đề thi thử đại học môn toán có đáp án khối chuyên đh sư phạm

TRUONG
DHSP
HA
NQI
TRUcD{c
rHpr
cHuytN
-
EHSp
DE
THI
utl
DAr
Hec
r,AN
vr
xAvr
zoro
M6n
thi
:
TOAN
Thdi
gian
ldm
bdi
; t
B0
philr,
kh6ng
ke thdt

gian
phdr
di
CAu
I.
1z
diafi:
Cho
hAm
s6
y
=
x4
-2a2x2
+b
v6.i
a,
b ld
tham
s5
(1)
.
1.
Khdo
s6tsubi6n
thi€n
vdve
dd thl
crja
hdm

sO
1ty
mi
u=
Evd b =4.
!2
2. Tim
cdc
gi6,
tri
crla
a *
0 vd
b di5 c6c
di6m
cuc
dai,
cuc
ti€u
cria
dO
thi hdm
s6
1t;
tao
thdnh
tam gi6c
d€u.
CAu II.
(2

dia@.
1)
Giii
phuong
trinh
:
cot2x
-
2tan4x
-
tan2x
=
-4^13
.
2)
ciei he
phucrng
trinh
:
[(x
-
+)G
+
])
=
v(v
+ 5)
,,,uw'6Lrrrrr.
I
logt"_rl(y

+Z)
:
T
C0u
III.
(t
die@,
rinh
tich
ph6n
r
:
f
fr,
a-
CAu
IV.
(1
die@.
Cho
hinh
ch6p
tam
gi5c
dOLr
S.ABC
c6
c4nh
d6y
bing

a vd
canh
b€n
tqo
v6.i
mdr
driy
m6t
g6c
60".
M6t
mdt
cAu
tam
o
ti6p
xric
v6'i
m4t
ddy
(ABC)
tai A
va
ti6p
xrlc
v6'i
duong
thing
BS
tai

H.
H6y
x6c
dinh
vi
tri
tuong
coi gina
H v6'i
hai
di6m
B,
S vd
tinh
di€n
tich
mdt
cAu
t6m
o.
C6u
V.
(l
di€m).
Cho
cdc
sO duong
x,
y,
zth6a

rndn
xlz*
y
+
y
-
z:
0.
Tim gi6
tri l6n
nh6t
cfia
bi6u
thilc
:
P= .2
-
3
xz+l y2+1
z2+L'
Cdu
VI.
(2
dia@.
1) Trong
mdt
phdng
oxy,
cho
ducrng

tron
(c)
:
x'
+
y2
-
6x
+
2y
-
15=
0.
Tim
toa
dd
di6m
M
tr€n
dudng
thhngd:3x-22y-6=0,saochotirdi6mMkdduo'ct6'i(a)haititiptuy6nMA,MB(A,Bldcricti6p
di€m)
md
dudng
thang
AB
di qua
di6m
C(0
;

l).
2)
Trongkhdnggianoxyz,chohinhldngtrudrmgABC.A'B'c'v6iA(a;0;
0),8(-a;0;
0),c(0;r;0)
vd
B'(-a;
0; b),
trong
d6
a vd
b rd
hai
si5
duong
thay
d6i
nhung
ru6n
th6a
mdn
a
+
u:
6lz.Tim
a,
b
dti
khoAng
c6ch gifi.a

hai
duong
thing
B,C
vd
AC,
l6n
nh6t.
CAu
VII.
(1
die@.
Cho
hai
s6
phric
Z1
=
cosf-
isin
fi
vit
z2=_
I
+iVT.
Hdy
x5c
dinh
d4ng
dai s6

crja
s6
phric
z=
(2,.22)ts.
H6r
CAU
I.
1.
Hoc
sinh
tu'gidi.
.
2. Tac6:
y'
=
4x3
-4a2x
Bing
bi6n
thi6n
oAp
AIv
ToM
TAT
+
y'
:0
<=+
4x(x2

-
ar)
:
0
*
[r]=:f
trt
vd
lim"_*
y:
+
oo
Dat
A(0;b),
B(-lal
;b-a4),
c(lal
,b_uo).
t(hi
d6di€mAthu6crrucrungcdnhai
ditim
ximg
nhau qua
truc
tung,
n6n
tarn giiic
ABC
cAn
tai

A.
E€
AABC
d6u
cAn
vd
drl
ld
AB
:
BC.
tuong
duong
v6'i
:
a'
+
at
-
4a2 e
a6:3 <=
a:
+
V3
.
Vdy
v6i
a
:
*V3

vd
b
ld s6
thuc
tuy
y.
Cdu
lI
:
1.
Di6u
ki€n
:
sinSx
#
0.
cos2x
sin2x
P
I
(+
-
Ztan4x
=
_4r8.
sin2x
cos2x
Zcos4x
^
sin4x

cosz4x
-
sinz4x
:
-
= tY5
c=-:
_l^,n
sin4x
-cos4x
rvr
"
sin4x.cos4x
Lvr
c+
cos8x
=
-€
sin8x
e+
cot
8x:
-v5
(
do
singx
I
0
).
'

€+
8x=-I*kn',=
"=
-l
l<n
6
+;*
u
(kez)'
f2<x+3
2.
Di€ukidn:l
y>-z
I
y*o
Tac6 phuorrgrrintr
(x-4)(x+
1):y(y+
5)
?
*,
_
3x
_y(y
+
5)
_
4:0
(*)
Coi(*)

ldphuo.ngtrinh
An
xc6
A
=(2y+5)2.
n6npt(*)
c6
nghi€m
le
lx
=
y+4
[x=_y_1
V6i
x
:
y
+
4,thay
vdo pt
thfr
liai
cria
h€,
ta
dugc
:
log(v+zt(y
+2)=t#*,#:t
€+

y2
-y-z:o
So
s6nh
v6'i
diOu
ki6n
chi
c6
x
= 6
th6a
rndn.
v6,x=-y-i,
dox>2n€n
-y-r
>
2ey
<
-3,
rar.ngth6amdndi.uki6n.
Vdy
nghi6rn
crja
h€ phu'ong
trinh
ld
(x,
y)
=

(6,
2).
B,
C d6i
^.).
ureu
nay
*'
[]:;'
-
ll:Z
\
y'ot
/+*
\ / \ /
\
b-ut
/
\
b_ uo
/
CAU III.
Tac6l
.:fi*o*=
I
.i
ti(*
-
*)0,.
=-ir"o(*)

:
-r* li
=1+lrnlrl
li
=
I
*1rn1
.
3 4
lx+1|
l0
3
4
3
Cdu IV.
Gqi G
ld trgng
tdm
crla AABC.
I(d
OI( I SG, I( €
SG.
Ifti d6
SEE
= 60" n€n SG
= GB.tan60o: "G /3
=
u.
3
ss

:\reEz;ZBz
:
tr
+t
:
r^,15
.
\33
Do BH
=
BA
=
a va
u.
+ndn
H
nim
gifr.a
S vd
B.
3
Tac6 oH2
+HS2
= oS2
:
oI(2
+KS2.
OA
:
oH

=
GK
=
R
(
R
-
b6n kinh mdt
c6u
tAm
O
)
n6n
n,
+
1&J3
-a)'
=
(+)' +
(a-R),
<+
Do
d6 di€n
tich m4t
cAu la
: S,,.
=
4ftp12
=
CAU

V.
A
(+-J5
)a
D :
i r-
l\
2t3
(rs
-eVr
)naz
3
Tac6
xyz*y
*y=z<=+x+
y=z(1-
xy)
<+
.=:+.
(vi
x,y>0n€n
1-xy
+0).
1-xy
Dat
x=tanq,
y=tanB
vo-ia,p
e
ro;|)khi

d6 z:
tan(a+
ilvdbi€uthrictr6.thdnh:
'
P:
-:
"
+ r-
-
-=:*
:
Zcos2a+3cos2f-2cos21a+81
r+tan2a
r+tanz1
l+an2(a+p)
-"""
*
:
cos2a+
I
+
3cos2/t-
[cos(2a
+
Zb+
1]
:
ZsinB.sin(2a
+
h

+3(1-
sinrB
).
Eat t:sinB
thi
p<
-3t,
+2t+3:-3(t-1lr*T=T
Edng thri'c
xAy ra
khi vd
chi
khi
{
sinB=+.*l
sinB-i
l
[sin(2c
+
F)
=
r
-
'
lz*
=]-
0.+
zkz
I
sinB

-
+
=
fcos'F
=
f,
=!r'=tun'F
=
*
cos?u-sinp
Icos2a
=1
l*,
=
tunro=i
J2
7
"12)
'
10
uooo
f,r*=
T
rar,chinghan
(x,
y,z)=(Q
'2'
Cdu Vl.
1) Duongtrdn(C)
c6tArn

I
(3;-
i)vdb6n
kinh R:5.
. 3t-6.
Xet M
(U#
)
e
a. Dr-rongthEngquaM
se
ldtieptuydn
cna(C)taiT(x;y)
khi vdchikhi
tWT.
tf
=O
22
<+
(x
-
t)
(x
-
3)
+
(y
-
+ ) 0
+

1)
-
0
<=+
x,
-
3x
-
rx
+
3r
+
y,
+
y
-
3t-6v
-
t'-u
=
0
22
'
)
"
22
t
22
<+
x2+

y'-6x+2y+3x-y-tx+3t
-ff,
T-0<+
l5+3x-y-rx
+zt-ffv
-tlru
=o
16+3t 53r+336
€(3-
t)x-
n
y+
n
=0
(*).
Nhu'vay
c6c
ti6p di6nr A,
B cria ti6p
tuyt5n kd
tu M d6n
duong
tron
(C)
c6
toa d6 th6a
mdrr
phuong
trinh
(*)

. Do
d6
(*)
chfnlr
ld
phuong
trinh
dudng
thdng AB.
Eu'd'ng
thing ndy
di
qua
di€m
C
(0;
1)
khi vd
chi
1 6+3t 63t+336
76 , 1 A
khi
-
: * :: 0
er
t-
-

Suy
radi6m

M
(-*:-1).
22223'3-/'
2) Tu'
giA
thi€t
suy ra:
CCi
:
BBi
+
C'(0; 1;
b)
,
-
B'
C
:
(a:
l;
-
b), AC'
=
(-
a; l;
b).
KhoAng
c6ch
gifi'a
hai

dud'ng
thing B'C
vd AC'
B
bing
khoAng
c6ch
tir di€rn A
d6n rndt
phdng (o)
chila B'C
vd song
song v6'i
AC'.
Vecto'ph6p
tuyiin
cria
mp(a) ld
i
:
tE,
i, ed
t
:
Qr,
-
ool,
l;u
_|,l,
l:,

1,
l)
=
rzu,
0; 2a)
Suy
ra
phuong
trinh
cira
mp(u) ld
:
bx
*
az=
A.
Do d6 khoing
c6clr tu
A d6n
mp(c,)
cfing
ld l<hoAng
cdch
., : I
-
ab
gifa
hai
dudng
thdng

B'C vd
AC'
bing
h:
;;ftr
i r 1t.,:
ab
ab
v'?'5 1
Ap dung
bat dang
tnuc
Co-sl ta
co
:
ffi
S
Um=
,/,
S
A.
DSng
thric
xdy ra
khi vd
chi khi
u=
6
=
jtfT.

VAy
khoang
c6ch
gifi'a
hai
dud'ng
thing
B'c vd
AC' t6'n
nhAt
bing
3 khi
a
:
b

3{2.
Cf;u VII.
rac6:
21
= cos(-;)+i
sin(-*)
yd
z2=r(-)*
rf)
=ztcosf,*rrinf,).
Suyra
Zr.zz=z1cos3*;rinf
)+
(21.22)tE=ztt(ror')n

*,rinf
):2't.i
.
B'
a*b
O"E
-___:
-
1
) 1^l')
/,"""
t.o
',
"'
t.
t