Bộ đề thi đại học môn toán năm 2014

BỘ GIÁO DỤC VÀ ĐÀO TẠO
VỤ GIÁO DỤC TUYỂN SINH ĐẠI HỌC 2014


Năm 2014 Nhà xuất bản Giáo dục Việt Nam được Bộ
Giáo dục và Đào tạo (Bộ GD&ĐT) giao nhiệm vụ tổ
chức biên soạn và phát hành tài liệu ngân hàng đề thi
phục vụ công tác tuyển sinh đại học, cao đẳng hệ
chính quy năm 2014. Các thông tin này được cập
nhật đến ngày 31/3/2014 dùng cho các đại học, học
viện, các trường đại học, cao đẳng và chịu trách
nhiệm. Bộ ngân hàng mã đề thi đáp án “Dùng cho
các trường đại học , cao đẳng về tuyển sinh năm
2014” làm căn cứ đổi mới để tuyển sinh đại học, cao
đẳng năm 2014. Nhằm cung cấp những thông tin
quan trọng về ngân hàng mã đề tuyển sinh đại học
(ĐH), cao đẳng (CĐ) trong toàn quốc : KIẾN THỨC
KỸ NĂNG HIỂU BIẾT CỦA HỌC SINH THPT về MÔN
TOÁN CƠ BẢN VÀ NÂNG CAO :CÓ 50 MÃ ĐỀ THI
MÔN TOÁN CÓ KÈM THEO LỜI GIẢI . nhằm mục đích
cho các trường tuyển sinh đầu vào đại học cao đẳng
năm 2014 .
*Lịch thi tuyển sinh (theo đề thi chung)
a) Đối với hệ đại học
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0DEF
Q S  d x y m+ + =
63
j
] 
m
0W
Q SC
#q
Q Sd
?A+,/#/$`2#, #

Ai(TI6
]^(1 điểm)
3./L,T`@,0hi&k#/K, cNF
QrS&sgkgbQtS&sgkgbQuS&gskgb
0DEF

∆



−
−x
b

+y
b

z
6_@

∆
(,/9;#!,QrSQtS6
;ND\.]0DEFQ$S9L-#TQuS#q#J,0DEF

∆


∆
6
]^(1 điểm) _JKIND\.](/

&
Q(/

Q=
&
sSS
≤

>>>>>>>>>>:;>>>>>>>>>>
BZB0),.62@
]I3MN&#0B
{ }
v D = ¡
32


l 
Q S
y x D
x
−
= < ∀ ∈
−
: +B#K;.Y##/J
Q PS−∞

QP S+∞
: +L#-#%#.B
_T?
x

Limy
+
→
= +∞

x
Limy
−
→
= −∞


x
Lim y
→+∞
=


x
Lim y
→−∞
=
[B#-` #M0H&b` #M,b
AJK;Y
Z0[B
]I?(3;N9;#!,Q7S?0W 
 
Q P Q SS Q SM x f x C∈
#-ND\.]
  

lQ SQ S Q Sy f x x x f x= − +
:,
 
  
Q S    x x y x x+ − − + − =
QS
X/J##40W QPS0;;N9;QSK^





 

 Q S
x
x
−
⇔ =
+ −

J0D#` 

x =


x =
M7#;N9;#w] 
 x y+ − =


 x y+ − =
]?IA;0GND\.]0-#/D\0D\T
/+  +   /+Q S C 
C
c x x c x
π
− + + + =

/+Q S  /+Q S  
 C
c x c x
π π
⇔ + + + + =

 /+ Q S  /+Q S  
C C
c x c x
π π
⇔ + + + + =
6_J0D#

/+Q S
C 
c x
π
+ = −

/+Q S 
C
c x

π
+ = −
Q(/?S
_J

/+Q S
C 
c x
π
+ = −
0D#` 


x k
π
π
= +



C
x k
π
π
= − +
]?I?A;0G`D\0D\T
  
 
Q S 
Q S 

x xy x y
x y x xy

− = −


− − = −


cxN"


x xy u
x y v

− =


=


,0D#`



u v
v u

= −


− = −

_J`.Y0D#` Q9PS(
QPSQ>P>S340-J0D#` Q&PS(QPSQ>PS
]eI(fg#%Vh32$b>+&$&0G#M&byb

x
π
=
]


t =
340-



 



( (t t
I dt dt
t t
= − =
∫ ∫
c


( Pu t dv dt

t
= =

 
Pdu dt v
t t
⇒ = = −
9.,




 
   
( ( 
 

 
I t dt
t t t
= − + = − −
∫
X;z9J

  ( 

I = − −

]AI(id
_@:(.90W A7#H 

Q SSH ABC⊥
{#0B0O-#*,, cNFQASQ7ST c0(

CSEH SFH= =
X|
HK SB⊥
(MN(9M+9.,-#*,, cNFQASQA7SK^
HKA
6
MN(9M20D#7bAb,


a
HA =



, C

a
SH HF= =
3, #:X9L?:#-
  
   

KH a
HK HS HB
= + ⇒ =
3, #:X9L?:#-




,



a
AH
AK H
KH
a
= = =

#/+

AKH⇒ =

]TA;0G
 
 Q SQ S
a b c c
ab c ab b a a b
+ − −
= =
+ + − − − −
340-
  
Q SQ S Q SQ S Q SQ S
c b a
VT

a b c a c b
− − −
= + +
− − − − − −
</,K#$D\,gKg#bY,K#9h#/JQPSb}>,>K>#$D\
N$"KI0FH#7L+#/K,+$D\,0D#

  
6 6 6
Q SQ S Q SQ S Q SQ S
c b a
VT
a b c a c b
− − −
≥
− − − − − −
bQ0N# S
FH#&J.,#d


a b c= = =
]j$I
∆
#-ND\.], +
 
 
x t
y t
= −



= − +

#-#N
Q PSu = −
ur
9h#
∆

Q  P   SA t t⇒ − − +
3,#-QAP
∆
Sb



/+Q P S

c AB u⇔ =
uuuur ur
6


6
AB u
AB u
⇔ =
uuuur ur
ur



 
C= C  
 
t t t t⇔ − − = ⇔ = ∨ = −
7#0W #w] (
 
   
Q P S Q P S
   
A A− −
]k$I(l$S0z9,

QP PSM −
#-#N

QP P Su = − −
uur
Q$mS0z9,

QPPSM
#-#N

QPPSu =
uur
3,#-
 
P Q P 5PSu u O
 
= − − ≠

 
uur uur ur

 
QPPSM M =
uuuuuuur
{~
   
P 6 C  u u M M
 
= − + =
 
uur uur uuuuuuur
 Q$SQ$mS0[NF6
_@QrS( cNF#H,Q$SQ$mSb}QrS#ON
QPP Sn = −
ur
0z9,U

Y#-
ND\.]
  x y z+ − + =
<•I0W UQP>PS9h# €QrS40-,#-0N# 
]m$I89`&}
3:&~&b(` 
3:&~
x ≠
K;0GND\.]D\0D\T

  

 (/ Q S  (/ Q S (/ Q S
x x x
x x x
+ =
+ + + + +
c
(/ Q S
x
x t+ =
,0D#ND\.]
  
  t t t
+ =
+ +
J0D#bb>
Tb
(/ Q S 
x
x⇒ + =
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QS

MI
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5
x =
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y t
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
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
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Q  P  P SAQg+Pg+P+SA t t t⇒ − − +

Q  P CP  SAB s t s t s t= + − + −
uuuur
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−
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A
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Z,,.,:)[)\B),<7,( 7 điểm )
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? 3]  0W0[B +#-0W #%#0?0W #%#W90[E##0W #%#
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


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  
5   5 5  x x x x x x− + ≤ − + − + −
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A
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Z,CF.,:)n.,Do.)C,le&+P
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


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ty
tx
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

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n 1 n 2 n 3 2n 1 2n 8
2n 1 2n 1 2n 1 2n 1 2n 1
C C C C C 2 1
+ + + -
+ + + + +
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6
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6
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−
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−−+− xxxx
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·
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AA H
K^
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6{~, #9L:
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·
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AA H
b
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a
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A
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7
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7
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7
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
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7
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#/, #A79L634N##!,0DE.…,#-a QP>Sub4|0D#
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ACAB ⊥
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m
m
m
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SPPQ tttHdH ++⇒∈
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SPPQQ6 ==⇒⊥ uuAHdAH
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n 1 n 2 n 3 2n 1 2n 8
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C C C C C 2 1
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6
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7
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1 x x x- + -
6
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+ - + + +
+ + + + + + + + +
+ = + + + + + + + + + +
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2 C C C C C C C C C C
+ + - + + + + -
+ + + + + + + + + +
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+
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4
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ë û
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4 4 4 4 4 4 4 4 4 4
C C x C x C x C x C C x C x C x C x= - + - + + + + +
^
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2
−=
R(N
QES
1
9
2
2
=+ y
x
67H .^QPS,/QES?0W NaK`#e^ .Y h
0DE.…6;ND\.]0DE.…0z9,0W 0-6
63./L,T`."#@,0hOxyz#/ c#w9QSS#-ND\.]
011642
222

=−−+−++ zyxzyx
 cNFQ
α
S#-ND\.]xgyszgb
6;ND\.] cNFQ
β
S+/+/TQ
α
S#qQSSR/,/9;(0DE
.…#-#9K^Cπ6
]^$Q0W S3] `+#!,+?#H,x
 
./,.WBH#9\#!,
n
x
x








+
4
2
1
   K;  .^ n (  +  9Y  $D\  f,  o
1

6560
1
2
3
2
2
2
2
1
2
3
1
2
0
+
=
+
++++
+
n
C
n
CCC
n
n
n
nnn

Q
k

n
C
(+GN#MNk#!,nNw'S
Zq?]^Q0W S
63./ cNFT`."#@,0hOxy#/,0DEFd

xgygbd

x
gy>b, #ABC#-AQPS.@a (0W GQPS0W B9h#d



0W
C9h#d

6;ND\.]0DE.…/?;N, #ABC6
63./L,T`."#@,0hOxyz#/, #ABCTAQPPSBQP
PSCQPPS cNFQPS&ssksb6_@M( h0W ,0G.Y
cNFQPS63] .BfI#!,KW9H#
222
MCMBMA ++
]^Q0W S_J`ND\.]



+−=
+=+
+
+−

1
)1(2
yxe
xee
yx
yxyx
Qxy
∈R
S
,Dr.s,[-):B2@e
Câu 1: 1, Khảo sát hàm số
43
23
+−= xxy
6Tập xác địnhu
6Sự biến thiên
,S_T?
+∞=+−=−∞=+−=
+∞→+∞→−∞→−∞→
)4x3x(limylim,)4x3x(limylim
23
xx
23
xx
KSAJK;Ylb&

>C&lb
⇔
&b&b
AJK;Y

& >
∞
g
∞
l g>g

g
∞
>
∞

>: +0[K;.YQ>
∞
PSQPg
∞
SB#K;.YQPS
>: +0?#%#0??&b
7
b0?#%#W9?&b
73
b6
6Đồ thị[B,/T."#9?QPS,/T."#/?Q>PSQPS6M
0W 9QPS( a 0&H
Câu1 : 2,Tìm m để hai tiếp tuyến vuông góc
$#-ND\.]b Q&sSg6
:/0h,/0W #!,$Q7S(` #!,ND\.]



=−

=
⇔=−−⇔+−=+−
0mx
3x
0)mx)(3x(4)3x(m4x3x
2
223
&

>

i



3R/K.,,#-089` }
1)m('y).m('y −=−
9
35318
m01m36m91)m6m3)(m6m3(
2
±
=⇔=+−⇔−=+−⇒
Qf, oS
Câu 2: 1, Giải hệ phương trình đại số
3,IbLNJ(` #!,`
:`ND\.]D\0D\T








=−+
+
=−++
+
1)2yx(
y
1x
22yx
y
1x
2
2
c
2yxv,
y
1x
u
2
−+=
+
=
3,#-`
1vu
1uv
2vu
==⇔




=
=+
9.,





=−+
=
+
12yx
1
y
1x
2
6
_J`.Y,0D#` #!,N0o#/(QPSQ>PS
Câu 2: 2,Giải phương trình lương giác
89`
0
3
xcos
6
xcos
3
xsin

6
xsin ≠






π
+






π
−






π
+







π
−
3,#-
1x
6
cot
6
xtan
3
xtan
6
xtan −=






−
π






π
−=







π
+






π
−
rD\.]0o#/D\0D\T
8
1
x3cosxcosx3sin.xsin
33
=+⇔
1 cos2x cos 2x cos 4x 1 cos2x cos 2x cos 4x 1
2 2 2 2 8
− − + +
⇔ × + × =
2
1
x2cos
8

1
x2cos
2
1
)x4cosx2cosx2(cos2
3
=⇔=⇔=+⇔






π+
π
−=
π+
π
=
⇔
k
6
x
(lo¹i) k
6
x

(k )∈Z
6MND\.]#-` 
π+

π
−=
k
6
x

(k )∈Z
Câu 3:Tính tích phân c





=
++
+
=
⇒



=
++=
2/xv
dx
1xx
1x2
du
xdxdv
)1xxln(u

2
2
2
1
1
2 3 2
2
2
0
0
x 1 2x x
I ln(x x 1) dx
2 2 x x 1
+
= + + −
+ +
∫
∫∫∫
++
−
++
+
+−−=
1
0
2
1
0
2
1

0
1xx
dx
4
3
dx
1xx
1x2
4
1
dx)1x2(
2
1
3ln
2
1
( )
11
1
0
2
1
0
2
I
4
3
3ln
4
3

I
4
3
)1xxln(
4
1
xx
2
1
3ln
2
1
−=−+++−−=
32


∫








+







+
=
1
0
2
2
1
2
3
2
1
x
dx
I
6c






ππ
−∈=+
2
,
2
t,ttan
2

3
2
1
x
9.,
9
3
t
3
32
ttan1
dt)ttan1(
3
32
I
3/
6/
3/
6/
2
2
1
π
==
+
+
=
∫
π
π

π
π
M
12
3
3ln
4
3
I
π
−=
7a9_@U(.90W #!,A7@:(]#;99L-##!,U(YmX
0-QrS
≡
QA7:S6</-#
·
A ' AM
@Y:^ *,m63;$`#!,(1."#q
K„  QrS  (  ,  #  A7:6  </  ,  #  A7  089  #?  ,  Y
3
3a
AM
3
2
AO,
2
3a
AM ===
3R/K.,
4

3a
HM
8
3a
BC.HM
2
1
8
3a
S
22
BCH
=⇒=⇒=
4
a3
16
a3
4
a3
HMAMAH
22
22
=−=−=
</,, #miU:0[$?Y
AH
HM
AO
O'A
=
+9.,

3
a
a3
4
4
3a
3
3a
AH
HM.AO
O'A
===
3W2#(1."
12
3a
a
2
3a
3
a
2
1
BC.AM.O'A
2
1
S.O'AV
3
ABC
====
Câu 5 : Tìm giá trị lớn nhất

3,#-,

gK

≥,KK


g≥K⇒
1bab
1
2
1
21bba
1
3b2a
1
22222
++
≤
++++
=
++
3D\%
1aca
1
2
1
3a2c
1
,

1cbc
1
2
1
3c2b
1
2222
++
≤
++
++
≤
++
2
1
bab1
b
ab1b
ab
1bab
1
2
1
1aca
1
1cbc
1
1bab
1
2

1
P
=
++
+
++
+
++
=
++
+
++
+
++
≤












2
1
P =

,bKb#b6Mr0?.B(TIK^
2
1
,bKb#b6
Câu 6a: 1,Viết phương trình đường tròn đi qua giao điểm của(E) và (P)
:/0h,/0W #!,Q‹SQrS(` #!,ND\.]
09x37x36x91)x2x(
9
x
23422
2
=−+−⇔=−+
QS
{~
9x37x36x9)x(f
234
−+−=
€Q&S(Y"#.Yu#-€Q>S€QS•
€QS€QS•€QS€QS•€QS€QS•+9.,QS#-` NaK`$/0-Q‹S

A
7
7m
Am
m
:
i
U
#q  QrS  ?    0W  Na  K`  3/?  0h  ##  ,/ 0W  #!,  Q‹S    QrS  f,  o `






=+
−=
1y
9
x
x2xy
2
2
2
09y8x16y9x9
9y9x
y8x16x8
22
22
2
=−−−+⇒



=+
=−
⇔
QS
QS(ND\.]#!,0DE.…#-a 







=
9
4
;
9
8
I
K2ub
9
161
 </0-
,/0W #!,Q‹SQrS#e^ .Y0DE.…#-ND\.]QS
Câu 6a: 2,Viết phương trình mặt phẳng (
β
)
</QβSQαSYQβS#-ND\.]&gskg<bQ<
≠
S
Uc#w9QS#-a QP>PSK2ub6DE.…#-#9CπY#-K2.
b6
X/J##4TQβS(b
435rR
2222
=−=−
</0-




=
−=
⇔=+−⇔=
−++
+−−+
(lo¹i) 17D
7D
12D54
)1(22
D3)2(21.2
222
MQβS#-ND\.]&gsk>b
Câu 7a : Tìm hệ số của x
2
3,#-
( )
∫∫
++++=+=
2
0
nn
n
22
n
1
n
0
n

2
0
n
dxxCxCxCCdx)x1(I 
2
0
1nn
n
32
n
21
n
0
n
xC
1n
1
xC
3
1
xC
2
1
xC







+
++++=
+

 +9  .,  
n
n
1n
2
n
3
1
n
2
0
n
C
1n
2
C
3
2
C
2
2
C2
+
++++=
+


QS
Uc#
1n
13
)x1(
1n
1
I
1n
2
0
1n
+
−
=+
+
=
+
+
QS
34QSQS,#-
n
n
1n
2
n
3
1
n
2

0
n
C
1n
2
C
3
2
C
2
2
C2
+
++++=
+

1n
13
1n
+
−
=
+
3R/K.,]
7n65613
1n
6560
1n
13
1n

1n
=⇒=⇔
+
=
+
−
+
+
3,#-,.W
( )
∑∑
−
−
=








=









+
7
0
4
k314
k
7
k
k
7
0
4
k7
k
7
7
4
xC
2
1
x2
1
xC
x2
1
x
?#H,&

 HTf, o 

2k2
4
k314
=⇔=
−
   M`+#w] (
4
21
C
2
1
2
7
2
=
Câu b:1, Viết phương trình đường tròn
</A∈$

YAbQ P> sS7∈$

Y7bQsPS
</_(.@a , #A7Y



=+−−
=−++
0.3n5m3
2.3n27m2





=
−=
⇔



=+−
−=−
⇔
1n
1m
2nm
3n2m
9.,AbQ>P>S7bQPS
_J+'0DE.…Q7S/?;N, #A7#-ND\.]
0cby2ax2yx
22
=++++
6</A7∈Q7SY,#-`





−=
=
−=

⇔





=++++
=+−−+
=++++
27/338c
18/17b
54/83a
0cb2a10125
0cb8a2161
0cb6a494

MQ7S#-ND\.]
0
27
338
y
9
17
x
27
83
yx
22
=−+−+
Câu 6b :2, Tìm giá trị nhỏ nhất _@_(.@a #!,, #A7+9.,_b







3;
3
8
;
3
7
3,#-
( ) ( ) ( )
222
222
GCMGGBMGGAMGMCMBMAF +++++=++=
22222222
GCGBGAMG3)GCGBGA(MG2GCGBGAMG3
+++=++++++=
ŒfI⇔U_

fI⇔U(]#;9#!,_(YQrS
⇔
33
19
111
333/83/7
))P(,G(dMG =
++

−−−
==
3
64
9
104
9
32
9
56
GCGBGA
222
=++=++
MŒfIK^
9
553
3
64
33
19
.3
2
=+









U(]#;9#!,_(YQrS
Câu 7b: Giải hệ phương trình mũ



+−=
++=
⇔



+−=
+=+
+
−
+
+−
1yxe
1yxe
1yxe
)1x(2ee
yx
yx
yx
yxyx
c9b&gb&>,#-`




−=−
+=
⇔



+=
+=
)2(uvee
)1(1ue
1ve
1ue
vu
v
u
v
>;99}]QS#-;.$D\;NJa YQSL`
>3D\%;99•]QSL` YQS
vu =⇔
3;/QS,#-R
9
b9gQS6{~€Q9SbR
9
>9>€lQ9SbR
9
>
AJK;Y
9 >
∞
g

∞
€lQ9S >g
€Q9S

3R/KJK;Y,#-€Q9Sb
0u =⇔
6
</0-QS#-` 9b



=
=
⇔



=−
=+
⇒=⇒
0y
0x
0yx
0yx
0v

M`ND\.]0o#/#- h` QPS
A•_Ži<•7••i3‘i2),8,9>?@A
UL3/UV>>A><
3E,( K5NOLWE,,/08

Z,,.,:)[)\B),<7,
]Q0W S7/ +
43
23
+−= xxy
6XJ/++%K;YZ0[BQCS#!, +6
6_@d(0DEF0z9,0W AQPS#-`+-#(m63] m0Wd#q
QCS?0W NaK`AMN+,/#/,;N9;#!,QCS?MN 9L-#T
,96
]Q0W S
6_J`ND\.]



=−++
=+++
yyxx
yyxyx
)2)(1(
4)(1
2
2
Qxy
∈R
S
6_JND\.]
8
1
3
tan

6
tan
3coscos3sin.sin
33
−=






+






−
+
ππ
xx
xxxx
]Q0W S322#Na
∫
++=
1
0
2
)1ln( dxxxxI


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α
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β
S+/+/TQ
α
S#qQSSR/,/9;(0DE
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n

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222
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


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+=+
+
+−
1
)1(2
yxe
xee
yx
yxyx
Qxy
∈R
S
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Câu 1: 1, Khảo sát hàm số
43
23
+−= xxy

6Tập xác địnhu
6Sự biến thiên
,S_T?
+∞=+−=−∞=+−=
+∞→+∞→−∞→−∞→
)4x3x(limylim,)4x3x(limylim
23
xx
23
xx
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⇔
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AJK;Y
& >
∞
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∞
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∞
>
∞
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>: +0[K;.YQ>
∞
PSQPg

∞
SB#K;.YQPS
>: +0?#%#0??&b
7
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73
b6
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0W 9QPS( a 0&H
Câu1 : 2,Tìm m để hai tiếp tuyến vuông góc
$#-ND\.]b Q&sSg6
:/0h,/0W #!,$Q7S(` #!,ND\.]



=−
=
⇔=−−⇔+−=+−
0mx
3x
0)mx)(3x(4)3x(m4x3x
2
223
3R/K.,,#-089` }
1)m('y).m('y −=−
9
35318
m01m36m91)m6m3)(m6m3(
2
±

=⇔=+−⇔−=+−⇒
Qf, oS
Câu 2: 1, Giải hệ phương trình đại số
3,IbLNJ(` #!,`
:`ND\.]D\0D\T







=−+
+
=−++
+
1)2yx(
y
1x
22yx
y
1x
2
2
c
2yxv,
y
1x
u
2

−+=
+
=
3,#-`
1vu
1uv
2vu
==⇔



=
=+
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




=−+
=
+
12yx
1
y
1x
2
6
&


>

i

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
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Câu 2: 2,Giải phương trình lương giác
89`
0
3
xcos
6
xcos
3
xsin
6
xsin ≠






π
+







π
−






π
+






π
−
3,#-
1x
6
cot
6
xtan
3
xtan
6
xtan −=







−
π






π
−=






π
+







π
−
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8
1
x3cosxcosx3sin.xsin
33
=+⇔
1 cos2x cos 2x cos 4x 1 cos2x cos 2x cos 4x 1
2 2 2 2 8
− − + +
⇔ × + × =
2
1
x2cos
8
1
x2cos
2
1
)x4cosx2cosx2(cos2
3
=⇔=⇔=+⇔






π+

π
−=
π+
π
=
⇔
k
6
x
(lo¹i) k
6
x

(k )∈Z
6MND\.]#-` 
π+
π
−=
k
6
x

(k )∈Z
Câu 3:Tính tích phân c





=

++
+
=
⇒



=
++=
2/xv
dx
1xx
1x2
du
xdxdv
)1xxln(u
2
2
2
1
1
2 3 2
2
2
0
0
x 1 2x x
I ln(x x 1) dx
2 2 x x 1
+

= + + −
+ +
∫
∫∫∫
++
−
++
+
+−−=
1
0
2
1
0
2
1
0
1xx
dx
4
3
dx
1xx
1x2
4
1
dx)1x2(
2
1
3ln

2
1
( )
11
1
0
2
1
0
2
I
4
3
3ln
4
3
I
4
3
)1xxln(
4
1
xx
2
1
3ln
2
1
−=−+++−−=
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

∫








+






+
=
1
0
2
2
1
2
3
2
1
x

dx
I
6c






ππ
−∈=+
2
,
2
t,ttan
2
3
2
1
x
9.,
9
3
t
3
32
ttan1
dt)ttan1(
3
32

I
3/
6/
3/
6/
2
2
1
π
==
+
+
=
∫
π
π
π
π
M
12
3
3ln
4
3
I
π
−=
7a9_@U(.90W #!,A7@:(]#;99L-##!,U(YmX
0-QrS
≡

QA7:S6</-#
·
A ' AM
@Y:^ *,m63;$`#!,(1."#q
K„  QrS  (  ,  #  A7:6  </  ,  #  A7  089  #?  ,  Y
3
3a
AM
3
2
AO,
2
3a
AM ===
3R/K.,
4
3a
HM
8
3a
BC.HM
2
1
8
3a
S
22
BCH
=⇒=⇒=


A
7
7m
Am
m
:
i
U
4
a3
16
a3
4
a3
HMAMAH
22
22
=−=−=
</,, #miU:0[$?Y
AH
HM
AO
O'A
=
+9.,
3
a
a3
4
4

3a
3
3a
AH
HM.AO
O'A
===
3W2#(1."
12
3a
a
2
3a
3
a
2
1
BC.AM.O'A
2
1
S.O'AV
3
ABC
====
Câu 5 : Tìm giá trị lớn nhất
3,#-,

gK

≥,KK



g≥K⇒
1bab
1
2
1
21bba
1
3b2a
1
22222
++
≤
++++
=
++
3D\%
1aca
1
2
1
3a2c
1
,
1cbc
1
2
1
3c2b

1
2222
++
≤
++
++
≤
++
2
1
bab1
b
ab1b
ab
1bab
1
2
1
1aca
1
1cbc
1
1bab
1
2
1
P
=
++
+

++
+
++
=
++
+
++
+
++
≤












2
1
P =
,bKb#b6Mr0?.B(TIK^
2
1
,bKb#b6
Câu 6a: 1,Viết phương trình đường tròn đi qua giao điểm của(E) và (P)

:/0h,/0W #!,Q‹SQrS(` #!,ND\.]
09x37x36x91)x2x(
9
x
23422
2
=−+−⇔=−+
QS
{~
9x37x36x9)x(f
234
−+−=
€Q&S(Y"#.Yu#-€Q>S€QS•
€QS€QS•€QS€QS•€QS€QS•+9.,QS#-` NaK`$/0-Q‹S
#q  QrS  ?    0W  Na  K`  3/?  0h  ##  ,/ 0W  #!,  Q‹S    QrS  f,  o `





=+
−=
1y
9
x
x2xy
2
2
2
09y8x16y9x9

9y9x
y8x16x8
22
22
2
=−−−+⇒



=+
=−
⇔
QS
QS(ND\.]#!,0DE.…#-a 






=
9
4
;
9
8
I
K2ub
9
161

 </0-
,/0W #!,Q‹SQrS#e^ .Y0DE.…#-ND\.]QS
Câu 6a: 2,Viết phương trình mặt phẳng (
β
)
</QβSQαSYQβS#-ND\.]&gskg<bQ<
≠
S
Uc#w9QS#-a QP>PSK2ub6DE.…#-#9CπY#-K2.
b6
X/J##4TQβS(b
435rR
2222
=−=−
</0-



=
−=
⇔=+−⇔=
−++
+−−+
(lo¹i) 17D
7D
12D54
)1(22
D3)2(21.2
222
MQβS#-ND\.]&gsk>b

Câu 7a : Tìm hệ số của x
2
3,#-
( )
∫∫
++++=+=
2
0
nn
n
22
n
1
n
0
n
2
0
n
dxxCxCxCCdx)x1(I 
2
0
1nn
n
32
n
21
n
0
n

xC
1n
1
xC
3
1
xC
2
1
xC






+
++++=
+

 +9  .,  
n
n
1n
2
n
3
1
n
2

0
n
C
1n
2
C
3
2
C
2
2
C2
+
++++=
+

QS
Uc#
1n
13
)x1(
1n
1
I
1n
2
0
1n
+
−

=+
+
=
+
+
QS
34QSQS,#-
n
n
1n
2
n
3
1
n
2
0
n
C
1n
2
C
3
2
C
2
2
C2
+
++++=

+

1n
13
1n
+
−
=
+
3R/K.,]
7n65613
1n
6560
1n
13
1n
1n
=⇒=⇔
+
=
+
−
+
+
3,#-,.W
( )
∑∑
−
−
=









=








+
7
0
4
k314
k
7
k
k
7
0
4
k7

k
7
7
4
xC
2
1
x2
1
xC
x2
1
x
?#H,&

 HTf, o 
2k2
4
k314
=⇔=
−
   M`+#w] (
4
21
C
2
1
2
7
2

=
Câu b:1, Viết phương trình đường tròn
</A∈$

YAbQ P> sS7∈$

Y7bQsPS
</_(.@a , #A7Y



=+−−
=−++
0.3n5m3
2.3n27m2




=
−=
⇔



=+−
−=−
⇔
1n
1m

2nm
3n2m
9.,AbQ>P>S7bQPS
_J+'0DE.…Q7S/?;N, #A7#-ND\.]
0cby2ax2yx
22
=++++
6</A7∈Q7SY,#-`





−=
=
−=
⇔





=++++
=+−−+
=++++
27/338c
18/17b
54/83a
0cb2a10125
0cb8a2161

0cb6a494

MQ7S#-ND\.]
0
27
338
y
9
17
x
27
83
yx
22
=−+−+
Câu 6b :2, Tìm giá trị nhỏ nhất _@_(.@a #!,, #A7+9.,_b






3;
3
8
;
3
7
3,#-
( ) ( ) ( )

222
222
GCMGGBMGGAMGMCMBMAF +++++=++=