ĐỀ THI THỬ ĐẠI HỌC NĂM 2011 MÔN: TOÁN - TRƯỜNG THPT CHUYÊN- ĐHSP ppt

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TRTIONG
THPT CUUVNTV
-
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DE THI
rnu DAI
HQC t
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Narr
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Mdn
thi : TOAN
Thdi
gian
tdm
bdi :
IB0
phtit,
kh6ng
ke
thdi gian
phdt
di
Ciu
1.
(
2,0 dilm

)
Cho
hAm
s6
.y:
Irt
-
1**'
+
(*2
-3)x,
trong do
m
littham s6.
32
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sg bi€n
thiOn vi v€
d6
thi
cta
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z
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g6c
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2. (2,0 diem)
1.
Giii
phuong
trinh
:
2.
Gidi
phuo-ng
trinh :
CAu 3.
(
2,0
di1m
)
1. Tim nguyOn
hdm
cria
hdm
sO f1x;
:
tanx.tan(x

+
];.tan1x
-
l;.
3" 3',
2. Tim c6c
gi6
tri cta
m
d6
phuong
trinh
sau
c6 nghiQm
duy nh6t
:
g-lz-xl
_
43-|2-xl=
p.
Ciu
4.
(
1,0 didm,
,
Cho, hinh ch6p
tu gi6c ttdu
S ABCD
tt6
UU

ddi
canh ddy
bing a,
cgnh
b6n bing
t'
ttnn
goc
tao
boi
'2
mdt b€n v6'i
mdt d6y
vi
the
tictr t<hOi
cau
ngopi
ti6p
hinh
ch6p
d6.
Cfru
5.
(
2,0
diem
)
.3
Trong

mdt
phdng
Oxy :
L Chohaidi€m
A(2;1),
B(-l;-3)vdhai
cluongthing d1:
x+y+3
=0;
cl2:
x-5y-
16:0.
Tim tga dQ
c6c cti6m
C, D lin luE
thuQc clr
vd dzsao cho t6'gi6c
ABCD
ld hinh
binh hdnh.
2. Vi6tphuongtrinh
tluo'ngthingtiOpxircv6'i
duongtron
(C),
xt+
y?-zr]
x+4y+4=0vdtao
v6'i
trr,rc tung
mdt

g6c
bing 60".
CAu 6.
(
1,0
diem
)
Xdtcdctam
thirc
bgc hai f(x):ax2
+
bx+ c,trotlgd6
a< bvnf(x)>
0 vd.i moi
x € R.
Hay
tiin
gi6
tri
nho nh6t
cira biriu thric
M
=
TT
Het
2.
Tim
t6t
cd
cdc

gi6
tr! oba
m ae
ham s6
c6
cuc d4i
t4i
x6p,
c!.rc ti6u t4i xcr ddng
thd'i
xss,
.rcr lh
dO
z+^[s-x,
+12 ,[s-*,1
sinal3x*|l
*
sinal3x
-?=:
x2
-l
Dy
kiAn
ki
ttti thrb
Egi
hgc
l6n
2
sE

ihrqc
t6 chrbc
vito ngdy
26,27/2/2011
www.laisac.page.tl
nAp
AN
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THANG
omirn
rru
fiillon
IAN rntl
Nnar
nAu zotl
Ciu
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e
aidm)
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tu
ei6i.
t.
2.
(1,0

itiiinr)
. Tim c6c
gi|trim
-
y'=x'-mx+m2-3
.
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sti c6
CD,
CT
vd Xco
)
0,
xcr
>
0
e
pt
y'
=
0
c6 hai nghiQrn duo'ng
phdn
biQt
0,25
(L:m2-4(m2-3)>0
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l"
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o
o
t
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m>o
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m
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ld dO dei
c6c cqnh
g6c
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gi6c
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f
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i
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e
xzru+
0,25

.
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dinh l)t Vi-et,
thi
(*)
trd thdnh : m'
-
21m'-
3) =
.l;
t
**=J;.
(fi,2)
0,25
il
(2
iliim)
l.
(
1,0
iti€m\ .
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phuong
trinh
.
a
EiAukiQn:-3<
x<3,
Phuong trinh trd
thenh

xl0. Dat 1=1f$Qz
+xt=
9-t2,t>0,1+3
g-tz
\
-+-=l
3+t
4(3-t)
a
0,50
(+
4Q-q2
-4Q-t)+
I
:
0
e
2(3-t)=
I
<+
*:9
-
E
o
*=*E( th6a mdn diOu
kiOn).
5
t-
-
2

e
0,50
2.
(1,0
iti€nt).
Gidi
phuong
oinf .
Phuongtrinh tuongduongv6i
phuongtrinh:
cosa(:*-l
)
+sin4(3x-T
l:i
'
4 4' 2
0,25
e
[cos2(3x
-l
I
*sin213x-i
lt'
-2
cos2(3x
-[
).rin'{:*
-on)
=
}

0,25
(+
t-]sin'{ox-
sin26x
=
0
<+
?I 1
-)=-
z' z
kn
x:
-
6
<+
sin2(6x
-
,
kez.
lt
-)=l
<+
2'
cos26x
=
I
(+
0,50
ilI
(2diim)

l.
(1,0
iliAm) . Tim nguyOn hdm
a
f(x):
sinx.sin(x +
l).sin
(x
-
T)
.or* or(* +
i).costx
-
i)
slnx.(cosf
-
coszx)
_
sinx.(zsin'x
-
i)
sin3x
:
cos3x
.orr.(.orf + .orz*) .os*.(zcoszx
-
])
0,50
.
Jf(x)dx=-JHo*

=
lJffi
=
llnlcos3xl
+
c.
0,50
/>Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay
2.
(1,0
.
DAt
t:
t- x
,
phuong
trinh tr6'thdnh
9-ltl
-
4.
3-ltl
:
m
(l
)
Phuong
trinh
dd cho
c6 nghiQm
duy

dr6t
khi
vd chi khi
pt
(l)
c6 nghiQm
dr-ry nh6t.
+
)
EiAu
kien
cAn
: Gid
sft
(l
)
c6
nghiQm
duy
nhAt t"
.
khi
d6
-
to
cfrng ld nghi€m.
Suy
ra
to
=

0, thay
vdo
(l
)
ta cluo.'c
m
=
-
3.
+)
DiAukigndrl:Khirn=-3,thi
(l)trdthdnh:
9-ltl
-4.3-ltl
:-3
(2).
Suy
ra
3-ltl
=
1
a:r
t
=
0, d0y
ld nghiQnr
duy
nh6t
cria
(2).

.
E6ps6:
m:-3.
t
(0,5
eti6@.
Gqi
H
ld t6m
cta
d6y
ABCD,
ta c6
SH I
(ABCD);
M td trung
di6m cfia
BC thi
BC
I
(SHM),
do
c6c
m{t ben
t4o
v6i mqt
d6y ctrng
mQt
g6c,
n€n 5fr8

bing
g6c
tao
bdi
m[t
b€n
voi
cl6y.
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r/ffi
-
4112
+
tan
sffE=
ffi=
vr
+fliliH=60o.
o
(0,5
diA@.
Hinh
ch6p
S.ABCD
ddu,
nOn tdm
I cria
t<trOi
cAu ngo4i
tii5p

hinh
ch6p
ld
giao
<ti6m c0a
club'ng
thing SH
v6'i
m{t
phing trung
trqc cria
mQt c4nli
b€n
ndo
d6 cta hinh
ch6p.
GqiN
ld trung
cli6m
ctra SC,
thi
IN ld trung
trr,rc
cria SC.
Suy ra:
ASNI
-
ASHC
SN.SC 5a
=rR=SI=-;fr-=m

*l
4 .
rzsa3{1i
A
V0y, V:
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:
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.
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rl
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tl
ll
I
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I
rl'
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t
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rl
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t
t
I
IV
Q
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t.
(1,0
V
Q
di6m\
Gi6
sri ABCD
ld hinh
binh
hdnh, ta c6
Cd
=
ffi
=
13;
+;
(+
[}3
-
;:
=

i
Vi
D
ed2 ndn
xe-5yo-
16=0
+ (xc+3)-5(ys+4)=
ViC€d1,n€n
xc+yc*3=0.
Tu d6 ta c6 hQ
phuong
trinh
:
fT l?It-=j=
(x'
=
3
(xo
=
6
-
(xc+yc=-3
<+
tv.=-o
ttvl=-z
Ta c6 :
el
=
(3;
a) ve Be =

(4;
-
3
)
n6n hai
vectcv
Bf, Be khdng
ctrng
phuong,
tric ld 4
dit5m A, B, C,
D kh6ng thdng
hing,
hay tri
gi6c
ABCD ld hinh
binh
hdnh.
Edp sd : C(3;
-6)
vi
D(6;
-2)
a? r-l'f
/>Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay
2.(1,0
@2)vib6nkinhR:J3;
Tir
gi6 thii5t
suy

ra
ti6p
tuyiin
cAn
tim
t?o
v6i
trr,rc
hodnh
mQt
g6c
bing
30o
,
n€n
ti6p
tuy6n
c6
h0s6g6cbing
** t€rrptti€ptuy6nc6d4ng:y=*rt
x*m
e
+*-V3y
+"13m=0'
Khoang
cich
htir
t6m
l(r/3;
-2)

den
ti6p
tuy€n
bing
b5n
kinh
R =
v3'
ItJs
+z\tr
+
VSml
r;
TfclA
ir=-7=\5
rfm
=
-5
*
|ilill
=22
*
lfn=-l
L[m=1
V{y
c6
4 tiiip
tuy€n
th6a
mdn

y6u cAu
bii
to6n
: x-rfgy-5r/3=o;
"+r/3y+3V3=0;
*-fsy-V3=o;
x+y'3y-J3=0.
Tim
gi6 tri
nh6
n
w
Q
diAm)
Tir
giAthi6t
suy
ra
a>
0
vd
A
=
b2
-
4ac<0
+
c
>
-yz

a+b+-
M>#
b-a
Dat
t=b-a>0+MZ
+a2
+
+a(t+a)+(t+a)z
-
gaz
+ 6at+
tz
4at
4at
3
gaz
+
t2 3
T''lw7
=-a-/-a-=J
2
4at
-Z
4at
(^_b'
Dingthftcxiyrakhi
vdchi
kf
ti
=

A
(+
b=c=4a
=+
f(x):a(x+2)2
vhminM =
3'
-
3t
/>Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay