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102 7 31
1
............................................................ 2
............................................................ 32
................................................. 45
................................................. 64
............................................................ 75
1...................................... 85
2................ 96
......................................................... 101
........................................ 111
2
97 1 24 0970011604B
102 7 31 1020071891A
IIIIIIIV
III
IIIIV
AB B A
3
I4
1. 1.1
1.2
1.3
1.2
2. 2.1
2.2
1.
1.1
1.2
1.3
1.3 4
2.
2.1
2.1
3. 3.1
3.2 n a
3.3
3.1
4.
4.1
4.1
1. 1.1
2. 2.1
3. 3.1
3.2
3.2
4. 4.1
5.
5.1
5.2
5.1
4
5.3
5.4
5.4
2
5
II4
1. 1.1
1.1.1
1.1.2
3
1.2 1.2
/ II
2. 2.1
1.
1.1
1.2
1.3
1.4
2. 2.1
2.2
2.1
3. 3.1
3.1
1.
1.1
2.
2.1 2.1
3.
3.1
6
1.
1.1 1.1
2. 2.1
2.1
1.
2.
7
III4
1.
1.1
2.
2.1
2.1 cot, sec, csc
I
I
2.2
2.3
2.2
3.
3.1
4. 4.1 4.1
5. 5.1
5.2
5.1
1.
1.1
1.2
2. 2.1
2.2
3.
3.1
3.2
3.2
1.
1.1
1.2
2.
2.1
2.2
8
3.
3.1
3.2
9
IV4
1. 1.1
1.1
2.
2.1
2.2
3.
3.1
4.
4.1
4.2
4.3
4.3
1. 1.1
2.
2.1
2.2
3.
3.1
3.2
1.
1.1
1.1
2. 2.1
3. 3.1
4.
4.1
4.2
4.2
1. 1.1
2. 2.1
3. 3.1
10
1.
2.
3.
4.
5.
1
2
3
6.
7.
8.
11
IIIIII IV
I
2
1.
1.1
12
1.2
2
1212
1
2a a
2
a bab
1.3
3
a b 2 2a b a ab b 2 2a b a ab b 2
a b c
21 1x x x 1 2x y x y
3 3 3 2 2 23 ( )( )x y z xyz x y z x y z xy yz zx
1 2
1 1 1
2
ab
a b
a b
2 2 2 2
1 c
a ba b
c c
5 2 6 3 2
2 2 12x x x x
2.
2.1
,a b ,a b 2:3 x
2.2
a b a b
3 2x 1 1x 1 2x
1 2 3x x
ncxy n=1234
13
ax
ax bx 2 1x 2 1x x xf
ax f a ax xf ax
xf a xf ax bx
,a ,b xf ax bx
I
n
1.
1.1
y f x
0y mx b m x x 0, ,m x b m
y x 1.2
22,32)(2 xxxxf
2 4x x
y c x a x b 2y ax bx c
2y a x h k
1.3
ny x 1, 2,3, 4n 1.5,1.5
14
n
ny cx
c ny cx
n
y c x h k
2.
2.1
1 2 1n n n n nx a x x a a x a n = 2,3,4
3322 ))(( axaaxxax
2 33 22 5 6 3 1 1 1f x x x x a b x c x d x , , ,a b c d
1.01f
3 22 5 6 3 1 1 2 1 2 3f x x x x a b x c x x d x x x
, , ,a b c d
xf ax bx , , ,a f a b f b f a,b f f x q x x a x b
1,1 , 2,3 , 3,7 1 1 2f x a b x c x x
, ,a b c 1
2f
15
)8,13(),5,12(),3,11(
)1213)(1113(
)12)(11(8
)1312)(1112(
)13)(11(5
)1311)(1211(
)13)(12(3)(
xxxxxxxf
11.5f
1,1 , 2,3 , 3,7
2f x a bx cx , ,a b c IV
3.
3.1
2 0ax bx c+ + =
2 5 3 0x x 2 2
3 3
1 1 3
1 2 2x x
3.2 n a
nx a a>0 3 22 3 4f x x x x
n 3.3
11 2 21 1 1mk
s sr r
k m mf x k x a x a x b x c x b x c
4 3 25 21 30 9 7f x x x x x 2x i
4.
4.1
2
1 2 4 0x x x 3 21 2 1 0x x x x
3 1 0x 4 22 3 0x x
1
0x
11
1x
11
x
16
10 , 0.1,0.2, ,0.9x x
0, 1a a
2 x 10x
logax b xa b
10
yxxy logloglog
log / log logx y x y xx loglog
10 1
log loglog
a x xa
logy x logy x
1.
1.1
n 1 51
3 6210 10 10 1 1 1
3 3 32 3 6
1 1
3 210 10<
1 1 1
( ) ( ) ( )a b c
a b c a b c a b c a b cx x x
2 2 3xa
3 3
6
x x
x x
a a
a a
17
2.
2.1
2 x
10x
3.
3.1
yxxy logloglog log / log logx y x y
log loglog log , log log log , x xm b an a a b aan
b b b c c a bm
3.2 1
log loglog
a x xa
10
4.
4.1
xy a logax y
1
log loga x x
loga
2
a bab
log loglog
2 2
a b a b
a b
5.
5.1
5.2
1002 10
1.18
5.3
5.4
xx loglog
18
II
/
1.
1.1
3
1n na a d 1n na ra 1n na a n 2
1n na a n 1 1n na n a
1.2
/ II
2.
2.1
1 1 1
n n n
k k k k
k k k
a b a b
1 1
n n
k k
k k
ca c a
1
1
1 2
n n
k k
k k
a a
1
n
k
k
21
n
k
k
11
1
n
k k k
19
1.
1.1
1.2
1.3
|S| S
10 8 3 5 7 21 4 1 3 6
10+8+3+5+7+21+4+1+3+6 = 68
51
51
50
1.4
A B |A B| = |A| + |B|
A, B A B |A B| = |A||B| A, B, C
1 |A B| = |A| + |B| |A B|
2 |A B C| = |A| + |B| + |C| |A B| |B C| |C A| + |A B C|
Principle of Inclusion and Exclusion PIE
Inclusion and Exclusion
PIE
2.
2.1
n n! 1 n 1 n n!
20
n k
)!(
!
kn
nPnk
1 k 1 n
nkP
50 1
n k nk
1 k 1 n nk
10 310
1 0 A={0,1} n
An = A A . . . A n 2n 2.2
!
!( )!
n
k
nC
k n k
n k !
!( )!
n
k
nC
k n k
k 1 n n
kC
n k
1n k
kC
k 1 n 1n k
kC
n k x1 + x2 + + xn = k 1n k
kC
3.
3.1
(x + yn
5
2 1 1xx
x
1.
21
1.1
3
2.
2.1
50
3.
3.1
ABC A 40%B
30%C 30% A 5%B
10%C 8%
A
90%
90%
90% 2%
1.
1.1
1
1 n
k
k
xn
1
1 2n
nx x x
2
1
1 n
k
k
xn
2
1
1 n
k
k
x xn
2 x=
ix
ix
22
2.
2.1
0
, , 1,2, ,k kx y k n , 2
1
( )n
k k
k
e r y rx
r 2 2 2 2
1 1
( ) ( 2 ) = 2( ) 1n n
i i i i i i
i i
e r y x y r x r r x y r
1
n
i i
i
r x y
y rx= ( )e r
II
1.
2.
III
23
360 r 0 360
X
1.
1.1
24
O
2 2cos ,sinB
1 1cos ,sinA
1,0
2.
2.1
X
150 , 30 ; 225 , 45 ; 300 , 60
cos , sin
2.2
2.3
r, 0 ,0 360r 3.
ABC B , 0c C
cos , sinb A b A
ABC 1
sin2
c b A
ABC 1
sin2
a c B
ABC 1
sin2
a b C
ABC A B , 0c C
cos , sinb A b A
2 22 2 2cos sin 2 cosa b A c b A b c bc A
4. 2 1 1 2 1 2cos cos cos sin sin
4.1
A,B
A B D
C
2 2 2 22 2
2 2
sin cos
2 cos
BC CD BD b A c b A
b c bc A
25
1 1 2 2cos ,sin , cos ,sin OAB
2 1 1 2 1 2cos cos cos sin sin
1 2cos 1 2sin 1 2tan cos2
sin2 cos2
sin
2
cos15
5.
5.1
5.2
1.
1.1
1.2
2.
2.1
2.2
ax by k
3.
3.1
3.2
2
26
a b
1 1 2 2cosa b a b a b
1 2 2 1sina b a b a b
1 1 1
2 2 2
a x b y c
a x b y c
c xa yb a b 0
a b
1.
1.1
1.2
1 2
0 1 ,0 12 1
x y x y
4
5
1
2
2
1
2.
27
a
b
1 2,b b
1 2,a a
2.1
1 2 1 2, , ,a a a b b b
2 22 2
1 1 2 2 2 cosa b a b a b a b
1 1 2 2 cosa b a b a b
,a b a b
a b b a a b c a c b c 2
a a a
2 2 2 2 2ax by a b x y
a b a b
4, 51, 2
2.2
3.
3.1
1.OABO0,0 1 2,A a a 1 2,B b b
2. ,a b
2 2 2
22 2 2 2
1 2 1 2 1 1 2 2 1 2 2 1
1 1 1sin 1 cos
2 2 2
1 1
2 2
OAB a b a b a b a b
a a b b a b a b a b a b
1 1 1 2 1 1
2 2 1 2 2 2
a b a a b a
a b b b b a
1 1 1 1 1 1 1
2 2 2 2 2 2 2
a c b a b c b
a c b a b c b
1 1 1 1
2 2 2 2
ca b a bc
ca b a b
3.2
D C
1 2,A a a
1 2,B b b
O x
y
1 2 2 2 1 1 1 2
1 2 2 1
1 1 1( )( )
2 2 2
1
2
OAB b b a b a b a a
a b a b
28
1 1 1
2 2 2
a x b y c
a x b y c
c a b a b
0
IV
0
0
1.
1.1
2.
2.1
2.2
1,2,3 0,1, 1 | 0 1t t
1,2,3 0,1, 1 | 0 1,0 2s t s t 3.
3.1
1 2 3, ,a a a 1 2 3, ,b b b
1 1 2 2 3 3 cosa b a b a b a b a b 1 1 2 2 3 3a b a b a b
4.
4.1
29
2 2 2
2 2 3 3 1 1 22 2 2
2 3 3 1 1 2
| | | |a a a a a a
A a b a bb b b b b b
4.2
, ,a b c )( cba
4.3
2
2
2
1
1
1
a ba ca
ab b cb
ac bc c
bacc
bcab
aacb
1.
1.1
2.
2.1
1
: 12 3
x zL y
: 2 3E x y z
2.2
3.
3.1
3.2
1 1 1 1
2 2 2 2
3 3 3 3
a x b y c z d
a x b y c z d
a x b y c z d
d a b c a b c
0
30
1.
2.
2.1
Caley-Hamilton
3.
3.1
4.
4.1
4.2
1 2
2 1A
A 1
0
0
1
1
2
2
1
1
2
3
4
1
2
2
1
31
1.
1.1
( )22x y c y c+ - = +
2.
2.1
2 22 2 2x c y x c y a
x x h
y y k
2 2
2 21
x h y k
a b
2 2
2 21
x y
a b
2 2
2 2
x yk
a b
,x y
x yt t
2 2
2
2 2
x yt
a b
2 2
2 21
x y
a b
2 2 0ax cy dx ey f
2 2 2 2a x h c y k ah ck f
3.
3.1
2 22 2 2x c y x c y a
32
97 1 24 0970011604B
102 7 31 1020071891A
I
II
I
II
1 I II II
2 III
I 4
II 4
I 3
II 3
I III
I
II
I
II
33
I 1
II 1
2~3
1
I 3~4
II 3~4
2
2
2
2
III
I4
1. 1.1
1.2
2. 2.1
3.
3.1
3.2
3.3
3.1
1.
1.1
1.2
1.3
1.1
2.
2.1
2.2
2.1
3.
3.1
3.2 n
II4
34
1. 1.1
1.2
1.3
1.4
1.2
1.4
2. 2.1
3. 3.1
3.2
1. 1.1
1.2
2.
2.1
2.2
3. 3.1
3.2
3.3
3.3
4. 4.1
I3
1. 1.1
2.
2.1
3. 3.1
4. 4.1
5.
5.1
5.2
5.3
5.1
1. 1.1 1.1
35
2.
2.1
2.2
II3
1. 1.1
1.2
1.2
2. 2.1
2.2
2.3
2.3
3. 3.1
4. 4.1
4.2
1.
2.
3.
4.
5.
1
2
3
6.
36
7.
8.
37
III III
I I
II
III
variables n
n n
X
Y
0
1.
1.1
X Y
X X=0,1,2,3
Y
1.2
38
2.
2.1
1/2 n k 1
2
n
n
kC
np 1np p
3.
3.1
3.2
3.3
p n
p
1 , 0.4, 100k n kn
kC p p p n
2
221
, , 1 , 2.7182
x
e np np p e
-0.01 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0 10 20 30 40 50 60 70 80 90 100
39
1 n
1.
1.1
1.2
1.3
2 2cos sin 1 2 21 tan sec
2.
2.1
0sinA t A 0t
0c o s s i n s i na t b t A t
2.2
3.
3.1
3.2 n
cos sin cos sin cos sini i i
n 2 11 n
2
1 1 1
1 1 1 n
II II
1.
1.1
1.2
40
1.3
ABCD 1 ABCD
1.4
n
2.
2.1
3
y x h 3y x
3y x
3
y x h
y x n
cy
x n=1,2
2,y x y ax bx c 2 2 1x y
3.
3.1
3.2
1.
1.1
1.2
2.
2.1
2.2
A B
C D
41
3.
3.1
1
n
k
k
21
n
k
k
2
0 0,
a a
xdx x dx
3.2
3.3
4.
4.1
20
2R
rdr R X
2
2 2 34
3
R
RR x dx R
A Z
2 2: :H z A A z 2
20
1
3
H Azdz AH
H
0z 0v t
0v t v gt t 2
0 0 00
1
2
t
z v t dt z v t gt
II
a 1
na
I I
II
III
variables n
n n
X
Y
42
0
1.
1.1
X Y
X X=0,1,2,3
Y
2.
3.
4.
4.1
1/2 n k
1
2
n
n
kC
np 1np p
5.
5.1
5.2
5.3
p n
p
43
1 , 0.4, 100k n kn
kC p p p n
2
221
, , 1 , 2.7182
x
e np np p e
1.
1.1
2.
2.1
2.2
2 2cos sin 1 2 21 tan sec
II II
1.
1.1
1.2
2.
2.1
-0.01 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0 10 20 30 40 50 60 70 80 90 100
44
ABCD 1 ABCD
2.2
2.3
n
3.
3.1
3
y x h 3y x
3y x
3
y x h
y x n
cy
x ,n=1,2
2,y x y ax bx c 2 2 1x y
4.
4.1
4.2
A B
C D
45
97 1 24 0970011604B
102 7 31 1020071891A
A
B
A
B
46
1. 1-1
1.5
1-2
2. 2-1
47
1.
1-1
2.5
1-2
1-3
2.
2-1
2-2
2-3
48
1.
1-1
4
2.2. 2-1
F=ma
2-2
3.
3-1
49
1. 1-1
3
1-2
2. 2-1
2-2
3. 3-1
3-2
50
1. 1-1
3
2. 2-1
51
1. 1-1
6
1-2
1- 1-3
2. 2-1
2-2
2-3
2-4
52
1. 1-1
4
1-2
2.
2-1
E
= MC2
3. 3-1
3-2
4.
4-1
53
1.
1-1
E
4
1-2
1-3
1-4 ()
1961
2. 2-1
2-2
2-3
54
1.
2
1-1
1-2
2. 2-1
32
1. 1-1
55
0.5
0.5
0.5
0.5
56
A
1. 1-1
6 1-2
1-3
1-4
1.
1-1
7 2.
2-1
3.
3-1
4. 4-1
1. 1-1
6
2. 2-1
3.
3-1
1.
1-1
3
2.
2-1
3.
3-1
57
A
1. 1-1
8
2.
2-1
3. 3-1
3-2
4. 4-1
1. 1-1
2
32
B
1. 1-1
8+2
1-2
1-3
2.
2-1
3. 3-1
4. 4-1
5.
5-1
1. 1-1
8+2
1-2
58
1-3
1-4
1-5
2. 2-1
2-2
1.
1-1
8+2
2.
2-1
3.
3-1
4. 4-1
1. 1-1
12
2. 2-1
3. 3-1
4.
4-1
5. 5-1
6. 6-1
59
7.
7-1
1.
1-1
4
2.
2-1
3.
3-1
1. 1-1
12
2.
2-1
3. 3-1
3-2
4. 4-1
1. 1-1
4 2. 2-1
56+8
()
60
B
2
1. 2.
2
1.
2
2.
2
61
62
63
64
97 1 24 0970011604B
102 7 31 1020071891A
65
1.
7
2.
3.
4.
1.
7
2.
1~18
3.
4.
66
1.
7
2.
3.
4.
1.
7 2.
3.
67
1.
8
2.
pH
3.
4.
1.
8
2.
3.
4.
5.
68
1.
3D
10
2.
3.
4.
5.
6.
1.
2
2.
3.
69
1.
8
2.
3.
4.
1.
10 2.
3.
1.
10
2.
3.
4.
70
()
1.
()
(
)
2.
(
~)
3.
()
(
)
(
)
4.(
)
(
)
()
()
5.
(
)
pH
6.
()
(
3D
)
71
()
7.
(
)
()
(
)
8.
(
)
(
)C12~C16
()
()
9.(
)
10.
(~)
Fe
3++SCN
FeSCN
2+
(
)
11.
()
MgC2O4
(
)
MgC2O4 (
)
()
()
()
72
()
()
()
()
()
()
()
()
()
()
()
()
()
73
()
()
()
()
()
()
()
()
()
74
75
97 1 24 0970011604B
102 7 31 1020071891A
76
1.
12
2.
3.
4.
5.
1.
d
12
2.
3.
77
1.
12
2.
HX
H2O
C=C
Br2
78
1.
12
2.
KaKb
3.
4.
1.
10
2.
3.
4.
1.
10
2.
3.
79
1.
3D
8
2.
3.
1.
6 2.
3.
1.
2.
24
3.
4.
5.
80
1
IV
2
3
4
5
6
V
IVIII
II
II
81
7
8
IR12050~100
9
(25 %
)
1-2-
()
10
82
()
()
()
()
()
()
()
()
()
()
()
()
()
()
83
()
()
()
()
()
()
()
()
()
()
84
()
()
85
1
97 1 24 0970011604B
102 7 31 1020071891A
1
(1)
1
2
86
8~9
(
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ATP
87
8~9
(symplast)
(apoplast)
12
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(
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(
)
(
)
88
(
T B
MHC Ig )
(
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(
)
(
)
89
8~10
(
)
ABO
(
)
DNA
DNA
(
)
(
)
90
DNA DNA
DNA
7~8
(Biological species
concept)
(
)
91
13~
14
(
)
15 2 60
1
92
prior knowledge
93
authentic assessment
portfolio assessment
norm-referenced assessment
criterion-referenced assessment
1.K
1
94
2
3
2.U
1
2
3
3.A
1
2
3
4.I
1
2
3
4
1
1
2
95
96
2
97 1 24 0970011604B
102 7 31 1020071891A
2
2
2
1
97
7~8
7~8
7~8
7~8
15230
2
1
1
98
1
prior knowledge
99
authentic assessment
portfolio assessment
norm-referenced assessment
criterion-referenced assessment
1.K
1
2
3
2.U
1
2
3
3.A
1
2
3
4.I
1
2
3
4
100
2
2
1
101
97 1 24 0970011604B
102 7 31 1020071891A
102
12~
13
(
)
8~9
(Carbon Reactions)
ATP
103
(catalase)
7~8
9~10
104
8~9
(
)
(
)
5~6
4~5
105
5~6
10~
11
(
)
106
7~8
ABO
13~
14
DNA RNA
DNA DNA
DNA
(PCR)
DNA
6~7
107
6-7
(
)
1. 15 13 4
112
2.
prior knowledge
108
109
authentic assessment
portfolio assessment
norm-referenced assessment
criterion-referenced assessment
1.K
1
2
3
2.U
1
2
3
3.A
1
2
3
110
4.I
1
2
3
4
111
97 1 24 0970011604B
102 7 31 1020071891A
1.
1-1
4
1-2
2.
2-1
112
2-2
1.
1-1
5~7
2.
2-1
2-2
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13
1-2
1-3
2.
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113
2-2
3.
3-1
3-2
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4~5
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2. 2-1
2-2
114
1. 1-1
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1-2
2.
2-1
2-2
1.
1-1
7~8
1-2
1-3
2.
2-1
2-2
1. 1-1
11~13
115
2. 2-1
3. 3-1
4. 4-1
5.
5-1
5-2
5-3
1. 1-1
12~13
1-2
2. 2-1
2-2
2-3
116
3. 3-1
3-2
4. 4-1
OBAFGKM
4-2
1.
1-1
2 2.
2-1
117
1.
1
118
2
()
3
4
2.
119
VCD
DVD
visualization technologies