TRIJONG
EAI HQC
VINH
TRIIONG
THPT
CHUYTN
of
xrrAo
sAr
cnArr,ugr\c
t
6p tzr,An
3, NAna zorr
m0n:
TOAN;
Thli
gian
lim
bhi: IBA
phrtt
r. rHAN cHUNc
cHo rAr cA rHi
slr.{H
1z,o
a$q
1
Ciu
I.
1Z,O
ei6m; Cho him s6
y

phuorg
trinh 2Iogo(l a
,l2y
a1= logz
(5
-
r) + log
,
(3
-
x).
2
2.
Gieiohuongtrinh
lsinZx-cos2x)tanr*
sin3x
=sinr+cosx.
Ciu III.
(1,0
di6m) Tinh thc
tich
khdi
trdn xoay tu":iah
khi
quay
hinh
phang gidi
han
boi d6
thi hem

1200
vd
<tudmg
ttrang A'C t4ovoim{tphdng
(ABB'A') g6c
300. GgiMldtrungdi6m
BB'.
TinhthCtichk*r6i
teng trU
dd cho vd khoang c6ch
gita
hai ttuong theng
AM,
CC'
theo a.
CAu V.
(1,0
iti6m) Tim
a dO
hq
phucrrg
trinh sau c6 nghiQm
II.
PHAN nrtNc
e,o
iti6m)
a. Theo
chuong trinh
Chu6n
CATVIa

elip
(E)
,t*t-=l.
Virit
'41
phuong
trinh
dudrng theng A
vu6ng
g6c
voi
d vit
cht
(D
t+ihai
di6m
A, B
saocho
diQn
tich tam
gifuc
OAB
bing 1.
2.
trong
kh6ng
gi*
tqu dg
oxyz, cho m{t
pheng

x6c
su6t e6
si5 vira vii5t
th6a mdn
trong s6
eo m5i
crrt so
dAu lon
hcrn
chit
s6 e,mg
tru6c
n6.
b. Theo
chrorrg
trinh
Ning
cao
Cf,u
VIb.
(z,o
ai6n;
1.
Trong
mat
ph6ng
tga d0
Oxy, cho
parabol
(P):

reng
tam
gi6c
OABliLtam
gi6c
vu6ng.
2.
Trong
kh6ng gian
tga
dO
Oxyz,cho
dudrng
thang
d,**=l
='.4
=l
vitc6c
<tii5m Ae;2;7),
-2t2
B(l;
5; 2),
C(3;2;
4). Tim
tqa
d0 di6m
MthuQc
d sao
ebo
MA2

ngyd
th*g
cuQc
vn tren
rliu
k6t
trtir.
rinfr:<a.
r"aida
trat
d6u t6t
ttnic
sau s6c
thf
tu, bitit rang
xac
su6t An
thing
trong
m8i
s6c
ld
0,4
vd s6c
ndo
ctng
c6 nguoi
th5"g.
.L
d-

'trR{i'#.}iil
T'l-{P I'
il}"ILryEN
DAP
EN+
BE
K}IAO
M$F{:
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3,
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gian
ihm bii:
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i) pltfit
I,
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rr^ \
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m
-
0

y,=0
e
I
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=
+Ji'
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ra
hdrn sd
ddng
bi0n
tr0n
c6c
o
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r'
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chiu.
x.
I
t-x
>
J,
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r

yr,
=1.
c"
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ss-tfri
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s#
nir$n
trgc
tung
limn
trui:
d6i
xr?ng.
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s&
dd
sho
c6 3
di6m
cgc
tri
€
3
nghiQm
phfin
bipt
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1)
va
gi6c ABC
a
!a+2!n
-
0.
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2m+2+2(-9m'-4m+1)-0
egmz
+
I(€t
hqp
vo'i
(1)
suy
ra
gifttri
cua
m|d
m
-+.
3
Diou
kiqn:
1=
x
<
3.

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-
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f
m
Zl3
3m-2-
0 e
I
L*
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1.
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1}
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tx
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hqp
di0u
kign
ta
co
nghigm cua
phuong
trinh
la
x:
l,

di€u
kiQn d6
phuong
trinh
tuong
cluong v6i
sin2.xsinx
-
cos2;rsinx
+
sin
3x
=
cosx(sinx
+
cosx)
e sin 2xsinx
-
cos2-rsinx +
sin
2xcosx
+
cosixsinx
=
cosr(sinx + cosx)
e cosx(2sinx
-
l)(sinx * cosx)
=
Q

e x
=
-!
+ kn.
4
Vfy
nghiem
cta
phuong
trinh
li ,
=[+
k2n,.
=+
+
k2r;,
=
-L
+
kn, k eZ.
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f:
HS c6 tnc viet
nghiQm
cria
PT: r
:
(-
ry
+*

Do
d6 &$ tfch
kiroi
triiii xilay le V
-
n'{-g
^
dx.
i
{-n.
-i-
1}'
hinh
thang
cong
dugc
gi6i
han bdi c6c
du'crng
(1)
015
015
Edt
u: x. dv
=
"'
=
d*.
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=

:-_tn
"l
l.
. e+l
lo
-lo
e+I
2
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(l)
ta iluqc th6 tich kh6i
trdn xoay li
v
='
,(
-
"

tn
'
*
1.).
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"'
z
)'
IV.
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di€rn
+)

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tr
AB
ffi-:ol,'
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+
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+
)
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ldng
trg
li
V
-
AA'.5
ABC
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a
az
Jj
_
a3Jl os
214
-
ACz
t
7

(1ro
di0m
{ t _
"
xz?
*
I
D+t,
=
Jtn
I
.
r 2 0
rrQ
trcr
rrranir
l;,
t
:utr;
==
o
+
Z
Rd
ran
g
z.
S khOng
thoa
rnfln

g6m
4 chf
s0
duo-c
viet ra
th6a
mdn
m6i
chfr
sd
16n
hon
chfi'
s
dung
tru6c
n6.
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d6
Q
=
{abcd
'.
a + 0,
d
e
{0,
2,
4, 6,8\\;
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tai
hai
diom
A,
B
+)
Ggi
A(2yt-m;
!t),
B(Zyz
.
mi
!)
trong
d6
h'
lz
ldnghiQm
ctia
(1)
+
!,:!,:+'!:!:
.#
.
: ;j.: ,
* ABz
=
5(yz
-
yr)'

=
0 hoa"
t
g
x-2y
+
m=0.
lx
-2y
+
, ,A
I
cua
hQ
1
x''
)
l-+ Y-
t4
J
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h9
c6
2 nghiQm
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ls"ut

+)
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fr4.M8
=
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+fr>fffi
+787
=
tui
+ u>fat
-
u)
=
MI'
-
IA2 .
+ffi.uE
datgi6trinhonhAt
e MInh6nhAtldo
u'
=lf
khongd6i)'
.?
4-44.bit'I
qt'i9r-v'l-ole eeg
gll+-{lt-"1-(1)'-
- -
-
lx=2+2t
I

xrit
cac tnrcvng
hqp
sau
+)
d
=0.
Trudng
hqp niy
c6
,
j
s6.
:
+)
d e{2,4,6,8}.
Truong
hqp
niy
"6
(4
-
efi.+ sA.
suyralol=4
++(4-4>72221___ _ __._
_.___-__ _
pe
tintr
lQn I
,u

c6 C;
sS.
Suyra
lCInl=t
*Cl.+Cl
-46-
Do
do
P(A)=l#
:
:? r=
0,02,
-/
lCIl
2296
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ie
d
ln
s*
cl-i1n
)
.
\
l.
(1,0
tti6m.
Ii}'
|
.l

9oo.
+)NCu
d
LOx*
pt
d:y-k{x-4)-
* M(4;
la$;
=+{
LB(A;
0),
4)
-4)
Tqa
6Q
A,
B la
nghiQm
cria
h$
li;la;G;'a;aist{uii,;iaiffi-pifi;i,i-ditii-(it;ltt;si;Gil;i'd;tilct
c+l';-d:
_.2
,2
Gii sri LtLq;
yr), B(?;
yr) trong
d6
/rr
v,

gi6c
OAB
vu}ngtrong mgi trudmg
hqp.
Tu
"9
!pg!n.
{v-b-4k l*-Y:
i'^
<+{
4
Ly'==4x
'
,
A., 1r
Itty'-4y-r6k-o
(1)
2.
(1,0
iti€nr
@thfcsau4s6c;Anbi6nc6Anlingudithdngchung,cuQc;l;1ibi6n
;6 A; itt"ne
te"rhi
t; B
auii5n
"6
Binh
li
ngudi
thdng chung cu6c vi.a,

Ao
;
B
:
"Trong
3 s6c
ciiu Binh
thing
2 s6c
vd
s6c
thri tu Binh
thing"
=
(B1B2A3
v
BrArB,
w ArBrBt)
B
o.
'
tt
;#
iildt
;l,r
*
"i;
i+
i,,
ti,;

-
PtA)+
P(B)
=
0,3744-
YIIb.
(1,0
tIi6m)
l*'!,4!
Lrr.j:!