Đề thi thử toán - Bà Rịa Vũng Tàu ppt

. TruOng Chuyen U
Quy
Don
BR
-
VT
DE
TID
TmJ
D~
HQC
-
CAO
DANG
LAN
1 (2010 - 2011)
Man:
Toan
- Kh8i: A & B .
DE
cHiNH
THiJ'c
Thitigian
liun btli: 180 phut.
I.
Ph
in
chnng cho
tit
ca
cac

thi
sinh
(7.0 diem):
Can
I (2.0 diem): Cho
ham
56
Y = x
3
-
3x
2
•
1) Khao sat S\l bien thien
va
ve db thi eua ham
56.
2) Tim m9i gia
tri
eua tham s6 m
d8
trong khoang
(1;
+cc), phuong trinh x
2
1x
-
31
=m
cO

hai
nghi~m
phan
bi~t.
Can
II
(2.0
diim):
1) Giai phuong trinh: eot
2x
- 2 tan
3x
= sin 2x(1 +tan x tan
2x)
.
2
2
2)
Giai bdt phuong trinh:
2(1 J
x -
2x)
S;
x
+.J
x -
3x
+ 2 .
Can
III

(1.0 diem): Tinh tich phan I
ln
(X
+
~)
dx .
I X
Can
IV
(1.0
diim):
Cho
Wnh
ch6p S.ABCD c6
m~t
ben (SAB) vuong g6c
vai
~t
day. Hinh thoi
ABCD
c6
g6c
ABC
=
60~
, tam giac,
SAB
vuong
can
t1ili

S va
SD
=
a.
Tinh theo a
th~
tich
Clla
kh6i ch6p S.ABCD
va
di~n
tich cua
m~t
cau
ngo~
tiep
t(r
di~n
SACD.
Can
V (1.0
diim):
Cho cac s6 th\lc x, y thay d6i trong
d01ilD
[1;2]. Tim tdt
ca
gia
tri
cua
56

th\lc z
d~
bi~u
thuc P =
(x
+
yz)(
x -
y)
+
xyz
c6 gia
tri
16n
nMt la M thoa man
M?
2 .
x2
_xy+
y2
II.
Phin
rieng (3.0 diem) : Thi sinh
chi
ilu(1c lam
m(jf
trong
hai
phdn
(phdn A holjc

phdn
B).
A. Theo
chvO'Dg
trinh
Chnin:
.
Can
VI.a (2.0 diem):
1)
Trong
m~t
pMng
vai
h~
t9a
dQ
Oxy,
cho
tam
giac
d~u
ABC
nQi
ti8p duang tron
(C): x
2
+
y2
-

2x
+ 4Y - 4 = 0
va
duang tMng
AB
~o
vai
dubng
tha.ng
d:
x - y +1= 0 g6c 45° . Viet
phuong trinh duang tha.ng
AB.
2) Trong khong gian v6i
h~
t9a
dQ
Oxyz,
cho lang
nv
tam giac
d~u
ABCAIB1CI
cO
dinh
AlJ3;l;l);
hai dinh B, C
thuQc
nvc
Oz

va
AAI
=1 . Tim
t01il
dQ
cac dinh A, B,
C.
.
Can
VII.a (1.0 diem): Cho s6 nguyen duong n thoa man 2
n
-
4
(C;-2 -C!_2
-n)
=
C:~12.
Tim
h~
s6
Clla
s6
h1ilDg
chUa
x~
trong
khai
tri€n
nhj
thuc

Newton
cU. (
<Jx'
+
~
rv(ri
x>
O.
B. Theo
chlfO'Dg
trinh
Nang
cao:
Can
VI.b(2.0 iliim):
1)
Trong
m~t
ph~ng
vai
h~
t9a
dQ
Oxy,
cho hai
di~m
A(l ;2)
va
BO
~-2).

Tim
t01il
dQ
di8m C tren
duang
tha.ng
d
1
:
x - y
-1
a
sao
cho duang tron
ngo1ili
ti8p
tam
giac
ABC
ti~p
xuc
vai
dubng tha.ng
d
2
:
x + y - 3 = a .
2) Trong khong gian
vai
h~

t9a
dQ
Oxyz,
vi8t phuong trinh
m~t
d.u
(S) c6
tam
thuQe
duang tha.ng
d :
~
=
~1
:;;;;
z;
1
,
(S) di qua giao di8m cua d
vai
m~t
pha.ng
Oxy
va
cat
m~t
pha.ng Oxy theo giao
tuy8n la duang tron e6 ban kinh
bkg
J5

.
•
{27(X+2
Y
)=4.3
X
-
Y
Can
VII.b(1.0 diem): Giro
h~
phuong trinh .
31og
2
(1
+ x.2-
Y
)
=
2x-5y
IIItT
Thi
sinh kbong
dU'q'c
sl1
dy.ng
tai
Iitu.
Can
bQ

coi
thi
khong giai
thich
gi
them.
B9
va.
ten
thi
sinh: .•• • ••••••••• •••••••.•• •.•• •••
Sa
bao danb:

.
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I
Tru'01lg
Chuy@n
U
Quy
Bon
BR
VT.
BAp
AN
VA
HlfONG
DAN CHAM

nt
THI
THU
B~I
HQC
-
CAO
BANG
LAN 1 (2010 - 2011). Mon: Toan Kh6i: A
& B
y
Cau
N{U
dung
Thang
Ghi eho
di~m
3
1.
Khao
sat
va
ve
etA
thi: y =x
-
3x
2
*
T~p

xae
dink
D =
lR
0.25
Gi&i
h~:
lim y = +00; lim y = -00 .
x-++co
x-+~
*
D~o
ham:
y'
= 3x
2
-
6x
0.25
y'
= 0
~
x =
0;
x = 2
*
Bimg
bi~n
thien:
x

-00
0 2 +00
0.25
y'
+ 0 - 0 +
0.25
*
Db
thi:
y"
= 6x
-6,
di~m
u6n 1(1;-2).
Db
thi qua
0,
A(3 ;0), B(
-1
;-4)
Db
thi
nh~
I lam
tam
d6i
xUn
.
2.
Tim

tham
s6
m: x
2
1x-31
= m (1)
0.25
*
S6~ghi~m
trong khoang
(1;
+(0) eua (1)
hI
s6 giao
di~m
e6 hoanh
dl)
> 1 eua
duemg
th~ng
d: y =m
va
(C*) : y = x
2
1x
-
31.
0.25
* Ve db thi
(C*):

y x
2
1x
-
31
(suy tir (C)).
va db thi d: y = m tren eimg M trve.
*K8t qua: 0 < m
:::;
2 ho"e m 4.
0.5
Cach khac: C6
th~
l~p
bang bi8n thien eua ham s6 y = x
2
1x
-
31
tren
(1;
+(0) .
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II
III
1. Giiii
pbU'O'llg
trinb:
cot

2x
- 2 tan
3x
= sin 2x(1 + tan x tan
2x)
(1)
* (1)
¢::>
cot
2x
2 tan
3x
= tan
2x
7r
7r
cos7x
X
=-+k-'kEZ
*¢::>
=o¢::> 14
7'
sin4xcos3x
{
. 4 3
0 (2)
sm
xcos
X;f;
*

:E>i~u
ki~n
(2)<=:>
X;f;
m
7r
;X;f;
7r
+ m
7r
,(m
E
Z)
4 6 3
7r 7r 7r 7r 7r
*
-+k-;f;-+m-'m-¢::>k;f;7/+3·/EZ.
14
7 6
3'
4 •
V~y
nghi~m
eua (1): x =
~
+
k;
;k
E Z
va

k;f;
71
+
3;1
E
Z.
*Cach khac:
(1)
<=:>
cot2x-tan2x
=
2tan3x
<=:>
cot4x
=cot(7r
-3x)
2
7r
jx
=
~
+ k
7r
{
7r
7r
4x= 3x+k7r
14 7 X=
+k-
<=:>

2
¢::>
<=:>
14
7
{
4X;f;m7r x;f;m!!'-
k;f;7/+3
4
2 2
2. Giiii
bit
pbU'O'llg
tnnb:
2(1 J
x -
2x)
:s;
x
+.J
x -
3x
+2 (1)
*
T~p
X3c
dinh eua
bAt
phuong
trinh: D = (-00;

0]
u [2;
+00
) .
(1)
<=:>
2.J x
2
-
2x
+ x - 2 +
.J
x
2
-
3x
+ 2
;;:::
0 : thoa
v6'i
mQi
x;;:::
2 .
*
V6'i
x:S;
0 :
(1)
<=:>
(J2-x

r
-2h.J2-x:S;
Jl-x'\/2-x
¢::>
J2-x:s;
2h
+.Jl-x.
*
¢::>
4x
+ 1
:s;
4.Jx
2
- x
(2):
thoa
v6'i
mQi
x:S;
_.!
4
" 1 0 (2) 1
* Vm

<
x:s;:
<=:>
x:S;

4 24
1
V~y
t~p
nghi~m
eua (1)
1a
S =(-00; - 2
4]
u [2; +00).
Tinb
tich
philn:
1=
I
ln
(X
+
~)
dx
1 X
~
1 1 1
*
u=ln(x+vl+x2)~
u'= Jl
;v':::::-~V= 2
3
.
x

2x
1
2
1.J3
1.J3
dx
*
I= 2
ln
(x+.Jl+x
)
+-
J
~.
2
1+ x
2
2x
1 2 I x
1r
7r
7r.J3
dx
3"
cost
1
~

*
d~t

x =tant,

< t < -

J
~
=
J-'-2-
dt
=
2 2 1 x
2
1+x
2
!!.
sm
t
sintl~
4
1 r;; 1
~
J2
J3
*
I=-ln(l+ ,2)-
1n(2+,,3)+
2 6 2 3
1
.J3
- 1 1

*Clich khac:
_dx==
_ J x dx - J tdt =
Jt2;l11
1
-1~X2-1
r
x
2
.J1
-2+
1
-fi"j
T3
x
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
I
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0.25
0.25
IV
Tinh
the
tich khoi chop SoAReD
va
S
mit
cAu

*
GOi
H la trung diam
Clla
AB, chUng
minhSH
J
(ABCD).
GOix =AB
2SH
thi
VS,ABCD
=
x::
.
2
2
* SD
2

=
SH
2
+
HC
2
+CD
2
nen x
=~
2
a
3
J6
B
V~yVS,ABCD
48
*
GQi
G la
tarn
dtron (ACD), d\ffig
dUOng
thAng d (qua G, song
song
SH) la
1:n,lc
cua
dUOng
tron (ACD). D\ffig N

sao
cho
SHAN
la hinh binh hanh,
chUng minh
dugc
(CRN)
la
m~t
trung
tnrc
do~
SA
.D\ffig 0 E d sao
cho
ON II AG, vi
AG
II
HC
nen 0 E
(CHN).
V~y
0 la
tarn
m~t
cAu
ngolJ,i
ti~p
SACD.
v

Tim
gia
tri
z: P =(x+
yz)(x-
y)+
xyz
x2
_xy+
y2
2
x x
+(2z
l) z
x 1
*
Chia
tir
va
m~u
cho
ita
co: P =
: c;: = ,
d~t
t =Y ~ t E
["2
;2]
2
P =

f(t)
=t +(2z
-1)t
- z .
t
2
-t+
1
*
j{t)
h\
ham
lien tvc tren [1/2 ;2J
nen
cO
Maxf(t)
= M .
I
le[2;2j
,
J,
(2
+(2z-1)t-z
,
'A
V~y
: M
~
2
<=>

bat
phuang
trinh (an t) : 2
~
2
co
nghlym
t
-t+1
tren [1/2 ;2J.
2
A
A
t
-t+2
, h'
(1/2
2J
*
<=>
z
~
co
ng
Hil
m
tren
;.
2t-1
t

2
-t+2
1
Lap
BBT
cua
get) = E
(-
;2].
.
2t-l
2
*T'hd
II'
()
J7
S
.,.
A,
•
I'
>J7
m
ugc
.J.Y.lmg
t = - . uy
ra
gla
tr!
can

tIm
cua
z
a:
z _ .
~!~
2 2
2
PHANT
CHON
VLa
A.Theo
chU'O'llg
trinh
chuan:
1. Binh hoc
toa
dO
phAng:
* (C)
cO
tarn(1
;-2), ban kinh R =3.
AB
tlJ,o
vOi
d
goc
45°
nen

tim
dugc
VTPT
la
n=
(1;
0)
ho~c
n (0;1).
V~y
phuang
trinh AB
co
d~ng:
x + C =0
ho~c
Y + D =0 .
* Tarn giac
ABC
d~u
nQi
ti~p
(C)
nen
khoang
cach d(I,AB) Rsin300 = l
2
* C = 1/2
ho~c
-5/2 .

Phuang
trinh AB:
2x
+ 1 =0;
2x
- 5 =
O.
* D = 7/2
ho~c
1/2.
Phuang
trinh AB:
2y
+ 7 =
0;
2y
+ 1
O.
0.25
0.25
0.25
0.25
0 25
.
025
.
0.25
0.25
0.25
0.25

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I
2.
mnh
hoc
toa
d6
kh6ng gian:
*
~(.J3;l;l)co
hinh
chi~u
tren
Oz
lit
1(0;0;1), ciing lit trung diem BC.
All
=2,
AAI
= 1 nen AI
.J3.
V~y
IB =IC =
1.
*Suy ra
B(O;O;O),
C(0;0;2)
ho~c
C(O;O;O),

B(0;0;2).
*Ptrinh
m~t
phing
(ABC) co
d{Ulg:
ax + by +
cz
+ d
O.
(a
l
+ b
2
+ c
2
> 0)
(ABC)
chua
Oz
vit d(
AdABC))
1 cho c =d =0, a =
.J3,
b =
-1
ho~c
c =d = 0, a
0,
b =

1.
V~y
pt
(ABC): .J3x- y =0
ho~c
y =
O.
*A lit hinh chiSu
cua
Al tren (ABC) nen A(.J3
;~;1)
ho~c
A(
.J3;O;l)
.
2 2
VILa
T6
h9l!:
2
C
l
C
n
*2
n
-
4
(c
n

-
-
)
-
-
-
2
(1)
D'
A
k'~
l~n:
n E tl.J
'71+
> 3(*)
n -
n-2
n
n-l
•
leu
,n_
V6i
di~u ki~n
(*), (1)
~
2
n
-
s

(n-4)
==
1.
*n = 3, n
4:
VT
< 0;
n>
5:
VT
>
1;
n 5
lit
nghi~m
duy
nhAt.
2)15
15
5
k
15
* V
+-
=
LCI~2IS-kX3
- .
(
X
k=O

5
* S6
h~g
chua
X
SI3
khi k = 10. Yay s6
h~g
cAn
tim
lit:
CII~25
x
3
VLb B.Theo
chtrO'llg
tnnb
nang cao:
1.
mnh
hoc
toa
d9
pbing:
*
Ta
co
A thuQc d
2
nen hili toan ttrong duong

vcri
vi~c
vi~t
phuong
trlnh
dUOng
tron
(T) di
qua
B vit
ti~p
xiic d
2
4J.i
A, sau do tim C
lit
giao
di~m
cua
(T) vit d
I.
*Tam I
cua
(T)
lit
giao diem
cua
trung
tnrc
do{Ul

AB
(y
= 0) vit dth d
qua
A, vuong
goc d
2
(d:
x - y + 1 =O);Vay 1(-1;0).
*Ban kinh cua (T): R
IA
=
.J8
,
v~y
phuong
trinh (T): (x +
Il
+ i = 8.
*
To~
dQ
C : ( J3; J3 -1);(.J3;.J3
-1).
2.
mnh
hoc
toa
d6
kh6ng gian:

* d n Oxy = A(2;-1;0).
GQi
J lit hinh
chi~u
cua tam
m~t
cAu
1 tren
Oxy
thi
AJ
lit
ban kinh giao
tuy~n
=
-J5
vit
iiJ
::::
(d,'iiXy) .
*
sine
d,
0;;)
==
lcos(d;
k)1
=
~
v~y

ban kinh
m~t
cAu
lit R =
A~
=
J6
.
v6
cosliU
* fA =
J6
&
lEd
nen 1(0;0;-1)
ho~c
1(4;-2; 1).
*Yay
phuong
trinh
m~t
cAu
lit:
x2+y2+(z+1)2
=6
ho~c
(X_4)2
+(y+2i+(z-li
=6.
VILb {27(X + 2

Y
)
=
4.3
x
-
y
(1)
Giii
he
phU'O'llg
tnnb:
31og
2
(1
+x.2-
Y
)
= 2x - 5y (2)
, ( 4
)x;Y
4
*The vito (1): -
=-~
x-
y=3
(4)
27
27
*(3)

~
2
Y
+Y = 1
~
y = 0
(pp
so
sinh
ho~c
dUng
hitm

)
*
V~y
nghi~m
cua
h~:
x = 3, y =
o.
0.25
0.25
-
Co
tM
tim A
trui)-c.
Tinh
a1P;1c

AB
=
AC
0.25
=
2.
r6i suy ra
B.
C
0.25
0.25
i 0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
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