ĐỀ THI THỬ ĐẠI HỌC LẦN 2 NĂM 2011 MÔN: TOÁN, KHỐI A - TRƯỜNG THPT NGUYỄN TRUNG THIÊN ppsx

SO
GD-DT
IIA
TINH
TRU,ONG
THPT
NGUYEX
TRUNG
TIIITX
DE THr rntlDAr
Hec LAN
2
(Kh6i
a,n;
Nim
hgc :
2010-2011
MOn :
Tofn
Thdi
gian
:
180
phut
c6u 1
(2
tli6m)
Cho
hdm s6
!
=

x3
-
3x',
+ 2
1)
Kh6o s6t
sr,r biiSn
thi6n
vd vE
AO tfri
(
C
)
cfa
hdm s6.
2)
Tim tr0n
dudng thing
(d):
y
:
-2
nhffng
di€m
md
tir
d6 ke dugc
Z tiep tuy{in t6i
1C;,
eOng thoi

2 ti6p
tuy6n do
vu6ng
g6c
v6i nhau.
Ciu
2
(
2 tli6m
)
Giii
chc
phuong
trinh
vd
hQ
phuong
trinh sau:
+
logr*,
(*'
-
2x + 1)
=
6
4)
=l
2)
2cos'
"r

+
cos
2x
+ sinx
-
0
C6u3(2tti6m'l
1)
Tinh tich
phdn
+4x+4
.
2) Hoi co bao
nhi€u
s6 tU
nhi6n
gO-
7 chii s6,
tuo cho chfi s6
dring sau nho
h<vn chir
sO
dring liOn
tru6c
n6.
i
-aau!-(
z rX!€aq)
Cho
hinh ch6p

tri
g
d6y
ABCD
ld hinh binh hdnh.
Goi B', D'
lAn luo,t
ld
trung
di6m
cira SB,
SD.
'D')
cit SC
tai C'.
1) Chring
minh SC:3
SC'
2)Tinhttr0
tich cria
S.AB'C'D'
theo th0
tictr V
cria S.ABCD.
Cffu5
(2tli6m)
1)
Trong mat
phdng
tea

dQ oxy
cho :
diemiu
r(2;2),
s,
f?;1),
H,
(1,?l
tu 3 chan
\)/).'5,5,, 5,5,
dunng
cao cfia tam
gi6c ABC lAn
luqt ha tri
A, B, C.
Tim tqa dQ c6c dinh
A, B, C
2) Cho
hai s6 thgc
avd b
th6a a-b
+
1
:
0.
Chring
minh
r6ng:
ffi
+

^ta'+b'-4a-4b+8
::::::::::::::::::::::::::-:
ii€r
::::::::
4
I
I
x4+2
?
x
)
2
dx
sen to www.laisac.page.tl
nUoNc
oAN
cnAvr roAN rnr
rHrl on
r,Ax
rntl2
-
KHor
A-B
l.Gi:ii hG
pt
2x+1)
I
l
6
(1)

(2)
log
,*r(l
-
x)'
:
6
+
2) + log
,*r(l
-
x
,,
(x-
2)'+
, (Y
y+
lop
_"(
<>
)
2)-
+4
-1
)Br-,
6€
:*
og
y+
,r(*

y+
+k
:)=
o
ov+
-).
2),
c)'
-x
-L
a
+
(1
v-
5)-
,r!
,(1
)
)
v+2
I
X
;dr
v
4
Lg
(
)n.
.r0t
o

bl-
r9t
.u
OT
ki,
T
llc
3ul
(1)
+2
let
(r
l+
-1,
Di
+,
pt
-)
.?
v
:
!=xt
-3x'+2
+,
TQp xd, Tim
dugc
y';
Tim c6c di6m
tdi
han;

Tim
y"
0,25
+,
Khoang
don diQir,
gioi
h?n,
bang biOn thiOn
0.25
+,
Tim c6c di6m d4c biQt: CUc dai
(0;2);
Cyc ti€u
(272):;
Di m
u6n
(1;0)
Oiem cdt tryc ox:
(1-".6;0); (l;0);
1f
*",6;0);
Di6m
c6
tsa dQ nguy€n
(3;2);
(-17
2)
0,25
+,

Ve dO thi
dgp, tron,
c6 tinh d6i xring, di
qua
c6c
di€m <l{c biet
0,25
+,
Gid sri c6c Oiem cAn tim ld X(m;-2); Dudng
ttrang
(A
)
di
qua
X v6i hp s6
g6c
k
co
pt
ld:
y
:
k(x-m)-2; khi
d6
(l
)
tiCp xirc
(
C
)

niSu
vd chi n6u hQ
:
ll*2
-6x-k
)
)3-r2
[x'-3x'+2 k(x-m)-2
(1),.
co nghiQm
(
6n
x
)
(2)
(/
0,25
ThC k tir
(l)
vdo
(2)
ta c6
pt:
x'
-3x'
+2=
(3r'
-
6x)(x
-

m)
-
2
<) x'
-3x'
+4=3x(x-2)(x-*) <>
HoA.
x:2,hoirc
2x'-(3m-l)x+2=0
(3)
0.25
rO rdng
kh6ng
co ti0p tuyOn nao
cdu d0 ra
thi
pt
(3)
phai
co
2
(3*i
-
6*,) .(3*',
-
6xr)
-
-1
Vdi x
:

2 thl ta duqc
ryQt
tiOp tuy0n
co
pt: y
:
-2,
vu6ng
goc
vdi ti6p tuyOn
ndy. NOn mu6n thoa
yOu
nghi0m
pb
x,, x2 thoa:
y'
(
x,
)
.V'(*r)
-
-
1. Tuc
:
<+
gxixl
-
18r,
xr(x,
*

xr)
+
36x,x,
-
-1
0,25
Do x,
,
xrld nghiQm cria
(3),
theo Viets ta c6:. xt.xz
=l;x,
+
x,
=
55
NOn
dugc 9
-9(3m-1)
+
36:
-1
Hay m=a;
Gi6 tri m ndy thoa
27'
nghiQm. k6t 1u0n eicm cdn tim tex1fi;-21
2\op.
(-xv
-2x
+ v+ 2) + los^

(x'
-2x
+1\
=
3m-1
2
pt
(3)
co
0.25
i iDat
t:
log,-"
(y +
2)
ta
co
Pt
sau:
-2
e
t-
1
'e
logr-r(Y'+Z)-I
e
Y:
-x-
1
t+-

t
0,25
2
D[t
t-x+-
x
)
ta
co
dt
-
(1
-
i>a*
;
dOi
cQn
t
x
A9
:J+-
2
-)
J
:
44
+,
Thay
gr;tri
y vao

pt
(2) vd
giai
thi
dugc
x:
0
;
x
-
-2
+,
Ket
hqp
diou
kiEn
ta
c6
nghiQm
|d
:
x:
-2,
y
:
1
1
|
2cos'x
+

cos2x
+
sinx
=
0
+,
Thay
2cos'
x
=
cosx.2cost
t
=
cos'x(co
sLx
+1)
thi
pt
vii5t
lai
ld:
Cosx.
Cos2x+
cosx*
cos2x+
sinx:0
ecos2x(cos"
i11+titt"*cosx:0
e
(cosx*sinx)

ftro,
x
-sin
x)(cos
x
+
1)
+
1l-0
<>
(cosx+sinx)
ft.o,
"
-
sin
x)(cos
x
+
1)
+
1.1:0
;
i;;-;;;ii-
sin'x
+ cosx(l-
sinx)
+
(1-
sinx)l:0
(cosx*sinxx

1
-sinxx
1
*sinx*cosx+
1
)
-
0
ept
co
2hqnghiQm
x-
-+
+
kn;x
-!
*2kn
42
(ke
z)
( Ttry
vho
lflp
lufln
tI6
cho
tti6m
thirnh
ph6n
chfnh

x6c
tl6n
0,25
)
1,00
l
I
0 )5
\t
)-
-'
Cflu
4
(2di6m)
I,Xtrc
dinh
tdm
O ctra
hbh
ABCD
+,
Xd
giao
O'
cfia
B'D'
vdi
SO
+,
Xd

giao
C' cira
AO'
v6i
SC
'
+,KeCPllSO(P€AS)
+,
Xd
giao
K cira
AC'
vdi
CP
+,Chung
minh
K
lA trung
diOm
CP
+,Chung
minh
S
ld trung
diOm
AP
+,
Suy
ra C'
ld trgng

tdm
HaySC-3SC'.
2. Chia
th6
tich
cria
S.AB'C'D'
thinh2
kh6i
chop
tam
gt6c:
S.AB'C'
vd
S.AC'D',
tdc6:
0,25
0,25
0,25
0,25
0,5
0
0,25
0,25
0,25
0,25
v(s.AB'c')
^sBo.,sc'
Tuong
tU thi:

v(s.AC'D')
v(s.ACD)
6
11
v(s.ABC)
SB.,SC
23
6
Suy
ra : v(S.AB'.'o'):*
ir6.nc)
+v(s.ACDll
:
f
rfs .ABCD)
1,
Tam
gi6c
ABC C6
AH1, BHz,
CH3
ld c6c dudng
cao. Nguoc l4i tam
giac
H'FzHr
se c6 AHr,
BFtrz
,
CH3
ld c6c dudng

ghdn
gi6c.
(
C6c
em dga vdo
tinh
ch6t
ndy
thi ldm
dugc
nhfing bdi
to6n
nhu th€.
)
+,
Ri€ng bdi
to6n
ndy cho d{c
biQt
hcrn:
<
H
,H,H
3cAn
tpi Hr.*,
Dinh
A nim tr€n
trung
tn;c(d) cria
H2H3.

Dinh
B vd
C nim tr€n
ducrng
ttring
(d')
di
qua H1
vd
vu6ng
g6c
v6i
(d).
+,
Vi6t
pt
ducrng
phdn
gi6c
cria
goc
do
I{zHr ho.
p
v6i
HzH:
(
c6
2
pt

)
+,
Giao
ctra
dt
co
pt
thf
nh6,tvdi
(d)
cho
ta
di6m
A( 0; 0
)
j
giao
vdi
(d')
cho ta
OiCm
B( 1; 3
),giao
cria
dt co
pt
thft
2 v6i
(d')
cho ta

C(
2, Ta c6
:
^lo'
+b'
-za+6b+10
+^la' +b'
-4a-4b+8:"/(a-1)'+
(b+3)'
*,l@-2)'
+(b-2)'
Trong
mpt
phEng
tqa
dO Oxy"ta
lBp tli€m A(1;-3),
eiem BQ;2) vd duong
thang
(d)
c6
pt:
x
-
y
+1
:
0
Khi d6
di6m

M(a,b)
ndm trOn
(d)
thi
cap
(a;b)
thoa
a-b+1:0
Ta co
lfo-
1)'
+
(b
+3)'
+
J
@
-2)'
+
(b
-2)'
:AM
+
BM
L6y
B' d6i
xung
vdi
B
qua

(d)
suy
ra :
B'(1;3)
0.25
0.25
0,25
0,25
Ta c6 ngay
AM
+
BM
>
AB'
:
6
. Suy
ra tliiju
phf,i
chfne
minh
QJ