Foundation Student's Book - Hodder Plus Home

ANSWERS TO THE STUDENT’S BOOK EXERCISES Chapter 1 Exercise 1.1 (page 3) 1 a) 99 d) 181 2 a) 41 d) 94 3 a) 69 d) 476 4 a) 21 d) 13 5 £69 6 £27 7 276p, £2.76 8 26

b) e) b) e) b) e) b) e)

91 418 37 107 76 738 24 24

c) f) c) f) c) f) c) f)

124 453 47 276 180 1048 15 46

4 a) 1920 b) 4320 d) 11 200 e) 25 200 g) 259 200 h) 232 000 5 a) 1728 b) 2356 d) 1764 e) 1914 g) 3321 h) 9240 j) 29 713 k) 43 902 6 a) 63 200p b) £56 7 47 000 metres 8 £240 9 156 000 metres or 156 kilometres 10 952p

1

1 a) 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96 b) 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 2 24, 48, 72, 96 3 a) 2, 6, 18, 30 b) 6, 15, 18, 30, 33 c) 15, 30 4 a) 12, 24, 36, 48, 60, 72, 84, 96 b) 15, 30, 45, 60, 75, 90 5 60 6 a) 1, 2, 3, 6, 9, 18 b) 1, 2, 3, 4, 6, 8, 12, 24 7 1, 2, 3, 6 8 a) 1, 2, 4, 5, 8, 10, 20, 40 b) 1, 2, 3, 4, 6, 9, 12, 18, 36 9 1, 2, 4 10 a) 23 000 b) 197 000 c) 8000 d) 148 000 e) 5 732 000 11 a) 7700 b) 17 600 c) 800 d) 654 300 e) 5000 12 a) 70 000 or 68 000 b) £5 000 000 c) 8000 or 7900 d) £700 000 or £690 000

Exercise 1.3 (page 11) 520 36 100 549 000 470 000 53 640 6754 1500 60 000 1 800 000 12 000 000

7020 23 400

c) f) i) l)

4674 6216 34 776 20 768

b) 81 e) 900 h) 40 000

c) f) i)

121 2500 160 000

b) 484 e) 7921 h) 32 400

c) f) i)

961 3136 69 169

c) f)

1331 50 653

c) f)

19 87

c)

50

c) c) c)

3 8°C 14°C

Exercise 1.4 (page 14)


1 a) d) g) j) 2 a) d) g) 3 a) d) g) j)

c) f)

b) e) h) k) b) e) h) b) e) h) k)

6300 560 000 810 000 92 300 000 140 6400 73 000 5600 24 000 300 000 2 800 000

c) f) i) l) c) f) i) c) f) i) l)

54 000 6000 530 000 62 000 000 532 53 600 5800 14 000 2000 5 600 000 72 000 000

2

3

4

5

a) d) g) j) a) d) g) j) a) d) g) a) d) g) a) d)

49 144 3600 640 000 196 2209 1156 555 025 216 2744 79 507 15 23 68 20 80

b) e) h) b) e) h) b) e)

729 15 625 3 176 523 14 39 54 30 200

Exercise 1.5 (page 16) 1 2 3 4

a) a) a) a) b) c) 5 3

3 b) 3 1°C b) 4°C 16°C b) 26°C 8, 3, 1, 7 6, 4, 0, 5 6, 4, 3, 1, 2, 5

Mixed exercise 1 (page 18) 1 a) 132 b) 44 c) 269 d) 348 e) 1016 f) 63 2 271p 3 a) 20, 40, 60, 80, 100, 120 b) 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 c) 60, 120 4 a) 1, 2, 3, 4, 6, 12 b) 1, 2, 3, 6, 9, 18 c) 1, 2, 3, 5, 6, 10, 15, 30 d) 1, 2, 3, 6

Foundation WJEC GCSE Mathematics © 2010, Hodder Education

Answers to the Student’s Book exercises

165

5 a) 5600 d) 273 500 6 a) 9300 d) 78 g) 21 000 j) 140 000 7 a) 1764 8 8370 km 9 a) 64 d) 100 000 10 a) 841 d) 22 11

b) e) b) e) h) k) b)

18 000 6 000 000 63 000 6300 1410 31 920 4731

c) f) c) f) i) l) c)

273 000 3500 572 000 4000 34 800 292 800 9728

b) e) b) e)

1600 8000 1728 72

c)

250 000

c)

3 a) 312 f) k)

1 a) c) e)

2809

2 a)

15

3

4

10

10° warmer

15

7

6

10

5° colder

10

8

9

15

3 4 5 6 7


9 a) 34

e) 2 a) b) 3 a) e) i) 4 a) e) i) m)

h)

1 9 2 18 4 2 4 5 30 15 3 35 7 5 7 1 2 1 6 5 7

30 50 3 21 28 70 3 4 3 5 1 2 2 3

d)

4 7

2 a) 215

b) 137

156

238

f)

166

g)

m)

d) 137 i) n)

e)

225

514 2181

j)

337

3 5 4 5

e)

12 17 2 63

e)

2 3

e)

15

o) 112

b) d) f) h) 4 5 3 4

c)

15 5 21 7 18 3 60 10 3 1228 7 8 1 24 3 4 d) 11 5 i) 6

2 5 1 2

b)

1 3 4

b) 25

c)

3 5

c)

27

d) 4

d)

3

h) l) d) h) l) p)

35


17

1 a) 4 tens b) 4 tenths c) 4 ten thousands d) 4 hundredths e) 4 thousandths 2 a) 0.3 b) 4.7 c) 0.09 d) 52.79 e) 0.021 3 a) 35 b) 4130 c) 14110 3 3 d) 4 e) 9100 4 £0.05, £0.07, £0.92, £1.42, £6.07, £8.60 5 9.207, 7.29, 0.927, 0.209, 0.072 6 a) 0.468 kg b) 1.645 kg c) 0.072 kg d) 0.006 kg e) 2.45 kg 7 a) 0.12 m b) 0.874 m c) 0.218 m d) 0.056 m e) 1.38 m 8 6.4 cm, 78 mm, 47.6 cm, 0.58 m, 1.07 m 9 1745 g, 1.54 kg, 785 g, 0.75 kg, 486 g 10 a) 0.1 b) 0.5 c) 0.4 d) 0.25 e) 0.03

140

c)

17

c)

16

c)

150

c)

100


Exercise 2.3 (page 26) b)

h)

212 712

Chapter 3

1 a) 5 b) 9 d) £25 e) £2.50 2 a) 6 b) 9 d) £24 e) 5.2 m 3 a) 18 b) 36 d) £42 e) £105 4 a) 25 b) 40 d) 35 cm e) £75 5 £1.60 6 a) £3 b) £9 7 56 m 8 72 9 210 10 58 of £120 £75, 34 of £96 £72; 5 8 of £120 is the larger.

3 5

112

10 445 metres

2 5 3 16


1 a)

5 9 3

d)

c)

of 200 is the larger.

8 a) 4 9 1 9

l)

229 2110

f) h) j) a) 8 b) 11 c) 45 d) 160 40 metres 10 800 28 km 7 3 of 180 135, of 200 140 10 4 7 10

1 b) 13 c) 2 2 1 f) g) 3 5 1 2 3 100 6 1 0 2 4 6 200 12 20 1 10 2 3 4 6 5 10 15 20 30 50 3 10 5 9 b) 16 8 c) 4 12 12 6 f) 27 1305 g) 18 9 2 6 j) 131 1424 k) 9 27 4 b) 16 c) 5 2 5 f) 6 g) 3 2 1 j) k) 3 2 4 8 n) 9 o) 5

g)

3 15 4 20 1 11 2 22 16 8 18 9 4 40 9 90 2 b) 3 3 g) 11

Chapter 2 1 a)

b) 115

Mixed exercise 2 (page 27)

g)

Temperature (°C)

212 445

c)

3 5

d)

c)

313

d) 612

h)

267

534

i)

8 9

e)

1 4

e)

423

j)

3130


1 a) 13.91 d) 14.63 2 a) 9.65 d) 8.31 3 a) £16.62 d) £97.10 4 £57.90 5 1.76 m 6 2.96 seconds 7 a) 1.2(00) kg 8 £5.90

b) e) b) e) b)

42.09 60.71 14.91 20.77 £24.90

c) f) c) f) c)

111.15 113.37 54.84 221.84 £114.47

b) £11.97


9 a) 16.32 m d) 7.88 m 10 a) 4.572 kg d) 1.475 litres 11 £14.11 12 £4.89 13 a) 3.5 b) e) 0.03 f) i) 0.08 j)

b) e) b) e)

11.15 m 6.8 cm 1.96 kg 1.872 litres

1.8 0.54 0.15

c) f) c) f)

c) 2.4 g) 15 k) 0.25

5.55 m 7.3 cm 1.614 kg 0.7 litre

d) 6.3 h) 42 l) 0.01

1 a) 6 thousands b) 6 tenths c) 6 tens d) 6 hundredths e) 6 units 2 0.068, 0.215, 0.4, 0.532, 0.71 3 8p, 26p, 87p, 156p 4 a) 0.9 b) 2.1 c) 0.07 d) 16.23 e) 0.019 5 a) 0.3 b) 0.2 c) 0.75 d) 0.7 e) 0.6 6 a) 236 cm b) 8.3 cm c) 57 cm d) 580 cm e) 47 cm 7 a) 9.31 b) 45.46 c) 118.84 d) 16.88 e) 51.51 f) 128.29 8 a) 13.61 b) 24.08 c) 46.54 d) 5.43 e) 6.83 f) 196.07 9 £60.13 10 3.1 m 11 £2.92 12 a) 1.2 b) 0.05 c) 0.56 d) 0.48

Chapter 4 Exercise 4.1 (page 42) 2 25

d) 115 c) 0.83 f) 0.04 i) 1.5 l) 0.125 c) 4% c)

35%

Exercise 4.2 (page 44) 1 2 5 6

Original price (£)

Reduction (£)

Sale price (£)

Television

150

30

120

Washing machine

360

72

288

40

8

32

550

110

440

DVD player

7 a) £76.16 b) £85.68 c) £72.76 d) £111.52 8 a) £255.84 b) £212.16 c) £283.92 d) £68.64 9 £7395 10 80 960 11 £399.50 (using a VAT rate of 17.5%) 12 £71.44

Exercise 4.4 (page 49) 1 4 7 10

10% 5% 7.5% 17%

2 25% 5 20% 8 53%

3 40% 6 13% 9 82.5%

Mixed exercise 4 (page 50) 1 a) 0.27 d) 0.165 2 a) 8% d) 40% 3 £8.40 5 £2.10 7 £29.75 9 4.2%

4 6 8 10

b) 0.96 e) 3.5(0) b) 70% e) 123% £7.50 £16 480 £216 28%

c)

0.02

c)

72%

Chapter 5 Exercise 5.1 (page 53) 1 5 9 13 17

70 136 73 92 117

2 6 10 14 18

31 37 72 99 122

3 7 11 15 19

74 57 91 73 105

4 8 12 16 20

89 60 73 116 183

3 7 11 15 19

41 41 69 35 82

4 8 12 16 20

23 16 46 67 17


a) £16 b) £10 c) £6 3 240 4 £1260 a) £8.16 b) £86.40 £18 7 38.4 m 8 21 280

£21

9 £83.60

Exercise 4.3 (page 46) 1 a) £480 b) £580 2 a) £168 b) £204 3 £12 480 4 £34.20

Item

Computer system


1 a) 270 b) 1230 c) 2 a) 0.16 b) 0.27 d) 0.07 e) 0.31 g) 0.17 h) 0.02 j) 2.5 k) 0.09 3 a) 62% b) 56% d) 16.5% e) 132% 4 a) 70% b) 60% d) 40% e) 34%

6

c) £424 c) £232.80 5 £129.60

d) £720 d) £96

1 5 9 13 17

70 72 65 37 7

2 6 10 14 18

25 22 21 19 69

Exercise 5.3 (page 55) 1 56 5 14 9 27


2 42 6 43 10 39

3 73 7 57

4 42 8 49


167

Exercise 5.4 (page 56) 1 5 9 13 17

12 35 36 18 49

2 6 10 14 18

12 12 15 36 18

3 7 11 15 19

45 48 28 50 54

4 8 12 16 20

4 5 6 7

45 27 40 56 63

Exercise 5.5 (page 57) 1 5 9 13 17

6 5 3 7 7

2 6 10 14 18

4 7 9 9 6

8 3 7 11 15 19

3 5 8 4 7

2 4 6 8 10

4.8 or 4.9 7.7, 7.8 or 7.9 6.8 or 6.9 7.3, 7.4 or 7.5 8.7, 8.8 or 8.9

4 8 12 16 20

4 9 7 8 4

9 10 11

Exercise 5.6 (page 58) 1 3 5 7 9

3.5, 3.6 or 3.7 9.2, 9.3 or 9.4 5.5, 5.6 or 5.7 6.1, 6.2 or 6.3 9.4, 9.5 or 9.6

12 13 14 15 16

Exercise 5.7 (page 63) 1 a) 14 d) 205 g) 320 j) 35 2 a) 5.2 d) 7.7 3 a) 5.24 d) 7.67 4 a) 1000 d) 40 g) 300 5 20 000

b) 17 e) 9 h) 924 b) e) b) e) b) e) h)

48.1 9.9 48.12 9.89 3000 600 000 4000

c) f) i)

581 28 1

Chapter 6

c)

0.9


c)

0.89

c) f) i)

60 000 9 000 000 600

Exercise 5.8 (page 65) 1 5 9 13 17

1 2 5 3 2

2 6 10 14 18

4 8 1 1 3

3 7 11 15 19

2 1 1 5 1

4 8 12 16 20

3 1 1 1 3

2 2 6 4 10 4

3 4 7 4

1 4 7 10

4 6 8 7

1 a) 58 b) 94 c) 82 d) 133 e) 62 2 a) 35 b) 36 c) 37 d) 24 e) 8 3 a) 21 45 66, 66 21 45, 66 45 21 b) 39 14 53, 53 14 39, 53 39 14 c) 15 52 67, 67 15 52, 67 52 15 d) 37 18 55, 55 18 37, 55 37 18 e) 36 54 90, 90 36 54, 90 54 36


b) 22.09 e) 0.3844 h) 3.24

c) f) i)

1444 0.0361 4.6656

b) 7.7 e) 36 h) 0.86

c) f) i)

1.6 0.31 3.75

b) 5.46 e) 48.46 h) 154.24

c) f) i)

9.38 0.59 1.37

2.419 3.450 41.33 26

2 5 8 11

3.84 12.606 0.417 6.983

3 6 9 12

34.2 62.41 4.48 2.545



168

1 a) 7.29 d) 107 584 g) 0.0049 j) 998.56 2 a) 4.1 d) 17.2 g) 0.49 j) 0.047 3 a) 4.16 d) 23.81 g) 0.95 j) 0.28 4 21.9 cm


Exercise 5.9 (page 66) 1 4 5 1 9 6

a) 43 b) 14 c) 16 d) 4 a) 15 b) 28 c) 48 d) 32 e) 63 a) 8 b) 8 c) 7 d) 2 e) 7 a) 6 7 42, 42 6 7, 42 7 6 b) 8 7 56, 56 8 7, 56 7 8 c) 8 5 40, 40 8 5, 40 5 8 d) 6 4 24, 24 6 4, 24 4 6 e) 6 9 54, 54 9 6, 54 6 9 a) 1 b) 25 c) 49 d) 64 e) 8 f) 125 g) 4 h) 6 a) 4.2 b) 9.4 c) 8.5 d) 6.7 e) 7.5 a) 47 b) 2 c) 98 d) 105 e) 7 a) 9.1 b) 1.6 c) 68.7 d) 1.4 e) 3.9 f) 16.4 a) 1.39 b) 3.88 c) 16.38 d) 43.95 e) 1.33 f) 2.67 a) 40 b) 30 000 c) 8000 d) 800 000 e) 10 000 20 000 a) 6 b) 2 c) 4 d) 2 e) 5 a) 6 b) 1 c) 6 d) 1

1 a) 50.41 d) 271 441 2 a) 4.8 d) 0.33 3 a) 6.11 d) 0.624 4 98.2 m 5 a) 7.529 d) 91.2

b) e) b) e) b) e)

40.96 0.2116 8.3 0.063 23.17 0.28

b) 10.536 e) 23.810

c)

1444

c)

24.3

c)

201.70

c) f)

19.36 2.494


Chapter 7

4 a) 54 5 a) 25

Exercise 7.1 (page 77) 1 3 5 6 7 8 9 10

b) 1011 b) 32

c) c)

1 a) d) 2 a) d) 3 a) d) 4 a) d)

1 3 1 100

16 67 114 3 10

0.4 6.25

b) e) b) e) b) e) b) e)

1 6 1 640

c)

1 49

9 1000 223 1212 2 0.3125

c)

52

c)

5 8

c)

0.008

1 4 22; 6 2 3; HCF 2; LCM 22 3 12 2 12 22 3; 16 24; HCF 22 4; LCM 3 24 48 3 10 2 5; 15 3 5; HCF 5; LCM 2 3 5 30 4 32 25; 40 23 5; HCF 23 or 8; LCM 25 5 160 5 35 5 7; 45 9 5; HCF 5; LCM 32 5 7 315 6 27 33; 63 32 7; HCF 32 9; LCM 33 7 189 7 20 22 5; 50 2 52; HCF 2 5 10; LCM 22 52 100 8 48 24 3; 84 22 3 7; HCF 22 3 12; LCM 24 3 7 336 9 50 2 52; 64 26; HCF 2; LCM 26 52 1600 10 42 2 3 7; 49 72; HCF 7; LCM 2 3 72 294



Chapter 8

12 28 5 9 21

2 6 10 14 18

20 16 8 7 6

3 7 11 15 19

30 18 3 4 9

4 8 12 16 20

54 4 2 12 20

Exercise 7.4 (page 86) 1 a) 49 b) 121 c) 6 e) 8 f) 1000 g) 4 2 6 cm 3 a) 625 b) 1600 d) 1024 e) 1.44 4 a) 1728 b) 15.625 d) 27 000 e) 157.464 5 a) 20 b) 23.98 d) 60.70 e) 124 6 a) 8 b) 8.78 d) 21.15 e) 21.54 7 1 and 64

d) 12 h) 1 c)

1225

c)

226.981

c)

35.83

c)

20

b) b) e) b) e)

73 107 26 103 20 1

1 a) 3 52 b) 22 5 7 2 c) 2 3 5 7 2 a) 24 23 3, 60 22 3 5, HCF 12, LCM 120 b) 100 22 52, 150 2 3 52, HCF 50, LCM 300 c) 81 34, 135 33 5, HCF 27, LCM 405 3 a) 12 b) 16 c) 8 d) 3 4 a) 16, 64 b) 36, 216 c) 100, 1000 5 a) 8 b) 14 6 a) 5 b) 3 7 a) 21.16, 97.336 b) 441, 9261 c) 8.41, 24.389 8 a) 9.43, 4.46 b) 11.14, 4.99 c) 31.40, 9.95 9 a) 57 b) 103 c) 82 d) 26 e) 33 1 1 10 a) 5 b) 8 c) 8 5 d) 10 e) 8 or 0.625

Exercise 8.1 (page 97) 1 a) 2 a) d) g) j) 3 a) d) g) j) 4 a) d) g) j)

9, 79 7 9 5 13 1 3 214 7 8 1 4 13 18 23 30 5170 3112 71118 51230

b) b) e) h) k) b) e) h) k) b) e) h) k)

24, 78 7 11 5 6 135 419 7 9 1130 112 13 36 318 738 1 26 11114

c) c) f) i) l) c) f) i) l) c) f) i) l)

40, 38

c) f)

13 2 17 12

c) f)

2 15

1 3

118 312 267 7 12 11238 11138 39 40 41114 4172 6211 5 6


Exercise 7.5 (page 87) 1 a) 35 2 a) 55 d) 310 3 a) 52 d) 32

d) 34 d) 73


23 2 25 35 4 37 2 2 2 2 2 25 2 2 3 3 22 32 2 2 5 7 22 5 7 2 5 5 5 2 53 3 3 5 7 32 5 7 2 2 3 5 7 22 3 5 7


1 5 9 13 17

82 54

c) c) c)

34 52 84 8

3

1 a) 149 d) 281 g) 167 2 a) 225 d) 438


b) 137 e) 273 h) 6121 b) 412 e) 251

9


169

3 a) d) g) j) 4 a) d) g) j)

3 16 138 4 27 159 7170 17 40

b) e) h) k) b) e) h) k)

10 225

4 27 135 7 8

c) f) i) l) c) f) i) l)

513 217 825 313 1812

5 24 15 28 20 27

4 5 6 7 8 9

7 32 147 1194 757 11309

Mixed exercise 8 (page 118) 5

1 a) 30, 6 2 a)

Exercise 8.3 (page 106) 1 a) d) g) 2 a) d) 3 a) d) 4 a)

13 21

7 20 51134 3494 5 8

b) e) h) b) e) 19 b) 71117 e) 8133 b) 2434 cm2

1175 1267 2 5 7 16

2115 445 2056 cm

c) f)

3 a)

5 22 11112

c)

7 15

c)

41135

4 a) 5 6 7 8 9 10 11 12

Exercise 8.4 (page 108) 0.8 b) 0.375 c) 0.182 0.111 e) 0.45 Terminating, 5 is a factor of 10 Recurring, 3 is not a factor of 10 Recurring, 9 is not a factor of 10 Terminating, 16 has only factors which are factors of 10 e) Recurring, 7 is not a factor of 10 3 a) 0.714 285 7… b) Six 1 a) d) 2 a) b) c) d)

7.7 2.2 5.7 16.5

2 5 8 11

7.9 7.1 3.8 0.9

3 6 9 12

3.6 8.1 12.2 5.8

1.2 0.24 0.06 40 20 80 6.3 113.4 5.08 49 53 2.9

b) f) j) b) f) j) b) f) j) b) f) j)

3.5 0.48 0.08 4 20 30 14.26 388.8 1.872 17 78 2.7

c) g) k) c) g) k) c) g) k) c) g) k)

1.8 12 0.49 4 30 3.1 35.99 49.84 3.822 24 5.7 3.7

d) h) l) d) h) l) d) h) l) d) h) l)

170

b) f) b) f)

1.2(0) 1.175 0.8(0) 0.77

c) g) c) g)

1.68 2(.00) 0.55 0.14

d) h) d) h)

b) b) b)

a) b) a) 0.125 b) a) 9.7 b) a) 2 b) d) 10.8 e) a) 30 b) d) 80 e) 1 a) 166 b) £5263 £29.52

1 a) 2 : 1 d) 1 : 3 : 5 2 a) 1 : 20 d) 16 : 3 3 5:6 4 5 : 8 : 10 5 4:2:3

c)

40, 20

5 6

c)

e)

c) c)

c) 0.222 5.3 0.07 9.18 8 79 11 40

c) c) c) f) c) f) c)

d)

13

d) 618

1

e)

1 210 17 44

e)

d)

d) 0.714 8.7 0.72 18.72 3 8.7 1 37

13 24 13 120 9 20 3 97

e) d) 0.273 d) 4.6

1

d) 39

b) e) b) e)

1:3 3:6:4 3 : 20 3 : 20

c)

5:1

c)

4:1


7.2 35 0.09 9 50 122 19.44 26.16 9.968 32 4.9 4.5

Exercise 8.7 (page 116) 1 a) 1.13 e) 1.02 2 a) 0.86 e) 0.97 3 £4.78

1

11 24 3 88 15 16 3 34

b) 21, 3 2 121 7 320 10 21 13 121


Exercise 8.6 (page 113) 1 a) e) i) 2 a) e) i) 3 a) e) i) 4 a) e) i)

2 15 5 512 2 5 2 33

Chapter 9

Exercise 8.5 (page 109) 1 4 7 10

£29.40 £2917 £34 696 £8736 £159 627 £2980.80

1.08 2.5(0) 0.93 0.835


1 a) 1 : 3 d) 1 : 1.75 g) 1 : 0.2 2 1 : 250 000 3 1:6

b) 1 : 5 c) e) 1 : 7.5 f) h) 1 : 500 000

1 : 2.5 1 : 125

Exercise 9.3 (page 126) 1 2 3 4 5 6 7 8 9 10

a) 12 cm b) a) 24 babies b) a) 6 litres b) 140 mm or 14 cm a) 28 miles b) a) 30 ml b) a) 100 ml b) a) 150 g b) £120 a) 500 g b)

3.5 cm 9 helpers 4 litres 10 inches 10 teaspoons 36 ml 48 g 180 g

Exercise 9.4 (page 128) 1 Dave £8, Sam £12 2 a) 15 litres b) 25 litres 3 30 kg sand


4 5 6 7 8

a) 50 ml b) 250 ml Amit £320, Bree £800, Chris £480 1560 £292 a) 400 g b) 80 g

4 250 g 5 a) 60 g 6 a) 500 ml

In questions 7 and 8 either cost per unit or number of units per pound or per penny can be used. Both are given in each answer.

Exercise 9.5 (page 131) In all these questions either cost per unit or number of units per penny can be used. Both are given in each answer. Where necessary, answers are rounded to 2 decimal places, unless otherwise indicated. 1 Cost per gram: 420 g bag 0.38p, 325 g bag 0.34p Grams per penny: 420 g bag 2.64 g, 325 g bag 2.98 g 325 g bag is better value. 2 Cost per litre: 2 litre bottle 42.5p, 5 litre bottle 35.8p Millilitres per penny: 2 litre bottle 23.53 ml, 5 litre bottle 27.93 ml 5 litre bottle is better value. 3 Cost per gram: 680 g pack 0.47p, 1.4 kg pack 0.39p Grams per penny: 680 g pack 2.125 g, 1.4 kg pack 2.59 g 1.4 kg pack is better value. 4 Cost per nail: 50 pack 2.5p, 144 pack 2.64p Nails per penny: 50 pack 0.4 nails, 144 pack 0.38 nails 50 pack is better value. 5 Cost per roll: 12 pack 14.92p, 50 pack 14.4p Rolls per penny: 12 pack 0.067 rolls, 50 pack 0.069 rolls (answers rounded to 3 decimal places) 50 pack is better value. 6 Cost per ml: 80 ml tube 3.49p, 150 ml tube 3.33p Millilitres per penny: 80 ml tube 0.29 ml, 150 ml tube 0.3 ml 150 ml tube is better value. 7 Cost per litre: 3 litres 66.33p, 2 litres 67.5p, 1 litre 57p Litres per pound: 3 litre 1.51 litres, 2 litre 1.48 litres, 1 litre 1.75 litres 1 litre bottle is the best value. 8 Cost per gram: 750 g 0.239p, 1.4 kg 0.229p, 2 kg 0.245p (answers rounded to 3 decimal places) Grams per penny: 750 g 4.19 g, 1.4 kg 4.38 g, 2 kg 4.09 g 1.4 kg packet is the best value.

10 : 7 9 : 20 1:4 1 : 250 000 60 cm

b) e) b) e)

5 : 12 c) 3:5 1 : 2.4 c) 1 : 0.4 b) 5 cm

7 Cost per litre: 5 litres £3.70, 2 litres £3.50 Litres per pound: 5 litres 0.270 litre, 2 litres 0.286 litre (answers rounded to 3 decimal places) 2 litres is better value. 8 Cost per millilitre: pint 0.076p, litre 0.075p (answers rounded to 3 decimal places) Millilitres per penny: pint 13.2 ml, litre 13.3 ml (answers rounded to 1 decimal place) Litres are better value.

Chapter 10 Exercise 10.1 (page 135) 1 a) 26 e) 80.4 i) 283 2 a) 16 e) 69.6 i) 85.7 3 a) 72 e) 800 i) 1000 4 a) 4 e) 13 i) 20 5 a) 4 e) 2 i) 24 6 a) 8 e) 40 i) 2 7 a) 36 e) 169 i) 0.49 8 a) 4 e) 15 9 a) 1 e) 0.027 10 £9.20 11 8 cm 12 £15.28 13 420 ml 14 a) 17 cm 15 8 and 5

b) f) j) b) f) j) b) f) j) b) f) j) b) f) j) b) f) j) b) f) j) b)

1.5 20.1 275 0.9 65 996 52 336 775 80 4 3 4 10 0 12 3 16 25 400 0.09 3

b) 125

c) 58 g) 661

d) 200 h) 10.1

c) 87 g) 69

d) 58 h) 277

c) 2.4 g) 185

d) 160 h) 520

c) 13 g) 0.08

d) 16 h) 6

c) 7 g) 6

d) 6 h) 4

c) 12 g) 4

d) 35 h) 3

c) 121 d) 100 g) 90 000 h) 0.16 c)

7

d) 13

c)

8

d) 64 000

20 1000 4000 20 0.6 0.07

d) h) l) d) h) l)

b) 18 cm2


Mixed exercise 9 (page 132) 1 a) d) 2 a) d) 3 a)

b) 250 g b) 240 ml

3:1 1 : 50

1 a) e) i) 2 a) e) i)


8 500 0.7 10 6000 1

b) f) j) b) f) j)

7 7 4000 200 0.01 20 000

c) g) k) c) g) k)

30 0.4 3 800 0.04 2000


171

3 a) 18 b) 180 e) 50 f) 0.17 i) 0.031 j) 0.99 4 a) 8.26 b) 69.8 e) 12 500 f) 7.10 i) 0.0386 j) 3.14 5 £180 or £200 6 3 7 54 cm2 or 50 cm2 8 21 cm or 20 cm 9 £2000 10 64 cm3 or 60 cm3 11 50 mph 12 a) 4000 c) 125 or 100 e) 24 000 or 20 000 g) 0.75 or 0.8 i) 43 or 40 k) 3.5 or 3 or 4

c) 5700 g) 0.039

d) 98 000 h) 0.0061

c) 16 300 d) 208 g) 50.9 h) 0.416

b) d) f) h) j) l)

9 49 or 50 0.1 36 000 or 40 000 60 60

Exercise 10.3 (page 142) 1 a) 8 d) 26 2 a) 14 d) 50 3 5:2 4 225 cm2 5 (64 4 ) cm2

b) e) b) e)

64 81 80 4

c) f) c) f)

36 7 32 16

4900 0.0016 560 000 9040 25 70 30 4000 2160 0.002 16 9880 38 408.51 4.0851

c) f) i) l) c) f) i) l) c) f) c) f) c) f)

0.04 30 000 120 300 0.06 0.13 90 15 000 1000 16 216 260 26 1530 15 300

b) 1.6 e) 441 h) 8.1

c) f) i)

141.9 7.2 383

b) 0.54 e) 1025 h) 0.82

c) f) i)

710 17 9

b) 6 e) 1 h) 9

c) f) i)

17 28 5

b) 0.81 e) 196

c)

144

b) e) h) k) b) e) h) k) b) e) b) e) b) e)

0.036 0.04 1120 0.12 0.05 0.006 35 0.013 1.35 1600 3.8 0.038 40 851 26.7

Mixed exercise 10 (page 145) 1 a) d) g) j) 2 a) d) g) j) 3 a) d) g) j) 4 a) d)

172

92 21.1 158 6.9 153 345 0.35 12 4 9 30 3 49 10 000

4 600 0.3

c) f) i)

b) d) f) h) j) 4.7 510 10.2 0.005 62 49 85 80 1539 70

30 6 0.6

10 36 or 40 0.1 15 000 or 20 000 21 or 20 c) 0.014

2.34 1900 38 682 30.7

c)

0.0219

c) f) c) f) i)

22 63 48 20 4500

c) f) c) f)

19 4.446 1260 1.26

Chapter 11

Exercise 10.4 (page 144) 1 a) d) g) j) 2 a) d) g) j) 3 a) d) 4 a) d) 5 a) d)

5 £15.41 6 a) 9 b) d) 30 e) g) 1000 h) j) 50 000 7 32 cm2 or 30 cm2 8 50 mph 9 a) 4000 c) 200 e) 4200 or 4000 g) 30 i) 300 10 a) 9.2 b) d) 160 000 e) 11 a) 1480 b) d) 21 000 e) 12 a) 10 b) d) 9 e) 13 a) 15 000 b) d) 0.09 e) g) 0.16 h) j) 12 000 14 a) 4446 b) d) 0.004 446 e) 15 a) 38.682 b) d) 3.8682 e)


Exercise 11.1 (page 150) 1 2 3 4 5 6 7 8 9 10

a) a) a) a) a) d) a) a) a) a) a)

6 5 5 13 x5 2x 4 4x 10 75p 2x 2m

b) b) b) b) b)

x2 2p x3 p9 x8

c) c) c) c) c)

br qr 2x 4q x2y

b) b) b) b) b)

xy 14 £1.50 5x m6

c) c) c) c)

2x x6 25x 7x

Exercise 11.2 (page 153) 1 a) (i) 8 b) g 7 2 a) (i) 2 b) p 3 3 a) 12 r 4 a) (i) 6 cm b) p 3 5 a) (i) 155 cm b) h 5 6 a) x 14 7 a) 12p 8 a) y 10 9 a) 25 a 10 b 5

(ii) 3 (ii) 7 b) s 8 (ii) 11 cm

c)

vt

c)

xp

c) c)

yg ba

(ii) 184 cm b) b) b) b)

x 21 a6 y 15 15 a


Mixed exercise 11 (page 155) 1 2 3 4 5 6 7 8 9 10

a) 35 f a) 15 r a) (i) 9 a) p 29 4x a) (i) £1.60 a 8 (£) a) t 4 a) x 6 a) p 2

b) 60 f b) x 5 (ii) 15 b) p 53

c) c f c) z y b) 3h c) p e

(ii) £2.40

b)

b) t 2 b) x 3 b) p 3 q

c) c) c)

20x (pence) 2t 3x prs

Chapter 12 5p 7p 2a 8a 2b

2 6 10 14 18

7a 6b 5c 2c 9x

3 7 11 15 19

5x 3p 7x 0 9a

4 8 12 16 20

4c 4s 4m p 5a

Exercise 12.2 (page 160) 1 4 7 10 13 16 19

a 3b 3p q 8pq 6a 4b 4 a 3c 2a 4 10a 2b

21x 8 22 3z 16n 9p 23d 6e h 11j

b) d) b) d) f)

14y 4 36 10x 21q 13r 14f g 6k 3m

Exercise 13.3 (page 167) 1 a) c) 2 a) c) 3 a) c)

5(2x 3) 4(2x 3) 7(2 x) 5(3 2x) x(3x 5) 4x(3x 2)

b) d) b) d) b) d)

2(x 3) 4(x 5) 4(2 3x) 3(3 4x) 5x(x 4) 2x(3x 4)


Exercise 12.1 (page 158) 1 5 9 13 17

3 a) c) 4 a) c) e)

2 5 8 11 14 17 20

x 3y 6a 6b 6x 4y 3ab 2bc 4ab 2a2 a 2b 3a2b2

3 6 9 12 15 18

4ab 2a 3c 3p2 a2 3s x 3y

1 a) c) 2 a) c) 3 a) c) 4 a) c) 5 a) c)

a2 10a 21 6 5c c2 9d 2 3d 20 6 5f 56f 2 4g2 20g 21 6j2 37j 56 10k2 23k 42 6 n 15n2 4 4p 63p2 4s2 20s 21

b) b2 11b 28 b) 8e2 2e 15 b) 4h2 28h 49 b) 6 11m 72m2 b) 6r2 37r 56

Exercise 13.5 (page 170) 1 2 3 4

a) a) a) a)

34 x5 m 2n 4 56k3

b) b) b) b)

73 y4 f 4 g5 120y3

c) c) c) c)

105 z7 p3r4 8d 3

Mixed exercise 12 (page 161) 1 4 7 10 13 16 19

4a y2 2y 3s 3x 2y 3ab 3ac 3 5x 2y 8pq

2 5 8 11 14 17 20

2a 3 abc 2c 6 4a b 6a b 9 2p2 3x 12 6ab 3x 2y 15 6a 3b 3ab2 18 6 a b c 2a 3b 7

Chapter 13 Exercise 13.1 (page 163) 1 3 5 7 9 11 13 15

20a 30b 15e 40f 10u 15v 21y 7z 12 42w 8g 6 6i 8j 10k 12r 18s 24t

2 4 6 8 10 12 14

6c 21d 28g 21h 30w 18x 16v 40 12 32a 35 20b 20m 12n 8p

Exercise 13.2 (page 166) 1 a) c) 2 a) c)

20a 38 12 37c 18s 43t 27x 77y

b) d) b) d)

27b 53 32 22a 14v 49w 38v 27w

Mixed exercise 13 (page 171) 1 a) c) e) g) i) k) 2 a) c) e) g) i) k) 3 a) c) e) g) i) k) m) o) 4 a) c) e) g) i) k)


24a 16b 36a 60b 12x 15y 20x 12y 15f 20g 7r 14s 12x 11 7x 12 15y 7 3a 6 6p 18 j 31 4(x 2) 3(3x 2) 2(3 5x) 8(3 x) 2(3x 4) 4(5 4x) x(2 x) z(5z 2) a2 9a 20 12 7a a2 x2 4x 45 3x2 31x 36 14 25p 6p2 4t2 23t 15

b) d) f) h) j) l) b) d) f) h) j) l) b) d) f) h) j) l) n)

20a 15b 9a 18b 18x 12y 8x 2y 6j 15k 12v 4w 20x 27 16y 5 21y 4 6m 1 14t 24 46 6(x 2) 6(2x 3) 5(2 3x) 4(4x 3) 4(8x 3) 5(3 4x) y(3 7y)

b) d) f) h) j) l)

a2 5a 6 x2 7x 8 x2 3x 2 2y2 y 21 6p2 8p 8 6a2 a 15


173

5 a) 46 e) j3 i) x3y5

b) 54 f) t6 j) 60p3

c) 25 g) v3w3

d) a7 h) d3e6

Chapter 14 Exercise 14.1 (page 174) 1 2 3 4 5 6 7 8 9 10

a) a) a) a) a) a) a) a) a) a)

£45 3 £24 £25 £90 9 cm2 40 mph £17 £35 £60

b) b) b) b) b) b) b) b) b) b)

£100 32 £60 £12 £150 75 cm2 80 km/h £28 £55 £400

c) c) c) c) c) c) c) c) c) c)

£60 16 £14 £280 £105 5 m2 8 m/s £50.50 £80 £10

d) d) d) d) d) d) d) d)

£75 37 £92 £18.50 £290 12.3 mm2 230 mph £37.50

d) £48

Exercise 14.2 (page 177) 1 c 5a

2 B J 14 m 4 a n bh 6 a 2

3 r 4m 5 c 50 10h d 7 s t 9 v lwh

8 t 6a 2.5c 10 t 0.2w

174

6 12 17 8 18 10 8

c) g) k) o) s) w)

b) 10 b) 6

1 a) 15 m b) 2 a) 50 °F b) 3 a) 2 hours c) 14 hours 4 a) C 3d d c) t s 5 a) 9 b) e) 15 f) i) 16 j) m) 25 n)

d) h) l) p) t) x)

c) 15 g) 9

d) 5 h) 90

c)

4

d) 612

c) c)

232 8.5

d) 8

42 m 32 °F

c) c) b) d) b)

75 m d) 10.5 m 86 °F d) 53.6 °F 4.5 hours 80 seconds F 1.8C 32

3 24 4 13

c) g) k) o)

30 37 5 8

d) h) l) p)

27 26 7.7 107

1 a) 90 minutes b) 210 minutes 2 4°C 3 £31 d 4 a) s b) 60 km/h t 5 490 6 18 7 a) 55 b) 20 8 a) 8x b) 3x2 9 a) 2 hours 10 minutes b) 1.5 kg 10 5 11 15 miles 12 a) 12 b) Number of posts, P

1

2

3

4

5

Number of chains, C

0

3

6

9

12 15

6

C 3P 3 or C 3(P 1) 87 24 cm2 b) 22.5 cm2 3 120 cm b) 216 cm3 £45 b) 43 miles

Exercise 15.2 (page 188) 1 a) b a c

3 10 28 8 2 20

1 4 27 39


c) d) 13 a) 14 a) 15 a)

Exercise 14.3 (page 179) b) f) j) n) r) v) z)

b) f) j) b)


11 t 4.5w t stands for the total amount saved w stands for the amount saved each week r 12 n 3 n stands for the number of strips of paper r stands for the length of a roll of paper 13 s n d s stands for the sale price n stands for the normal price d stands for the discount d 14 f 3 5 f stands for the fare d stands for the distance covered 15 c 100 7s c stands for the total cost s stands for the number of students

9 10 2 1 40 3 100

5 11 15 19 14.5 10 4

Chapter 15

Note that in questions 11 to 15, different letters could be used.

1 a) e) i) m) q) u) y)

2 a) e) i) 3 a) e) 4 a) 5 a)

11 19 14 40 25 12


4a y b) x w

c)

vu t a

pc d) t 3

e)

A pr A q or q r p p

f)

p 2f g 2

Ft m g) n 4


sbn 2 u 3v 2a 3 h b 100I 4 R PT 3V 5 a) h 2 r 6 a) 140°F 7 r

2

a)

b) rule 4

rule 3

c)

rule 4

b) 16.6 cm b) C (F 40) 59 40

3V h

v2 u2 8 a) a 2s

d)

Exercise 16.3 (page 196) 1 a) c) e) 2 a) d)

2 b) u v as 2

Mixed exercise 15 (page 189) a) 104°F b) 32°F c) 23°F 95p a) 12 cm2 b) 21.6 cm2 a) 34 minutes b) 47.8 minutes xs 5 a) q p 2r b) r 5 ms tx A x A c) r d) y or y pq 2t 2 2t

1 2 3 4

T 40 6 a) w b) w 2.4 kg 45 7 a) 4 cm b) 8 cm 8 a) 30 words b) 60 words

rule 5

11, 15, 19, 23, 27 b) 13, 21, 29, 37, 45 12, 19, 26, 33, 40 d) 2, 5, 8, 11, 14 13, 18, 23, 28, 33 f) 16, 25, 34, 43, 52 603 b) 799 c) 2194 1202 e) 2413 f) 1795

Mixed exercise 16 (page 196) 1 a) c) 2 a) c) 3 a) c) 4 a) c) 5 a)

1, 6, 11, 16, 21 6, 4, 2, 0, 2 26; rule 4 34; rule 5 9, 5; rule 4 2, 15; rule 13 22, 27, 37; rule 5 26, 37, 70; rule 11 rule 3

b) 50, 46, 42, 38, 34 b) 51; rule 8 b) 5, 2; rule 3 b) 22, 13, 7; rule 3

rule 6

6 a)

Chapter 16

rule 3

b)

rule 7

b)

Exercise 16.1 (page 193) 1 a) c) e) 2 a) c) e) 3 a) c) e) 4 a) c) e)

1, 5, 9, 13, 17 21, 18, 15, 12, 9 100, 60, 20, 20, 60 25, 29; 4 47, 54; 7 38, 43; 5 7, 5; 2 9, 3; 6 1, 5; 4 15, 36; Add 7 65, 21; Subtract 11 22, 30; Add 8

b) d) f) b) d) f) b) d) f) b) d) f)

4, 1, 2, 5, 8 5, 10, 15, 20, 25 1, 112, 2, 212, 3 39, 45; 6 25, 28; 3 77, 86; 9 9, 5; 4 4, 0; 4 2, 7; 5 17, 35; Add 6 66, 30; Subtract 9 18, 2; Subtract 5

Exercise 16.2 (page 194) 1 a)

c)

rule 3 b)

rule 5

d)

rule 2

7 a) 5, 9, 13, 17; 601 c) 10, 18, 26, 34; 738

b) 4, 13, 22, 31; 697

Chapter 17 Exercise 17.1 (page 200) 1 a) Multiply the pattern number by 2 b) 200 2 a) Pattern number

1

2

3

4

5

Number of matchsticks

4

6

8

10 12

b) They go up by 2 each time; they are the 2 times table plus 2. c) 102 3 a)

rule 4 b) 36 You add 1 more to the difference each time, so T4 10, T5 15, T6 21, T7 28, T8 36



175

4 a) 3 1 5 2 5 a) 4, 10, 16, 22 c) 4, 2, 0, 2 6 a) 1, 4, 9, 16, 25 c) 1, 8, 27, 64, 125 7 2, 4, 8, 16, 32 8 5, 2, 1, 4 9 For example

6 a) Tn 3n 2 b) c) Tn 7 5n 7 a) Linear: 24, 29 b) c) Not linear d) 8 a) 3, 9, 27, 81, 243 b) 9 A suitable answer is as follows.

b) 1, 4, 7, 10 b) 5, 9, 13, 17 b) 3, 6, 11, 18, 27

1

3

6

Not linear Linear: 12, 18 Powers of 3

10

15

b) Tn n 4 2

10 a) 1, 4, 9, 16, 25

and so on. 10 For example

Tn 6n 5

Chapter 18 Exercise 18.1 (page 209) and so on.

1 A(2, 1) E (7, 2) I(5, 3) 2 y

Exercise 17.2 (page 205) 1 a) 2n 3 b) 3n 1 c) n 6 2 a) 20 3n b) 10 5n c) 1 n 3 a) Linear: 17, 20 b) Not linear c) Linear: 30, 36 d) Not linear 4 a) 6, 0, 6, 12, 18 b) 14 6n 5 a) Number of tickets 1 2 3 4 Cost in £

8 7 6 5 4 3 2 1

17 32 47 62

b) 15n 2 c) 7 6 1, 3, 6, 10, 15, 21, 28, 36, 45, 55 7 210 8 a) 10, 100, 1000, 10 000, 100 000 b) Powers of 10 9 a) 1, 4, 9, 16, 25 b) (i) Each term is 3 more than the equivalent term in the sequence of square numbers. (ii) n2 3 (iii) 10 003 10 a) Each term is 3 times the equivalent term in the sequence of square numbers. b) 3n2 c) 1200

0

176


D(1, 8) H(9, 4)

B C E

A D 1 2 3 4 5 6 7 8 x

B(3, 1) F(2, 3) J(2, 3)

1 A(1, 2) E(3, 1) I(0, 3) 2

y 5 4 D 3 2 1

543210 1 C 2 3 4 5

C(2, 4) G(3, 3)

D(0, 2) H(4, 2)

A

1 2 3 4 5 x B

Square 3

C

b) 64. This is the sequence of square numbers; the 8th pattern has 8 8 stars. 3 a) T1 1 6 2 4 b) 10, 16, 22, 28 4 a) 7, 12, 17, 22 b) 2, 5, 10, 17 c) 88, 86, 84, 82 5 4, 8, 16, 32, 64

C(7, 7) G(0, 4)


Mixed exercise 17 (page 207) 1 a) 300 b) Multiply the term number by 3 or start with 3 and add 3 each time. 2 a)

B(4, 6) F(6, 0) J(10, 1)

y 5 4 3 2 1

543210 1 2 3 4 5

A

1 2 3 4 5 x B

Isosceles triangle


4


y 5 4 3 2 1

D

543210 1 2 3 C 4 5

1 a) x 3 c) x 4 2

A

1 2 3 4 5 x

y 5 4 3 2 1

C

543210 1 2 3 4 5

yx4

B

5

6

7

yx2

5

4

3

2

1

0

1

1 0

x xy6

A

7

6

1

2

3

4

5

6

5

4

3

2

1

0

1 2 3 4 5 x B

yx4

A

1 2

3

4

y 7 6 5 4 3 2 1

xy6

0 7 5 3 1 3 5 1 1 2 y x 2 3 4 5 6 7

5 x

5

B

7 x

x

2

1

0

1

2

y 3x 1

5

2

1

4

7

For graph, see question 6. 6

2 1 0

x y5x

4 3 1 1 2

3 4 B

3 4 5

A

7 y 7 6 5 4 3 2 1

A

2

543210 1 2 3 4 C 5

4

3

y 5

D

3

2

4

D(2, 3)

y 5 4 3 2 1

2

For graph, see question 4.

4 5

8

1

1

3

C(3, 1)

3

0

1

5 4 3 2 1 0 1 C 2

2

1

2

D

1

2

D

3

7

0

3

4

5 4 3 2 1 0 1 2 C

1

x

y 5 D

2

For graph, see question 4.

Rhombus 6

3

3

Trapezium 5

x

b) y 2 d) y 1

5 x

0 7 5 3 1 1 2 3 4 5 6 7

6

5

1

2

3

4

5

4

3

2

1

0

y 3x 1 y5x

1

3

5

7 x

7 (1, 4)

1 2 3 4 5 x B

C(3, 4) Foundation WJEC GCSE Mathematics © 2010, Hodder Education


177

6 There are two possible answers to this question.


y

1 A(5, 1), B(2, 1), C(2, 1), D(4, 0), E(1, 3), F(0, 2), G(2, 4) 2 y

5 4 3

5

2

4

A

3 B

2

1 5 4 3 2 1 0 1

G

1 5 4 3 2 1 0 1 3

F

2

1

3

5 x

4

5

D

(5, 4), (1, 4) or (2, 1), (2, 5) 7 yx1

y 5

C

4

2 1 A

B

5 4 3 2 1 0 1

2

1

3

4

5 x

3

2

1

0

1

2

3

y

2

1

0

1

2

3

4

x

3

2

1

0

1

2

3

4

y

5

4

3

2

1

0

1

2

For graph, see question 9. 9 y 2x 1

2 3 4

x

2

1

0

1

2

3

4

5

y

5

3

1

1

3

5

7

Parallelogram B

x

For graph, see question 9. 8 xy2

3

4

y

y

5

7

C

3

5

2

4

1

3

5 4 3 2 1 0 1

C

6

4

1

2

3

4

A

2

5 x

1

D

2 A

5 x

4

5

D

4

3

C

4

3

3

2

E

2

2

1

3

7 6 5 4 3 2 1 0 1

4

2

5

3

y

5

5

6

4

7

1

2

3

4

5

6

7 x

B

4

Trapezium 5 A

3

10 a) (2, 3)

B

2

b) (1, 1)

c)

1

1

(2, 12)

1 5 4 3 2 1 0 1

1

2

3

4

5 x

2 D

3 4 5

C

D(1, 3) 178



Chapter 19

Chapter 20



1 4 7 10 13 16 19

a5 m2 n 12 n4 b 16 x 5 x 4

2 5 8 11 14 17 20

p5 a7 h3 x 28 p 36 x 4 x 14

3 6 9 12 15 18

x8 x3 r 11 m 13 x4 x 8

3 6 9 12 15

b8 x4 x2 x9 x8

3 6 9 12 15 18

p 25 m 48 d 18 x 18 x 72 x 30

Exercise 19.2 (page 224) 1 4 7 10 13 16

x6 p8 x7 x4 x 14 x 1

2 5 8 11 14

m 11 x3 x5 x5 x8

Exercise 19.3 (page 225) 1 4 7 10 13 16 19

x6 x 18 t4 y 1000 x4 x 24 x 10

2 5 8 11 14 17 20

p 12 a6 b 128 x 54 x 21 x 80 x 16

Exercise 19.4 (page 226) 1 2 3 4 5 6

a 59° b 92° c 149° x 2 16, x 18 8x 72, x 9 2x 5 13, x 4 3x 6 18, x 8 3x 5 10, x 5

d 98°

Mixed exercise 19 (page 227) 1 3 5 7 9 11 13 15 17 19 21

x4 x7 x 23 x 14 x7 m3 y8 x5 x2 x 75 10x 5 95; x 9

2 4 6 8 10 12 14 16 18 20

x6 x6 x 26 x 1 x5 p2 x4 x6 x 16 x 16

1 3 5 7 9 11 13 15 17 19

x7 x7 x1 x5 x 10 x 5 or x 5 y 8 or y 8 m 5 or m 5 x 8 or x 8 x 2 or x 2

2 4 6 8 10 12 14 16 18 20

x 0.5 x7 x7 x4 x6 x 7 or x 7 m 9 or m 9 x 10 or x 10 x 4 or x 4 x 10 or x 10

Exercise 20.2 (page 229) 1 4 7 10 13 16 19

p 16 x1 x 14 x 10 x1 x3 x2

2 5 8 11 14 17 20

x3 x 15 x5 x 10 x3 x8 x 5.5

3 6 9 12 15 18

x7 x1 x 4 a1 x2 x4

3 6 9 12 15 18

x2 x2 x3 x1 x4 x2

Exercise 20.3 (page 231) 1 4 7 10 13 16 19

x3 x 10 x 10 x2 x3 x6 x 3

2 5 8 11 14 17 20

x3 x3 x 2 x2 x 4.5 x1 x7

Exercise 20.4 (page 232) 1 4 7 10

x 16 y 50 m 24 y 33

2 a 40 5 y 30 8 x 64

3 x 20 6 p 35 9 x 27

Exercise 20.5 (page 234) 1 x 1.7 2 a) 23 5 × 2 2 33 5 × 3 12 b) x 2.8 3 a) 43 4 60 53 5 120 b) x 4.6 4 a) 3.73 3.7 47 (nearest whole number) 3.83 3.8 51.1 (1 d.p.) b) x 3.77 5 x 2.6 6 x 4.33 7 22 8 31.6 9 a) x(x 4) 621, i.e. x2 4x 621 b) 27, 23 10 7.8



179

Chapter 21

Exercise 20.6 (page 237) 1 x 13 6

Exercise 21.1 (page 240) 8

10

12

14

16

1

2

3

4

5

8

10

12

14

16

1

2

3

4

5

1 Three points plotted, e.g. (3, 12), (0, 0), (3, 12), straight line drawn through them. 2 Three points plotted, e.g. (3, 0), (0, 3), (3, 6), straight line drawn through them. 3 Three points plotted, e.g. (2, 10), (0, 4), (4, 8), straight line drawn through them. 4 Three points plotted, e.g. (2, 10), (0, 2), (3, 10), straight line drawn through them. 5 Three points plotted, e.g. (4, 8), (0, 4), (2, 10), straight line drawn through them.

2 x4 0

3 x 13 6

4 x 4 0


5 x 3 0

1

2

3

4

5

2

4

6

8

10

6 x 8 0

7 10 13 16 19

x2 x 1 x 2 x 0.25 x 4

8 11 14 17 20

x 5 x 5 x 6 x 2 x4

9 12 15 18

x 9 x 9 x 5 x 3


Mixed exercise 20 (page 238) 1 a) c) e) g) i) k) m) o) 2 a) b) 3 a) b) 4 a) 5 a)

m9 b) p 2 x8 d) x 3 p8 f) x 4 or 4 x 6 or 6 h) p 4 or 4 x 4 or 4 j) a 5 or 5 x 25 l) x 30 y 18 n) y 49 a 36 13 4 1 5, 23 4 2 16 x 1.7 33 32 18, 43 42 48 x 3.4 x3 x 100 b) x 4.6 x 2 0

1

2

3

4

5

b) x 3 0

1 Three points plotted, e.g. (2, 4), (0, 1), (4, 5), straight line drawn through them. 2 Points (0, 3) and (7.5, 0) plotted, straight line drawn through them. 3 Points (0, 7) and (2, 0) plotted, straight line drawn through them. 4 Three points plotted, e.g. (3, 6), (0, 112), (3, 9), straight line drawn through them. 5 Points (0, 7) and (3.5, 0) plotted, straight line drawn through them.

1 a) She walked at 3 km/h for 20 minutes (distance 1 km), waited for 5 minutes, travelled in a bus (or car) at 45 km/h for 12 minutes (distance 9 km). b) Approximately 35 minutes c) (i) 0.25 km/minute (ii) 15 km/h d) (i) Approximately 0.75 km/minute (ii) Approximately 45 km/h 2 Description to include: ● A winning, B second, C third ● A ran at a steady speed, B started off quickly but gradually slowed down, C ran in a series of sprints and rests. May also mention approximately when overtaking took place. 3 a) £2 b) 80p c) 30

1

2

3

4

5

1

2

3

4

5

25

0

d) x 4 0

1

2

3

4

5

e) x 2 0

Charge (£)

c) x 3

20 15 d) 10 5

1

2

3

4

5 0

10

20 30 40 Distance (km)

50

d) £24 e) 69p (to nearest penny) 180



Cost (£)

4 a) D b) H c) 5 a) £49.50 b) £46.50 c)

F

2 a)

d) C

x

60

x2

50

4x

40

y x 4x

30

b)

1

2

3

4

5

1

0

1

4

9

16

25

4

0

4

8 12 16 20

5

0

3

4

y 5 4 3 2 1

10 0

Charge (£)

0

2

20

6 a)

1

1 2 3 4 5 6 7 8 9 10 11 12 Number of boxes

180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0

1

b)

0 1 2 3 4 5

2

1

3

5 x

4

(ii) 0.6 or 3.4

4 3 2 1

0

1

2

3

1

0

1

4

9

x

4 3 2 1

0

1

2

3

3

3 3 3 3 3 3 3 3

x x

2

16

y x2 x 2 20

x2

9

2

4

1

0

1

4

3


181

4

9

3

2 2 2 2 2 2 2

y x 2 2

b)

2 1 2 1

2

7

c)

(i) 1.8

2

110 2 3 4

y x2 x 3

1

2

3 x

(ii) 2.3 or 1.3

y 8 7 6 5 4 3 2 1

y x 2 2

2

7

3 1 3 3 1 y 9 8 7 6 5 4 3 2 1

Exercise 21.4 (page 253) Answers read from graphs may be approximate. 1 a) x 3 2 1 0 1 2

4

9

b)

9

9

3

b) Less than 91 cubic metres

c)

5

3 a)

60 100 140 40 80 120 160 Water used (cubic metres)

3

0

y x2 4x

(i) 0.8 to 0.9

c)

3

1

0 1 2 3 4

1

2

3 x

(i) 3.3 (ii) 2.4 to 2.5 or 2.4 to 2.5


4 a)

b) 2 1

x 2

0

1

2

3

4

5

1

4

9

16

25

4

1

0

6

3

0 3 6 9 12 15

4

4

4

4

4

4

4

4

y x 3x 4 14

8

4

2

2

4

8

14

x

3x 4 2

b)

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

c)

1

y 7 6 5 4 3 2 1

y x2 x 5

3

110

2

2x

2

18

5 y 2x 5 b) 0

2

1

3

5 x

4

0

1

2

3

4

5

3x

6 3

0

3

6

9

12

15

4 1

0 1 4 9 16 25

10 4

b)

0

2

2

4 10

0

y 3 2 1 2

3

1

0 1 2 3 4 5 6 7 8 9 10

2

1

3

2

1

5 x

4

2

0

2

8 18

3 3 5 3

13

3 13

y 13 12 11 10 9 8 7 6 5 4 3 2 1

y 2x2 5

(ii) 1.4 or 4.4

2 1

8

3

5 5 5 5 5 5 5 2

x

y 3x x

4 x

3

c) (i) 1.8 or 2.8 (ii) 2.4 or 3.4 7 a) x 3 2 1 0 1 2

5 a)

2

2

2 3 4 5 6

y x2 3x 4

(i) 1.75

x2

1

0 1 2 3 4 5 6

1

3 x

2

c) (i) 1.6 or 1.6 8 a) x 0

1

2

3

4

5

A 6x

6

24

54

96

150

y 3x x2

2

b)

(ii) 2.7 or 2.7

0

A 160

c)

(i) 2.25 (ii) 0.5 to 0.6 or 3.5 to 3.6

120

6 a)

100

3 2 1

x

0

1

2

3

4

1

4

9 16

x2

9

4

1

0

x

3

2

1

0 1 2 3 4

5

80 60 40

5 5 5 5 5 5 5 5

y x2 x 5

7

1 3 5 5 3

1

20

7

0

c)

182

A 6x2

140


(i) 1.8

1

2

3

4

5

x

(ii) 3.6 to 3.7



y

y 2x 1

7 6 5 4 3

x

2

x

1 1 0 1

1

2

3

2

5

4

3

2

1

0

1

2

25

16

9

4

1

0

1

4

6

3

0

3

6

2

2

0

4

10

15 12 9

3x

4 x

y x 3x 2

2

10

4

0

b)

3

2

She stopped (e.g. waited for bus) 68 minutes c) 27 km/h (i) 1 km (ii) 10 km Quadratic, b) Not quadratic Quadratic, d) Quadratic, Not quadratic f) Not quadratic Quadratic,

6 a) b) d) 7 a) c) e) g) 8 a)

y

y

10

8 7

2x y 8 0

6

8

5

6

4 3

4

2 1

2

0

2

1

3

3 a) £39 4 a)

4 x

b) (i) £11

(ii) 8p

5

4

3

2

2 x

1

2

50

4

c) (i) 2.25 9 a)

40 Cost (£)

0

1

(ii) x 3.8 or x 0.8

30

x

4 3 2 1

0

1

2

3

20

(x 3)

1

3

4

5

6

10

(x 2)

6 5 4 3 2 1

0

1

4 6 6 4

0

6

y (x 3)(x 2) 0

200

400

600

800

1000 1200 1400 1600

6

0

1

0

2

b)

Gas used (kWh)

y

b) Gas by £20 5 a) d

6 5 4 3 2 1 4

3

t

b)

2

1

0 1

1

2

3 x

2

d

3 4 5 6 7 8

t

c)


(i) 6.25 (ii) x 2.5 to 2.6 or x 1.5 to 1.6 Answers to the Student’s Book exercises

183

10 a)

obtuse reflex right angle obtuse

b) acute e) obtuse h) acute

x

2

1

0

1

2

3

4

x2

4

1

0

1

4

9

16

2x

4

2

0

2

4

6

8


1

1

1

1

1

1

1

1

7

2

1

2

1

2

7

a 55° e 70° i 39°

y x2 2x 1

b)

a 50° e 105° i 87°

8 7 6 5

1 2 3 4 5 6 7 8 9 10

3 2 1 1

0 1

1

2

4 x

3

2 3 4

c)

(i) x 0.4 or x 2.4 (ii) x 1.4 to 1.5 or x 3.4 to 3.5

x

1

0

1

2

3

4

5

6

5x

5

0

5

10

15

20

25

30

x2

1

0

1

4

9 16 25 36

y 5x x2

6

0

4

6

6

4

0

6

b) y 6 5 4 3 2 1 0 1

1

2

3

4

6 x

5

2 3 4 5 6

c)

d 81° h 37°

b 110° f 122° j 60°

c 120° g 135°

d 100° h 57°

(i) x 0.7 or x 4.3

(ii) 6.25

Chapter 22 Exercise 22.1 (page 262) 1 e, c, b, d, a 2 a) right angle d) reflex g) obtuse

b) obtuse e) acute h) right angle

c) f)

a 60° d 20° g 135° j 47° n 114° r 28° w 143° z 47° a 40° e 40°

b 120° e 160° h 45° k 133° p 66° s 152° x 37°

c 120° f 160° i 45° m 133° q 66° t 152° y 37°

b 90° f 40°

c 50° g 140°

d 50°


11 a)

1

c 132° g 17°


4

2

b 110° f 35° j 45°

reflex reflex reflex

c) f) i)


y

184

3 a) d) g) j)

1 a) right angle b) obtuse c) right angle d) reflex 2 a 140° b 95° c 54° d 91° 3 a 90° b 44° c 77° d 120° 4 a 100° Vertically opposite angles are equal. b 80° Angles on a straight line add up to 180°. c 80° Angles on a straight line add up to 180° or Vertically opposite angles are equal or Angles around a point add up to 360°. d 138° Vertically opposite angles are equal. e 42° Angles on a straight line add up to 180°. f 42° Angles on a straight line add up to 180° or Vertically opposite angles are equal or Angles around a point add up to 360°. g 70° Vertically opposite angles are equal. h 110° Angles on a straight line add up to 180°. i 110° Angles on a straight line add up to 180° or Vertically opposite angles are equal or Angles around a point add up to 360°. j 52° Vertically opposite angles are equal. k 128° Angles on a straight line add up to 180°. l 128° Angles on a straight line add up to 180° or Vertically opposite angles are equal or Angles around a point add up to 360°.

acute reflex



Chapter 23



1

2

3

4

5

6

1 a 51° b 113° c 60° d 114° 2 a 50° b 130° c 20° d 130° e 137° f 25° g 68° h 128° i 64° 3 a 74° b 41° c 56° d 76.5° 4 a) (i) a 54° (ii) b 45° (iii) c 36° b) It is an isosceles triangle.

Exercise 23.2 (page 274) 1 C, F and G

2 triangles a, b, d and f

Exercise 23.3 (page 276) 1 A right-angled triangle B isosceles triangle C parallelogram D rhombus E trapezium 2 a) A, B, F and G b) C and D or H and I c) F, G, H and I

Exercise 23.4 (page 278) 1 a) F b) CB c) 2 Note: this diagram is not full-size.

3 a) 4 b) A 4 1 1, C 2 2 1,

LK

B 3 2 1, D511

Mixed exercise 23 (page 281) 1 a 55° 2 x 115°

b 80° c 37° d 65° Base angles of an isosceles triangle are equal; angles on a straight line add up to 180° y 50° The sum of the angles in a triangle is 180° 3 a) cuboid b) 2 cm 2 cm 4 cm 4 Sides Quadrilateral Square

4 equal sides

Parallelogram

2 different pairs of equal sides

2 pairs of parallel sides

Only one pair of parallel sides

Trapezium Kite

Parallel sides

Equal diagonals

Rectangle Rhombus

Diagonals



185

5 a) Trapezium b) Square, rhombus, kite c) Square, rectangle d) Rhombus, kite 6 7

Exercise 25.2 (page 293) 1 2 3 4

a) a) a) a)

45 seconds £20 000 06:00 7.3 years

b) b) b) b)

160° 6.2 years 21°C £1400

c) c)

£13 500 21:00 (20°)


Chapter 24 Exercise 24.1 (page 285) 1 a) Radius b) Centre 2 a) Hexagon b) (Regular) octagon c) (Isosceles) triangle 3 5 For example

c)

Diameter

4 20 For example

5 6 7 8

36° 40° Check student’s hexagons. 5 cm Check student’s hexagons. 4.6 cm



1 a) €30 b) $46.50 c) $1.35 2 a) July b) Moscow c) (i) March to April (ii) April to May 1 3 Ian leaves home at 7:30 a.m. and walks 2 km to the bus stop. It takes 10 minutes. He waits 5 minutes for the bus. The bus travels 6 km and arrives at 8:05 a.m. Ian then walks 1 km in 15 minutes. 4 a) 23°C b) 6.5°C c) November d) May 5 a) 0.7 second b) 1 hour c) After the first hour, reaction time gets longer (slower).

1 a) Radius b) Circumference c) Diameter 2 Check students’ diagrams. 10 cm 3 It does not have eight equal angles. 4 Square 5 Rhombus 6 6 7 45° 8 a) Isosceles triangle b) Pentagon 9 Check student’s diagrams. 10 Check student’s diagrams.

Chapter 26

Chapter 25


Exercise 25.1 (page 291) 1 a) $53 2 a) 22.5 litres 3 a) 25 miles

186

1 During stage 1, from 08:00 to 08:45, the car travels 10 miles. It is travelling slowly as it leaves London. During stage 2, from 08:45 to 09:45, the car travels 60 miles. It is travelling quickly on a motorway or major road. During stage 3, from 09:45 to 10:00, the car is stationary. The driver could have stopped for petrol or a break. During stage 4, from 10:00 to 11:30, the car travels 100 miles. It is travelling quickly on a motorway or major road. 2 The tortoise travels steadily without stopping. It covers 100 m in 100 minutes. The hare covers the first 50 m in 10 minutes. It then stops for 20 minutes. It then covers another 40 m in 10 minutes but then stops for 60 minutes. The tortoise wins the race. 3 a) The bicycle travels from Hereford to Birmingham steadily without stopping. It covers 60 miles in 4 hours. The car travels from Birmingham to Hereford. It leaves Birmingham at 14:30 and travels 20 miles in 12 hour. It then stops for 34 hour, between 15:00 and 15:45, before continuing for a further 40 miles and arriving in Hereford after 1 hour at 16:45. b) They pass going in opposite directions.

b) £46 b) 8.8 gallons b) 24 km

c) c) c)

$1.52 4.5 litres 1.6 km


1 2 3 4

a 74° b 65° c 125° d 65° e 65°

(Alternate angles) (Allied angles) (Corresponding angles) (Alternate angles) (Corresponding or vertically opposite angles)


5 f 110° g 110°

(Alternate angles) (Corresponding or vertically opposite angles) 6 h 55° (Allied angles) i 125° (Corresponding angles) j 125° (Alternate or vertically opposite angles) 7 k 65° (Corresponding angles) l 65° (Alternate or vertically opposite angles) m 115° (Allied angles) n 115° (Vertically opposite angles) 8 o 101° (Corresponding angles) p 101° (Corresponding angles) q 101° (Alternate angles) 9 r 97° (Allied angles) s 83° (Corresponding angles) t 29° (Angles in a triangle add up to 180°) 10 u 45° (Alternate angles) v 67° (Corresponding angles) w 68° (Angles on a straight line add up to 180° or angles in a triangle add up to 180°)

2 a) b) c) d) e) 3 a)

a 35° b 41° c 43° d 35° e 60° f 55°

7 g 141° h 39° 8 i 115° 9 j 123° k 57° 10 l 100° m 84°

(Angles in a triangle add up to 180°) (Angles in a triangle add up to 180°) (Angles in a triangle add up to 180°) (Angles in an isosceles triangle) (Angles in an equilateral triangle) (The exterior angle of a triangle is equal to the sum of the opposite interior angles) (The exterior angle of a triangle is equal to the sum of the opposite interior angles) (Angles on a straight line add up to 180°) (Angles in a quadrilateral add up to 360°) (Angles in a quadrilateral add up to 360°) (Angles on a straight line add up to 180°) (Angles on a straight line add up to 180°) (Angles in a quadrilateral add up to 360°)

6 4 2 0

2

4

6

8 x

6

8 x

6

8 x

Rhombus b)

y 4 2 0

2

4

Trapezium c)

y 4 2 0

2

4

Parallelogram d)

y 4 2 0

2

4

6

8 x

Kite 4 All the angles are 90° and the diagonals are equal length. 5 Isosceles trapezium, parallelogram or rhombus 110°

110°

70°

70°

Isosceles trapezium 70°

110°

110°

70°

Parallelogram

Exercise 26.3 (page 308) 1 A: trapezium B: rhombus C: square D: kite E: rectangle F: square G: arrowhead H: parallelogram I: trapezium J: rhombus K: parallelogram

y 8

Exercise 26.2 (page 305) 1 2 3 4 5 6

Square, rhombus Rectangle, parallelogram, kite, arrowhead Rectangle, parallelogram Trapezium Square, rhombus, kite

110° 70°

70°

110°

Rhombus

Exercise 26.4 (page 312) 1 2 3 4 5 6 7 8

2340° 3240° a) 131° a) 58° e 30°; e 3.6°; 15 20


b) 86°, 130°, 95°, 49° b) 90°, 100°, 123°, 105°, 122° i 150° i 176.4°


187



1 a) a 110° b 70° b)

c)

2 a) b) c)

3 a) b)

4 a) b) c) 5 a) b) c)

Corresponding angles. Allied angles or Angles on a straight line. c 50° Alternate angles. d 50° Corresponding angles or vertically opposite angles. e 36° Alternate angles. f 72° Angles on a straight line. g 72° Corresponding angles or angles in a triangle. a 19° Angles in a triangle add up to 180°. b 47° Base angles in an isosceles triangle are equal. c 31° Exterior angle of a triangle is equal to the sum of the opposite, interior angles. d 77° Angles on a straight line add up to 180° or Angles in a triangle add up to 180°. a 126° Angles in a quadrilateral add up to 360°. b 129° Angles on a straight line add up to 180°. c 53° Angles in a quadrilateral add up to 360°. Rectangle, parallelogram, kite, arrowhead Rhombus, isosceles trapezium, parallelogram Square, rectangle, isosceles trapezium 900° Exterior angle 24°, interior angle 156° 36

Chapter 27 Exercise 27.1 (page 315) 1 a) d) g) j) 2 a) d) 3 a) c)

6 cm b) 3.4 cm e) 2.9 cm h) 8.7 cm 7 cm b) 6.8 cm 4 cm 3 cm 3.4 cm 3.4 cm

4.5 cm 7.8 cm 1.3 cm

c) f) i)

9 cm 10.2 cm 5.6 cm

3.5 cm

c)

2.2 cm

b) 2 cm 2.4 cm

b 64° f 73° j 136° n 119° r 270°

c 50° g 90° k 40° o 29° s 128°

d 61° h 310° l 300° p 302° t 218°

Exercise 27.3 (page 324) Check students’ drawings.

188

C 23° C 72° B 30° B 32° C 40° XY 5.5 cm XY 7.1 cm YZ 3.8 cm YZ 4.5 cm XZ 3.4 cm

Exercise 27.5 (page 330) Check students’ drawings. 1 a) A 65° B 65° b) A B C 60° c) A 35° B 84° d) A 78° B 57° e) A 59° B 35° 2 a) X 65° Y 43° b) Y 38° Z 91° c) Y 41° Z 21° d) Y 81° X 64° e) X 52° Y 56°

C 49° C 60° C 44° C 86° YZ 6.7 cm XY 6.4 cm XY 3.2 cm YZ 6.7 cm XZ 6.1 cm

Exercise 27.6 (page 333) 1 a) 12 m b) 20 m c) 26 m d) 10 m 2 a) 40 km b) 100 km c) 55 km d) 27 km 3 Check students’ drawings. The lines should be the lengths given below. a) 5 cm b) 5 cm c) 12 cm d) 7.5 cm 4 a) 11 m b) Living room: 10 m 5 m Dining room: 6 m 4 m Bedroom 1: 5 m 5 m Bedroom 2: 3 m 4 m Bathroom: 3 m 3 m Kitchen: 4 m 3 m c) 13 cm 7.5 cm 5 a) (i) 90 km (ii) 270 km (iii) 110 km (iv) 66 km (v) 126 km (vi) 272 km b) 16 cm


Exercise 27.2 (page 320) a 30° e 125° i 127° m 109° q 67°

Check students’ drawings. 1 a) BC 7.6 cm B 67° b) BC 6.7 cm B 43° c) AB 9.1 cm A 20° d) AB 4.6 cm A 65° e) BC 9.6 cm B 22° 2 a) Y 70° YZ 4.9 cm b) Y 45° YZ 5 cm c) Y 33° XY 7.2 cm d) Y 60° XY 7.2 cm e) Y 65° XY 6 cm


Diagrams are not full size. The measurements given are correct for the suggested scale. 1 A: 005° B: 050° C: 090° E: 240° F: 300° G: 345° 2 Park: 3 km, 035° Swimming pool: 6 km, 060° Youth club: 4.5 km, 100° Shop: 7 km, 127° Hairdresser: 3 km, 188° Church: 4.5 km, 231° School: 6.5 km, 266° Cinema: 3.5 km, 315°

D: 145°


3 Check students’ drawings.

Chapter 28

N

Exercise 28.1 (page 351) 085° 5 cm Ashton 150°

Bradbury

Diagrams are not full size. The measurements given are correct for the suggested scale. 1

4 cm Charlton

5 cm

A

4 a) Check students’ drawings. N

C

2 Scale 1 cm 20 m

N

125° 5 cm

2.5 cm

L

5 cm

250° 7.5 cm P

b) 1.24 km

c)

029°

3 Scale 1 cm 10 m

5 Check students’ drawings.

Hedge

N A 6 cm 4 cm

Tree

B

Coastguard

6 cm

4 5 cm

5.5 cm 6.5 cm

E

60° 30°

C D

5 B

5 cm

C 3 cm

Mixed exercise 27 (page 339) 1 7.5 cm, 4.7 cm, 4.3 cm, 3.4 cm 2 a 52°, b 37°, c 125°, d 98°, e 217°, f 296° 3 Check students’ diagrams. 4 Check student’s diagrams. a) BC 2.9 cm, B 53°, C 92° b) E 50°, ED 6.8 cm, EF 7.4 cm c) HI 4 cm, H 125°, I 55° 5 Check student’s diagrams. a) K L M 60° b) OP 4.3 cm, O 48°, N 32° c) QR 3.9 cm or 10 cm 6 a) 2 m b) 14 m c) Study 8 m 4 m, lounge 8 m 10 m, dining room 8 m 7 m, kitchen 8 m 7 m d) 113 cm 52.5 cm 7 a) 450 m, 105° b) 400 m, 329° c) 325 m, 225° 8 a) Check students’ diagrams. b) 106 miles, 335°

5 cm

A

D

6 Scale 1 cm 1 m 4 cm

2 cm 1 cm

7

N NW

NE

W

E

SW

SE S



189

5

8

C

3 cm

7 cm

9 cm

7 cm

3 cm

Locus

9

A

C 7 cm

B

11 cm

6 Scale 1 cm 1 m

6 cm

5 cm A

8 cm

B

3 cm

10 Scale 1 cm 10 m (Note: other scales are also acceptable.)

2 cm

7 1 cm 20 m

8 cm 2 cm

Castle 6 cm Locus

2.5 cm

7 cm

Exercise 28.2 (page 354) Diagrams are not full size. The measurements given are correct for the suggested scale. 1

8 Scale 1 cm 1 km C

6 cm 5 cm

3 cm A

9.5 cm 5 cm 5 cm A

2 Scale 1 cm 1 km

B

7 cm


5 cm Q 4 cm

2 cm House

P

2.5 cm

3.5 cm 2 cm

7 cm

3 A

10 Scale 1 cm 5 miles

B

5 cm 3 cm

3 cm 5 cm H

3 cm D

8 cm

H

4 cm G

T 6 cm

190

K

C

4 Scale 1 cm 1 m

E

2 cm

5 cm

F



Mixed exercise 28 (page 355) Diagrams are not full size. Measurements given are correct for the suggested scale.

8

G

6 cm

5 cm

1 70° 8 cm

E 100°

F


2

5 cm

8 cm

5 cm

3

3 cm

10 Scale 1 cm 1 m

3 cm 7 cm

10 cm 3 cm

4

C

3 cm

3 cm 3 cm

6 cm

A

8 cm

3 cm

5.2 cm 9 cm

8 cm

3 cm

B

Area 23.4 cm2 5 S

R

Chapter 29

5 cm


P

8 cm

Q

6 Scale 1 cm 5 km

6 cm

b)

8 cm

6 cm

c) 7 Scale 1 cm 1 m D

C 3 cm

A

5 cm

B

2 a) 1


b) 0

c)

2


191

5

3

4 Isosceles triangle 5 Other answers with more squares shaded are possible. G B

G

R Y

G green B blue Y yellow R red

6 Check students’ patterns. 7

8

R B

6 Other answers with more squares shaded are possible. Purple Orange

9 Check students’ patterns.

Pink


b)

c)

d)

7 Check students’ patterns. 8 a)

e) b)

2 a)

b)

c) c)

3

Exercise 29.2 (page 363) 1 a) 2 b) 1 d) 4 e) 1 2 6, 6 3 Equilateral triangle 4

192

c) f)

4 8


B

y 5 4 3 2 1

0 87654321 1 2 3 4 mirror 5 line

A

1 2 3 4 5

x

C


4

9

y 5

y 5

4

4

3 B

B

A

2

2

1 5 4 3 2 1 0 1 2

1 2

3

4

1

5 x

5 4 3 2 1 0 1

C

3

2

1

3

4

5 x

2

4 5

3 5

Chapter 30 Exercise 30.1 (page 377)

Mixed exercise 29 (page 372) b) 4 b) 4

C

4

5 a) 90° anticlockwise b) 180° 6 a) 120° b) 240° 7 a) 180° (or 12 a turn) b) 90° anticlockwise (or 14 of a turn) 8 a) B, E, F b) C, D

1 a) 1 2 a) 1 3

A

3

1

0 1

c) c)

y 4

yx B

3 2 y1

C

1

4 3 2 1 0 1 2

1

2

3

4 x

3

4 x

A

3 4

4 2 y x

y 4 3

y2

A

2 B

1

5 a)

b)

4 3 2 1 0 1 2 C

1

2

3 4

6 a) 90° clockwise 7 B, E, F 8 a)–b)

b) 90° anticlockwise

3 a)

b)

y 5

c)

4 3 A

C

2 1

5 4 3 2 1 0 1 B

1

2

3

2

D

3 4 5

c)

4

mirror line

5 x

4 a) b) c) 5 a) b) c)

A reflection in the line y 2 A reflection in the line x 3 A reflection in the line y x A reflection in the line y 0 A reflection in the line y x A reflection in the line y x

90° anticlockwise



193


5

y 4 3 2 1

A C

4 3 2 1 0 1

1

2

4 x

3

90°

O

B

2 3 4

2

y 4

6

A

A

3 2

B

C

1 4 3 2 1 0 1

2

1

3

C

4 x

B

120°

2 3

A

D

B

4

3

y 8 7 6 5 4 3 A C 2 1 4321 0 1 2 B 3 4

4

D 1 2 3 4 5 6 7 x

7 a) A rotation of 90° (anticlockwise) about the origin b) A rotation of 180° about (1, 0) c) A rotation of 90° clockwise or 90° about (1, 2) 8 a) A rotation of 90° clockwise or 90° about the origin b) A rotation of 180° about (2, 1) c) A rotation of 90° (anticlockwise) about (1, 1) 9 A rotation of 150° clockwise about O 10 a) A reflection in the line x 0 b) A rotation of 90° (anticlockwise) about (2, 4) c) A reflection in the line y x d) A rotation of 90° (anticlockwise) about the origin e) A reflection in the line y x

A

Exercise 30.3 (page 386) 1 C

B 90°

y 6 5 4 3

B

A

B A

2 1 D 2 1 0 1

C

1

2

3

4

5

6 x

2

194



2

2 a)

y 6 5

B

4 D 3 C

2

A

1

2 1 0 1

1

2

3

4

5

6 x

2

12 1 A translation by vector 2 2 A translation by vector 1 4 A translation by vector 2 5 A translation by vector 2

b)

3 a) A translation by vector b) c) d) 4 a)

b) A rotation of 90° (anticlockwise) about the origin c) A rotation of 90° clockwise or 90° about (2, 2) 3 d) A translation by vector 4

3

y 4 3 B

2

A

1 4 3 2 1 0 1

A reflection in the line y 0 A reflection in the line y x 2 g) A translation by vector 6 e) f)

2

1

3

4 x

3

4 x

2

3

C

4

h) A rotation of 180° about (0, 2) 4

y C


4

y

2

4

1

3

4 3 2 1 0 1 D 2

2 B

1 4 3 2 1 1

2

1

3

4

x

A

2

A

3

3

1

2 B

4

3 4

C



195

Chapter 31


Exercise 31.1 (page 394) Note: Diagrams not full-size. 1 a)

y 8 7 6 5 4 3 2 1 0

b) b)

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

y 8 7 6 5 4 3 2 1 0

c) c)

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

y 8 7 6 5 4 3 2 1 0

d)

d)

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

y 8 7 6 5 4 3 2 1 0

e)

e)

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

y 8 7 6 5 4 3 2 1 0

2 a) 2 b) 3 c) 4 d) 3 3 a) No: for an enlargement, all the lengths must be enlarged by the same scale factor. AC 4 and DF 8 so DF is twice as long as AC but AB 4 and DE 10 so DE is more than twice as long as AB. b) No: for an enlargement, all the lengths must be enlarged by the same scale factor. AB 2 and DE 8 so DE is four times as long as AB but the height of the triangle ABC, from side AB to C, is 4 and the height of triangle DEF, from side DE to F, is 15, which is less than four times as long.

2 a) b) c) d) e)

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

3 4 2 3 2

(i) (i) (i) (i) (i)

(ii) (ii) (ii) (ii) (ii)

Exercise 31.3 (page 402) 1 a), b) y 6 5 4 A

3 2

B

1 0

c)

196


(0, 0) (0, 1) (2, 6) (5, 4) (5, 3)

1

2

3

4

5

6 x

An enlargement with scale factor 2, centre the origin


2 a), b) y 8 7

A

6 5 4

B

3 2

C

1 0

c)

1

2

3

4

5

6

7

8 x

An enlargement with scale factor 3, centre (1, 2)

7 a) A reflection in the line x 1 b) An enlargement with scale factor 2, centre (1, 0) c) A rotation of 90° (anticlockwise) about the origin d) A reflection in the line y x e) An enlargement with scale factor 12, centre the origin 1 f) A translation by vector 4

8 a) A reflection in the line y 2 b) A rotation of 90° clockwise or 90° about the origin 2 c) A translation by vector 2

3 a), b) y 8 7

d) A reflection in the line y 0 e) An enlargement with scale factor 12, centre (0, 2) f) An enlargement with scale factor 13, centre (2, 1) g) An enlargement with scale factor 3, centre (2, 1)

B

6 5 4 3 2

A

1 0

c)

1

2

3

4

5

6

7

8 x

An enlargement with scale factor 14, centre the origin

Mixed exercise 31 (page 405) 1 a)

4 a), b) y 8 7 6 5

B

4 3 2

C

1 0

b)

A

1

2

3

4

5

6

7

8 x

c) An enlargement with scale factor 23, centre (2, 1) 5 a) An enlargement with scale factor 2, centre (0, 3) b) An enlargement with scale factor 12, centre (0, 3) c) An enlargement with scale factor 112, centre the origin d) An enlargement with scale factor 23, centre the origin 6 a) A reflection in the line y 0 b) An enlargement with scale factor 2, centre (0, 4) 8 c) A translation by vector 3

d) An enlargement with scale factor 212, centre the origin 6 e) A translation by vector 4

f)

An enlargement with scale factor 13, centre (5, 3)

2 a)

y 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 x

b) y 10 9 8 7 6 5 4 3 2 1 0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 x


197

3 a) (i) 3 b) (i) 2 4

4 a) 2.4 kg 5 a) A: 4°C, B: 18°C

(ii) (0, 0) (ii) (8, 9)

y

1 100 ml, 0.75 litre, 1500 ml, 1.6 litres, 2 litres 2 a) centimetres b) metres c) metres d) kilometres e) metres f) metres g) centimetres or millimetres 3 1.1 m 4 0.72 5 34 kg, 1500 g, 1.6 kg, 2 kg, 10 000 g 6 a) 140 ml b) 25 ml c) 5000 ml d) 5230 ml 7 3.627 kg

8 7 6 5 A

4 3 2 B

1

5

400 g or 0.4 kg 22°C


9

0

b) b)

1

2

3

4

5

6

7

8

9 x

y


9

1 a) 900 g or 0.9 kg b) 2250 g or 2.25 kg c) 10 800 g or 10.8 kg d) 225 g or 0.225 kg 2 a) 48 km b) 22 pounds c) 264 pounds d) 40 miles e) 20 kg 3 200 miles

8 7 6 A

5 4 3

B

2 1 0

1

2

3

4

5

6

7

8


9 x

6 a) A reflection in the line x 0 b) A rotation of 90° clockwise about the origin. c) An enlargement with scale factor 3, centre (4, 3) 0 d) A translation by vector 3 1 e) An enlargement with scale factor 2, centre the origin 3 f) A translation by vector 2

g) A reflection in the line y x 7 a) A reflection in the line x 0 1 b) A translation by vector 3 c) An enlargement with scale factor 3, centre (0, 2) d) A rotation of 90° (anticlockwise) about (2, 2) 1 e) An enlargement with scale factor 2, centre the origin f) A rotation of 180° about the origin 3 g) A translation by vector 2

Chapter 32 Exercise 32.1 (page 410) 1 7.8 cm 2 1150 g or 1.15 kg 3 0.7 litre or 700 ml 198


The answers may vary a little from those given. 1 a) 3 m b) 25 cm c) 30 g d) 2 litres e) 70 kg f) 50 cm 2 a) 2.5 m b) 7 m 3 16 m 4 7m

Mixed exercise 32 (page 418) 1 a) 60 mm b) 350 mm c) 4500 mm d) 620 mm e) 37.2 mm 2 a) 5000 m b) 4320 m c) 46 700 m d) 1234 m 3 a) 5 km b) 6.7 km c) 12.345 km d) 0.543 21 km 4 31.04 cm, 1623 mm, 2.42 m, 284 cm, 9.044 m 5 a) m b) m c) cm or mm d) cm 6 a) 9000 g b) 1129 g c) 3100 g d) 300 g 7 a) 90 cm b) 40 km c) 0.5 kg d) 8 kg 8 55 miles 88 km 9 9m 10 3.75 kg

Chapter 33 Exercise 33.1 (page 421) 1 a) c) 2 a) c)

2500 cm 236 cm 30 000 cm2 95 200 cm2

b) d) b) d)

420 mm 5100 mm 230 mm2 1.4 mm2


3 a) 900 cm2 b) 81.4 cm2 2 c) 720 m d) 9.4 m2 3 4 a) 3 200 000 cm b) 0.000 042 m3 3 c) 0.005 m d) 6 420 000 cm3 3 5 a) 2610 cm b) 9.5 litres c) 2400 ml d) 0.91 litre 6 All the units need to be the same; change 50 cm to 0.5 m. 5 2 0.5 5 m3

Exercise 33.2 (page 423) 1 a) 56.5 m and 57.5 m b) 567.5 ml and 568.5 ml c) 23.925 seconds and 23.935 seconds 2 a) 633.5 g and 634.5 g b) 233.5 ml and 234.5 ml c) 8.25 m and 8.35 m 3 a) 28 to 32 m2 b) 15 cans (100 7 14.2) 4 a) 4.965 mm b) 4.975 mm 5 No; 595.5 mm is greater than 59.5 cm. 6 a) 14.9 cm and 15.1 cm b) 1.95 cm and 2.05 cm c) 1.95 cm and 2.05 cm 7 Maximum d: longest rod minus least depth 35.5 19.5 16 mm Minimum d: shortest rod minus greatest depth 34.5 20.5 14 mm 8 2 (14.5 8.5) 46 cm and 2 (15.5 9.5) 50 cm

Exercise 33.3 (page 425) 1 a) c) 2 a) c)

3.5 minutes 3 kg 3 5.7 m (or 54 m) 665 km

b) d) b) d)

3 weeks 2m £16 0.1 cm2

3 a) 2130 ml b) 5.1 litres c) 421 000 ml d) 0.0917 litre 4 a) 26.5 cm and 27.5 cm b) 5.55 cm and 5.65 cm c) 1.225 m and 1.235 m 5 Greatest speed: greatest distance least time 100.05 5.5 18.19 m/s 6 a) 33.5 mm and 34.5 mm b) Greatest perimeter: greatest length 3 34.5 3 103.5 mm 7 a) 1 hour 15 minutes b) 8 km/h 8 a) 60 mph b) 190 miles 9 5394 m2

Chapter 34 Exercise 34.1 (page 430) 1 a) 22 cm d) 14.9 cm 2 16.8 m 4 15 m

b) e) 3 5

8 cm 17.6 cm 18.8 cm 83.3 m

1 a) 12 cm2 d) 9 cm2

b) 8 cm2 e) 5 cm2

15 cm2 25 cm2

c) f) i)

80 cm2 17.6 m2 9.66 cm2

Exercise 34.3 (page 433) 1 a) 24 m2 d) 75 m2 g) 30.66 m2 2 16.92 cm2 3 6.76 m2 4 15.023 cm2 5 15.68 m2 6 36 m2 7 a) 14 m2 8 a) 15 m2

b) 36 cm2 e) 8 cm2 h) 10.24 m2

b) £343 b) £375

1 3 5 7 9

16 cm2 160 m2 64 cm2 55 cm2 150 m2

2 4 6 8 10

50 cm2 75 mm2 17.5 cm2 144 cm2 120 m2




b) d) b) d)

c) f)


62.5 m/s 2 43 mph 7.5 miles 4 5 hours 278 cm3 6 60 mph 9 g/cm3 8 100 km/h 7.8 g/cm3 a) 8.9 g/cm3 b) 151.3 g 19.3 kg a) 58.5 kg b) (i) 0.7692 m3 (ii) 769.2 m3 13 a) 60 km/h b) 64.3 km/h 14 10.6 g/cm3 15 1156 people per square kilometre 1 3 5 7 9 10 11 12

120 000 cm2 4200 cm2 3 000 000 mm2 94 cm2

18.4 cm 33 cm



1 a) c) 2 a) c)

c) f)

371 mm2 5 mm2 41.25 m2 600 cm2

1 3 5 7 9

1 2 4 6 8 10

24 cm2 64 m2 14 cm2 42 cm2 42 cm2

a) 60 cm3 150 m3 4500 cm3 42.875 cm3 189 000 cm3 750 cm3


2 4 6 8 10

b) 3 5 7 9

72 cm2 35 cm2 30 cm2 144 m2 16 cm2

128 cm3 125 cm3 72 m3 252 cm3 1800 cm3


199

Mixed exercise 34 (page 441) 1 a) 20.6 cm b) 16.9 cm c) 28 cm d) 15.4 cm 2 perimeter 17.4 cm, area 18.02 cm2 3 perimeter 54 m, area 180 m2 4 perimeter 18.4 cm, area 21.16 cm2 5 perimeter 13 m, area 10 m2 6 a) 4.41 m2 b) 23.68 m2 2 c) 28.09 m d) £21.07 (to the nearest penny) 7 a) 9 cm2 b) 8 cm2 c) 30 cm2 2 2 8 a) 28 cm b) 300 cm c) 18 cm2 3 9 120 cm 10 19.683 cm3 11 3000 cm3 12 360 000 cm3 or 0.36 m3

g) h) i) j) k) l)

2290 cm2 (nearest whole number) 15.2 cm2 (1 d.p.) 75.4 cm2 (1 d.p.) 11.3 m2 (1 d.p.) 6.2 m2 (1 d.p.) 4.30 m2 (2 d.p.)

Exercise 35.3 (page 448) 1 2 3 4 5 6

160 cm2 126 cm2 340 cm2 227 cm2 108 cm2 212 cm2

Exercise 35.4 (page 450) 1 a) 515 cm3 d) 385.5 cm3 2 18 000 cm3

Chapter 35 Exercise 35.1 (page 445) These answers have been calculated using the button on a calculator. 1 2 3 4 5 6 7 8 9 10 11 12

37.7 cm (1 d.p.) 78.5 cm (1 d.p.) 282.7 cm (1 d.p.) 116.2 mm (1 d.p.) 207 mm (nearest whole number) 84.8 cm (1 d.p.) 163.4 cm (1 d.p.) 14.8 cm (1 d.p.) 28.9 cm (1 d.p.) 22.9 m (1 d.p.) 9.1 m (1 d.p.) 3.86 m (2 d.p.)

200


219.6 cm3 780 cm3

Exercise 35.5 (page 452) 1 a) 1233 cm3 d) 396.8 cm3 2 119 000 mm3

b) 17 334 cm3 c) e) 2253.42 cm3 f)

2092.8 cm3 528.82 cm3

These answers have been calculated using the button on a calculator.

These answers have been calculated using the button on a calculator. 616 cm2 (nearest whole number) 2463 cm2 (nearest whole number) 20 106 cm2 (nearest whole number) 3848 mm2 (nearest whole number) 12 076 mm2 (nearest whole number) 5809 cm2 (nearest whole number) 9503 cm2 (nearest whole number) 75.4 cm2 (1 d.p.) 295.6 cm2 (1 d.p.) 36.3 m2 (1 d.p.) 21.2 m2 (1 d.p.) 4.91 m2 (2 d.p.) 201 cm2 (nearest whole number) 452 cm2 (nearest whole number) 3848 cm2 (nearest whole number) 1018 mm2 (nearest whole number) 5281 mm2 (nearest whole number) 1810 cm2 (nearest whole number)

c) f)



1 a) b) c) d) e) f) g) h) i) j) k) l) 2 a) b) c) d) e) f)

b) 1376 cm3 e) 192 cm3

1 a) 7037 cm3 (nearest whole number) b) 25 862 cm3 (nearest whole number) c) 113 097 cm3 (nearest whole number) d) 24 881 mm3 (nearest whole number) e) 11 781 mm3 (nearest whole number) f) 115 mm3 (nearest whole number) g) 707 m3 (nearest whole number) h) 370 m3 (nearest whole number) 2 11 045 cm3

Exercise 35.7 (page 456) These answers have been calculated using the button on a calculator. 1 a) b) c) d) e) f) g) h) 2 a) b) c) d) e) f) g) h)

1810 cm2 (nearest whole number) 2281 cm2 (nearest whole number) 2827 cm2 (nearest whole number) 3958 mm2 (nearest whole number) 377 mm2 (nearest whole number) 465.6 mm2 (1 d.p.) 131.9 m2 (1 d.p.) 77.0 m2 (1 d.p.) 2111 cm2 (nearest whole number) 6993 cm2 (nearest whole number) 10 336 cm2 (nearest whole number) 3054 mm2 (nearest whole number) 4869 mm2 (nearest whole number) 1176.5 mm2 (1 d.p.) 190.0 m2 (1 d.p.) 59.7 m2 (1 d.p.)


Exercise 35.8 (page 459) 1 Plan

Front elevation

Side elevation

3 Plan

5

Plan

6 Plan

2 Plan

Front elevation

Front elevation

Side elevation

Side elevation

Front elevation

Side elevation

4 Plan

Front elevation

Front elevation

Side elevation

Side elevation

Mixed exercise 35 (page 461) Where necessary, the button on a calculator has been used to work out these answers. 1 a) 44.6 cm b) 93.3 cm c) 204 cm d) 100.8 mm b) 24.45 m2 2 a) 127.08 cm2 2 c) 237.79 mm d) 69.40 mm2 2 e) 124.69 cm f) 72.08 m2 3 Check students’ diagrams. 4 a) 89.54 cm2 b) 75 cm2 2 c) 176.5 cm d) 178.23 cm2 3 5 a) 208 cm b) 156 cm3 3 c) 169.32 cm d) 192 cm3 3 e) 257.544 cm f) 655.2 cm3 3 6 a) 20 308.2 cm b) 1578.46 mm3 3 c) 5617.5 cm d) 0.8874 m3 3 7 a) 2601 mm (nearest whole number) b) 3268.5 mm3 (1 d.p.) c) 106 437 cm3 (nearest whole number) d) 181 cm3 (nearest whole number) e) 23 091 m3 (nearest whole number) f) 27.5 m3 (1 d.p.) 8 a) 1659 m2 (nearest whole number) b) 2432 cm2 (nearest whole number) c) 16.0 cm2 (1 d.p.) d) 672 mm2 (nearest whole number) 9 a) 5202 mm2 (nearest whole number) b) 113 m2 (nearest whole number) c) 174 cm2 (nearest whole number) d) 546 cm2 (nearest whole number)



201

10 a)

b)

Plan

Side elevation

4 Yes 7.52 182 19.52 (This is 1.5 the 5, 12, 13 triangle) 5 Yes 3.52 122 12.52 (This is 0.5 the 7, 24, 25 triangle) 6 No 52 102 112 7 No 4.52 92 102 8 Yes 28.82 122 31.22 (This is 2.4 the 5, 12, 13 triangle)

Plan

Side elevation


Front elevation

1 a) c) e) 2 a) c) e)

Front elevation

(6.5, 3) (1.5, 6) (0.5, 5) (1, 6) (5, 4.5) (1, 2)

b) d) f) b) d) f)

(3, 5) (4.5, 0) (5.5, 4.5) (4, 4) (5.5, 4.5) (5, 7)


c)

d)

Plan

1 a) 20 cm2 b) 23 cm2 2 a) 11.40 cm b) 7.55 cm c) 6.27 cm d) 4.99 cm 3 a) No 52 82 92 b) Yes 92 122 152 (This is 3 the 3, 4, 5 triangle) c) Yes 17.52 602 62.52 (This is 2.5 the 7, 24, 25 triangle) d) No 5.22 8.32 9.72 4 a) (3, 4) b) (4, 512) c) (412, 412) 5 1.93 m 6 30.3 cm2 7 15.66 m

Plan

Side elevation

Side elevation

Chapter 37 Exercise 37.1 (page 478)

Front elevation

Front elevation

1 2 3 4 5

6

Chapter 36 Exercise 36.1 (page 465) 1 12 cm2 3 50 cm2

2 4

7 8 9 10 11

85 cm2 28 cm2

Exercise 36.2 (page 467) 1 a) 13 cm d) 24 cm g) 30.50 m 2 4.53 m 3 23.66 inches

b) 5.83 m e) 7.64 cm h) 9.35 m

c) f) i)

6.24 cm 6.34 cm 6.57 cm

Exercise 36.3 (page 470) 1 Yes 62 82 102 (This is 2 the 3, 4, 5 triangle) 2 No 42 72 82 3 No 82 82 112 202


14:25 a) 09:35 b) 00:13 1 hour and 20 minutes 5 minutes to 6 a) 33 minutes b) c) 39 minutes d) e) 45 minutes f) a) 3:35 b) c) 13:10 d) e) 5 past 10 f) 08:21 9:20 16:35 11:15 1 hour and 35 minutes

20 minutes 40 minutes 33 minutes 3:05 13:23 25 past 5

Exercise 37.2 (page 482) 1 3 5 7 8 9 10

54 km 3 hours 1470 m 10.44 m/s a) 14 hour a) 150 seconds 162.5 km

2 2.8 mph 4 12 km/h 6 4.5 hours b) 52 km/h, yes b) 1.2 m/s


Exercise 37.3 (page 484) 1 14 ounces 2 1.5 pounds 3 a) Imperial

b)

Metric

5 feet

1.5 m or 150 cm

12 pounds

6 kg

5 pints

2.9 litres

Metric

Imperial

20 km

12.5 miles

3m

10 feet

10 litres

17.5 pints

15 kg

30 pounds

Exercise 37.4 (page 486) 1 a) b) c) 2 a)

17.5 pence A 7-minute call to Jamaica, by 0.5 pence 3 509 km b) 15 km

Mixed exercise 37 (page 487) 1 2 3 4 5 6 7 8 9 10 11

23:50 and 01:50 a) £9 a) £69.65 50 m/s 30 mph 10.5 miles 7.5 hours a) 215 second a) 13 a) 48 km/h a) 31.5 litres

b) £6 b) £3.95

b) b) b) b)

c) c)

40 seconds 8 50 mph 225 litres c)

£5.11 £2.52

1350 litres

Chapter 38 Exercise 38.1 (page 491) 1 4 7 10

5 3.45 1.20 2.65

2 5 8 11

3.84 9.2 2.68 1.78

3 6 9 12

4.5 62.41 4.48 1.85

Exercise 38.2 (page 494) 1 Check students’ answers. Possible answers include the following. a) positive negative negative b) Multiplying by number less than 1 should make answer smaller. c) 3 60 180 and answer should be more than this. d) 64 8 and answer should be less than this.

2 Check students’ answers. Possible answers include the following. a) Answer is too large, since 0.9 is near 1. b) negative negative positive c) 62 36 and answer should be less than this. d) 8 3 11 so last digit should be 1. 3 a) 1000 20 20 000 b) 0.4 0.4 0.16 c) 20 5 4 4 a) 7 £9 £63 b) 30 £15 £450 or 30 £10 £300 c) 3 £6 3 £2 £24 5 a) 62 067.5 81.4 762.5 or 62 067.5 762.5 81.4 b) 1466.8 9 38.3 c) 17.6 3.8 66.88 d) 278.93 18.2 297.13, 297.13 4.3 69.1 6 a) 468.38 b) 6.80 7 a) 12.647 b) 896.874 8 a) 61.1 b) 4.8 9 a) (i) 403 64 000 (ii) 20 0.2 4 2 (iii) 7 42 49 6 1 33 6 10 30 4000 40 (iv) 500 0.08 8 0.08 b) (i) 60 236.288 (ii) 3.496 (iii) 5.93 (to 2 d.p.) (iv) 516 (to nearest whole number)

Exercise 38.3 (page 500) 1 a) 2 hours and 51 minutes b) 9 minutes 2 a) 1.45 hours b) 0.9 hour 3 3 hours and 15 minutes 4 1 hour and 48 minutes 5 5 6 £31.32 and £20.88 7 700 ml or 0.7 litre 8 54 mph 9 £191.11 or £191.12 10 66 834 11 200.8 12 2.2 g/cm3 13 15.2 cm

Mixed exercise 38 (page 502) 1 a) 3 b) 3.5 2 2.32 (to 2 d.p.) 3 a) The answer should be more than 72, which is 49. b) Multiplying 2.4 by a number less than 1 should give an answer less than 2.4. c) 120 49 120 50 6000, not nearly 60 000 (or equivalent argument). d) The answer should be negative. 4 a) 900 30 27 000 b) 0.62 0.36 c) 48 6 8 or 50 6 8



203

13 a)

5 a) 1270.26 b) 2.88 (ii) 30 0.3 9 6 a) (i) 203 8000 2 (iii) 8 42 64 6 1 48 7 30 50 80 (iv) 2000 0.04 0.04 b) (i) 9800.344 (ii) 7.743 (iii) 6.93 (to 2 d.p.) (iv) 2054 (to nearest integer) 7 3 8 a) 3 hours 42 minutes b) 2 hours 45 minutes c) 48 minutes d) 51 minutes 9 34.3 mph (to 1 d.p.) 10 48.75 cm3 11 £96.91 or £96.92

Dice

Spinner

1

2

3

4

5

6

1

2

3

4

5

6

7

2

3

4

5

6

7

8

3

4

5

6

7

8

9

4

5

6

7

8

9

10

b) 10 c) 24 14 a) (Order can be different)

d)

2 24

112

First scoop

C

C

C

V

V

V

S

S

S

Second scoop

C

V

S

C

V

S

C

V

S

b)

2 9


Chapter 39 Unlikely (or Impossible) Evens Likely Arrow at Certain Arrow at Very unlikely Arrow at Likely (if answering this at school) Unlikely Evens Impossible All 1s All not 1 Two 1s and three others Four 1s and one other

38 or 0.375

2 a) b) c) 3 a) b) c)

Exercise 39.1 (page 506) 1 a) b) c) 2 a) b) c) 3 a) b) c) 4 a) b) c) d)

24 64

1230 or 0.65 About 100 Do many more tosses. (i) 35070 or 0.19 (ii) 33090 or 0.13 (i) 0.167 (ii) 0.167 They could do although the experimental probabilities are different from the theoretical probabilities, but more throws are needed to check. 130 200

Mixed exercise 39 (page 516) 1 a) Impossible b) Evens c) Likely (this depends on the local climate) 2 0

0.5

1

a)

b)

Exercise 39.2 (page 511) 1 a) Arrow at 0.5 b) Arrow at 1 c) Arrow at 13 (3rd tick mark from the left) 2 a) Unlikely b) R at 0.5, G at 0.3, B at 0 3 a) 15 or 0.2 b) 25 or 0.4 1 4 a) 6 b) 46 23 c) 0 5 a) 0.1 b) 0.7 c) 0.3 6 a) 28 14 b) 18 c) 0 7 a) 6 b) 12 8 5 orange, 3 blue, 2 red, no green 9 a) Red b) 3 red and 1 purple 10 a) Arrow at 0.4 b) Arrow at 0.6 11 78 12 a) 156 b) 176 c) 196

c)

3 a) 5 1 4 a) 5 5 6 7 8 9 10

1

a) 8 1 a) 6 4 0.65 72 200 0.36 a) T-shirt

b)

204


b) 0 3 b) 5 b)

2 8

1

or 4

c)

2 5

c)

0

b) 0.7

Jeans

Red

Blue

Red

Black

White

Blue

White

Black

Yellow

Blue

Yellow

Black

1 6


6 a) 200 is a large number of trials. b)

Chapter 40 Exercise 40.1 (page 519) 2 56 5 0.57

1 0.9 4 130

Method of travel

3 0.15 6 1479

Estimate of probability


Car

Bike

Walk

0.245

0.24

0.115

0.4


2 260 or 130 5 0.11

1 0.7 4 141

Bus

3 0.35 6 210

1 2 3 4 5 6

7 9

0.35 0.13 7 a) 20 b) 5 red, 8 white, 7 blue 12 days 10 1 a) 20 2, which is the probability of getting heads with a fair coin. b) She is not necessarily correct. She should carry out more trials. 7 a) About 67 279 121 3 9 b) (i) (ii) (iii) 400 400 400

Exercise 40.3 (page 523) 1 4 2 12 3 17 4 £300 5 a) 50 b) 150 6 50 yellow, 75 blue, 125 green

Exercise 40.4 (page 525) 1 a) 1

Score Relative frequency

2

3

4

5

6

0.14 0.09 0.17 0.22 0.11 0.27

1 6

b) or 0.17 (to 2 d.p.) c) Yes, the dice is biased. The relative frequency for 2 seems too low and the relative frequencies for 4 and 6 seem too high. 2 Small number of trials. Cannot be predicted from these past events. 3 a) Party Relative frequency

Chapter 41 Exercise 41.1 (page 530) 1 Discrete: Number of pets, Money, Age in years Continuous: Weight, Distance, Temperature 2 Check students’ answers. 3 a) Month of Tally Frequency birth January February March

Labour

0.30

Conservative

0.47

Lib. Dem.

0.17

June

Other

0.06

July

b) 0.3 4 a) 1200 0.5, which is the probability of tossing a fair coin and getting a head. b) 130020 0.34, which is very different from 0.5. c) Emma. More trials give a more reliable indication. 5 a) Score 1 2 3 4 Relative frequency

April May

August September October November December b)

0.27 0.23 0.26 0.24

Day of birth

Tally

Frequency

Monday Tuesday

b) Yes. All values are approximately equal to 0.25. c) Either 225, 225, 225, 225 (if the spinner is fair) or Score 1 2 3 4 Relative frequency

Wednesday Thursday Friday Saturday

240 204 237 219

Sunday c)–e) Check students’ answers. 4 Check students’ answers.



205


c) Frequency

12 10 8 6 4 2

12 10 8 6 4 2

lu e ro w n G re en G re y O th er

0 0

B

B

Frequency

1 a)

1p

2p

5p

20p £1 10p 50p £2

Eye colour

Type of coin

d) 12 10 8 6 4 2

Frequency

Frequency

b)

0

1

4 More than 4 Number of cars

0

2

3

16 14 12 10 8 6 4 2 0

0

1

2

3 More than 3 Number of fillings

12 10 8 6 4 2

e)

O S& V O th er

en

&

f

hi

C

0

ee

5 More than 5 Number of bedrooms

ck

4

C

3

n

2

ai

1

Pl

0

60 50 40 30 20 10

B

Frequency

Frequency

c)

Favourite crisps 12 10 8 6 4 2


0

Fish Horse Rabbit Other

1 a) Bird Cat Dog

Frequency

2 a)

35

65

100

Not red

72

438

510

107

503

610

b) 610 2 a)

b) 12 10 8 6 4 2 0

0

1

2

3 More than 3 Number of brothers

107

d) 72

e)

100

New drug

Total

Symptoms eased

700

550

1250

No change in symptoms

350

250

600

1050

800

1850

Total b) 1850


c)

Existing drug

3

206

Total

Red Total

Type of pet

Frequency

Japanese Not Japanese

c)

550

Riding

Sport

Total

Boys

8

18

26

Girls

15

7

22

Total

23

25

48


4 a) Hockey

Not hockey

Total

Badminton

33

13

46

Not badminton

24

15

39

Total

57

28

85

Frequency

2 a) 50 40 30 20 10 0

b) 15

30– 50– 70– 90– 110 49 69 89 109 or more Grapes per bunch

5 a) Silver

Bronze

Total

USA

31

18

10

59

Germany

18

16

9

43

China

22

9

11

42

Total

71

43

30

144

c)

c)

1 a) Frequency

1 to 5

12

6 to 10

25

11 to 15

13

16 to 20

5

21 to 25

3

26 to 30

2

0

7

11 to 20

16

21 to 30

18

31 to 40

13

41 to 50

0

100 80 60 40 20 0

1

c)

1 to 20

Tally

Frequency

f)

4

21 to 40

15

41 to 60

25

61 to 80

13

81 to 100

3


Frequency

Number of cars

Less 30– 50– 70– 90 than 49 69 89 or 30 more Number of ants

e)

5

51 to 60 61 to 70

50 40 30 20 10

Frequency

Frequency

1 to 10

0– 20– 40– 60– 80– 100 19 39 59 79 99 or more Greenfly per plant

d)

b) Tally

50 40 30 20 10 0

Frequency

Tally

Number of stamps

1– 26– 51– 76– 101 25 50 75 100 or more Leaves per branch

China

Exercise 41.4 (page 536) Number of birds

40 30 20 10 0

Frequency

b) The USA

Frequency

b) Gold

50 40 30 20 10 0

0–9 10– 20– 30– 40 19 29 39 or more Eggs per day

140– 150– 160– 170– 180– 190– 200 149 159 169 179 189 199 or more

Apples per box


207


4 a)

1 Discrete: Hair colour, Vehicle type, Number of sisters, Crowd size, Score on a dice Continuous: Height, Length 2 Check students’ data collection sheets. 3 a)

35

20

2 0 1

2

3

4

5

Other

4

Volvo

0

6

Volkswagen

5

8

Toyota

10

10

Nissan

15

12

Vauxhall

Frequency

14

25

Ford

Frequency

30

Make of car

6

Score

b)

b)

16 16

14

14

12 Frequency

Frequency

12 10 8 6

10 8 6

4

4

2

2 0

0 1

2

3

4

5

Number of goals

0

More than 5

1

2

3

Number of pets

c)

More than 3

c) 30

20

20 Frequency

15 10 5 0

5

Other

Hair colour

Other

PC

Gamecube

5 X-box

0

Make of phone

Playstation

Frequency

50 40 30 20 10

Games console owned

208

Other

Motorola

0

d)

Siemens

Grey

Ericsson

Red

10

Nokia

Brown Black Blonde

15

Samsung

Frequency

25


Alton Towers

Legoland

Thorpe Park

Total

Girls

31

25

27

83

Boys

43

11

21

75

Total

74

36

48

158


6 a)

c) Tally

30

Frequency

11 to 10

14

11 to 20

11

21 to 30

18

31 to 40

10

41 to 50

18

51 to 60

16

61 to 70

13

25 Frequency

Number of CDs owned

20 15 10 5 0 1–5

6–10

11–15

16–20

21–25

Number of mice in a nest

Chapter 42

b) Number of flowers per plant

Tally

Frequency

represents 10 kilos of apples.

1 M

11 to 20

12

21 to 40

22

41 to 60

28

18

61 to 80


Tu W Th F Sa

7 a) 20

Su

Frequency

15

represents two pairs of spectacles.

2 10

M Tu

5

W Th

0 1–5

6–10

11–15

16–20

Number of flowers on a plant

More than 20

F Sa

b) Su 40

represents four people.

3 Frequency

30

M Tu

20

W Th F

10

Sa Su

0 0–9

10–19

20–29

30–39

40–49

50–59

Number of passengers on a bus



209

4

2

represents 20 boxes of bananas.

䡵

a) Beef

Jan Other

Feb

Chicken

Salt and vineger

March April

Cheese and onion

May June

b)

July

Other Blue

Aug Sep

Grey Brown

Oct Green

Nov Dec

c)

Other

Red

You can use any symbol to represent ten ice creams. Here is used.

5

Black

M

Brown

Blonde

Tu W

3 a)

Th

Scotland

F

Northern Ireland

Wales

Sa Su

England


More than 3 cars No cars

b)

Oats and nuts

3 cars Sugar

1 car

Butter

2 cars

Flour

b)

More than 4 bedrooms

1 bedroom

2 4 bedrooms bedrooms

Exercise 42.3 (page 547) 1 24 22

More than 3 pets

3 pets

No pets

Temperature (°C)

3 bedrooms

c)

Fruit

20 18 16 14

2 pets 1 pet

12 M Tu W Th F Sa Su Day

210



2


24

Sales ( £1000)

Represents 4 skips

1

22 20

Monday

18

Tuesday

16

Wednesday

14

Thursday

12

Friday

10

Saturday J F MAM J J A S O N D Month

Sunday Represents 100 tickets

2

3 Temperature (°C)

100

Monday

90

Tuesday

80 70

Wednesday

60

Thursday

50

Friday 0

5

10 15 20 25 30 Time (minutes)

Saturday Sunday

4 3

900

Protein

Other

Number of visitors

800 700 600

Carbohydrate

500 400

4

300 M Tu W Th F Sa Su Day

Savings

Entertainment

5

Rent

140 120

Clothes

Sales (£)

100

Food

80 60 40 20 0 1

2

3

4

5

6

7

9 11 13 8 10 12 14 Day



211

4

Temperature (°C)

5

Speed (mph)

Tally

Total

28

30 s < 35

2

24

35 s < 40

9

20

40 s < 45

10

45 s < 50

8

50 s < 55

1

16 12 8 4

Modal class 40 s 45 mph

0

Mon

Tues

Wed

Thurs

Fri

Sat

Day

6

Sales (¥ million)

26 24 22 20 18 16 14 0

J

F M A M

J

J

A

S

O N D

Month

Chapter 43 Exercise 43.1 (page 551) 1 a) 6 d) 4 2 48 3 a) 5 or more

b) 7 e) 8

c) f)

4 7.5

c) c)

6.5 6

c)

756

b) 6

Exercise 43.2 (page 552) 1 2 3 4

18 73 kg 19 There are two modes: 47 and 50.

Exercise 43.3 (page 553) 1 a) 6 2 a) 5 3 11.1 minutes

b) 9 b) 7.2

Exercise 43.4 (page 554) 1 a) 19 2 a) £32

b) 3.2 b) £92

Exercise 43.5 (page 555) 1 121–130 cm 2 £8–£11.99 3 11–15 words

212


Sun

Mixed exercise 43 (page 556) 1 a) Tom: mode 7, median 7, mean 6, range 5 Freya: mode 3, median 3, mean 5, range 9 b) Possible answers include: Tom’s scores are more consistent (the range of his scores is smaller). Tom’s scores are higher on average (higher mode, median and mean). 2 a) 4 b) 45 mm c) 200.3 mm 3 a) Football team: mean 12.9 seconds, median 13 seconds, range 4 seconds Hockey team: mean 13.1 seconds, median 13 seconds, range 4 seconds b) Mean 12.4 seconds, median 12 seconds, range 4 seconds c) PE staff: lower mean and lower median times 4 a) Data set A: range 6, mean 3.6, median 3, mode 3 Data set B: range 6, mean 3.6, median 3, mode 3 Data set C: range 12, mean 7.2, median 6, mode 6 b) The range, mean, median and mode for data sets A and B are the same. The results for data set C are double those of data sets A and B. 5 a) (i) Mean 3, median 3, mode 3 (ii) Mean 30, median 20, mode 20 (iii) Mean 130, median 120, mode 120 (iv) Mean 13, median 13, no mode b) The values for set (iii) are 100 more than the corresponding values in set (ii) so the values of the mean, median and mode are also 100 more. 6 a) Boys: mean 14.7 hours, median 15 hours, mode 13 hours and 15 hours, range 23 hours Girls: mean 12.1 hours, median 12 hours, mode 9 hours, 12 hours and 15 hours, range 9 hours b) Yes, the boys watch more television than the girls. 7 a) Median 7, no mode b) Median 36 kg, no mode 8 Median 124 cm, mode 123 cm


9

Mass (grams)

Tally

Frequency

200 m 220

冟冟

2

220 m 240

冟

1

240 m 260

冟

1

260 m 280

冟

1

280 m 300

冟冟冟

3

300 m 320

冟冟

2

320 m 340

冟冟

2

340 m 360

冟

1

360 m 380

冟冟

2

380 m 400

冟冟冟冟

5

400 m 420

冟冟冟冟

4

The modal class is 380 m 400

Chapter 44 Exercise 44.1 (page 559) 1 a) 630 b) 45 2 a) Saturday b) Wednesday c) 21 d) 150 3 a) 60 b) 45 4 a) 70 b) 105 5 a) Wednesday b) 75 c) 195 6 a) 325 (June) b) 500 (January) c) 5150 d) Approximately 429

c)

Monday

c) c)

275 415

Exercise 44.2 (page 564) 1 a) 12 b) About 13 2 a) The Mail b) The Sun, magazines, and other newspapers 3 a) 36 b) 6 4 a) 28 b) 16 5 a) 14 b) 10 c) 18 6 a) 44 b) 16 c) 24

Exercise 44.3 (page 568) 1 a) c) 2 a) c) 3 a) c)

75°C 21°C 44 115 22°C 23 18 5°C

b) d) b) d) b) d)

5 minutes 19°C Friday 162 18°C (Monday) 147 7 21°C

4 a) b) c) d) 5 a) b) c) 6 a) b) c) d)

November £22 000 £15 000 £7000 £223 000 223 000 12 £18 583.33 10 500 1500 1850 1300 550 The café is closed. £100 The second Monday (£40) 540 8 £67.50

Exercise 44.4 (page 572) 1 a) England b) Wales c) Scotland is a relatively large country with a relatively small population. 2 a) 8 b) 0 c) 7 d) 10 1 9 e) The girls did better in the test. The shape of the charts show that there are more girls getting higher scores. The mean for the boys is 5.6 and the mean for the girls is 6.2. 3 a) $38 000 b) $35 000 c) $31 000 > $31 200 d) 2003 range $15 000, 2009 range $63 000 e) Student’s own answer f) Check students’ bar charts.

Mixed exercise 44 (page 574) 1 a) 60 b) 75 c) 270 d) 45 2 a) 240 b) 1760 c) 251 (to nearest whole number) d) 300 3 a) County council b) (i) Any answer from £275 to £285 (ii) Any answer from £157.50 to £167.50 (iii) Any answer from £75 to £85 4 a) Spain b) Spain: any answer from 41 to 43, USA: any answer from 23 to 25, France: any answer from 15 to 17, Asia: any answer from 11 to 13, Italy: any answer from 5 to 7, Other: any answer from 19 to 21 5 a) Week 7 b) 28 c) 250 d) 28 (to the nearest whole number) 6 a) July and August b) 14 cm c) 5°C d) 113 cm 7 a) (Just over) half b) North America. The ‘Forest’ sector is larger in the pie chart for North America. c) The total areas are different d) A greater proportion of land is used for pasture and grazing and for farming (arable) in North America than in Australia, and a smaller proportion is non-productive.



213

4

8 a) Germany, $23 billion b) USA, $15 billion c) France and Italy d)

Lifetime of lightbulb (h hours)

Frequency

300 h 400

3

400 h 500

9

500 h 600

12

600 h 700

15

Tourist Spending and Earnings

20

700 h 800

13

10

Earnings

800 h 900

19

5

900 h 1000

13

0

1000 h 1100

10

1100 h 1200

6

SA U

m G

er

U

It al y

an

nc Fr a

K

Spending

y

15

e

$ (billion)

25


Chapter 45

1


Frequency

20

1 20

Frequency

15

10 5 0

0

6

12 18 24 30 Weight (kg)

10

2 140

5 Frequency

120

0 15 20 25 30 35 40 45 50 Age (years)

100 80 60 40

2 a)

20 0

20

25

0 50

70

90 110 130 150 170 Rainfall (cm)

b) 70 r 90

c)

90 r 110

20 15 10 5 0 168 172 176 180 184 188 192

3 a) 30

Height (cm)

4 a)

20

30 Book 2

25 Frequency

Frequency

15 30 45 60 75 90 105 Time (minutes)

3

10

Frequency

Frequency

30

10 0 60

70

80

90 100 110

b) 80 w 90

c)

20 15 10

Book 1

5

Weight (kg)

214

15

80 w 90


0

0

10 20 30 40 50 60 70 No. of words


b) Possible answers include: Book 1 has a wider variety of sentence length. Book 2 has more shorter sentences.

Mixed exercise 45 (page 589) 1 a)

Time (t mins)

Frequency

0t5

6

5 t 10

7

6

10 t 15

5

5

15 t 20

2

Exercise 45.3 (page 587) Number of bad peaches

1 a), d), e)

4

b)

3

Frequency

2 1 0 0 2 4 6 8 10 12 14 16 18 Delivery time (hours)

5 10 15 20 Time (minutes)

20

20 10 0 0

10 20 30 40 Paper 1

15 10 5 0 30 40 50 60 70 80 90 Mark

b) Strong positive correlation c) 29 > 29.1 f) About 32

b) Suitable comments include the following. The marks range from 30 to 90. There are few low and high marks. Most of the marks are around 50 to 60. c) 50 m 60 d) 70 2 e) 7

50 40 30 20 10 0

3 0

a), c) 1800

1 2 3 4 5 Engine size (litres)

1600 Average weight (g)

Petrol consumption (mpg)

2

2 a)

30

Frequency

Paper 2

40

b) Strong negative correlation c) 32.9 d) About 32 mpg 4 a), d) 50 Mark

4

c) 5 t 10 d) 5 t 10

2 a), d), e)

1400 1200 1000 800 600

40

400

30

200

20

0

10 0 400

1

2

3

4

5

6

7

8

9

Age of rabbit (months) 500

600

Circumference of head (cm)

b) c) e) f)

6

0

b) Strong positive correlation c) 10.4 f) About 3

3 a), e)

8

No correlation 34.1 No Don’t know the ages of the people involved.

b) Strong positive correlation d) (i) About 800 g (ii) About 1700 g e) No. A rabbit’s weight cannot keep increasing.



215

2 £11.36 3 2.71 (2 d.p.) 4 a) (i) 20 (ii) 22.09 b) (i) 100 (ii) 30.11 c) (i) 50 (ii) 59.33 d) (i) 25 (ii) 55.8 5 a) 10 x 20 b) 10 x 20 c) 19.31 6 £24 888.89 (or £24.89 thousand)

Chapter 46 Exercise 46.1 (page 594) 1 a) (i) (iii) b) (i) (iii) c) (i) (iii) d) (i) (iii) 2 a) 1.96 3 a) 4.51 4 £1.07 5 7.52

3 5 50 5 1 5 2 4

(ii) 3 (iv) 3.456 (ii) 50 (iv) 49.632 (ii) 1 (iv) 1.443 (ii) 2 (iv) 1.728 b) 1.04 c) 2.987 b) 27.04 c) 12.75

Chapter 47 d) 4.456 d) 3.1625

Exercise 46.2 (page 599) 1 a) b) c) d) 2 a) b) c)

d)

(i) 50 (ii) (i) 20 (ii) (i) 40 (ii) (i) 20 (ii) (i) 0–4 (ii) (i) 0–9 (ii) (i) 250–299 (ii) 250 (iii) 164.7 (i) 30–44 (ii) 45 (iii) 31.5 (i) 3–5 (ii) (i) 4–7 (ii) (i) 30–39 (ii) (i) 75–99 (ii)

3 a) b) c) d) 4 30.3 5 179.5

13.6 7.22 14.1 6.55 20 40

(iii) 6.98 (iii) 15.5

3.62 7.3 32.25 75

Exercise 46.3 (page 603) 1 a) (i) 50 b) (i) 40 c) (i) 16 d) (i) 50 2 a) (i) 0 x 3 b) (i) 120 x 130 c) (i) 22 x 26 d) (i) 50 x 55 3 a) 250 x 300 c) £270.00 4 18.3 g 5 166 (165.71) pence

(ii) (ii) (ii) (ii) (ii) (ii) (ii) (ii) b)

31.46 25.11 68.56 16.04 9.85 121.36 21.2 54.83 250 x 300

Mixed exercise 46 (page 606) 1 a) b) c) d) e) f)

216

(i) (i) (i) (i) (i) (i)

6 50 1 6 2 18

(ii) (ii) (ii) (ii) (ii) (ii)

7 7 6 5 5 5

(iii) (iii) (iii) (iii) (iii) (iii)

4.488 50.27 1.42 6.36 3.47 17.54


Exercise 47.1 (page 613) 1 a) Primary b) Secondary c) Primary d) Secondary 2 Possible answers include the following. a) Those not in the phone book have no chance of being included. b) Those working on Saturday would not be included. 3 Possible answers include the following. Make the categories exclusive (in Paul’s first draft, for example, 1 hour could go in two categories). Have more categories, for example, split the groups into classes of 30 minutes rather than 1 hour. 4 Possible faults include the following. a) The person’s favourite sport might be one that isn’t listed. b) This question is vague: it needs categories, such as hours spent. c) This is a leading question. Check students’ new questions. 5 a) Possible answers include the following. Q1 is too vague. Q2 is an open question and the answers would be very difficult to analyse. b) Check students’ rewrites of Q1. It should have better categories. 6 Check students’ questions.

Mixed exercise 47 (page 615) 1 Secondary. Jan did not collect the data herself. 2 a) Possible answers include the following. Ask people to draw a 70° angle without a protractor. Show people three drawn angles and ask them to estimate what size the angles are. b) Possible answers include the following. Choose 30 students from Year 7, 30 from Year 9 and 30 from Year 11. Choose a random sample of students from a mixed-age group. c) Check students’ data collection sheets. The sheets should include the age or year-group of the student as well as data on the angle(s) drawn/estimated. 3 Check students’ answers.


Chapter 48 1 a) 8th, 6th, 3rd, 4th b) 18 c) Wong and Selby 2 a) 47 b) 145 c) 15 3 Any answer so long as it is justified, e.g. taxi is the quickest but most expensive at £32.50, cycling is the cheapest but the longest at 2 hours. 4 a) 120 m2 b) 108 m2 c) £42 5 a) Starters £16.25 Main course £45.00 Dessert £18.50 Tea or coffee £5.25 Total £85.00 b) £1.50 6 a) 9, 8, 16:30, 7 12 , 08:00, 12 , 1 12 b) £360 c) Yes: 360 2.5 24 £420 7 SOS: ABC £75 for 20, ET £70 for 20, SOS £70 for 21 8 Expected income £1250, expected cost £900, expected profit £350 9 a) 74 b) 132 c) (i) 6 (ii) 14 10 a) 1°C b) Stockholm c) Friday d) 13°C 11 a) 45 m2 b) Grass seed by £45.75 c) (i) Small box: 50p/m² Large box: 40p/m² (ii) 2 large boxes and 1 small box 12 a) £3.75 b) £13.75 13 a) (i) £130 (ii) No. The total amount collected on Sunday is not known. b) (i) Possible answers include: no timescale, categories overlap, options are exhaustive. (ii) Possible answers include: not a representative sample of the population, rugby is probably played on a Saturday afternoon and the people who watch it are unlikely to be in the supermarket at this time. 14 Any answer so long as it is justified, e.g. bus is cheapest at £32 in total but have to catch the bus at 07:50, car costs £63 but don’t have to leave until 11a.m. 15 a) $1008 b) £950 16 Hotel £1740 the most expensive but includes use of leisure facilities. Guest house £1140 includes evening meal (but not flexible) and breakfast. Cottage £880 all meals must be paid for and prepared. 17 a) Player

Mean

Range

A

50

8

B

33

106

C

50

99

b) Any answer, so long as reasoning is justified, e.g. player A as they are the most consistent. 18 a) (i) £3025 (ii) Six hundred and five pounds > six hundred and twenty-five pounds b) 6541

19 a) 102 b) 317 20 a) £33 b) £12.55 21 a) 10 miles b) 12 litre milk, 2 kg potatoes 22 Possible answers include: Ann £12, Gareth £6, Lucy £2. 23 a) €456 b) £53

Chapter 49 Number (page 627) 1 2 3 4 5 6

7

8

9

10 11

12

a) 1248 b) 8 11 Yes: water 52 18 936, lunches 45 20 900 a) 54.81 b) 548.1 c) 0.63 a) $1780 b) £1202.70 a) 1200, 1200, 30, 1950, 2100, 30 b) 700 (grams) c) No: 2 80 160 grams are needed but 5 ounces 125 grams a) 97, 99, 101, (103), 105, 98, 100, 102, 104, 106 b) 9, 11, 13, 15, 17 strategy: must be odd numbered, 65 ÷ 5 or algebraic method c) 9 and 10 a) 6 p.m. b) Between 12:30 p.m. and 2 p.m. UK time and 8:30 p.m. and 10 p.m. HK time c) Hotel Bear and reason, e.g. four dinners for £1. Hotel Gelton 4 80 £320, Hotel Bear 3 107 £321. a) False: counter example, e.g. 10 ÷ 5 2 b) False: counter example, e.g. 14 ÷ 2 7 c) True: one or other must be even, and even odd even a) 1000 (ml), 1000 (ml), 460 (g), 60 (ml) b) 44 The 4 m roll rectangle is 280 cm by 350 cm so either 350 cm of 3 m roll (3.5 3 10.5 m2) or 280 cm of 4 m roll (2.8 4 11.2 m2) both must be seen. Area from 3 m roll 6 £63. Area from 4 m roll 5 £56. a) 26 cm b) 9 c) 39

Algebra (page 631) 1 a) n 4m b) y x 3 c) (i) 50 (ii) 20 d) 20° 2 a) (4, 2) b) D marked at (2, 2) c) E(4, 4), F(2, 4) 3 a) A(3, 4), B(3, 2) b) C marked at (3, 1) c) E marked at (3, 1) 4 a) 15 b) 20, 33, 46, 59 5 a) A(12, 10) b) B(12, 5) c) C(7, −12) 6 a 3, b 6, c 7, d 5 7 A(12, 4), B(0, 8), C(16, 16) 8 a) (i) X marked at 2 cm above sea level (ii) Y marked at 1 cm below sea level b) 300 m c) 220 m



217

9 a) c) 10 a) b) c)

(4, 2) b) T marked at (3, 2) (1, 1) xx2x3x7 (i) 4x 12 40 (ii) x 7 7 cm, 9 cm, 10 cm, 14 cm

Geometry and measure (page 636) 1 2 3 4 5 6

a) 60° b) 40° c) 50° a) 36 cm b) 56 cm2 a) 62° b) 75° S, P, Q, R 14 cm3 a) (i) 26 cm (ii) 6.5 cm b) (i) 36 cm2 (ii) 6 cm 7 ⬔DCB 40°, ⬔DBC 100°, ⬔DBA 80°, x 20° 8 Check students’ diagrams. AB 6 cm, AC 7 cm, BC 9 cm 9 a) Statement Rectangle The diagonals are not equal in length

10 11 12 13 14

All angles are equal

The sum of the interior angles is 360°

b) (i) square-based pyramid (ii) triangular prism General explanation, e.g. decimals are not accurate enough not rounded correctly. Specific 1 2 explanation, e.g. 3 0.33…, 3 0.66... . Not possible: angle sum of polygon 720°, sum of remaining angles 720 – 3 140 300°, 3 89 < 300° Arc centre X, radius DX 2 mm; arc centre corner of building, correct radius 2 mm Use of a 90° angle from the rectangle. Angles in a triangle: angle AGD 70°, angle BFC 70°. BFC AGD, so triangle EFG is isosceles. a) Statement Square

Parallelogram

Rhombus

Parallelogram

Trapezium

The diagonals are equal in length

Opposite angles are equal

Only one pair of opposite sides are parallel

The diagonals are lines of symmetry

b) 3 + 5 < 10 c) 100° 15 AD 11.2 cm (AC 10 cm) 16 a) AB 4.5 cm

b) 22.1 > 22.05

Statistics (page 643) 1 a) c) 2 a) c) 3 a) 4 a)

£40.09 b) £22 10 a.m. next day Louise b) 1 hour 45 minutes Nell d) Betweeen 5:45 and 6:00 p.m. 138 b) 20 c) 28 25% b) No: you need to know the total numbers of boys and girls. 5 4, 6, 10, 12, 16 6 5, 6, 9, 10, 10

218

