đề toán thi thử năm 2015

ĐỀ THI THỬ ĐẠI HỌC LẦN I NĂM 2015
Môn: TOÁN; Khối A, A1, B và D
Thời gian làm bài: 180 phút, không kể thời gian phát đề
Câu 1 (2,0 ).




 !"!##$%
&'(!)*!)+,-./#0)12314'(!)*!)+56
478!0.9:9; 7- !%6:#;#-<!))#=!-
Câu 2 (1,0 ). >7'?!)@3!


A
B! CDA E!   !
  
x c x x
π π π
π
     
+ + − = + −
 ÷  ÷  ÷
     
Câu 3 (1,0 ). 236!)F
G
@!)1@4!!F%!F
B




n
x
x
 
+
 ÷
 

H !IJ!
 
D
D  D
   DC
n
n n n
n
n
n n n
C C C
C n
C C C
−
+ + + + =

Câu 4 (1,0 ). >K7'?!)@3!
2 2
1 2
9 1 10.3
x x x x+ − + −
+ ≥

.
Câu 5 (1,0 ). 2@!)L7*!)#=0MNO9PQ77'?!)@3!'(!)*!)+,-:/
#5O6./C95O6HC/)O.H+0!RS!)DG9 #
+'?!)
Câu 6 (1,0 ).3!7T.HUP3!V!Q/N+6!.H/
H  =

6!"!S!)!-#S!)>M:9;'?!)F!)P@-!)46!.U#H9P
4@"!.U
 
.

=
2R!W4R3!7T.HU#1!))V
'(!)*!):;#T
Câu 7 (1,0 ).4.DC//ED#'(!)*!)+7'?!)@3!

D
D
D −
==
− zyx
XQ7
7'?!)@3!L7*!)Y,-.9!)!)#=+#1!)Z+=YPP=!!K
Câu 8 (1,0 ).>07'?!)@3![
 B  
 B B
 D D   D
      D


+ + = −

− = + +

#=
9∈¡
Câu 9(1,0 ).+'?!)99IJ!
Da b c
+ + =
23)@!I!K%4-
F
D D D
P
a bc b ac c ab
= + +
+ + +

Hết
 !
\M#"!R![T+![
Đề gồm 01 trang.
T]>U^&2T_;X.
TRƯỜNG THPT THUẬN CHÂU
ĐÁP ÁN – THANG ĐIỂM
ĐỀ THI THỬ ĐẠI HỌC LẦN I NĂM 2015
Môn: TOÁN; Khối A, A1, B và D
(Đáp án – Thang điểm gồm 04 trang)
" #$ #
1
(2,0

)
a) (1,0 ) Khảo sát sự biến thiên và vẽ:
 
 y x x= − +
`2Q7![
= ¡D

`T !"![
>=6![
→−∞
= −∞
x
lim y
/
→+∞
= +∞
x
lim y
%&'(
a- !"![

b  Gy x x= −
/
b  Cy x = ⇔
CL
\!) !@"!1!)
( )
/C−∞
#
( )

/+∞
/!) !@"!1!)
( )
C/

@[\666

C/ x y= =
Đ
/64-6
2
/ x y= = −


%&'(
H!) !"![
%'(
`&[


O
EDD

E
%'(
b) (1,0 ) Đường thẳng (d) đi qua A(3; 2) và có hệ số góc k
&'(!)*!)+[1
Y'?!)@3!!N)4[




1

 C
C
x
x k
− =

⇔

− =


%&'(
+564.9:9;78!0

Cx k⇔ − =
!)078!01

C ck⇔ < ≠
Y'?!)@3![

Cx k− =
x k
x k

=
⇔


= −


%&'(
\0)% 7- !6:#;Pd!P'eP[
( ) ( )
b  G / b  G
k k
y k k y k k
−
= − = +
2 7- !6:#;#-<!))
( ) ( )
b  b D
k k
y y
−
⇔ = −
%&'(

( ) ( )

Df  A
 G  G D c G D C  g 
c
k k k k k k k t m
±
⇔ − + = − ⇔ − + = ⇔ =
%'(


−∞
C
+∞

h C
−
C
 
+∞
−∞
E
2
(1,0
)
(1.0 )Giải phương trình:

A
B! CDA E!   !
  
x c x x
π π π
π
     
+ + − = + −
 ÷  ÷  ÷
     
Y2

B      c x c x c c x⇔ − − = −
%&'(

 c x c x
⇔ =
%&'(
 
 
x x k
x x k
= + π

⇔

= − + π

 %&'(

x k
π
⇔ =
 %&'(
3
(1,0
)
Tìm hệ số của x
6
trong khai triển
ij1@4!
D
D
k
n

k
n
C n k
C k
+
−
=
+
#=
C / 9k n k n≤ ≤ ∈¥
k7+l!)Pd!P'e#=1C/D///!D
2'e[!!D!DDC
%&'(
DA
 D
DC
DG 

n
n n
n loai
=

+
⇔ = ⇔

= −

 %&'(
2

( )
DA
DA
DA
D D DA
DA DA
 B  B
DA DA
B
C C
  
     
 

k k
k
k
k k
k k
k k
x C x x C x
x
−
−
− −
−
= =
   
 
 

+ = =
 ÷  ÷
 ÷
 ÷
 
 
   
∑ ∑
 %&'(
\0%6!)F
G
'?!)F!)#=
DA
G
 B
k k−
− =
k
⇔ =
m=10%6!)F
G
P[

 DA   DD 
DA DA

    DcAGC

C C
−

 
= =
 ÷
 
%&'(
4
(1,0
)
(1.0 )Giải bất phương trình:
2 2
1 2
9 1 10.3
x x x x+ − + −
+ ≥
&L


x x
t
+
=
9nC %&'(
HK7'?!)@3!@o![

DCc≥C⇔≤DL≥c
%&'(
≤D⇒


 D C D C

x x
t x x x
+
= ≤ ⇔ + ≤ ⇔ − ≤ ≤

%&'(
≥c⇒



 c  C
D
x x
x
t x x
x
+
≤ −

= ≥ ⇔ + − ≥ ⇔

≥


%&'(
 e7#Q7!)0%7P[TE∞/Ep∪qED/Cp∪qD/∞
5
(1,0
)
LYp phương trình đường thẳng d (1,0 )

>M7'?!)@3!+'(!)*!)+d!3+6!)[
D
x y
a b
+ =
&1[
Cab ≠
 %&'(
 
/   D   D
   /C/  C/  /
M d a b ab
a b
d Ox A a d Oy B b OA a a OB b b
∈ ⇒ + = ⇔ + =
∩ = ∩ = ⇒ = = = =
D
 

ABC
S OAOB ab= ⇔ =
%&'(
2ZD#0[
f
 f

  B
D
ab a
a

hoăc
a b ab b
b

= =
=
 

⇔
  
+ = =
 

=

%&'(
m=
f
B
a
b
=


=

'e+[
D  f C
f B
x y

x y+ = ⇔ + − =
m=
f

D
a
b

=



=

'e+[

D c  B C
f D
x y
x y+ = ⇔ + − =
%&'(
6
(1,0
)
*) Tính thể tích hình chóp S.ABCD theo a. (0,5 )
A
B
C
M
S

E
F
K
H
D
O
N
%&'(


  
 D
B
B 
a a
SO SA OA a= − = − =

%&'(

D


S ABCD ABCD
V SO S=


D D D G
    
   G
S ABCD ABCD

a a
V SO S a a= = =
#
*) Tính khoảng cách giữa MN và SK theo a.(0,5 )
r
ggKE MN

%&'(
9
gg MN SEK
!"!
+:;9T  9   9 d MN SEK d O SEK= =
>MsP@-!)4t2[
/KE OF KE SO⊥ ⊥
 KE SOF⇒ ⊥

2@!)
 SOF
+!)
OH SF⊥

9
  +:;9T  9 OH SKE d O SEK OH⊥ ⇒ = =

Os:..:

G
a

  

D D D
OH OS OF
= +
  
D B G
D OH a a
⇔ = +


D D
f f
a
OH OH a⇔ = ⇒ =
%&'(
7
(1,0
)
LYp phương trình mặt phẳng (P).(1,0 )
>M\P3! -%.@"!+9L7*!)Y,-.#Ygg+91
1!))V+#YP1!)Z\ !Y
%&'(
>u4vP3! -%\P"!Y9
HIAH ≥
n\vP=!!K1
IA ≡
mQYd!3PL7*!),-.#!Q!
AH
P#j?77- !
%&'(
:L  19 

D//D tttHdH ++⇒∈
#3  \  P  3!   -  %  .  @"!  +  !"!
. 0 ( (2;1;3)AH d AH u u
⊥ ⇒ = =
uuur r r
P#j?w7'?!)%+
A/D/xB/D/ −−⇒⇒ AHH

%&'(
mQ[Y[xDCAyDC
⇔
xAyxxC %&'(
8
(1,0
)
Giải hệ phương trình:
 B  
 B B
 D D   D
      D

+ + = −

− = + +

#=
9 ∈¡
\7
A   B B
 G   B A

  DD
   D
xy xy x y y
x y xy x y xy

− − − =
⇔

− − − =

XK@ZD'e[


G
B
A

B
C
%&'(
>M
AC BD O∩ =
.
UT.THTTU
T-@
 SO ABCD⊥
( )
B

C

C
D
 B D C
D

y
y
xy
xy xy
xy


=

=

⇔ ⇔ =


− + =



=


%&'(
m=C#7D1<!)IJ!T-@0#<!)0
m=D#7D2'e[
B 

D A
 D

y y y
±
= + ⇔ =
m=
D A A D
 
y x
+ −
= ⇒ =
/
D A A D
 
y x
− − −
= ⇒ =
%&'(
m=
D

xy =
#7D'e[
B


C#<!)0
mQ0!)0
A D D A

/
 
 
− +
 ÷
 
#
A D D A
/
 
 
− − −
 ÷
 
%&'(
9
(1,0
)
 )**+,-
F!)![
( )
D D D D D D c
cx y z
x y z x y z x y z
 
+ + + + ≥ ⇔ + + ≥
 ÷
+ +
 
D D D c

P
a bc b ca c ab a bc b ca c ab
⇒ = + + ≥
+ + + + + + + +
%&'(
2[
T-@
    
  
 
a b a c a b c
a bc a b a c
+ + + + +
+ = + + ≤ =

2'?!)[
    
  
 
b a b c a b c
b ca b a b c
+ + + + +
+ = + + ≤ =

    
  
 
c a c b a b c
c ab c a c b
+ + + + +

+ = + + ≤ =
%&'(
T-@[
  
  
a b c a b c a b c
a bc b ca c ab
+ + + + + +
+ + + + + ≤ + +
B 


a b c
a bc b ca c ab
+ +
⇒ + + + + + ≤ =
mQ
c

P ≥
%&'(
mQY6>2;;S!)
c


D
D
D

a b c

a b a c a b c
a b c
b a b c a b c
c a c b
+ + =


+ = + + + =


⇔ ⇔ ⇔ = = =
 
+ = + = =



+ = +

%&'(
./0123,&45678
,+,"2