6 đề-đáp án thi thử ĐH-Hà nội -2011

TRU,ONG
EHSP HA
NOI
TRTIONG
THPT CUUVNTV
-
EHSP
DE THI
rnu DAI HQC t AN
I Narr ZOrt
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
I .
I(hAo s6t sg bi€n
thiOn vi v€
d6
thi
cta
hdm
s6 khi
z
=
l.
diri cdrc canh
g6c
vudng cira mQt tam
giirc
vudng c6 dQ ddi
c4nh
huy€n birg
F
.
"{2
Cdu
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
aa
TRUONC
DFISP
HA
NQI
TRI'OI{G
TFIPT
CHUYEN
-
EFTSP
rJE THr rHU
DAr
Fr-oc LAN u
ruann
zolr
tr{l-
'l^:
-
rzl i xr
'
lvluil Lill
, lt ftl!
T'hdi
gian tdm bdi : 180
philt,

kh6ng
k€
thdi gian phdt
di
CAU
1.
(
2,0 di|m
)
|
2x+L
Cho hanr
s0
V
=

-
x-2
l'I(hios6tsLr.bi6nthi0nviv€d6th!(C)cirahims6.
2. Tim
t6t
cd
c6c
gi6tri
cttam
d6
cluongtiring
y
=
m(x-2)+

Z cit AO thi
(C)
t4i hai
di6m
phAn
biQt
A, B sao cho
doan AB
c6
dO dei
nho nhAt.
C0u
2.
(2,0
diilm)
t. Giii
phuo'ng
trinh
: sin2x.(l
+
tanx)
:
3sinx.(cosx
-
sinx)
+
3
x+3
gx-7
2.

Giai bAt
phuong
trinh:
3sx-,
-4>5.3sx-,
Cffu 3.
(
1,0 di6m
)
-
rinh
tich
phan
I
=;€$o*
Ciu 4.
(
1,0 rtiAm
)
Cho hinh
lAp
phuo'ng
ABCD.A'B'C?D'
c6 clQ ddi
canli
bing a vi
di6m
N4 thu6c
canh
CC'

sao cho
1c
CM
=
T.
tUat
phing
(a)
di
qua,t,
M vir
song
song
vdi BD
chia
khOi
l4p phu'o'ng
thdnh
hai
khoi
3
e o
da cli6n.
Tinh thO
tich
hai t<tr6i
Aa diQn
d6.
CAu 5.
(

1,0
diem)
Ba
s6 duo'ng
thay
d6i a, b, c
till0c
doan
[a,
F]
md
B
-
o
{2.
Chri'ng
minh
ring
:
GETf
+/[611a1ffi1
1>
a+b+c.
C6u
6.
(
2,0 dient)
l.
Trong
mdt

phing
toa
dg
Oxy, cho tam
gi6c
ABC
c6
C( I
:
2),
hai rh-rong
cao
xuAt
ph6t
til.A vd
B
iin
luqtc6
phuongtrinh
ld
x
*
y
:
0 vir
2x-y+
I
=0.
Tlnli
di€rr

tich
tarri
gi6c
ABC.
2. Trongkhonggiantoa116
oxyz,
cho mf,tphing(p)c6phuo-ngtrinh:
\-zy
+zz+
l=0vdrn[t
cAu
(S)
c6
phuong
trinh :
x2
+
y2
+
z2
-4x
+
Sy
+
6z+ l7
:
0.
Tim
toa
dQ

tAm vir
b6n kinh
cria drLdng
trdn
(C)
ld
giao
crira
m{t
ptring
(p)
vd
mat
cAl
(S).
C6u7.(l,0diim)
Giai
h9
phuong
trinh
:
f*t+xyz=40y
ty'+xzy=10x
TI6t
Dqr
kiiin
ki thi
thfr Dgi
hgc
tfrn

thft
3 sd itwqc
fi
chftc
vdo
ngdy
X\,Z0/S/2011
TRI'ONG
TIIPT
DAo
DUY TTI
-
IIA
NoI
of
rrn rrnlDAr
Hgc
r,Arv
r
(2010 2011)
nndx,
roAN
rn6r a
Thdi gian:
180
phtu (kh6ng
*6 nm
g*n
giaa
di)

CAu
I.
Cho
him
s5
y:
x3
-
3x (l)-
/
U Xnaosft
sg bi6n
thi€n
vi
v€
eO tni narn
sO
(t;.
'.t
u
2/
Tl^m etii
phuong
trinh
x3
-3x
=
+
c6
3 nghiQm phdn

biQt.
m" +l
3/ V6iO(0;
0) vd
A(2;2)
h
hai ttiiAm nim
tr6n
AO
tni
hdm
sd
(1),
rim
di€rn
lvi
nim
trOn cung OA
crha dd thihAm
sO
(t)
sao
cho khodng
c6ch
tu
M cli5n
OA ld
ld.n
nh6t,
Cffu II.

1/ Cho
b6t
phuong
trinh:
JT3x+2)
7n-rt7
1x+4
l,
v
al
Giai bdt
phuong
trinh khi
m
:4.
b/ Tim tdt
cir chc
giittri
cria
m
ee
UAt
phucrng
trinh
tr€n
nghiQnr
ding
viii
riiqi
x

>:i.
,,1
2/ Gi6i
phucrng
trinh:
tanx+cosx-cos2x
=sinx(l
+tan!-tarrx).
Cffu III.
V
ttTrCn
m{t
phdne
tqa d0
Oxy, tim
phuong
trinh
tludrng
thingr
di
qua
di6rn
M(l; 3) sao cho dudng theng
d6 ctrng
v6i2
dudrng
thang
(d1):
3x-{-
4y

+
5
:
{j
vi
(d2):
4x
+
3y
-
I
:
0
t4o
th'nnh
mQt tam
gitlc
cdn
c6
dinh
ld
giao
di6m
cria
(d1)
,,,d
(d2).
(
2l
Cho hinh ch6p SABC

c6 dhy
ABC
li
tam
gi6c
cdn,
c6 AB
:
AC
:
?,a;
RC
-
2a
c6c m{t
bon ctrng tao vdi ttax,m0t
g6c
600.
Hinh
chitiu
H
cia dinh
s xu6ng
(ABC)
nam
O trong tam
gi6cABC.
'/
at
cntng

minh t6ng H h tem
dulng
trdn
nQi
ti6p cria
tam
gi6c
ABC.
b/ Tfnh thiS
tich
cria trl di0n SABC
Cffu
IV.
Cho tflp hW A
gdm
n
phAn
tri
(n
>
4).
nii5t
ra"g
sO tgp con
gOm
4
pfran
tri
cria
A

bing}} Hn
sO
tdp
con
g6m
2
phan
tfr
cria
A.
Tim
k e
{1,2,3, ,n}
sao cho
si5
tfp
con
g6m
k
phAn
trl cria A ln lcrn nhdt.
Cf,uY,
Cho 3 sO
kh6ng
6m
a,b,c. Chung minh
ring:
a3 +bt +c'> a'Jbc
+b'Ji
+t'^[on

.
I'R{'GNG
PTTE{ EAO
NUIT
TTI
HA NOn
Bn
rrur
B4r
FIgc L.&N rn-lt^Ana
Hqc 2010
- zfitt,
na6m
roAn
E[ec xa6i a
Thdi
gianldmbdi:
I8Tphfit
+/-
(
KH1NG
XE
rnU
CUU rn
irDE)
/
efurn:
cho
hdrn
16

y:
(m+l)x+m
x+m
1)
Khno
sit
vi
ve
dd thi
hem sO ttri
m
:
1.
Tim tr6n
dd
thi
nhimg di6m
c6 t6ng khoing
c6ch d€n
hai
tiQm
can
nhO
nhAt.
2) Chtmg minh
rdng
v6i
moi
m
l0

aO tni hdm sd
lu6n
tii5p xric
voi
mQt
duimg thing
cO a6n.
@I!:
Gi6i
phucrng
trinh:
"'/i+
ti""
+
Ji
_siil
=
2cosx .
CAU ItrI:
1) Giai
cdc
phuong trinh sau:
,
a)
(4x
-
l)
fi'?
+1
:2x2

+2x+
1.
b) log*+r
p
-
Jt-zx*;
=)-
2)
Tim
m
d€
phuqng
trinh sau c6 nghiQm duy nhAt.
3m-z=
h
C6u XV:
1)
Trong
m4t
ph6ng
voi
h€
tga dQ Oxy cho tanl
gi6c
ABC
c6 A(-2; l), B(3;
5),
C(2;1). Tim
tqa
t10 truc tem H, t6m I ctra dudngfirdn

ngo4i ti6p
vd trgng tem G
cira tam
gi6o
ABC.
Chrmg minh H,
I,
G tha"g hang
.
2) Ctro tam
gi6c
ABC
vu6ng t4i A,
AE
:
a, BC
:2a.Haitia
Bx
vi Cy cring
vuOng
g6c
voi
m{t
pb5-ng (ABC)
-rir
nim v0
mOt
phia
d6i v<ri mit
phang

d6. Tr6ri
Bx, Cy lAn luqt 16y
c6c
diAm
B', C'
sao
cho BB'
:
a, CC'
:
m.
a,Yrn
gi6
tri nio ctra m thi AB'C'
ld tarn
giAc
vudng.
b, Khi
tam
gi6c
AB'C' vuOng
t4i B',
ke
AH vu6ng
g6c
voi BC.
Chrng minh
ring B'C'H
idr
tarn

gi6c
vu0ag,
Tinh
gbc, glftahai
m4t
phAng
(
ABC
)
vd
(AB'C').
e6g-Y'
Chr.rng
miiih ring khi
a
l0
thi
hQ
phuong
trinh sau
c6 nghiQm
duy nhAt:
7
a
=y
-F-
v
a'
a"
-

L'T
I,*,
i,,'
;-
GiAm
thi coi
tfui
kFr0ng
gidi
thich
gi
thdm
,/
T'R{IffiG TE#T s}ao
puv
T{l,
pm
s's{x
rmalo4r
noc x,AN
rm,
xAla F{EC 2010
-
20Il
nndlol
:
Todn, m6i a
Thdi
gian
ldm bdi

: 180
phrit
(
kh6ng
te tn}i
gian
phdt
d0
)
tsAi
t.
(2
di}m) Cho hdm
s0
!
=
x3
+3x2
-mx+2
c6 AO
mi
(C*).
1" Kh6o sdt vd ve dd thi
hdm
s6 vdi m:0.
'
2. Timm'd}hdm s6 c6 cgc d4i, cgc ti6u sao cho
khoing-crlch tu trung
di€m cfa
do4n

thdng
n,5i hai di6m
cuc
tri cria
(C*)
d6n tiiSp tuytin
cria
(C-)
tai
cii€m c6
hoinh elQ bing
1
le
lorr
nhdt.
Eei It.
(
3
diCm
)
Giai
c6c
phucrng
trinh,
hQ
phucrng
trinh sau :
-
fry-3x-
2y+6:A

L
i,
.,
l*"
+y'-2x-4y+3=0.
2.
4sin2x-cotx=
Jj
-
3. 2losr(3x+5)+logo(lx+l)8
=
4logr(l2x+8).
Bii III.
(
I
diem
)
Tim sd hang khdng chfta
x
trong
khai triiSn
nhi thric Newton
cria
r'
Bni Iv.
(
3
di€m
)
1 . Trong

m{t
phing
vdi
hQ,fa dQ O*y
,
cho
du}ng thing
d : 3x
-
4y +2011
=
0, vd
duong trdn
(C)
:
,' +
y'
-6x
-2y+1=
0 . ViCt
phucrng
trinh dudrng
thing A
song
song v6i d
vd cft
(C)
theo mQt dAy
cung c5
dQ

dni
bing
4.
2. ChotudiQnABCD
c6AB
:a,AC-
Za,AD=
3a
vit A)C
=C)n:fAn=600
.
Tinh th6 tfch
tri
di6n
ABCD.
3. Trong
kh6ng
gian
v6i hQ tga dQ Oxyz,cho
m{t
phing (P)
: r+ 2y-
"-4
:0
vd
duong
thing
a
'
*

:4
=
+
Tim ditim M tr€n
tnp
oz
sao
cho cdc khodng
2t-1
c6ch tir
M d6n m{t
phAng (P)
vd tludmg
thdng d
bing nhau.
tsni V"
(
i diem
)
Cho c6c
sd thuc duon
g
a,b"c
th6a
m6n
a+b
+c
=3
. Chring
minh

ring
: G.trh-b+c
a6.111-rao
+r.l,h-o+b.3.
HA NOI
P(x)=
(r*r-+l'
\
r-l.
Gi6m thi
coi thi
kh6ng
gi6i
thfch
gi
th6m
rci
rHr rnrl
DAr Heqr,AN rHrI
NnAl
xAnn
Hec 2010-_
zltt
DE
THI
MON:
TOAN
xlr6t.L,n
Thoi
gian

ldm bii:
180
phirt,
kh6ng kC
thoi
gian giao
d6
Cffu I:
(2,0
itiAm) Cho him
sd
!
=
x3
-3(nt+1)x2
+9x-m,vti
m ldtharnsd
thgc.
l.
Kh6o
s6t sy bi6n thi6n
vh vE OO
ttri cria hdm
sti
ea cho ring v6i
m
=1.
2. XAc
dinh
m

ee fram
sO ea cho
d4t cuc
tri t4i
xr,x2 sao
cho
la
-*rl:2.
Cflu
II:
(2,0
iti6m)
l.
Gi6i
phucrng
trinh:
1
+ 3 cos
x + cos 2x
-
2cos 3x
=
4sin
x.sin 2x
2.
Giai
he
phuong
trinh:
lxt

+2x+y'+y:3-xy
j
^
"
(x,y€R)
l*y+*+Zy-1
"'
cf,uIII:
(1,0ili0m)
r\m
J
ff-;d.
sinx.sinl
x+: I
\
4)
Cf,u
IV:
(1,0
ili6m) Cho
l6ng tru tam
gi6c
ABC.ATBTCT c6
tdt ch
cdc canh
bang
a,
g6c
tao b&i
canh b€n vi

mdt
phing
d6y
bang 300.
Hinh
chidu
H cfra didm
A
tr€n
mat
phftng
(ArBrCr)
rhuoc
doong thing
B,C,. Tfnh thd tfch
khdi ldng tru
ABC.ATBTC, vi
tinh
khoang cdchgifa
hai dudng
thing AA,
vi
B,C, theo a.
Cffu
V:
(1,0
ifiAm)X6t
chc
sd
thgc

ducrng a,b, c
thoa mdn
di€u kiQn
a+b+c=1.
Tim
gie
d
nh6 nh6t cria
:
":m
?
. h
Cflu VI
(2,0
iiidm)
'
I
1. Trong mat
phing
vdi hQ
tga
ttQ
Oxy cho hai dudng
trdn
:
.
(C1):
x2
+
f

,:13
vd
(C2):
(x:
6)'+
t'
,:
ZS
cit nhau tqi
A(2;3).
Vi6t
phuong
trinh ducrng thdng
ili
qua
A vi 16n
lugt
cdt
(Cr),
(Cz)
theo hai
ddy cung
phAn
biQt
c6 elQ dii
blng
nhau.
2. Trong
kh6ng
gian

v6i h0 tqa d6
Oxyz
cho
tam
gi6c
vu6ng
c0n ABC
c6
BA
:
BC. Bi6t
A(5
;
3
;
- 1),
C
(2
;
3
;
-
0vd
B ld ditim nim
tr6n m{t
phing
c6
phuong
trinh
:

x+
y
-
z
-6
:0.
Tim tga c10 tli€m B.
Cflu VII
(1,0
iti6m)
Gi6i
phucmg
trinh
:
(z
-
tog,
x)logn,,
-;ft;
=
t
utlt
TRUONG THPT
CHUYfi,N
NGUYEN HUE
Thi
sinh kh6ng duqc
s* d4ng
tdi li€u.
Cdn bQ coi thi

kh6ng
gidi
th{ch
gi
thent