Đề ôn thi ĐH số 6 có đáp án

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Thời gian: 120 phút (không kể phát đề)
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 !"#"$%&
3 2
1
2 3 1
3
y x x x= − + −
' (")#%*+,$,-.+"/C01'"$%&+234
5 64"784+60""94":";4<<=">45?C,$0*0@A4<+";4<
0, 2, 3y x x= = =

B !
64"0*0+60":"4%'

3
2
0
x
I dx
1 x
=
+
ò
B
( )
5
1
ln
e

I x x x dx= +
∫
! 
9C401'%&:"D0z5E+2F4<
( )
1 2 (4 5 ) 1 3i z i i− + − = +

GH!
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 "Q#0"@J4<+294""R4
S 'B 
2#4<T"C4<<'4,="8+I'UVWX0"#"'
A(1;2;0)

B(3;4; 2)-
,$P+:";4<
Y
x y z 4 0- + - =

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B IM$+"_'`4
IA IB 0+ =
uur
uur
r
 `W,E+:"@J4<+294"P+0N+,$+E:Va0,=
P+:";4<
b ' 
Tìm
x (0; )Î +¥

thỏa mãn :
( )
x
2
0
2sin t 1 dt 0- =
ò

B "Q#0"@J4<+294"4<0'#
S 5B 
2#4<T"C4<<'4,="8+I'UVWX0"#"'
A(1;2;0)

B(3;4; 2)-
,$P+:";4<
Y
x y z 4 0- + - =

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B IM$+"_'`4
3IA 2IB 0- =
uur
uur
r
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b 5 
cd+%&:"D0
( )
z x yi x,y R= + Î

9VW%'#0"#
( )
2
x yi 8 6i+ = +

Hết
HƯỚNG DẨN ĐỀ 6
I. PHẦN CHUNG;(7 điểm)
e'fcY
¡
f
2
' 4 3y x x= − +
gh
2
1
' 0 4 3 0
3
x
y x x
x

=
= ⇔ − + = ⇔

=

f=">4
lim
x

y
→+∞
= +∞
,$
lim
x
y
→−∞
= −∞
• ^)4<5E4+"34
- $%&.4<5E4+2340*0T"#)4<
( )
;1−∞
,$
( )
3;+∞

- $%&4<"/0"5E4+234
( )
1;3

- 0i0>
1
1;
3
 
 ÷
 
- 0i0+
( )

3; 1−
f.+"/ 
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lU+%&+"U0.+"/
x   B ! S
y
1−
1
3
1
3
−
1−
1
3
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0, 2, 3y x x= = =
M$
3
3 2
2
1
2 3 1
3
S x x x dx= − + −
∫
3
3 2
2
1

2 3 1
3
x x x dx
 
= − − + −
 ÷
 
∫
3
4 3
2
1 2 3
12 3 2
x x x x
 
= − − + −
 ÷
 
3
4
=

B'64"0*0+60":"4%'
3
2
0
x
I dx
1 x
=

+
ò
P+
2
u 1 x du 2xdx= + Þ =
m0n4Y
u 4
x 3
u 1
x 0
=
=
Þ
=
=

o#OY
4
1
4
1
I du u 1
1
2 u
= = =
ò
ZnW
I 1=
B5
( )

5 5 6
1 1 1
ln ln
e e e
I x x x dx x xdx x dx= + = +
∫ ∫ ∫
64"
5
1
1
ln
e
I x xdx=
∫
P+
5 6
1
ln
6
du dx
u x
x
dv x dx x
v

=


=
 

⇒
 
=



=


6 5 6 6 6
1
1
1 1 1
ln ln 5 1
6 6 6 36 36
e e e
e
x x x x x x e
I dx
+
= − = − =
∫
f64"
7 7
6
2
1
1
1
7 7

e
e
x e
I x dx
−
= = =
∫
ZnW
6 7
5 1 1
36 7
e e
I
+ −
= +
!'0O
( ) ( ) ( )
( ) ( )
( ) ( )
+ = + = + = +
+ +
+ + + +
= = = = = +
+ +
2
2 2
1 2 (4 5 ) 1 3 1 2 1 3 (4 5 ) 1 2 3 8
3 8 1 2
3 8 3 6 8 16 19 2 19 2
1 2 1 2 1 2 1 2 5 5 5

i z i i i z i i i z i
i i
i i i i i
z z z i
i i i
o#O
2 2
19 2 19 2 73 365
5 5 5 5 5 5
z i


= + = + = =
ữ ữ

GH!
Hc sinh hc chng trỡnh no thỡ ch c lm phn dnh riờng cho chng trỡnh ú (phn 1 hoc phn 2)
"Q#0"@J4<+294""R4
SB
1. Vit phng trỡnh mt phng (Q) i qua hai im A, B v vuụng gúc vi mt phng (P).
Mt phng (P) cú vect phỏp tuyn l :
P
n (1; 1;1)= -
uur
,
AB (2;2; 2)= -
uuur
Vỡ (Q) qua A,B v vuụng gúc vi (P) nờn (Q) cú mt vect phỏp tuyn l:

( )

Q P
1 1 1 1 1 1
n n ;AB ; ; 0;4;4
2 2 2 2 2 2
ổ ử
- -
ữ
ỗ
ộ ự
ữ
ỗ
= = =
ữ
ỗ
ờ ỳ
ữ
ở ỷ
ỗ - -
ữ
ỗ
ố ứ
uuur
uur uur
Do ú phng trỡnh mt phng (Q) l

4(y 2) 4(z 0) 0
y z 2 0
- + - =
+ - =
Vy phng trỡnh (Q):

y z 2 0+ - =
2. Gi I l trung im ca AB. Hóy vit phng trỡnh mt cu tõm I v tip xỳc vi mt phng (P).
Do I tha món
IA IB 0+ =
uur
uur
r
nờn I l trung im ca AB
Ta trung im I ca AB l:
I(2;3; 1)-
Gi (S) l mt cu cú tõm I v tip xỳc vi (P)
Bỏn kớnh ca mt cu (S) l:

R d(I,(P))
2 3 1 4 6
2 3
3 3
=
- - - -
= = =
Vy phng trỡnh mt cu (S) l
2 2 2
(x 2) (y 3) (z 1) 12- + - + + =

b '
Tỡm
x (0; )ẻ +Ơ
tha món :
( )
x

2
0
2sin t 1 dt 0- =
ũ
(1)
Ta cú:
( )
x x
2
0 0
x
1 1
2sin t 1 dt cos2tdt sin2t sin2x
0
2 2
- = - = - = -
ũ ũ
Do ú:

1
(1) sin2x=0 sin2x=0
2
2x k
k
x
2
-
= p
p
=

Do
x (0; )ẻ +Ơ
nờn ta chn
k
x
2
p
=
vi
k Z
+
ẻ
2 "Q#0"@J4<+294"4<0'#
S5B#
1. Vit phng trỡnh mt phng (Q) i qua hai im A, B v vuụng gúc vi mt phng (P).
Mt phng (P) cú vect phỏp tuyn l :
P
n (1; 1;1)= -
uur
,
AB (2;2; 2)= -
uuur
Vỡ (Q) qua A,B v vuụng gúc vi (P) nờn (Q) cú mt vect phỏp tuyn l:

( )
Q P
1 1 1 1 1 1
n n ;AB ; ; 0;4;4
2 2 2 2 2 2
ổ ử

- -
ữ
ỗ
ộ ự
ữ
ỗ
= = =
ữ
ỗ
ờ ỳ
ữ
ở ỷ
ỗ - -
ữ
ỗ
ố ứ
uuur
uur uur
Do ú phng trỡnh mt phng (Q) l

4(y 2) 4(z 0) 0
y z 2 0
- + - =
+ - =
Vy phng trỡnh (Q):
y z 2 0+ - =
2. Gi I l im tha món
3IA 2IB 0- =
uur
uur

r
. Hóy vit phng trỡnh mt cu tõm I v tip xỳc vi mt phng.
Gi I(x;y) l im tha món
3IA 2IB=
uur
uur
, ta cú:
( ) ( )
( ) ( )
( )
( )
3 1 x 2 3 x
x 3
3IA 2IB 3 2 y 2 4 y y 2
z 4
3 0 z 2 2 z
ỡ
ỡ
ù
ù
- = -
= -
ù
ù
ù
ù
ù
ù
ù ù
= - = - = -

ớ ớ
ù ù
ù ù
ù ù
=
- = - -
ù ù
ù
ợ
ù
ợ
uur
uur
. Suy ra:
I( 3; 2;4)- -
Gi (S) l mt cu cú tõm I v tip xỳc vi (P)
Bỏn kớnh ca mt cu (S) l:

3 2 4 4 1 3
R d(I,(P))
3 3 3
- + + - -
= = = =
Vy phng trỡnh mt cu (S) l
2 2 2
1
(x 3) (y 2) (z 4)
3
+ + + + - =
b 5

Xột s phc
( )
z x yi x,y R= + ẻ
. Tỡm x, y sao cho
( )
2
x yi 8 6i+ = +
Ta cú:
( )
2
2 2
4 2 2
2
2 2
2
x yi 8 6i x y 2xyi 8 6i
x 3
9
x 8x 9 0 x 9
x 8
y 1
x y 8
x
3 3
3
xy 3 x 3
y y
y
x x
x

y 1
+ = + - + = +
ộ
ỡ =
ù
ù
ờ
ỡ
ù
ớ
ỡ ỡ
ờ
- - = =
ù ù
ù
- =
ỡ ù
=
ù ù
- =ù
ù
ờ
ù
ù ù
ù ợ
ù
ù ù ù ù
ờ

ớ ớ ớ ớ

ờù ù ù ù
ỡ= = -
ù
= =
ù ù ù ù
=
ù
ợ ù
ờ
ù ù ù
ù ù
ợ ợ
ớ
ù
ờ
ù
ợ
ù
= -
ờ
ù
ợ
ở
Vy giỏ tr x, y cn tỡm l
x 3
y 1
ỡ =
ù
ù
ớ

ù
=
ù
ợ
hoc
x 3
y 1
ỡ = -
ù
ù
ớ
ù
= -
ù
ợ
f