA
vdB.
VC hinh binh henh OCO'B.Chrmg
minh ring
ACIIOO'.C6u
L0. Cho tam gi6c nhqnABC
nQi ti6p dudng tron (O). C6c ducrng caoAD,
BE,CF
.(D e BC, E e AC, F e
AB)
criatam
gi6c chtnhau tpi H. Chrmg minh.irg'
a) Tir gi6c AEFtr' nQi ti6p dugc mQt dudng trdn.
b) DE + DF', < BC.
--- n6t
Hq vd
ftn
thisinh;
...Sd bdo danh;UBND THANH PHO THAI NGUYEN PHdNG GrAo DUC
vA
DAorAo
nuoxc nAN
cHAnnKrEM
TRAxuAo sAr cnAr LtIgI,{G
HQC SINHLOP 9
naON
roAN
I. Hudng din
chung- Gi6m kh6o cA, n6.n
vimg
y6u cAu cria hu6ng d6n ch6m OC Aann giq dring bdi ldm criathi
sinh.Thi
sinh ldrm c6chkh6c
dap 6nn6u dirng vdn cho di6mt6i
da.
- Khi
vQndpng
ddp6nvd
thangdi6m,
gi6m kh6o cdn chir dQng,linh
ho4tv6i
tinh th6n tr6n trgng bdi ldm ctra hgc sinh.- N6u c6 viQc chi
titit
h6adi6m
cdcy
cAnphii
d6m b6o kh6ng sai lQchv6i
t6ng di6m vd dugc th6ng nh6t trong todn hQi d6ng ch6m thi.- Di0m todn bdi ld t6ng
di6m
diua cilc c6u hoi trong dOthi,
ch6m di6m 16 d6n 0,25 vitkh6ng ldm trdn.II. Dfp
rin n vir Yath
tha eIi6mBni N6i
dung Di6m1
o:(Jt -3Jr.Jo)"0-J-s
=
(rJi -3nry. fi)
.",!-2- Ji
=(-.lr.Jo) Jr-Ji
=
-Jr.J, *
Jto.Ji - J5
=
-(Jr)' * Jn - J5
T: I:
:-l+lV)-V) .,
17--l,-r!J
chf j:
IYdu
thi
sinhra luin
bw6c,rili cins,
khbngbi\n
d6t cho 0,5 ctiAm.0,25
0,5
0,25
2
Vfly he phucrng
trinh
co nghiQm(*;y)= ''/ \7'7) f+,+)
Chri
f:
.+
Niiu
thf sinhgidi
theo phwong phdp thiiitfing
vdn choiliiim
t6i ita;+
Nilathi sinhiW atug-MTCT, ia
nghiQmitfing
cho 0.5 tti6m;+
Nilu
th{ sinhsirti ittiis nhtng khilng *ih
tuAn cho di6mfii
cta.lZ*-r=-3 lZ*-!:-3 lty--tt
< <>< <f<
lx+3y=4 l2x+6y=8 lx+3y=4
t rt I ll
lr'-- lt'--
^)' t ^)"
7e1 e1
_l.r=+-3.11 l*=:l lzlz
0,5
0,5
Ja
Phuong
trinh:
2x2-6x+2m-5 - 0
(1)v6i
m ld tham s6.a)
V6i m:
2 ta c6 phucrngtrinh:
2x2-6x -
1 = 0A'=11>0
Phucrng
trinh
c6 hai nghiQm phAn biQt::+J1 3-d1
"r= 2 i xz=
Z
;chf f:
+ Ndu thi
sinh tfnh
theoL itfing
vdn cho itihmfii
ita.+ Nhu HS sfr d4ng
MTCT, ra
nghiQm drtngthi
cho 0,25 iti6m.0,25
0,25
b) Phucrng
trinh
(1) co hai nghiCm phdn biet khi:A' > 0 <>3' -212m-5)> o <>
*.*
4
[.. + r,
:3
Ap dung dinh
li Vi-et
taco:
]^ ^' z) -s
l.'''t':
2Theo Ae Uai ta
c6: l*l -
6 <+xt+
x2 = 6xrx,xt
x2e
3-
U.2m-52
e2m-5=1 em-3(rlm)
Vfly
m:3
thoa mdn y6u cAu cira AC Uai.0,25
0,25
4
a)
V6i x)
0,x + 4,x +9 ta
co,_ zJi-g _..,[+g *2Ji+l x-s.'[+6 Ji-z J*-s
2.,[i -g (Ji * 3XJ; - 3)
,e^[;
+r;1Ji -
zy:Grxf=;-m-rxf5-@
_zJi -g -d; +sLd; -zL+eJ; +ttrJ; -zt (# - zt<Ji -e)
_z^,li -s -(*-s)+(z*-sJ; -z)
(#
-2)(J; -z)
0,25
x-J;-2 (J,-zltJi-sl
r,,!*
-zl(Ji -
gl'[i +t
r/x
-3
0,25
b)Voi x)0,x+4,x+9
p
>le p_
1>o e
Vxr
+1 _1 > oe_J-ro
Jx -3 Jx -3
oJr-3>0<>r>9
K6t ho. p
v6i
di6uki6n
x)
O,x*
4,x*9 taduoc
x >9 .0,25
0,25
5
Vi
ducrng thdng (d) c6t trpc hoirnh tai di6m c6 hodnh d0 - 2, thay x =-2 , !
= 0vdo phuongtrinh
dudng thEng ta dugc:.l
(l-2k).(-2)+3:0 oO:;
.l _l
Vav 'J
k:-
thoa man veu cau.4 '
0,25
0,5
0,25
6
Ggi
vfn
t6c cria b4n Lankhi
di hgc bdng xe dpplir x
(km/h), (x
> 0) Thdi gian hdng ngey Lan di xe dpptt
nhd d6n trucmg ta:1
1fr)x Thdi gian Lan
di
1 km bdng xe dpph: l(ko/h)
x Vpn tdc ctra xe m6y ld:
x+
24(ko/h)
Thdi gian Lan di nhd xe m6y i16n truong
a ld: 4 x+24 =-16<mltr) x+24\
/Vi
h6m nay Lan d6n truong sorn hon trinh:10
phrit: I
SiO n6n ta c6 phucrng4 (t 3 )
l--l -r- l-
x [r, ,+Z+)-O 331
rr x+24
6e
x2+24x-432=O
[x
= l2 (rh6a min),'-O
t\
Ilx=-36
(loai)L
0,25
0,25
0,25
0,25
Vpy hdng ngay Lan di hgc
bing
xe dppv6i vfn
t6c 12 km/h7
Ap
dung h6 thuc lugng trong tam gi6c vu6ngta
c6:1 1 1 1 r (S)'
HA' - A# * Atr: Cn n':
t;.,J
e
AH:7,2(cm)
X6t AAHC vu6ng tai H c6:AC2
:
AH2 + uC21or
Pytago)e HC JAc'-AH'
<+
HC ,[r' J J :
e.6(cm )X6t AABC vu6ng tai
A
c6tanll: AC124 =0=530 AB93
0,25
0,25
0,25
0,25
8
Ke
oHLAB. X6t (o)
c6:(1) Hai titip tuy6n
DN
vdDH
cdt nhau taiD = DN: DH
(2) Haitii5p tuy6n
BH
vdBI cit
nhau tpiB = BI : BH
Tir (1)
vd(2)
suyra: fdD =90'
(g6c tpobdi
haitia ph6n
gi6ccinhai
g6c kC bu).
Xdt LD)B
vu6ng tpi O c6dulng
cao OH, 6p dpng hQ !hit9 luqng trong tarfl gi6c vu6ngta
c6; OH2 = DH.BH = DN.BI = 120,25
0,25
0,25 0,25
Chri
f: Thf sinh kh6ns
vEhinh
khdne cho cli6m.9
Gqi
I
ld giao di6m criaOO'
vd BC.Vi tf
gi6cOCO'B
le hinh binh hdnh n6nI
ld trung di6m ctra BC.(O) va
(O') clt
nhau taiA vi B
n6nOO'
lddulng
trungtrgc
criathdng
AB.
Gqi
H
ld giao di6m criaOO'
vdAB + H
ld trung diOm criaAB X6t AABC
c6H vd I
lAnluqt
ld trung di6m criaAB vi BC
n6n ducrng trung binhcta
AABC.=HI ll
ACVfy AC ll OO'
(dpcm)Chf f
:Thi sinh
kh6ng vEhinh
kh6ng cho tli6m.do4n
HI
1e0,25
0,25
0,25
0,25
10
a) Ta c6:
0,25
BEIAC=ffi=900 CFIAB=ffi:9OO
Tri gi6c
AEHF c6: frpL: trA:
eo"V4y
tir
gi5^AEHF
n6i ti6p ducrng trdn duhng kinhAH
(dpcm). 0,25b) Gqi
F'
ld di6m doi xungvoi
FquaBC
=DF:DF';0 :fr (f)
Vi ATa: ffia:
eoo=
AFDC n6iti6p = fl :6Ib
Vi ffiE:
ADB:900= AEDB
n6ititlp = pDc:6IL
3
D,: EDC
(2)Tir (1) vd (2) suy
ra: 0 :
EDa=
D, + BDE^
= EDC + BDE:1800=
E, D,F' thing
hdng.Do d6: DE + DF
:
DE +DF' :
EF'Vi F vdF'd6i xirng quaBC n6n 6FB:BFC=900vd tu
giirc BFEC n6i tiep duong tron duong ,ikinh
BC.3
B, F, E, C,F'
cirng thuQc dudng trdndulng
kinh BC.Gqi
M
ld trung di6m cua canh BC.X6t ducmg trdn
(M)
duong kinh BC co:EF'
le dAy cung BC ld duong kinhDo do:
EF'
<BC eDE
+DF <BC
(dpcm) Ddu":" xiy
rakhi D :M =
AABC cdn tai A.Chri
y:
-
Thi sinh
khdng vEhinh
khdng cho tli6m.- y b): Thf sinh kh6ng x6t d6u $-D
xayra khi D =M vin
choeli6m
t6i
Aa.0,25
0,25
Lu'u rt
: Hgc
sinh lcim cdch khtic ctfing vdn cho ttiOmtili
cta.t