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
  3. 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

 

  3. (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)       {}
  4. (i)         C = {s, e}
    (ii)        There are four subsets: {}, {s}, {e} and {s, e}
  5. {2}, {4}, {6}, {8}
  6. {}, {1}, {2}, {1, 2}
  7. F = {d, o, r}
    The eight subsets are: {}, {d}, {o}, {r}, {d, o}, {d, r}, {o, r}, {d, o, r}
  8. (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}
  4. #F = #{e, l, m, n, t} = 5
  5. {}, {1}, {2}, {1,2}

 

EXERCISE 2A

 

  1. 9732
  2. 1578
  4. (i) 1368            (ii) 300             (iii) 270            (iv) 2000
  5. Each row, column and main diagonal sums to 34.
  6. (i) 111              (ii) 222             (iii) 333            (iv) 444            (v) 555
  7. (i) 9801            (ii) 98901         (iii) 989901
  8. (i) 24                (ii) 19               (iii) 121            (iv) 32
  9. (i) 19                (ii) 43               (iii) 56              (iv) 28
  10. (i) 362              (ii) 12345         (iii) 6789
  12. 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}
  3. {11, 13, 17, 19}
  4. {23, 29}
  5. 3, 11, 19 and 23 are prime.
  8. 37 and 73
    79 and 97
  9. p+r+i+m+e = 16+18+9+13+5 = 61, which is a prime number.
  10. 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.
  3. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
  5. (i) 8                  (ii) 7                 (iii) 6
  6. (i) 40                (ii) 45               (iii) 96
  7. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
  8. (i) 8                  (ii) 243             (iii) 625            (iv) 81
  9. (i) 100 (102)                (ii) 450 (450)
  10. (i) 800 (722)                (ii) 6000 (5535)
  11. (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

 

  3. (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
  12. 100
  13. 424

 

CHAPTER TEST 4

 

  1. (i) 66                (ii) 15
  10. €30
  11. €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

 

  6. (i) 5678900                  (ii) 24200                     (iii) 2560
  7. (i) 981                          (ii) 65                           (iii) 1400
  8. (i) 0.0244                     (ii) 0.00576                  (iii) 0.39
  9. (i) 0.00322                   (ii) 0.04115                  (iii) 0.000112
  10. (i) 22340                      (ii) 6500                       (iii) 577
  11. (i) 0.197                       (ii) 0.0333                    (iii) 0.001
  12. 558
  13. 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

 

  13. (i) 7                  (ii) 2                 (iii) 9
    (iv) 5                (v) 8                 (vi) 6
  14. (i) 20                (ii) 2.5              (iii) 3.8
    (iv) 6.1             (v) 0.0240        (vi) 1.5
  15. (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
  3. (i) 95.64           (ii) 678.95        (iii) 298.9
  4. (i) 23.6             (ii) 9.8168        (iii) 77.2
  5. 16.09
  6. 0.0007
  7. €27, €28.24
  9. 51.87
  11. (i) 0.025           (ii) 9.8
  12. 19.59
  14. (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%
  5. (i) 19%            (ii) 40%           (iii) 0.5%         (iv) 320%
  6. (i) 60%            (ii) 35%           (iii) 40.5%       (iv) 175%
  7. (i) 80%            (ii) 2.5%          (iii) 220%        (iv) 12.5%
  11. (i) 0.16             (ii) 3.2              (iii) 0.04           (iv) 0.0011
  12. (i) 0.155           (ii) 0.0325        (iii) 1.1275       (iv) 0.0035
  13. (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

 

  5. (i) 1:3               (ii) 2:5              (iii) 1:7
  6. (i) 2:3               (ii) 5:6              (iii) 1:3
  7. (i) 6:7               (ii) 3:4              (iii) 8:9
  8. (i) 1:2               (ii) 9:10            (iii) 6:7
  9. €1000 and €800
  10. €50 and €75
  11. €274 and €137
  12. €560
  13. €120 and €200
  14. €100 and €200
  15. €40, €80 and €160
  16. €640, €320 and €1280
  17. €30 and €20
  18. €16.80
  19. €180
  20. €30
  21. €15, €30 and €45
  22. 3000 m and 4800 m
  23. €45, €60 and €75
  24. €200, €250 and €300
  25. €15 and €5

 

CHAPTER TEST 6

 

  3. (i) 0.35             (ii) 0.2404        (iii) 0.0025       (iv) 0.165
  4. (i) €228            (ii) €4,473         (iii) €3,600
  5. €195
  6. 600 g
  7. (i) 200%          (ii) 30%
  9. (i) 4:7               (ii) 5:9
  10. €39 and €26
  11. €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
  14. 41, 43, 47, 53, 61, 71, 1681 = 412
  15. 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)(x-6)
  12. (i) (x-5)(x+2)               (ii) (x-9)(x-4)               (iii) (x+2)(x+1)

 

CHAPTER TEST 9

 

  1. (i) 3(5x+2)       (ii) 4y(y-2)       (iii) 5a(a2+2)    (iv) 7(b+3)
  2. (i) (a+b)(5x+y)            (ii) (r-s)(5x-y)
  3. (i) (b+2d)(2a+5c)        (ii) (s-2t)(3p+q)
  4. (i) (g-8)(g+8)               (ii) (3w-1)(3w+1)        (iii) 5(x-2)(x+2)
  5. (i) (x+8)(x+3)              (ii) (x-49)(x-1)             (iii) (x-100)(x+1)

 

EXERCISE 10A

 

  1. €68
  2. €45
  3. €76
  4. €81
  5. €28
  6. €17.10
  7. 30%
  8. 12%
  9. (i)  €36                         (ii)  €204
  10. €105
  11. €160
  12. €133.52
  13. 2.25%

 

EXERCISE 10B

 

  1. €105
  2. €142.50
  3. €300
  4. €400
  5. €182.40
  6. €71.50
  7. €61.80
  8. €6,750
  9. €13.34
  10. €26.32
  11. 5%
  12. 12%
  13. 15%
  14. 5%
  15. 8%
  16. 12%
  17. €532
  18. €88.50
  19. €200

 

EXERCISE 10C

 

  1. €5,100
  2. €624
  3. €927
  4. €1,908
  5. €40.80
  6. €2,227.89
  7. €66.56
  8. €8,112
  9. €30.75
  10. €1,389.15
  11. €3,993
  12. €20.40
  13. €865.28
  14. €2,142.45
  15. €1,260.75
  16. €662
  17. €5,824
  18. €4,630.50
  19. €10,927.27
  20. €1,230.25

 

EXERCISE 10D

 

  1. (i) €4,120                     (ii) €3,419.60
  2. (i)  €8,200                    (ii) €9,635
  3. (i)  €624                       (ii) €284.96
  4. (i)  €927                       (ii) €542.81
  5. (i) €2,070                     (ii) €3,177.45
  6. (i)  €820                       (ii) €635.50
  7. €28.25            
  8. €626.40          
  9. €30.36            
  10. €1,011.15       
  11. €203.40          
  12. (i)  €2,520                    (ii) €1,701
  13. (i)  €1,908                    (ii) €2,446.48
  14. €33.45            
  15. €890.40          
  16. (i) €1,560                     (ii) €1,102.40

 

CHAPTER TEST 10

 

  1. €44
  2. (i) €3.88                       (ii) 8%
  3. 6%
  4. €8,200
  5. €42.63
  6. (i) €3,090                     (ii) €1,637.70
  7. €14.24

 

EXERCISE 11A

 

  1. (i) 3                  (ii) 5                 (iii) 7
  2. (i) 4                  (ii) 6                 (iii) 2
  3. (i) 5                  (ii) 3                 (iii) 4
  4. (i) 27                (ii) 16               (iii) 32
  5. (i) 2                  (ii) 5                 (iii) 7
  6. (i) 4                  (ii) 3                 (iii) 8
  7. (i) 20                (ii) 30               (iii) 12
  8. (i) 18                (ii) 24               (iii) 36
  9. (i) 7                  (ii) 5                 (iii) 9
  10. (i) 6                  (ii) 4                 (iii) 3
  11. (i) 2                  (ii) 3                 (iii) 5
  12. (i) 6                  (ii) 4                 (iii) 2
  13. (i) 28                (ii) 35               (iii) 73
  14. (i) 100              (ii) 60               (iii) 224
  15. (i) 76                (ii) 57               (iii) 42
  16. (i) 49                (ii) 38               (iii) 19

 

EXERCISE 11B

 

  1. (i) 3                  (ii) 9                 (iii) 0.5
  2. (i) 2                  (ii) 10               (iii) 1.5
  3. (i) 5                  (ii) 18               (iii) 3.5
  4. (i) 9                  (ii) 6                 (iii) 2.5
  5. (i) 5                  (ii) 10               (iii) 4.5
  6. (i) 2                  (ii) 3
  7. (i) 6                  (ii) 8
  8. (i) 4                  (ii) 7
  9. (i) 5                  (ii) -3
  10. (i) 2                  (ii) 7
  11. (i) 2                  (ii) -4
  12. (i) 3                  (ii) 2

 

 

EXERCISE 11C

 

  1. (i) 3                  (ii) 4                 (iii) 2
  2. (i) -1                (ii) 10               (iii) 3
  3. (i) 5                  (ii) 2                 (iii) 7
  4. (i) 3                  (ii) 4                 (iii) 2
  5. (i) 10                (ii) 6.5              (iii) 1
  6. (i) 2                  (ii) 3                 (iii) 4
  7. (i) 3                  (ii) 6
  8. (i) 5                  (ii) 2
  9. (i) 6                  (ii) 10
  10. (i) 3                  (ii) 4
  11. (i) -2                (ii) -5               (iii) -3
  12. (i) -1                (ii) -4               (iii) -2

 

EXERCISE 11D

 

  2. 2x+1 = 9,         x = 4
  3. 3x-2 = 88,       x = 30
  4. 5x+4 = 79,       x = 15
  6. 4x+20 = 52,     x = 8
  7. 4x+3 = 51,       x = 12
  8. 5x-9 = 76,       x = 17
  9. 6x+77 = 125    x = 8
  10. 2x+4 = 16,       x = 6
  11. (i) x+10                       (ii) 2(x+10)+3x            (iii) €15

 

CHAPTER TEST 11

 

  1. (i) 72                (ii) 23               (iii) 20              (iv) 34
  2. (i) 3                  (ii) 19               (iii) 30
  3. (i) 79                (ii) 1                 (iii) 1.5
  4. (i) 8                  (ii) 10
  6. 12x-31 = 5,     x = 3

 

EXERCISE 12E

 

  1. A = 40º, B = 105º, C = 100º, D = 75º.
  2. x = 30, y = 20.
  3. <4, <3.
  1. x = 35, y = 145.
  2. 260º
  1. 72º.
  2. 76º.
  3. 60º.

 

CHAPTER TEST 12

 

  1. 45º.
  2. x = 60º, y = 120º.
  3. x = 78º.

 

 

EXERCISE 13A

 

  1. (i) 7                  (ii) 5                 (iii) 3                (iv) 5                (v) 6
    (vi) 33              (vii) 20             (viii) 8              (ix) 2                (x) 6
    (xi) 7                (xii) 14             (xiii) 35            (xiv) 19            (xv) 128
    (xvi) 248          (xvii) 13600     (xviii) 5            (xix) 700          (xx) 11
  2. (i) 4                  (ii) 3.4              (iii) 1.5             (iv) 1.8             (v) 222
    (vi) 2                (vii) 0               (viii) 3              (ix) -3              (x) €7.19
    (xi) €13.45       (xii) 13.8          (xiii) €21.51     (xiv) €12.99     (xv) €18.30
  3. 54
  4. 60
  5. 56
  6. 52
  7. 5
  8. 7
  9. 5
  10. 20
  11. 50
  12. 136
  13. 41
  14. 13
  15. 42

 

EXERCISE 13B

 

  1. (i) Friday          (ii) 30               (iii) 120            (iv) 45
  2. (i) Athens         (ii) 24               (iii) 17              (iv) Paris
  3. (i) November   (ii) 80 mm        (iii) 55
  1. 65 mm
  2. €40
  3. 20º
  4. 68
  1. 45
  2. (i) 40                (ii)  €10            (iii) 89

 

EXERCISE 13C

 

  1. (i) 6                  (ii) 1                 (iii) 0                (iv) 23              (v) 18
  2. (i) 5                  (ii) 28                          
  3. (i) 1.5               (ii) 210 (iii) -1              (iv) 3.2             (v) 2 and 9

 

EXERCISE 13D

 

  1. (i) Age                         4          5          6          7          8
    Number of children       8          6          3          7          2
    (ii) 4 years        (iii) 26
  2. (i) Number of cereals                0          1          2          3          4
    Number of pupils                      3          7          12        5          2
    (ii) 2 types        (iii) 29              (iv) 7
  3. (i) Marks                      1          2          3          4          5
    Number of pupils          3          5          6          9          2
    (ii) 4 marks      (iii) 25              (iv) 8
  4. (i) Shoe Size                 5          6          7          8          9
    Number of people        3          4          6          2          1
    (ii) size 7          (iii) size 9         (iv) 16
  5. (i) Number of books     2          3          4          5          6
    Number of pupils          7          3          5          4          2
    (ii) 2 books      (iii) 13              (iv) 21
  6. (i) Shirt Size                 38        39        40        41        42
    Number of men            2          3          6          4          3
    (ii) size 40        (iii) 3
  7. (i) Rainfall (mm)            0          5          8          11        12        13        14
    Number of days            6          1          11        1          3          2          6
    (ii) 8 mm          (iii) 6 days
  8. (i) Marks                      0          2          4          6          8          10
    Number of pupils          1          4          6          9          3          2
    (ii) 6 marks      (iii) 20 pupils

 

EXERCISE 13E

 

  1. 6
  2. 2
  3. 7
  4. 2
  5. (i) 4                  (ii) 3                 iii) 13
  6. (i) 24                (ii) €5               (iii) 9                (iv) 5
  7. (i) 8                  (ii) 30               (iii) 14              (iv) 5
  8. (ii) 30               (iii) 3.4             (iv) 4                (v) 20%
  9. (i) 1                  (iii) 60              (iv) 135            (v) 2.25
  10. (ii) 2.5              (iii) 19
  11. (i) 13                (ii) 2
  12. (i) 12, 12          (ii) 6, 9             (iii) 8, 8
    (iv) €37.50, €38.00                  (v)14, 12
    (vi) 48, 60        (vii) 70, 69       (viii) 75, 65
    (ix) 3.5, 3         (x) 2, 1

 

EXERCISE 13F

 

  1. (i) 4º                (ii) 11º            
    (iii) Tuesday, Wednesday, Thursday                 (iv) Tuesday, Wednesday, Sunday
  2. (i) 40                (ii) April, May, October
    (iii) June, July               (iv) February
  3. (i) €110            (ii) 1993                      
    (iii) 1993, 1997, 1999              (iv) 1995, 1996, 2000
  4. (i) 14                (ii) Saturday                
    (iii) Monday, Friday, Sunday                (iv) Tuesday, Wednesday, Saturday
  5. (i) February, March                  (ii) July, December                  
    (iii) February, March, April, September                       
    (iv) July, November, December
  1. (ii) 48 hours     (iii) 160 hours              (iv) 5.2 hours = 5 h 12 m
  2. (ii) October      (iii) 40 mm       (iv) September, October                      (v) 600 mm

 

EXERCISE 13G

 

  1. (i) 51                (ii) 41               (iii) 28
  2. (i) 23                (ii) 18               (iii) 19
  3. (i) 75                (ii) 44               (iii) 61
  4. (i) 42                (ii) 28               (iii) 20
  5. (i) 29                (ii) 18               (iii) 25
  6. (i) 36                (ii) 55               (iii) 29
  7. (i) 30                (ii) 20               (iii) 40
  8. (i) 24                (ii) 29               (iii) 7
  9. (i) 69                (ii) 46               (iii) 65
  10. (i) 21                (ii) 33               (iii) 18
  11. (i) 84º              (ii) 32               (iii) 21              (iv) 37
  12. (i) 102º            (ii) 81               (iii) 48              (iv) 51
  13. 6
  14. 21
  15. 266
  16. 25
  17. (i) 144              (ii) 30

 

EXERCISE 13H

 

  1. 35
  2. 32
  3. 18
  4. 43
  5. 52
  6. 26
  7. (i) 150              (ii) 2.5              (iii) 500
  8. Game               A         B          C         D
    Pupils               6          4          12        2
  9. Amount in €                  4          5          6          7
    Number of people        2          5          10        3

    (i) €6                (ii) 65%           (iii) €5.70        

 

CHAPTER TEST 13

 

  1. €14.33
  2. 140
  3. 3
  4. (ii) 620 mm                  (iii) 465 mm     (iv) 75%
  5. (i) 20                (ii) 1                 (iii) 13              (iv) 2
  6. (ii) Friday, Saturday, Sunday, (mean = €8.)
  7. (i) 96º              (ii) 49               (iii) 32              (iv) 39
  8. 40

 

EXERCISE 14A

 

  1. (i) 60                (ii) 90               (iii) 32
  2. (i) 30                (ii) 18
  3. (i) 50                (ii) 75
  4. (i) 90                (ii) 68               (iii) 56
  5. (i) 124              (ii) 131
  6. (i) 65                (ii) 56               (iii) 68
  7. (i) 66                (ii) 80               (iii) 32
  8. (i) <pcd            (ii) 80

 

EXERCISE 14B

 

  1. 30º
  1. 115º
  2. 20º.

 

EXERCISE 14C

 

  1. A = 70º            B = 40º            C = 60º            D = 30º
  2. 23º
  3. 80º
  1. 70
  2. X = 50º            Y = 60º            Z = 48º
  3. x = 30, y = 15
  4. x = 18, y = 72
  5. (i) <bca            (ii) 60º
  6. f = 55,  g = 70
  1. x = 40, y = 95, z = 115
  2. x = 30, y = 15
  3. (i) 100º            (ii) 40º

 

CHAPTER TEST 14

 

  1. x = 42
  2. z = 74, w = 58
  3. z = 144
  1. (i) 60º              (ii) 120º
  2. (i) 104º            (ii) 76

 

EXERCISE 15A

 

  1. (i) 22 cm          (ii) 34 cm         (iii) 56 cm        (iv) 82 cm        (v) 70 cm
  2. (i) 32 cm2         (ii) 15 cm2        (iii) 294 cm2
    (iv) 3456 cm2   (v) 625 cm2      (vi) 2268 cm2
  3. (i) 154 cm2       (ii) 1080 cm2
  4. 1472 m2
  5. 6 cm
  6. 12 cm
  7. 16 cm
  8. 19 cm
  9. 15 cm
  10. 8 cm
  11. 1440 cm2
  12. 30400 cm2
  13. 113.4 m2, 315.
  14. 20 m2, 500, €450.
  15. 24 m2, 39 m2, 624

 

EXERCISE 15B

 

  1. (i) 52 cm2         (ii) 236 cm2      (iii) 202 cm2     (iv) 180 cm2     (v) 166 cm2
  2. (i) 54 cm2         (ii) 600 cm2      (iii) 24 cm2       (iv) 6 cm2         (v) 294 cm2
  3. (i) 48 cm3         (ii) 105 cm3      (iii) 192 cm3    
    (iv) 648 cm3     (v) 320 cm3 (vi) 3000 cm3
  4. (i) 99 000 cm3  (ii) 288
  5. (i) 180 000 cm3            (ii) 28.57%
  6. 4 cm
  7. 8 cm
  8. 5 cm
  9. 2 cm
  10. 7 cm
  11. 13.5 cm2
  12. 7 cm

 

EXERCISE 15C

 

  1. (i) 5 m2             (ii) 900 cm2                  (iii) 0.3 m2
  2. (i) 3 ha                         (ii) 35 m2                      (iii) 1.5 ha
  3. (i) 45 cm2                     (ii) 18 m2                      (iii) 0.4 ha
  4. (i) 15,000 cm2              (ii) 1.5 m2
  5. (i) 54,000 m2                (ii) 5.4 ha
  6. (i) 112,000 cm2                (ii) 11.2 m2
  7. (i) 44.1 m2                    (ii) 441,000 cm2
  8. (i) 2,500 cm2                (ii) 0.25 m2, 32 tiles
  9. (i) 3 litres                      (ii) 0.25 litres                (iii) 8,400,000 cm3
  10. (i) 7,000 cm3                (ii) 0.9 litres                  (iii) 25,000,000 cm3
  11. (i) 40,000 cm3              (ii) 40 litres
  12. (i) 6,000 cm3                (ii) 6 litres
  13. (i) 1,200 cm3                (ii) 36   litres
  14. 20 cm
  15. 60 cm

 

EXERCISE 15D

 

  1. (i) 10                (ii) 20               (iii) 25              (iv) 29
    (v) 40               (vi) 30              (vii) 35             (viii) 28
    (ix) 9                (x) 26
  2. (i) 3.61             (ii) 5.83            (iii) 2.65           (iv) 4.47
  4. 20
  5. 30
  7. (i) yes               (ii) no               (iii) yes
    (iv) yes             (v) no
  8. 3
  9. 5
  10. 8

 

EXERCISE 15E

 

  1. (i) 14                (ii) 48               (iii) 72              (iv) 33
  2. (i) 6                  (ii) 7.5              (iii) 30              (iv) 54
  3. 10
  4. 9
  5. (i) 30                (ii) 80               (iii) 108
  6. 6
  7. 6
  8. 48
  9. (ii) 24
  10. (i) 90º              (iii) 80º            (iv) 2
  12. (iii) 6
  13. (iii)51
  14. (i) 4                  (ii) 32.8            (iii) 6.56

 

CHAPTER TEST 15

 

  1. (i) P = 80 cm, A = 400 cm2     (ii) P = 62 cm, A = 84 cm2     
    (iii) P = 100 cm, A = 576 cm2
  2. 208 m2
  3. 7 cm
  4. 150 cm2
  5. 11 cm
  6. (i) 168,000 m2              (ii) 16.8 ha
  7. 50 cm
  8. 4
  9. 6
  10. 5

 

 

EXERCISE 16A

 

  1. (i) yes               (ii) no               (iii) no              (iv) yes
  1. 91º
  2. 21º
  1. 58º
  2. 86º

 

EXERCISE 16B

 

  1. 2.9 cm
  2. 72º
  3. 43º, 64º

 

EXERCISE 16C

 

  1. 8.4 cm, 5.5 cm, 29º, smallest angle 29º, opposite side 4.5 cm.
  2. 1.9 cm, 3.0 cm
  3. 75º
  4. 6 cm, 6 cm, 60º, equilateral.
  5. 3.8 cm, 4 cm, 84º, largest side 5.2 cm, opposite angle 84º.

 

EXERCISE 16D

 

  1. 41º
  2. 52º, 38º, 4.3 cm, longest side 7cm, opposite angle 90º.
  3. 33º
  4. 3 cm
  5. 6 cm, 23º.

 

EXERCISE 16E

 

  3. RHS
  4. SAS
  5. SAS

 

EXERCISE 16I

 

  1. 4.3 cm
  2. 105º
  3. 3.6 cm
  4. 3.4 cm
  5. 30º

 

CHAPTER TEST 16

 

  1. 90º
  1. 4.4 cm, 6.1 cm, 54º, smallest angle 46º, opposite side 4.4 cm.
  2. 4.2 cm, 40º.
  3. SAS
  4. 4.3 cm.

 

 

EXERCISE 17A

 

  1. (i) 62.8 cm       (ii) 31.4 cm      (iii) 125.6 cm               (iv) 94.2 cm
  2. (i) 88 cm          (ii) 22 cm         (iii) 8.8 cm                    (iv) 15.4 cm
  3. (i) 188.4 cm     (ii) 251.2 cm    (iii )157 cm                  (iv) 75.36 cm
  4. (i) 196 cm        (ii) 98 cm
  5. (i) 224 cm        (ii) 112 cm
  6. (i) 182 cm        (ii) 91 cm
  7. (i) 140 cm        (ii) 70 cm
  8. 250
  9. 800
  10. 400
  11. (i) 210 cm        (ii) 105 cm
  12. (i) 75.4 cm       (ii) 25.1 cm      (iii) 100.5 cm
    (iv) 50.3 cm     (v) 37.7 cm
  13. (i) 44 cm          (ii) 55 cm         (iii) 176
    (iv) 7.7 cm       (v) 99 cm
  14. 128 cm
  15. 100 cm
  16. (i) 400 m          (ii) 6.25 m/s

 

EXERCISE 17B

 

  1. (i) 1,386 cm2                (ii) 2,464 cm2               (iii) 7,546 cm2
    (iv)18,634 cm2             (v) 5,544 cm2
  2. (i) 12.56 cm2                (ii) 314 cm2                  (iii) 78.5 cm2   
    (iv)28.26 cm2                (v) 113.04 cm2
  3. (i) 1,256.4 cm2             (ii) 5,025.6 cm2            (iii) 31,410 cm2
  4. 35 cm
  5. 4 cm
  6. 15 cm
  7. 70 cm
  8. 21 cm
  9. 5 cm
  10. (i) 3,773 cm2                (ii) 4,928 cm2               (iii) 308 cm2
  11. (i) 154 cm2                     (ii) 221 cm2
  12. (i) 21 m                        (ii) 882 m2                    (iii) 189 m2
  13. (i) 78.5 cm2                    (ii) 10 cm                     (iii) 48%
  14. 1050 cm2
  15. 616 cm2

 

EXERCISE 17C

 

  1. (i) 880 cm2, 6 160 cm3             (ii) 220cm2, 550 cm3
    (iii) 660 cm2, 6 930 cm3           (iv) 3 080 cm2, 75 460 cm3
    (v) 528 cm2, 1 848 cm3                            (vi) 528 cm2, 1 584 cm3
  2. (i) 188.4 cm2, 282.6 cm3          (ii) 75.36 cm2, 113.04 cm3
    (iii) 25.12 cm2, 25.12 cm3        (iv) 314 cm2, 785 cm3
    (v) 263.76 cm2, 791.28 cm3     (vi) 401.92 cm2, 1 607.68 cm3
  3. (i) 141.28 cm2              (ii) 4 224 cm2
  4. (i) 8 cm            (ii) 628 cm3
  5. (i) 4 cm            (ii) 251.3 cm2
  6. (i) 30 cm          (ii) 9 425 cm3
  7. (i) 80 cm          (ii) 157.1 litres
  8. (i) 8 cm            (ii) 1.2 litres
  9. (i) 70 cm          (ii) 351.9 litres
  10. (i) 198 cm3       (ii) 252 cm3
  11. (i) 412.5 cm3    (ii) 525 cm3      (iii) 79%
  12. 7 700 cm3
  13. 88 000 cm3, 220 cm3, 400
  14. 1100 cm3         (i) 20 cm          (ii) 10 cm         (iii) 2800 cm3,
  15. 198 cm3, 49 500 cm3, 9 900 cm3, 11 cm
  16. (i) 4.224 cm3    (ii) 26.88 cm3   (iii) 5.78 cm3

 

EXERCISE 17D

 

  1. (i) 1 386 cm2, 4 851 cm3                      (ii) 887.04 cm2, 2 483.71 cm3
    (iii) 3 118.5 cm2, 16 372.13 cm3          (iv) 346.5 cm2, 606.38 cm3
    (v) 221.76 cm2, 310.46 cm3                   (vi) 498.96 cm2, 1 047.82 cm3
  2. (i) 113 cm2, 113 cm3                            (ii) 452 cm2, 904 cm3
    (iii) 1 809 cm2, 7 235 cm3                    (iv) 1 256 cm2, 4 187 cm3
    (v) 5 024 cm2, 3 3493 cm3                   (vi) 11 304 cm2, 113 040 cm3
  3. 7 cm
  4. 28 cm
  5. 28 cm
  6. 1.5 cm
  7. 4.5 cm
  8. 3 cm
  9. 6 cm
  10. 15 cm
  11. (i) 4 cm            (ii) 201 cm2
  12. (i) 2 cm            (ii) 50
  13. (i) 3 052.08 cm3           (ii) 18 cm         (iii) 5 832 cm3              (iv) 52%
  14. (i) 904.32 cm3              (ii) 3 456 cm3
  15. (i) 36 cm          (ii) 2 187 cm3               (iii) 1 458 cm3              (iv) 729 cm3

 

CHAPTER TEST 17

 

  1. (i) 75.384 cm               (ii) 452.304 cm2
  2. (i) 96 cm                      (ii) 614.25 cm2
  3. 700
  4. 1.4 cm
  5. (i) 21 cm2                        (ii) 21.43%
  6. (i) 24 cm          (ii) 30 159.3 cm3
  7. 10.5 cm
  8. 1 767.15 cm3, 10 125 cm3, 52.4%

 

EXERCISE 18A

 

  1. €180
  2. €66
  3. €228
  4. €92
  5. €242
  6. €180
  7. €500
  8. €280
  9. €400
  10. €40
  11. €70
  12. €228
  13. 12%
  14. 15%
  15. 16%
  16. 21%
  17. 23%
  18. €140.36
  19. €95
  20. 12.5%

 

EXERCISE 18B

 

  1. €80
  2. €25
  3. €23
  4. €56
  5. €122
  6. €78.65
  7. €51.47
  8. €54.63
  9. €47.14
  10. (i) €287            (ii) €48.84
  11. (i) €296            (ii) €46.76
  12. (i) €414            (ii) €76.43
  13. (i) €206.60       (ii) €14.75        (iii) €191.85
  14. (i) €447            (ii) €111.18      (iii) €335.82
  15. (i) €6,627.60    (ii) €4,250.11
  16. (i) €4,361         (ii) €3,049.35
  17. (i) €3,769.70    (ii) €2,826
  18. (i) €3,114.40    (ii) €1,856.54
  19. (i) €4,983.30    (ii) €3,429.58
  20. (i) €7,933.50    (ii) €5,389.25
  21. €25.90
  22. 20%
  23. €550.40
  24. €39.90

 

EXERCISE 18C

 

  1. €200
  2. €45
  3. €68
  4. €174
  5. €14.58
  6. 848 Rupees
  7. 2184 Krone
  8. €76.18
  9. €770.83
  10. €1,409.72

 

EXERCISE 18D

 

  1. (i) €5.54            (ii) €24.46       (iii) €20.82
  2. (i) €13.81         (ii) €6.19          (iii) 46 minutes (iv) 47
  3. (i) €87.75         (ii) €12.25        (iii) 6 hours      (iv) €4,563

 

EXERCISE 18E

 

  1. 9317 15 14a
  2. www.esb.ie
  3. 1850372999
  4. 1877
  5. 1877
  6. 9.52 c
  7. 178.6904
  8. 178.69
  9. 10.85
  10. 23.6925
  11. 23.69
  12. 213.23
  13. 193.79
  14. 259.74
  15. 259.74
  16. 19 MAR 02 – 16 MAY 02
  17. 01 JUNE 02

 

EXERCISE 18F

  1. 1120    €107.52           €122                €15.25             €137.25
  2. 880      €83.60             €92                  €11.50             €103.50
  3. 970      €91.18             €102                €14.28             €116.28
  4. 1040    €96.72             €108.60           €16.29             €124.89
  5. 960      €88.32             €99.60             €12.45             €112.05
  6. 840      €78.96             €95.40             €14.31             €109.71
  7. (i) 1250, 970, 810, 1450.
    (ii) €144.00 , €114.39, €97.47, €165.15
    (iii) 4480          (iv) €521.01     (v) €1.43

 

CHAPTER TEST 18

 

  1. €333
  2. €200
  3. €71.31
  4. (i)  €6,619.70   (ii) €2,551.99  
  5. (i)  €585            (ii) €245.70     (iii) €207.25
  6. €526.29
  7. (i)  1030           (ii) €96.82        (iii) €108.80    
    (iv) €13.60       (v) €122.40

 

EXERCISE 20A

 

  1. (i) {1, 2, 3}                  (ii) {4}             (iii) {1, 2, 3, 4}, 4.
  2. (i) {d}                          (ii) {e}             (iii) {i, j, k}
  3. (i) {1, 2, 3, 4, 5, 6, 7}              (ii) {1, 2, 3, 4}
    (iii) {1, 2, 3, 5, 6, 7, 8, 9}, 8.
  4. (i) {p, q, r}                  (ii) {l, m, r}                 (iii) {l, m, n, o}
  5. (i) {7, 8, 9, 10}            (ii) {3, 4, 5}                 (iii) {3, 4, 9, 10}
  6. (i) {u, v, w, x}             (ii) {r, s, x}                  (iii) {r, s}                     (iv) { }
  7. (i) {s, t, u, v, w, x, y, z}           (ii) {s, t}                      (iii) {w, v, u}
    (iv) {s, t, y, z, x}                      (v) {s, t, y, z}
  8. (i) {10, 14, 6, 18}        (ii) {8, 12, 16}             (iii) {2, 4, 10, 14, 6, 18}
    (iv) {6, 18}
  9. (i) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
    (ii) {8, 9, 10, 11, 12, 13, 14}
    (iii) {1, 2, 3, 7, 11, 12, 13, 14}
    (iv) {1, 2, 3, 7, 8, 9, 10, 11, 12, 13, 14}
    (v) {4, 8, 9}                 (vi) {1, 2, 3, 7, 11}
  10. (i) {b, g, c, f, d, h, i, j, k, m}    (ii) {k, i, j, m}              (iii) {i, j, h, d}
    (iv) {b, c, h, i, j}                      (v) {g, f, h}                  (vi) {b, c, d, k, i, j, m}

 

EXERCISE 20B

  1. (ii) 7                 (iii) 4
  2. (ii) 5                 (iii) 11
  3. (ii) 5                 (iii) 7
  4. (ii) 4                 (iii) 5
  5. (ii) 4                 (iii) 7
  6. 10

9.      28-x = 22,   x = 6

10.  (ii) 6                 (iii) 6

11.  (ii) 7                 (iii) 9

12.  9

13.  2

14.  (ii) 5                 (iii) 10+12+2 = 24

 

CHAPTER TEST 20

 

 

  1. (i) {t, e, l, v, i, s, o, n}             (ii) {v, i, d, e, o, g, a, m}
    (iii) {e, v, i, o}                         (iv) {t, e, l, v, i, s, o, n, d, g, a, m}
  2. {}, {m}, {n}, {m, n}
    (ii) {}, {2}, {4}, {6}, {2, 4}, {2, 6}, {4, 6}, {2, 4, 6}
  3. #{d, i, f, c, u, l, t, y} = 8
  1. (i) {1, 2, 3}      (ii) {6, 7, 8, 9, 10}       (iii) {9, 10}, 3
  2. (i) {o, u, s, e, m, a, t}              (ii) {m, a, t, p, c}
  3. (ii) 3                 (iii) 6

 

EXERCISE 21A

 

1.      5x+3y = 18

2.      9a+4b = 20

3.      12p+6q = 34

4.      6x = 6

5.      11a = 20

6.      12c = 27

7.      2x = 6

8.      2a = 10

9.      2c = 12

10.  8x = 34

11.  8x+6y = 10

12.  9a-21b = 24

13.  20c+8d = 44

14.  15p-20q = 30

15.  42x+18y = 54

 

EXERCISE 21B

 

1.      x = 2, y = 3.

2.      x = 5, y = 2.

3.      x = 7, y = 3.

4.      x = 8, y = 5.

5.      x = 4, y = 6.

6.      x = 10, y = 5.

7.      x = 1, y = 3.

8.      x = 9, y = 6.

9.      x = 2, y = 3.

10.  x = 4, y = 1.

11.  x = 3, y = 3.

12.  x = 4, y = 2.

13.  x = 6, y = 5.

14.  x = 1, y = 3.

15.  x = 5, y = 2.

16.  x = 2, y = 1.

17.  x = 3, y = 2.

18.  x = 3, y = 2.

19.  x = 4, y = 3.

20.  x = 2, y = 2.

21.  x = 1, y = 3.

22.  x = 10, y = 2.

23.  x = 2, y = 2.

24.  x = 16/3, y = 19/3

25.  x = 3, y = 7.

26.  x = 2, y = 5.

27.  x = 5, y = 8.

28.  x = 5, y = 5.

29.  x = 8, y = 6.

 

EXERCISE 21C

 

1.      x = 4, y = 3.

2.      x = 10, y = 2.

3.      x = 7, y = 1.

4.      x = 5, y = 3.

5.      x = 2, y = 1.

6.      x = 6, y = 10.

7.      x = 12, y = 4.

8.      x = 2, y = 3.

9.      x = 4, y = -2.

10.  x = 1, y = -1.

11.  x = 4, y = -3.

12.  x = 5, y = -5.

13.  x = -2, y = 3.

14.  x = 5, y = -1.

15.  x = 4, y = 2.

16.  x = 2, y = 3.

17.  x = 20, y = 4.

18.  x = 10, y = 2.

19.  x = 2, y = 1.

 

EXERCISE 21D

 

1.      (i) 5x+2y = 76,   2x+y = 32                 (ii) x = 12, y = 8

2.      (i) 3x+4y = 40,   x+y = 12                   (ii) x = 8, y = 4

3.      (i) x+y = 60,   x-y = 24                        (ii) x = 42, y = 18

4.      (i) 4x+5y = 44,   3x+2y = 26               (ii) x = 6, y = 4

5.      (i) 2x+3y = 60,   x-y = 5                      (ii) x = 15, y = 10

6.      Tom is 14, Ann is 16 years of age.

7.      140 people at €12 and 60 people at €20.

 

EXERCISE 21E

 

1.      (i) 3, 9              (ii) 6, 7             (iii) 10, 12.

2.      (i) 4, 7              (ii) 2, 5             (iii) 0, 8.

3.      (i) 3, -2            (ii) 6, -4            (iii) 1, -5.

4.      (i) 0, -19                      (ii) -16, 9                      (iii) 5, -3.

5.      (i) -3, -6                       (ii) 0, -2                        (iii) -7, -20.

6.      (i) 3, 4              (ii) 3, 2

7.      (i) 3, 5              (ii) 3, 6

8.      (i) 2, 2              (ii) 1, 4

9.      (i) 1, 3              (ii) 5, 5

10.  (i) 1, 5              (ii) 2, 6

11.  (i) 3, 7              (ii) 1, 6

12.  (i) 4, 4              (ii) 2, 7

13.  (i) 2, 4              (ii) 1, 1

14.  (i) 5, 6              (ii) 1, 8

15.  (i) 6, 7              (ii) 1, 2

16.  (i) 6, 6              (ii) 2, 8

 

EXERCISE 21F

 

1.      (i) -5, -2                       (ii) -3, -2

2.      (i) -5, -5                       (ii) -6, -2

3.      (i) -5, -4                       (ii) -8, -2

4.      (i) -7, -6                       (ii) -5, -3

5.      (i) -2, 4                        (ii) -3, 7

6.      (i) -1, 5                        (ii) -2, 7

7.      (i) -4, 6                        (ii) -7, 8

8.      (i) -5, 7                        (ii) -1, 8

9.      (i) -8, 3                        (ii) 1, -4

10.  (i) -6, 1                        (ii) -8, 5

11.  (i) -9, 2                        (ii) -6, 4

12.  (i) 3, 4                          (ii) -4, 1

13.  (i) -1, 7                        (ii) -10, 5

14.  (i) 10, 10                      (ii) -7, -7

15.  (i) -1, 12                      (ii) -6, 4

 

EXERCISE 21G

 

1.      x2+x-6 = 0,                  2, 3

2.      x2+x-30 = 0,                5, 6

3.      x2+x-12 = 0,                3, 4

4.      x2+3x-10 = 0,              2, 5

5.      x2+4x-45 = 0,              5, 9

6.      x2-x-30 = 0,                 5, 6

7.      x2-3x-28 = 0,               3, 7

8.      x2 -36 = 0,                   -6, 6

9.      x2 -25 = 0,                   -5, 5

10.  x2 -64 = 0,                   -8, 8

11.  x2 -16 = 0,                   -4, 4

 

EXERCISE 21H

 

1.                        3

2.                        2

3.                        4

4.                        1

5.                        3

6.                        5

7.                        7

8.                        13

9.                        14

10.                    6

11.                    5

12.                    7

13.                    5

14.                    6

15.                    9

 

EXERCISE 21I

 

1.     

2.      x > 3

3.     

4.      x < 2

5.      x < 4

6.      x < 3

7.     

8.     

9.     

10. 

11. 

12.  x < 5

13.  x > 2

14.  x < 4

15.  x < 6

16. 

17.  x < 2

18. 

19. 

20.  x < 2

21.  x < 3

22.  {0, 1, 2, 3, 4}

23.  {0, 1, 2}

24.  x < 5

25.  {0, 1, 2, 3, 4}

26. 

27.  {0, 1, 2}

28.  x = 6

29.  {0, 1, 2}

30.  x < 6

 

CHAPTER TEST 21

 

1.      (i)         x = 2, y = 1      (ii)        x = 4, y = 3

2.      (i)         x = 6, y = 5      (ii)        x = 6, y = 7

3.      x+y = 450, 4x+6y = 2100
They sold 300 tickets at €4 each and 150 tickets at €6 each.

4.      (i)         x = 0, x = -9    (ii)        x = 1, x = 6      (iii)       x = -3, x = 11

5.      (i)         x = 4, x = 6      (ii)        x = 7

6.      (i)         x = -10, x = 3  (ii)        x = -8, x = 2    (iii)       x = -11, x = 5

7.      x(x+1) = 42,    x = 6, x = 7

8.      x = 7

9.     

10. 

 

EXERCISE 22A

 

3.      (i) 0.50             (ii) 0.64            (iii) 0.77           (iv) 0.87
(v) 0.94            (vi) 0.19           (vii) 0.75          (viii) 0.39
(ix) 0.99           (x) 0.10

4.      (i) 13°              (ii) 18°              (iii) 70° (iv) 54°
(v) 30°             (vi) 43° (vii) 11°            (viii) 57°
(ix) 22° (x) 45°

 

EXERCISE 22B

 

2.      sin B = 0.75, cos B = 0.66, tan B = 1.13

3.      sin C = 0.56, cos C = 0.83, tan C = 0.68

4.      1.92

5.      0.79

6.      0.89

8.      (i) 0.67             (ii) 0.96            (iii) 0.78           (iv) 0.48
(v) 3.27            (vi) 0.26           (vii) 0.88          (viii) 57.29
(ix) 1.00           (x) 0.98

9.      (i) 69°              (ii) 64°              (iii) 18° (iv) 30°
(v) 87°             (vi) 47° (vii) 14°            (viii) 13°
(ix) 81° (x) 45°

 

EXERCISE 22C

 

1.   3.5 cm

2.   5.5 cm

3.   10.0 cm

4.   11.3 cm

5.   32º

6.   56º

7.   58º

8.   (i) 43º   (ii) 14.5 cm

9.   33.8 cm

10. 11.4 cm

11. (i) 61º   (ii) 29.6 cm

12. (i) 36º   (ii) 54.7 cm

13. 84.9 cm

14. 44º

 

EXERCISE 22D

 

1.                  2.9 m

2.                  3.4 m

3.                  4.6 m

4.                  40º

5.                  247 m

6.                  118 m

7.                  210 m

 

EXERCISE 22E

 

1.   (i) 8 km            (ii) 3756 m

2.   (i) 2.6 km         (ii) 974 m

3.   (i) 5.4 km         (ii) 2781 m

4.   (i) 55 m/s          (ii) 1067 m

5.   42º

6.   49º

7.   53º

8.   68º

9.   (i) 17.3 m         (ii) 23º

10. (i) 15.6 m         (ii) 5.4 m

 

EXERCISE 22F

 

1.   (i) N34ºE         (ii) N55ºW       (iii) E25ºS
(iv) N42ºE        (v) N37ºW       (vi) W63ºS

2.   (i) 80 km          (ii) 130 km       (iii) 32.5 km/hr

3.   (i) 36 km          (ii) 51 km         (iii) 25.5 km/hr

4.   (i) 69 km          (ii) 142 km       (iii) 47.3 km/hr

5.   15 898 m

6.   20.0 km/hr

7.   16.7 km/hr

8.   (i) 15 km          (ii) 53º

9.   (i) 17 km          (ii) 28º

10. (i) 20 cm          (ii) 53º

 

CHAPTER TEST 22

 

1.                  sin D = 0.65, cos D = 0.76, tan D = 0.86

3.                  13.5 cm

4.                  (i) 37º         (ii) 20.7 cm

5.                  (i) 40 m/s    (ii) 309 m

6.                  20 km, 40 km

 

EXERCISE 23A

 

1.                  a(-2, 2), b(3, 5), c(4, 2), d(3, -2), e(-2, -2), f(-3, 5), g(5, -2),
h(2, 7), i(-1, 6), j(1, -4), k(-4, -3), l(-2, -4), m(2, 3)

2.                  a(5, 4), b(4, 3), c(3, 2), d(2, 1), e(-3, 3), f(-3, 4), g(-3, 2),
h(2, -2), i(3, -2), j(4, -2), k(-3, -2), l(-2, -3), m(-1, -4)

3.                  a(1, 3), b(3, 3), c(5, 3), d(-6, 6), e(-4, 4), f(-2, 2), g(-4, -1),
h(-3, -2), i(-2, -3), j(4, -3), k(1, 0), l(7, -6), m(-4, -5), n(1, -3)

 

EXERCISE 23B

 

1.                  (3, 10)

2.                  (4, 11)

3.                  (7, 9)

4.                  (5, 5)

5.                  (4, 10)

6.                  (4, 3)

7.                  (8, 13)

8.                  (15, 16)

9.                  (18, 9)

10.              (1, 8)

11.              (-2, 4)

12.              (-1, 3)

13.              (3, -2)

14.              (0, -2)

15.              (-4, -4)

16.              (-3, 5)

17.              (-1, 3)

18.              (-2, 3)

19.              (-1, -8)

20.              (5, 10)

 

EXERCISE 23 C

 

4.                  (i) (-5, 3)                (ii) (2, 9)           (iii) (-8, 7)
(iv) (-6, 4)              (v) (-5, -5)       (vi) (0, 0)

5.                  (i) (-7, 1)                (ii) (2, 6)           (iii) (-8, 0)
(iv) (-3, -5) (v) (3, -5)         (vi) (-2, 9)

6.                  (i) (6, -8)                (ii) (-10, -2)      (iii) (3, 7)
(iv) (-8, -2) (v) (4, 0)          (vi) (-6, -5)

7.                  (i) (-7, 0)                (ii) (3, 8)           (iii) (2, 10)
(iv) (5, -3)              (v) (0, 9)          (vi) (-1, -6)
(vii) (7, 7)               (viii) (-3, 5)       (viii) (-8, 3)
(x) (-6, 1)

 

EXERCISE 23D

 

1.                  (3, 5)

2.                  (4, 3)

3.                  (3, 5)

4.                  (3, 7)

5.                  (5, 2)

6.                  (-5, -2)

7.                  (-1, -3)

8.                  (-1, 1)

9.                  (-8, 5)

10.              (-9, -2)

11.              (-5, -4)

12.              (4, 6)

13.              (13, 15)

14.              (25, 35)

15.              (10, 80)

 

EXERCISE 23E

 

1.                  5

2.                  3.61

3.                  17

4.                  10

5.                  5

6.                  13

7.                  10

8.                  1.41

9.                 

10.              5

12.             

13.             
(Note: It is not necessary to reduce surds at Ordinary level.)

14.              (i)   (7, 7)    (iii)

15.              (i) 3            (ii)            (iii) 9

 

EXERCISE 23F

 

1.                 

2.                  -1

3.                 

4.                 

5.                 

6.                 

7.                  (i) 1            (ii) 1

8.                  (i) 2            (ii) (-3, 3)         (iii)

9.                  (i) (1.5, 4.5)           (ii) -3    (iii) -3

10.             

 

EXERCISE 23G

 

1.                  x = 1

2.                  x = 4

3.                  y = 3

4.                  y = 5

5.                  x = 2,        p(2, 0)

6.                  y = 4          k(0, 4)

 

EXERCISE 23H

 

1.                  (i) x-y-2 = 0           (ii) x-y+4 = 0               (iii) x-y+5 = 0
(iv) 2x-y-5 = 0        (v) 3x-y+1 = 0

2.                  (i) 3x+y-7 = 0        (ii) 4x+y-2 = 0             (iii) 2x+y = 0
(iv) x+y+2 = 0       (v) 3x+y+10 = 0

3.                  (i) x-2y+1 = 0        (ii) x-3y-1 = 0               (iii) x-5y+3 = 0
(iv) 2x-3y-5 = 0      (v) 3x-4y-7 = 0

4.                  (i) 1            (ii) x-y+2 = 0

5.                  (i) 3            (ii) 3x-y-9 = 0

6.                  (i) -1          (ii) x+y-6 = 0

7.                  (i) -3          (ii) 3x+y-15 = 0

8.                  (i) 2            (ii) 2x-y-5 = 0

9.                  (i) 3            (ii) 3x-y-2 = 0              (iii) midpoint = (2, 4)

 

EXERCISE 23I

 

1.                  (6, 0)

2.                  (3, 0)

3.                  (2, 0)

4.                  (4, 0)

5.                  (5, 0)

6.                  (0, 4)

7.                  (0, 4)

8.                  (0, 1)

9.                  (0, 9)

10.              (0, 2)

 

CHAPTER TEST 23

 

1.                  (iii) 0.5       (iv) x-2y+6 = 0 (v) (0, 3)

2.                 

3.                  (iii) -2         (iv) 2x+y-2 = 0 (v) (1, 0)
(vi) k = -12            (vii) (2, 2)

4.                  (ii) (2, -1)               (iii) -1               (iv) x+y-1 = 0
(v) k(1, 0)              (vi) (1, -2)

5.                  (iii) 1                      (iv) x-y+3 = 0              (v) q(-3, 0)
(vi) (2, 1)

6.                  (ii) -1                      (iii) (2, 1)          (iv) (0, 3)          (v) A = 3

 

EXERCISE 24A

 

1.                  (i) {0, 1, 2, 3}        (ii) {0, 1, 8, 27}

2.                  (i) {1, 2, 3}            (ii) {4, 5, 6}

3.                  (i) {Galway, Leitrim, Mayo, Roscommon, Sligo}
(ii) {1127, 145, 610, 220, 279}

5.                  (i) 7            (ii) 23

6.                  (i) 12          (ii) 22

7.                  (i) 2            (ii) -4

8.                  (i) 5            (ii) -9

9.                  (i) -2          (ii) -5

10.              (i) -1          (ii) 3

11.              (i) 6            (ii) 2

12.              (i) 23          (ii) 3

13.              0

14.              0

15.              (11, 5), (6, 0)

16.              (1, 2), (2, 1), (3, 0)

17.              (5, 3), (9, 11), (3, -1)

18.              (0, -2), (1, 1), (2, 4)

 

EXERCISE 24B

 

1.                  y = 4

2.                  y = 5

3.                  x = 2

4.                  x = 3

5.                  y = -10

6.                  (1, 3), (3, 5)

7.                  (1, 0), (3, 4)

12.              y = 55

13.              y = 14

14.              x = 2.5

15.              x = 3.5

 

EXERCISE 24C

 

1.                  (iii) x = 1, y = 3

2.                  (iii) x = 1.5, y = 3.5

3.                  (iii) x = 1, y = -2

4.                  (iii) x = 3, y = -1

5.                  (iii) x = 2, y = 2

6.                  (iii) x = 2, y = -1

7.                  (iii) x = 2.5, y = 3

8.                  (iii) x = 3, y = 1

9.                  (iii) x = 2, y = 4

10.              (iii) x = 1, y = 3

11.              (iii) x = 1, y = -1

12.              (iii) x = 12, y = 4

 

EXERCISE 24D

 

  1. x = 0.8, x = 3.2
  2. x = 0.5, x = 1.5
  3. x = 2.5, x = 4
  4. x = 0.4, x = 3.6
  5. x = 0.2, x = 2.3
  6. (i) x = -2, x = 1            (ii) y = 1.75
  7. (i) x = -1, x = 3            (ii) y = 2.25
  8. (i) x = 1, x = 5             (ii) y = 5.25
  9. (i) No solution i.e. the graph does not cross the x-axis.
    (ii) 6.75
  10. (i) x = -1, x = 3            (ii) Axis of symmetry: x = 1
  11. (i) 4.15 p.m.     (ii) x = -1.6 i.e. October, x = 1.6 i.e. February
  12. (i) x = 0.6 i.e. 36 minutes after midnight, x = 3.4 i.e. 3. 24 a.m.
    (ii) 8.6 km/hr
  13. (i) 1.25
    x = 3.

 

CHAPTER TEST 24

 

1.                  -16

2.                  (1, 5), (3, 9), (4, 11)

3.                  (i) y = 3.5               (ii) x = 2.5

4.                  (ii) x = 2, y = 3

5.                  (i) 0.6 seconds and 5.4 seconds      (ii) x = 3 seconds.