1
()
1.
2.
3.
21 (1)(2)(3)()(4)
1.
2.
2
3.()()()
4.
5.
6.()()
3
()
7.
8.()
9.
4
()
3-4 ()
1. 2. 3. 4.
1.()
2.()
3.()
4.()
5
()
NSAD 1234 C RTSCE
6
1.
N-1-01 1000 N-1-02 N-1-03 N-1-04 N-1-05 N-1-06 N-1-07 () N-1-08 N-1-09 N-1-10 () N-1-11
N-2-01 10000
N-2-02 () N-2-03
N-2-04
N-2-05 N-2-06 () N-2-07
N-2-08 ()
N-2-09
N-2-10
N-2-11 N-2-12 N-2-13 N-2-14 N-2-15
7
N-2-16 N-2-17 N-2-18 N-2-19
N-2-20
N-2-21 N-2-22 (S-2-08) N-2-23 N-2-24 N-2-25 () N-2-26 N-3-01 N-3-02 N-3-03 N-3-04
N-3-05
N-3-06 N-3-07 N-3-08 N-3-09 () N-3-10 () N-3-11 ()
N-3-12 ()
N-3-13
N-3-14
N-3-15 N-3-16
N-3-17
8
N-3-18 (A-3-02)N-3-19 N-3-20 (S-3-05) N-3-21 N-3-22 (S-3-06)N-3-23 (S-3-07) N-3-24 (S-3-10) N-3-25 (S-3-11) N-4-01
N-4-02
N-4-03 N-4-04 N-4-05 N-4-06
N-4-07
N-4-08 N-4-09 N-4-10 N-4-11 N-4-12 N-4-13 N-4-14
S-1-01 S-1-02 S-1-03 S-1-04 S-2-01 S-2-02 S-2-03
9
S-2-04 S-2-05 S-2-06 S-2-07 S-2-08 (N-2-22) S-3-01
S-3-02 180
S-3-03
S-3-04
S-3-05 (N-3-20) S-3-06 (N-3-22)S-3-07 (N-3-23) S-3-08 S-3-09 S-3-10 (N-3-24) S-3-11 (N-3-25) S-4-01 S-4-02 S-4-03 S-4-04 S-4-05 S-4-06 S-4-07 S-4-08 S-4-09 S-4-10 S-4-11 S-4-12 ()
S-4-13 ()
10
S-4-14 S-4-15 S-4-16 S-4-17
S-4-18 (A-4-19)
S-4-19 (A-4-20)
A-1-01
A-1-02
A-1-03 A-2-01 A-2-02 A-2-03
A-3-01
A-3-02 (N-3-18)A-3-03
A-3-04
A-3-05 A-3-06
A-4-01 ()
A-4-02
A-4-03 xy()
A-4-04 ()
A-4-05
A-4-06
11
A-4-07 A-4-08 A-4-09 A-4-10 A-4-11 A-4-12 A-4-13 A-4-14 A-4-15 () A-4-16 A-4-17
A-4-18
A-4-19 (S-4-18)
A-4-20 (S-4-19)
D-1-01 D-2-01 D-2-02 D-3-01
D-4-01
D-4-02 D-4-03 D-4-04
C-R-01 C-R-02 C-R-03 C-R-04
12
C-T-01 C-T-02 C-T-03 C-T-04
C-S-01 C-S-02 C-S-03 C-S-04 C-S-05
C-C-01 () C-C-02 C-C-03 C-C-04 C-C-05 C-C-06 C-C-07
C-C-08
C-E-01 C-E-02 C-E-03
C-E-04
13
2. (1)
N-1-01 1000 N-1-02 N-1-03 N-1-04 N-1-05 N-1-06 N-1-07 () N-1-08 N-1-09 N-1-10 () N-1-11
S-1-01 S-1-02 S-1-03 S-1-04
A-1-01
A-1-02
A-1-03
D-1-01
14
(2)()
N-2-01 10000
N-2-02 () N-2-03
N-2-04
N-2-05 N-2-06 () N-2-07
N-2-08 ()
N-2-09
N-2-10
N-2-11 N-2-12 N-2-13 N-2-14 N-2-15 N-2-16 N-2-17 N-2-18 N-2-19
N-2-20
N-2-21 N-2-22 (S-2-08) N-2-23 N-2-24 N-2-25 ()
15
N-2-26
S-2-01 S-2-02 S-2-03 S-2-04 S-2-05 S-2-06 S-2-07 S-2-08 (N-2-22)
A-2-01 A-2-02 A-2-03
D-2-01 D-2-02
16
(3)()
N-3-01 N-3-02 N-3-03 N-3-04
N-3-05
N-3-06 N-3-07 N-3-08 N-3-09 () N-3-10 () N-3-11 ()
N-3-12 ()
N-3-13 N-3-14 N-3-15 N-3-16
N-3-17
N-3-18 (A-3-02) N-3-19 N-3-20 (S-3-05) N-3-21 N-3-22 (S-3-06)N-3-23 (S-3-07) N-3-24 (S-3-10) N-3-25 (S-3-11)
17
S-3-01
S-3-02 180
S-3-03
S-3-04
S-3-05 (N-3-20) S-3-06 (N-3-22)S-3-07 (N-3-23) S-3-08 S-3-09 S-3-10 (N-3-24) S-3-11 (N-3-25)
A-3-01
A-3-02 (N-3-18) A-3-03
A-3-04
A-3-05 A-3-06
D-3-01
18
(4)()
N-4-01
N-4-02
N-4-03 N-4-04 N-4-05 N-4-06
N-4-07
N-4-08 N-4-09 N-4-10 N-4-11 N-4-12 N-4-13 N-4-14
S-4-01 S-4-02 S-4-03 S-4-04 S-4-05 S-4-06 S-4-07 S-4-08 S-4-09 S-4-10 S-4-11 S-4-12 ()
19
S-4-13 ()
S-4-14 S-4-15 S-4-16 S-4-17
S-4-18 (A-4-19)
S-4-19 (A-4-20)
A-4-01 ()
A-4-02
A-4-03 xy()
A-4-04 ()
A-4-05
A-4-06
A-4-07 A-4-08 A-4-09 A-4-10 A-4-11 A-4-12 A-4-13 A-4-14 A-4-15 () A-4-16 A-4-17
A-4-18
20
A-4-19 (S-4-18)
A-4-20 (S-4-19)
D-4-01
D-4-02 D-4-03 D-4-04
21
3.
19 nsad ()
1-n-01 100
N-1-01
1-n-02 1 5 10 1 10
N-1-01
1-n-03 N-1-01
1-n-04
N-1-02 A-1-01
1-n-05 N-1-02 1-n-06 N-1-02
1-n-07 2 5 10 N-1-01 N-1-04
1-n-08
N-1-11
1-n-09 N-1-08 S-1-01 S-1-03
1-n-10
N-1-08
1-s-01 S-1-01 1-s-02 S-1-01 1-s-03 S-1-02
22
1-s-04 S-1-02
1-a-01 A-1-02 1-a-02 A-1-03
1-d-01 D-1-01 1-d-02 D-1-01
23
2-n-01 1000 N-1-01
2-n-02 100 10 100 N-1-01
2-n-03 ( 2-a-01)
N-1-01 A-1-01
2-n-04 N-1-02 N-1-03
2-n-05 () N-1-02 N-1-03
2-n-06
N-1-04 A-1-01
2-n-07 N-1-05 N-1-06
2-n-08 N-1-06 A-1-02 2-n-09 () N-1-07
2-n-10 () N-1-07
2-n-11 N-1-02 2-n-12 N-1-11
2-n-13 N-1-11
2-n-14 N-1-08
2-n-15
N-1-08 N-1-09
2-n-16 N-1-10 2-n-17 N-1-10
2-n-18 ( 2-s-04) N-1-10 S-1-03
2-s-01 () S-1-03
24
2-s-02 S-1-04
2-s-03 N-1-08 S-1-02
2-s-04 ( 2-n-18) N-1-10 S-1-03
2-s-05 N-1-08 S-1-01 S-1-03
2-a-01 ( 2-n-03)
N-1-01 A-1-01
2-a-02 A-1-02
2-a-03 A-1-02 2-a-04 A-1-03
25
()
3-n-01 10000 N-2-01
3-n-02 (10000) N-2-03
3-n-03 N-2-06 N-2-07 3-n-04 N-2-05
3-n-05 () N-2-04
3-n-06 N-2-05
3-n-07 () N-2-06
3-n-08 () N-2-06
3-n-09
N-2-14 N-2-15
3-n-10 N-2-03
3-n-11
N-2-09 N-2-10
3-n-12 N-2-13
3-n-13
N-2-24
3-n-14
N-2-17 N-2-26
3-n-15 ()
N-2-18 N-2-26
3-n-16
N-2-19 N-2-26
3-n-17 ( 3-s-04) N-2-20 S-2-04
3-n-18 ( 3-s-05)
N-2-21 S-2-02
26
3-s-01 S-2-01
3-s-02 N-2-17 S-2-01
3-s-03
S-2-04 S-2-05
3-s-04 ( 3-n-17) N-2-20 S-2-04
3-s-05 ( 3-n-18)
N-2-21 S-2-02
3-s-06 S-2-02 3-s-07 S-2-04
3-a-01 A-2-01
3-d-01 D-2-01
27
4-n-01 () N-2-02
4-n-02 N-2-03 4-n-03 N-2-05
4-n-04
N-2-06 N-2-07 A-2-02
4-n-05 () N-2-07 A-2-03
4-n-06 () N-2-08
4-n-07 N-2-11
4-n-08
N-2-10
4-n-09
N-2-12 N-2-16
4-n-10 N-2-16 4-n-11 N-2-13
4-n-12 N-2-13
4-n-13 N-2-24 N-2-25
4-n-14 () N-2-17 N-2-18 N-2-19 N-2-25
4-n-15 N-2-17
4-n-16 ( 4-s-04) N-2-20
4-n-17 N-2-21
28
4-n-18 ( 4-s-09)
N-2-22 S-2-08
4-n-19 N-2-23
4-s-01 S-2-04 4-s-02 S-2-05 4-s-03 S-2-06
4-s-04 ( 4-n-16) N-2-20
4-s-05 () S-2-07
4-s-06 N-2-20 S-2-03
4-s-07 S-2-02 S-2-03 S-2-04
4-s-08
S-2-03 S-2-04
4-s-09 ( 4-n-18)
N-2-22 S-2-08
4-a-01 A-2-02
4-a-02 N-2-07 A-2-01
4-d-01 D-2-02 4-d-02 D-2-02
29
()
5-n-01 N-3-01
5-n-02 N-3-02 A-3-01
5-n-03 N-3-02 A-3-01
5-n-04 N-3-03
5-n-05 N-3-03
5-n-06 N-3-06 5-n-07 N-3-07
5-n-08 N-3-09
5-n-09 N-3-10
5-n-10 N-3-08
5-n-11 N-3-09 N-3-11
5-n-12 N-3-11 N-3-13
5-n-13 N-3-11 N-3-13 5-n-14 () N-3-14 5-n-15 N-3-19
5-n-16 N-3-19
5-n-17 N-3-19
5-n-18 ( 5-s-05)
N-3-22 S-3-06
5-n-19 N-3-19
30
5-n-20 ( 5-s-07)
N-3-20 N-3-25 S-3-05 S-3-11
5-n-21 N-3-21
5-s-01 180 S-3-02 5-s-02 S-3-02 5-s-03 S-3-01 5-s-04 S-3-03
5-s-05 ( 5-n-18)
N-3-22 S-3-06
5-s-06 S-3-09
5-s-07 ( 5-n-20)
N-3-20 N-3-25 S-3-05 S-3-11
5-a-01
N-3-02 A-3-01
5-a-02 A-3-01
5-a-03 N-3-02 A-3-01
5-a-04
A-3-04 A-3-05
31
6-n-01 (2020100) N-3-04
6-n-02 N-3-05 6-n-03 N-3-05
6-n-04 N-3-10
6-n-05
N-3-02 A-3-01
6-n-06 N-3-10 N-3-11
6-n-07 () N-3-12
6-n-08
N-3-02 A-3-01
6-n-09 N-3-15 6-n-10 N-3-15 6-n-11 N-3-16
6-n-12 N-3-16 N-3-17
6-n-13 ( 6-a-04)
N-3-18 A-3-02 A-3-03 A-3-04 A-3-05
6-n-14 ( 6-s-03)
N-3-23 S-3-07
6-n-15 ( 6-s-05)
N-3-24 S-3-10
32
6-s-01 S-3-01
6-s-02 S-3-04
6-s-03 ( 6-n-14)
N-3-23 S-3-07
6-s-04 S-3-08
6-s-05 ( 6-n-15)
N-3-24 S-3-10
6-a-01 A-3-03
6-a-02
A-3-04 A-3-05
6-a-03 A-3-06
6-a-04 ( 6-n-13)
N-3-18 A-3-02 A-3-03 A-3-04 A-3-05
6-d-01 D-3-01 6-d-02 D-3-01
6-d-03 D-3-01
33
7-n-01 100 N-4-01
7-n-02
N-4-01 N-4-02 N-4-09
7-n-03 N-4-02
7-n-04 N-4-05
7-n-05 N-4-05
7-n-06 ()
N-4-05 N-4-06 N-4-08
7-n-07 N-4-08 A-4-02
7-n-08 N-4-07
7-n-09 N-4-07 A-4-08
7-n-10 N-4-09 7-n-11 N-4-09 7-n-12 N-4-10
7-n-13 N-4-03
7-n-14 N-4-04
7-n-15
N-4-03 N-4-04
34
7-a-01 A-4-01 A-4-02
7-a-02 A-4-03 A-4-04
7-a-03
A-4-03 A-4-06 A-4-07
7-a-04 A-4-05 A-4-07
7-a-05 A-4-07
7-a-06
A-4-03 A-4-09
7-a-07
A-4-03 A-4-12
7-a-08 A-4-12
7-a-09 A-4-01 A-4-04
7-a-10 A-4-01 A-4-04
7-a-11 A-4-10 7-a-12 A-4-11 7-a-13 A-4-11
7-a-14 A-4-11 A-4-12
7-a-15 A-4-08
7-a-16 A-4-03 A-4-08
7-a-17 A-4-08 7-a-18 a x b y=cxd A-4-11
35
8-n-01 N-4-11 N-4-12
8-n-02 N-4-11 8-n-03 N-4-12 8-n-04 N-4-13
8-n-05
N-4-13 N-4-14
8-n-06
N-4-13 N-4-14
8-s-01 S-4-01
8-s-02 S-4-01 S-4-04
8-s-03 S-4-06
8-s-04 S-4-01 S-4-04
8-s-05
S-4-01 S-4-07
8-s-06 S-4-08
8-s-07 S-4-09
8-s-08 (Pythagorean Theorem) ( 8-a-05)
S-4-05 A-4-15
8-s-09 S-4-05 A-4-10
8-s-10
S-4-08 S-4-09 S-4-11 S-4-12
8-s-11 S-4-10
36
8-s-12
S-4-02 S-4-03 S-4-04 S-4-08 S-4-12 S-4-13
8-s-13
S-4-02 S-4-04 S-4-07 S-4-13
8-s-14
S-4-08 S-4-12 S-4-13
8-s-15 S-4-13
8-s-16 S-4-18
8-s-17 S-4-19
8-s-18 S-4-03 S-4-04
8-s-19 S-4-04
8-s-20 () S-4-17
8-s-21 S-4-17
8-a-01 A-4-13 8-a-02 N-4-12 8-a-03 A-4-14 8-a-04 A-4-14
8-a-05 Pythagorean Theorem ( 8-s-08)
S-4-05 A-4-15
8-a-06 A-4-16 8-a-07 A-4-16 8-a-08 A-4-16
37
8-a-09
A-4-06 A-4-16
8-a-10 A-4-16 8-a-11 A-4-16 8-a-12 A-4-16
38
9-s-01 S-4-14 9-s-02 S-4-15 9-s-03 S-4-15 9-s-04 S-4-07 9-s-05 S-4-15 9-s-06 S-4-17 9-s-07 S-4-17
9-s-08 S-4-16 S-4-17
9-s-09 S-4-16 S-4-17
9-s-10 S-4-16
9-s-11 ()
S-4-08 S-4-13 S-4-17
9-s-12 S-4-19 A-4-20
9-s-13 S-4-01
9-s-14 S-4-01 S-4-02
9-s-15
S-4-01 S-4-04
9-s-16 S-4-01 S-4-04
39
9-a-01 A-4-04 9-a-02 A-4-18 9-a-03 A-4-17
9-a-04 A-4-17 A-4-18
9-d-01
D-4-01 D-4-02 D-4-03
9-d-02 D-4-01 D-4-03
9-d-03 D-4-02 D-4-03
9-d-04 1025507590 D-4-03
9-d-05 D-4-04
40
()
1.
2.
3.
4.
5.
6. (
)
7.
8.
9.
10.
41
()
1. (1)
(2)
(3)
(4)
(5) (6)
(7)
(8)
(9)
42
(10)()
(11)()
(12)
(13)()
2. (1)
(2)
(3)
(4)
43
(5)
3. (1)
() (2)
(3) (4)
4.
(1)
(2)
(3)
44
1. 1-a-01 ()
2. 3.
4.() 5.
6.
45
1. 1-n-01 100
N-1-01
100
( 1-s-02)( 1-n-03)( 1-n-02)
87 8 7 8 7
( 1-n-02)
4 16 16 1 6 4 5 6 56 56
1-n-02 1 5 10 1 10
N-1-01
10 10
55 15 10
22 55 10
60 5
14 5 40 5
46
65 10 50
65 25 50
2 5 10 (1-n-07)
10 1 1 10
5
25 1-n-04
25
(1)10 5
(2)105 1
(3)5 1
( 1-n-01)
47
1-n-03 N-1-01
5 4 3
()8 ()6 ()
() 1 2
1-n-04
N-1-02A-1-01
()()()()()
( 1-n-05)
7 3 10 7310 7 3 4 734
48
( 1-a-02)
() 3 2 8 2
2 6
6 1
5
6
18 3
6 4
8 5
12 5
36 15
17 5
5 6
17 8
16 4
14 17
4 3
15 5
()
0 0
49
1-n-05 N-1-02
(1) 1 1(2) 10 10(3) 10
10(4)(4812)(5)(1284)
3971510748
293214
1821()5322()
147()4711()111021
1-n-06 N-1-02
( 1-n-05)
159 1910 10515
50
1898 188 1091
1-n-07 2 5 10 N-1-01N-1-04
2 5 10
( 2-n-062-a-03)
2 24680
5 5 0
1-n-08 N-1-11
1 3
1( 2) 8 2
1-n-09 N-1-08S-1-01S-1-03
1-n-10 N-1-08
51
(
)
()
( 2-n-15)( 3-n-09)
5 55
9 5 95
1-s-01 S-1-01
()()
1-s-02 S-1-01
()
1-d-011-d-02
1-s-03 S-1-02
52
1-s-04 S-1-02
1-a-01 A-1-02
()(1-n-04)()
3 4 3+4 4+3
1-a-02 A-1-03
()(1-n-04)()
7 6 13 13 6 7 13 7 6
( 1-n-04) 5 12 7 125 7 125
( 1-n-04) 6 4
( 1-n-04) 17 8
53
( 2-a-04)
1-d-01 D-1-01
( 1-s-02)
1-d-02 D-1-01
54
2. 2-n-01 1000
N-1-01
1-n-011-n-02 10010 1
99100101()109110111()
4 16 5 6 560 560
19933013
2-n-02 100 10 100 N-1-01
1-n-02 (1 5 10 100 ) 1
10 5 100 10 10
2-n-03
( 2-a-01) N-1-01A-1-01
16 1412 1113 14 27 45
55
2-n-04 N-1-02N-1-03
1992 502
( 1-n-05)
978 8 35 978 97 3 100 1005 105
1037 100 1003 1037 100 7 3 96
( 2-a-02)
2-n-05 () N-1-02 N-1-03
56
100
57
2-n-06
N-1-04A-1-01
( 2-n-08)
( 1-n-06)( 1-n-07)2 4 24824 2 4 ()()
( 2-n-08) 232 23 3
(1)()
(2)(1 54 )()()
(3)5 4 5
(4)(3)
58
5 4 4 5
(5)(5 420 )
( 2-a-03 3-a-01) 3 24 3 24324243 24242472() 3 24
2-n-07 N-1-05N-1-06
()()
12 1 4
1 4 3
12 2
24 3
59
2-n-08 N-1-06A-1-02
10
( 2 5 10 2510 4 36978 )
23 32 74 47
2-n-09 () N-1-07
()
1 20 3 2 25 20 15
3 67 35 25
4 35 9 4
5 30 25 60
1
23 ()
60
2-n-10 () N-1-07
()
8 3 2 3 (83) 2 (242)
7 3 19
55 10 5 7 6 4
9 6 4
(3 47 ) 594545247
10 8 100
5 3 6 538 8648
20 15 6
6 2 4
2-n-11 N-1-02
3249( ) 3
61
70 80 90 32 3049 503050 80
7129( ) 3 30 40 50 71 7029 307030 40
8, 9, 0, 1, 2
2-n-12 N-1-11
1-n-08 5 5 1 1
7 55 8 8 8 5 8 8
7 9
2-n-13
N-1-11
12
7 8 ()4
62
2-n-14
N-1-08
()
8 6 86 6 8
4 7 ()
2-n-15
N-1-08N-1-09
1 100 123 1 23
1
0
0 5 8 3 5 6 16 7 1 7 8 1 3 5678 4
20 3 ( 2-n-09)
25 20 15
63
( 2-n-09)
10 6 ( 2-n-06)
175 2 ( 2-n-06)
()
( 1 )( 10 )
() 1
2-n-16 N-1-10
3-n-15
2-n-17 N-1-10
()
(
64
)
3-n-16
2-n-18 ( 2-s-04) N-1-10S-1-03
2-s-01 () S-1-03
( 1-s-02)
2-s-02 S-1-04
2-s-03 N-1-08S-1-02
65
15
()
2-s-04 ( 2-n-18) N-1-10S-1-03
2-s-05 N-1-08S-1-01S-1-03
()
2-a-01
( 2-n-03) N-1-01A-1-01
2-a-02 A-1-02
()()
66
3 4 7 3 7 10 4 14
2-a-03 A-1-02
()( 2-n-062-n-08)()()
7 4 7 4 74 4 7 47( 2-n-06)
( 2-n-08)
2-a-04 A-1-03
()(2-n-04)()
1-a-03
65 90 906525()
65 25 652590()
18( )2722( )14( )1230( )2510( )
67
3.
3-n-01 10000 N-2-01
1-n-011-n-032-n-01 100010010 1
10
1000 (2-n-02)
206720000607 30063060 3600
257 700
0579
( 1327 4)( 2498 3)( 3998 3)
15 1 5 8 2 7 12
3-n-02 (10000) N-2-03
2-n-042-n-05
3-n-03 N-2-06N-2-07
68
1299
T 250
180
4500 1470 1528
570 50 319
500 3000 1250
3-n-04 N-2-05
(1)
(2)(305)(2004)
(3)(326)(326 306 26 )
(4)(3)
(1)(340)
(2)(3040)
(3)(5300)
1 1 5 2 1
69
3 2
2 3
70
3-n-05 (
) N-2-04
2-n-07
3265 232652
82 2 82 8
20 3 6 7 2 10 75 10 7 5
8 2 () 2 8 4 ()
()() 2-n-06
36 3 30 3 10 6 3 2 12
71
(103313)
( 3-n-09 3-n-11 )
()80 8 80810
()80 10 80108 10
36 9
130 2
2 0 1
3-n-06 N-2-05
( 2-n-08)
(1) 2-n-08
(2)(283396)
(3)(353785)( 3-n-05)()
(4)(3)
3-n-07 () N-2-06
2-n-10
72
( 3-n-05)
400 560 6 6 4005609609606160
400 70 3 70 400703303303110
399 300 300 3993133300133167
1 6 300 1 615300560
3-n-08 () N-2-06
5 2 2
4 6 5 4624 5 245120
8 6 5 ()
3-n-09
N-2-14N-2-15
1-n-03
0
0
73
1 1 1
0.1 0.9
7 7 7 7
1 14 1 10 14104
2 6 2 11 1165516
3-n-10 N-2-03
()
1896114-n-06
302299( ) 3 400 500 600 302 300299 300300300 600
701599( ) 3 100 200 300 701 700599 600700600
74
100
3-n-11
N-2-09N-2-10
12
1
1214
310
()() 6
6 16
6 16
()(
)
1214
18
12
75
14
3 1 3 2 3
8 8 1
2 1
13
23
33
43
63
2 13233
15
35
()
3-n-12 N-2-13
( 10 1 ) 1
1100.1
10 0.1 1.010101
1 0.1 (100 ) 0.1
76
0.50.60.70.80.911.1
23.4 5.7 12.1
3-n-09 (
)
3-n-13
N-2-24
31 30
1 24 1 60 1 60
24 4 24
124
21 30 21 30 21129 9 21 30 9 30
1 1 1 55 40 1
(24 60 ) 10
7 40 7 50 5040
7 40 8 8 7 60 40 60
77
6040
7 48 10 4810
8 20 40 2040 60 8 60 9
8 40 4
11 20 2 30
10 10 3 30
1 30 8 40
7 30 3
14 2 10
7 3 7 17
3-n-14
N-2-17N-2-26
1 10 1 100 1 1000
0.1 ( 110) 1
2.1 2 1
40 15 7
30 7 6 6 8
3 4
78
8 3 4
5 6
3-n-15 ()
N-2-18N-2-26
1 1000 ml cc
100ml 10 1
(100ml) 0.1 110
(1000 ) 10
1 450 2 450
600 1
6 4
5 300
8 4 1
3-n-16
N-2-19N-2-26
1 1000
(1000 ) 10
2 150 1 450
79
1 800 120
3 500 12 800
600 3 10 2
3-n-17 ( 3-s-04) N-2-20S-2-04
3-n-18 (3-s-05) N-2-21S-2-02
()
1
6 4 6 6 6 4 4 4
80
1
1
6
1
1
20
1
1
81
3-s-01 S-2-01
()
3-s-02 N-2-17S-2-01
()
(
)
4 5 6 456
5 54
6 4 62 42
4 5
5
6
82
8 4
1
1
3-s-03
S-2-04S-2-05
()()
3-s-04 ( 3-n-17) N-2-20S-2-04
4
6
83
3-s-05 (3-n-18) N-2-21S-2-02
3-s-06 S-2-02
1-s-04 ()
12
3-s-07 S-2-04
()
4-s-01
3-a-01 A-2-01
()()
84
728 287
696 966
728 728
118 811
7 28 287
8 10 108
3-d-01 D-2-01
()()
85
4. 4-n-01 (
) N-2-02
1-n-011-n-032-n-013-n-01
503000000 3203000
11608767 11349593 1160 1134
4-n-02 N-2-03
3-n-02
8 6 9 7 3 4 9 2 960 1 4820
4-n-03 N-2-05
3-n-023-n-043-n-06
86
4-n-04
N-2-06N-2-07A-2-02
2-n-103-n-033-n-073-n-08
3 15 153245290 15(32)156120
12 3 7 12(37)120
12 5 10 5 12560 601070 (125)1070
80 5 5735 80 35 803545 805745
8 10 432 1 81018 1 4321824 43281024
36 3 2 36312 2 12224
87
(363)224
24 2 3 2 24248 3 48316 (242)316
48 3 1 8 48 48316 16 1682 (483)82
72 4 6 1 72418 6 1863 (724)63
4-n-05 () N-2-07A-2-03
(1)
(2)
(3)
4-a-02
4-n-06 (
) N-2-08
( 6-n-7)
2007 5 11589667 11304616
11589667 1159 11304616 1130 115911302289()
88
4-n-07 N-2-11
( 2323
2323)
( 3-n-11)
1 3 13
1 313 1313
2 3
3 13 13
2 2323
23 2
13 23
()2
23
4 3 () 2 4 ()
(5 3 )(5 3 )
89
()
35 4 ( 4 ) 35
4 8() 3 3 4 34
3 34
354834() 8 34()
()
4-n-08
N-2-10
20 234581012151620 100
()()
(1) (9 1494 )
(2)
(3)
(4)
90
4-n-07 23
3 (3 )23 32
1 10
4-n-07
16301
4530
1630
4530
1725
3425
51252
125
22042
12142
99422
1542
23 32
98 3
278
21332133 ()
100 110
4-n-09
N-2-12N-2-16
( 5-n-06) 5-n-07
2 4 4 1 2
24
12
24
12
91
14
1242
28
( 4-n-07) 3 9
1 3 39391313 3913
( 5-n-04)
2510100
2233
441
24 ()
3468
()3468
58
2510100
4-n-10 N-2-16
4-n-09 2510 4-n-07() 23410
4-n-11 N-2-13
11000.01
(4-n-01)10 0.01 0.1 0.230.120.0130.0123
2 (
92
)
0.23
0.27 0.5 0.3 0.29()
1 0.01 100 0.1
4-n-12
N-2-13
4-n-09 4-n-11 3.25 24.56 5.32
4-n-13 N-2-24N-2-25
2 35 60 235 155 60 2 12 135 135602 15135 2 15 2880 28806048482422880 2 1 45
1 30
2 15 57
7 45 20 ( 7 50 )
10 30
8 22
23 8
93
4-n-14 () N-2-17N-2-18N-2-19N-2-25
3-n-14 1
10 10 1
3-n-15 3-n-16
1001 10001
4-n-15
N-2-17
1 1000 1 100000 ( 4-n-06)
5 1 ( 200 ) 7 1 400
1 30 15
4 300 3 800 7 1100 8 100
4-n-16
( 4-s-04) N-2-20
()
0
30 45 60 90 120 135 150180
4-n-17 N-2-21
94
1 10000
4-n-18 ( 4-s-09) N-2-22S-2-08
()2 4
()
4-n-19 N-2-23
1
4-s-01 S-2-04
()
2-s-012-s-05
95
()()
()
4-s-02 S-2-05
()
4-s-03 S-2-06
()
(1-s-043-s-06)
( 4-s-02) 4-s-04
( 4-n-16) N-2-20
96
4-s-05 () S-2-07
() 90 120
90 90 180 () 360 ()
4-s-06 N-2-20S-2-03
()
()()()
( 4 ) 4 4
4-s-07 S-2-02S-2-03S-2-04
4-s-08 S-2-03S-2-04
97
4-s-09 ( 4-n-18) N-2-22S-2-08
4-a-01 A-2-02
()(4-n-05)()()
3 10 6 310 6 106 3 (310)63(106)
8 6 5
2 60242
2511425411100111100
4-a-02 N-2-07A-2-01
()()
98
4-d-01 D-2-02
108
12
2
02468
101214
A B O AB
15
7 812
85
810
14 13
0
5
10
15
20
1
2
99
157 8 12 8
58 10
1413
0
10
20
30
15
7
8
12
8
5
8
10
14
13
0 5 10 15 20
4
4-d-02 D-2-02
5
130
136138
143
125
130
135
140
145
1 2 3 4
3
5
100
5. 5-n-01 N-3-01
0 23400021008400002803200000
2000
5-n-02 N-3-02A-3-01
() 2200 1800 500
(22001800500)3450031500()
() 3
5-n-03 N-3-02A-3-01
5-n-04 N-3-03
1-n-07()2-n-08()3-n-05()
5-n-05()
101
(5-n-07)
2510 3 11
5-n-05 N-3-03
(6-n-02)
5-n-06 N-3-06
4-n-09
63
3231
21 =
= 31
3933
93 =
= 31
93
93
3
1
=//=
5-n-07 N-3-07
(1)(2) 100(3) 2345 ( 12 18)
(6-n-03)
5-n-08 N-3-09
102
3-n-11
1 300 2 600
1 (12)
1315
1213
15( 2)
( 3)( 5)
5 1 52 10
12 5252
(4-n-18) 4-n-18
10 1 13
(10110) 1013103
103
122133
1 32
()23
3232112( 1 )
5 3253253
2 152
54
32
5432
534 2
5342
158
3254
15 1214 1
181815
158
5-n-09 N-3-10
6-n-04 (
)
312 4 312
14
3 12 4
72
14
78
m 1m
6-n-04
104
5-n-10
N-3-08
() 34
()
0.0003 0.00001 10 ()
5-n-11 N-3-09N-3-11
5-n-08
0.1 0.01
( 1101
100
5-n-12) 0.2( 210)
1.2(1210)
5-n-12 N-3-11 N-3-13
4-n-06 4-n-08
245810100
105
(6-n-06)
5-n-13 N-3-11 N-3-13
23410
106
5-n-14 () N-3-14
1 1
1 1 120
100 75
751000.75 10.750.25
500
53100 50053100
265
( 6-n-046-n-06)
100 1 751000.75 75
75 25 1751007525
500 75 500 275
10015012
2514753420
1540
2560
3580
45
10 110
75 600 60034450
17525
(
107
6-d-01)
5-n-15 N-3-19
5 30
31 15
2 30 1
5-n-16
N-3-19
1 1000 (
)
5-n-17
( 5-s-05) N-3-19
1 100 1 100 1 1000000
1 11000000 0.000001
1 10000 100 1
5-n-18
( 5-s-05) N-3-22S-3-06
3-s-06
()2
() 2
108
5-n-19
N-3-19
1 1000000
1 11000000 0.000001
5-n-20
( 5-s-07) N-3-20N-3-25S-3-05S-3-11
5-n-21 N-3-21
1
109
1 1000
1 1c.c.
110
5-s-01 180 S-3-02
180
180 60
45-45-90 30-60-90
5-s-02 S-3-02
()
5-s-03 S-3-01
180
14 90
18 45
13
120 16 60
180 360 ( 4-s-05)
5-s-04 S-3-03
()
()
()
111
5-s-05
( 5-n-18) N-3-22S-3-06
5-s-06 S-3-09
()
5-s-07 ( 5-n-20)
N-3-20N-3-25S-3-05S-3-11
112
5-a-01
N-3-02A-3-01
()(5-n-025-n-03)
41241042
12 37 12336 12784 3684120 3710 1210120 12(37) 123127
10 12 7 7 10770 12784 154 101222 227154 (1012) 7107127
312333
1239
3210
12
5-a-02
A-3-01
()(5-n-025-n-03)()
113
15 7 5 (157105)(105521) 5 ( 1553 )7 (3721)15751557
2-n-06 (632623)
4-n-04 48 3 1 8 3824 483848(38)48242
4-n-04 72 4 6 1 6424 724672(46)72243
603212601232532160
(6-n-056-n-08)
5-a-03 N-3-02A-3-01
5-a-01 5-a-02
4-n-044-n-05
5-a-04
A-3-04A-3-05
2-a-04(3-a-01)
x y
114
x y
8 13 8 x 13 x 1385
7 28 7 x 28 x 2874
8 x 13 x 516
x 1010 20 x 15
7 x 28 x 520
x 963 40 x 5
115
6. 6-n-01 20
20100 N-3-04
5-n-04 1 1 ( 3 )
()
60610(23)(25)2235 60154(35)(22)2235
( 6-n-02)20100
235711131719 100
6-n-02 N-3-05
(5-n-05) 6-n-01 6-n-01
(6-n-03)
6-n-03 N-3-05
1 14 15
116
6-n-04 N-3-10
(5-n-09)
()
4 13
413 1
13 1 3 13
3 3 12 ()
4 23
1313
23
2 23132 3 2 5-n-08
32 4234
326
3 25
152 () 7 12
325 715
25
12
(
117
) 1 12 25
1 12 1510
25
410
110
154 3 34 34
310
25 (
410 )
34
274 95
274
59
27549
154
50 1
100 212
9 30
1 2 1 50 2 100
a a 12 =50 a 2=50
a 502=100()
3235
910
910
53
32(35
53)
6-n-05 N-3-02A-3-01
6-n-06 N-3-10N-3-11
3 0.1100.01100
118
60.12 6(0.0112)60.01126001250
6-n-04 3.241.2324100120100324120
()13.3 1.8 7 0.7 71.80.712.60.713.3
( 13
0.3333)(6-n-07)
( 0.3 0.33 13)()
6-n-07 (
) N-3-12
(4-n-06)
(5-n-14)
32 18 1832 0.5625
56 56.3
6-n-08 N-3-02A-3-01
6-n-05
119
6-n-09 N-3-15
1 16 2 32 3 48
1 2 3 4 5 16 32 48
1:162:323:48 16:132:248:3 4:645:80
16 1 116
1 112
6-n-10 N-3-15
6-n-11
6-n-10 16 16 1 16 2 32 3 48
120
6-n-11 N-3-16
()(///)
60 5 300 5 60
80000 20 100 1
20 100 ( )80000
( ) 800002010040 (/) 40
4000 40 1 15 1
4000 4000
1540 ( 1 15 1 40 )
4000 1540 1500
1500
80 50 /
80 50 ( )
( ) 80501.6()
90 / 1
90 90
100060
90 100060
1500
121
1500
6-n-12 N-3-16N-3-17
100 20 25
5 25 10 50 15 75 20 100 () 5-n-14 5 1 0.2 4 54
15 1.5
(/)(/)(/) 1 / 160603600 3.6
1 3.6
( 6-n-09)
3.6 3.6
10003600
3.610003600 1 /
122
20 13
6-n-13 ( 6-a-04)
N-3-18A-3-02A-3-03A-3-04A-3-05
()
() 12 24
() 90 88
() 5 4 40
() 100 22
6-n-14 (6-s-03) N-3-23S-3-07
() 3.14
1418
123
6-n-15 ( 6-s-05) N-3-24S-3-10
6-s-01 S-3-01
180 ( 5-s-01) 360
6-s-02 S-3-04
( 50)()
6-s-03 (6-n-14) N-3-23S-3-07
(1213
23
14
16)
124
6-s-04
S-3-08
6-s-05 ( 6-n-15) N-3-24S-3-10
6-a-01 A-3-03
( 5-a-04 6-a-02)
6-a-02
A-3-04A-3-05
113 x 3 x
121
13
x 612 212 x 1
12 x 12 x
13
12
125
x 1253
34 x
35
6-a-03 A-3-06
a a a
a b a b
A h A h
6-a-04 ( 6-n-13)
N-3-18A-3-02A-3-03A-3-04A-3-05
6-d-01 D-3-01
(
88.6)
1.14 1.09 1.10 1.09 2.00 1.07 1.34 1.53 1.58 1
0
0.5
1
1.5
2
2.5
()
1
126
50 1 2
1 15 7 8 12 8
30 14 16 24 16
30%
14% 16%
24%
16%
0%
10%
20%
30%
40%
2
6-d-02 D-3-01
2 3
2 6 10 12 14 16 18 20 C 32 34.5 37 38 37 36.5 35
127
3
6-d-03 D-3-01
( 6-d-01) 50 1 3 4
15
78
12
8
3
128
30%
14%
16%
24%
16%
4
129
7. 7-n-01 100 N-4-01
100
(Eratosthenes)100
7-n-02
N-4-01N-4-02N-4-09
48
48 = 2 2 2 2 3 = 16 3 23 48 12346812162448 48 48 12346812162448
4872 72 1234689121824
3672 24
(7248)= 23 3 24
130
[7248] = 24 32 = 144
487290 (4872) = 24 (487290) = (2490) = 6
[4872] = 144 [487290] = [14490] =720
100 1 (2435) = 1 24
35 24 35
2 3
30 30 = 5 6 56 = 56 = 11 80
80 = a b a b a b 1 80 5 80 = 1 80 = 5 16 180 516
7-n-03
N-4-02
N-2-03N-2-06
424
212
381
386
387
193
387 ==
7-n-04 N-4-05
5 5
5 12.32
110 0 5 12.3
2
110
131
10 10 4 4 5000 5000 1000 1000
1325 4578 1038 4238 1325457810384238 =53 1325(4578)(1038)4238 =53 53
5 5 5 5
5 0 5 8 0 8 5858
7-n-05 N-4-05
a 0 a = a a 0 a = a a = 0 a = 0 0 0
31
131
1 = ()
31
131
1 =
10 6 10(6)
7-n-08
15 = 15 18 = 18 15 18 1518
7-n-06 () N-4-05N-4-06N-4-08
132
a a a
221
1 a
a a = a
a b a b a b a a a a a a ba + ab ba + a b
a a a a a ( a ) = 0
a b a (b ) = a b a (b ) = a b
ba + ba ( ba + ) = ba ba + ( ba ) = ba + ba = 0 ba ba + ba +
)( ba + )( ba + = ba ba ba +
ba + a b 2300298 =+ 598300298 =
( ) = = =
2 22 21
3 33 3
a a 0
7-n-07 N-4-08A-4-02
133
abba +=+ abba = )()( cbacba ++=++ )()( cbacba = cbcacba +=+ )( cbcacba = )( bcacbac +=+ )(
bcacbac = )(
b11 === cabc
ac
bacba
)(111 cbacb
acb
acba ===
cb
ac)(ba +=+1
)11(11cb
ac
ab
acaba +=+=+
baba =+ )( baba += )(
1 98076376 = 980( 76376 ) = 980300 = 680 2 25 89 4 = ( 25 4 ) 89 = 8900
3 76
3976
39372
1337
213 =+=+=
4 5839
5819
1151
5819
1514
151
5819
1514 ==+=
5 87
81
1492
162
4947
491
161
24947 ==+=
6 baababa =+=+ )( 7 1=
ac
cb
ba
( a 0 b 0 c 0)
8 bac
bc
acb
a == (b 0 c 0)
1 1 1 1 1 1
134
7-n-08 N-4-07
0 ()10030101003010
A 2A(2)
2 22 |2| = 2
23 5 |32| | 2(3)|
310 3 10 310 3 10
a b 5 10 a b
7-n-09 N-4-07A-4-08
x 1 1
3x 3
31
135
a 0 a 0 ( a 0 a 0 )
( c 0 c 0 )
( a b )
7-n-10 N-4-09
na n a 2222225 =
4
44
3
2
3
2
3
2
3
2
3
2
3
2 ==
5
5
2
1
2
1
2
1
2
1
2
1
2
1
2
1 ==
(1) 6 = (1) (1) (1) (1) (1) (1) =1
a 0 0a = 1 3248 4 = [36 48] = 24 32
( )22
4
42
22
42
2
4
24
3
13
2
2
1
3
2
2
1
3
4
2
1
3
4
2
1 ====
3
9
8
2
9
8
0 a 1 n na
3
9
10
2
9
10
a 1 n na
a 0 -a
-c 0 c
a b
1
1
136
7-n-11 N-4-09
mnmn aaa += nmmn aa =)( nnn baba = )( m n 0 a b
mnmn aaa = a 0 n m 0a = 1 a 0
7-n-12 N-4-10
na 10 1 a
137
5 94
95
45
94
95 =
425
455 =
A B
A = B 23
A B 23
a b c a : b = 3 : 2 c : b = 8 : 7
a c a b 23 a b c b
78 a c
( 7-n-15 )
() 3% 500 15%3500 = 3% 500 7% 1500
%606.0)1500500(%)71500%3500( ==++ 180 cm 1 m 150 cm
80 56 110
90 km 45
138
50000:1
10% 1000 100 100 100 100
6 740 6 820 : = 740 : 820 = 37 : 41 75 90 1000 ( 1000 ) : = 90 : 75 () = 6 : 5
7-n-14 N-4-04
dcba :: =
dc
ba = bcad =
dcba :: = dbca :: = dcba :: = cka = dkb = xx :)1(4:3 = 3 x = 4 x 4 x = 4 7:3: =ba 24= ab ka 3= kb 7= 100=AB D AB 5:2: =DBAD
kDBkAD 5,2 ==
7200
522
522 =+=+= ABABkk
kAD
7500
525
525 =+=+= ABABkkkDB
7-n-15
N-4-03N-4-04
2:1: =ba 4:3: =cb 8:6:3:: =cba
139
8:6:3:: =cba 863cba ==
8:6:3:: =cba kk,ck,ba 863 === 3400 3 : 6 : 8
cba 543 == 51:
41:
31:: =cba
ABC AB BC CA 101215
151:
121:
101
= 6 : 5 : 4
A B 25 : 12 C B 3 : 4 A C C B 3 : 4 B C 4 : 3 = 12 : 9 A B C 25 : 12 : 9 AC 25 : 9 5 : 3 A B 25 : 12 C B 3 : 4
A = B x1225
C = B x43
925
34
1225
43
1225
43
1225
43
1225
====
=B
B
CA
A C 25 : 9 5 : 3
8 9 10
5 6 4
100 500 1000 16500 100 500 1000 5 : 4 : 3
140
20 10 300 15 20
7-a-01 A-4-01A-4-02
a b c x y z x 2 x x (1) x
y 2 x x 2 2 x 2 x y 1 x 1 x 1 x x (1) x (2) x x 2 x y
74
74 xx = x
74 x
74
74x 4 x 7
74
74
74 xxx ==
5 x 18 x 2 2 x y 5 x 2 y 1
a b =b aa (b c) = a b a cx y x = x ( y 1)
7-a-02 A-4-03A-4-04
x y
5 x 5 x 5 x 2 y ( 5 x 2 y )
x2 y 2 14
7-a-03
A-4-03A-4-06A-4-07
32
141
2 8 x 2322 x = 8
50 1 7 x 7 x 1 = 50
() 12 24 = 12 =(1224) x 1224 x = 2 (12 x )
7-a-04 A-4-05 A-4-07
( 0)
a =b a c = b c a c =b c a c = b c a c = b c ( c 0)
7-a-05 A-4-07
a=b b = a 23 = 5 5 = 23 2 = 3 x 3 x = 22 = 8 x 8 x =2
3 x= 6 x= 6 (3) x = 2
x 8 = 7 x 6 (1) 2 = 8 x (2) 8 x= 2 (3) x= 1/4 (2)(3)()(2)
142
7-a-06
A-4-03 A-4-09
x y x y
60 5 2 5 x2 y 5 x2 y = 60
3 2 3 9 3
x 9 x3 2 x3 3 9 x3 = 3 ( 2 x3 ) x= 4 33 11 y 3 y ( y 3) 2 9 3 3 y = 9 ( y 3) 23 y = 11 33 11
75 5 3
6 5 400 8 : 9
7-a-07
A-4-03 A-4-12
x y x y
() 100 22
x y
143
10046 =+ yx 22=+ yx
7-a-08 A-4-12
7-a-09 A-4-01 A-4-04
() 0 3 6 9 12 15 18
( ) 25 45 65 85 100 100 100
100
f( x )g( x )
7-a-10 A-4-01 A-4-04
y x y = a x+b a 0 y x y = c
3259 += xy Cox Foy
7-a-11 A-4-10
()
144
()
() 100
7-a-12 A-4-11
32
59 += xy
7-a-13 A-4-11
cbyax =+ a b 0
dy =
7-a-14 A-4-11 A-4-12
7-a-15 A-4-08
a 5 (1) 5 (2) a 5
a b a b 0 a b a b 0
7-a-16 A-4-03 A-4-08
145
cbax + bax + c fedx + edx + f dbaxc +
20 1 50 x 20 x 1 50
100 30 20 x x 20 x +30 100
7-a-17 A-4-08
( a b b c a c a b b c a c )
x 582 x 865 x 72 x 62
( 0)
3 5 10
x 3x
5x
10
3x
+5x 10
475
8150 =x ()
a d x
(1) a 0 cbax + a
bcx
bax + c x a
bc
(2) a 0 cbax + a
bcx
bax + c x a
bc
146
dbaxc +
7-a-18 a x b y=cxd A-4-11
baxy += x bax +
147
8.
8-n-01 N-4-11N-4-12
a >0 a a () a
a a
2)2( 2 = 3)3( 2 =
3 3 3 3 3 3
32 =x 2 3 2 3
2 3 2
2 3
2 3
13169 = 4248 2)2(2256 ===
353575 2 ==
23)
23(
49 2 ==
36
3332
32 =
=
0,0 >> ba baba =2 baab =
ba
ba =
3232 2 = 3223 >
148
8-n-02 N-4-11
132
1.4< 2
149
8-n-04 N-4-13
179182185 2471116
na 1357
12 = nan 1248 12 = nna na na na = 43 n 5a = 435=11
na nba n
8-n-05
N-4-13N-4-14
12345 n
36912153 n
581114173 n +2
1
3
3 2 3 2
n dnaan )1(1 += 807774 14 7 5 7 8 a 7 8 1 a
5 8 5 d 5313
8-n-06 N-4-13N-4-14
naaaa ++++ L321 n dnnnan
aaS n
nn +=+= 2
)1(S 2
)(1
1 d
150
++++ L)27()29(31 6 285
12 n = 528 n
8-s-01
S-4-01
8-s-02 S-4-01S-4-04
8-s-03 S-4-06
180 360
180
360 n 180)2(n 3n
n 360
151
n
8-s-04 S-4-01S-4-04
L P PQ
L L Q Q PQ L
PQ P L P
Q PQ P L
8-s-05 S-4-01S-4-07
//
L M , N P Q
L M N
L M N
L M N
L M N (1)
(2)
(3)
M N
L // M L M
152
8-s-06 S-4-08
()
()
8-s-07 S-4-09
ABC DEF ABC DEF ABC DEF
ABC DEF CBA ,, FED ,,
SASSSSASAAASRHS y
y
y
153
y y y y
8-s-08 (Pythagorean Theorem)( 8-a-05) S-4-05A-4-15
( 222 bac += )
SSS RHS SSS
154
8-s-09 S-4-05A-4-10
A ( a , b ) B ( c , d ) 22 )()( dbcaAB +=
8-s-10
S-4-08S-4-09S-4-11S-4-12
;
8-s-11 S-4-10
()
155
8-s-12
S-4-02S-4-03S-4-04S-4-08S-4-12S-4-13
SSS
30 60 90 45 45 90
8-s-13
S-4-02S-4-04S-4-07S-4-13
()
156
8-s-14
S-4-08S-4-12S-4-13
8-s-15 S-4-13
8-s-16
S-4-18
157
8-s-17 S-4-19
ABCD CDAB = BCAD =
BD BCAD //
CBDADB = () BDBD = ()
CDAB // BDCABD = () BCDABD (ASA ) BCAD = CDAB =
8-s-18 S-4-03S-4-04
8-s-19 S-4-04
= () 2 = =
21
()
a 243 a
8-s-20 () S-4-17
A
B C
D
158
8-s-21 S-4-17
= 2
360q q
= 360q
= 21
q
8-a-01 A-4-13
bcaccba +=+ )(
222 2)( bababa ++=+ 222 2)( bababa += 22))(( bababa =+ bdbcadacdcba +++=++ ))((
(1) 99913100)3100()3100(97103 22 ==+= (2) 9801111002100)1100(99 2222 =+== (3) 98011)199()199(119999 2222 =++=+=
8-a-02 N-4-12
8-n-03
8-a-03 A-4-14
2312 xx
159
123 2 + xx 23x 23x x2 1 3 2 1
8-a-04 A-4-14
8-a-01
8-a-05 (Pythagorean Theorem)( 8-s-08) S-4-05A-4-15
8-a-06 A-4-16
)22)(2(422 2 += xxxx (1) )1)(42( += xx (2) )1)(2(2 += xx (3) (1)(2)(3)
8-a-07 A-4-16
)3))(1()2(()3)(1()3)(2( ++=+++ xxxxxxx = )3)(32( + xx )1)(()1()1( 222 ++=+++ xbaxbxa
)3)(6()3(6)3(18632 +=+=+ xxxxxxxx
160
)()( bdbcadacbdbcadac +++=+++
)()( dcbdca +++= ))(( badc ++=
8-a-08 A-4-16
)2)(1(232 =+ xxxx
)5)(5(252 += xxx 22 )1(12 +=++ xxx 22 )2(44 =+ xxx
120232 + xx 23 120 8152454031201120 ==== )8)(15(120232 =+ xxxx
8-a-09 A-4-06A-4-16
12 4 x x 4 xxxx 4)4( 2 +=+ ( )
1242 =+ xx 02 =++ cbxax 0a
8-a-10 A-4-16
161
)3(3)3)(1( +=+ xxx 03 =+x 3=x 0 3=x x 3 03 +x 3+x 31 =x 4=x 3=x 4
0=ba 0=a 0=b
0)7(5)7( 2 =+++ xx 0)5)(5)7(( =+++ xx 012 =+x 05 =+x 12=x 5=x 01)7(2)7( 2 =++++ xx 0)1)7(( 2 =++x 0)8( 2 =+x 8=x 0)3()7( 22 =++ xx
0))3()7))((3()7(( =+++++ xxxx 0)102(4 =+x 5=x
201
21
11 =++ xx
201
)2)(1()1(2 =++
++xxxx
201
)2)(1(1 =++ xx
20)2)(1( =++ xx 3=x 6 x 1 x 2 0
8-a-11 A-4-16
162
02 =++ cbxax
aacbbx
242 = 0a acb 42
2x 1 1 y 182 =+ xx y 232 =+ xx
8-a-12 A-4-16
180 20 / 45
x / )20( x /
6045180
20180 = xx )20( xx
)20(43)20(180180 = xxxx
014400603 2 = xx 0)60)(80(3 =+ xx 80=x 60=x 80=x 60=x
80=x 60=x
6045180
20180 = xx
80=x
163
80 / 60 /
164
9. 9-s-01 S-4-14
O A OA A OAAO 2= AO A 2
O 2 O 2
O AB 2
O ABC 21
6-s-02
r
r l lr
r
165
9-s-02 S-4-15
ABC DEF ABC DEF
ABC DEF A B C D E F
n
9-s-03 S-4-15
AASASSSS
ABC 090=A AD BC ABC DBA DAC
BDBCAB =2 DCBCAC =2 CDBDAD =2
ADE BCE
9-s-04 S-4-07
A B
C
D
E
166
ABC D AB E AC DE BC
ECAEDBAD :: = ACAEABAD :: = ECACDBAB :: = BCDEABAD :: =
()
ABC D AB E AC
ECAEDBAD :: = ACAEABAD :: = ECACDBAB :: =
DE BC BCDEABAD :: =
A
D
B
C
167
41
21
L 3 L 4 L 5 L 1 L 3 L 4 L 5 ACE L 2 L 3L 4L 5 BDF
DFBDCEAC :: =
9-s-05 S-4-15
ABC D AB E AC DE BC
ECAEDBAD :: = ACAEABAD :: = ECACDBAB :: = BCDEABAD :: =
ABC AD A BC D DCBDACAB :: =
168
() : C AD AB E AD
CE CADACE = BADAEC = )1(L
DC:BDAE:BA = Q AD A CADBAD = )2(L (1)(2)
AECACE = ACAE = DCBDACAB :: =
() : DG AB DF AC
Q D A DFDG = Q ADB : ADC = ACAB : ( DFDG = ) AH BC
ADB : ADC = DCBD : ( AH )
ACAB : = DCBD :
9-s-06 S-4-17
169
9-s-07 S-4-17
()
()
9-s-08 S-4-16S-4-17
170
9-s-09 S-4-16S-4-17
ABC s r ABC 2sr
r () 2
9-s-10 S-4-16
9-s-11 () S-4-08S-4-13S-4-17
()
9-s-12 S-4-19A-4-20
8-s-17
171
1 O ABCD
O ABCD
AB AB BC BC
CD CD DA DA AB + BC + CD + DA
AB + BC + CD + DA O ABCD
()
()
2 AB CD O AC = BD
AD
AB CD BADADC = AC = BD
() () ()
3 cba 222 cba =+ bc 2a
222 cba =+ 222 bca = b)b)(c(c +=
()
()
172
bcb)(ca +=2 bc 2a
9-s-13 S-4-01
L A P A P L
173
9-s-14 S-4-01S-4-02
9-s-15
S-4-01S-4-04
9-s-16 S-4-01S-4-04
9-a-01 A-4-04
cbxaxy ++= 2 ( 0a ) y x 2xy =
y x
9-a-02 A-4-18
174
y x
2axy = ( 0a )
kaxy += 2 ( 00 ,ka )
2axy = 2h)a(xy =
( 00 ,ha ) 2axy =
kh)a(xy += 2 hx = 0>a ( kh, ) 0
175
9-d-01
D-4-01D-4-02D-4-03
(9-d-029- d-03)
1
1 2 3 4 5 6 7 8 5 64 35 78 36 43 44 82 9 10 11 12 13 14 15 16 83 48 52 55 58 64 65 68 17 18 19 20 21 22 23 24 69 70 74 35 79 80 78 45 25 26 27 28 29 30 47 33 84 75 85 89
2 0-20 20-40 40-60 60-80 80-100 1 4 8 11 6
30 0~20 0 20
20~40 20 40
176
40~60 40 60
60~80 60 80
80~100 80 100
3 0-20 20-40 40-60 60-80 80-100 0.03 0.13 0.27 0.37 0.20
4
0-20 20-40 40-60 60-80 80-100 1 5 13 24 30
5
0-20 20-40 40-60 60-80 80-100 0.03 0.16 0.43 0.80 1.00
13 43%
1 ( 2)
177
02468
1012
0-20 20-40 40-60 60-80 80-100
1
0%10%20%30%40%
0-20 20-40 40-60 60-80 80-100
2
()( 3 4)( 5 6)
02468
1012
0-20 20-40 40-60 60-80 80-100
3
178
0%
10%
20%
30%
40%
0-20 20-40 40-60 60-80 80-100
4
5
6
()()
179
9-d-02 D-4-01D-4-03
{ 1, 2, 3, 4, 5 } { 1, 2, 3, 4, 500 } 102
0
9-d-03 D-4-02D-4-03
89 5 84
1 2 3 (Q 1 Q 2 Q 3 )Q 1Q 2Q 3 2 3 1 Q 3 Q 1 Q 1 Q 2 Q 3 4564.578 33
7 Q 1 Q 3 8
180
1 25 (9-d-04) 3 75
( 1)
9-d-04 1025507590 D-4-03
8
7
181
25 Q 1 50 75 Q 3
10 90 10 158 90 176 10 158 10 176
9-d-05 D-4-04
()
0 1
()
10
100
80
182
()
21
183
1.
()() (1)()
A.
0
()
a.
b.()
c.
d.
e. f.
a.
b.
184
c.
d. e.
B.
()
a.
b.
c.
d.
()
185
a.
b. c.(ccml)
d.
C.
/
a.
b./
c.
d.//( 1)
186
D.
()
7527 205070 25 40 80
(2)()
() A.
()
187
B.
C.()
()()
a. 2
b.
c.
d.
D.
()()
188
2.
(1)()
A.
B.
()()
(2)()
189
A.
B.()
C.()
AA
190
3. (1)()
82
A. , < , > +, -, , , , , x, y
B.
, < , >
C.
D.
()
E. (2)()
()()() A.
(
191
)
()()
B.
()
()
C.
()
D.
x y
y=f(x) y=f(x)
()
192
4.
(1)
(2)
(3)
(4)()()
5. (1)
3443 +=+ 7
193
()
A. B.
A
B abba +=+ 0180
(2)
()
194
()
()
195
92
6 13 09204608060
(m) (cm) (km) (mm)
1 1000 1 100 1 10
(kg) (g) (t)
1 1000 1 1000
(l L) (mlcc) 1 1000
360
(m2) (cm2) (km2)
1 100 1 100 1 106 1 104
(m3)
(cm3) 1 106 1 1000
(d) (h) (min) (s)
1 24 1 60 1 60
196
1.
1234567890
()
197
()()
()
()
198
%
()
199
()
()
x y
( )
( )
200
()
n
( )
()
201
2. () 43=7 4 4 4 4
4 4 4 4 4
4 4 43=74 3 7 43=14 3 1 43=124 3 12 144=3214 4 3 2
0 1243 123
0 02468
202
13579 a0|a|=a a a|7|=7 a0
|a| =a |7|=(7)=7
q p pq p0p
q 0q p q p q p
312
()
a ba b b a
a a
a a
1 1 1 1
55=2525 5 a 2=bb0 a b () 22=4(2)2=4
22 4 2 2 b
() 5 0() 5 1 0()325587
203
3260003.1416 3.14 ( 7 )
5643 2600
3:4 3 4 0.75
100 % 0.23=23% x y y = kxk ()
xy 0 x y xy=kk 0 x
y ()
90 90 90 180 360 180 90
204
()
() 180
180
90 ()
L MN L M N
L
M 1 2
N
7 8
1 52 63 74 8
3 4 5 6
205
3 54 6 3 64 5
3.14 ()
206
( 0)
(1)(2)(3)(4) -3x6 x6(-3)
x-2
AB A B B A
,.....,,, 15
6143 2 ++ xxxx
432 + xx ,1 , 3 ,() 4
0 bax + a, b ba cbyax ++ a, b, c a, b 0
cbxax ++2 a, b, c 0a
02 =++ cbxax acbD 42 =
207
()
()
50
255075 1 2 3 2
3 1
bar chart
pie chart
histogram
1 2 3 box chart 50%
208
()
()()()
()D-4-01D-4-02D-4-03D-4-04D-4-01D-4-02D-4-03D-4-04