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5 31 36 13

a b b 0 15 0,-3 , , 0.54, 3.512, .. 2

, , 4.323323332 , ...

4.23 , 0.25000 3 1. 2. 3. ..

Integer

... 1, 2, 3, 1 1 a a -a -a a

3 -3 -3 -(- 3) -(-3) -3 -3 3 -(-3) = 3 ...

a = 4 4 -4 a = -4 -4 -(-4) = 4 -1,-2,-3, ...

... 0 2 + (-2) = 0 * 0 -0 = 0

... 1 1.) 23 2.) -543.) -314.) -(-43)

1.) 23 = 2.) -54 = 3.) -31 = 4.) -(-43) =

-23314354

... 2 2, 4, 6, 8, 10, 2 1, 3, 5, 7, 9,

... 20 1, 2, 4, 5, 10 20

... 12 18 12 1, 2, 3, 4, 6 12 18 1, 2, 3, 6, 9 18 12 18 1, 2, 3 6

2 10 12 10 1, 2, 5, 10 12 1, 2, 3, 4, 6 12 10 12 1 2

...

...

1

... 2 1 2 1 2 2 13 1 13 13

n n n n 1 n n n ...

... n p n p n p p

3 59 1. 59 22 = 4 < 59 , 32 = 9 < 59, 52 = 25 < 59 , 72 = 49 < 59, 112 = 121 > 59

...( 59 )

2. 2, 3, 5 7 59 59 59 ...

1 100 1 1 2 2 3 3 5 5 7 7

...

21 22 23 24 25 26 27 28 29 30 ...31 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 1-100

1 - 100 25 2357111317192329313741434753616771737983899397...

... 4 108 1 2)108

3 = =

... 2 108 12 9 3 4 3 33 2 2 3 3 108 =

... ... 12 1, 2, 3, 4, 6, 12 30 1, 2, 3, 5, 6, 10, 15 30 12 30 1, 2, 3 6 12 30 6 6 ...

... 5 .. 42, 60 120

42 1, 2, 3, 6, 7, 14, 21 4260 1, 2, 3, 4, 6, 5, 10, 12, 15, 20, 30 60120 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 120

...

... 42, 60 120 1, 2, 3 6 42, 60 120 6 6 ...

... ...

...2. 3. ...

... .. 12, 28 40 2 ) 12 28 40 2 ) 6 14 20 3 7 10 ... 12, 28 40 2 2 = 4

... 6 .. 24, 36 48 2 ) 24 36 48 2 ) 12 18 24 3 ) 6 9 12 2 3 4 ... 24, 36 48 2 2 3 = 12

... ... 1. ... 2. ...

... ... 12 32 12 = 2 2 3 32 = 2 2 2 2 2 ... 2 2 ... 12 32 2 2 = 4

... 7 ... 18 30 18 = 2 3 3 30 = 2 3 5 ... 2 3 ... 18 30 2 3 = 6

... ...

... 12 12, 24, 36, 48, 60, 72, 30 30, 60, 90, 12 30 60, 12 30 660 ... 12 30 60

... 8 ... 15 25 15 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 25 25, 50, 75, 100, 125, 150, 15 25 75, 150, 75 ... 15 25 75

... ... 1. ... 2. ...

... ... 8 20 8 = 2 2 2 20 = 2 2 5 ... 2 2 2 5 ... 8 20 2 2 2 5 = 40

... 9 ... 18 30 18 = 2 3 3 30 = 2 3 5 2 3 3 5 ... 18 30 2 3 3 5 = 90

... 1. 2.

...3. 4. ...

... ... 8, 12 32 2) 8 12 322) 4 6 16 2) 2 3 8 1 3 4 ... 8, 12 32 2 2 2 3 4 = 96

2 2 8 2 3 3

... 10 ... 8, 30 42 2) 8 30 423) 4 15 21 4 5 7 ... 8, 30 42 2 3 4 5 7= 840

3 4

0, 1, 2, 3, 4, 5, 6, 7, 8, 9 10 10

225415

11 58,936 58,936

0 = 021 = 122 = 1023 = 1124 = 10025 = 10126 = 11027 = 110128 = 100029 = 10012 10 = 10102 11 = 10112

12 110102 110102 = (1 24) + (1 23) + (0 22) + (1 2) + (0 1) = (1 16) + (1 8) + (0 4) + (1 2) + (0 1) = 16 + 8 + 0 + 2 + 0 = 26 110102 = 26

13 26 2 ) 262 ) 13 0 2 ) 6 1 2 ) 3 0 2 ) 1 1 0 1 26 = 110102

5 0, 1, 2, 3, 4

0 = 051 = 152 = 253 = 354 = 455 = 1056 = 1157 = 1258 = 1359 = 145 10 = 205 11 = 215

14 1325 1325 = (1 52) + (3 51) + (2 1) = (1 25) + (3 5) + (2 1) = 25 + 15 + 2 = 42 1325 = 42

15 42 5 ) 42 5 ) 8 2 5 ) 1 3 0 1 42 = 1325

2 1. 0.2500 0.25 4.750 4.75 ...

2. 0.777 0.7 0.3181818 0.318 ...

161.) 2.)

1.) 2 ) 17 16 10 100 2.) 12 )73 72 100 96 40 36 40 36 40

08.506.0833.

17 4 1 23 2 41 3 34 4 12

1 23 25 2 41 40 3 34 35 4 12 15 110 115

1 = 4 1 = 2 1 = 12

19 3 1 = 4 3 = 4 3 = 12 1 = 2 12 = 2 12 = 24 1 = 12 24 = 12 24 = 288 3 = 288

10 1 35 4 10

a b a : b - a b a b ab

100 % 1) 5 5 %

2) 27 27 %

20 9,400 15%

100 85 15 9,400 x

= 7,990 7,990

= 15 8 = 4 + 3 , 4(x + 3) = 20

21 x + 12 = 25 x + 12 = 25 10 10 + 12 = 25 22 = 25 13 13 + 12 = 25 25 = 25 13

22 3(y - 1) = 24 3 ( y - 1) = 24 9 3(9 - 1) = 24 3 8 = 24 24 = 24 9

1. a b a = b b = a 2 = -(-2) (-2) = 2

2. a , b c a = b b = c a = c x - 2 = 8 8 = 2x x - 2 = 2x3. a , b c a = b a + c = b + c 12 = 6x 12 + 4 = 6x + 4

4. a , b c a = b ac = bc 6 = 3x 6 x 3 = 3x x 3

1. 2. 3. 4. 5.

23 2 564 3 7 108

x 108 x 3 3x 3 7(108 - x)

3x + 7 (108 - x) = 564 () 3x + 756 -7x = 564 () 756 - 4x = 564

756 - 4x = 564 (-564) () (756 - 4x ) + (-564) = 564 + (-564) 192 - 4x = 0

192 - 4x = 0 (-192) () (192 - 4x ) + (-192) = 0 + (-192) - 4x = -192 -1 4x = 192

= x = 48 144 420

x 48 3x + 7 (108 - x) = 564 3(48) + 7 (108 - 48) = 564 144 + 420 = 564 564 = 564 x = 48 x = 48

, , < >

8 3x-4 > 18 x 8 2 3x-4 > 8 x 2

y 4 4 x 10 10 x+3 > x+1 x+5 < x

1. a , b c a > b b > c a > c

a = 2x , b = 3 , c = 5-2x

2. a , b c a > b a+c > b+c

a = 2x , b = 5 , c = -5

3. a , b c 3.1 a > b c > 0 ac > bc

a = x , b = 3 , c = 2

3.2 a > b c < 0 ac < bc

4. a , b c a+c > b+c a > b

a = 5x , b = 10 , c = -2a = 12x , b = 25 , c = 2

5. a , b c 5.1 ac > bc c > 0 a > b

5.2 ac > bc c < 0 a < b

a = 2x , b = 5 , c = 3a = 4x , b = 12x , c = -1

24 4x-3 > 2x+3 4x-3 > 2x+3 -2x 4x-3-2x > 2x+3-2x 2x-3 > 3

3 2x-3+3 > 3+3 2x > 6 2x > 6 x > 3 3

25 x - 4 < 20 4 x 4 + 4 < 20 + 4 x < 24 24

1 a n a n a n an n an a n

261.) 2 2 2 2 22.) 25 53.) 625

1.)2.)3.)

a , b , c

abc 2abc

c2 = a2 + b2* c

27 c a = 12 , b = 5c2 = a2 + b2ACBbca

c2 = a2 + b2 c2 = 122 + 52 = 144 + 25 c2 = 169 c = = c = 13 c = 13

1.) 3, 4, 52.) 5, 12, 133.) 6, 8, 104.) 7, 24, 255.) 9, 12, 156.) 12, 16, 207.) 11, 60, 618.) 20, 21 29

28 ABC A(1, 1) , B(4, 1) C(3, 3) ABC X 5

0 1 2 3 4 5 6 7 8 9 10 YXCAB

ABC X 5 A(1, 1) (1 + 5, 1) (6, 1)B(4, 1) (4 + 5, 1) (9, 1)C(3, 3) (3 + 5, 3) (8, 3) ABC X 5

(a , b) a b ( a , b ) ( b , a ) a = b (a , b) = (c , d) a = c b = d

29 () ()12345246810

(1, 2) , (2, 4) , (3, 6) , (4, 8) , (5, 10)()

= (2 )+ = = =

= = = (2 )+

= h r

h r = = = + = + = l

30 6 7 = 3 7 = = = 66 = 66

31 20 30 50 = x x = 20 x 30 x 50 = 30,000 1,000 = 1 30,000 = = 30 30

32 1.2 1.5 80 1.2 = 120 1.5 = 150

= x x = 120 x 150 x 80 = 1,440,000 = = 1,440 = x 1,440 = 1,080 = 1,440 - 1,080 = 360 360

33 O OA 3 O OA OA3.P

OA 1.5 O OA3P.

3 14.14

1 a n a n a n an n an a n

1. 2. 3. 34 1.) 33 2.) 54 3.) 72

35 x y = 3y = 27 x + y = 3y = 27 = = 3 3 3 3y = 33 = y = 3

x = 4 x + y = 4 + 3 = 7

36 3.5 x 10-4 5.8 x 103 ( 3.14 = x ) =

= x = x 3.5 x 10-4 x 3.5 x 10-4 x 5.8 x 103 = 3.14 x 3.52 x 5.8 x 10-5 = 223.097 x 10-5 = 2.23097 x 10-3

c2 = a2 + b2 BC = c AB = a AC = b

BAcC

37 43 , 281 , 6,500, 91,200 43 40 281 300 6,500 7,000 91,200 90,000

38 4,152,367 4,152,367 4,000,000 4,152,367 4,200,000 4,152,367 4,150,000 4,152,367 4,152,000

39 1) 9.478 2) 9.578 3) 12.706 5 9

5 1 9 10 5 1 12 131)2)3)

45 20 45.20 70 89 70.89 23 20 23.20 45.20 + 70.89 + 23.20 + 32 171.29 171 40

41 9,492 15% 15 % 100 15 9,492 X

100X = 9,492 x 15

1,424

42 15 5.4

2rh 5.4 = 2.7 = 15 = 2 3.14 2.7 15 254.34 255

1 = 3 (1 )2 = (3 )2 1 = 9

43 57 9 1 57 x

1 . = 100 . (1 . )3 = (100 .)3 1 .. = (102)3 ..

44 2 . X 2 . X 2 . = 8 200 . X 200 . X 200 . = 800 = 8 X 102 X 106 = 8 X 108

45 8 6 c2 = a2 + b2 x x2 = 82 + 62 x 6 . x2 = 64 + 36 = = x = 10 11

8 .

46 6 8 ABC ~ EBD 1 = 3 8 = 24 E B D C AC = 18 18 6 8 12 24

1 ax + b = 0 a , b a 0 2x+3 = 0

47 40 50 10

X x + 1 x 50x x + 1 40(x + 1) 10 50x - 40(x + 1) = 10 50x - 40x - 40 = 10 50x-40x = 10 + 40 10x = 50 X = 5 5 10

x = 5 50x - 40(x + 1) = 10 50(5) - 40(5 + 1) = 10 250 240 = 1010 = 10 x = 5

48 20 .. 30 .. 50 .. = x x = 20 x 30 x 50 = 30,000 1,000 = 1 30,000 = = 30 30

( = ) 5 + 4 = 9 x + 1 = 2

49 40 3 8 3 8 40 (3 x 40)+(8 x 4) = x 120 + 32 = x 152 = x 152 152

1 ax + b = 0 a , b a 0

50 475 1,456

x 2 2x 475 x 4 4(475 - x) 2x + 4(475 - x) = 1,456 2x + 1,900 4x = 1,456 1,900 2x = 1,456 1,900 1,456 = 2x 444 = 2x 222 = x

2 x 222 = 444 4 x 253 = 1,012 1,456 222 475 222 = 253

51 ABC AC c2 = a2 + b2 172 = x2 + 152 289 = x2 + 225 289 - 225 = x2 64 = x2 = = x = 8 AC = 81517xACB

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