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oE
BE CHINH THUC
xrru
rRA HQC rci' u NAU Hqc
nt0N: roAN g
2017 - 2a18
Thdi gian ldnt bhi 90 phtit, khhng kA thdi gian giao di'
I. TRAC NGHIpM (2,0 tli6m)
drtng.
Ghi vdo bdi tdm chi mQt cttib ctii A, B, C hofic D tlwdc yhuong tin trd ldi
cAu 1. Phuong trinh nio sau t16y li phucrng trinh bac ntr6t rrai ry *,y?
D.2x+5y=10
C.2+5=10
A.2x+5y2=1g B.Zxy+Sy=lg
A
Ciu Z.Cho parabo-l (f) ,y =+vi dudng thang(d) :! =Zx-3cit nhau tai hai di6m
Khi d6,
diQn
tfch tam giitc OAB b{ng:
c. s (dvd| '
cAu 3. Cho rtudmg trdn (o;n) c6 AB =JZn DO dai cung nh6 AB bing:
A.6
(dvdt)
8.7
(dvdt)
c6u 4. Cho mQt hinh
cAu c6 thc tich bang
5002gnlza
8.50r
["
3
D. tA}r cm2
C.25tt cltt2
5 (1,5 tri6m). cho hQ phuong trinh:
(mx-v=l - ..1
(*,v ln 6n; lrr li
IT^;;, : z
a) Gi6i hQ Phuong trinh vdi m = -3;
b) Tim m d0 hQ cl nghiQm duy nhat
Ciu
,rr'. Di€n tich mflt ciu d6 1i:
3
cm2
- Tu LU4.N'(8,0 cli6m)
u. PrrAN
ciu
50:o
(dvdt)
nR
D.4
c"ry
B.ZrR
A. nR
D.9
vi B'
tham sd)
y deu nh4n gi6 tri UY*n
trinh: x' -Zna+4m-4= 0 (1), (x li dn; mli tham sO)
(r;y)
sao cho
x
vit
6 (1,5 tliam)Cho phuong
a) Tim m d6 phuong trinh (1) c6 hai nghiQm ph6n biQt;
b) Tim m d6 hai nghiQm x,;x, cria phucrng trinh (1) th6a rndn:
( n-2)(*'-2)=x"
+x" -8'
km, sau
CAu 7 (1,5 rli6m). MOt ca nd xudi ddng tr6n mOt t
thdi
hon
ft
d6 lai ngogr ddng rtiin dia di€m C c6ch btin B 721
;i"r rdnr aOng Ia tS pftit. Tinh v6n t5c ri6ng cria ca nO bi6t vfn t6c ddng nudc le 4 km/h.
cAu 8
3;l
t[i*
.odn (o)ngo4i tirip ram gi6c
nhen
ABC .c6c
du&ns cao AD, BE,
cF
cta
tam gi6c ABC cht nhau tPi I{.
a) Chrmg minh rAng tr: gi6c BDHF vd BCEF n6i tiiSp dudmg trtn;
b) Chring rninh rlngFH li tiaphfln gi6c cria g6c DFE;
c) Gqi MldtrungdiErn cua aC. Cfrung rninh rang tu gi6c DMEFnQi. ti6p dudrng trdn;
d) Gqi K h gial di6m cria dudrng thAng EF vitBC. Chung minh rang H Id tr.uc tdm cria
tam gihc AMK.
CAu 9 (0,5 di6m)
Tim gi6 tri l6n nh6t cria bi6u thric
Cho ba sii ducrng a,b,c th6a mdn a + b + =
2c
2b
--=L- +2018 r/b' +2018- Jc2 +2018
"
JM.
Jo'
--
-- -- - - -- H e t
Gido vihn coi kidm
Ho vd ftn lqc sinh:
ta
--- - --
--'
khdng gidi thich gi thAm.
SBD:
PHONG GD&ET \IINH YEN
oB
I.
HDC KIEM TRA
Hgg rci, rr xAm Hgc zafi
MON:
roAx
2
J
4
A
C
D
cnixH THUc
- 2018
q
TRic NGHIEM qz,o aiaml:: M6i
ME c6u drine 0.5 di em
I
D
CAu
D6p 6n
II. Tr/ LUaN
CAU
18,0 diOm1.
NQi dung
Di0m
a) Vdi ln : -3 thi he phucrng trinh tro thinh
Ir
l-l*- ! =7- l'= -t I
12*-3y=2 1.._ 8
0r75
l.'--11
NghiQrn cria hQ phuong trinh
( t 8\
li (x,y')=[-11;-n)
fntx-y=1 fy=ntx-L
fy=mx-L
'l.2x+ nry-2 [2x+ nt(ntx-1)=2
[(m'+Z)x=m+2
nt+2 lIX m+2
I
l V = tn._;_ _l
b)
5 (1,5
cli6m).
m'+2
IlX=- rn+2
I tn'+2
1l"
0,25
I =--___-__
mz +2
Il1r---2m-Z
[' m2+2
<=<
V6i rnoi gi6 tr! cria ra hQ pt c6 nghiQrn duy nhdt. Ta c6
x
vit
y
ddu duong
khi:
I
m+2
lm+2>0<i{ lnt> -z e
trro._.J*= r;*1>tt <><
"
2nt-2
lyroIlY=:--:-:>Q
\r'
t-
a) A
=
l2nt-2>0
ln'+Z
l*rl
0r5
m>1.
(nt-2)2
Phucrng trinh ( 1) c6 hai nghiQrr phAn biQr x, ;x,
khi:
A' > 0 e(m-2)'
r0e
0r75
m*2.
b) Vdi moi m thi phucrng trinh (1) lu6n c6 hai nghiern-
vi
Theo h6 thric
6 (1,5
eli6m).
- dt, ta c6: {x,
|.',
(x,
-2)(x, -Z)=x,'+xr'
o
(r,
**r)'
(2m)'
Ta co:
^I
-8e
+
x, = 2nt
'',
=4nt-4
xtxz-2(n*xr)+4=(x,
+
*r)'-2xrxr-g
0,25
-3x,xr+2(xr+xr)=12
- 3.(4nt - 4) + 2.2m = t2 e
4m(nt
-
2) = 0
fm=O
lnt-)
L"'
vay m :0 hodc m:2.
0r5