ĐỀ THI KHẢO SÁT CHẤT LƯỢNG LỚP 12 LẦN 3 NĂM 2011 Môn Toán - Trường THPT CHUYÊN pps

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

=
1*o
-(3m+l)xz
+2(m+l),
m ldtham
s5.
"4
l.
Kh6o s6t sg bitin thi6n vd
vC dO thi hdm
sb c16 cho khi
z
=
0.
2.
Tinr llr A6 A6 fti ham
sii da cho co 3 tli6m
cgc ti l$p thanh
mQt tam
gf6c
e6 trgng
t6m ld
g6c
toa
d0.
CAu II.
(2,0
tti6m)
I
. Giai

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

1(:.1
')L-
s6
y
=
E,trqc
hoanh vi dudmg
thdng x
=
1 xung quanh
truc
hoanh.
A*
e- *
-l-
t-4r
ttl
Ciu IV.
(1,0
di6m)
Cho
hinh
Hng tru dtmg ABC.A'
B'C'
c6 AC
=
a, BC
=2a,
ZACB
=

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

(a0
di6n$
l*'
^[y
a
-2xy
-2x
=1
ft'
-rr-:
x!
=
a+2
Thi
sinh chi tlugc
ldm mQt
trong hai
phdn
(phin
a,
hoic
b)
l.
Trong mat
phdng
tga ilQ
Oxy, chodudrng
thang
d:2x+y+3=0
vd

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

Q):2x-y+22+9:0
vd
hai
di6m Ae;-l;2),
B(1;-
5; 0). Tim
tqa d0
cta diOm MthuQc
(P)
sao
cho ffi.uE
d4t
gid
tri
nh6 nhAt.
Cf,u VIIa.
(1,0
tli6m) Vitit
ng6u nhi€n
mQt
s6 tw nhi6n
ch8n
gdm.4
ght
s6 eoi
mQt kh6c
nhau
l€n
bang.
Tinh

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):

y'
=
4x
c6 ti€u
diOm
F.
Gqi M
h <ti6m
th6a
man
didu
kiQn
Ffr
=
-3fu;
d ld
ttuong
th5"g
U6t ti
tli
qua
M,
d cgt(P)
tai hai
di6m
phdn
biQt
A vit-y.
Chtmg
minh

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

-
MBz
-
MCz
dat
gi6
tri lcrn
nh6t.
Ciu
VIIb
(1,0.tli6m)
Hai
ban An
vd Binh
thi
it6u voi
nhau mQt
t'{n
b6ng
ban.
Hq
quy
u6c
choi
v<yi nhau
nrlAu.nh6t
5 s6c,
ai theng
tru6p
3. s6c li

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-

/n-
n6t
Ghi
chrt:
L Bfg
s€ trd bdi
vdo
cdc ngdy
21, 22/05/2AI
I.
DA
nhSn
iluqc
bdi thi,
thi
sinh
phdi
ngp
lqi
phidu
du
thi
cho BTC.

sent to
www.laisac.page.tl
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m
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2
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do
phuong
trinh
dd
cho
e
logr(1
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e
logz(1
+
JZx
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-
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x)
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g
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;al'
;
:
r,;;,',i '
-
"'
-' -
Theo
c6ng
thirc
tinh
x6c
su6t
ta
c6
P(l)
=
3.19
,412
.0,6.0,4:0,1152,
P
(B)
=3'10,6;2'0'4'0'6
=
0'2592'
Suy
ra
P(H)

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