Junior High Math

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