TIBND THANH PHO HAI DUONG

DE KHAo SAT HQC SINH LoP 9
xAvr Hec zoz? - 2023

PHOI{G GrAo Duc vA DAO TAO
,,

MON: TOAN

DE CHINH THITC

Thdi gian ldm bdi: 120 philt
(EC thi g6m 05 c6u, 01 trang)

Ciu I (2,0 tli6m). Giei phuong trinh vd hQ phucrng trinh sau:

a)x(3*x)-4

g [2(*-l)+ !=3

'

lx-3,y=-8

Ciu2 (2,0 tli6m).
a) Rft ggn bi6u thirc:

t: I

ili-z
- (--'z*?G-4)[
f#-,l Lm.#]
p=(

ftoi x)o,x +2,x*t1

b) cho hdm s6 b0c nh6t ,=(2m-r)x+ m'-2 (m ldtham so; co d6
thi ld ducrng
(d).
thdng
Tim m dc (d) c6t (d'): y - x-r tpi di6m A c6 tung dQ bing

I.

C6u 3 (2,0 tli6m).
a) Hai c6ng nhdn cirng ldm chung mQt c6ng viQc thi hodn thenh
sau 10 gio.
N6u ngudi thf nh6t ldm mQt minh trong 6 gid rdi nghi, sau d6
ngudi thir hai ldm ti6p
trong 3 gid thi dugc 40d/o c6ngvi6c. Hoi n6u ldm mQt minh thi m6i
c6ng nh6n ph6i
ldm trong bao 16u hodn thdnh c6ng viQc d6?
b) Cho phucrng trinh: x, _'2x * m _1 _ 0 (m ld tham sO;. fim

m nguyOn

duong dc phucrng trinh c6 hai nghiOm xt;xz th6a m6n
C6u 4 (3,0 tli6m).

*i

+

d<

r5.

Cho AC ld mQt dAy kh6c ducrng kinh cria ducrng trdn (O), B
lA mQt ditim tr6n
cung nh6 AC sao cho AB < BC, ke ddy BD cria dulng trdn (O)
vudng g6c v6i AC tpi
H. Ke BI vudng g6c v6i CD (I thuQc CD)
a) Chung minh b6n di6m B, H, I, C ctng thuQc mQt dudrng
trdn.

b) Ke BK vu6ng g6c v6i

Bk : m

ducrng th6ng

AD (K

thuQc AD). chrmg minh

vd ba di6m H, I, K thEng hdng.
c) Gqi M, N lAn luqt ld trung di6m ctra AD vir HI. Chrmg
minh
C6u 5 (1,0

rli6m).

ring Bff L MI\t

r

Cho ba s6 thuc ducrng x,U,z th6a mdn di6u kiQn x, > y, +
zr.

Tim gi6 t l ,,h6 nh6t cua bi6u thric: p =

n
+ 2018.
). +l
#(r, ,,).
' *(\Y'
z')

sg1--H9 vd t6n thi sinh:
Chfr ki si6m thi s61 : ....

SO Uao

Chitl.i

niA^ +l:

danh:
o.

UBND THANH PHO HAI DUONG
PHoNG crAo DUC vA DAo rAo

'

EE

HtIoNG nAN cuAvr
on xnAo sAr Hec srNH Lop
Nim hgc: 2022 - 2023
M6n: TOAN

cniNn THtIc

e

(Hadng ddn chtim gim 04 trang)

Y

Cf,u

NOi dune cAn clat

Di6m

x(3+x)=1<>"2+3x- 4=0.
Tac6:a+b*c=1+3-4-O
a

0,5

3*t =I;xr=
Vpy phucrng trinh c6 hai nghiQm ph6n biQt le x,

Ciu

1fz$-l)+y=3
€)i |

1

2x+y=5 [Ox+3y=15
!)(
x-3y=-g
t
[x-3y=-g

[x-3y=-s
(

(2,0d)

-t

,-b

)

:1;x, - -4.

0s
" )r

I

0,5

7x=7
[x=l
<>{
2x+y=5 [Z.t+y=5

0,25

[x=l

?Hbllr

lv=3

0,25

,:( ,*rE-!l [ :J;-z *J;-l
( 3 -2Jx ) LtJ* +t)(2",1x-3) "./i+r_]
( il-:_z J;_j
:(g-oE_*4-4)
-[trtr

3-2ft]:[@.ffi.1
_a-+Ji+z,li-q.( sJi-z
Jirz",li -sl
T:[@
-

0,25

0,25

.f-r-

a

(Vx + i)(2Vx

2-zJ;

2x-2

=-_

3-2J* (J, + tX2Ji-:)

_z(Ji -p ' 2(J;-rXJr+rl

Cdu 2
(2,0d)

-z

"

(J, + DQJ; -3)
VayP:1v6ix20x *2,x+l
z",lx

PO nam s6

ld hdm
b

sO

6
Y

"

0,25

y = (2m -1).x + mi I

Upc--rthfu. zm-l*

+ Di6u kiQn dC (d)

2m-1*l<+ m*l

o

o

**!

4,25

,=(2m-1).r+m'-Z cit (d,): y=.r_1

+Vi(d)cdt(d'):y:x-l
thayy: l vdo(d') +x:2

ld:

A c6 tung d6 bdng 1 ndn

4,25
0,25

tt

t'\

\a

m'

+

4m-5 = 0 e (m-l).(nt+

em-I;

m=-5.Do

5)

:

0

m*l:,u*!

nen

m- -5

Yqy m--5.
Goi x (gio) ld thdi gian c6ng nh0n thri nhAt m6t minh ldrn xong
cdng vi6c vd y (gio) ld thdi gian c6ng nhdn thf hai m6t minh ldm
xong cdng viQc. (Ei6u kiQn: x; y > 10)
Trong 1 gio nguoi thu nh6t ldm dugc 11.Orrg viec). ngudi
x

ldm duoc

Vi

I

thf

hai

0,25

(cong viec).

-v

cd hai c6ng nh6n ldm xong c6ng viQc trong 10 gid, do do trong

gio cA hai c6ng nhdn cung ldm duoc
'
phuongtrinh:

l*l:l

*l0

1

(.Ong viQc) n6n ta co

(l)

x y

10

Khi c6ng nhdn thf nh6t ldm 6 gio vd cdng nhdn thli hai ldm 3 gio
thi hoan thdnh duoc

632^.

40Yo (c6ng

vi6c) n6n ta c6 phuong trinh:

Q)

-+-:l
xy5

.,HU

It 1

I

lx v

10

I'

Tn'(1) va (2) ta c6 h0 phuong trinh: (I) !"

la
I- r 3-

a

C6u 3
(2,0d)

DAt

0,25

11 )0i
-=u
-=v
xy

|..r

-y

}G!N
nAO,
rs
L

2
5

i'fto

;'0.

Khi d6 (I) tro thdnh:

1,,*r:L
l0

]
I

lu,,

..-,j
t-l

*6r=!:3
l0

5

')

[6zr+rr=i [.6ir+tr=i

[r,:1
s

[,

=

Ils

0,25

o]
.-l
I:
lu*r:L
1,,:lI
t0 l. l0 15 30

(tho6 mdn DK)

I

[t l; 30 t, =11 (thoa rndn Dr()
-l I 1:1y=r5
r

t-

l.Y ls
V$y thdi gian d6 cOng nh6n thf nh6t rrQt mirt tu,, xort .6rg
"iC..
1A 30 gicr vd thdi gian dO cdng nhdn thri hai mQt minh ldm xong
c6ng viQc ld 15 gid
x2

0,25

-2x*m-1-o

Tac6:

A'=1-(m-l)=Z-*

d6 phucrng trinh c6 hai nghiQm

xtix,

,

0,25

-,

2-m>0em<2
Theo
b

hQ

De xi

rl)
(--

thtic Vi-et, ta co:

+xj

,

< ts

ItttAt-L

-n

0,25

t', ', =m-r

.1

e (x, +x, )- -3x,x, (x, *x,)< 15
\

t

: /

r

z \

L/

t

-

<+8-3(m-1).2<15
\./

0,25

++8-6m*6<15

e -6m 1l
I

(2)

6

ftit hqrp (1) va (2),ta c6

-l<
6

Do m nguy€n ducrng n6n m e

m<2

0,25

{t;z\

VE hinh dring cdu

a
:i DlJI

"i,10

0?5

b

a

Cdu 4
(3,0d)

6i

Ta c6 EfiC :9oo ,
=9oo
Suy ra H. I ndm tr6n dudns trdn dulne kinh BC
Do vpy 4 di6m B, H, I, C ctrng ndm tr6n ducmg trdn ducrng
kinh BC
Chirng minh dugc

tu

gi6c

BFIAK nQi ti6p'=ffiR

=@ =frD
66
Do BHIC ld tu gi6c nQi ti6p =fr)=frD (3)
Suv ra BR = iffi
Do <16 ffi*ffi=ffi*ffi=1800

Do ABCD ld tir gi6c nQi titip
Tir (1) vd (2\ suy ra Bk =
b

Suy ra ba di6m K. H. I hine hdne

qz1

=fu

0)

0,25
0,25
0,25

or{
fl ?5
0,25

0,25

Tir gi6c BHIC nQi ti6p BeI = BrE
=
Tri gi6c ABCD nQi ti6p ecA- = EDI
=
^
^
BIH
BDA
=
=
C6 tf gi6c BHIC vd tu gidc ABCD nQi ti6p + BAD
= BHI
(cing bu v6i BeD)
Do d6 ABHr .o aBAD (g.g)

* BH=_HI _ BH= 2.FIN
-'BA

BH

AD
BA 2,ANI BA
Tir d6 suy ra ABHN c,: ABAM +
+ tri gi6c ANMK ri6i tii5p

Me BRM

= 9oo

=

Tt

d6 suy ra

,=

.
#(y' t ).

(1,0d)

BMI

BNIMN

r(i.

t' /
=p>[Y'*r'*-.r')
[-7-. y, .,,
5

=

EfrM = qo"

--)

Lau

ffi

Do t:!rx'

x'

r.2018

>

+3. R

3x'

+2078
).i .,,

, ).

ry2+'z-''

,,2y,+z',=j{=r3
y'+z'

2P

>2+3+2018

-2023

- yJi = r,fi
Vpy Min P -2023 khi x yJ, _ rJz'
D6u bing xhy rara khi *

Chri

y:

+ 2o1B

- Gido vi€n c6 thd chia nh6 bi€u didm;
- Hqc sinh rdm cdch khdc, fiing vdn chrim
di€m ttii da.

0,25