EXERCISE 1A

 

  1. A = {a, b, c}
    B = {9, 10, 11}
    C = {d, o, g}
    D = {green, white, orange}
    E = {x, y, z}
    F = {f, o, t, b, a, l}
    G = {hearts, diamonds, clubs, spades}
    H = {Maggie, Lisa}
    I = {March, May}
    J = {Monday, Friday, Sunday}
    K = {head, tail}
    L = {13, 14, 15, 16, 17, 18, 19}
    M = {a, b, r, c, d}
    N = {b, c, d, f}
  2. A = {p, r, s}
  3. B = {2, 4, 6}
  4. C = {2, 4, 6, 8}
    D = {8, 3, 5}
    C and D = {8}
  5. E = {d, e, f, h}
    F = {f, h, a, b, c}
    E but not F = {d, e}
  6. G = {10, 30, 5, 15, 25}
    H = {5, 15, 25, 20}
    G and H = {5, 15, 25}
    G but not H = {10, 30}
    H but not G = {20}
  7. I = {i, h, f, a, d}
    J = {f, a, d, e, g}
    K = {h, a, d, e, b, c}
    I and J and K = {a, d}
  8. L = {3, 7, 9, 1, 2}
    M = {9, 1, 2, 10}
    N = {7, 1, 2, 12}
    L and N = {7, 1, 2}
    L and M = {9, 1, 2}

 

EXERCISE 1B

 

  1. A = S, B = P, C = R, D = Q
  2. A = {}, B ≠ {}, C = {}, D ≠ {}, E = {}, F = {}, G ≠ {}, H = {}
  1. #I = 5, #J = 6,
    #K = #{c, a, l, u, t, o, r} = 7,
    #L = #{15, 16, 17, 18, 19, 20, 21, 22} = 8
    #M = #{g, m, t, r, y} = 5
    #N = 0

 

EXERCISE 1C

 

  1. (i)         There are ten possible answers e.g. {a, e, i} etc.
    (ii)        There are five possible answers e.g. {a, e, i, o} etc.
    (iii)       {a, e, i, o, u}
    (iv)       {}
  2. (i)         C = {s, e}
    (ii)        There are four subsets: {}, {s}, {e} and {s, e}
  3. {2}, {4}, {6}, {8}
  4. {}, {1}, {2}, {1, 2}
  5. F = {d, o, r}
    The eight subsets are: {}, {d}, {o}, {r}, {d, o}, {d, r}, {o, r}, {d, o, r}
  6. (i)         G has 2 = 21 subsets
    (ii)
            H has 4 = 22 subsets
    (iii)
           I has 8 = 23 subsets.

 

EXERCISE 1D

 

 

EXERCISE 1E

 

 

CHAPTER TEST 1

 

  1. (i)         A = {red, amber, green}
    (ii)        B = (1c, 2c, 5c, 10c, 20c, 50c, 1 euro, 2 euro}
    (iii)       C = {s, u, m}
  2. #F = #{e, l, m, n, t} = 5
  3. {}, {1}, {2}, {1,2}

 

EXERCISE 2A

 

  1. 9732
  2. 1578
  3. (i) 1368            (ii) 300             (iii) 270            (iv) 2000
  4. Each row, column and main diagonal sums to 34.
  5. (i) 111              (ii) 222             (iii) 333            (iv) 444            (v) 555
  6. (i) 9801            (ii) 98901         (iii) 989901
  7. (i) 24                (ii) 19               (iii) 121            (iv) 32
  8. (i) 19                (ii) 43               (iii) 56              (iv) 28
  9. (i) 362              (ii) 12345         (iii) 6789
  10. 5050

 

EXERCISE 2B

 

  1. (i) {1, 2, 4, 8}              (ii) {1, 2, 5, 10}           (iii) {1, 2, 3, 4, 6, 12}
    (iv) {1, 2, 4, 5, 10, 20}            (v) {1, 2, 3, 4, 6, 8, 12, 24}
  2. {11, 13, 17, 19}
  3. {23, 29}
  4. 3, 11, 19 and 23 are prime.
  5. 37 and 73
    79 and 97
  6. p+r+i+m+e = 16+18+9+13+5 = 61, which is a prime number.
  7. 23 is a prime neighbour of 24
    29 and 31 are prime neighbours of 30
    37 is a prime neighbour of 36
    53 is a prime neighbour of 54
    59 and 61 are prime neighbours of 60.

 

EXERCISE 2C

 

  1. (i) 3                  (ii) 2                 (iii) 6
  2. (i) 6                  (ii) 5                 (iii) 10
  3. (i) 7                  (ii) 1                 (iii) 18
  4. (i) 4                  (ii) 9                 (iii) 8
  5. (i) 4                  (ii) 6                 (iii) 2
  6. (i) 42                (ii) 35               (iii) 42
  7. (i) 30                (ii) 60               (iii) 15              (iv) 105
  8. (i) 8                  (ii) 14

 

EXERCISE 2D

 

  1. (i) 3, 6, 9, 12, 15, 18                (ii) 8, 16, 24, 32, 40, 48
    (iii) 10, 20, 30, 40, 50, 60                    (iv) 15, 30, 45, 60, 75, 90
  2. (i) 12, 24, 36, 48, 60                (ii) 18, 36, 54, 72, 90
    (iii) 45, 90, 135, 180, 225                    (iv) 60, 120, 180, 240, 300
  3. (i) 6                  (ii) 12               (iii) 40
  4. (i) 18                (ii) 24               (iii) 8
  5. (i) 60                (ii) 30               (iii) 20
  6. (i) 36                (ii) 24               (iii) 60
  7. (i) 48                (ii) 180             (iii) 60
  8. (i) 192              (ii) 135             (iii) 616            (iv) 432

 

EXERCISE 2E

 

  1. (i) 81                (ii) 1000                       (iii) 25
  2. (i) 36                (ii) 27               (iii) 16
  3. (i) 10                (ii) 100             (iii) 1 000         (iv) 10 000
  4. (i) 144              (ii) 216             (iii) 225            (iv) 6561
  5. (i) 1                  (ii) 8                 (iii) 27              (iv) 64
    (v) 125             (vi) 216            (vii) 343           (viii) 512
    (ix) 729
  6. 52 = 25 and 25 = 32 thus 25 > 52
  7. (i) 1                  (ii) 1                 (iii) 1
    (iv) 1                (v) 1                 (vi) 1
  8. 8 = 23, 16 = 24, 64 = 26.
  9. (i) 1                  (ii) 121             (iii) 12321                    (iv) 1234321
    (v) 123454321
  10. (i) 16                (ii) 1156                       (iii) 111556                  (iv) 11115556
    (v) 1111155556
  11. (i) 33                (ii) 11               (iii) 3                (iv) 1
  12. (i) 15                (ii) 21               (iii) 28 
  13. 53 = 125 = 21+23+25+27+29
    63 = 216 = 31+33+35+37+39+41
    73 = 343 = 43+45+47+49+51+53+55

 

EXERCISE 2F

 

  1. (i) 494 (500)                (ii) 861 (850)
     (iii) 145 (140)             (iv) 5017 (5000)
  2. (i) 4653 (5000)                        (ii) 576 (600)
    (iii) 2189 (2000)                      (iv) 3952 (4000)
    (v) 189 (200)                           (vi) 3599 (3600)
  3. 3000
  4. 120
  5. (i) 800 (805)                (ii) 200 (201)               (iii) 590 or 600 (605) 

 

EXERCISE 2G

 

  1. (i) 8                  (ii) 3                 (iii) 18
  2. (i) 26                (ii) 13               (iii) 19
  3. (i) 3                  (ii) 4                 (iii) 7
  4. (i) 42                (ii) 11               (iii) 100
  5. (i) 22                (ii) 25               (iii) 1

 

EXERCISE 2H

 

  1. (i) 11                (ii) 14
  2. (i) 27                (ii) 13
  3. (i) 6                  (ii) 11
  4. (i) 22                (ii) 10
  5. (i) 10                (ii) 75
  6. (i) 60                (ii) 90
  7. (i) 32                (ii) 60
  8. (i) 8                  (ii) 1
  9. (i) 101              (ii) 11
  10. (i) 45                (ii) 64               (iii) 4375                      (iv) 96
  11. (i) 18                (ii) 36               (iii) 500                        (iv) 8000
  12. (i) 14                (ii) 36               (iii) 98
  13. (i) 6                  (ii) 10               (iii) 2
  14. (i) 1                  (ii) 4                 (iii) 4
  15. (i) 1                  (ii) 20               (iii) 7
  16. (i) 4                  (ii) 2
  17. (i) 5                  (ii) 3
  18. (i) 9                  (ii) 9                 (iii) 36              (iv) 36
    (v) 100             (vi) 100            (vii) 225           (viii) 225
  19. (i) 8                  (ii) 27

 

CHAPTER TEST 2

 

  1. sum = 16, product = 48, difference = 8, quotient = 3.
  2. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
  3. (i) 8                  (ii) 7                 (iii) 6
  4. (i) 40                (ii) 45               (iii) 96
  5. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
  6. (i) 8                  (ii) 243             (iii) 625            (iv) 81
  7. (i) 100 (102)                (ii) 450 (450)
  8. (i) 800 (722)                (ii) 6000 (5535)
  9. (i) 13                (ii) 48               (iii) 45              (iv) 7

 

EXERCISE 3A

 

  1. (i) -5, -4, 0, 2, 3                       (ii) -10, -2, 0, 6, 10                  (iii) -8, -3, 0, 2, 4
  2. (i) -7, -3, -1, 3, 12                   (ii) -5, -2, 1, 4, 6                      (iii) -7, -3, 0, 8
  3. (i) -2, -1, 0, 1, 3, 4                   (ii) -9, -6, -3, 0, 2                    (iii) -5, -3, 1, 2, 4
  4. (i) <                 (ii) >                (iii) <
  5. (i) >                 (ii) >                (iii) <
  6. (i)-5, -3, 2, and 4 are missing
    (ii) -6, -4, -2, 1 and 3 are missing
    (iii) -5, -3, -2, and 0 are missing
    (iv) -9, -7, -4, -3, -1, 0 and 2 are missing.
  7. (i) 5                  (ii) -8               (iii) -3              (iv) -3
    (v) 7                 (vi) -8              (vii) 2               (viii) -4
    (ix) 9                (x) -8               (xi) 2                (xii) -4
    (xiii) 3              (xiv) -3                        (xv) -2
  8. (i) 2                  (ii) -5               (iii) 9                (iv) -8
    (v) 0                 (vi) -1              (vii) 9               (viii) 7
    (ix) 3                (x) -8               (xi) -3              (xii) 3
    (xiii) 0              (xiv) -6                        (xv) -4
  9. (i) 8                  (ii) -3               (iii) -4              (iv) -2
    (v) 3                 (vi) -6              (vii) -5             (viii) 1
    (ix) -2              (x) 2    

 

EXERCISE 3B

 

  1. (i) 30                (ii) 3                 (iii) -12                        (iv) -37
  2. (i) -11              (ii) 15               (iii) -30                        (iv) 11
  3. (i) 27                (ii) -4               (iii) -13                        (iv) -38
  4. (i) 67                (ii) -56             (iii) -7                          (iv) -350
  5. (i) -12              (ii) -26             (iii) -67                        (iv) 30
  6. (i) 272              (ii) 47               (iii) -148                      (iv) -384
  7. (i) 106              (ii) -37             (iii) -153                      (iv) -1790
  8. (i) -3358          (ii) 27               (iii) -181                      (iv) -613
  9. (i) -1                (ii) 3                 (iii) 4
  10. (i) 0                  (ii) 9                 (iii) -24
  11. (i) 15                (ii) -8               (iii) 9
  12. (i) 0                  (ii) 0                 (iii) 0
  13. (i) -28              (ii) 6                 (iii) -50
  14. (i) 37                (ii) 4                 (iii) 11
  15. (i) -136            (ii) 14               (iii) -83

 

EXERCISE 3C

 

  1. (i) -8                (ii) -21                         (iii) -24
  2. (i) 16                (ii) 50                           (iii) -16
  3. (i) -80              (ii) 80                           (iii) -30
  4. (i) 0                  (ii) -15                         (iii) -9
  5. (i) -2                (ii) 6                             (iii) 64
  6. (i) 168              (ii) 0                             (iii) -48
  7. (i) 2                  (ii) -2                           (iii) -9
  8. (i) -1                (ii) -7                           (iii) -2
  9. (i) -8                (ii) -19                         (iii) 32
  10. (i) -63              (ii) 147                         (iii) -325
  11. (i) -1                (ii) 7
  12. (i) -5                (ii) 2
  13. (i) 0                  (ii) 157
  14. (i) 2                  (ii) -1
  15. (i) -1                (ii) 10

 

EXERCISE 3D

 

  1. (i) 81                            (ii) 25                           (iii) -216
  2. (i) 64                            (ii) -343                       (iii) -100 000
  3. (i) -1                            (ii) 1                             (iii) -1
    (iv) 1                            (v) -1                           (vi) 1
  4. (i) -125                        (ii) -64                         (iii) 81
  5. (i) 405                          (ii) 48                           (iii) -162
  6. (i) 160                          (ii) -1000                     (iii) -486
  7. (i) -1024                      (ii) 320                         (iii) -1701
  8. (i) -392                        (ii) 106
  9. (i) 19                            (ii) 2827
  10. (i) 6380                        (ii) -65 182
  11. (i) -54                          (ii) -496 074

 

CHAPTER TEST 3

 

  1. (i) -8, -6, -3, 2, 12                   (ii) -5, -1, 0, 4, 7
  2. (i) >                                         (ii) <
  3. (i) -5                (ii) 5                 (iii) -7              (iv) 9
  4. Like, minus.
  5. (i) -6                (ii) -10             (iii) -7              (iv) 7
  6. (i) 4                  (ii) 24               (iii) -17
  7. (i) 192              (ii) -84
  8. (i) 36                (ii) 25
  9. (i) 2                  (ii) 1
  10. (i) 4                  (ii) -4700

 

EXERCISE 4A

 

  1. (i) 2                  (ii) 3                 (iii) 4
  2. (i) 2                  (ii) 7                 (iii) 5
  3. (i) 6                  (ii) 15               (iii) 4
  4. (i) 30                (ii) 15               (iii) 12
  5. (i) 28                (ii) 171             (iii) 4

 

EXERCISE 4B

 

 

EXERCISE 4C

 

  1. (i) 15                (ii) 14               (iii) 40

 

EXERCISE 4D

 

1.     

2.     

3.     

4.     

5.     

6.     

7.     

8.     

9.     

10. 

11. 

 

EXERCISE 4E

 

 

EXERCISE 4F

 

  1. €3
  2. €2
  3. €5
  4. €12
  5. €12
  6. €20
  7. €20
  8. €10
  9. 24
  10. 100
  11. 424

 

CHAPTER TEST 4

 

  1. (i) 66                (ii) 15
  2. €30
  3. €280

 

EXERCISE 5A

 

  1. (i) 0.3               (ii) 0.09            (iii) 0.19           (iv) 0.007
  2. (i) 0.5               (ii) 0.25            (iii) 0.125         (iv) 0.0625
  3. (i) 1.5               (ii) 0.75            (iii) 0.375         (iv) 0.02           (v) 0.0002
  4. (i) 0.05             (ii) 0.025          (iii) 0.02           (iv) 0.0125

 

EXERCISE 5B

 

  1. (i) 12.55                       (ii) 17                           (iii) 90.3
  2. (i) 8.924                       (ii) 17.76                      (iii) 16.725
  3. (i) 1.504                       (ii) 0.5993                    (iii) 2.504
  4. (i) 6.7                           (ii) 9.09                        (iii) 46.88
  5. (i) 43.759                     (ii) 146.216                  (iii) 34.545
  6. (i) 60.14                       (ii) 27.36                      (iii) 160.32
  7. (i) 551.46                     (ii) 18.356                    (iii) 126.243
  8. (i) 1430                        (ii) 862                         (iii) 100.9883
  9. (i) 1.2                           (ii) 2.6                          (iii) 23.3
  10. (i) 0.583                       (ii) 0.1624                    (iii) 0.0287
  11. (i) 2.5                           (ii) 7.5                          (iii) 40
  12. (i) 14                            (ii) 35                           (iii) 50
  13. (i) 73.374                     (ii) 129.024
  14. (i) 25.3                         (ii) 26
  15. (i) 39.8                         (ii) 67.7
  16. (i) 127.66                     (ii) 63.11
  17. (i) 53.248                     (ii) 131.24
  18. (i) 41.3                         (ii) 33.2                        (iii) 69.7
  19. (i) 11.3                         (ii) 12.175
  20. (i) 45.7                         (ii) 1.776

 

EXERCISE 5C

 

  1. (i) 1.7               (ii) 35.7            (iii) 681.5         (iv) 25.0           (v) 2.0
  2. (i) 28.58           (ii) 1.82            (iii) 3.40           (iv) 19.64         (v) 2.40
  3. (i) 2.7               (ii) 2.9  0.4
  4. (i) 27.57           (ii) 361.40
  5. (i) 2.8               (ii) 7.42            (iii) 9.899

 

EXERCISE 5D

 

  1. (i) 1259.244, 1200                   (ii) 6.12, 6
  2. (i)  €103.48, 100                      (ii)  €17.19, 17
  3. (i) 4.15 4, 4                              (ii) 365.89854, 380
  4. (i)  €135.80, €150                    (ii) €341.91, €400
  5. €8.00, €9.51
  6. €9.00, €8.69
  7. €19.00, €19.64
  8. €22.00, €24.00

 

EXERCISE 5E

 

  1. (i) 5678900                  (ii) 24200                     (iii) 2560
  2. (i) 981                          (ii) 65                           (iii) 1400
  3. (i) 0.0244                     (ii) 0.00576                  (iii) 0.39
  4. (i) 0.00322                   (ii) 0.04115                  (iii) 0.000112
  5. (i) 22340                      (ii) 6500                       (iii) 577
  6. (i) 0.197                       (ii) 0.0333                    (iii) 0.001
  7. 558
  8. 164220

 

 

EXERCISE 5F

 

  1. (i) 9.8               (ii) 3.7              (iii) 2.1             (iv) 6.8
  2. (i) 18                (ii) 18.5            (iii) 22.6           (iv) 17.2
  3. (i) 64.25           (ii) 37.3            (iii) 51.95
  4. (i) 0.05             (ii) 0.01            (iii) 0.125
  5. (i) 0.16             (ii) 23.81          (iii) 0.39           (iv) 14.29
  6. (i) 0.889           (ii) 617.284      (iii) 0.008         (iv) 0.147
  7. (i) 66                (ii) 1.35
  8. (i) 59.39           (ii) 1.9625
  9. (i) 4.1               (ii) 1.25
  10. 16.45
  11. (i) 8.660           (ii) 0.235          (iii) 0.649
  12. (i) 1.48             (ii) 0.32
  13. 16
  14. 2.88
  15. (i) 0.149           (ii) 0.122          (iii) 0.385

 

EXERCISE 5G

 

  1. (i) 7                  (ii) 2                 (iii) 9
    (iv) 5                (v) 8                 (vi) 6
  2. (i) 20                (ii) 2.5              (iii) 3.8
    (iv) 6.1             (v) 0.0240        (vi) 1.5
  3. (i) 14                (ii) 17               iii) 30  
    (iv) 1.2             (v) 2.7              (vi) 50

 

CHAPTER TEST 5

 

  1. (i) 0.6               (ii) 0.49            (iii) 0.4             (iv) 1.125
  2. (i) 95.64           (ii) 678.95        (iii) 298.9
  3. (i) 23.6             (ii) 9.8168        (iii) 77.2
  4. 16.09
  5. 0.0007
  6. €27, €28.24
  7. 51.87
  8. (i) 0.025           (ii) 9.8
  9. 19.59
  10. (i) 2.42             (ii) 14

 

EXERCISE 6A

 

  1. (i) 10%            (ii) 20%           (iii) 75%          (iv) 5%
  2. (i) 12.5%         (ii) 37.5%        (iii) 4%            (iv) 87.5%
  3. (i) 550%          (ii) 160%         (iii) 245%        (iv) 142.5%
  4. (i) 19%            (ii) 40%           (iii) 0.5%         (iv) 320%
  5. (i) 60%            (ii) 35%           (iii) 40.5%       (iv) 175%
  6. (i) 80%            (ii) 2.5%          (iii) 220%        (iv) 12.5%
  7. (i) 0.16             (ii) 3.2              (iii) 0.04           (iv) 0.0011
  8. (i) 0.155           (ii) 0.0325        (iii) 1.1275       (iv) 0.0035
  9. (i) 0.15             (ii) 2                 (iii) 0.03           (iv) 0.005

 

EXERCISE 6B

 

  1. (i) 24                (ii) 253             (iii) 689
  2. (i) 84                (ii) 45               (iii) 705
  3. (i) €44              (ii) €71             (iii) €195
  4. (i) €475            (ii) €141           (iii) €96
  5. (i) €64.20         (ii) €223.30      (iii) €397.86
  6. (i) €733.60       (ii) €23.15        (iii) €5.96
  7. (i) €5.75           (ii) €6.93          (iii) €2.05
  8. (i) €168            (ii) €1,494        (iii) €256
  9. (i) €25             (ii) €252           (iii) €33
  10. 23
  11. 66
  12. €1,533.32
  13. €669.64
  14. €120
  15. €57
  16. €33
  17. €36
  18. €31.20
  19. 52
  20. 90
  21. 102 kg
  22. €276,640

 

EXERCISE 6C

 

  1. (i) 5%                          (ii) 25%
  2. (i) 60%                        (ii) 80%
  3. (i) 75%                        (ii) 10%
  4. (i) 30%                        (ii) 70%
  5. (i) 5%                          (ii) 55%
  6. (i) 95%                        (ii) 16%
  7. (i) 24%                        (ii) 75%
  8. (i) 12.5%                     (ii) 37.5%
  9. (i) 45%                        (ii) 31.25%
  10. (i) 40%                        (ii) 42.5%

 

EXERCISE 6D

 

  1. (i) 1:3               (ii) 2:5              (iii) 1:7
  2. (i) 2:3               (ii) 5:6              (iii) 1:3
  3. (i) 6:7               (ii) 3:4              (iii) 8:9
  4. (i) 1:2               (ii) 9:10            (iii) 6:7
  5. €1000 and €800
  6. €50 and €75
  7. €274 and €137
  8. €560
  9. €120 and €200
  10. €100 and €200
  11. €40, €80 and €160
  12. €640, €320 and €1280
  13. €30 and €20
  14. €16.80
  15. €180
  16. €30
  17. €15, €30 and €45
  18. 3000 m and 4800 m
  19. €45, €60 and €75
  20. €200, €250 and €300
  21. €15 and €5

 

CHAPTER TEST 6

 

  1. (i) 0.35             (ii) 0.2404        (iii) 0.0025       (iv) 0.165
  2. (i) €228            (ii) €4,473         (iii) €3,600
  3. €195
  4. 600 g
  5. (i) 200%          (ii) 30%
  6. (i) 4:7               (ii) 5:9
  7. €39 and €26
  8. €8, €12 and €16

 

 

EXERCISE 7A

 

  1. (i) 6                  (ii) 16               (iii) 5
  2. (i) 20                (ii) 22               (iii) 4
  3. (i) 18                (ii) 21               (iii) 2
  4. (i) 9                  (ii) 18               (iii) 14
  5. (i) 16                (ii) 48               (iii) 27
  6. (i) 1                  (ii) 3                 (iii) 4
  7. (i) 4                  (ii) 22               (iii) 15
  8. (i) 3                  (ii) 60               (iii) 14
  9. (i) 22                (ii) 20               (iii) 21
  10. (i) 13                (ii) 60               (iii) 33

 

EXERCISE 7B

 

  1. -11
  2. -5
  3. -9
  4. 6
  5. 5
  6. 4
  7. 10
  8. 1
  9. 1
  10. 2
  11. -1
  12. 2
  13. 41, 43, 47, 53, 61, 71, 1681 = 412
  14. 41, 43, 47, 53, 61, 71, 1681 = 412

 

EXERCISE 7C

 

  1. €210
  2. (i) 15 mg          (ii) 2.5 mg        (iii) For a 25-year-old the rule gives 32.5 mg which is greater than the recommended adult dose
  3. (i) 101 cm        (ii) 125 cm       (iii) 137 cm      (iv) 257 cm i.e. more than 8 feet tall!
  4. (i) 5 m              (ii) 20 m           (iii) 500 m

 

EXERCISE 7D

 

  1. (i) 2                  (ii) -5               (iii) 11
    (iv) -10                        (v) -7               (vi) 15
    (vii) -21           (viii) 8              (ix) -3
    (x) -25             (xi) 30              (xii) -9
  2. (i) 8x+1           (ii) 6a+10        (iii) 3b+3
  3. (i) x+6             (ii) 3a+6          (iii) 4y+1
  4. (i) 3x+10y+5   (ii) a+2b+7      (iii) 2p+3q+2
  5. (i) 2x+3y+3     (ii) 14a+11b-1            (iii) 3p-4q+6
  6. (i) 5x2+3x-8     (ii) 8x2+6x-3    (iii) 3x2+3x+3
  7. (i) 2y2-4y         (ii) -3y2+3y-5   (iii) 3y2+3y-1
  8. (i) 5z2+6z-2      (ii) 3z2+5z+7   (iii) 3z2+5z-3
  9. (i) 14x+18       (ii) 21x+7
  10. (i) 2x+10         (ii) 9x+10
  11. (i) 15x2                        (ii) 8x3              (iii) 14a2          (iv) 12b3
  12. (i) 8x2+4x        (ii) 15a2-10a               (iii) 4y2+2y       (iv) 9x2+6x
  13. (i) 6y2+19y+10            (ii) 5y2+14y+8             (iii) 8y2+14y+6
  14. (i) 4x2+6x-4                 (ii) 6x2-x-2                  (iii) 15x2-19x+6
  15. (i) x-11y                      (ii) 6a-14b
  16. (i)-15x-6y                    (ii) 5a+3b
  17. (i) 6x                            (ii) 12a-b

 

EXERCISE 7E

 

  1. (i) 6x2+7x+2                (ii) 12x2+11x+2                       (iii) 4x2+12x+9
  2. (i) 4x2+2x-12               (ii) 3x2-5x-2                            (iii) 8x2+10x-3
  3. (i) x2+2xy+y2               (ii) x2-2xy+y2               (iii) x2-y2
  4. (i) 4x2-8x+4                 (ii) 12x2-2x-4              (iii) 9x2-24x+16
  5. (i) 6x2+7xy+2y2           (ii) 8x2+10xy+3y2        (iii) 10x2+19xy+6y2
  6. (i) 2x2+5xy-3y2            (ii) 2x2+5xy-3y2           (iii) 16x2-25y2
  7. (i) a2+2a+1                  (ii) a2+4a+4                 (iii) a2+6a+9                (iv) a2+8a+16
  8. (i)16x2-24x+9              (ii) 49x2-14x+1           
    (iii) 100x2-60xy+9y2    (iv)
    4x2+20x+25
  9. (i) 8x3 +22x2+17x+3    (ii) 8x3 +34x2+29x+6   (iii) x3 +3x2+3x+1
  10. (i) 2x3 -5x2+3x-2         (ii) 2x3 -15x2+32x-21  (iii) x3 -8x2+9x+18
  11. (i) x3 -2x2y+2xy2-y3     (ii) 2x3 -5x2+3x-2        (iii) 3x3 -11x2+9x-2
  12. (i) x3 +6x2+5x-12        (ii) 27x3 -27x2y+9xy2-y3

 

EXERCISE 7F

 

 

CHAPTER TEST 7

 

  1. (i) 55                (ii) 0                 (iii) 1
  2. 4
  3. 1
  4. €170.37
  5. (i) 12y2-11y+2             (ii) 4y2+12y+9             (iii) 9y2-12y+4
  6. (i)-3x-10y                    (ii) 9a-9b
  7. (i) 4x2-9y2        (ii) 25x2+40xy+16y2                (iii) 8x3 -12x2+6x-1

 

EXERCISE 8A

 

  1. (i) 9 m              (ii) 14 cm         (iii) 25 m          (iv) 4 km
  2. (i) 400 cm        (ii) 20 cm         (iii) 0.75 km     (iv) 26 m
  3. (i) 4 m              (ii) 160 cm       (iii) 2500 m      (iv) 130 cm
  4. 15 cm
  5. 2 m
  6. 3 km
  7. 255 cm
  8. 130 m
  9. 15
  10. 550
  11. 1600
  12. 25
  13. 30
  14. 2 m

 

EXERCISE 8B

 

  1. (i) 3 kg             (ii) 25 kg          (iii) 4000 kg     (iv) 1700 kg
  2. (i) 8 t                (ii) 6.2 t            (iii) 0.3 t          (iv) 1.4 t
  3. 2 kg
  4. 3 t
  5. 4 kg
  6. 19.5 kg
  7. 125
  8. 980
  9. 25
  10. 20
  11. 5 t
  12. 4
  13. 4 t

 

EXERCISE 8C

 

  1. (i) 60                (ii) 240             (iii) 150
  2. (i) 15                (ii) 75               (iii) 420
  3. (i) 1 m 40 s      (ii) 3 m 20 s     (iii) 11 m 40 s
  4. (i) 24                (ii) 72               (iii) 168
  5. (i) 1 h 25 m      (ii) 1 h 13 m     (iii) 1 h 42 m
    (iv) 1 h 30 m    (v) 1 h 51 m     (vi) 1 h 8 m
  6. (i) 720              (ii) 10080         (iii) 525600
  7. (i) 520              (ii) 5200           (iii) 3640
  8. (i) 3600            (ii) 86400         (iii) 604800
  9. (i) 12                (ii) 150             (iii) 480
  10. (i) 8                  (ii) 3                 (iii) 26
  11. (i) 4                  (ii) 7                 (iii) 47
  12. 300

 

EXERCISE 8D

 

  1. (i) 12 h 50 m                (ii) 05 h 58 m
  2. (i) 10 h 32 m                (ii) 11 h 18 m
  3. (i) 04 h 25 m                (ii) 07 h 22 m
  4. (i) 11 h 22 m                (ii) 18 h 17 m
  5. (i) 03 h 30 m                (ii) 04 h 40 m
  6. (i) 06 h 08 m                (ii) 06 h 37 m
  7. (i) 04 h 47 m                (ii) 04 h 53 m
  8. (i) 02 h 52 m                (ii) 05 h 53 m
  9. (i) 12 h 49 m                (ii) 11 h 51 m
  10. 28 h 10 m
  11. 4 h 55 m
  12. 2 h 32 m

 

EXERCISE 8E

 

  1. (i) 1600                        (ii) 1300                       (iii) 0500
    (iv) 2030                      (v) 1425                       (vi) 1145
    (vii) 1510                     (viii) 0720                    (ix) 2155
  2. (i) 8 p.m.                      (ii) 3 a.m.                     (iii) 5.32 p.m.
    (iv)
    11.59 p.m.             (v) 8.42 a.m.                (vi) 6.12 p.m.
    (vii)
    10.14 a.m.            (viii) 7.45 p.m.             (ix) 2.26 p.m.
  3. 2 h 35 m
  4. 2 h 22 m
  5. (i) 02 h 09 m                (ii) 1619
  6. 2 h 13 m
  7. 1 h 30 m
  8. 2 h 53 m
  9. 2 h 39 m
  10. 1802
  11. (i) 1 h 48 m                  (ii) 1445
  12. 55 m
  13. (i) 1647                        (ii) 02 h 37 m
  14. 2 h 55 m
  15. (i) 2 h 24 m                  (ii) 36 m
  16. (i) 2 h 32m                   (ii) 28 m
  17. (i) 58 m                        (ii) 2015
  18. 1334
  19. (i) 02 h 40 m                (ii) 2 h 16 m                 (iii) 2 h 24 m
  20. (i) 45 m                        (ii) 1 h 10 m                 (iii) 50 m
  21. (i) 1 h 44 m                  (ii) 1859
  22. (i) 2 h 41 m                  (ii) 19 m
  23. (i) 2 h 36 m                  (ii) 24 m
  24. 1723
  25. (i) 2 h 25 m                  (ii) 2 h 17 m                 (iii) 2 h 32 m
  26. 2118
  27. (i) 2 h 28 m                  (ii) 1815
  28. 1545

 

EXERCISE 8F

 

  1. 30 km/hr
  2. 45 km/hr
  3. 42 km/hr
  4. 141 km
  5. 106 km
  6. 140 km
  7. 3 h
  8. 5 h
  9. 6 h
  10. 20 km/hr
  11. 96 km
  12. 5 h
  13. 2 h
  14. 135 km
  15. 40 km/hr
  16. 50 km/hr
  17. 54 km
  18. 120 km
  19. 65 km
  20. 40 km/hr
  21. 126 km
  22. 153 km
  23. 57 km/hr
  24. 12 km
  25. 36 km
  26. 44 km/hr
  27. 36 km/hr
  28. 100 km/hr
  29. 60 km/hr

Puzzle:        2 seconds

 

CHAPTER TEST 8

 

  1. (i) 250 cm        (ii) 125 m         (iii) 326 mm     (iv) 54 cm
  2. 7 km

 

  1. (i) 3 kg             (ii) 3000 g
  2. 380
  3. (i) 17 minutes   (ii) 84 minutes
  4. (i) 10 h 15 m                (ii) 5 h 50 m
  5. 5 h 4 m
  6. (i) 1622            (ii) 0615
  7. (i) 5.48 p.m.     (ii) 2.10 a.m.
  8. 1 h 55 m
  9. (i) 2 h 53 m      (ii) 1355
  10. (i) 2 h 49 m      (ii) 11 minutes
  11. 2010
  12. 44 km/hr
  13. 3 h 30 m
  14. 94 km/hr

 

EXERCISE 9A

 

  1. (i) 2(x+2)         (ii) 5(a+3)        (iii) 3(y+3)       (iv) 7(z+2)
  2. (i) 2a(x+2)       (ii) 5a(b+3)      (iii) 3y(y+3)     (iv) 7z(z+2)
  3. (i) 5(x+2)         (ii) 4x(x+2)      (iii) 10a(b+10)             (iv) 5x(y-4)
  4. (i) x(x+3)         (ii) a(a-4)         (iii) y(2y+1)     (iv) c(c+5)
  5. (i) 2(x+3)         (ii) 6x(x+2)      (iii) 8a(b-2)      (iv) 12(x+2)
  6. (i) 3(3a+4)       (ii) 5(2y+3)      (iii) 2(3c+4)     (iv) 4z(3z+2)
  7. (i) 2y(3x+4)     (ii) 2x(5x+6)    (iii) 2y(2y+3)   (iv) 5x(2x-3y)
  8. (i) 2xy(x+2)     (ii) 3ab(a-2)     (iii) 4cd(2+3d)             (iv) 5xy(3x+4y)
  9. (i) -3(a+2)       (ii) -2b(2b+5)  (iii) -2xy(x+2)              (iv) -4(2p+6q)
  10. (i) -6x(x-2)      (ii) -10b(a2-2)  (iii) -c(4c-b)     (iv) -5xy(3x-4y)
  11. (i) -3x(3x+5)   (ii) -2b(2a-3)   (iii) -2ac(9b+2)            (iv) -20x(5x-1)
  12. (i) 10(x+3)       (ii) -5(a-4)       (iii) -2x(x+3)   (iv) a(4a+3b)

 

EXERCISE 9B

 

  1. (i) (x+y)(3+a)              (ii) (c+d)(a+b)
  2. (i) (p+q)(2+y)              (ii) (f+g)(m+n)
  3. (i) (c-d)(2+b)               (ii) (p-q)(4x+y)
  4. (i) (x+w)(x+y)              (ii) (x+b)(2x+a)
  5. (i) (c+3d)(2a+b)          (ii) (p+2q)(5x+y)
  6. (i) (r-3s)(4m+n)           (ii) (c+2d)(10a+b)
  7. (i) (y+w)(y+z)              (ii) (x+2)(3x+a)
  8. (i) (p-3r)(2p+q)           (ii) (x+2y)(5x+3)
  9. (i) (f+g)(e-h)                (ii) (y+r)(x-s)
  10. (i) (2c+b)(2a-d)           (ii) (7x+a)(2x-y)
  11. (i) (x+2y)(2x-z)            (ii) (2x+3y)(3x-z)
  12. (i) (3a+4b)(4a-c)         (ii) (2y+3z)(5y-w)
  13. (i) (c+d)(a+b)              (ii) (r+s)(x+y)
  14. (i) (j+k)(m+n)              (ii) (2f+g)(d+e)
  15. (i) (r+s)(p+3q)             (ii) (c+2d)(a+3b)

 

EXERCISE 9C

 

  1. (i) (r-d)(r+d)                (ii) (m-n)(m+n)                        (iii) (p-q)(p+q)
  2. (i) (a-2)(a+2)               (ii) (b-3)(b+3)                          (iii) (c-4)(c+4)
  3. (i) (x-2y)(x+2y)           (ii) (z-4w)(z+4w)                     (iii) (p-8q)(p+8q)
  4. (i) (a-5b)(a+5b)           (ii) (c-10d)(c+10d)                  (iii) (e-11f)(e+11f)
  5. (i) (2a-3b)(2a+3b)       (ii) (4c-5d)(4c+5d)                  (iii) (10x-7y)(10x+7y)
  6. (i) (x-1)(x+1)               (ii) (y-4)(y+4)                          (iii) (2p-1)(2p+1)
  7. (i) (3-x)(3+x)               (ii) (5-y)(5+y)                          (iii) (4-8a)(4+8a)
  8. (i) 3(a-2b)(a+2b)         (ii) 2(b-1)(b+1)                        (iii) 10(x-2)(x+2)
  9. (i) 7(c-1)(c+1)             (ii) 2(a-5)(a+5)                        (iii) 3(y-3)(y+3)
  10. (i) 5(p-1)(p+1)             (ii) 10(x-4)(x+4)                      (iii) 2(y-2)(y+2)

 

EXERCISE 9D

 

  1. (i) (x+4)(x+2)              (ii) (x+5)(x+3)             (iii) (x+5)(x+1)
  2. (i) (x+5)(x+2)              (ii) (x+3)(x+3)             (iii) (x+2)(x+1)
  3. (i) (x+8)(x+1)              (ii) (x+4)(x+3)             (iii) (x+8)(x+2)
  4. (i) (x+2)(x+2)              (ii) (x+4)(x+4)             (iii) (x+7)(x+1)
  5. (i) (x+9)(x+1)              (ii) (x+5)(x+5)             (iii) (x+5)(x+2)

 

EXERCISE 9E

 

  1. (i) (x-5)(x-2)                (ii) (x-6)(x-2)               (iii) (x-6)(x-5)
  2. (i) (x-5)(x-4)                (ii) (x-3)(x-2)               (iii) (x-7)(x-2)
  3. (i) (x-8)(x-2)                (ii) (x-6)(x-3)               (iii) (x-6)(x-4)
  4. (i) (x-4)(x-2)                (ii) (x-6)(x-1)               (iii) (x-10)(x-3)
  5. (i) (x-25)(x-2)              (ii) (x-7)(x-2)               (iii) (x-5)(x-3)
  6. (i) (x-25)(x-1)              (ii) (x-14)(x-1)             (iii) (x-20)(x-1)

 

EXERCISE 9F

 

  1. (i) (x+10)(x-3)             (ii) (x-6)(x+3)              (iii) (x+10)(x-2)
  2. (i) (x-4)(x+2)               (ii) (x+7)(x-2)              (iii) (x-5)(x+3)
  3. (i) (x+14)(x-2)             (ii) (x+12)(x-1)            (iii) (x+25)(x-2)
  4. (i) (x-20)(x+5)             (ii) (x-10)(x+6)            (iii) (x-8)(x+5)
  5. (i) (x-20)(x+3)             (ii) (x-9)(x+5)              (iii) (x-20)(x+2)
  6. (i) (x+6)(x-5)               (ii) (x+10)(x-8)            (iii) (x+5)(x-2)
  7. (i) (x+5)(x+4)              (ii) (x-30)(x-1)             (iii) (x+50)(x-2)
  8. (i) (x-10)(x-4)              (ii) (x-9)(x+2)              (iii) (x+6)(x+4)
  9. (i) (x-25)(x-4)              (ii) (x+16)(x+1)           (iii) (x+30)(x-2)
  10. (i) (x-15)(x+4)             (ii) (x+50)(x+4)           (iii) (x-30)(x-5)
  11. (i) (x+24)(x+2)            (ii) (x+8)(x-2)              (iii) (x-6)(