Ôn Tập thi tot nghiep THPT theo chu de

Chủ đề 1 : Khảo sát hàm số
Câu 1: 
4 2
2y x x= - +

 !"#$%&!'()&*+,
4 2
2 0x x m- + =

Câu 2: 
4 2
2 3y x x+ -= -

-
.'()&*+'#/01234&5
Câu 3: 
4 2
1
4
y x x= -
2

.'()&*+'#/012#&34&
3
4
-

Câu 4: 
4 2
2 1y x x= - -
2


 !"#$%&!'()&*+
4 2
2 0 x x m- - =

Câu 5:,/678
9
78

:

.'()&*+'#/;

!&2;4&7<
Câu 6:
4 2
1 5
3
2 2
y x x= - +


.'()&*+'#/='#/&&>;,/6?98:@
Câu 7:/68
9
78

:5=2"

.'()&*+'#/>='#/#A&&2>;,/6

1
6
-
8:@
Câu 8: ,
2
1
x
y
x
-
=
-

 B&*4&>C&*(D&E&;,
y x m= - +
"#AF01'G!
Câu 9:
1
1
x
y
x
+
=
-


H+1(D&E&;,/68:F01'G!
Câu 10: 

2 1
1
x
y
x
+
=
-
2

.'()&*+'#/>0IJK
Câu 11:
2
2 1
x
y
x
-
=
+


.'()&*+'#/>='#/2!&2L6?K
Câu 12:
2 1
2
x
y
x
+

=
-

-
.'()&*+'#/01*2#&3
3y = -

Câu 13:,/6
1
1
x
x
-
+
2

.'()&*+'#/0&1>*M#&
Câu 14:
3 5
2 2
x
y
x
+
=
+
2
-
.'()&*+'#/01234&
Câu 15:

2 1
1
x
y
x
+
=
-
2

.'()&*+'#/>0&1>*MN8
Câu 16:,/6O86
2 3
1
x
x
+
-

-
.'()&*+'#/='#/#A&&2>;,
1
2011
5
y x= - +

Chủ đề 2 : TÌM GIÁ TRỊ LỚN NHẤT, GIÁ TRỊ NHỎ NHẤT CỦA HÀM SỐ
Bài 1. H+PHQR=PHRR#,

2

4 3y x x= + +

3 4
4 3y x x= -

4 2
2 2y x x= + -
;
2
2y x x= + -
%
2
1
2 2
x
y
x x
-
=
- +
O
2
2 4 5
1
x x
y
x
+ +
=
+

&
2
1
( 0)y x x
x
= + >

2
1
1
x x
y
x
- +
=
+

4 2
1
( 0)
x x
y x
x
+ +
= >

Bài 2. H+PHQR=PHRR#,

3 2
2 3 12 1y x x x= + - +

*S7JKT 
3
3y x x= -
*S7J5T

4 2
2 3y x x= - +
*S75JT ;
4 2
2 5y x x= - +
*S7JT
%
3 1
3
x
y
x
-
=
-
*S@JT O
1
1
x
y
x
-
=
+
*S@J9T

&
2
4 7 7
2
x x
y
x
+ +
=
+
*S@JT 
2
1
1
x x
y
x
- +
=
+
*S@JT

2
100y x= -
*S7<JUT L
2 4y x x= + + -
Bài 3. H+PHQR=PHRR#,

2sin 1
sin 2

x
y
x
-
=
+
 
2
sin 2sin 3y x x= + +
 
2
2sin cos 1y x x= - +
;
cos2 2sin 1y x x= - -
%
2
4 1
2
x
x
y
+
=
OO86
2
2x x+ -

&
x
y xe

-
=
*
[ ]
0;2
 
2
8ln y x x= -
*SJ%T 
2
2 1
2
x x
y
- -
=
*S@JT
V
lny x x= -
L
2
2 x
y x e= -
*
[ ]
1;1-
 "
lny x x= -



x
x
e
y
e e
=
+
*
[ln2 ; ln4]
 /6878*
;
2 2
p p-
é ù
ê ú
ê ú
ë û
 /687*S@JWT
Chủ đề 3 : PHƯƠNG TRÌNH, BẤT PHƯƠNG TRÌNH MŨ VÀ LÔGARÍT
Bài 1. P'()&*+#,

2
6 8
3 1
x x+ +
=
J 
( )
2
2

1
3
27
x
x
-
+
=
J 5
2.9 3 3
x x
- =
J 9
1
9 2.3 9 0
x x+
- + =
K
2
4
5 25
x x- +
=
J <
2
2
4 3
1
2
2

x
x
-
-
æö
÷
ç
=
÷
ç
÷
ç
è ø
J X
7 1 2
1 1
. 2
2 2
x x+ -
æö æö
÷ ÷
ç ç
=
÷ ÷
ç ç
÷ ÷
ç ç
è ø è ø
J U
2

3 2 1
2 3
x x x- + -
=
Y
2
3 5
9 3
x x +
=
J @
1
9 2.3 9 0
x x+
- + =
J 
2 1 1
3.5 2.5 0,2
x x- -
- =
J 
2 5 2
3 3 2
x x+ +
= +
5
25
5 24
5
x

x
- =
J9
3 4.3 3 0
x x-
- + =
J K
1
3 .2 72
x x+
=
J <
2 3 1
2 4
x x- -
=
X
1 2 4 3
7.3 5 3 5
x x x x+ + + +
- = -
U
3 2 3
7 9.5 25 9.7
x x x x
+ = +
Y
2 2
5 3 2(5 3 )
x x x x

= + +
J @
2 1 2 2 1 1 2
2 3 5 2 3 5
x x x x x x- + + +
+ + = + +

2 2 2 2
1 2 1
2 2 3 3
x x x x- + -
+ = +
J 
1 1
5 6. 5 – 3. 5 52
x x x+ -
+ =
5
2
4 5.4 4 0
x x
- + =
9
1
4 2 8 0
x x+
+ - =
K
1 1
4 6.2 8 0

x x+ +
- + =
J <
4 8 2 5
3 4.3 27 0
x x+ +
- + =
X
16 17.4 16 0
x x
- + =
J U
1
49 7 8 0
x x+
+ - =
Bài 2. P'()&*+#,
"&
5
8:K76@ 
1
2
2
log (3 5 ) 3 0x x- + =
5
5 5
log (2 1) log (2 ) 0x x+ + - =
9
2 2
log ( 5) log ( 2) 1x x+ - + =


K
1
2
2 2
log ( 5) log (2 1) log 6x x- + + =
 <"&K:"&8:@?6"&8?@?"&8?
X"&
U
8:"&
<9
86
1
2
U
5 5 5
log log ( 6) log ( 2)x x x= + - +
Y
5 25 0,2
log log log 3x x+ =
@
2
log (2 5 4) 2
x
x x- + =

2 2
log ( 3) 1 log ( 1)x x+ = + -

1

2
3
log (log ) 0x =
5
[ ]
1
2
2 1
log log (log 9 0
x-
=
9
2
log (9 2 ) 3
x
x- = -

K
1
2
3 3 3
log ( 5) log 2 log (3 20)x x- - - -
<
5
log ( 20).log 5 1
x
x + =
X
3 2
1

log (2 2 3 1) 3
x
x x x
+
+ - + =
U
4 2 2 4
log (log ) log (log ) 2x x+ =
Y
4 2 4
log ( 3) log ( 1) 2 log 8x x+ - - = -
@
1
3
3
3
log log log 6x x x+ + =

2 2
lg 3lg lg( ) 4x x x- = -

2 4
log log 3 2x x= +
5
2
3 3
2(log ) 5log 9 3 0x x- + =
9
1 1
3 3

log 3 log 2 0x x- + =
K
1
2
2 2
log ( 5) log (2 1) log 6x x- + + =
<
2
log log 8 2
x
x - = -
X
7
6
4
log 2 log 0
x
x- + =
U
1 2
1
4 lg 2 lgx x
+ =
- +
Bài 3. PZ'()&*+#,

2 3 4 1 2
2 2 2 5 5
x x x x x+ + + + +
- - > -


1 2
3 3 3 11
x x
x
- -
+ - <
5
2 2
3 2 3 2
9 6 0
x x x x- + - +
- <
9

2 3 7 3 1
6 2 .3
x x x+ + -
<

K
2
2 2
1
2 2
4 .2 3.2 .2 8 12
x
x x
x x x x
+

+ + > + +
<
2 1 2
6. 3 . 3 2.3 . 3 9
x x x
x x x x
+
+ + < + +
X
1 2 1 2
9 9 9 4 4 4
x x x x x x+ + + +
+ + < + +
U

1 3 4 2
7.3 5 3 5
x x x x+ + + +
+ £ +
Y
2 1 2
2 5 2 5
x x x x+ + +
+ < +
@
1 2
2 .3 36
x x- +
>


8
?5
8:
:5[@ U
8
≤997
8

5K
8
[<K
8
7K 99
8
:
8:
7U@\@
K
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K
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7K
8:
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( )
2
4 15 13
3 4

1
2
2
x x
x
- +
-
<
X
( )
2 3
2 1
1
2
2 21. 2 0
x
x
+
+
- + >
U
2
3.7 37.140 26.20
x x x
- £
Y
1
2
2
log ( 4 6) 2x x- + < -

@
1
2
2
log ( 1) log (2 )x x+ £ -

1
5
4 6
log 0
x
x
+
³

1
2
log (2 1) 1x + > -
Chủ đề 4 : Tích phân - Ứng dụng của tích phân
Bài 1:H]]'G#G/,

( )
6
3
0
cos
2sin 1
xdx
x
p

+
ò

( )
1
3ln 2
e
dx
x x +
ò

2
3
6cos 1sinx xdx
p
p
+
ò
 ;
19
2
3
0
8
xdx
x +
ò
Bài 2: H]]'G#G/,

( )

1
2
0
2
4 5
x dx
x x
-
- +
ò
 
( )
2
2
6
3cot 1 sin
dx
gx x
p
p
+
ò

4
2
2
0
cos
tgx
e dx

x
p
ò
 ;
4
2 1
1
x
dx
e x
+
ò
Bài 3:H]]'G#G/,

3
3
0
cos
tgxdx
x
p
ò

6
4 4
0
sin2
cos sin
xdx
x x

p
-
ò

2
2 3
6
sin cosx xdx
p
p
ò
 ;
( )
4
2
0
cos2
sin cos
xdx
x x
p
+
ò
Bài 4:H]]'G#G/,

3
3
4
0
sin

cos
xdx
x
p
ò
 
6
0
sin2
2sin 1
xdx
x
p
+
ò

3
2 3
0
1x x dx+
ò
 ;
4
3
6
dx
tgx tg x
p
p
+

ò
Bài 5:H]]'G#G/,

( )
0
2 1 sinx xdx
p
+
ò
%
( )
1
2
2
0
1
x
x e dx+
ò

( )
2
0
2 cosx x xdx
p
+
ò
O
1
0

3 2
x
x
dx
e
-
ò

4
2
0
cosx xdx
p
ò
&
1
0
( 3)2
x
x dx-
ò
;
4
2
0
cos
xdx
x
p
ò

 
( )
1
2
0
x
x e dx+
ò
Bài 6:H]]'G#G/,

( )
3
2
1
3 1 lnx xdx+
ò

2
1
ln
e
xdx
ò

( )
1
0
ln 1x x dx+
ò
;

( )
1
2
0
ln 1x x dx+
ò
Bài 1:H];!]+'E&&>0^(D&&
( )
( )
2
: 3C y x x= -
*MN8
Bài 2:H];!]+'E&&>0^(D&&
( )
4 2
:C y x x= -
*MN8
Bài 3:H];!]+'E&&>0^(D&&
( )
3
: 3 1C y x x= - +
(D&E&
: 3d y =

Bài 4:(D&&
( )
3 2
: 3 4C y x x x= - +
.'()&*+'#/
d


( )
C
0&C3NH_2];!
]+'E&&>0^
( )
C

d

Bài 5:'*"
( )
2
: 6 5P y x x= - +

.'()&*+'#/
( )
P
0&1
( )
P
>*MN8
H];!]+'E&&>0^
( )
P
'#/2^G#
Bài 6:H];!]+'E&&>0^'*"
( )
2
: 4P y x=

(D&E&
: 2 4d y x= -

Bài 7:(D&&
( )
4 2
:C y x x= -
PC`"+'E&&>0^
( )
C
*MN8H]1]+*a
8/(b*Lc#/`8#&c#*MN8
Chủ đề 4 : Số Phức
Bài 1:H+8=/

( ) ( ) ( ) ( )
2 3 1 2 3 2 2 4 3x y x y i x y x y i+ + + - + = - + + - -


( ) ( )
2 1 1 2 2 3 2x y i x y i+ + - = - + -

5
( )
( ) ( )
( )
4 3 2 2 1 3x y i y x i+ + - = + - -

9
( ) ( )

2 2 2 2x y y x i x y x y i+ - - = + + +

Bài 2H+A#='B"b'1;d*e'E&C3'B#
:5 5? 5?9: 9??5
Bài 3 :H]
:K:?5:  5:5?  5::K? 9
7 2 2 5
4 3 3 6
i i
æ ö æ ö
÷ ÷
ç ç
- + - +
÷ ÷
ç ç
÷ ÷
ç ç
è ø è ø
K5:?K:  <9?K?5? X?7K?
U@=K?5=K:=K:@=K:?7 Y9?7??5:? @:9:5????K

( ) ( )
4 3 2i i- +
 
( ) ( )
1 3i i+ - -
5
( )
( )
2 3 0,2 0,5 3i i i- -


9
( )
2
1 i-
 K
1
1
i
i
+
-
 <
2
1
i
i-
 X
3
1 2i+
U
( ) ( ) ( )
2 1 4 3
3 2
i i i
i
+ + + -
+
Y
( ) ( )

3 4 1 2
4 3
1 2
i i
i
i
- +
+ -
-
Bài 4 :H]

( ) ( ) ( )
2 4 3 5 7 4 3i i i+ - + -
 
( ) ( ) ( )
2
1 2 2 3 3 2i i i- - - +
 5
( )
10
1 i+
9
( )
2
3 4i-
 K
( )
3
2 3i+
 <

( ) ( )
[ ]
2
4 5 4 3i i+ - +
X
( )
2
2 3i-
U
( )
2008
1 i+
 Y
( )
2010
1 i-
@
3
1 3
2 2
i
æ ö
÷
ç
÷
- +
ç
÷
ç
÷

ç
è ø
 
3
1 3
2 2
i
æ ö
÷
ç
÷
+
ç
÷
ç
÷
ç
è ø
Bài 5 :P'*$''B+8
58::5?6K:9 
( ) ( ) ( )
5 7 3 2 5 1 3i x i i- + = - +
5
( ) ( )
5 2 3 4 1 3ix i i- = + -
9
( ) ( ) ( )
3 4 1 2 4i x i i+ = + +
K
2 3 5 4ix x i+ = +

   <
( ) ( )
2 3 1 2 1 3i x ix i i- + = + +
Bài 6 :P'#*$''B
8

:8:X6@ 8

:58:96@ 558

?8:X6@
98
5
?U6@ K8
5
:U6@ <8
9
:58

?K6@
Bài 7 :H+'$2&!"

1 2 ;1 2i i+ -

3 2 ; 3 2i i+ -
5
3 2 ; 3 2i i- + - -
Bài 1 :H]

( )

5 2 3 7 6i i+ - - +
 
( )
1
2 3 3
2
i i
æ ö
÷
ç
- +
÷
ç
÷
ç
è ø
5
( )
2
1 2i+
9
2 15
3 2
i
i
-
+
K
( ) ( )
2 2

1 3 1 3P i i= + + -
Bài 2 :H]'B#=+A#=8'fB='f2

( )
( ) ( )
0 2 3 7 8z i i i= - - - + +
,
5 5z =

( )
( ) ( )
0 2 3 5 2 : 377z i i i kq z= - + + =
5
6 481
:
3 2 13
i
z kq z
i
-
= =
+
9
( ) ( )
2
2
7 3 2 : 2813z i i kq z= - - - =
K
( )
3

4 3 1 : 29z i i kq z= - + - =
Bài 3 :'Bg6975H]

2
z
,
7 24i-

1 4 3
:
25 25
kq i
z
+
5
z
9
2 3
: 33 144z z z kq i+ + - -
Bài 4 :P'#*$''B

2
6 29 0x x- + =

2
1 0x x+ + =
 5
2
2 5 0z z- + =
9

2
4 7 0z z- + =
K
2
6 25 0z z- + =
<
2
2 3 5 0x x- + =

X
2
3 10 9 0x x- - - =
U
2
72 1297 0x x- - - =
Y
2
600 2008 2009 0x x+ + =
Chủ đề 5 : Phương Pháp Tọa Độ Trong Không Gian
Bài 1:H*&LA&&>!C3N8/g;2'",
  
  5
x y z− + −
= =
'h2'",87/:5g:6@
H+';
H+C3&1I;'h
5H+&1'h*MC3
9.';


#A&&2'h0I
K.''iB;#A&&2'h
Bài 2 : H*&LA&&>!C3N8/g'
( )
α
,8:/:g?6@
( )

,
  
x y z
d
−
= =
−
1I?9JKJ?<
.''hc#I&&'
( )
α
.''ic#I#A&&2;
5.';

c#I&&;
9.';

c#I#A&&2'
( )
α
KH+&1;'
( )

α

<H]L&_I'
( )
α
XH]1]LB;!j k=j= ="&1()&B&'
( )
α
>*MC3N8=N/=Ng=
ak"&;'N8/
U.'ef#lc#91j= ==k
Bài 3 :H*&LA&&>!C3N8/g
( ) ( ) ( )
J@J  = JJ = @JJ@A B C−
PCP"*C&G&j 
.'NP
.'ef#lc#91N=j= =
5.''#A&&2>NP'8m>l
Bài 4 : H*&LA&&>!C3N8/g
( ) ( ) ( ) ( )
9J5J = 5J@J@ = @J5J@ = @J@J5A B C D

.''hc#51 ==kB&nj k"B;!
.'
( )
∆
c#j*C&GP& k
5.'ef#l2Gj'8m>' k
Bài 5:H*&LA&&>!C3N8/g
( ) ( ) ( )

J@J@ = @J5J@ = @J@J<A B C

.''hc#j= =
H++#&C3N"'hl#/*C31N
o
8B&>Nc#'h
5.';c#1j= 
9H++#1";l#/*C31
o
8B&>Nc#;
KPCP"*C&G&j .'ef#l22(D&L]NP
Bài 6 :H*&LA&&>!C3N8/g
( ) ( ) ( )
JJ = @JJ = J@J9A B C−

B&&j #A&.'j 
PCI"1
MB MC= −
uuur uuuur
.''c#I#A&&2> 
Bài 7:l,
2 2 2
2 2 4 3 0x y z x y z+ + - + + - =

1
2
: 1
x t
y t
z t

ì
=
ï
ï
ï
ï
D = -
í
ï
ï
=
ï
ï
î
J
2
1
:
1 1 1
x y z-
D = =
- -
*
 
=∆ ∆
p#
H+&1

∆
>'C3

5.''h'8m&&>*
Bài 8:H*&LA&&jJ?J= J5J=9J5J=k9J?J
*j= ==k"91&'E&
PCI=R=h"f"(b"+# "'C3N8/=N/g=N8g.''c#51I=R=h
5PCj
o
"+##A&&2j"'N8/`q/'lc#91j
o
= ==k
9.''
( )
α
'8ml01j
o
r,
5 9   @x y z+ + + =
Bài 9 :H*&LA&&1j= ==k2C38^!B,
( ) ( )
J9J  = 9 = J9J5 =  A OB i j k C OD i j k− = + − = + −
uuur r r ur uuur r r r
*j #A&&2jJj#A&&2jkJjk#A&&2j H]1]B;!j k
.'(D&#A&&2#&
∆
j k
5.'ef#lc#91j= ==k.''
( )
α
'8ml&&>'j k
Bài 10:H*&LA&&>!C3N8/g
( ) ( )

  
J@J@ = JJ = J J
5 5 5
A B C
 
 ÷
 
.''
( )
α
#A&&2>N0B&51N= =E&&
.';"+##A&&2j "'
( )
α
Bài 11:H*&LA&&h,8?5/:9g7K6@l,
  
5 9 K < @x y z x y z+ + + + − + =
sGt]L]u
H]L&_t'h
5H_2#/**4&'hF%&#/"3#D&vL]!#"sG`L]*
(D&*a
Bài 12 :sp*]()&
 
,  9
5
x t
d y t
z t
= +



= +


= +

>'#,
h

,8:/:g:6@
h

,98:U/:g:X6@B&n#A&&2'
5h
5
,8?/:g:K6@
9h
9
,8?/:9g?@6@
Bài 13 :s=1'h,98:/:<g?@6@=i,8?/?g:96@&&H]L&&w'/
Bài 14 :H++##A&&2IJ?5J"'h,8:5/?g:6@l#/*CI
o
8B&>I
c#'h
Bài 15 :H++##A&&2IJ?J"
1 2
: 1
2
x t
d y t

z t
ì
ï
= +
ï
ï
ï
ï
= - -
í
ï
ï
ï
=
ï
ï
î
l#/*CI
o
8B&>Ic#;
Bài 1 :sGL]2',

2 2 2
8 2 1 0x y z x y+ + - - + =
t9JJ@u69 
2 2 2
2 1
2 0
3 9
x y z x y+ + - + + =

5
2 2 2
4 2 6 5 0x y z x y z+ + + - + + =

( )
2;1; 3I - -
u65
Bài 2 :l2',
2 2 2
2 4 4 0x y z x y z+ + - - - =
sGL]tJJu65
s&1l>*MC3N8=N/=Ng
Bài 3 :Q$''*&*(D&b'#,
2GtJ?J?9L]u6<
2Gt@?J5c#1IJJ?9
52Gt5J?5Jc#1IKJ?J
92Gj9J?9Jc#&CN
K2(D&L]j >j?JJ= @JJ5
<2(D&L]j >j<J9J?5= JUJ
X2Gt?JJ'8m>'h,8:/?g:K6@
U2GIJ?J5'8m>'h,8?/?g:56@
Y2GtJ?J5'8m>'N8/
@2GtJ?J5'8m>'N8g
2GtJ?J5'8m>'N/g
Bài 4 :Q$'''h*&*(D&b'#,
c#51
( ) ( )
2;0; 1 , (1; 2;3), 0;1;2A B C- -

c#51

( ) ( ) ( )
1;2;3 , 2; 4;3 , 4;5;6A B C- -

5c#51
( ) ( ) ( )
1;0;0 , 0; 2;0 , 0;0;3M N P-

9c#1IJ5J?&&'h87/:5g:96@
Kc#1R@JJ@&&'h8:5/79g76@
<c#1jUJYJ?@&&'N8/
Xc#1jUJYJ?@&&'N/g
Uc#1IJ5J?#A&&2 > @JJ?5=J?9J
Yc#1IJJ#A&&2;
2 1 1
1 2 2
x y z+ - +
= =
-

@c#1R?JJ?5#A&&2;
1 6
2 2
1 3
x t
y t
z t
ì
ï
= +
ï

ï
ï
ï
= -
í
ï
ï
ï
= - -
ï
ï
î

c#1IJ5J?#A&&2>*MN/
c#1IJ5J?#A&&2>*MNg
5c#1IJ5J?#A&&2>*MN8
9"'*#&*0j >jJ5JX= 9JJ5
K"'*#&*0hi>hJ?9J=iXJJ?K
<c#1j@JJ= ?J@J#A&&2'i,87/:g:6@
Xc#1IJJ5=RJ?J9&&*MN/
Bài 5 :Q$''=';*&*(D&b'#,
c#1jJ5J?= JJ9
c#1IJ?J5=R5J@J@
5c#&C3N1IJ9J?<
9c#1I5JJ?&&
1 1
:
2 3 4
x y z- +
D = =

-

Kc#1kJ@J?5&&
1 2
: 3 3
4
x t
y t
z t
ì
ï
= +
ï
ï
ï
ï
D = - +
í
ï
ï
ï
=
ï
ï
î

<c#1I?5JJ#A&&2'h8?/:9g:6@
Xc#h@J@?5@&&*MNgx"$''
Uc#1jJ@J?#A&&2'h8?/:g:Y6@
Yc#1 KJJ?9#A&&2'C3N8/

Bài 6 :sp*]()&
1 1 5
:
2 3 1
x y z- + -
D = =
>#,

1
3 2 6
:
4 6 2
x y z- - -
D = =
J 
2
4 1 3
:
6 9 3
x y z- - -
D = =

5
3
3 2 6
:
4 3 5
x y z- - -
D = =
J 9

4
1 2 1
:
4 2 2
x y z- + +
D = =

Bài 7 :sp*]()&
3 2
: 2 3
6 4
x t
d y t
z t
ì
ï
= - +
ï
ï
ï
ï
= - +
í
ï
ï
ï
= +
ï
ï
î


'
' '
'
5
: 1 4
20
x t
d y t
z t
ì
ï
= +
ï
ï
ï
ï
= - -
í
ï
ï
ï
= +
ï
ï
î

R#m&F#++C3&1
Bài 8 :sp*]()&
1 1

:
2 1 1
x y z
d
- +
= =
-

'
' '
'
3
: 2
1
x t
d y t
z t
ì
ï
= -
ï
ï
ï
ï
=
í
ï
ï
ï
= - +

ï
ï
î
R#m&F#++C3&1
Bài 10 :H+C3&1
1 2
: 1
x t
d y t
z t
ì
= +
ï
ï
ï
ï
= - +
í
ï
ï
= -
ï
ï
î
'h,8:/:g?6@
Bài 11 :H+C3&1
: 1 2
1
x t
d y t

z t
ì
ï
=
ï
ï
ï
ï
= +
í
ï
ï
ï
= -
ï
ï
î
'h,8:/:g?56@
Bài 12 :H+C3&1
1 2
:
2 1 3
x y z
d
- +
= =
-
'h,8:/:g?6@
Bài 13 :H++##A&&2IJ?J"'h,87/:g:6@
Bài 14 :H++##A&&2kJJ"'h,X8:K/:g?5X6@

Bài 15 :H++##A&&2&C3N""'hc#51jJJ= ?JJ?=J?J?
Bài 16 :H++##A&&2I9J?5J"
2 3
: 2 2
x t
d y t
z t
ì
= - +
ï
ï
ï
ï
= - +
í
ï
ï
= -
ï
ï
î

Bài 17 :H++##A&&2jJJ"
2 1 1
:
1 2 2
x y z
d
+ - +
= =

-
Bài 18 :H++##A&&2j?J5J";c#1 9J@J?5=KJ?J9
Bài 19 :H*&LA&&>!C3N8/g
( ) ( ) ( ) ( )
J@J = @JJ@ = JJU = 5JJA B C D −
.'='j .''
( )
α
c#51j= =B&nj k"B;!
H]3;(D&B;!j kLy_k
5.'2(D&L]j
9.'Gkc#1 
K.'Gk'8m>'
( )
α
