tefchos a solutions.pdf

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  • B

    2013 14

  • :

  • :

    :

    9

    1. () () () () () 2. () > () <

    () > () > () > () <

    3. () 5 () 47 () 21 () 7 () 23 () 0 () 13 () 72 () 24 () 0 () 7 7

    12 () 1 2

    15

    () 5 518

    () 1 521

    4. () 0 () 5 () 0 () 20 () 14 () 21 () 6 () 7 () 4 () 24

    5. = 10 6. (32,48,80) = 16, (32,48,80) = 480 7. () 4 () 4 () 27 () 1 () 1 () 1

    49 () 25 () 6

    () 64 () 225 8. () (11)8 () (6)5 () 220 () (3)4

    () 40 () (1,2)3 () 32

    14 () 212

    () 24 () 36 9. () = 10 () = 11 () = 8 10. 11. () = 1 () = 4 () = 2 () = 5

    () = 6 () = 4 () = 0 () = 7 12. () () () () () () () () 13. () = 55 () = 35, = 145 () = 22 () = 20 () = 65, = 115

  • :

    14. () = 60, = 60 () i. iii.

    15. () = 4, = 3 () = 8, = 2 () = 72, 1 = 2 = 18 16. ()

    = 72 = 108 ,

    ()

    = 45 = 45 = 135 ,

    17. () = 40 () 1 = 2 = 30 = 30 = 30

    18. ()

    (0,3) (3,0) (0,0) ,

    () = + 3 19. () (0,0) 20. () = 20 () = 5 21. () = 7

    10 () = 400 () = 56

    22. 32000 23. 12% 24. () = 1, () = 1

    2, () = 1

    2, () = 5

    6, () = 0

    25. () 40 () 30 () i. 14 ii. 7

    10

  • :

    1:

    - 19

    1. : +2, 37, 6

    , 223

    , 1234, 5

    3.

    -

    +32

    8

    3

    8 2 2

    22 1 22 4 335 3 35 8

    2

    73 + 4 323

    1

    4 1

    4 1

    4. () 3 () ..22, 14

    3 () 32 () .. 43 5. () = 2 () = 4, = 6 6. 223 7. () () ()

    () () ()

    24

    1. () v () vi () ii () i

    2.

    2 5 : 2 43 3 62 15 162 8 41 82 163 402 325 164 82

    3. () 6 () 2 () 2 () 52 () 73 6 () 5

    32

  • :

    4. () 25 () 125 () 313 () 653 () 63 () 1055 () 46 () 424 () 125 () 3

    8

    5. () 6 () 2 () 2 () 74 () 63 () 1

    23

    6.

    2 62 2 0 22 42 52 22 32

    7. () 42 () 192 () 32 () 7 8. () 102 () 923 () 85 () 93

    () () 63 () 52 () 67 9. = 9 10. () 32 () 132

    30

    1. () 3 + 32 + 2 () 4 + 43 22 + 1 2. () 2 + 7 () 32 + + 6 () 22 + 3 () 32 3 + 2 () 52 2 + 1 () 2 + 6 3. () 103 22 11 + 11 () 53 + 2 7 () 22 + 7 + 3 4. () 3 + 2 + 5 () 2 + 2 4

    () 2 5 + 9 () 1 5.

    () 32 8 4 + (92 + 8) = 122 9 + 4 () 83 + 212 7 93 + 72 + 5 + 3 = 3 + 142 + 5 10 () (2 + 3) + 22 + 3 = 2 + 6 () (2 2 + 3 ) (2 3 + 3) =

    6. 62 12

  • :

    7.

    52 3 2 + 3 92 3 22 + 7 + 2 22 + 7 + 2 152 11 10 82 4 5 162 7 8 92 + 14 + 7

    8. () = (7 + 181) () = 76, = 31, = 73

    35

    1. () 2 + () 2 + 5 () 53 152 () 62 + 30 () 2 + 2 () 63 + 223

    2. () 2 + 3 + 2 () 2 + 7 + 12 () 2 16 () 2 + 6 + 9 () 2 + 6 8 () 2 2 + 1 3.

    () 3 2 + 4 = 6 + 122 () 12 ( + 3) = 36 + 122

    42 ( + 3) = 43 + 122 () 45 5 2 = 206 86 () ( + 1)( + 3)=2 + 4 + 3 () + 3( 2) = 2 + 6

    4. () 2 3 + 1 () 3 () 2 + 9 () 122 + 4 5

    5. () 8 10 () 42 9 + 5 () 2 2 + 1 () 32 + 11 10 () 42 5

    6. 20 + 52 7. 62 + 16 9. 7

  • :

    10. .. 1, 202 + 4

    11.

    2, 102 + 2 4, 52 + , 20 + 4

    12. .

    13. = 43 262 + 40

    40

    1. () 22 + 6 () 22 + 42 () 25 + 1 () 4

    + 5

    2 () + () 2 52

    2 33

    () + 3 4 () 2 + 1 3

    2. 62 + 3 32 1 8 4

    3. () 2 () () 2 () 2, = 2 4. () 4 () + 2 () + 2 () + 2, = 1

    () 1, = 4 () 3 + 1

    5.

    () 63 3 2

    3=22 1

    2

    3

    () 632 5 2

    2 =32+5

    + 1

    () ()

    2 + 2 8 2 + 2 +4 8 4 + 8 0

    2 32 + 2 4 32 + 3 +5 4 5 + 5 +1

    1 + 4 3 + 5

    6. 32 + 14 2

  • :

    7. 33 + 52 + 3 + 4 8. . 9. = 12

    42

    1. () 52 + 9 () 8 () 36 () 88 () 9623 () 1555 () 32 () 73

    2

    2. () 42 7 6 () 62 () 33 62 () 23 42 + 6 () 5 + 6 () 2

    2+

    () 2 4 () 2 + 2 + 2 () 7 () 2 6 + 9

    3. () 22 + 4 () 22 + 3 7 () 23 92 8 + 15 () 2 + 11, = 52 () 2 () 2

    4. () 2 3

    () 2 3 () 5, = 5 () 4 2, () 2 1, = 4

    6. () 142 () 82 () 3 () 2 () 2

    34 () 823

    () 1277 () 2, 7 () 9, 34 () 2, 2

    7. () () () ()

    8. 32 5 7 9. 2, = 6 11. 33 52 2 14. () 42 () 2800 2 15.

    . . 1, 22 + 4 2, 2 + 2 , 2 + 4

    16. 52 2

  • :

    45

    2. = 3 3. () = 5 . , = 4 . 4. 1200000 + 1000 52 6. = 5 , = 8 8. 4 9. 10. = 300 5000 11.

    = 2 = 2 = 4

  • :

    2:

    52

    1. () 8 () 5 () 2 () 0,6 () 7 () 1,5 () 0,3 () 0,01 () 0,4 () 18 () 23 () 13

    2. 30 3. = 6 4. () () ()

    () () () 4. () 13 () 11 () 26

    () 8 () 27 () 12 () 53 () 9

    5. () () () () ()

    6. () = 28 () = 36 () = 44 7. () 10 () 6 () 3

    () 2 () 2 () 3 9. 230 10. 5,8,13,20

    13 (132 + 4 = 173) 11. = 11

    58

    1. () () () ()

    2. () 72 () 135 + 2 () 3 + 233 () 210 + 103

    3. () 8 () 10 () 35 () 150 () 9 () 32 () 9 () 12

    4. i. ii. iii. iv.

  • :

    5. () = 19 () = 1 34 () = 1 6. ()

    = 45 2 = 125 () = 106 2 = 43 + 102

    7. = 4 8. () 12 () 1 () 4 2 () 1 9. () i. = 6,4 / ii. = 9,6 / iii. = 16 /

    ()

    67

    1. () 25. . () 100. . 2. () = 15 () = 20

    () = 8 () = 24 3. = 50 4. ()

    = 48 2 = 36 () = 432 2 = 84

    5. () ()

    6. , 52 = 32 + 42 7. () = 90

    () 8.

    9. = 5 = 4

    10. = 136,5

    75

    1. () 5 () 4 () 7 () 12 () 6 () 9

    2. () 7, 50, 9, 85 () 5, 38, 7, 91 () 0,474 , 0,47 , 0,47 , 0,23

  • :

    3. .. = 51, = 59 4. () 2,65 () 1,87

    () 11,18 () 1,44

    5.

    13 8,4 3

    5

    25 24

    5 8, 17

    6 53

    73 36 273

    20 0,44444

    6. , 25 = 5 7. () < () >

    () > () = 8. () () ()

    () () 9. () 5,8 () 2,5 () 2,8 11. () = 50 () = 41 12. 23 13. 297,32 14. 13

    15

  • :

    78

    1. () () () () () () ()

    2. () 8 () 13 () 1,1 () 5 () 5 () 10 () 2 () 0,3

    3. () 7 () 5 () 10 4. () 2, () 93 , () 13,

    () 133 , () 5, () 253 , 5. () < () < () =

    () < () = () > 7. 83 , 5 , 2,5 , 293 , 29 8. .. = 70 = 8,3 9. () = 48 () = 1184 () = 464 10.

    210 1 6000000 11. 25 12. = 13 13. = 17 14.

    = 10 = 26 = 32

    81

    3. () = 13 . () = 17 . () = 3 . () = 18 . () = 20 .

    4. = 8 5. = 8

  • :

    6. () , , 2 () = = 2 () 2, , () = = 2

    7. = 34 2 8. () ()

    () () 9. () 21, 20, 1

  • :

    3:

    88

    1. , , ,

    4. () .. = 6, = 0 () = +6 () +3 5. () 3 () 1,8,0 () 2 ,4, 5, 6, 7, 9 9. () () () () 11. () () 1 () 3

    97

    1. () 8 () 9 () 101 () 80 2. () = = 63 () = =109

    = =71 3. () = 9 () = 24 6. () = 24 2

    = 22 () = 84 2 = 42 () = 90 2 = 48 7. = 8 8. 1 = 4

    2 = 2,5 9. (3, 4) (3, 4) (1,6)

    101

    1. = 18 2.

    = = = = 30 = = = = 60 = = 60 = = 120

    3. () = 8 . . () (3,2) 4. () = 6 .

    = 52 . () = 20 . 5.

    6. () = 6 () = 12

  • :

    7. 1 = 4,8 2 = 4,8

    8. = 16 = 4

    9. = 1050 25 2 = 502 25 2

    106

    1. () 90 () = 4,5 () = 10 , = 8 , = 12

    2. () 60, 120, 30, 60, 90 () = 40 3. () = 120 2 () = 52 4. = 6 5. () = 40 () = 96 2 6. () 1 = 8 () 2 = 32 7. () 1 = 12 () = 40 8. () = 192 2 () = 216 2

    111

    1. = 7 = 45

    2. () = = = = = = = = 90 () = = = = = = = 45 () = = = = 2 () = = 8 () = = = = 2

    4. = = = = 3 6. () () ()

    () ()

    8. () () ()

    9. = 5 2 10. , 11. = = 42 + 4 , = 4 2

  • :

    = = 22 + 2 , = 1 2 = 42 , = 2 2 = 4 + 22 , = 2 2 = 4 + 22 , = 2 2

    117

    1. () = = 120 = = 60 () = = 85 = = 95 () = = 100 = = 80

    2. () () () () ()

    3.

    1 2 3 4

    -

    5. , , , 6. () = 25 2 () = 247,5 2 7. () = 35 . . () = 25 . . 8. = 6 9. = 96 2 10. () = 28 2 () = 24 11. 1 = 5

    2 = 9

    125

    1. = 20 62,8 3. 20 31,4 4. () = 4 () = 8 5. = 0,55

  • :

    6. 1000 7. = 40192 8. 24 9. = 6 10. () = 53 () = 256 11. () = 6 + 3

    2 () = (20 + 6)

    () = (8 + 2) () = (24 + 3) 12. : 72,22 . : 920,81 13. 31

    131

    1. () = 100 314 2 () = 25 78,5 2 () = 4 12,56 2 () = 36 113,04 2

    2. = 6 3. = 6 4. = 6 5. = 12 2 6. = 4 7. .

    . 8. = 1050 2 = 3297 2 9. . 10. () = 1296 2 () = 1116 2 11. = 1296 2, = 1256 2.

    . 12. () = (36 8) 2 () = 2 2

    () = 60 2 () = (57 9)2 () = (40 6) 2 () = (64 96) 2

  • :

    133

    1. () = = 119 = 61 () = 53 = 37

    = 90 2. = 30 . 3. () 5 () 8 () 3

    () 42 () 84 () 96

    4.

    -

    -

    -

    . . . . . . 90. .

    . .

    5. ()

    ()

    6. () () () () () ()

    8. = 120 2 = 52

    9. = 4 = 40

    10. = 120 2 11. () = 10

    = 20 () = 103 = 503

    2 12. = 162 2 13.

    12

    31

    32

    12

    24

    36

    1

    2 3 3

    2

    14. = 2 15. () = 100 25

    2 2 () = (100 25) 2

    () = (100 25) 2 () = 754

    2

  • :

    136

    1. ()

    = = 45 = = 20 = = 65

    ()

    = = = = 20 = 5 = = 210

    () = 18 . () = 20 . 2.

    = 60 = 75 = 45 = 7

    4. = 400 2 10. = 8 2