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. 
3. A = {}, B ≠ {}, C = {}, D ≠ {}, E = {}, F = {}, G ≠ {}, H = {}

5. #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. 
2. 
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

1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 

EXERCISE 1E

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

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. 
3. 
4. #F = #{e, l, m, n, t} = 5
5. {}, {1}, {2}, {1,2}
6. 
7. 

EXERCISE 2A

1. 9732
2. 1578
3. 
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
11. 
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}
2. 
3. {11, 13, 17, 19}
4. {23, 29}
5. 3, 11, 19 and 23 are prime.
6. 
7. 
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
9. 

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. 
3. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
4. 
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
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 

EXERCISE 4B

1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 

EXERCISE 4C

1. 
2. 
3. (i) 15 (ii) 14 (iii) 40
4. 
5. 
6. 
7. 
8. 
9. 
10. 

EXERCISE 4D

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

EXERCISE 4E

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

EXERCISE 4F

1. €3
2. €2
3. €5
4. €12
5. €12
6. €20
7. €20
8. €10
9. 24
10. 
11. 
12. 100
13. 424

CHAPTER TEST 4

1. (i) 66 (ii) 15
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
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
5. 
6. 
7. 
8. 

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. 
2. 
3. 
4. 
5. 
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
14. 

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. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
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
2. 
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
8. 
9. 51.87
10. 
11. (i) 0.025 (ii) 9.8
12. 19.59
13. 
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%
4. 
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%
8. 
9. 
10. 
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

1. 
2. 
3. 
4. 
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

1. 
2. 
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%
8. 
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
13. 
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

1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 

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
8. 

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

3. (i) 3 kg (ii) 3000 g
4. 380
5. (i) 17 minutes (ii) 84 minutes
6. (i) 10 h 15 m (ii) 5 h 50 m
7. 5 h 4 m
8. (i) 1622 (ii) 0615
9. (i) 5.48 p.m. (ii) 2.10 a.m.
10. 1 h 55 m
11. (i) 2 h 53 m (ii) 1355
12. (i) 2 h 49 m (ii) 11 minutes
13. 2010
14. 44 km/hr
15. 3 h 30 m
16. 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)(