Đề thi thử đại học môn toán 2014 khối D đề 1

sở giáo dục và đào tạo hà tĩnh

Tr"ờng THPT Nguyễn Trung Thiên

Đề THi thử đại Học LầN I năm 2014
Mụn thi: Toán - KHI D
Thi gian lm bi: 180 phỳt
I. Phần chung cho tất cả thí sinh (7,0 điểm)
Câu I (2,0 điểm) !"# "$% &'
42
24
yxmx
=+
() *+ ,"-
()
m
C
./0 % 1$ ,"2% &' ,"3(
45 6"7# &8, &3 90:; ,"0<; .$ .= *+ ,"- (>2 "$% &' ?"0 % @ A
A5BC% ,D, (7 (8( E08 ,F- (>2 % GH (8( *0H% (3( ,F- (>2 *+ ,"-
()
m
C
;I% ,F<; (8( ,FJ( ,K2 *L5
Câu II (2,0 điểm)
45 M070 N"OP;E ,FC;"Q
sin2cos2cos3sin2
xxxx
+=+
5
A5 M070 N"OP;E ,FC;" Q

222
41
2
log(4)2log8326
xx
+=++

Câu III (1,0 điểm) M070 "R N"OP;E ,FC;"Q
222
710
1310
xyyx
xyyxy
++=


++=



Câu IV (1,0 điểm) !"# "C;" (")N S5TU!V () *8W TU!V 1$ "C;" ,"2;E .XY;E ,Z0 T .$ V5
U0:, TU @ A2 [ TV @ !V @ 2[ ST @ \2 .$ ST .XY;E E)( ./0 *8W5 B];" ,"H ,](" ?"'0 (")N S5U!V .$
?"#7;E (8(" ,^ U *:; %N _S!V` ,"a# 25
Câu V (1,0 điểm) !"# \ &' ,"3( GOP;E bc Wc d5 !"e;E %0;" FI;E Q

222
0
xxyyyzzzx
xyyzzx

++
+++
5
II. Phần riêng (3,0 điểm): Thí sinh chỉ đ"ợc làm một trong hai phần (phần A hoặc phần B)
A. Theo ch"ơng trình chuẩn
Câu VI. a. (1,0 điểm) BF#;E %f, N"g;E ./0 "R ,K2 *L hbW ("# ,2% E08( TU! () ,F3( ,i% j _4[k4`5
BFX;E *0H% (>2 (Z;" T! 1$ l_k4[ A`[ (Z;" U! () N"OP;E ,FC;"
d:2xy +10
=
5 m8( *-;" ,K2 *L (8(
*n;" (>2
ABC

5
Câu VII. a. (1,0 điểm) BF#;E %f, N"g;E ./0 "R ,K2 *L hbW ("# *Oo;E ,Fp;
22
():2220
Cxyxy
+=
5 qrN N"OP;E ,FC;" *Oo;E ,"g;E G (8(" E'( ,K2 *L %L, ?"#7;E 9I;E A .$
,0:N bs( ./0 _!`5
Câu VIII. a. (1,0 điểm ) BC% "R &' (>2
2
x
,F#;E ?"20 ,F0H; ;"- ,"e( t0X,P; (>2Q

()
2
2

n
Pxx
x

=+



(0)
x

5
U0:, FI;E ; ,"u2 %v;Q \
32
1
352(1)
nn
CAn
+
=
5
B. Theo ch"ơng trình nâng cao
Câu VI. b. (1,0 điểm) BF#;E %f, N"g;E ./0 "R ,K2 *L hbW ("# "C;" 9C;" "$;" TU!V ,i% wc () G0R;
,](" 9I;E x5 y"OP;E ,FC;" *Oo;E ,"g;E
:xy0
BC
=
5 U0:, z_A[4` 1$ ,FX;E *0H% (>2 (Z;" TU5 BC% ,K2
*L *0H% w5
Câu VII. b. (1,0 điểm) BF#;E %f, N"g;E ./0 "R ,K2 *L hbW ("# *Oo;E ,"g;E

:4320
dxy
+=
.$ *Oo;E
,Fp;
22
():26150
Cxyxy
++=
5{0:, N"OP;E ,FC;" *Oo;E ,"g;E
1
d
.XY;E E)( ./0
d
(|, *Oo;E ,Fp;
_!` ,Z0 T .$ U &2# ("#
6
AB
=
5
Câu VIII. b. (1,0 điểm) !) 4A "K( &0;" E0u0 E+% \ "K( &0;" ?"'0 4A[ x "K( &0;" ?"'0 44 .$ } "K( &0;"
?"'0 4~5 !"K; ;EX ;"0<; 6 "K( &0;"5 B];" b8( &XD, &2# ("# %ỗ0 ?"'0 () ], ;"D, 4 "K( &0;"5

kkkkkkkkkkkkkkkkkkkkk Hết kkkkkkkkkkkkkkkkkkkk



Đáp án K-D gồm có 5 trang.
L"u ý : Mọi cách giải đúng đều cho điểm tối đa.

Câu Đáp án và h"ớng dẫn chấm Điểm

1 (1,0 điểm)
________________________________________________________________________
{/0 %@A "$% &' ,Fở ,"$;"
42
44
yxx
=+

+BrN b8( *-;"Q
DR
=

+ M0/0 "Z;Q lim
x
y

=
[ lim
x
y
+
=

________________________________________________________________________
_ S3 90:; ,"0<;Q
3
'48
yxx

=+
c
,
0
0
2
x
y
x
=

=

=



+ U7;E 90:; ,"0<;Q

b



2

~
2


+

W

+ ~ k ~ + ~ k
W ~ ~



kx


kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
SXW F2Q
j$% &' *+;E 90:; ,F<; %ỗ0 ?"#7;E
(
)
;2

.$
(
)
0;2
5
j$% &' ;E"-(" 90:; ,F<; %ỗ0 ?"#7;E
(
)
2;0

.$
(

)
2;
+
5
Đ0H% (3( *Z0 (>2 *+ ,"- 1$
(
)
2;0

.$
(
)
2;0
5 Đ0H% (3( ,0HX (>2 *+ ,"- 1$
(
)
0;4

5
________________________________________________________________________
+ Đ+ ,"- Q
Đ+ ,"- (|, ,FJ( ,X;E ,Z0
(
)
0;4

.$ (|, ,FJ( "#$;" ,Z0 *0H%
(
)
2;0

.$
(
)
2;0
5
+ t"r; bé,Q Đ+ ,"- _!` ;"r; ,FJ( ,X;E 1$% ,FJ( *'0 be;E5




~cA}








~cA}

~cA}






~5A}

Câu
I.
2,0
điểm

2 (1,0 điểm)
________________________________________________________________________
B2 ()Q
(
)
32
'444
yxmxxxm
=+=+
[
2
0
'0
x
y

xm
=

=

=


________________________________________________________________________
t:X
0
m

,"C
(
)
m
C
("n () %L, *0H% (3( ,F- .$ *) 1$ *0H% (3( *Z0 ;I% ,F<; ,FJ( ,X;E5
________________________________________________________________________
t:X
0
m
>
,"C
(
)
m
C
() \ *0H% (3( ,F-5

zL, (3( ,0HX ;I% ,F<; ,FJ( ,X;E .$ "20 (3( *Z0 () ,K2 *L
(
)
2
;4
mm

c
(
)
2
;4
mm

5
________________________________________________________________________
ĐH "Z0 *0H% ;$W ;I% ,F<; ,FJ( "#$;" ,"C
2
402
mm
==
5
{C
0
m
>
;<; ("K;
2
m
=

5
{rW
(
]
{
}
;02
m 1$ ;"ữ;E E08 ,F- (ầ; ,C% ,"u2 %v; W<X (ầX 9$0 ,#8;5



~5A}



~cA}


~cA}



~5A}
Câu
II.
2,0
1 (1,0 điểm)
________________________________________________________________________
yB

2
2sincos12sincossin32
xxxxx
+=+





⇔
2
(2sincoscos)(2sin3sin1)0
xxxxx
−−−+=


⇔
(#&b_A&0;bk4` – _A&0;bk4`_&0;bk4` @ ~

⇔
(2sin1)(cossin1)0
xxx
−−+=

________________________________________________________________________
1
sin
2
sincos1
x

xx

=

⇔

−=


1
sin
2
2
sin
42
x
x
π

=


⇔


−=





________________________________________________________________________
2
6
5
2
6
2
2
2
xk
xk
xk
xk
π
π
π
π
π
π
ππ

=+



=+

⇔



=+


=+


k
∈





~c}





~c}








~cA}

®iÓm

2 (1,0 ®iÓm)
________________________________________________________________________
B2 ()
22
12
2
2log8322log832
xx
+=−+

(
)
2
4
2log832
x=−+

(
)
(
)
22
444
2log4log82log43
xx

=−++=−+−


5
y"OP;E ,FC;"
(
)
(
)
222
44
log42log430
xx
⇔+++−=

________________________________________________________________________
§f,
(
)
2
4
log4
xt
+=
c N"OP;E ,FC;" ,Fë ,"$;"
2
2301
ttt
+−=⇔=
[
3
t
=−

5
________________________________________________________________________
{/0 , @ 4c ,2 ()
(
)
2
4
log410
xx
+=⇔=
5
{/0 , @k\c ,2 ()
(
)
2
4
log43
x
+=−
_.Y ;E"0R%`5
{rW N"OP;E ,FC;" () ;E"0R% b @ ~5




~c}

~cA}



~cA}
C©u
III.
1,0
®iÓm

t"r; bÐ, W@~ ?"Y;E ,"u2 %v; "R N"OP;E ,FC;" *v ("#5
jR N"OP;E ,FC;" *v ("#
2
2
1
7
1
13
x
x
yy
x
x
yy

++=


⇔



++=



________________________________________________________________________
§f,
1
ux
y
=+
[
x
v
y
=
5 SXW F2Q
22
2
1
2
x
ux
yy
=++

22
2
1
2

xuv
y
⇒+=−
5
6"0 *)c ,2 *Oî(Q
2
7
13
uv
uv
+=


−=


2
7
200
uv
uu
+=

⇔

+−=


4
3

5
12
u
v
u
v
=



=


⇔

=−



=




________________________________________________________________________



~cA}

~cA}







~cA}
{/0
1
4
3
ux
y
x
v
y

=+=





==



3
1
34
xy
y
y
=


⇔

+=



2
3
3410
xy
yy
=

⇔

−+=


1
3
1
3
1
y
x
y
x
=



=



⇔

=






=



________________________________________________________________________
{/0
1
5
12
ux
y
x
v
y

=+=−




==



12
1
125
xy
y
y
=



⇔

+=−



2
12
12510
xy
yy
=

⇔

++=

_.Y ;E"0R%`5
6:, 1Xr;Q jR N"OP;E ,FC;" *v ("# () "20 ;E"0R%
3
1
x
y
=


=

.$
1

1
3
x
y
=



=


5








~cA}




C©u
IV.
1,0
®iÓm

V0R; ,](" "C;" ,"2;E TU!V 1$
()
2
13
2
22
a
Saaa=+=5
V0R; ,](" ,2% E08( TUV 1$
2
1
.
2
ABD
SABADa
∆
==
5
V0R; ,](" ,2% E08( U!V 1$
2
2
BCDABD
a
SSS
∆∆
=−=5
________________________________________________________________________
B"H ,](" ?"'0 (")N S5U!V 1$
23
.

11
3.
3322
SBCDBCD
aa
VSASa
∆
===
5
________________________________________________________________________
B2 ()Q
22
910
SDaaa=+= 5
{C
()
SAABCD
⊥

SACD
⇒⊥
5
zf, ?"8(
ADCD
⊥
5
SXW F2
CDSD
⊥
5

V0R; ,](" ,2% E08( S!V 1$
2
1
10
2
sCD
Sa
∆
= 5
________________________________________________________________________
MK0 G 1$ ?"#7;E (8(" ,^ U *:; _S!V`5 B2 ()Q
3
.
1
.
32
SBCDSCD
a
VdS
∆
==
3
2
3310
10
10
aa
d
a
⇔==5

~cA}





~cA}





~cA}





~cA}
C©u
V.
1,0
®iÓm

B2 ()
(
)

2
2
2
xxyxy
xxyxy
x
xyxyxy
+−
−
==−
+++
5
V# bcW GOP;E ;<;
2
2
xyxy
xy
+
≤
+
5
SXW F2
2
22
xxyxyxy
x
xy
−+−
≥−=
+

5
________________________________________________________________________
BOP;E ,3 ,2 (ò;E ()
2
2
yyzyz
yz
−−
≥
+
[
2
2
zzxzx
zx
−−
≥
+
5
B^ *) &XW F2
222
0
222
xxyyyzzzxxyyzzx
xyyzzx
−−−−−−
++≥++=
+++
_*N(%`5

~c}






~c}

A. Theo ch"¬ng tr×nh chuÈn
C©u
VI. a.
1,0
®iÓm

M07 &ö
(
)
;21
Cmm
+
5
{C
(
)
1;2
E − 1$ ,FX;E *0H% T! ;<;

(
)
2;32
Amm
−−−[
(
)
3;42
AHmm
=+−+

5
________________________________________________________________________
{C .a(,P ("n N"OP;E (>2 U! 1$
(
)
1;2
BC
u =

5
{C
AHBC
⊥
;<;
(
)
.22420
BC
AHumm

=++−+=


1
m
⇔=
5
{rW
(3;1)
A
−
.$
(1;3)
C 5
______________________________________________________________
M07 &ö
(
)
;21
Bnn
+
5
!)
(
)
1;22
BHnn
=−−−

[

(
)
4;2
BC
u =

5
{C
BHAC
⊥
;<;
.4(1)2(22)0
BC
AHunn
=−+−−=


1
n
⇔=
5
{rW
(0;1)
B 5


~cA}

~c}





~cA}
C©u
VII.
a.
1,0
®iÓm

MK0 N"OP;E ,FC;" *Oo;E ,"g;E G 1$
0
axbyc
++=

(
)
22
0
ab
+≠
c

22
(;)22
c
ddO

ab
=⇔=
+
5
________________________________________________________________________
§Oo;E ,Fp; () ,i% w_4[4` 98; ?];" R @A5
{C G ,0:N bs( ./0 _!` ;<;
22
(;)22
abc
ddO
ab
++
=⇔=
+

________________________________________________________________________
SXW F2
abcc
++=

2
ba
ab
c
=−


⇔
+


=−


______________________________________________________________
{/0
ba
=−
c ("K;
1
a
=

1;22
bc⇒=−=± ,2 *Oî( N"OP;E ,FC;"
220
xy
−±=
5
{/0
2
ab
c
+
=− c ,2 ()
22
152150
aabb
−+=

0
ab
⇔==
_?"Y;E ,"u2 %v;`5


~cA}




~cA}




~cA}




~cA}
C©u
VIII.
a.
1,0
®iÓm

B^ *Ò 9$0c ,C% *Oî( ; @4\5
________________________________________________________________________

13
13
22(13)
13
0
2
2
kkkk
k
xCxx
x
−−
=

+=


∑
5
M070 ,C% *Oî( ? @85
________________________________________________________________________
jR &' (Ç; ,C% 1$
88
13
2.
C
5
~c}

~cA}



~cA}










B. Theo ch"¬ng tr×nh n©ng cao
C©u
VI. b.
1,0
®iÓm

§Oo;E ,"I;E zw qX2 z .$ &#;E &#;E ./0 U! ;<; () N"OP;E ,FC;" b – W – 4 @ ~5
________________________________________________________________________
1
(,)
2
dMBC =
[
42(,).422
ABCD

SdMBCBCBC=⇔=⇔=
2
2
BC
MI ==5
________________________________________________________________________
MK0
(;1)
Iaa
−
[
3
2
1
a
MI
a
=

=⇔

=


________________________________________________________________________
SXW F2 w_\[ A` "#f( w_4[ ~`5
~cA}

~cA}




~5A}


~cA}
C©u
VII.
b.
1,0
®iÓm

_!` () ,i% w_4[ k\`c 98; ?];" R @}5
{C
1
dd
⊥
;<; N"OP;E ,FC;" *Oo;E ,"g;E
1
d
() GZ;E
340
xyc
++=
5
______________________________________________________________
6"#7;E (8(" ,^ w *:;

1
d
1$
1
9
(;)
5
c
dId
−+
= 5
zf, ?"8(
2
2
1
(;)2594
2
AB
dIdR

=−=−=


5
________________________________________________________________________
SXW F2
9
4
5
c−+

=

920
c
⇔−+=


920
920
c
c
−+=

⇔

−+=−


29
11
c
c
=

⇔

=−


______________________________________________________________

{rW
1
d
() N"OP;E ,FC;"
34290
xy
++=
"#f(
34110
xy
+−=
5

~cA}





~cA}




~cA}




~cA}

C©u
VIII.
b.
1,0
®iÓm

S' (8(" ("K; 6 "K( &0;" ,F#;E 4A "K( &0;" 1$
6
12
924
C = 5
S' (8(" ("K; 6 "K( &0;" ("n () "K( &0;" ?"'0 4A .$ 44 1$
6
7
C
5
S' (8(" ("K; 6 "K( &0;" ("n () "K( &0;" ?"'0 44 .$ 4~ 1$
6
9
C
5
S' (8(" ("K; 6 "K( &0;" ("n () "K( &0;" ?"'0 4A .$ 4~ 1$
6
8
C
5
________________________________________________________________________
⇒
S' (8(" ("K; 6 "K( &0;" &2# ("# %ç0 ?"'0 () ], ;"D, 4 "K( &0;" 1$

(
)
6666
12798
805
CCCC−++=5
________________________________________________________________________
{rW b8( &XD, (Ç; ,C% 1$
805115
924132
P ==5


~c}





~cA}


~cA}