answers to the student’s book exercises... 2, 3, 6 answers to the student’s book exercises ......

Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 165

Chapter 1Exercise 1.1 (page 3)

1 a) 99 b) 91 c) 124d) 181 e) 418 f) 453

2 a) 41 b) 37 c) 47d) 94 e) 107 f) 276

3 a) 69 b) 76 c) 180d) 476 e) 738 f) 1048

4 a) 21 b) 24 c) 15d) 13 e) 24 f) 46

5 £696 £277 276p, £2.768 26

Exercise 1.2 (page 7)1 a) 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78,

84, 90, 96b) 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

2 24, 48, 72, 963 a) 2, 6, 18, 30 b) 6, 15, 18, 30, 33

c) 15, 304 a) 12, 24, 36, 48, 60, 72, 84, 96

b) 15, 30, 45, 60, 75, 905 606 a) 1, 2, 3, 6, 9, 18 b) 1, 2, 3, 4, 6, 8, 12, 247 1, 2, 3, 68 a) 1, 2, 4, 5, 8, 10, 20, 40

b) 1, 2, 3, 4, 6, 9, 12, 18, 369 1, 2, 4

10 a) 23 000 b) 197 000 c) 8000d) 148 000 e) 5 732 000

11 a) 7700 b) 17 600 c) 800d) 654 300 e) 5000

12 a) 70 000 or 68 000 b) £5 000 000c) 8000 or 7900 d) £700 000 or £690 000

Exercise 1.3 (page 11)1 a) 520 b) 6300 c) 54 000

d) 36 100 e) 560 000 f) 6000g) 549 000 h) 810 000 i) 530 000j) 470 000 k) 92 300 000 l) 62 000 000

2 a) 53 b) 140 c) 532d) 640 e) 6400 f) 53 600g) 6754 h) 73 000 i) 5800

3 a) 1500 b) 5600 c) 14 000d) 60 000 e) 24 000 f) 2000g) 1 800 000 h) 300 000 i) 5 600 000j) 12 000 000 k) 2 800 000 l) 72 000 000

4 a) 1920 b) 4320 c) 7020d) 11 200 e) 25 200 f) 23 400g) 259 200 h) 232 000

5 a) 1728 b) 2356 c) 4674d) 1764 e) 1914 f) 6216g) 3321 h) 9240 i) 34 776j) 29 713 k) 43 902 l) 20 768

6 a) 63 200p b) £567 47 000 metres8 £2409 156 000 metres or 156 kilometres

10 952p

Exercise 1.4 (page 14)1 a) 49 b) 81 c) 121

d) 144 e) 900 f) 2500g) 3600 h) 40 000 i) 160 000j) 640 000

2 a) 196 b) 484 c) 961d) 2209 e) 7921 f) 3136g) 1156 h) 32 400 i) 69 169j) 555 025

3 a) 216 b) 729 c) 1331d) 2744 e) 15 625 f) 50 653g) 79 507 h) 3 176 523

4 a) 15 b) 14 c) 19d) 23 e) 39 f) 87g) 68 h) 54

5 a) 20 b) 30 c) 50d) 80 e) 200

Exercise 1.5 (page 16)1 a) 3 b) �3 c) �32 a) �1°C b) 4°C c) �8°C3 a) 16°C b) 26°C c) 14°C4 a) �8, �3, 1, 7

b) �6, �4, 0, 5c) �6, �4, �3, 1, 2, 5

5 �3

Mixed exercise 1 (page 18)1 a) 132 b) 44 c) 269

d) 348 e) 1016 f) 632 271p3 a) 20, 40, 60, 80, 100, 120

b) 12, 24, 36, 48, 60, 72, 84, 96, 108, 120c) 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, 30d) 1, 2, 3, 6

ANSWERS TO THE STUDENT’SBOOK EXERCISES

50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 65

166 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education

5 a) 5600 b) 18 000 c) 273 000d) 273 500 e) 6 000 000 f) 3500

6 a) 9300 b) 63 000 c) 572 000d) 78 e) 6300 f) 4000g) 21 000 h) 1410 i) 34 800j) 140 000 k) 31 920 l) 292 800

7 a) 1764 b) 4731 c) 97288 8370 km9 a) 64 b) 1600 c) 250 000

d) 100 000 e) 800010 a) 841 b) 1728 c) 2809

d) 22 e) 7211


1 a) �12� b) �

13� c) �

49� d) �

25�

e) �23� f) �

15� g) �

19� h) �1

36�

2 a) �12� � �

24� � �

36� � �1

62� � �

12

00� � �12

00

00�

b) �15� � �1

20� � �1

35� � �2

40� � �3

60� � �

15

00�

3 a) �34� � �1

92� b) �

11

06� � �

58� c) �

12� � �1

98� d) �

3500� � �

35�

e) �11

28� � �

69� f) �

27� � �

13

05� g) �

45� � �

23

40� h) �2

31� � �

17�

i) �29� � �2

67� j) �1

31� � �

14

24� k) �

13

55� � �

37� l) �

2780� � �1

40�

4 a) �45� b) �

16� c) �

57� d) �

34�

e) �23� f) �

56� g) �

12� h) �

35�

i) �23� j) �

12� k) �

16� l) �

12�

m) �45� n) �

89� o) �

57� p) �

23�


d) £25 e) £2.502 a) 6 b) 9 c) 16

d) £24 e) 5.2 m3 a) 18 b) 36 c) 150

d) £42 e) £1054 a) 25 b) 40 c) 100

d) 35 cm e) £755 £1.606 a) £3 b) £97 56 m8 729 210

10 �58� of £120 � £75, �

34� of £96 � £72;

�58� of £120 is the larger.

Exercise 2.3 (page 26)1 a) �

35� b) �

47� c) �

35� d) �

89� e) �

14�

2 a) 2�15� b) 1�

37� c) 3�

13� d) 6�

12� e) 4�

23�

f) 1�56� g) 2�

38� h) 2�

67� i) 5�

34� j) 3�1

30�

3 a) 3�12� b) 1�

15� c) 1�

12� d) 1�

37� e) 2�

25�

f) 2�12� g) 2�

29� h) 2�

12� i) 5�

14� j) 3�

37�

k) 4�45� l) 2�1

10� m) 7�

12� n) 2�1

81� o) 1�

12�

Mixed exercise 2 (page 27)1 a) �

34� � �

12

50� b) �

12

51� � �

57�

c) �12� � �

12

12� d) �

16

80� � �1

30�

e) �11

68� � �

89� f) �

37� � �

1228�

g) �49� � �

49

00� h) �2

84� � �

13�

2 a) �23� b) �

45� c) �1

41� d) �

35� e) �

25�

f) �131� g) �

34� h) �

56� i) �

45� j) �

12�

3 a) 8 b) 11 c) 45 d) 1604 40 metres5 10 8006 28 km7 �

34� of 180 � 135, �1

70� of 200 � 140

�170� of 200 is the larger.

8 a) �59� b) �

13� c) �

35� d) �

11

27� e) �

23�

9 a) 3�34� b) 2�

45� c) 2�

47� d) 6�

23� e) 1�

35�

10 4�45� metres


1 a) 4 tens b) 4 tenthsc) 4 ten thousands d) 4 hundredthse) 4 thousandths

2 a) 0.3 b) 4.7 c) 0.09d) 52.79 e) 0.021

3 a) �35� b) 4�1

30� c) 14�1

10�

d) �34� e) 9�1

300�

4 £0.05, £0.07, £0.92, £1.42, £6.07, £8.60

5 9.207, 7.29, 0.927, 0.209, 0.0726 a) 0.468 kg b) 1.645 kg c) 0.072 kg

d) 0.006 kg e) 2.45 kg7 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 g10 a) 0.1 b) 0.5 c) 0.4

d) 0.25 e) 0.03

Exercise 3.2 (page 36)1 a) 13.91 b) 42.09 c) 111.15

d) 14.63 e) 60.71 f) 113.372 a) 9.65 b) 14.91 c) 54.84

d) 8.31 e) 20.77 f) 221.843 a) £16.62 b) £24.90 c) £114.47

d) £97.104 £57.905 1.76 m6 2.96 seconds7 a) 1.2(00) kg b) £11.978 £5.90

Temperature (°C) 15 �3 �4 �10

10° warmer 15 �7 �6 �10

5° colder 10 �8 �9 �15

50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 166


9 a) 16.32 m b) 11.15 m c) 5.55 md) 7.88 m e) 6.8 cm f) 7.3 cm

10 a) 4.572 kg b) 1.96 kg c) 1.614 kgd) 1.475 litres e) 1.872 litres f) 0.7 litre

11 £14.1112 £4.8913 a) 3.5 b) 1.8 c) 2.4 d) 6.3

e) 0.03 f) 0.54 g) 15 h) 42i) 0.08 j) 0.15 k) 0.25 l) 0.01

Mixed exercise 3 (page 38)1 a) 6 thousands b) 6 tenths

c) 6 tens d) 6 hundredthse) 6 units

2 0.068, 0.215, 0.4, 0.532, 0.713 8p, 26p, 87p, 156p4 a) 0.9 b) 2.1 c) 0.07

d) 16.23 e) 0.0195 a) 0.3 b) 0.2 c) 0.75

d) 0.7 e) 0.66 a) 236 cm b) 8.3 cm c) 57 cm

d) 580 cm e) 47 cm7 a) 9.31 b) 45.46 c) 118.84

d) 16.88 e) 51.51 f) 128.298 a) 13.61 b) 24.08 c) 46.54

d) 5.43 e) 6.83 f) 196.079 £60.13

10 3.1 m11 £2.9212 a) 1.2 b) 0.05 c) 0.56 d) 0.48


1 a) �270� b) �

12

30� c) �2

25� d) 1�

15�

2 a) 0.16 b) 0.27 c) 0.83

d) 0.07 e) 0.31 f) 0.04

g) 0.17 h) 0.02 i) 1.5

j) 2.5 k) 0.09 l) 0.1253 a) 62% b) 56% c) 4%

d) 16.5% e) 132%4 a) 70% b) 60% c) 35%

d) 40% e) 34%

Exercise 4.2 (page 44)1 a) £16 b) £10 c) £212 £6 3 240 4 £12605 a) £8.16 b) £86.406 £18 7 38.4 m 8 21 280 9 £83.60

Exercise 4.3 (page 46)1 a) £480 b) £580 c) £424 d) £7202 a) £168 b) £204 c) £232.80 d) £963 £12 480 4 £34.20 5 £129.60

6

7 a) £76.16 b) £85.68c) £72.76 d) £111.52

8 a) £255.84 b) £212.16c) £283.92 d) £68.64

9 £739510 80 96011 £399.50 (using a VAT rate of 17.5%)12 £71.44

Exercise 4.4 (page 49)1 10% 2 25% 3 40%4 5% 5 20% 6 13%7 7.5% 8 53% 9 82.5%

10 17%

Mixed exercise 4 (page 50)1 a) 0.27 b) 0.96 c) 0.02

d) 0.165 e) 3.5(0)2 a) 8% b) 70% c) 72%

d) 40% e) 123%3 £8.40 4 £7.505 £2.10 6 £16 4807 £29.75 8 £2169 4.2% 10 28%


1 70 2 31 3 74 4 895 136 6 37 7 57 8 609 73 10 72 11 91 12 73

13 92 14 99 15 73 16 11617 117 18 122 19 105 20 183

Exercise 5.2 (page 54)1 70 2 25 3 41 4 235 72 6 22 7 41 8 169 65 10 21 11 69 12 46

13 37 14 19 15 35 16 6717 7 18 69 19 82 20 17

Exercise 5.3 (page 55)1 56 2 42 3 73 4 425 14 6 43 7 57 8 499 27 10 39

Item Original Reduction Saleprice (£) (£) price (£)

Television 150 30 120

Washing 360 72 288

machine

DVD player 40 8 32

Computer 550 110 440

system



Exercise 5.4 (page 56)1 12 2 12 3 45 4 455 35 6 12 7 48 8 279 36 10 15 11 28 12 40

13 18 14 36 15 50 16 5617 49 18 18 19 54 20 63

Exercise 5.5 (page 57)1 6 2 4 3 3 4 45 5 6 7 7 5 8 99 3 10 9 11 8 12 7

13 7 14 9 15 4 16 817 7 18 6 19 7 20 4

Exercise 5.6 (page 58)1 3.5, 3.6 or 3.7 2 4.8 or 4.93 9.2, 9.3 or 9.4 4 7.7, 7.8 or 7.95 5.5, 5.6 or 5.7 6 6.8 or 6.97 6.1, 6.2 or 6.3 8 7.3, 7.4 or 7.59 9.4, 9.5 or 9.6 10 8.7, 8.8 or 8.9


d) 205 e) 9 f) 28g) 320 h) 924 i) 1j) 35

2 a) 5.2 b) 48.1 c) 0.9d) 7.7 e) 9.9

3 a) 5.24 b) 48.12 c) 0.89d) 7.67 e) 9.89

4 a) 1000 b) 3000 c) 60 000d) 40 e) 600 000 f) 9 000 000g) 300 h) 4000 i) 600

5 20 000

Exercise 5.8 (page 65)1 �1 2 4 3 2 4 �35 2 6 8 7 1 8 �19 5 10 �1 11 �1 12 1

13 �3 14 �1 15 �5 16 117 2 18 �3 19 1 20 3

Exercise 5.9 (page 66)1 4 2 2 3 4 4 65 1 6 �4 7 �4 8 �79 6 10 �4

Mixed exercise 5 (page 67)1 a) 58 b) 94 c) 82 d) 133 e) 622 a) 35 b) 36 c) 37 d) 24 e) 83 a) 21 � 45 � 66, 66 � 21 � 45, 66 � 45 � 21

b) 39 � 14 � 53, 53 � 14 � 39, 53 � 39 � 14c) 15 � 52 � 67, 67 � 15 � 52, 67 � 52 � 15d) 37 � 18 � 55, 55 � 18 � 37, 55 � 37 � 18e) 36 � 54 � 90, 90 � 36 � 54, 90 � 54 � 36

4 a) 43 b) 14 c) 16 d) 45 a) 15 b) 28 c) 48 d) 32 e) 636 a) 8 b) 8 c) 7 d) 2 e) 77 a) 6 � 7 � 42, 42 � 6 � 7, 42 � 7 � 6

b) 8 � 7 � 56, 56 � 8 � 7, 56 � 7 � 8c) 8 � 5 � 40, 40 � 8 � 5, 40 � 5 � 8d) 6 � 4 � 24, 24 � 6 � 4, 24 � 4 � 6e) 6 � 9 � 54, 54 � 9 � 6, 54 � 6 � 9

8 a) 1 b) 25 c) 49 d) 64e) 8 f) 125 g) 4 h) 6

9 a) �4.2 b) �9.4 c) �8.5d) �6.7 e) �7.5

10 a) 47 b) 2 c) 98d) 105 e) 7

11 a) 9.1 b) 1.6 c) 68.7d) 1.4 e) 3.9 f) 16.4

12 a) 1.39 b) 3.88 c) 16.38d) 43.95 e) 1.33 f) 2.67

13 a) 40 b) 30 000 c) 8000d) 800 000 e) 10 000

14 20 00015 a) �6 b) 2 c) �4

d) 2 e) 516 a) 6 b) �1 c) 6

d) 1


1 a) 7.29 b) 22.09 c) 1444d) 107 584 e) 0.3844 f) 0.0361g) 0.0049 h) 3.24 i) 4.6656j) 998.56

2 a) 4.1 b) 7.7 c) 1.6d) 17.2 e) 36 f) 0.31g) 0.49 h) 0.86 i) 3.75j) 0.047

3 a) 4.16 b) 5.46 c) 9.38d) 23.81 e) 48.46 f) 0.59g) 0.95 h) 154.24 i) 1.37j) 0.28

4 21.9 cm

Exercise 6.2 (page 73)1 2.419 2 3.84 3 34.24 3.450 5 12.606 6 62.417 41.33 8 0.417 9 4.48

10 26 11 6.983 12 2.545

Mixed exercise 6 (page 74)1 a) 50.41 b) 40.96 c) 1444

d) 271 441 e) 0.21162 a) 4.8 b) 8.3 c) 24.3

d) 0.33 e) 0.0633 a) 6.11 b) 23.17 c) 201.70

d) 0.624 e) 0.284 98.2 m5 a) 7.529 b) 10.536 c) 19.36

d) 91.2 e) 23.810 f) 2.494




1 2 � 3 2 2 � 53 3 � 5 4 3 � 75 2 � 2 � 2 � 2 � 2 � 25

6 2 � 2 � 3 � 3 � 22 � 32

7 2 � 2 � 5 � 7 � 22 � 5 � 78 2 � 5 � 5 � 5 � 2 � 53

9 3 � 3 � 5 � 7 � 32 � 5 � 710 2 � 2 � 3 � 5 � 7 � 22 � 3 � 5 � 7

Exercise 7.2 (page 81)1 4 � 22; 6 � 2 � 3; HCF � 2;

LCM � 22 � 3 � 122 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 � 304 32 � 25; 40 � 23 � 5; HCF � 23 or 8;

LCM � 25 � 5 � 1605 35 � 5 � 7; 45 � 9 � 5; HCF � 5;

LCM � 32 � 5 � 7 � 3156 27 � 33; 63 � 32 � 7; HCF � 32 � 9;

LCM � 33 � 7 � 1897 20 � 22 � 5; 50 � 2 � 52; HCF � 2 � 5 � 10;

LCM � 22 � 52 � 1008 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 � 160010 42 � 2 � 3 � 7; 49 � 72; HCF � 7;

LCM � 2 � 3 � 72 � 294

Exercise 7.3 (page 84)1 �12 2 �20 3 �30 4 �545 �28 6 �16 7 �18 8 �49 �5 10 �8 11 �3 12 �2

13 �9 14 �7 15 �4 16 �1217 �21 18 �6 19 �9 20 �20

Exercise 7.4 (page 86)1 a) 49 b) 121 c) �6 d) �12

e) 8 f) 1000 g) 4 h) 12 6 cm3 a) 625 b) 1600 c) 1225

d) 1024 e) 1.444 a) 1728 b) 15.625 c) 226.981

d) 27 000 e) 157.4645 a) �20 b) �23.98 c) �35.83

d) �60.70 e) �1246 a) 8 b) 8.78 c) 20

d) 21.15 e) 21.547 1 and 64

Exercise 7.5 (page 87)1 a) 35 b) 73 c) 34 � 52

2 a) 55 b) 107 c) 84

d) 310 e) 26

3 a) 52 b) 103 c) 83

d) 32 e) 20 � 1

4 a) 54 b) 1011 c) 82 d) 34

5 a) 25 b) 32 c) 54 d) 73


13� b) �

16� c) �4

19�

d) �1100� e) �6

140�

2 a) 16 b) 9 c) 52

d) 67 e) 1000

3 a) 1�14� b) 2�

23� c) �

58�

d) �130� e) 12�

12�

4 a) 0.4 b) 2 c) 0.008d) 6.25 e) 0.3125

Mixed exercise 7 (page 91)1 a) 3 � 52 b) 22 � 5 � 7

c) 22 � 3 � 5 � 72 a) 24 � 23 � 3, 60 � 22 � 3 � 5, HCF � 12,

LCM � 120b) 100 � 22 � 52, 150 � 2 � 3 � 52, HCF � 50,

LCM � 300c) 81 � 34, 135 � 33 � 5, HCF � 27, LCM � 405

3 a) �12 b) �16 c) 8 d) 34 a) 16, 64 b) 36, 216 c) 100, 10005 a) �8 b) �146 a) 5 b) 37 a) 21.16, 97.336 b) 441, 9261

c) 8.41, 24.3898 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

10 a) �15� b) �

18� c) 8

d) 10 e) �58� or 0.625


1 a) 9, �79� b) 24, �

78� c) 40, �

38�

2 a) �79� b) �1

71� c) �

13�

d) �153� e) �

56� f) 1�

18�

g) �13� h) 1�

35� i) 3�

12�

j) 2�14� k) 4�

19� l) 2�

67�

3 a) �78� b) �

79� c) �1

72�

d) �14� e) 1�1

30� f) 1�

1238�

g) �1138� h) 1�

12� i) 1�

1138�

j) �2330� k) �

1336� l) �

3490�

4 a) 5�170� b) 3�

18� c) 4�

1114�

d) 3�112� e) 7�

38� f) 4�1

72�

g) 7�1118� h) �2

16� i) 6�2

11�

j) 5�1230� k) 1�

1114� l) �

56�


149� b) �

137� c) �

123�

d) �281� e) �

273� f) �

1172�

g) �167� h) �

6121�

2 a) 2�25� b) 4�

12� c) �1

25�

d) 4�38� e) �2

51� f) 9



3 a) �136� b) �2

47� c) �2

54�

d) 1�38� e) 1�

35� f) �

1258�

g) �247� h) �

78� i) �

2207�

j) 1�59� k) 5�

13� l) �3

72�

4 a) 7�170� b) 2�

17� c) 1�

47�

d) �14

70� e) 8�

25� f) 1�1

94�

g) 10 h) 3�13� i) 7�

57�

j) 2�25� k) 18�

12� l) 1�

1309�


12

31� b) �2

70� c) �2

52�

d) 1�175� e) 5�

11

34� f) 1�

1112�

g) 12�67� h) 3�4

94�

2 a) �25� b) �

58� c) �1

75�

d) �176� e) �

19�

3 a) 2�115� b) 7�

11

17� c) 4�

1135�

d) 4�45� e) 8�1

33�

4 a) 20�56� cm b) 24�

34� cm2

Exercise 8.4 (page 108)1 a) 0.8 b) 0.375 c) 0.182

d) 0.111 e) 0.452 a) Terminating, 5 is a factor of 10

b) Recurring, 3 is not a factor of 10c) Recurring, 9 is not a factor of 10d) Terminating, 16 has only factors which are

factors of 10e) Recurring, 7 is not a factor of 10

3 a) 0.714 285 7…b) Six

Exercise 8.5 (page 109)1 7.7 2 7.9 3 3.64 2.2 5 7.1 6 8.17 5.7 8 3.8 9 12.2

10 16.5 11 0.9 12 5.8

Exercise 8.6 (page 113)1 a) 1.2 b) 3.5 c) 1.8 d) 7.2

e) 0.24 f) 0.48 g) 12 h) 35i) 0.06 j) 0.08 k) 0.49 l) 0.09

2 a) 40 b) 4 c) 4 d) 9e) 20 f) 20 g) 30 h) 50i) 80 j) 30 k) 3.1 l) 122

3 a) 6.3 b) 14.26 c) 35.99 d) 19.44e) 113.4 f) 388.8 g) 49.84 h) 26.16i) 5.08 j) 1.872 k) 3.822 l) 9.968

4 a) 49 b) 17 c) 24 d) 32e) 53 f) 78 g) 5.7 h) 4.9i) 2.9 j) 2.7 k) 3.7 l) 4.5

Exercise 8.7 (page 116)1 a) 1.13 b) 1.2(0) c) 1.68 d) 1.08

e) 1.02 f) 1.175 g) 2(.00) h) 2.5(0)2 a) 0.86 b) 0.8(0) c) 0.55 d) 0.93

e) 0.97 f) 0.77 g) 0.14 h) 0.8353 £4.78

4 £29.405 £29176 £34 6967 £87368 £159 6279 £2980.80

Mixed exercise 8 (page 118)1 a) 30, �

56� b) 21, �

13� c) 40, �

12

30�

2 a) 1�25� b) 1�2

21� c) �

12

14� d) �

56� e) �

12

34�

3 a) 5�152� b) 3�2

70� c) 8�

38� d) 6�1

18� e) 1�

12

30�

4 a) �25� b) �

12

01� c) �

11

56� d) 2�1

10� e) �2

90�

5 a) 3�23� b) 1�

12

31� c) 3�

34� d) �

14

74� e) 9�

37�

6 a) 0.125 b) 0.222 c) 0.714 d) 0.2737 a) 9.7 b) 5.3 c) 8.7 d) 4.68 a) 2 b) 0.07 c) 0.72

d) 10.8 e) 9.18 f) 18.729 a) 30 b) 8 c) 3

d) 80 e) 79 f) 8.7

10 a) 1�616� b) �

14

10� c) 3�

17� d) 3�

19�

11 £526312 £29.52


1 a) 2 : 1 b) 1 : 3 c) 5 : 1d) 1 : 3 : 5 e) 3 : 6 : 4

2 a) 1 : 20 b) 3 : 20 c) 4 : 1d) 16 : 3 e) 3 : 20

3 5 : 64 5 : 8 : 105 4 : 2 : 3

Exercise 9.2 (page 122)1 a) 1 : 3 b) 1 : 5 c) 1 : 2.5

d) 1 : 1.75 e) 1 : 7.5 f) 1 : 125g) 1 : 0.2 h) 1 : 500 000

2 1 : 250 0003 1 : 6

Exercise 9.3 (page 126)1 a) 12 cm b) 3.5 cm2 a) 24 babies b) 9 helpers3 a) 6 litres b) 4 litres4 140 mm or 14 cm5 a) 28 miles b) 10 inches6 a) 30 ml b) 10 teaspoons7 a) 100 ml b) 36 ml8 a) 150 g b) 48 g9 £120

10 a) 500 g b) 180 g

Exercise 9.4 (page 128)1 Dave £8, Sam £122 a) 15 litres b) 25 litres3 30 kg sand



4 a) 50 ml b) 250 ml5 Amit £320, Bree £800, Chris £4806 15607 £2928 a) 400 g b) 80 g

Exercise 9.5 (page 131)In all these questions either cost per unit or number of unitsper 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 � 0.34pGrams per penny: 420 g bag � 2.64 g, 325 g bag � 2.98 g325 g bag is better value.

2 Cost per litre: 2 litre bottle � 42.5p, 5 litre bottle � 35.8pMillilitres per penny: 2 litre bottle � 23.53 ml, 5 litre bottle � 27.93 ml5 litre bottle is better value.

3 Cost per gram: 680 g pack � 0.47p, 1.4 kg pack � 0.39pGrams per penny: 680 g pack � 2.125 g, 1.4 kg pack � 2.59 g1.4 kg pack is better value.

4 Cost per nail: 50 pack � 2.5p, 144 pack � 2.64pNails per penny: 50 pack � 0.4 nails, 144 pack � 0.38 nails50 pack is better value.

5 Cost per roll: 12 pack � 14.92p, 50 pack � 14.4pRolls 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 � 3.33pMillilitres per penny: 80 ml tube � 0.29 ml, 150 ml tube � 0.3 ml150 ml tube is better value.

7 Cost per litre: 3 litres � 66.33p, 2 litres � 67.5p, 1 litre � 57pLitres per pound: 3 litre � 1.51 litres, 2 litre � 1.48 litres, 1 litre � 1.75 litres1 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 g1.4 kg packet is the best value.

Mixed exercise 9 (page 132)1 a) 10 : 7 b) 5 : 12 c) 3 : 1

d) 9 : 20 e) 3 : 52 a) 1 : 4 b) 1 : 2.4 c) 1 : 50

d) 1 : 250 000 e) 1 : 0.43 a) 60 cm b) 5 cm

4 250 g5 a) 60 g b) 250 g6 a) 500 ml b) 240 ml

In questions 7 and 8 either cost per unit or number ofunits per pound or per penny can be used. Both aregiven in each answer.

7 Cost per litre: 5 litres � £3.70, 2 litres � £3.50Litres 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.


1 a) 26 b) 1.5 c) 58 d) 200e) 80.4 f) 20.1 g) 661 h) 10.1i) 283 j) 275

2 a) 16 b) 0.9 c) 87 d) 58e) 69.6 f) 65 g) 69 h) 277i) 85.7 j) 996

3 a) 72 b) 52 c) 2.4 d) 160e) 800 f) 336 g) 185 h) 520i) 1000 j) 775

4 a) 4 b) 80 c) 13 d) 16e) 13 f) 4 g) 0.08 h) 6i) 20 j) 3

5 a) 4 b) �4 c) �7 d) 6e) �2 f) 10 g) �6 h) �4i) 24 j) 0

6 a) �8 b) �12 c) 12 d) �35e) 40 f) �3 g) �4 h) 3i) �2 j) 16

7 a) 36 b) 25 c) 121 d) 100e) 169 f) 400 g) 90 000 h) 0.16i) 0.49 j) 0.09

8 a) 4 b) 3 c) 7 d) 13e) 15

9 a) 1 b) 125 c) 8 d) 64 000e) 0.027

10 £9.2011 8 cm12 £15.2813 420 ml14 a) 17 cm b) 18 cm2

15 8 and 5

Exercise 10.2 (page 140)1 a) 8 b) 7 c) 20 d) 30

e) 500 f) 7 g) 1000 h) 0.4i) 0.7 j) 4000 k) 4000 l) 3

2 a) 10 b) 200 c) 20 d) 800e) 6000 f) 0.01 g) 0.6 h) 0.04i) 1 j) 20 000 k) 0.07 l) 2000



3 a) 18 b) 180 c) 5700 d) 98 000e) 50 f) 0.17 g) 0.039 h) 0.0061i) 0.031 j) 0.99

4 a) 8.26 b) 69.8 c) 16 300 d) 208e) 12 500 f) 7.10 g) 50.9 h) 0.416i) 0.0386 j) 3.14

5 £180 or £2006 37 54 cm2 or 50 cm2

8 21 cm or 20 cm9 £2000

10 64 cm3 or 60 cm3

11 50 mph12 a) 4000 b) 9

c) 125 or 100 d) 49 or 50e) 24 000 or 20 000 f) 0.1g) 0.75 or 0.8 h) 36 000 or 40 000i) 43 or 40 j) 60k) 3.5 or 3 or 4 l) 60


d) 26 e) 81 f) 72 a) 14 b) 80 c) 32

d) 50 e) 4 f) 163 5 : 24 225 cm2

5 (64 � 4) cm2

Exercise 10.4 (page 144)1 a) 4900 b) 0.036 c) 0.04

d) 0.0016 e) 0.04 f) 30 000g) 560 000 h) 1120 i) 120 300j) 9040 k) 0.12 l) 0.06

2 a) 25 b) 0.05 c) 0.13d) 70 e) 0.006 f) 90g) 30 h) 35 i) 15 000j) 4000 k) 0.013 l) 1000

3 a) 2160 b) 1.35 c) 16d) 0.002 16 e) 1600 f) 216

4 a) 9880 b) 3.8 c) 260d) 38 e) 0.038 f) 26

5 a) 408.51 b) 40 851 c) 1530d) 4.0851 e) 26.7 f) 15 300

Mixed exercise 10 (page 145)1 a) 92 b) 1.6 c) 141.9

d) 21.1 e) 441 f) 7.2g) 158 h) 8.1 i) 383j) 6.9

2 a) 153 b) 0.54 c) 710d) 345 e) 1025 f) 17g) 0.35 h) 0.82 i) 9j) 12

3 a) �4 b) 6 c) 17d) �9 e) 1 f) �28g) 30 h) �9 i) 5j) �3

4 a) 49 b) 0.81 c) 144d) 10 000 e) 196

5 £15.416 a) 9 b) 4 c) 30

d) 30 e) 600 f) 6g) 1000 h) 0.3 i) 0.6j) 50 000

7 32 cm2 or 30 cm2

8 50 mph9 a) 4000 b) 10

c) 200 d) 36 or 40e) 4200 or 4000 f) 0.1g) 30 h) 15 000 or 20 000i) 300 j) 21 or 20

10 a) 9.2 b) 4.7 c) 0.014d) 160 000 e) 510

11 a) 1480 b) 10.2 c) 0.0219d) 21 000 e) 0.005 62

12 a) 10 b) 49 c) 22d) 9 e) 85 f) 63

13 a) 15 000 b) 80 c) 48d) 0.09 e) 1539 f) 20g) 0.16 h) 70 i) 4500j) 12 000

14 a) 4446 b) 2.34 c) 19d) 0.004 446 e) 1900 f) 4.446

15 a) 38.682 b) 38 682 c) 1260d) 3.8682 e) 30.7 f) 1.26


1 a) 6 b) x � 2 c) b � r2 a) 5 b) 2 � p c) q � r3 a) 5 b) x � 3 c) 2 � x4 a) 13 b) p � 9 c) 4 � q5 a) x � 5 b) x � 8 c) x � 2 � y

d) 2x � 46 a) 4 � x b) x � y c) 2x7 a) 10 b) 14 c) x � 68 a) 75p b) £1.50 c) 25x9 a) 2x b) 5x c) 7x

10 a) 2m b) m � 6

Exercise 11.2 (page 153)1 a) (i) 8 (ii) 3

b) g � 72 a) (i) 2 (ii) 7

b) p � 33 a) 12 � r b) s � 8 c) v � t4 a) (i) 6 cm (ii) 11 cm

b) p � 35 a) (i) 155 cm (ii) 184 cm

b) h � 56 a) x � 14 b) x � 21 c) x � p7 a) 12p b) a � 68 a) y � 10 b) y � 15 c) y � g9 a) 25 � a b) 15 � a c) b � a

10 b � 5



Mixed exercise 11 (page 155)1 a) 35 � f b) 60 � f c) c � f2 a) 15 � r b) x � 5 c) z � y3 a) (i) 9 (ii) 15 b) 3h4 a) p � 29 b) p � 53 c) p � e5 4x6 a) (i) £1.60 (ii) £2.40 b) 20x (pence)7 a � 8 (£)8 a) t � 4 b) t � 2 c) 2t9 a) x � 6 b) x � 3 c) 3x

10 a) p � 2 b) p � 3 � q c) p � r � s


1 5p 2 7a 3 5x 4 4c5 7p 6 6b 7 3p 8 4s9 2a 10 5c 11 7x 12 4m

13 8a 14 2c 15 0 16 p17 2b 18 9x 19 9a 20 5a

Exercise 12.2 (page 160)1 a � 3b 2 x � 3y 3 4ab4 3p � q 5 6a � 6b 6 2a � 3c7 8pq 8 6x � 4y 9 3p2

10 6a � 4b � 4 11 3ab � 2bc 12 a2

13 a � 3c 14 4ab � 2a2 15 3s16 2a � 4 17 a2b 18 x � 3y19 10a � 2b 20 3a2b2

Mixed exercise 12 (page 161)1 4a 2 2a 3 abc4 y2 5 2c 6 4a � b7 2y � 3s 8 6a � b 9 2p2

10 3x � 2y 11 3x 12 6ab13 3ab � 3ac 14 3x � 2y 15 6a � 3b16 3 � 5x � 2y 17 3ab2 18 6 � a � b � c19 8pq 20 2a � 3b � 7


1 20a � 30b 2 6c � 21d3 15e � 40f 4 28g � 21h5 10u � 15v 6 30w � 18x7 21y � 7z 8 16v � 409 12 � 42w 10 12 � 32a

11 8g � 6 12 35 � 20b13 6i � 8j � 10k 14 20m � 12n � 8p15 12r � 18s � 24t

Exercise 13.2 (page 166)1 a) 20a � 38 b) 27b � 53

c) 12 � 37c d) 32 � 22a2 a) 18s � 43t b) 14v � 49w

c) 27x � 77y d) 38v � 27w

3 a) 21x � 8 b) 14y � 4c) 22 � 3z d) 36 � 10x

4 a) 16n � 9p b) 21q � 13rc) 23d � 6e d) 14f � ge) �h � 11j f) 6k � 3m

Exercise 13.3 (page 167)1 a) 5(2x � 3) b) 2(x � 3)

c) 4(2x � 3) d) 4(x � 5)2 a) 7(2 � x) b) 4(2 � 3x)

c) 5(3 � 2x) d) 3(3 � 4x)3 a) x(3x � 5) b) 5x(x � 4)

c) 4x(3x � 2) d) 2x(3x � 4)

Exercise 13.4 (page 169)1 a) a2 � 10a � 21 b) b2 � 11b � 28

c) 6 � 5c � c2

2 a) 9d2 � 3d � 20 b) 8e2 � 2e � 15c) 6 � 5f � 56f 2

3 a) 4g2 � 20g � 21 b) 4h2 � 28h � 49c) 6j2 � 37j � 56

4 a) 10k2 � 23k � 42 b) 6 � 11m � 72m2

c) 6 � n � 15n2

5 a) 4 � 4p � 63p2 b) 6r2 � 37r � 56c) 4s2 � 20s � 21


2 a) x5 b) y4 c) z7

3 a) m2n4 b) f 4g5 c) p3r4

4 a) 56k3 b) 120y3 c) 8d3

Mixed exercise 13 (page 171)1 a) 24a � 16b b) 20a � 15b

c) 36a � 60b d) 9a � 18be) 12x � 15y f) 18x � 12yg) 20x � 12y h) 8x � 2yi) 15f � 20g j) 6j � 15kk) 7r � 14s l) 12v � 4w

2 a) 12x � 11 b) 20x � 27c) 7x � 12 d) 16y � 5e) 15y � 7 f) 21y � 4g) 3a � 6 h) 6m � 1i) 6p � 18 j) 14t � 24k) �j � 31 l) 46

3 a) 4(x � 2) b) 6(x � 2)c) 3(3x � 2) d) 6(2x � 3)e) 2(3 � 5x) f) 5(2 � 3x)g) 8(3 � x) h) 4(4x � 3)i) 2(3x � 4) j) 4(8x � 3)k) 4(5 � 4x) l) 5(3 � 4x)m) x(2 � x) n) y(3 � 7y)o) z(5z � 2)

4 a) a2 � 9a � 20 b) a2 � 5a � 6c) 12 � 7a � a2 d) x2 � 7x � 8e) x2 � 4x � 45 f) x2 � 3x � 2g) 3x2 � 31x � 36 h) 2y2 � y � 21i) 14 � 25p � 6p2 j) 6p2 � 8p � 8k) 4t2 � 23t � 15 l) 6a2 � a � 15



5 a) 46 b) 54 c) 25 d) a7

e) j3 f) t6 g) v3w3 h) d3e6

i) x3y5 j) 60p3


1 a) £45 b) £100 c) £60 d) £752 a) 3 b) 32 c) 16 d) 373 a) £24 b) £60 c) £14 d) £924 a) £25 b) £12 c) £280 d) £18.505 a) £90 b) £150 c) £105 d) £2906 a) 9 cm2 b) 75 cm2 c) 5 m2 d) 12.3 mm2

7 a) 40 mph b) 80 km/h c) 8 m/s d) 230 mph8 a) £17 b) £28 c) £50.50 d) £37.509 a) £35 b) £55 c) £80

10 a) £60 b) £400 c) £10 d) £48

Exercise 14.2 (page 177)1 c � 5a 2 B � J � 14

3 r � 4m 4 a � �m

n�

5 c � 50 � 10h 6 a � �b

2

h�

7 s � �d

t� 8 t � 6a � 2.5c

9 v � lwh 10 t � 0.2w

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

11 t � 4.5wt stands for the total amount savedw stands for the amount saved each week

12 n � �3

r�

n stands for the number of strips of paperr stands for the length of a roll of paper

13 s � n � ds stands for the sale pricen stands for the normal priced stands for the discount

14 f � �d

5� � 3

f stands for the fared stands for the distance covered

15 c � 100 � 7sc stands for the total costs stands for the number of students

Exercise 14.3 (page 179)1 a) 9 b) 6 c) 3 d) 11

e) 10 f) 12 g) 10 h) 19i) 2 j) 17 k) 28 l) 14m) 1 n) 8 o) 8 p) 40q) 40 r) 18 s) 2 t) 25u) 3 v) 10 w) 20 x) 12y) 100 z) 8

2 a) 5 b) �1 c) 15 d) 5e) 11 f) 4 g) 9 h) 90i) 15 j) 27

3 a) 19 b) 39 c) 4 d) 6�12�

e) 14.54 a) 10 b) 10 c) 2325 a) 4 b) 6 c) 8.5 d) 8

Mixed exercise 14 (page 182)1 a) 15 m b) 42 m c) 75 m d) 10.5 m2 a) 50 °F b) 32 °F c) 86 °F d) 53.6 °F3 a) 2 hours b) 4.5 hours

c) 14 hours d) 80 seconds4 a) C � 3d b) F � 1.8C � 32

c) t � �d

s�

5 a) 9 b) 3 c) 30 d) 27e) 15 f) 24 g) 37 h) 26i) 16 j) 4 k) 5 l) 7.7m) 25 n) 13 o) 8 p) 107


1 a) 90 minutes b) 210 minutes2 4°C3 £31

4 a) s � �d

t� b) 60 km/h

5 4906 187 a) 55 b) 208 a) 8x b) 3x2

9 a) 2 hours 10 minutes b) 1.5 kg10 511 15 miles12 a) 12

b)

c) C � 3P � 3 or C � 3(P � 1)d) 87

13 a) 24 cm2 b) 22.5 cm2

14 a) 120 cm3 b) 216 cm3

15 a) £45 b) 43 miles

Exercise 15.2 (page 188)

1 a) b � a � c b) x � �4a

w

� y�

c) t � �v �

a

u� d) t � �

p �

3

c�

e) q � �A �

p

pr� or q � �

A

p� � r

f) g � �p �

2

2f� g) n � �

Ft �

4

m�

Number of posts, P 1 2 3 4 5 6

Number of chains, C 0 3 6 9 12 15



2 u � �s

3

b

v

n�

3 h � �2

b

a�

4 R �

5 a) h � �

3V

r2� b) 16.6 cm

6 a) 140°F b) C � (F � 40) � �59� � 40

7 r � ��8 a) a � �

v2

2

�

s

u2

� b) u � �v2 � 2�as�

Mixed exercise 15 (page 189)1 a) 104°F b) 32°F c) 23°F2 95p3 a) 12 cm2 b) 21.6 cm2

4 a) 34 minutes b) 47.8 minutes

5 a) q � p � 2r b) r � �x �

5

s�

c) r ��m

pq

s� d) y � �

tx �

2t

A� or y � �

x

2� � �

A

2t�

6 a) w � �T �

45

40� b) w � 2.4 kg

7 a) 4 cm b) 8 cm8 a) 30 words b) 60 words


1 a) 1, 5, 9, 13, 17 b) �4, �1, 2, 5, 8c) 21, 18, 15, 12, 9 d) 5, 10, 15, 20, 25e) 100, 60, 20, �20, �60 f) 1, 1�

12�, 2, 2�

12�, 3

2 a) 25, 29; �4 b) 39, 45; �6c) 47, 54; �7 d) 25, 28; �3e) 38, 43; �5 f) 77, 86; �9

3 a) 7, 5; �2 b) 9, 5; �4c) 9, 3; �6 d) 4, 0; �4e) �1, �5; �4 f) �2, �7; �5

4 a) 15, 36; Add 7 b) 17, 35; Add 6c) 65, 21; Subtract 11 d) 66, 30; Subtract 9e) 22, 30; Add 8 f) 18, �2; Subtract 5

Exercise 16.2 (page 194)1 a) rule �3 b) rule �2

c) rule �5 d) rule �4

3V�h

100I�PT

2 a) b)

rule �4 rule �3

c) d)

rule �4 rule �5

Exercise 16.3 (page 196)1 a) 11, 15, 19, 23, 27 b) 13, 21, 29, 37, 45

c) 12, 19, 26, 33, 40 d) 2, 5, 8, 11, 14e) 13, 18, 23, 28, 33 f) 16, 25, 34, 43, 52

2 a) 603 b) 799 c) 2194d) 1202 e) 2413 f) 1795

Mixed exercise 16 (page 196)1 a) 1, 6, 11, 16, 21 b) 50, 46, 42, 38, 34

c) �6, �4, �2, 0, 22 a) 26; rule �4 b) 51; rule �8

c) 34; rule �53 a) 9, 5; rule �4 b) 5, 2; rule �3

c) �2, �15; rule �134 a) 22, 27, 37; rule �5 b) 22, 13, 7; rule �3

c) 26, 37, 70; rule �115 a) rule �3 b) rule �3

6 a) rule �6

b) rule �7

7 a) 5, 9, 13, 17; 601 b) 4, 13, 22, 31; 697c) 10, 18, 26, 34; 738


1 a) Multiply the pattern number by 2b) 200

2 a)

b) They go up by 2 each time; they are the 2 timestable plus 2.

c) 1023 a)

b) 36You add 1 more to the difference each time, soT4 � 10, T5 � 15, T6 � 21, T7 � 28, T8 � 36

Pattern number 1 2 3 4 5

Number of matchsticks 4 6 8 10 12



4 a) 3 � 1 � 5 � �2 b) 1, 4, 7, 105 a) 4, 10, 16, 22 b) 5, 9, 13, 17

c) 4, 2, 0, �26 a) 1, 4, 9, 16, 25 b) 3, 6, 11, 18, 27

c) 1, 8, 27, 64, 1257 2, 4, 8, 16, 328 5, 2, �1, �49 For example

and so on.10 For example

and so on.

Exercise 17.2 (page 205)1 a) 2n � 3 b) 3n � 1 c) n � 62 a) 20 � 3n b) 10 � 5n c) 1 � n3 a) Linear: 17, 20 b) Not linear

c) Linear: 30, 36 d) Not linear4 a) 6, 0, �6, �12, �18 b) 14 � 6n5 a)

b) 15n � 2 c) 76 1, 3, 6, 10, 15, 21, 28, 36, 45, 557 2108 a) 10, 100, 1000, 10 000, 100 000

b) Powers of 109 a) 1, 4, 9, 16, 25

b) (i) Each term is 3 more than the equivalentterm in the sequence of square numbers.

(ii) n2 � 3(iii) 10 003

10 a) Each term is 3 times the equivalent term in thesequence of square numbers.

b) 3n2 c) 1200

Mixed exercise 17 (page 207)1 a) 300

b) Multiply the term number by 3 or start with 3and add 3 each time.

2 a)

b) 64. This is the sequence of square numbers; the8th pattern has 8 � 8 stars.

3 a) T1 � 1 � 6 � 2 � 4 b) 10, 16, 22, 284 a) 7, 12, 17, 22 b) 2, 5, 10, 17

c) 88, 86, 84, 825 4, 8, 16, 32, 64

6 a) Tn � 3n � 2 b) Tn � 6n � 5c) Tn � 7 � 5n

7 a) Linear: 24, 29 b) Not linearc) Not linear d) Linear: �12, �18

8 a) 3, 9, 27, 81, 243 b) Powers of 39 A suitable answer is as follows.

10 a) 1, 4, 9, 16, 25 b) Tn � n2 � 4


1 A(2, 1) B(4, 6) C(7, 7) D(1, 8)E (7, 2) F(6, 0) G(0, 4) H(9, 4)I(5, 3) J(10, 1)

2

Exercise 18.2 (page 214)1 A(1, 2) B(3, �1) C(�2, 4) D(0, �2)

E(�3, �1) F(2, �3) G(3, 3) H(�4, 2)I(0, 3) J(�2, �3)

2

Square

3

Isosceles triangle

�5�4�3�2�10 1

1C

B

A

�1�2�3�4�5

2345y

x2 3 4 5

�5�4�3�2�10 1

1

C B

D A

�1�2�3�4�5

2345y

x2 3 4 5

0

1

2

3

4

5

6

7

8y

x1 2 3 4 5 6 7

E

C

A

B

D

8

1 3 6 10 15

Number of tickets 1 2 3 4

Cost in £ 17 32 47 62



4

Trapezium

5

Rhombus

6

D(�2, 3)

7

C(�3, �1)

8

C(�3, �4)

�5�4�3�2�10 1

1

C

B

D

A

�1�2�3�4�5

2345y

x2 3 4 5

�5 �4 �3 �2 �10 1

1

C B

D A

�1�2

�3

�4

�5

2

3

4

5y

x2 3 4 5

�5 �4 �3 �2 �10 1

1

C B

D A

�1�2

�3

�4

�5

2

3

4

5y

x2 3 4 5

�5�4�3�2�10 1

1C

B

D

A

�1�2�3�4�5

2345y

x2 3 4 5

�5�4�3�2�10 1

1

C

B

DA

�1�2�3

�4�5

2345y

x2 3 4 5


1 a) x � 3 b) y � 2

c) x � �4 d) y � �12

For graph, see question 4.3

For graph, see question 4.

4

5

For graph, see question 6.

6

7 (1, 4)

x

y

y � 5 � x

y � 3x � 1

�7�6�5�4�3�2�1

10

234567

�7 �5 �3 3 5 7�1 1

x

y

y � x � 4

y � x � 2

x � y � 6

�7�6�5�4�3�2�1

10

234567

�7 �5 �3 1 3 5 7�1

x �3 �2 �1 0 1 2 3

y � x � 4 1 2 3 4 5 6 7

x �3 �2 �1 0 1 2 3

y � x � 2 �5 �4 �3 �2 �1 0 1

x �1 0 1 2 3 4 5 6

x � y � 6 7 6 5 4 3 2 1 0

x �2 �1 0 1 2

y � 3x � 1 �5 �2 1 4 7

x �2 �1 0 1 2 3 4 5

y � 5 � x 7 6 5 4 3 2 1 0



Mixed exercise 18 (page 220)1 A(5, 1), B(2, �1), C(�2, 1), D(�4, 0),

E(�1, �3), F(0, �2), G(2, 4)2

3

Parallelogram4

Trapezium5

D(�1, �3)

�5 �4 �3 �2 �1 0 1

D

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

A

B

C

�5 �4 �3 �2 �1 0 1

A

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

B

C

D

�5 �4 �3 �2 �1 0 1

A

D

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

C

B

�5 �4 �3 �2 �1 0 1

F

D

G

A

C

E

B

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

6 There are two possible answers to this question.

(5, 4), (�1, 4) or (2, 1), (2, �5)7 y � x � 1

For graph, see question 9.8 x � y � 2

For graph, see question 9.9 y � 2x � 1

10 a) (2, 3) b) (1, 1) c) (�12�, 1�

12�)

�7 �4�5�6 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

�6

�7

2

3

4

5

6

7 C

A

B

y

x2 3 4 5 6 7

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 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

x �2 �1 0 1 2 3 4

y �5 �3 �1 1 3 5 7




1 a � 5 2 p � 5 3 x � 84 m � 2 5 a � 7 6 x � 37 n � 12 8 h � 3 9 r � 11

10 n � 4 11 x � 28 12 m � 1313 b � 16 14 p � 36 15 x � 416 x � �5 17 x � �4 18 x � �819 x � �4 20 x � �14

Exercise 19.2 (page 224)1 x � 6 2 m � 11 3 b � 84 p � 8 5 x � 3 6 x � 47 x � 7 8 x � 5 9 x � 2

10 x � 4 11 x � 5 12 x � 913 x � 14 14 x � 8 15 x � 816 x � �1

Exercise 19.3 (page 225)1 x � 6 2 p � 12 3 p � 254 x � 18 5 a � 6 6 m � 487 t � 4 8 b � 128 9 d � 18

10 y � 1000 11 x � 54 12 x � 1813 x � 4 14 x � 21 15 x � 7216 x � 24 17 x � 80 18 x � 3019 x � �10 20 x � �16

Exercise 19.4 (page 226)1 a � 59° b � 92° c � 149° d � 98°2 x � 2 � 16, x � 183 8x � 72, x � 94 2x � 5 � 13, x � 45 3x � 6 � 18, x � 86 3x � 5 � 10, x � 5

Mixed exercise 19 (page 227)1 x � 4 2 x � 63 x � 7 4 x � 65 x � 23 6 x � �267 x � 14 8 x � �19 x � 7 10 x � 5

11 m � 3 12 p � 213 y � 8 14 x � 415 x � 5 16 x � 617 x � 2 18 x � 1619 x � 75 20 x � �1621 10x � 5 � 95; x � 9


1 x � 7 2 x � 0.53 x � 7 4 x � 75 x � 1 6 x � 77 x � 5 8 x � 49 x � 10 10 x � 6

11 x � 5 or x � �5 12 x � 7 or x � �713 y � 8 or y � �8 14 m � 9 or m � �915 m � 5 or m � �5 16 x � 10 or x � �1017 x � 8 or x � �8 18 x � 4 or x � �419 x � 2 or x � �2 20 x � 10 or x � �10

Exercise 20.2 (page 229)1 p � 16 2 x � 3 3 x � 74 x � 1 5 x � 15 6 x � 17 x � 14 8 x � 5 9 x � �4

10 x � 10 11 x � 10 12 a � 113 x � 1 14 x � 3 15 x � 216 x � 3 17 x � 8 18 x � 419 x � 2 20 x � 5.5

Exercise 20.3 (page 231)1 x � 3 2 x � 3 3 x � 24 x � 10 5 x � 3 6 x � 27 x � 10 8 x � �2 9 x � 3

10 x � 2 11 x � 2 12 x � 113 x � 3 14 x � 4.5 15 x � 416 x � 6 17 x � 1 18 x � 219 x � �3 20 x � 7

Exercise 20.4 (page 232)1 x � 16 2 a � 40 3 x � 204 y � 50 5 y � 30 6 p � 357 m � 24 8 x � 64 9 x � 27

10 y � 33

Exercise 20.5 (page 234)1 x � 1.72 a) 23 � 5 × 2 � �2

33 � 5 × 3 � 12b) x � 2.8

3 a) 43 � 4 � 6053 � 5 � 120

b) x � 4.64 a) 3.73 � 3.7 � 47 (nearest whole number)

3.83 � 3.8 � 51.1 (1 d.p.)b) x � 3.77

5 x � 2.66 x � 4.337 228 31.69 a) x(x � 4) � 621, i.e. x2 � 4x � 621

b) 27, 2310 7.8



Exercise 20.6 (page 237)1 x 13

2 x � 4

3 x � 13

4 x � 4

5 x 3

6 x 8

7 x � 2 8 x �5 9 x � �910 x 1 11 x 5 12 x � 913 x � 2 14 x 6 15 x 516 x � 0.25 17 x 2 18 x 319 x � 4 20 x � 4

Mixed exercise 20 (page 238)1 a) m � 9 b) p � 2

c) x � 8 d) x � 3e) p � 8 f) x � 4 or �4g) x � 6 or �6 h) p � 4 or �4i) x � 4 or �4 j) a � 5 or �5k) x � 25 l) x � 30m) y � 18 n) y � 49o) a � 36

2 a) 13 � 4 � 1 � 5, 23 � 4 � 2 � 16b) x � 1.7

3 a) 33 � 32 � 18, 43 � 42 � 48b) x � 3.4

4 a) x3 � x � 100 b) x � 4.65 a) x � 2

b) x 3

c) x � 3

d) x 4

e) x 2

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 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.

Exercise 21.2 (page 242)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, 1�

12�),

(3, 9), straight line drawn through them.5 Points (0, 7) and (3.5, 0) plotted, straight line drawn

through them.

Exercise 21.3 (page 245)1 a) She walked at 3 km/h for 20 minutes (distance

� 1 km), waited for 5 minutes, travelled in abus (or car) at 45 km/h for 12 minutes (distance� 9 km).

b) Approximately 35 minutesc) (i) 0.25 km/minute

(ii) 15 km/hd) (i) Approximately 0.75 km/minute

(ii) Approximately 45 km/h2 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 ofsprints and rests.

May also mention approximately when overtakingtook place.

3 a) £2 b) 80pc)

d) £24e) 69p (to nearest penny)

100 20 30Distance (km)

Ch

arg

e (

£)

40 50

5

10

15

20

25

30

d)

6 8 10 12 14 16

0 1 2 3 4 5

6 8 10 12 14 16

0 1 2 3 4 5

0 1 2 3 4 5

0 2 4 6 8 10



4 a) D b) H c) F d) C5 a) £49.50 b) £46.50

c)

6 a)

b) Less than 91 cubic metres

Exercise 21.4 (page 253)Answers read from graphs may be approximate.

1 a)

b)

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

�3 �2 �1 0 1 2 3

1

�1�2�3�4

2345678y � x2 �2

y

x

40

0

80 120Water used (cubic metres)

Cha

rge

(£)

16020 60 100 140

2010

40

60

80

100

120

30

50

70

90

110

130140150160170180

b)

20

4 6Number of boxes

Cos

t (£)

8 10 121 3 5 7 9 11

10

20

30

40

50

60

2 a)

b)

c) (i) 0.8 to 0.9 (ii) 0.6 or 3.4

3 a)

b)

c) (i) �1.8 (ii) �2.3 or 1.3

�3�4 �2 �1 0 1 2 3 x

y

1

�1�2�3�4

23456789

y � x2 � x � 3

�1 1 30 2 4 5 x

y

�2�3�4�5

�1

12345 y � x2 �4x

x �3 �2 �1 0 1 2 3

x2 9 4 1 0 1 4 9

�2 �2 �2 �2 �2 �2 �2 �2

y � x2 � 2 7 2 �1 �2 �1 2 7

x �1 0 1 2 3 4 5

x2 1 0 1 4 9 16 25

�4x 4 0 �4 �8 �12 �16 �20

y � x2 � 4x 5 0 �3 �4 �3 0 5

x �4 �3 �2 �1 0 1 2 3

x2 16 9 4 1 0 1 4 9

x �4 �3 �2 �1 0 1 2 3

�3 �3 �3 �3 �3 �3 �3 �3 �3

y � x2 � x � 2 9 3 �1 �3 �3 �1 3 9



4 a)

b)

c) (i) 1.75 (ii) �1.4 or 4.4

5 a)

b)

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

6 a)

y

�10�9�8�7�6�5�4�3�2�1

123

y � 3x � x2

�2 �1 10 2 3 4 5 x

y

123456789

1011121314

y � x2 �3x � 4

�2 �1 10 2 3 4 5 x

b)

c) (i) �1.8 or 2.8 (ii) �2.4 or 3.47 a)

b)

c) (i) �1.6 or 1.6 (ii) �2.7 or 2.78 a)

b)

c) (i) 1.8 (ii) 3.6 to 3.7

x

A

A � 6x2

10 2 3 4 5

20

40

60

80

100

120

140

160

�3 �2 �1 0 1 2 3 x

y

1

�1�2�3�4�5�6

23456789

10111213

y � 2x2 � 5

�3 �2 �1 0 1 2 3 4 x

y

1

�1�2�3�4�5�6

234567

y � x2 � x � 5

x �2 �1 0 1 2 3 4 5

x2 4 1 0 1 4 9 16 25

�3x 6 3 0 �3 �6 �9 �12 �15

4 4 4 4 4 4 4 4 4

y � x2 � 3x � 4 14 8 4 2 2 4 8 14

x �2 �1 0 1 2 3 4 5

3x �6 �3 0 3 6 9 12 15

�x2 �4 �1 0 �1 �4 �9 �16 �25

y � 3x � x2 �10 �4 0 2 2 0 �4 �10

x �3 �2 �1 0 1 2 3 4

x2 9 4 1 0 1 4 9 16

�x 3 2 1 0 �1 �2 �3 �4

�5 �5 �5 �5 �5 �5 �5 �5 �5

y � x2 � x � 5 7 1 �3 �5 �5 �3 1 7

x �3 �2 �1 0 1 2 3

2x2 18 8 2 0 2 8 18

�5 �5 �5 �5 �5 �5 �5 �5

y � 2x2 � 5 13 3 �3 �5 �3 3 13

x 0 1 2 3 4 5

A � 6x2 0 6 24 54 96 150

50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 2


Mixed exercise 21 (page 256)1

2

3 a) £39 b) (i) £11 (ii) 8p4 a)

b) Gas by £205 a)

b) d

t

d

t

1200 1400 1600600 800

Gas used (kWh)

Cos

t (£)

10000

200 400

10

20

30

40

50

2x � y � 8 � 0

x

y

2 41 3

1

0

3

5

2

4

6

7

8

x

yy � 2x � 1

�1 2 41 3

�3

�1

1

0

3

5

�2

2

4

6

7

6 a) She stopped (e.g. waited for bus)b) 68 minutes c) 27 km/hd) (i) 1 km (ii) 10 km

7 a) Quadratic, � b) Not quadraticc) Quadratic, � d) Quadratic, �e) Not quadratic f) Not quadraticg) Quadratic, �

8 a)

b)

c) (i) �2.25 (ii) x � �3.8 or x � 0.89 a)

b)

c) (i) �6.25(ii) x � �2.5 to �2.6 or x � 1.5 to 1.6

x

y

�1�2�3�4 1 2 3

�3

�1

1

0

3

5

�4

�5

�6

�7

�8

�2

2

4

6

x

y

�1�2�3�4�5 1 20

�4

�2

2

4

6

8

10

x �5 �4 �3 �2 �1 0 1 2

x2 25 16 9 4 1 0 1 4

3x �15 �12 �9 �6 �3 0 3 6

y � x2 � 3x 10 4 0 �2 �2 0 4 10

x �4 �3 �2 �1 0 1 2 3

(x � 3) �1 0 1 2 3 4 5 6

(x � 2) �6 �5 �4 �3 �2 �1 0 1

y � (x � 3)(x � 2) 6 0 �4 �6 �6 �4 0 6



10 a)

b)

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

11 a)

b)

c) (i) x � 0.7 or x � 4.3 (ii) 6.25


1 e, c, b, d, a2 a) right angle b) obtuse c) acute

d) reflex e) acute f) reflexg) obtuse h) right angle

x

y

�1 1 2 3 4 5 6

�3

�1

1

0

3

5

�4

�5

�6

�2

2

4

6

x�1�2 1 2 3 4

�3

�1

1

0

3

5

�4

�2

2

4

6

7

8

y

3 a) obtuse b) acute c) reflexd) reflex e) obtuse f) reflexg) right angle h) acute i) reflexj) obtuse

Exercise 22.2 (page 265)a � 55° b � 110° c � 132° d � 81°e � 70° f � 35° g � 17° h � 37°i � 39° j � 45°

Exercise 22.3 (page 266)a � 50° b � 110° c � 120° d � 100°e � 105° f � 122° g � 135° h � 57°i � 87° j � 60°

Exercise 22.4 (page 268)1 a � 60° b � 120° c � 120°2 d � 20° e � 160° f � 160°3 g � 135° h � 45° i � 45°4 j � 47° k � 133° m � 133°5 n � 114° p � 66° q � 66°6 r � 28° s � 152° t � 152°7 w � 143° x � 37° y � 37°8 z � 47°9 a � 40° b � 90° c � 50° d � 50°

10 e � 40° f � 40° g � 140°

Mixed exercise 22 (page 269)1 a) right angle b) obtuse

c) right angle d) reflex2 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 to180°.

c � 80° Angles on a straight line add up to180° or Vertically opposite angles areequal or Angles around a point add upto 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 areequal or Angles around a point add upto 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


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


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

y � x2 � 2x � 1 7 2 �1 �2 �1 2 7

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



Exercise 23.5 (page 280)1 2

3 4

5 6

Sides Diagonals Parallel sides

Quadrilateral 4 equal sides 2 different pairs Equal 2 pairs of Only one pair of equal sides diagonals parallel sides of parallel sides

Square � � �

Rectangle � � �

Rhombus � �

Parallelogram � �

Trapezium �

Kite �


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 triangleC � parallelogramD � rhombusE � trapezium

2 a) A, B, F and G b) C and D or H and Ic) F, G, H and I

Exercise 23.4 (page 278)1 a) F b) CB c) LK2 Note: this diagram is not full-size.

3 a) 4b) A � 4 � 1 � 1, B � 3 � 2 � 1,

C � 2 � 2 � 1, D � 5 � 1 � 1

Mixed exercise 23 (page 281)1 a � 55° b � 80° c � 37° d � 65°2 x � 115° Base angles of an isosceles triangle are

equal; angles on a straight line add upto 180°

y � 50° The sum of the angles in a triangle is180°

3 a) cuboid b) 2 cm � 2 cm � 4 cm4



5 a) Trapezium b) Square, rhombus, kitec) Square, rectangle d) Rhombus, kite

6 7


1 a) Radius b) Centre c) Diameter2 a) Hexagon

b) (Regular) octagonc) (Isosceles) triangle

3 5For example

4 20For example

5 36°6 40°7 Check student’s hexagons. 5 cm8 Check student’s hexagons. 4.6 cm

Mixed exercise 24 (page 287)1 a) Radius b) Circumference

c) Diameter2 Check students’ diagrams.

10 cm3 It does not have eight equal angles.4 Square5 Rhombus6 67 45° 8 a) Isosceles triangle

b) Pentagon9 Check student’s diagrams.

10 Check student’s diagrams.


1 a) $53 b) £46 c) $1.522 a) 22.5 litres b) 8.8 gallons c) 4.5 litres3 a) 25 miles b) 24 km c) 1.6 km

Exercise 25.2 (page 293)1 a) 45 seconds b) 160°2 a) £20 000 b) 6.2 years c) £13 5003 a) 06:00 b) 21°C c) 21:00 (20°)4 a) 7.3 years b) £1400

Exercise 25.3 (page 296)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 travels60 miles. It is travelling quickly on a motorway ormajor road.During stage 3, from 09:45 to 10:00, the car isstationary. The driver could have stopped for petrolor a break.During stage 4, from 10:00 to 11:30, the car travels100 miles. It is travelling quickly on a motorway ormajor 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 another40 m in 10 minutes but then stops for 60 minutes.The tortoise wins the race.

3 a) The bicycle travels from Hereford toBirmingham steadily without stopping. Itcovers 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 fora further 40 miles and arriving in Hereford after1 hour at 16:45.

b) They pass going in opposite directions.

Mixed exercise 25 (page 297)1 a) €30 b) $46.50 c) $1.352 a) July b) Moscow

c) (i) March to April (ii) April to May3 Ian leaves home at 7:30 a.m. and walks �

12� 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°Cc) November d) May

5 a) 0.7 second b) 1 hourc) After the first hour, reaction time gets longer

(slower).


1 a � 74° (Alternate angles)2 b � 65° (Allied angles)3 c � 125° (Corresponding angles)4 d � 65° (Alternate angles)

e � 65° (Corresponding or vertically oppositeangles)



5 f � 110° (Alternate angles)g � 110° (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°)

Exercise 26.2 (page 305)1 a � 35° (Angles in a triangle add up to 180°)2 b � 41° (Angles in a triangle add up to 180°)3 c � 43° (Angles in a triangle add up to 180°)4 d � 35° (Angles in an isosceles triangle)5 e � 60° (Angles in an equilateral triangle)6 f � 55° (The exterior angle of a triangle is equal

to the sum of the opposite interiorangles)

7 g � 141° (The exterior angle of a triangle is equalto the sum of the opposite interiorangles)

h � 39° (Angles on a straight line add up to180°)

8 i � 115° (Angles in a quadrilateral add up to360°)

9 j � 123° (Angles in a quadrilateral add up to360°)

k � 57° (Angles on a straight line add up to180°)

10 l � 100° (Angles on a straight line add up to180°)

m � 84° (Angles in a quadrilateral add up to360°)

Exercise 26.3 (page 308)1 A: trapezium

B: rhombusC: squareD: kiteE: rectangleF: squareG: arrowheadH: parallelogramI: trapeziumJ: rhombusK: parallelogram

2 a) Square, rhombusb) Rectangle, parallelogram, kite, arrowheadc) Rectangle, parallelogramd) Trapeziume) Square, rhombus, kite

3 a)

Rhombusb)

Trapeziumc)

Parallelogramd)

Kite4 All the angles are 90° and the diagonals are equal

length.5 Isosceles trapezium, parallelogram or rhombus

Exercise 26.4 (page 312)1 2340°2 3240°3 a) 131° b) 86°, 130°, 95°, 49°4 a) 58° b) 90°, 100°, 123°, 105°, 122°5 e � 30°; i � 150°6 e � 3.6°; i � 176.4°7 158 20

Rhombus

110°

110°

70°

70°

110°

110°

70°

70°

Parallelogram

Isosceles trapezium

110°110°

70°70°

0 2

2

4

y

x4 6 8

0 2

2

4

y

x4 6 8

0 2

2

4

y

x4 6 8

0 2

2

4

6

8

y

x4 6 8



Mixed exercise 26 (page 313)1 a) a � 110° Corresponding angles.

b � 70° Allied angles or Angles on astraight line.

b) c � 50° Alternate angles.d � 50° Corresponding angles or vertically

opposite angles.c) e � 36° Alternate angles.

f � 72° Angles on a straight line.g � 72° Corresponding angles or angles in

a triangle.2 a) a � 19° Angles in a triangle add up to 180°.

b) b � 47° Base angles in an isosceles triangleare equal.

c) c � 31° Exterior angle of a triangle is equalto the sum of the opposite, interiorangles.

d � 77° Angles on a straight line add up to180° or Angles in a triangle add upto 180°.

3 a) a � 126° Angles in a quadrilateral add up to360°.

b) b � 129° Angles on a straight line add up to180°.

c � 53° Angles in a quadrilateral add up to360°.

4 a) Rectangle, parallelogram, kite, arrowheadb) Rhombus, isosceles trapezium, parallelogramc) Square, rectangle, isosceles trapezium

5 a) 900°b) Exterior angle � 24°, interior angle � 156°c) 36


1 a) 6 cm b) 4.5 cm c) 9 cmd) 3.4 cm e) 7.8 cm f) 10.2 cmg) 2.9 cm h) 1.3 cm i) 5.6 cmj) 8.7 cm

2 a) 7 cm b) 3.5 cm c) 2.2 cmd) 6.8 cm

3 a) 4 cm � 3 cm b) 2 cm � 2.4 cmc) 3.4 cm � 3.4 cm

Exercise 27.2 (page 320)a � 30° b � 64° c � 50° d � 61° e � 125° f � 73° g � 90° h � 310°i � 127° j � 136° k � 40° l � 300°m � 109° n � 119° o � 29° p � 302°q � 67° r � 270° s � 128° t � 218°

Exercise 27.3 (page 324)Check students’ drawings.

Exercise 27.4 (page 327)Check students’ drawings.1 a) BC � 7.6 cm B � 67° C � 23°

b) BC � 6.7 cm B � 43° C � 72°c) AB � 9.1 cm A � 20° B � 30°d) AB � 4.6 cm A � 65° B � 32°e) BC � 9.6 cm B � 22° C � 40°

2 a) Y � 70° YZ � 4.9 cm XY � 5.5 cmb) Y � 45° YZ � 5 cm XY � 7.1 cmc) Y � 33° XY � 7.2 cm YZ � 3.8 cmd) Y � 60° XY � 7.2 cm YZ � 4.5 cme) Y � 65° XY � 6 cm XZ � 3.4 cm

Exercise 27.5 (page 330)Check students’ drawings.1 a) A � 65° B � 65° C � 49°

b) A � B � C � 60°c) A � 35° B � 84° C � 60°d) A � 78° B � 57° C � 44°e) A � 59° B � 35° C � 86°

2 a) X � 65° Y � 43° YZ � 6.7 cmb) Y � 38° Z � 91° XY � 6.4 cmc) Y � 41° Z � 21° XY � 3.2 cmd) Y � 81° X � 64° YZ � 6.7 cme) X � 52° Y � 56° XZ � 6.1 cm

Exercise 27.6 (page 333)1 a) 12 m b) 20 m c) 26 m d) 10 m2 a) 40 km b) 100 km c) 55 km d) 27 km3 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 mb) Living room: 10 m � 5 m

Dining room: 6 m � 4 mBedroom 1: 5 m � 5 mBedroom 2: 3 m � 4 mBathroom: 3 m � 3 mKitchen: 4 m � 3 m

c) 13 cm � 7.5 cm5 a) (i) 90 km (ii) 270 km

(iii) 110 km (iv) 66 km(v) 126 km (vi) 272 km

b) 16 cm

Exercise 27.7 (page 337)Diagrams are not full size. The measurements given arecorrect for the suggested scale.

1 A: 005° B: 050° C: 090° D: 145°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°



3 Check students’ drawings.

4 a) Check students’ drawings.

b) 1.24 km c) 029°

5 Check students’ drawings.

Mixed exercise 27 (page 339)1 7.5 cm, 4.7 cm, 4.3 cm, 3.4 cm2 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 cmc) 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 mc) Study 8 m � 4 m, lounge 8 m � 10 m,

dining room 8 m � 7 m, kitchen 8 m � 7 md) 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°

4 cm

6 cm

5.5 cm

6.5 cm

Coastguard

5 cm

E

D

C

B

A

N

125°

250°

5 cm

7.5 cm

C

P

L

N

N

N

085°

150°

5 cm

4 cm

Ashton Bradbury

Charlton

Chapter 28Exercise 28.1 (page 351)Diagrams are not full size. The measurements given arecorrect for the suggested scale.1

2 Scale 1 cm � 20 m


4

5


7 N

S

NW NE

SW

W E

SE

1 cm

4 cm

2 cm

A

B

5 cm

5 cm

3 cm

D

C

60° 30°

6 cm

Hedge

Tree

5 cm

2.5 cm

A5 cm



8

9

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

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

1

2 Scale 1 cm � 1 km

3


8 cm

6 cm 5 cm

E F

H G

T

7 cm

3 cm

3 cm

3 cm

3 cm

5 cm

5 cmA

D

B

C

7 cm

5 cm

4 cm

P Q

6 cm

3 cmA

6 cm2 cm

8 cm

Castle

7 cm 6 cm

8 cmA B

C

5


7 1 cm � 20 m



10 Scale 1 cm � 5 miles

9 cm7 cm

11 cmA B

C

Locus

H K2 cm

3 cm

4 cm

5 cm

3.5 cm

2 cm

2.5 cm

Hou

se

2 cm

B

C

A 7 cm

9.5 cm

5 cm

5 cm

5 cm

2.5 cm

7 cm

Locus

3 cm

2 cm

5 cm



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

1

2

3

4

Area � 23.4 cm2

5



100°

D C

A B5 cm

3 cm

8 cm

6 cm

6 cm

S R

P Q

5 cm

8 cm

9 cmA B

C

5.2 cm6 cm 8 cm

7 cm

3 cm 3 cm

8 cm

8



Chap ter 29Exercise 29.1 (page 359)

1

2 a) 1 b) 0 c) 2

70°

5 cm

8 cmE F

G

6 cm

10 cm

3 cm

3 cm8 cm

3 cm

3 cm

3 cm

3 cm

3 cm

5 cm

5 cm

a)

b)

c)



3

4 Isosceles triangle5 Other answers with more squares shaded are

possible.

6 Other answers with more squares shaded arepossible.

7 Check students’ patterns.8 a)

b)

c)


d) 4 e) 1 f) 82 6, 63 Equilateral triangle

4

Purple

Orange

Pink

G G � greenB � blueY � yellowR � red

G

BR

R Y

B

5

6 Check students’ patterns.

7

8

9 Check students’ patterns.

Exercise 29.3 (page 369)1 a) b)

c) d)

e)

2 a) b)

c)

3

�5�6�7�8 �4�3�2�1 0 1

1

�1�2�3�4�5

2345y

x2 3 4 5

A

C

B

mirrorline



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

Mixed exercise 29 (page 372)1 a) 1 b) 4 c) 02 a) 1 b) 4 c) 13

4

5 a) b)

6 a) 90° clockwise b) 90° anticlockwise7 B, E, F8 a)–b)

c) 90° anticlockwise

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

A

B

C

D

mirrorline

�5 �4 �3 �2 �10 1

1

C

AB

�1�2

�3

�4

�5

2

3

4

5y

x2 3 4 5

9


1

2

3 a) b)

c)

4 a) A reflection in the line y � 2b) A reflection in the line x � 3c) A reflection in the line y � x

5 a) A reflection in the line y � 0b) A reflection in the line y � �xc) A reflection in the line y � x

�4 �3 �2 �10 1

1

�1

�2

�3

�4

2

A

C

B3

4y

y � 1

y � x

x2 3 4

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2

C

AB

3 4 5

�4 �3 �2 �10 1

1

�1

�2

�3

�4

2

3

4y

y � �x

y � 2

x2 3 4

A

B

C




1

2

3

4

�4 �3 �2 �10 1

A

C

D

B1

�1

�2

�3

�4

2

3

4y

x2 3 4

�4 �3 �2 �10

A

C

1

1

�1

�2

�3

�4

2

3

4y

x2

B

3 4

C B90°

A

B� A�

�4�3�2�10 1

CA

D

B

1

�1�2�3�4

2345678y

x2 3 4 5 6 7

5

6

7 a) A rotation of 90° (anticlockwise) about the originb) 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

originb) A rotation of 180° about (2, 1)c) A rotation of 90° (anticlockwise) about (1, 1)

9 A rotation of 150° clockwise about O10 a) A reflection in the line x � 0

b) A rotation of 90° (anticlockwise) about (2, 4)c) A reflection in the line y � xd) A rotation of 90° (anticlockwise) about the origine) A reflection in the line y � �x

Exercise 30.3 (page 386)1

C

B�

B120°

A�

A

90°O

�2 �1 1

D0

A

B

C

2 3 4 5 6

�2

�1

1

2

3

4

5

6y

x



2

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

4 a) A translation by vector � �b) A rotation of 90° (anticlockwise) about the

originc) A rotation of 90° clockwise or �90° about

(2, 2)

d) A translation by vector � �e) A reflection in the line y � 0f) A reflection in the line y � x

g) A translation by vector � �h) A rotation of 180° about (0, 2)

Mixed exercise 30 (page 388)1

2�6

�3�4

�52

�42

�21

�1�2

2�1

�2 �1 1 2 3 4 5 6

�2

�1

1

2

3D

C

0

A

B4

5

6y

x

y

x1

C

A

B

2 3 4�4 �3 �2 1

�4

�3

�2

�1

1

2

3

4

2 a)

b)

3

4

�4 �3 �2 �1 0 1

1

�1

�2

�3

�4

2

3

4

y

x2 3 4

A

B

C

D

�4 �3 �2 �1 0 1

1

�1

�2

�3

�4

2

3

4

y

x2

C

B

3 4

A



Chapter 31Exercise 31.1 (page 394)Note: Diagrams not full-size.1 a)

b)

c)

d)

e)

2 a) 2 b) 3 c) 4 d) 33 a) No: for an enlargement, all the lengths must be

enlarged by the same scale factor. AC � 4 andDF � 8 so DF is twice as long as AC but AB � 4 and DE � 10 so DE is more than twiceas long as AB.

b) No: for an enlargement, all the lengths must beenlarged by the same scale factor. AB � 2 andDE � 8 so DE is four times as long as AB butthe height of the triangle ABC, from side ABto C, is 4 and the height of triangle DEF, fromside DE to F, is 15, which is less than fourtimes as long.

Exercise 31.2 (page 398)1 a)

b)

c)

d)

e)

2 a) (i) 3 (ii) (0, 0)b) (i) 4 (ii) (0, 1)c) (i) 2 (ii) (�2, 6)d) (i) 3 (ii) (5, 4)e) (i) 2 (ii) (5, �3)

Exercise 31.3 (page 402)1 a), b)

c) An enlargement with scale factor 2, centre theorigin

10 2 3 4 5

B

A

6

1

2

3

4

5

6y

x

0 1

12345678y

x2 3 4 5 6 7 8 9 10 11 12

0 1

12345678y

x2 3 4 5 6 7 8 9 10 11 12

0 1

12345678y

x2 3 4 5 6 7 8 9 10 11 12

0 1

12345678y

x2 3 4 5 6 7 8 9 10 11 12

0 1

12345678y

x2 3 4 5 6 7 8 9 10 11 12



2 a), b)

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

3 a), b)

c) An enlargement with scale factor �14�, centre the

origin

4 a), b)

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 1�12�, centre the

origind) An enlargement with scale factor �

23�, centre

the origin6 a) A reflection in the line y � 0

b) An enlargement with scale factor 2, centre (0, 4)

c) A translation by vector � �d) An enlargement with scale factor 2�

12�, centre

the origin

e) A translation by vector � �f) An enlargement with scale factor �

13�, centre (5, 3)

�64

10 2 3 4 5

A

6 7 8

1

2

3

4

5

6

7

8y

x

B

C

�8�3

10 2

C

A

B

3 4 5 6 7 8

1

2

3

4

5

6

7

8y

x

10 2

A

B

3 4 5 6 7 8

1

2

3

4

5

6

7

8y

x

7 a) A reflection in the line x � 1b) An enlargement with scale factor 2, centre

(1, 0)c) A rotation of 90° (anticlockwise) about the

origind) A reflection in the line y � xe) An enlargement with scale factor �

12�, centre the

origin

f) A translation by vector � �8 a) A reflection in the line y � 2

b) A rotation of 90° clockwise or �90° about theorigin

c) A translation by vector � �d) A reflection in the line y � 0e) 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)

Mixed exercise 31 (page 405)1 a)

b)

2 a)

14

0 1

12345678y

x2 3 4 5 6 7 8

2�2

0 1

123456789

10y

x2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

b)



3 a) (i) 3 (ii) (0, 0)b) (i) 2 (ii) (8, 9)

4

5

6 a) A reflection in the line x � 0b) A rotation of 90° clockwise about the origin.c) An enlargement with scale factor 3, centre

(�4, 3)

d) A translation by vector � �e) An enlargement with scale factor �

12�, centre the

origin

f) A translation by vector � �g) A reflection in the line y � x

7 a) A reflection in the line x � 0

b) A translation by vector � �c) An enlargement with scale factor 3, centre

(0, 2)d) A rotation of 90° (anticlockwise) about

(2, �2)e) An enlargement with scale factor �

12�, centre the

originf) A rotation of 180° about the origin

g) A translation by vector � �


1 7.8 cm2 1150 g or 1.15 kg3 0.7 litre or 700 ml

32

1�3

�32

0�3

10

1

2

3

4

5

6

7

8

9

y

x2 3 4 5 6 7 8 9

A

B

10

1

2

3

4

5

6

7

8

9

y

x2 3 4 5 6 7 8 9

B

A

4 a) 2.4 kg b) 400 g or 0.4 kg5 a) A: �4°C, B: 18°C b) 22°C

Exercise 32.2 (page 413)1 100 ml, 0.75 litre, 1500 ml, 1.6 litres, 2 litres2 a) centimetres b) metres

c) metres d) kilometrese) metres f) metresg) centimetres or millimetres

3 1.1 m4 0.725 �

34� kg, 1500 g, 1.6 kg, 2 kg, 10 000 g

6 a) 140 ml b) 25 mlc) 5000 ml d) 5230 ml

7 3.627 kg

Exercise 32.3 (page 415)1 a) 900 g or 0.9 kg

b) 2250 g or 2.25 kgc) 10 800 g or 10.8 kgd) 225 g or 0.225 kg

2 a) 48 km b) 22 poundsc) 264 pounds d) 40 milese) 20 kg

3 200 miles

Exercise 32.4 (page 417)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 cm2 a) 2.5 m b) 7 m3 16 m4 7 m

Mixed exercise 32 (page 418)1 a) 60 mm b) 350 mm c) 4500 mm

d) 620 mm e) 37.2 mm2 a) 5000 m b) 4320 m

c) 46 700 m d) 1234 m3 a) 5 km b) 6.7 km

c) 12.345 km d) 0.543 21 km4 31.04 cm, 1623 mm, 2.42 m, 284 cm, 9.044 m5 a) m b) m

c) cm or mm d) cm6 a) 9000 g b) 1129 g c) 3100 g d) 300 g7 a) 90 cm b) 40 km c) 0.5 kg d) 8 kg8 55 miles � 88 km9 9 m

10 3.75 kg


1 a) 2500 cm b) 420 mmc) 236 cm d) 5100 mm

2 a) 30 000 cm2 b) 230 mm2

c) 95 200 cm2 d) 1.4 mm2



3 a) 900 cm2 b) 81.4 cm2

c) 720 m2 d) 9.4 m2

4 a) 3 200 000 cm3 b) 0.000 042 m3

c) 0.005 m3 d) 6 420 000 cm3

5 a) 2610 cm3 b) 9.5 litresc) 2400 ml d) 0.91 litre

6 All the units need to be the same; change 50 cm to0.5 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 mlc) 23.925 seconds and 23.935 seconds

2 a) 633.5 g and 634.5 gb) 233.5 ml and 234.5 mlc) 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 mm5 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 cmc) 1.95 cm and 2.05 cm

7 Maximum d: longest rod minus leastdepth � 35.5 � 19.5 � 16 mmMinimum d: shortest rod minus greatestdepth � 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) 3.5 minutes b) 3 weeks

c) 3 kg d) 2 m2 a) 5.7 m (or 5�

34� m) b) £16

c) 665 km d) 0.1 cm2

Exercise 33.4 (page 426)1 62.5 m/s 2 43 mph3 7.5 miles 4 5 hours5 278 cm3 6 60 mph7 9 g/cm3 8 100 km/h9 7.8 g/cm3

10 a) 8.9 g/cm3 b) 151.3 g11 19.3 kg12 a) 58.5 kg

b) (i) 0.7692 m3 (ii) 769.2 m3

13 a) 60 km/h b) 64.3 km/h14 10.6 g/cm3

15 1156 people per square kilometre

Mixed exercise 33 (page 428)1 a) 120 000 cm2 b) 371 mm2

c) 4200 cm2 d) 5 mm2

2 a) 3 000 000 mm2 b) 41.25 m2

c) 94 cm2 d) 600 cm2

3 a) 2130 ml b) 5.1 litresc) 421 000 ml d) 0.0917 litre

4 a) 26.5 cm and 27.5 cmb) 5.55 cm and 5.65 cmc) 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 mmb) Greatest perimeter: greatest length � 3

� 34.5 � 3 � 103.5 mm7 a) 1 hour 15 minutes b) 8 km/h8 a) 60 mph b) 190 miles9 5394 m2


1 a) 22 cm b) 8 cm c) 18.4 cmd) 14.9 cm e) 17.6 cm f) 33 cm

2 16.8 m 3 18.8 cm4 15 m 5 83.3 m

Exercise 34.2 (page 431)1 a) 12 cm2 b) 8 cm2 c) 15 cm2

d) 9 cm2 e) 5 cm2 f) 25 cm2

Exercise 34.3 (page 433)1 a) 24 m2 b) 36 cm2 c) 80 cm2

d) 75 m2 e) 8 cm2 f) 17.6 m2

g) 30.66 m2 h) 10.24 m2 i) 9.66 cm2

2 16.92 cm2

3 6.76 m2

4 15.023 cm2

5 15.68 m2

6 36 m2

7 a) 14 m2 b) £3438 a) 15 m2 b) £375

Exercise 34.4 (page 435)1 16 cm2 2 50 cm2

3 160 m2 4 75 mm2

5 64 cm2 6 17.5 cm2

7 55 cm2 8 144 cm2

9 150 m2 10 120 m2

Exercise 34.5 (page 437)1 24 cm2 2 72 cm2

3 64 m2 4 35 cm2

5 14 cm2 6 30 cm2

7 42 cm2 8 144 m2

9 42 cm2 10 16 cm2

Exercise 34.6 (page 440)1 a) 60 cm3 b) 128 cm3

2 150 m3 3 125 cm3

4 4500 cm3 5 72 m3

6 42.875 cm3 7 252 cm3

8 189 000 cm3 9 1800 cm3

10 750 cm3



Mixed exercise 34 (page 441)1 a) 20.6 cm b) 16.9 cm

c) 28 cm d) 15.4 cm2 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

c) 28.09 m2 d) £21.07 (to the nearest penny)7 a) 9 cm2 b) 8 cm2 c) 30 cm2

8 a) 28 cm2 b) 300 cm2 c) 18 cm2

9 120 cm3

10 19.683 cm3

11 3000 cm3

12 360 000 cm3 or 0.36 m3

Chapter 35Exercise 35.1 (page 445)These answers have been calculated using the buttonon a calculator.

1 37.7 cm (1 d.p.)2 78.5 cm (1 d.p.)3 282.7 cm (1 d.p.)4 116.2 mm (1 d.p.)5 207 mm (nearest whole number)6 84.8 cm (1 d.p.)7 163.4 cm (1 d.p.)8 14.8 cm (1 d.p.)9 28.9 cm (1 d.p.)

10 22.9 m (1 d.p.)11 9.1 m (1 d.p.)12 3.86 m (2 d.p.)

Exercise 35.2 (page 446)These answers have been calculated using the buttonon a calculator.

1 a) 616 cm2 (nearest whole number)b) 2463 cm2 (nearest whole number)c) 20 106 cm2 (nearest whole number)d) 3848 mm2 (nearest whole number)e) 12 076 mm2 (nearest whole number)f) 5809 cm2 (nearest whole number)g) 9503 cm2 (nearest whole number)h) 75.4 cm2 (1 d.p.)i) 295.6 cm2 (1 d.p.)j) 36.3 m2 (1 d.p.)k) 21.2 m2 (1 d.p.)l) 4.91 m2 (2 d.p.)

2 a) 201 cm2 (nearest whole number)b) 452 cm2 (nearest whole number)c) 3848 cm2 (nearest whole number)d) 1018 mm2 (nearest whole number)e) 5281 mm2 (nearest whole number)f) 1810 cm2 (nearest whole number)

g) 2290 cm2 (nearest whole number)h) 15.2 cm2 (1 d.p.)i) 75.4 cm2 (1 d.p.)j) 11.3 m2 (1 d.p.)k) 6.2 m2 (1 d.p.)l) 4.30 m2 (2 d.p.)

Exercise 35.3 (page 448)1 160 cm2

2 126 cm2

3 340 cm2

4 227 cm2

5 108 cm2

6 212 cm2

Exercise 35.4 (page 450)1 a) 515 cm3 b) 1376 cm3 c) 219.6 cm3

d) 385.5 cm3 e) 192 cm3 f) 780 cm3

2 18 000 cm3

Exercise 35.5 (page 452)1 a) 1233 cm3 b) 17 334 cm3 c) 2092.8 cm3

d) 396.8 cm3 e) 2253.42 cm3 f) 528.82 cm3

2 119 000 mm3


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


1 a) 1810 cm2 (nearest whole number)b) 2281 cm2 (nearest whole number)c) 2827 cm2 (nearest whole number)d) 3958 mm2 (nearest whole number)e) 377 mm2 (nearest whole number)f) 465.6 mm2 (1 d.p.)g) 131.9 m2 (1 d.p.)h) 77.0 m2 (1 d.p.)

2 a) 2111 cm2 (nearest whole number)b) 6993 cm2 (nearest whole number)c) 10 336 cm2 (nearest whole number)d) 3054 mm2 (nearest whole number)e) 4869 mm2 (nearest whole number)f) 1176.5 mm2 (1 d.p.)g) 190.0 m2 (1 d.p.)h) 59.7 m2 (1 d.p.)



Exercise 35.8 (page 459)1 2

3 4Plan

Front elevation

Side elevation

Plan

Front elevation

Side elevation

Plan

Front elevation

Side elevation

Plan

Front elevation

Side elevation

5 6

Mixed exercise 35 (page 461)Where necessary, the button on a calculator has beenused to work out these answers.

1 a) 44.6 cm b) 93.3 cmc) 204 cm d) 100.8 mm

2 a) 127.08 cm2 b) 24.45 m2

c) 237.79 mm2 d) 69.40 mm2

e) 124.69 cm2 f) 72.08 m2

3 Check students’ diagrams.4 a) 89.54 cm2 b) 75 cm2

c) 176.5 cm2 d) 178.23 cm2

5 a) 208 cm3 b) 156 cm3

c) 169.32 cm3 d) 192 cm3

e) 257.544 cm3 f) 655.2 cm3

6 a) 20 308.2 cm3 b) 1578.46 mm3

c) 5617.5 cm3 d) 0.8874 m3

7 a) 2601 mm3 (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)

Plan

Front elevation

Side elevation

Plan

Front elevation

Side elevation



10 a) b)

c) d)


1 12 cm2 2 85 cm2

3 50 cm2 4 28 cm2

Exercise 36.2 (page 467)1 a) 13 cm b) 5.83 m c) 6.24 cm

d) 24 cm e) 7.64 cm f) 6.34 cmg) 30.50 m h) 9.35 m i) 6.57 cm

2 4.53 m3 23.66 inches

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

Plan

Side elevation

Front elevation

Plan

Side elevation

Front elevation

Plan

Side elevation

Front elevation

Plan

Side elevation

Front 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)

Exercise 36.4 (page 473)1 a) (6.5, 3) b) (3, 5)

c) (�1.5, 6) d) (�4.5, 0)e) (�0.5, �5) f) (5.5, �4.5)

2 a) (1, 6) b) (4, 4)c) (5, 4.5) d) (5.5, 4.5)e) (1, 2) f) (�5, �7)

Mixed exercise 36 (page 474)1 a) 20 cm2 b) 23 cm2

2 a) 11.40 cm b) 7.55 cmc) 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, 5�12�) c) (4�

12�, 4�

12�)

5 1.93 m6 30.3 cm2

7 15.66 m


1 14:252 a) 09:35 b) 00:133 1 hour and 20 minutes4 5 minutes to 65 a) 33 minutes b) 20 minutes

c) 39 minutes d) 40 minutese) 45 minutes f) 33 minutes

6 a) 3:35 b) 3:05c) 13:10 d) 13:23e) 5 past 10 f) 25 past 5

7 08:218 9:209 16:35

10 11:1511 1 hour and 35 minutes

Exercise 37.2 (page 482)1 54 km 2 2.8 mph3 3 hours 4 12 km/h5 1470 m 6 4.5 hours7 10.44 m/s8 a) �

14� hour b) 52 km/h, yes

9 a) 150 seconds b) 1.2 m/s10 162.5 km



Exercise 37.3 (page 484)1 14 ounces2 1.5 pounds3 a)

b)

Exercise 37.4 (page 486)1 a) 17.5 pence

b) A 7-minute call to Jamaica, by 0.5 pencec) 3

2 a) 509 km b) 15 km

Mixed exercise 37 (page 487)1 23:50 and 01:502 a) £9 b) £6 c) £5.113 a) £69.65 b) £3.95 c) £2.524 50 m/s5 30 mph6 10.5 miles7 7.5 hours8 a) �2

15� second b) 40 seconds

9 a) 13 b) 810 a) 48 km/h b) 50 mph11 a) 31.5 litres b) 225 litres c) 1350 litres


1 5 2 3.84 3 4.54 3.45 5 9.2 6 62.417 1.20 8 2.68 9 4.48

10 2.65 11 1.78 12 1.85

Exercise 38.2 (page 494)1 Check students’ answers. Possible answers include

the following.a) positive � negative � negativeb) 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 includethe following.a) Answer is too large, since 0.9 is near 1.b) negative � negative � positivec) 62 � 36 and answer should be less than this.d) 8 � 3 � 11 so last digit should be 1.

3 a) 1000 � 20 � 20 000b) 0.4 � 0.4 � 0.16c) �20 � 5 � �4

4 a) 7 � £9 � £63b) 30 � £15 � £450 or 30 � £10 � £300c) 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� � 38.3c) 17.6 � 3.8 � 66.88d) 278.93 � 18.2 � 297.13, 297.13 � 4.3 � 69.1

6 a) 468.38 b) 6.807 a) 12.647 b) 896.8748 a) 61.1 b) 4.89 a) (i) 403 � 64 000

(ii) 20 � 0.2 � 4

(iii) �72 � 4�2� � �49 � 1�6� � �33� 6

(iv) �10

0

�

.08

30� � �

0

4

.0

0

8� � �

40

8

00� � 500

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 minutes2 a) 1.45 hours b) 0.9 hour3 3 hours and 15 minutes4 1 hour and 48 minutes5 56 £31.32 and £20.887 700 ml or 0.7 litre8 54 mph9 £191.11 or £191.12

10 66 83411 200.812 2.2 g/cm3

13 15.2 cm

Mixed exercise 38 (page 502)1 a) 3 b) 3.52 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 000b) 0.62 � 0.36c) �48 � 6 � �8 or �50 � 6 �8

Imperial 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

3 m 10 feet

10 litres 17.5 pints

15 kg 30 pounds



5 a) 1270.26 b) 2.886 a) (i) 203 � 8000 (ii) 30 � 0.3 � 9

(iii) �82 � 4�2� � �64 � 1�6� � �48� 7

(iv) �30

0

�

.04

50� � �

0

8

.0

0

4� � 2000

b) (i) 9800.344 (ii) 7.743(iii) 6.93 (to 2 d.p.)(iv) 2054 (to nearest integer)

7 38 a) 3 hours 42 minutes

b) 2 hours 45 minutesc) 48 minutesd) 51 minutes

9 34.3 mph (to 1 d.p.)10 48.75 cm3

11 £96.91 or £96.92


1 a) Unlikely (or Impossible)b) Evensc) Likely

2 a) Arrow at Certainb) Arrow at Very unlikelyc) Arrow at Likely (if answering this at school)

3 a) Unlikelyb) Evensc) Impossible

4 a) All 1sb) All not 1c) Two 1s and three othersd) Four 1s and one other

Exercise 39.2 (page 511)1 a) Arrow at 0.5

b) Arrow at 1c) Arrow at �

13� (3rd tick mark from the left)

2 a) Unlikelyb) R at 0.5, G at 0.3, B at 0

3 a) �15� or 0.2 b) �

25� or 0.4

4 a) �16� 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) 128 5 orange, 3 blue, 2 red, no green9 a) Red b) 3 red and 1 purple

10 a) Arrow at 0.4b) Arrow at 0.6

11 �78�

12 a) �156� b) �1

76� c) �1

96�

13 a)

b) 10 c) 24 d) �224� � �1

12�

14 a) (Order can be different)

b) �29�

Exercise 39.3 (page 514)1 �

2644� � �

38� or 0.375

2 a) �123000� � �

1230� or 0.65

b) About 100c) Do many more tosses.

3 a) (i) �35070� or 0.19 (ii) �3

3090� or 0.13

b) (i) 0.167 (ii) 0.167c) They could do although the experimental

probabilities are different from the theoreticalprobabilities, but more throws are needed tocheck.

Mixed exercise 39 (page 516)1 a) Impossible b) Evens

c) Likely (this depends on the local climate)2

3 a) 5 b) 04 a) �

15� b) �

35� c) �

25�

5 a) �18� b) �

28� or �

14� c) 0

6 a) �16� b) 0.7

7 48 0.659 �2

7020� � 0.36

10 a)

b) �16�

0 10.5

c) a) b)

Dice

1 2 3 4 5 6

1 2 3 4 5 6 7

Spinner2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

First scoop C C C V V V S S S

Second scoop C V S C V S C V S

T-shirt Jeans

Red Blue

Red Black

White Blue

White Black

Yellow Blue

Yellow Black




1 0.9 2 �56� 3 0.15

4 �130� 5 0.57 6 �

1479�

Exercise 40.2 (page 521)1 0.7 2 �2

60� or �1

30� 3 0.35

4 �141� 5 0.11 6 �2

10�

Exercise 40.3 (page 523)1 4 2 123 17 4 £3005 a) 50

b) 1506 50 yellow, 75 blue, 125 green


b) �16� or 0.17 (to 2 d.p.)

c) Yes, the dice is biased. The relative frequency for2 seems too low and the relative frequencies for 4and 6 seem too high.

2 Small number of trials. Cannot be predicted fromthese past events.

3 a)

b) 0.34 a) �

12

00� � 0.5, which is the probability of tossing a

fair coin and getting a head.b) �

13

00

20� � 0.34, which is very different from 0.5.

c) Emma. More trials give a more reliableindication.

5 a)

b) Yes. All values are approximately equal to0.25.

c) Either 225, 225, 225, 225 (if the spinner is fair)or

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

Mixed exercise 40 (page 527)1 �

79�

2 0.353 0.134 a) �2

70� b) 5 red, 8 white, 7 blue

5 12 days

6 a) �12

00� � �

12�, 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

b) (i) �43090� (ii) �

24

70

90� (iii) �

14

20

10�


1 Discrete: Number of pets, Money, Age in yearsContinuous: Weight, Distance, Temperature

2 Check students’ answers.3 a)

b)

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

Score 1 2 3 4 5 6

Relative0.14 0.09 0.17 0.22 0.11 0.27

frequency

Party Relative frequency

Labour 0.30

Conservative 0.47

Lib. Dem. 0.17

Other 0.06

Score 1 2 3 4

Relative0.27 0.23 0.26 0.24

frequency

Score 1 2 3 4

Relative240 204 237 219

frequency

Method of travel Bus Car Bike Walk

Estimate of0.245 0.24 0.115 0.4

probability

Day of birth Tally Frequency

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

Month of Tally Frequencybirth

January

February

March

April

May

June

July

August

September

October

November

December




b)

c)

2 a)

b)

2

0

468

1012

0 1 2 3 Morethan 3

Number of brothers

Freq

uenc

y

2

0

468

1012

Bir

d

Type of pet

Freq

uenc

y

Cat

Dog

Fish

Hor

seR

abbi

tO

ther

2

0

468

1012

1

Number of bedrooms

Freq

uenc

y

2 3 4 5 Morethan 5

2

0

468

1012

0

Number of cars

Freq

uenc

y

1 2 3 4 Morethan 4

2

0

468

1012

1p

Type of coin

Freq

uenc

y

2p5p

10p20p

50p£1

£2

c)

d)

e)


b) 610 c) 107 d) 72 e) 1002 a)

b) 1850 c) 550

3

10

0

2030405060

Plain

Beef

Chicken

C&O

S&V

Favourite crisps

Freq

uenc

y

Oth

er

2

0

468

10121416

0 1 2 3 Morethan 3

Number of fillings

Freq

uenc

y

2

0

468

1012

Blue

Brown

Gre

enG

rey

Oth

er

Eye colour

Freq

uenc

y

Japanese Not Japanese Total

Red 35 65 100

Not red 72 438 510

Total 107 503 610

Existing New Totaldrug drug

Symptoms eased 700 550 1250

No change in350 250 600

symptoms

Total 1050 800 1850

Riding Sport Total

Boys 8 18 26

Girls 15 7 22

Total 23 25 48



4 a)

b) 15

5 a)

b) The USA c) China


b)

c)

2 a)

b)

c)

d)

e)

f)

0

10

20

30

40

50

Apples per box

Freq

uenc

y

140–149

150–159

160–169

170–179

180–189

190–199

200or

more

10

0

20304050

0–19

20–39

40–59

60–79

80–99

100or

moreGreenfly per plant

Freq

uenc

y

10

0

203040

1–25

26–50

51–75

76–100

101or

moreLeaves per branch

Fre

quen

cy

10

0

20304050

30–49

50–69

70–89

90–109

110or

moreGrapes per bunch

Freq

uenc

y

20

0

406080

100

0–9 10–19

20–29

30–39

40or

moreEggs per day

Freq

uenc

y

10

0

20304050

Lessthan30

30–49

50–69

70–89

90or

moreNumber of ants

Fre

quen

cy

Hockey Not hockey Total

Badminton 33 13 46

Not badminton 24 15 39

Total 57 28 85

Gold Silver Bronze Total

USA 31 18 10 59

Germany 18 16 9 43

China 22 9 11 42

Total 71 43 30 144

Number Tally Frequencyof birds

1 to 5 � � 12

6 to 10 � � � � � 25

11 to 15 � � 13

16 to 20 � 5

21 to 25 3

26 to 30 2

Number Tally Frequencyof stamps

1 to 10 � 7

11 to 20 � � � 16

21 to 30 � � � 18

31 to 40 � � 13

41 to 50 � 5

51 to 60 0

61 to 70 1

Number Tally Frequencyof cars

1 to 20 4

21 to 40 � � � 15

41 to 60 � � � � � 25

61 to 80 � � 13

81 to 100 3



Mixed exercise 41 (page 538)1 Discrete: Hair colour, Vehicle type, Number of

sisters, Crowd size, Score on a diceContinuous: Height, Length

2 Check students’ data collection sheets.3 a)

b)

c)

d)

10

0

20304050

Pla

ysta

tion

Games console owned

Fre

quen

cy

X-b

ox

Gam

ecub

e

PC

Oth

er

1

2

0

4

6

8

10

12

14

16

2 3 4 5 Morethan 5

Number of goals

Freq

uenc

y

1

2

0

4

6

8

10

12

14

2 3 4 5 6

Score

Freq

uenc

y

Brown

5

0

10

15

20

25

30

Black Blonde Red Grey Other

Hair colour

Freq

uenc

y

4 a)

b)

c)

5

0 1 2 3 Morethan 3

2

0

4

6

8

10

12

14

16

Number of pets

Freq

uenc

y

Mot

orol

a

Sam

sung

Nok

ia

Eri

csso

n

Siem

ens

Oth

er

0

5

10

15

20

Make of phone

Fre

quen

cyF

ord

5

0

10

15

20

25

30

35

Vau

xhal

l

Toy

ota

Nis

san

Vol

ksw

agen

Oth

er

Vol

vo

Make of car

Fre

quen

cy

Alton Legoland Thorpe TotalTowers Park

Girls 31 25 27 83

Boys 43 11 21 75

Total 74 36 48 158



6 a)

b)

7 a)

b)

0

5

1–5 6–10 11–15 16–20 Morethan 20

10

15

20

Number of flowerson a plant

Freq

uenc

y

c)


1 represents 10 kilos of apples.

2 represents two pairs of spectacles.

3 represents four people.

0

10

1–5 6–10 11–15 16–20 21–25

20

30

5

15

25

Number of mice in a nest

Freq

uenc

y

M

Tu

W

Th

F

Sa

Su

M

Tu

W

Th

F

Sa

Su

M

Tu

W

Th

F

Sa

Su

Number of Tally FrequencyCDs owned

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

Number of Tally Frequencyflowers per

plant

11 to 20 � � 12

21 to 40 � � � � � � � � � � � � � � � � 22� �

41 to 60 � � � � � � � � � � � � � � � � 28� � � � � � �

61 to 80 � � � � � � � 18

0

10

0–9 10–19 20–29 30–39 40–49

20

30

40

Number of passengers on a bus

Freq

uenc

y

50–59


4 � represents 20 boxes of bananas.

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


b)

c)

Jan

Feb

March

April

May

June

July

Aug

Sep

Oct

Nov

Dec

M

Tu

W

Th

F

Sa

Su

No cars

1 car

2 cars

3 cars

More than 3 cars

No pets

1 pet

2 pets

3 pets

More than3 pets

1 bedroomMore than4 bedrooms

2bedrooms

3 bedrooms

4bedrooms


2 a)

b)

c)

3 a)

b)


Black

BlondeBrown

RedOther

OtherBlue

Brown

Green

Grey

Cheeseand onion

Beef

ChickenSalt andvineger

Other

England

Wales

Scotland NorthernIreland

FruitFlour

Butter

Sugar

Oatsand nuts

12

14

16

18

Tem

pera

ture

(°C

)

Day

20

22

24

M Tu W Th F Sa Su



2

3

4

5

12

10

J F M A M J JMonth

A S O N D

14

16

18

Sale

s (�

£10

00) 20

22

24

5 10 15Time (minutes)

20 25 30

50

60

70

80

90

100

Tem

pera

ture

(°C

)

0

12

34

56

78

910

1112

1314

Day

20

40

60

80

100

120

Sale

s (£

)

140

0

300

400

500

600

Num

ber

of v

isit

ors

700

800

900

M Tu W ThDay

F Sa Su

Mixed exercise 42 (page 548)1 Represents 4 skips

2 Represents 100 tickets

3

4

Rent

Food

Clothes

Entertainment

Savings

Carbohydrate

OtherProtein

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday



5

6

Chap ter 43Exercise 43.1 (page 551)

1 a) 6 b) 7 c) 4d) 4 e) 8 f) 7.5

2 483 a) 5 or more b) 6

Exercise 43.2 (page 552)1 182 73 kg3 194 There are two modes: 47 and 50.

Exercise 43.3 (page 553)1 a) 6 b) 9 c) 6.52 a) 5 b) 7.2 c) 63 11.1 minutes

Exercise 43.4 (page 554)1 a) 19 b) 3.2 c) 7562 a) £32 b) £92

Exercise 43.5 (page 555)1 121–130 cm2 £8–£11.993 11–15 words

4

Modal class � 40 � s � 45 mph

Mixed exercise 43 (page 556)1 a) Tom: mode � 7, median � 7, mean � 6,

range � 5Freya: mode � 3, median � 3, mean � 5, range � 9

b) Possible answers include: Tom’s scores aremore consistent (the range of his scores issmaller). Tom’s scores are higher on average(higher mode, median and mean).

2 a) 4 b) 45 mm c) 200.3 mm3 a) Football team: mean � 12.9 seconds,

median � 13 seconds, range � 4 secondsHockey 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 times4 a) Data set A: range � 6, mean � 3.6,

median � 3, mode � 3Data set B: range � 6, mean � 3.6, median � 3, mode � 3Data set C: range � 12, mean � 7.2, median � 6, mode � 6

b) The range, mean, median and mode for datasets A and B are the same. The results for dataset 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 thecorresponding values in set (ii) so the values ofthe 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 hoursGirls: 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 thegirls.

7 a) Median � 7, no modeb) Median � 36 kg, no mode

8 Median � 124 cm, mode � 123 cm

0 Mon

Tem

pera

ture

(°C

)

4

8

12

16

20

24

28

Tues Wed Thurs

Day

Fri Sat Sun

0 J F M A M J J A S O N D

14

16Sale

s (¥

mill

ion)

18

20

22

24

26

Month

Speed (mph) Tally Total

30 � s < 35 2

35 � s < 40 � 9

40 � s < 45 � � 10

45 � s < 50 � 8

50 � s < 55 1



9

The modal class is 380� m � 400


1 a) 630 b) 45 c) Monday2 a) Saturday b) Wednesday

c) 21 d) 1503 a) 60 b) 45 c) 2754 a) 70 b) 105 c) 4155 a) Wednesday

b) 75c) 195

6 a) 325 (June)b) 500 (January)c) 5150d) Approximately 429


12� b) About �

13�

2 a) The Mailb) The Sun, magazines, and other newspapers

3 a) 36 b) 64 a) 28 b) 165 a) 14 b) 10 c) 186 a) 44 b) 16 c) 24

Exercise 44.3 (page 568)1 a) 75°C b) 5 minutes

c) 21°C d) 19°C2 a) 44 b) Friday

c) 115 d) 1623 a) 22°C b) 18°C (Monday)

c) 23� 18� 5°C d) 147� 7� 21°C

4 a) Novemberb) £22 000� £15 000� £7000c) £223 000d) 223 000� 12� £18 583.33

5 a) 10 500b) 1500c) 1850� 1300� 550

6 a) The café is closed.b) £100c) The second Monday (£40)d) 540� 8� £67.50

Exercise 44.4 (page 572)1 a) England

b) Walesc) Scotland is a relatively large country with a

relatively small population.2 a) 8 b) 0 c) 7

d) 10� 1� 9e) The girls did better in the test. The shape of the

charts show that there are more girls gettinghigher scores. The mean for the boys is 5.6 andthe mean for the girls is 6.2.

3 a) $38 000b) $35 000c) $31 000 > $31 200d) 2003 range � $15 000, 2009 range � $63 000e) Student’s own answerf) Check students’ bar charts.

Mixed exercise 44 (page 574)1 a) 60 b) 75 c) 270 d) 452 a) 240 b) 1760

c) 251 (to nearest whole number)d) 300

3 a) County councilb) (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) Spainb) 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) 250d) 28 (to the nearest whole number)

6 a) July and August b) 14 cmc) 5°C d) 113 cm

7 a) (Just over) halfb) North America. The ‘Forest’ sector is larger in

the pie chart for North America.c) The total areas are differentd) A greater proportion of land is used for pasture

and grazing and for farming (arable) in NorthAmerica than in Australia, and a smallerproportion is non-productive.

Mass (grams) Tally Frequency

200� m � 220 � � 2

220� m � 240 � 1

240� m � 260 � 1

260� m � 280 � 1

280� m � 300 � � � 3

300� m � 320 � � 2

320� m � 340 � � 2

340� m � 360 � 1

360� m � 380 � � 2

380� m � 400 � � � � 5

400� m � 420 � � � � 4



8 a) Germany, $23 billionb) USA, $15 billionc) France and Italyd)


1

2 a)

b) 70 � r � 90 c) 90 � r � 110

3 a)

b) 80 � w � 90 c) 80 � w � 90

0

10

60 70 80 90 100 110

20

30

Weight (kg)

Freq

uenc

y

France

Ger

man

yIta

lyU

KU

SA

5

0

10

15 Spending

Earnings

20

Tourist Spending and Earnings

25

$ (b

illio

n)

0

10

50 70 90 110 130 150 170

20

30

Rainfall (cm)

Freq

uenc

y

0

5

15 20 25 30 35 40 45 50

10

15

20

Age (years)

Freq

uenc

y

4


2

3

4 a)

5

0

10Freq

uenc

y

15

20

100 20 30No. of words

40 50 60 70

25

30

Book 1

Book 2

5

0

10

Freq

uenc

y

15

20

172168 176 180

Height (cm)

184 188 192

25

20

0

40

Freq

uenc

y

60

80

3015 45 60Time (minutes)

75 90 105

100

120

140

5

0

10Fr

eque

ncy

15

20

60 12 18Weight (kg)

24 30

Lifetime of lightbulb Frequency(h hours)

300 � h � 400 3

400 � h � 500 9

500 � h � 600 12

600 � h � 700 15

700 � h � 800 13

800 � h � 900 19

900 � h � 1000 13

1000 � h � 1100 10

1100 � h � 1200 6



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

Exercise 45.3 (page 587)1 a), d), e)

b) Strong positive correlationc) 10.4 f) About 3

2 a), d), e)

b) Strong positive correlationc) 29 > 29.1f) About 32

3 a), e)

b) Strong negative correlationc) 32.9d) About 32 mpg

4 a), d)

b) No correlationc) 34.1e) Nof) Don’t know the ages of the people involved.

10

0

20Mar

k 30

40

400 500

Circumference of head (cm)

50

600

10

0

20

Pet

rolc

onsu

mpt

ion

(mpg

)

30

40

10 2 3Engine size (litres)

4

50

5

10

0

20

Pape

r2 30

40

100 20 30

Paper 1

40

1

0

2

Num

ber

ofba

dpe

ache

s

3

4

20 4 6

Delivery time (hours)

8 10 12 14 16 18

5

6

Mixed exercise 45 (page 589)1 a)

b)

c) 5 � t � 10d) 5 � t � 10

2 a)

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 � 60d) 70

e) �27�

3 a), c)

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

04030

5

10

Fre

quen

cy 15

20

50 60Mark

70 80 90

0 5

2

4

Freq

uenc

y

6

8

10 15Time (minutes)

20

0 1 2 3 4 5

Age of rabbit (months)

6 7 8 9

200

400

600

800

1000

1200

1400

Ave

rage

wei

ght(

g)

1600

1800

Time (t mins) Frequency

0 � t � 5 6

5 � t � 10 7

10 � t � 15 5

15 � t � 20 2




1 a) (i) 3 (ii) 3(iii) 5 (iv) 3.456

b) (i) 50 (ii) 50(iii) 5 (iv) 49.632

c) (i) 1 (ii) 1(iii) 5 (iv) 1.443

d) (i) 2 (ii) 2(iii) 4 (iv) 1.728

2 a) 1.96 b) 1.04 c) 2.987 d) 4.4563 a) 4.51 b) 27.04 c) 12.75 d) 3.16254 £1.075 7.52

Exercise 46.2 (page 599)1 a) (i) 50 (ii) 13.6

b) (i) 20 (ii) 7.22c) (i) 40 (ii) 14.1d) (i) 20 (ii) 6.55

2 a) (i) 0–4 (ii) 20 (iii) 6.98b) (i) 0–9 (ii) 40 (iii) 15.5c) (i) 250–299

(ii) 250(iii) 164.7

d) (i) 30–44(ii) 45(iii) 31.5

3 a) (i) 3–5 (ii) 3.62b) (i) 4–7 (ii) 7.3c) (i) 30–39 (ii) 32.25d) (i) 75–99 (ii) 75

4 30.35 179.5

Exercise 46.3 (page 603)1 a) (i) 50 (ii) 31.46

b) (i) 40 (ii) 25.11c) (i) 16 (ii) 68.56d) (i) 50 (ii) 16.04

2 a) (i) 0 � x � 3 (ii) 9.85b) (i) 120 � x � 130 (ii) 121.36c) (i) 22 � x � 26 (ii) 21.2d) (i) 50 � x � 55 (ii) 54.83

3 a) 250 � x � 300 b) 250 � x � 300c) £270.00

4 18.3 g5 166 (165.71) pence

Mixed exercise 46 (page 606)1 a) (i) 6 (ii) 7 (iii) 4.488

b) (i) 50 (ii) 7 (iii) 50.27c) (i) 1 (ii) 6 (iii) 1.42d) (i) 6 (ii) 5 (iii) 6.36e) (i) 2 (ii) 5 (iii) 3.47f) (i) 18 (ii) 5 (iii) 17.54

2 £11.363 2.71 (2 d.p.)4 a) (i) 20 (ii) 22.09

b) (i) 100 (ii) 30.11c) (i) 50 (ii) 59.33d) (i) 25 (ii) 55.8

5 a) 10 � x � 20 b) 10 � x � 20c) 19.31

6 £24 888.89 (or £24.89 thousand)


1 a) Primary b) Secondaryc) 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 groupsinto 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 wouldbe very difficult to analyse.

b) Check students’ rewrites of Q1. It should havebetter 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 aprotractor.Show people three drawn angles and ask themto estimate what size the angles are.

b) Possible answers include the following.Choose 30 students from Year 7, 30 from Year9 and 30 from Year 11.Choose a random sample of students from amixed-age group.

c) Check students’ data collection sheets. Thesheets should include the age or year-group ofthe student as well as data on the angle(s)drawn/estimated.

3 Check students’ answers.



Chapter 481 a) 8th, 6th, 3rd, 4th

b) 18c) Wong and Selby

2 a) 47 b) 145 c) 153 Any answer so long as it is justified, e.g. taxi is thequickest but most expensive at £32.50, cycling isthe cheapest but the longest at 2 hours.

4 a) 120 m2 b) 108 m2 c) £425 a) Starters £16.25

Main course £45.00Dessert £18.50Tea or coffee £5.25Total £85.00

b) £1.506 a) 9, 8, 16:30, 7 �

12� , 08:00, �

12� , 1 �

12�

b) £360c) Yes: 360� 2.5� 24� £420

7 SOS: ABC £75 for 20, ET £70 for 20, SOS £70 for 218 Expected income £1250, expected cost £900,expected profit £350

9 a) 74 b) 132c) (i) 6 (ii) 14

10 a) �1°C b) Stockholmc) Friday d) 13°C

11 a) 45 m2 b) Grass seed by £45.75c) (i) Small box: 50p/m² Large box: 40p/m²

(ii) 2 large boxes and 1 small box12 a) £3.75 b) £13.7513 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 Saturdayafternoon and the people who watch itare unlikely to be in the supermarket atthis time.

14 Any answer so long as it is justified, e.g. bus ischeapest at £32 in total but have to catch the bus at07:50, car costs £63 but don’t have to leave until 11a.m.

15 a) $1008 b) £95016 Hotel £1740 � the most expensive but includes use

of leisure facilities. Guest house £1140 � includesevening meal (but not flexible) and breakfast.Cottage £880 � all meals must be paid for andprepared.

17 a)

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 poundsb) 6541

19 a) 102 b) 31720 a) £33 b) £12.5521 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 49Number (page 627)1 a) 1248 b) 82 113 Yes: water 52� 18� 936, lunches 45� 20� 9004 a) 54.81 b) 548.1 c) 0.635 a) $1780 b) £1202.706 a) 1200, 1200, 30, 1950, 2100, 30

b) 700 (grams)c) No: 2� 80� 160 grams are needed but

5 ounces� 125 grams7 a) 97, 99, 101, (103), 105, 98, 100, 102, 104, 106

b) 9, 11, 13, 15, 17 � strategy: must be oddnumbered, 65 ÷ 5 or algebraic method

c) 9 and 108 a) 6 p.m.

b) Between 12:30 p.m. and 2 p.m. UK time and8:30 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.

9 a) False: counter example, e.g. 10 ÷ 5� 2b) False: counter example, e.g. 14 ÷ 2� 7c) True: one or other must be even, and

even� odd� even10 a) 1000 (ml), 1000 (ml), 460 (g), 60 (ml)

b) 4411 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 280cm of 4 m roll (2.8� 4� 11.2 m2) � both must beseen. Area from 3 m roll� 6� £63.Area from 4 m roll� 5� £56.

12 a) 26 cm b) 9 c) 39

Algebra (page 631)1 a) n � 4m

b) y � x � 3c) (i) 50 (ii) 20d) 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, 595 a) A(12, 10) b) B(�12, 5)

c) C(7, −12)6 a � 3, b � 6, c � 7, d � 57 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 levelb) 300 mc) �220 m

Player Mean Range

A 50 8

B 33 106

C 50 99



9 a) (4, 2) b) T marked at (�3, 2)c) (�1, 1)

10 a) x � x � 2� x � 3� x � 7b) (i) 4x � 12� 40 (ii) x � 7c) 7 cm, 9 cm, 10 cm, 14 cm

Geometry and measure (page 636)1 a) 60° b) 40° c) 50°2 a) 36 cm b) 56 cm2

3 a) 62° b) 75°4 S, P, Q, R5 14 cm3

6 a) (i) 26 cm (ii) 6.5 cmb) (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)

b) (i) square-based pyramid(ii) triangular prism

10 General explanation, e.g. decimals are not accurateenough � not rounded correctly. Specificexplanation, e.g.

13 � 0.33…,

23 � 0.66... .

11 Not possible: angle sum of polygon� 720°,sum of remaining angles � 720 – 3� 140� 300°,3� 89 < 300°

12 Arc centre X, radius DX � 2 mm; arc centre cornerof building, correct radius � 2 mm

13 Use of a 90° angle from the rectangle. Angles in atriangle: angle AGD� 70°, angle BFC� 70°.BFC�AGD, so triangle EFG is isosceles.

14 a)

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) £40.09 b) £22

c) 10 a.m. next day2 a) Louise b) 1 hour 45 minutes

c) Nell d) Betweeen 5:45 and 6:00 p.m.3 a) 138 b) 20 c) 284 a) 25% b) No: you need to know the

total numbers of boys and girls.5 4, 6, 10, 12, 166 5, 6, 9, 10, 10

Statement Rectangle Parallelogram Rhombus

The diagonals are not equal in length � �

All angles are equal �

The sum of the interior angles is 360° � � �

Statement Square 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 �


answers to the student’s book exercises... 2, 3, 6 answers to the student’s book exercises ......

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