.fRUONG
D}.iSP
I-IA
NOI
TR.UOI\G
TT{PT'
CHUVEF{
.
}}FISP
pn
:r'm
rFIU'F]Ar
ri-oc
LAI{
Ir
ruAnr
zolt
lvidii
ilii
:
TOAI{
7'hd'i gian
ldm hdi
:
I
B0 phtit,
khong
kA
thdi
gian
phfrt

di
CAu
1.
(
2,0
diAnt
)
Cho hdnr
sd
.y:
?+
I. I(hAo
s6t
su
bi6n
rhi6n
vA v6
c16
thi
(C)
cfra
hArn
s6.
2' Timtdt
citcircgi6tri
cirantd6drrongtirang
y:m(x_
2)+2citci6rhi
(C)tai
hai

di6rnphAnbi€t
A,
B
sao
cho
doan
AB
c6
dQ
dii'nho
nhAt.
Cdrr
2.
(2,0
diem)
l.
Giei phLlo-ng
trinh
:
sin2x.(l +
tanx)
:
3sinx.(cosx
_
sinx)
+
3
2.
Gi6i
bat

phuong
rrinh
:
3*=
-
4>
5.3#
Cflu
J.
(,
1,0
cliem
)
-
.V3ln\fizTJ
Tinh
tich
phAn
I
:
J,
"
il-J '6*
Cf,u
4. (
1,0
diem
)
Cho
hinh

lAp
plruo'ng
ABCD.A'B'C'D'
cci
do
cldi
canh
bing
a
vd
cii6rn
M t5Lr6c
ca'6
CC,
sao
cho
cM
:
?
*Ut phang
@)
diqLra
A,
M
vd
song
song
v6'i
BD
chia

kn6i
tap
phu.ong
thdnh
hai
l<h6i
da
cti6n.
Tinh
th€
tich
hai
I<h6i
da diQn
d6.
Cdtr
5.
(
t,0
dietn
)
tla
s6
clu'ong
thay
d6i
a,
b,
c thu6c
doan

[',
B]
md
F
-
o
{2.
crrfi.ng
mi'h
rdrig
:
Gilf
+/66a1+rtra+f
>
a*b*c.
Cflu
6.
(
2,0
didm
)
l'
Trong
rndt
phlng
toa
d0
oxy,
cho
tam

gi6,eABC
c6
c(
I
:
2),
hai
dildng
cao
xu6r
ph6t
tLr
A vd
B
lAn
lu'otc6
phLLongtrinh
IA
x
+
y
:
0
vd
2x-y
+
I
=
0.
Tinh

cli6n
tic6
ta'r gi6cABC.
2.
Trong
l<h6ng
gian
toad6
Oxyz,
cho
mdtphing
(p)
c6 phLrong
trinh:
x*2y
1,22+
l=
0 vd
rndt
cAu (S)
c6 phLrong
trinh
:
x2
+
yz
+
z2
-
4x

+
gy
+
6z+
17
:0.
Tinr
toa
dd
tam
vd
b6n
kinh
crla
du'o'ng
tron
(c)
la giao
cira
niir
plidng
(p)
vd
rnat
cAir (S).
Cf,u
7. (
t,0
ttient
)

Giei
he phLLong
trinh
:
nat
t*t
+ xyz
:40y
Lyt+x'y=10x
DqE
kiare
ki
tki
thft
fr$i
hpc
rftn
tratu
s
sE
dwgc
t6
chs?c
vda
rcgdy
rg,z#/s/zL!i
sap Ani
-
THANc
DIEM

rnr rrrtl oH r.An
rnU
nar
NAivr
zor
r
CAU
oAp
AN
olBtvt
I
7z
AiAml
L
(1.0
man.
Hoc
sinh tu
sidi.
i.
(t,o
aiiiml
. Tim c6c
gi|tri
m
Euong
thang
y
=
m(x-2)

+
2 cttd0
thi
(C)
tai
hai di'5m
phdn
bi6t
<+
c6 hai nghiQm
phdn
bi€t
<+
pt nrx'
-
4mx
+
4m
-
5
=
0
(*)
c6 hai
2x+1
Pt;=m(x-2)+z
nghiQm
phdn biQt khbc2
0,25
(m*0

c+ Jo'
:
4m?
-m(4m-s)
> o
o
m
>o
I
\+m-Bm*4m-5+o
0,2s
Gi6 srlr
A(x,,y,), B(xr;yr)
trong
d6
xr, Xz
ld
hai nghiQm c0a
(E).
Khi d6
yr
=
lnXr
-Zm*Z
vit
y2=
lrlx2
-
2m+2
Tac6 AB2

=
(*,
-
4,)t
+
(y,
-y,)2
=
(xz
-
xr)2(m2
+
l)
:
[(x2
+
x1)2
-
4x1x2](m2
+
l)
0,2 5
4(4m-5) .
20(m2
+ 1) 2o,2m
:
Il6
-=;=
X*t
+

l)
=
:-:il"-:1/
Z"#:40
vdi mgi
m
>
0.
Eing thri'c
xdy ra
khi vd
chi
khi m
:
L
Vdy, v6'i
rh: I thi
AB ngdn nhat Uing
V40
.
0,25
II
(2
cti6m)
l.
(
1,0 clilnt\
. Gi6i
phLro-ng
trinh

.
Ei6u kiQn : cosx
f
0.
Phuong
trinh dd cho
tuong duong v6i
pt
:
sinzx
^
sinx
.
3
) ,, l ,
#
(tun* +
1):3:lla(l-
tanx)
+


c+
tan2x
(l+
tanx):3tanx(l-tanx)
+
3(l+ tan x,t
cos'x'
'

cosx
cos'x
0,50
(+
tan2x
(l+
tanx)
=
3(l+
tanx)
e
).
dreu Klgn Dal toanJ.
[tanx =
-1
[*
=
Itan2x=3
H
l*:
(kez) (
th6a rndn
-i+tn
*I+kn
-3
0,50
2.
(1,0
cli1nt). Giai
bat

phuong
trinh .
DiAuki€n:xl
BAt
phu'o'ng
trinh
dE cho tuong
duo'ng
v6'i
bpt
x+3
.
x+3
3sx-,
-
4,5.3"-t*u
')
;
0,25
AfJ
D{t1=3sx-2, t>0.'Bpttr6ntrdthanh
t2
-4t 45>0
+
t:9(dot> 0)
0,25
x+3
ATJ
'isx-z>
ge

-
5x-z
27
>2
e
-<x<
-
5
-9
Ddp
sd :
a1
x€(-:-l
'5'9'
0,50
III
(1,tti€nl
(1,0
diAm).
Tinh
tich
phAn
rrc6 r-
-
I,fitnVTJ?d1=
-11nur1
1p
lf
-llr"1otrn.,rTT7;
=

rn,/z
-
*^o
*
lr/t*=a*
:#rnz
*f
"lo*.
0,50
L
Tas€tinh.l
=f*clx,
ddt
x:tanr
=r
dt:-+
dr:(l .of,)d,
,
x=
r/3
thi
IV
(1
ili1nt)
o
(0,50
ilid@.
Dung
thirit
diQn

cira
mat
phing
di
qua
A,
M
va
song
song
v6.i
BD.
Gqi
o=AC
o BD,
o'
=A'c' n B'D'
va I
=AM
n oo'.
eual
k6tluo.ngth6ngsong
song
v6'i
BD
cit
BB'
vri
DD'
lan

luo.t
t4i K, N. Khi
d6
AKMN
la
thi€t
di€n
can
dung.
DAt
Vr
=
Ve.scvr*
Ve,.oouru
,
Vz= Veaco.a,s.c.o,-
Vt.
t
(0,50
tlie@.racO
ff
=#=
1
=+
DN=BK=Ot
=;a*
=; .
Hinh
ch6p
A.BCMK

c6
chi€u
cao
ld AB
=
a,
I
ddy
ld
hinh
thang
BCMI(.
1
Suy ra
vo.scrr,
::aB
o
-
AB
Bc(BK+cM)
a3
3
'.recvrc:T
z
:T
B'
Hinh
ch6p
A.CDNM
c6

chi€Lr
cao ld
AD
=
a,
tf6y
ld
hinh
thang
CDNM.
1
.
-
AD
CD(ND+CM)
a3
Suy
ra
Ve.coN"
=:AD
3
'.Jcolrlr:T
,
=;
r(
a3
.3 t^3
V?y,
Vr
=-:-

,
Vz:
ai
-a'
-2a"
B
'333
t.
(1,0
TtLgi6thi6tsuyra
lg
llSF-o
<2
+(a-b)t<
4=+(a+b)2
_4abs
4
suy
ra
a*
b
<
2lr+a,
tlro'ngtu'tacfingc6
:
b+c
<2fi1fi
,
a+
c

szrlr+
ac
Dod6:
a*b*c<V1
+ab+/1
+bc+/1
+a;(dpcnr)
(1,0
ttiAm).
Tinh
di6n
tich tarn gihc

VI
(2
tli€n)
DLld'ng
thdng
BC c6 vecto
chi
phLro-ng
il la vecto
phap
cira
dLLdtrg
thing
x
+y
:
0,

n€n
d=(l;
l).
Phuo'ngrrinh
cira*a'
[i:1il
tu,
ra
B(l+t;2
+t).
B
rhu6cdr-rongcaoxu6t
phSttrrB
n€ntead6th6amdrr
phuongtrinh:2(l
+t)-z-r+
I
-0
+t:-
l.
vay
B(0;
I).
ruo'ng
ts,
phuong
trinh
AC
,
[;

=
i:i'
vd
A(-
5;
5)
Tac6:
BC=J2
Duo'ng
thing
BC
vitit va
d4ng t6ng
qurit
:
x
-
y +
l-s-s+r I
9
Goi
AH
ld
dudng
cao,
ta c6
AH
-
:-:
-

I
-j
-
-
'lZ
,/Z
(1,0
tti€m).
'lim
toa
d0
tdrn vd
bAn kinh
.
Mat
cAu
(S)
c6
tdrn IQ;
-
3;
-3)
vd
bdn
kinh
R
:
\i5
.
I(ho6ngc6chtiL1t1iinmp(P)lith=w=l<R=V5,n€nmp(P)cdt

rn{t cAu
(S)
theo
mQt tfud'ng
trdn
c6 b6n kinh bing r
:
,lP P
=
2.
0,50
Tdm K cria
dudng
trdn
(C)
ld
giao
di€m cria mp(P)
vdi
dub'ng
thingd tli
qua
di€m 1vd
vudng
g6c
v6{
mp(P). Vecto
chi
phuong.c0a
duong thhng d Li vecto phrip

tuytin
cria
mp(p), n6n
ui:rt;1
:2)vi
phuongtrinh
cria
o,[;='-{ir,
Dod6
K(2+t
;-3
-2t;-3
+zt)
\z:
-3
{
2t.
Tqad0tem
K cira(C).th6amdn phuongtrinh:
2+t+6+4t-6+4t +
I
:0
+
t
=-+.,
\
7
11
Vay
tAm

I((il ;-
).
bdnkinh
r:2
'J',
3' 3"
0,50
WI
,Q
iliem)
(1,0
cli€nt). Giei
he
phLro'ng
trinh
N6u x=0thi
y:0
=+
(0;0)
ld
mQtnghiQm
crhahQ
phuongtrinh.
Ntiu
x
I
0. D?t
y
=
tX, khi

d6 hQ
pt
tro thAnh
:
fx3
+ x3t2
=
4otx
fx3(t
+ tt)
:
4otx
tt3x3+*tt=10*
:
["t1rt+tj=1gx
(+
(x.(t
+t')
:4ot
(
"t
=
#
(1)
I
*'(r'
* t)
=
1s
€

lt##
:
to (z)
Tt(l)
+
t>0,k6tho.pv6'i(2)
-
t::.Thay
t=
)
,eo(l)raduo-c
x=+4
+
y=r2.
Drip
sti : HQ
pt
c6 3 nghiOm
(0;
0),
(4;
Zj
,
e
a;
-
2).
I,00