中華民國 102 年7月31 日 發布 - k12ea.gov.tw · 2...
TRANSCRIPT
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102 7 31
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1
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1...................................... 85
2................ 96
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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.
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84
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97 1 24 0970011604B
102 7 31 1020071891A
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DNA DNA
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92
prior knowledge
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93
authentic assessment
portfolio assessment
norm-referenced assessment
criterion-referenced assessment
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97 1 24 0970011604B
102 7 31 1020071891A
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97 1 24 0970011604B
102 7 31 1020071891A
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104
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-
105
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106
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DNA RNA
DNA DNA
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102 7 31 1020071891A
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113
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-
115
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116
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-
117
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-
118
2
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-
119
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DVD
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