Đề-đáp án thi thử lần 2-ĐHSP

@
'rRU'a,NG
DHSp
r{A
NOl
Dt THr rrrrl DAr Hgc rAN
rr NAvr
zoog
rliol
T'HPT ciruvtlx
M6n
thi:
To6n
Thoi
gian
ldm bii: 180
ph0t
lr**
clu
I
(2
di€m):
Cho
hdm
sd
r
=-lP
f
rl
1) KhAo
s6t

vi
ve
d6 thi
(C)
crha him
s5 khi m
=
0.
?)
Tim
nr AE A6 tbi
hAm sO
(t)
cit tryc
Ox
t+i
hai di,im
phdn
biQt
c6
hoinh d0
ldn luqt
li x1,
x2
sao cho
r
=
I
xr
-

x2
I
dat
gii
tri nh6 nhAt.
C6u
2
(2
di6nr).
i.
GiAi
phuong
trir*r :
2sin2
(x
-
.5
=
2sin2x
-
tarx
.
2. V6'i gi6
tri
ndo
cia
m,
phuong
trinh
sau c6'nghiQm

duy
nhdt :
2log'
(mx
+
28)
=
-
log5(12
-4x
-
x2).
Cdu 3
(l
di€nr).
Tinh tich
phan
:
Cnu 4
(1
di€m).
-a'

Tan
gi6c
MNP c6
dinh P nim trong
mflt
phang (a),
hai dinh

M
vi
t'f nirn
vB
mQt
phia
cia
(o)
c6
hinh chiiiu
vu6ng
g6c
tren
(s)
Dn luqt
li M' vi
N' sao cho
PM'N' li
tam
gi6c
dAu
canh
a.
CiAsirMM'=
2NN'=
a.
j
-
Tinh diQn
tfch tam

gi6c
PMN, tu d6
suy
ra
gi6
tri eua
g6c
gita
hai mflt
pheng
(c)
vA
(MNP).
-
:
Ciu
5
(l
ditim).
Cho tlp hpp
A
c6
l0
phan
*.
H6i c6
bao
nhi€u cich chia tfp
hqp A thenh
hai tip

-/.
:
cau 6
(2
dirim).
/
:./
1)
Trong
m{t
phing
voi
hQ
tga dQ
Oxy, cho
elip
@)
c6
phuong
rriot, r
{
*.*
=
,.
9
'4
:
MQt
g6c
vu6ng

tOv
quay
xung
quanh
di6m
O c6 c6c
canh
Ot
vi
ov
cit
(E)
lan luqt t4i
M
viN.
chil11113ng
mrnn rang:
6F
" ON,
=
36
.
Trong
kh6ng
gian
v6i
hQ toa d0
Oryz,
cho ducrngthang
O'

T=?=
|
tamit
phturg
CI)
:
x
+
!
+
z- 3
=
0.
Vi6t phuong
trinh
tluong
thang
A nim tong
mit
phang
(P),
vu6ng g6c
vsi
d vi
c6
khoang cach d6n
d mQt khoing
h=
'#
.

Ciu
7 (l
di€m).
C6c
s6 thpc
x,
y
thay d6i sao
cho x*
y
=
2.
Hdy
tim
gi6
tri
lon nh6t
cua
bi€u
thric
:
P
=
1x3
+
4(f
+
4.
-
,.li xdx

l=l
'
J1
x+y;l['

M4t
khdc
lim*-s+
f(x)
=
+ oo
vi
lim*_e-
f(x)
=
_
-
,
Tac6f(x)>0v6i
-4>x>
-6vdf(x)<0voi
x
e(-4;0)
u (0;2)
.
Bing
bi€n
thi€n
:
Nhu

vfy,
tu
bing
biiin thi€n
suy
ra
phuong
trinh
(3)
hay
ciing
Ii
phuong
tdnh (2)
c6 nghiQm
duy
nhAt thuQc ( -
6; 2) \
{0}
khi
vA
chi
khi
:
cAum.
(
1,0
di6m).
|
-^>

t!.
lm
<
_L4
l ;,=l-rT
L-m=-4
L
m=4.
3,13-
2,12
-t
3
rac6
r=
1€$ff=
Jfxzdx
-
J€x\Fldx
e.,6-1
lis-,y'
=
't-'
zfi
=
t'lf
-itf
r.,-
r)ia(*,
-
1)

=+
-*ic.,-,)-lf
cAu
rv.
(
1,0 di6m).
K6o dAi
MN cit
M'N'tai
E,
khi d6
NN'
li duong
trung
binh
trong
AEMM',
mi
M,N'
=
pN'=
a
n€n
EN'
=
4
suy ra
APEM'
li tam giac
n?ng

tei
p
vi
EP
=
rGMryffi7?
=
816
,
d6ng
tiroi
Ep .t-
pM.
Trong
tam.gi6c
vu6ng
c6n
pMM',
c6
pM
=
a.,12
,
nAn FP PM
=
a.E
"^17-
:
^2-17
Ta c6

.966p
=
2Suup +
Suup=
|
fe.ru
=l*^f, .
Viy
S,r.1up
=I^'#
Vi
EP
la
giao
tuy6n
cria
hai
mpt
pheng
(a)
ve
@Ia}Q
vi
EP
1PM,
n€n
g6c
a
giiia
t.rai

m{t phing
nay
bAng
g6c
frFFf
=
450
Cht
)t
;
C6
th6
tinh
g6c
a
bing
c6ch
sri
dsng
c6ng
thrlc
SpM,N,
=
Spyy.cos
g.

cAU v.
(
1,0 didm).
GiA

sri
k li
sii'cdch
chia
r{p
A rh6a
man
y€u
c6u
bAi
to6n.
Ta
nhin th{y
ring,
'''si
mdi
c6ch chia ta dugc
hai
tip
con
kh6c
r6ng cua
A.
Suy
ra
s6
cdc
t6p
con
kh6c

r6ng
cria
bing
2k.
Tri d6 ta
c6
:
2k
=
Cls*Crzo* +Cio
=zta
-Z
s
ft=2e-
I
=511.
Viy,
si5 c6ch
chia theo
y€u
cAu
bii toan
bang
5l L
cAu
u.
(
2,0
di,im).
l)

(1,0
di6m).
Dat
@;ffi1=a
(0
S
oS2Tr)
vA
(d;
}]f)=c+l
Tac6:
Mf*"=oMcosc
"'tYr,r
=
OMsina,
Do
Me(E)ndn'
xft*Yil-,
4
OM?cos2c
OM2sinza
,
;-= i
.
1
coszrt
sin2cr
-m=J-=
4'
1

sin2q
cos2cr
.r
usrg
rU', ra
cung co
&
=
T
*
T
^
7
1_
_
coszd.
sinzc
*
sin2c
,
cos2c
:1
-
1
suYra
6fr?*o=il,
s
r'i+:r=;*;.
1113
_T_

=
_
oMz
0N2
36'
2)
(1,0
ditim).
cia sir aa
dgmg
duo.
c A th6a
mEn
bii to64
tlf
a
se nin
trong
m{t
phang
(e
vu6ng g6c
v6i
d,n€n
m(Q)
nh4n vdc
t?hi phusnC
cria
d
lA

i(-2;3;2)
tAm v6c
to ph6p
tuy6n.
Phuong
trinh
cria
*(O
g
:
-2x+3Y+22+a=0
(1).
GqiA li
giao
di6m
cuad vr5'i
mf(fi,
thi
tga
ttg
giao
diiim
cria
A tn
nghi€in
ctia
he phucrng
ft+3 v-9 z-6
r-:-:_
trinh

:
J
-2
3
2
e+
A(3:
0:
0)
(2).
(x*y*z-3=0
Ke
AB
J.
A, B
e
A.
Ggi
C
ld
giao
di6m cria
m(e) voi
d
vi g
ld
g6c
giGa
d
vA

(P)
thi
g
=
ffie
,tac6
fi(l;
l; t) h
mQt
vdc
to
ph6p
tuy6n
cria
(p),
Khi d6 :
-,
t-2+3+21
li l;
sne
=
JE!t7-
=
{;
+
Ianp
=
J14-
@

Ta
c6
BC li duong
vu6ng
g6c
chung
cira
d vi
A,
d6ng
thoi
dg
dai
troqn
BC
=
h
=
'#
.
Suy
ra:
Ac
=
:
Bc
<=+
AC
-z'iE'
. E

=
g
tane
11
'
.,,/
a
rry'?'
"1*"
AC cfing
tA
khoang
c6ch
hr
A dAn
m(e,
n€n
tir
(r)
vi
(2)
ta c6 :
o.=#=ffi
ea-6=*#,
Do
A
nim trong
mf@),
n€n
A li

giao
ruyiin
cua
hai
mft
pheng (P)
va
(e.
T6m
lai ta
c6
hai
rtuong
theng
A th6a
m6n
bAi torin
lA:
,",.,.f
x+y+z-3=
[
x+y+z-3=0
tv'i
:
[-zx+3y+
2z*6*#=
o
ua (a)'[-zx+3yr
zz*
6_#=

o
cAu
ylr.
(
l,o
di6m).
Tac6
P
=x3y3
*2(x3
+f;
+
4=*tf +Z(x+yXxz-xy
+yt1++
=
x3y3
+
2(x
+
y)[(x +y)2
_
3xy
]
+
+
Theo
giithitit
x
+
y

=
2
n€n
p
=
x3y3
-
l2xy
+2A.
D6t
1
=
xy, do
(x
+
y)2:
4xy
n6n t
<
l.
DAtf(t)
=f -lzt+20,
te(-oo;
U,thif(D=3f
-
12=0et=-2.
Ta c6
f( 2)
=
36,lim,*-*

f(g
=
-
o,
f(r)
=
9
vi
f(t)
>
0 voi
t
<
-'
2
c6n
f
(t)
.
o voi -2
<
t
<
l
Tir
c6c
t6t
qua
tr€n,
suy

ra
maxf(t)
:36
khi t
=
-
2.
Vsi
i
=
-2,tac6
hQ
phuong
trinh
:
(x*y=2
IuL-l
e
x=lt16;y=lTG.
Y
4y,
gtdtri
lsn
nh6t
cfra
p
b6ng
36,
khi
x

=
I
*
16,
y
=
I
_
16
ho4c
x
=
I
_y'3,
y
=
!
*
.fi
.
Dy
kiiin
k)
thi
tht?
tin
sau
sE vdo
cdc
ngdy

2b
-
29
thdng
3 ndm
2009
'5