ANSWERS TO THE HOMEWORK BOOK · PDF fileFoundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises219 1 Integers, powers and roots 1 Exercise

Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 219

1 Integers, powers and roots 1Exercise 1.1H

1 a) 78 b) 103 c) 145d) 204 e) 417 f) 534

2 a) 45 b) 46 c) 33d) 152 e) 125 f) 358

3 a) 128 b) 168 c) 114d) 392 e) 945 f) 1390

4 a) 23 b) 18 c) 16d) 23 e) 33 f) 58

5 £70 6 £247 304p 8 78

Exercise 1.2H1 a) 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

b) 12, 24, 36 48, 60, 72, 84, 962 36, 723 a) 4, 16, 18, 30, 42

b) 9, 18, 21, 30, 42c) 7, 21, 42

4 a) 20, 40, 60, 80, 100, 120b) 25, 50, 75, 100, 125

5 1006 a) 1, 2, 4, 5, 10, 20

b) 1, 2, 3, 4, 6, 9, 12, 18, 367 1, 2, 4, 68 a) 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

b) 1, 2, 3, 4, 6, 8, 12, 249 1, 2, 3, 4, 6, 12

10 a) 32 000 b) 204 000 c) 7000d) 243 000 e) 3 504 000

11 a) 8400 b) 21 800 c) 400d) 757 000 e) 7000

12 a) 8000 or 7800b) £2 000 000 or £2 100 000c) £35 000 000d) 12 000

Exercise 1.3H1 a) 710 b) 8400 c) 26 000

d) 40 200 e) 780 000 f) 8000g) 617 000 h) 280 000 i) 140 000j) 840 000 k) 97 400 000 l) 76 000 000

2 a) 59 b) 290 c) 648d) 920 e) 9200 f) 78 900g) 4582 h) 84 000 i) 7100

3 a) 1200 b) 5400 c) 24 000d) 160 000 e) 35 000 f) 3000g) 3 200 000 h) 100 000 i) 7 200 000j) 12 000 000 k) 1 800 000 l) 63 000 000

4 a) 1060 b) 2520 c) 8250d) 29 200 e) 57 400 f) 35 400g) 429 600 h) 288 000

5 a) 1728 b) 2304 c) 6816d) 1357 e) 3432 f) 11 844g) 22 620 h) 45 318 i) 76 032j) 32 640

6 a) 58 900 b) 49 m7 630 000 square metres 8 £2409 94 000 miles 10 £3588

Exercise 1.4H1 a) 1 b) 64 c) 16

d) 1600 e) 4900 f) 6400g) 90 000 h) 250 000 i) 360 000j) 12 100

2 a) 324 b) 1156 c) 2704d) 6084 e) 7396 f) 2209g) 3249 h) 57 600 i) 151 321j) 413 449

3 a) 343 b) 512 c) 1728d) 5832 e) 39 304 f) 110 592g) 175 616 h) 12 326 391

4 a) 16 b) 21 c) 24d) 32 e) 63 f) 74g) 58 h) 89

5 a) 40 b) 70 c) 90d) 100 e) 300

Exercise 1.5H1 a) 2 b) �4 c) �42 a) �3°C b) 3°C c) �13°C3 a) 18°C b) 15°C c) 12°C4 a) �6, �4, 2, 5 b) �8, �5, 0, 7

c) �8, �7, �2, 3, 6, 95 91°C

2 FractionsExercise 2.1H

1 a) �13� b) �

34� c) �

35� d) �

23�

e) �12� f) �

14� g) �

18� h) �

27�

2 a) �13� � �

26� � �

39� � �1

42� � �

13

00� � �

13

00

00�

b) �17� � �1

24� � �2

31� � �2

48� � �

17

00� � �

17

00

00�

3 a) �35� � �1

95� b) �

11

08� � �

59� c) �

12� � �

12

24�

d) �57

00� � �

57� e) �

12

22� � �1

61� f) �

47� � �

12

21�

g) �151� � �

36

06� h) �2

37� � �

19� i) �

29� � �3

86�

j) �143� � �

13

29� k) �

24

55� � �

59� l) �

67

30� � �1

90�

ANSWERS TO THEHOMEWORK BOOK EXERCISES

50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 219

220 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education

4 a) �57� b) �

16� c) �

45� d) �

35�

e) �35� f) �

35� g) �

23� h) �

47�

i) �113� j) �

12� k) �

18� l) �

15�

m) �13� n) �

34� o) �

56� p) �

35�

Exercise 2.2H1 a) 10 b) 12 c) 23

d) £30 e) £52 a) 7 b) 11 c) 18

d) £28 e) 7.2 m (or 7 m)3 a) 27 b) 45 c) 75

d) £51 e) £1354 a) 50 b) 30 c) 75

d) 40 cm e) £1255 £66 a) £4 b) £67 £4808 809 450

10 �38� of £160 � £60, �

45� of £80 � £64, �

45� of £80 is larger.

Exercise 2.3H1 a) �

56� b) �

49� c) �

45� d) �

23� e) �

13�

2 a) 2�34� b) 2�

25� c) 4�

23� d) 10�

12� e) 5�

34�

f) 3�56� g) 4�

18� h) 1�1

11� i) 4�

34� j) 7�1

90�

3 a) 5�12� b) 2�

25� c) 1�

57� d) 4�

27� e) 1�

79�

f) 2�12� g) 1�

45� h) 3�

34� i) 4�

15� j) 3�1

21�

k) 6�23� l) 8�1

10� m) 6�

14� n) 3�

13� o) 1�

23�

3 DecimalsExercise 3.1H

1 a) 8 hundreds b) 8 tenths c) 8 thousandsd) 8 units e) 8 thousandths

2 a) 0.9 b) 8.3 c) 0.07d) 61.23 e) 0.183

3 a) �25� b) 5�1

10� c) 27�

12� d) �

14� e) 1�1

1030�

4 £0.08, £0.12, £0.82, £4.09, £5.79, £13.845 60.1, 8.61, 1.806, 0.816, 0.0686 a) 0.25 litres b) 1.5 litres

c) 0.185 litres d) 0.005 litrese) 2.25 litres

7 a) 120 cm b) 8.4 cm c) 385 cmd) 5.6 cm e) 0.7 cm

8 7.3 cm, 83 mm, 48.1 cm, 0.61 m, 2.08 m9 Check student’s diagrams.

10 a) 0.7 b) 0.5 c) 0.8d) 0.75 e) 0.13

Exercise 3.2H1 a) 13.02 b) 97.55 c) 108.95

d) 24.53 e) 90.76 f) 410.742 a) 13.03 b) 31.74 c) 172.33

d) 9.71 e) 33.91 f) 484.763 a) £6.34 b) £20.01 c) £164.92 d) £70.744 £80.70

5 5.68 m6 5.37 seconds7 a) 1.35 kg b) £2.978 £2.169 a) 14.27 m b) 10.35 m c) 3.32 m

d) 3.93 m e) 11.4 cm10 a) 4.506 kg b) 2.65 kg

c) 0.814 kg or 814 g d) 1.27 litrese) 1.74 litres

11 £7.1112 £5.3013 a) 2.4 b) 1.4 c) 1.5

d) 7.2 e) 0.04 f) 0.56g) 35 h) 24 i) 0.12j) 0.06 k) 0.49 l) 0.04

4 PercentagesExercise 4.1H

1 a) �290� b) �

12

70� c) �2

15� d) 1�1

30�

2 a) 0.18 b) 0.26 c) 0.92 d) 0.08e) 0.42 f) 0.03 g) 0.12 h) 0.01i) 1.7 j) 3.5 k) 0.05 l) 0.145

3 a) 73% b) 28% c) 6%d) 23.5% e) 168%

4 a) 30% b) 80% c) 65%d) 28% e) 45%

5 a) 0.25 b) �12�

c) 0.3 d) 0.5, 30%, �14�

6 a) 0.4 b) �14�

c) 0.1 d) 10%, 0.25, �25�

7 a) (i) 0.5 (ii) �25�

(iii) 0.6 (iv) 0.4, �12�, 60%

b) any 6 sectors shaded

8 a) 0.8 b) �1270�

9 a) 40% b) �290�

Exercise 4.2H1 £21 2 21 kg 3 £10.504 £5600 5 66 6 £1807 £6.84 8 88.8 metres 9 £69.12

10 29 440 11 £87 12 £8.75

Exercise 4.3H1 a) £980 b) £945 c) £1190 d) £8472 a) £156 b) £390 c) £488.80 d) £4163 £16 4804 £3 910 0005

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

Bookcase 180 72 108

Dining table and840 336 504

chairs

Sofa 440 176 264

Display unit 260 104 156



6 £266.407 a) £95.76 b) £114.24

c) £91.56 d) £144.488 a) £329.56 b) £269.64

c) £398.04 d) £132.689 £14 784 10 6912

11 731 000 12 £672

Exercise 4.4H1 8% 2 20% 3 30% 4 4%5 15% 6 16% 7 45% 8 35%9 12.5% 10 2%

5 Mental methods 1Exercise 5.1H

1 32 2 81 3 114 4 895 137 6 35 7 57 8 589 70 10 61 11 88 12 95

13 64 14 85 15 92 16 12817 120 18 131 19 152 20 112

Exercise 5.2H1 30 2 60 3 16 4 195 61 6 24 7 25 8 619 13 10 21 11 64 12 33

13 16 14 68 15 38 16 5917 57 18 67 19 65 20 27

Exercise 5.3H1 75 2 37 3 53 4 235 42 6 32 7 49 8 469 56 10 27

Exercise 5.4H1 6 2 6 3 42 4 425 14 6 32 7 81 8 209 9 10 24 11 54 12 40

13 21 14 24 15 90 16 6417 30 18 35

Exercise 5.5H1 4 2 8 3 4 4 65 7 6 2 7 3 8 69 7 10 8 11 5 12 9

13 8 14 4 15 6 16 617 9 18 10

Exercise 5.6HAccept answers �0.1.

1 4.4 2 6.4 3 8.6 4 3.25 5.1 6 9.1 7 9.8 8 7.19 6.5

Exercise 5.7H1 a) 24 b) 562 c) 81 d) 418

e) 82 f) 128 g) 40 h) 627i) 5 j) 5

2 a) 2.4 b) 8.2 c) 9.5 d) 12.7e) 8.9 f) 12.9 g) 9.6 h) 7.5i) 6.2 j) 2.0

3 a) 2.84 b) 1.62 c) 5.47 d) 5.19e) 1.23 f) 7.38 g) 6.25 h) 7.32i) 7.90 j) 9.60

4 a) 60 b) 400 c) 9000 d) 100e) 9000 f) 50 000 g) 3000 h) 50 000i) 2000 j) 2000

5 £4 000 000

Exercise 5.8H1 �2 2 3 3 2 4 �25 �1 6 7 7 2 8 09 �3 10 3 11 �5 12 �1

13 �1 14 �11 15 �5 16 �717 �1 18 �1 19 �3 20 �2

Exercise 5.9H1 3 2 �1 3 2 4 15 �2 6 �1 7 1 8 09 5 10 �4

Review Exercise 5H1 a) 7097

b) (i) 47 � 53 � 100 (ii) 42 � 29 � 13c) (i) 57 300 (ii) 57 000

2 a) 7085b) (i) 303 (ii) 505c) 400

3 a) 8037 b) 631 c) 19d) (i) 5840 (ii) 5800e) (i) 2596 (ii) 9625f) 50 � 5 � 250

4 a) 6708b) (i) 47 � 53 � 100 (ii) 70 � 24 � 46c) 9752 d) 6 tens or sixtye) 3 hundreds f) 8 units

5 a) (i) £1080 (ii) 12 million poundsb) (i) 27 (ii) 57c) (i) 901 (ii) 987d) 200 � 10 � 2000

6 a) £264 b) £16c) (i) £273 (ii) £298

7 a) 17 � 32 � 49 b) 38 � 9 � 29c) 2 � 42 � 84 d) 9

8 a) 627.8 b) 6278 c) 86

6 Using a calculatorExercise 6.1H

1 a) 18.49 b) 51.84 c) 3136d) 175 561 e) 0.5476 f) 0.6724g) 0.0081 h) 10.24 i) 22.1841j) 4070.44

2 a) 3.8 b) 8.3 c) 1.9d) 14.8 e) 62 f) 0.34g) 0.76 h) 0.18 i) 3.21j) 0.085

3 a) 6.73 b) 8.65 c) 6.63d) 28.76 e) 75.05 f) 0.68g) 0.63 h) 238.42 i) 0.64j) 0.25

4 26.8 cm



Exercise 6.2H1 2.1875 2 2.6 3 24.84 4 5.8405 7.963 6 22.09 7 46.53 8 5.0919 53.36 10 4.347 11 2.626 12 4.309

7 Integers, powers and roots 2Exercise 7.1H

1 2 � 7 2 24

3 22 � 7 4 5 � 75 2 � 3 � 7 6 72

7 22 � 33 8 22 � 3 � 139 32 � 52 10 23 � 53

Exercise 7.2H1 6 � 2 � 3, 8 � 23, HCF � 2, LCM � 242 8 � 23, 18 � 2 � 32, HCF � 2, LCM � 723 15 � 3 � 5, 25 � 52, HCF � 5, LCM � 754 36 � 22 � 32, 48 � 24 � 3, HCF � 12, LCM � 144 5 25 � 52, 55 � 5 � 11, HCF � 5, LCM � 275 6 33 � 3 � 11, 55 � 5 � 11, HCF � 11, LCM � 1657 54 � 2 � 33, 72 � 23 � 32, HCF � 18, LCM � 2168 30 � 2 � 3 � 5, 40 � 23 � 5, HCF � 10,

LCM � 1209 45 � 32 � 5, 63 � 32 � 7, HCF � 9, LCM � 315

10 24 � 23 � 3, 50 � 2 � 52, HCF � 2, LCM � 600

Exercise 7.3H1 6 2 �40 3 12 4 �245 �35 6 �21 7 20 8 �49 �5 10 �5 11 4 12 5

13 �5 14 �8 15 �3 16 �217 �18 18 �3 19 6 20 �15

Exercise 7.4H1 a) 1 b) 169 c) �8 d) �14

e) 27 f) 125 g) 2 h) 32 64 cm3

3 a) 400 b) 1764 c) 26.01d) 3600 e) 0.81

4 a) 343 b) 42.875 c) 830.584d) 8000 e) 1 000 000

5 a) �30 b) �8.66 c) �16.85d) �178 e) �201

6 a) 9 b) 5.24 c) 2.1d) 16.92 e) 46.42

7 8.94 cm

Exercise 7.5H1 a) 26 b) 74 c) 22 � 34 � 53

2 a) 26 b) 38 c) 45 d) 57

3 a) 53 b) 76 c) 22 d) 34

4 a) 26 b) 30 or 1 c) 54 d) 71 or 75 a) (i) 22 � 32 (ii) 72 (iii) 26

(iv) 22 � 52 (v) 22 � 34

b) All indices are even numbers.

6 50 � 2 � 52. Multiply by 27 a) (i) 22 � 3 (ii) 33 (iii) 22 � 3 � 5

(iv) 3 � 52 (v) 24 � 7b) (i) �3 (ii) �3 (iii) �15

(iv) �3 (v) �7


14� b) �

19� c) �6

15�

2 a) 6 b) 10 c) 253 a) 1�

23� b) 2�

14� c) �1

52�

4 a) 0.04 b) 5 c) 0.156 25

8 Fractions, decimals andpercentages

Exercise 8.1H

1 a) 8, �78� b) 99, �1

71� c) 60, �

16�

2 a) �57� b) �

11

15� c) �1

51�

d) �137� e) �

11

06� � �

58� f) �

191� � 1�

29�

g) �122� � �

16� h) �

11

31� � 1�1

21� i) 5�

57�

j) 3�46� � 3�

23� k) 5�1

53� l) 2�

68� � 2�

34�

3 a) �59� b) �

11

02� � �

56� c) �

12

30�

d) �176� e) 1�2

54� f) 1�

1390�

g) �12

14� h) 1�2

40� � 1�

15� i) 1�

1535�

j) 1�16

70� k) �

12

74� l) �

16

90�

4 a) 7�172� b) 5�

29� c) 5�

58�

d) 3�196� e) 6�1

12� f) 4�

1138�

g) 8�14

30� h) �

13

03� i) 8�2

18�

j) 3�172� k) 4�

11

18� l) �

12�


253� b) �

245� c) �

275�

d) �194� e) �

269� f) �

71

30�

g) �389�

2 a) 2�17� b) 3�

13� c) �2

30�

d) 2�181� e) �1

18� f) 24

3 a) �12

01� b) �4

58� c) �

14

45�

d) �56� e) 1�

18� f) �

29

09�

g) �238� h) �1

70� i) �3

72�

j) �22

78� k) 1�

12

75� l) �

19�

4 a) 8�49� b) �

11

15� c) 1�

47�

d) �141� e) 16�

12� f) 1�

13�

g) 5�19� h) 1�

14

94� i) 18�

13�

j) 3�15� k) 13�

29� l) 2�

2236�


11

12� b) �

15

96� c) �2

54� d) 1�2

10�

e) 4�12

10� f) 4�2

21� g) 22�

25� h) 3�

12

91�

2 a) �285� b) �

47� c) �

38�

d) �194� e) �

19�


3 a) 1�23� b) 11�1

73� c) 4�

11

09�

d) 3�59� e) 17�

1137�

4 a) 15�170� cm

b) 12�35� cm2

Exercise 8.4H1 a) 0.875 b) 0.07 c) 0.556 d) 0.1822 a) Terminating. 4 is a multiple of 2 which is a

factor of 10.b) Recurring. 6 is not a factor of 10.c) Recurring. 11 is not a factor of 10.d) Terminating. 25 is a multiple of 5 which is a

factor of 10.e) Terminating. 32 is a multiple of 2 which is a

factor of 10.3 a) 0.029 702 970 ...

b) 4 digits

Exercise 8.5H1 9.5 2 7.9 3 3.5 4 3.55 6.3 6 9.2 7 6.3 8 1.99 11.3 10 11.5 11 0.9 12 3.4

Exercise 8.6H1 a) 2 b) 4.8 c) 2.8 d) 5.4

e) 0.21 f) 0.36 g) 35 h) 32i) 0.07 j) 0.08 k) 0.64 l) 0.04

2 a) 20 b) 24 c) 4 d) 18e) 30 f) 40 g) 30 h) 50i) 80 j) 160 k) 3.1 l) 95

3 a) 5.04 b) 15.08 c) 34.83 d) 20.8e) 125.8 f) 243.2 g) 22.04 h) 36.48i) 20.16 j) 2.403 k) 10.14 l) 17.424

4 a) 59 b) 29.25 c) 26 d) 52e) 47 f) 63 g) 17.6 h) 10.8i) 316 j) 5.7 k) 2.7 l) 6.3

Exercise 8.7H1 a) 1.17 b) 1.3 c) 1.73 d) 1.06

e) 1.01 f) 1.125 g) 2.62 a) 0.87 b) 0.6 c) 0.65 d) 0.92

e) 0.96 f) 0.73 g) 0.8453 £7004 £14 7905 £3926 £42587 £10 352 (to the nearest pound)8 33.8 million9 Jane should choose 3% interest every 6 months.

She will receive £13.66 more (to the nearest penny).10 £34.46 (to the nearest penny)

9 Ratio and proportionExercise 9.1H

1 a) 4 : 3 b) 2 : 5 c) 7 : 11 d) 1 : 3 : 4 e) 3 : 5 : 4

2 a) 2 : 5 b) 1 : 5 c) 12 : 5d) 5 : 2 e) 1 : 6

3 2 : 14 4 : 7 : 95 1 : 2 : 5

Exercise 9.2H1 a) 1 : 5 b) 1 : 6 c) 1 : 4.5

d) 1 : 2.25 e) 1 : 0.6 f) 1 : 20g) 1 : 24 h) 1 : 0.35 i) 1 : 250 000

2 1 : 250 0003 1 : 6

Exercise 9.3H 1 a) 75 cm b) 9 cm2 a) 6 buckets b) 5 buckets3 a) 2.5 kg b) 900 g4 24 cm5 a) 50 km b) 16.5 cm6 480 g7 a) 125 ml b) 80 ml8 a) 10 cm b) 3 cm9 a) 200 ml b) 750 ml

10 a) 6000 votes b) 3000 votes

Exercise 9.4H 1 Paula £15, Tariq £252 a) 4 litres b) 6 litres3 Copper 150 g , iron 200 g, nickel 100 g4 3 hours 30 minutes5 £5206 £2.507 728 a) 3 : 2

b) Iain 126 000 euros, Stephen 84 000 euros

Exercise 9.5H In all these questions either cost per unit or number ofunits per penny can be used.

Both are given in each answer. Where necessary,answers are rounded to 2 decimal places, unlessotherwise indicated.

1 Cost per gram: 80 g bag � 1.24p, 200 g bag � 1.10pGrams per penny: 80 g bag � 0.808 g, 200 g bag � 0.913 g (to 3 d.p.)200 g bag is the better value.

2 Cost per litre: 2 litre bottle � 64.5p, 3 litre bottle � 66.3pLitres per pound: 2 litre bottle � 1.55 litre, 3 litre bottle � 1.51 litre2 litre bottle is the better value.




3 Cost per gram: 200 g tub � 0.48p, 450 g tub � 0.47pGrams per penny: 200 g tub � 2.11 g, 450 g tub � 2.14 g450g tub is the better value.

4 Cost per tub: 4 tubs � 19.75p, 12 tubs � 18.25pTubs per penny: 4 tubs � 0.051,12 tubs � 0.055 (to 3 d.p.)Pack of 12 tubs is the better value.

5 Cost per kilogram: 1.8 kg pack � £1.39, 1.5 kg pack � £1.33Kilograms per pound: 1.8 kg pack � 0.72 kg, 1.5 kg pack � 0.75 kg1.5 kg pack is the better value.

6 Cost per millilitre: 75 ml bottle � 1.59p, 200 ml bottle � 1.45pMillilitres per penny: 75 ml bottle � 0.63 ml,200 ml bottle � 0.69 ml200 ml bottle is the better value.

7 Cost per can: 12 can pack � 35.8p, 20 can pack � 36.25pCans per pound: 12 can pack � 2.79 cans, 20 can pack � 2.76 cans12 can pack is the better value.

8 Cost per gram: 750 g pack � 0.42p, 1.5 kg pack � 0.40p, 2.5 kg pack � 0.28pGrams per penny: 750 g pack � 2.38 g, 1.5 kg pack � 2.50 g, 2.5 kg pack � 3.57 g2.5 kg pack is the best value.

10 Mental methods 2Exercise 10.1H

1 a) 33 b) 62 c) 5.8 d) 201 e) 212 f) 18.4g) 335.3 h) 539 i) 1331j) 9170

2 a) 7 b) 27 c) 9.6d) 11 e) 43 f) 114g) 0.5 h) 167 i) 226j) 1047

3 a) 63 b) 96 c) 154d) 132 e) 40 f) 133g) 240 h) 200 i) 252j) 882

4 a) 6 b) 6 c) 500d) 23 e) 12 f) 6g) 6 h) 0.16 i) 80j) 4

5 a) 4 b) 4 c) 2d) �12 e) �5 f) �6g) 8 h) 20 i) 5j) �4

6 a) �24 b) �20 c) 18d) 40 e) �400 f) �2g) �3 h) 5 i) 7j) �8

7 a) 49 b) 81 c) 144d) 196 e) 1 f) 900g) 40 000 h) 0.25 i) 0.64j) 0.04

8 a) 6 b) 2 c) 8d) 11 e) 12

9 a) 27 b) 64 c) 1000d) 125 000 e) 0.008

10 a) 19.2 cm b) 23 cm2

11 £32.1912 11 cm13 £10.8014 9 and 515 568 g

Exercise 10.2H1 a) 10 b) 40 c) 7

d) 300 e) 1000 f) 0.8g) 0.6 h) 0.05 i) 2000j) 0.01

2 a) 8 b) 20 c) 700d) 8000 e) 100 f) 0.7g) 0.005 h) 0.02 i) 400j) 20 000

3 a) 29 b) 150 c) 7800d) 47 000 e) 21 f) 0.19g) 0.049 h) 0.0036 i) 0.051j) 0.90

4 a) 7.39 b) 24.8 c) 28 500d) 309 e) 16 400 f) 3.92g) 60.7 h) 0.914 i) 0.004 16j) 2.24

5 £66 £20 0007 50 mph8 5 cm9 £120

10 80 cm11 48 cm2 or 50 cm2

12 a) 4200 or 4000 b) 7c) 1200 or 1000 d) 400e) 480 000 or 500 000 f) 0.3g) 0.6 h) 320 000 or 300 000i) 4000 j) 70

Exercise 10.3H1 a) 12� b) 49� c) 144�

d) 7.6� e) 121�2 a) 19� b) 45� c) 48�

d) 126� e) 93 30� cm4 9 : 45 (144� � 25) cm2

Exercise 10.4H1 a) 36 b) 0.009 c) 0.036

d) 0.0025 e) 0.09 f) 400 000g) 150 000 h) 1530 i) 40 600j) 9100

2 a) 15 b) 0.03 c) 0.18d) 7 e) 0.0008 f) 80g) 20 h) 250 i) 5000j) 400



3 a) 75 600 b) 0.45 c) 168d) 0.007 56 e) 4500

4 a) 1800 b) 18 c) 7020d) 0.39 e) 7.02

5 a) 3480 b) 75 168 000 c) 75.168d) 21.6 e) 751.68

11 Algebra 1Exercise 11.1HThe order of letters does not matter when adding.

1 a) 10 b) 6 � w c) m � w2 a) 7 b) x � 3 c) x � y3 a) 11 b) x � 7 c) 4 � x4 a) 8 b) p � 5 c) 3 � q5 a) 2x b) x � 6 c) x � 4 � y6 a) x � y � 2 b) 2x � 5 c) 2x � y7 a) (i) 18 cm (ii) 22 cm

b) w � 6 cm8 x � 59 a) (i) 95p (ii) 83p

b) x � 10 pence10 a) 2c pence b) 4c pence c) 8c pence

Exercise 11.2H1 a) (i) 5 (ii) 13

b) b � 72 a) (i) 50p (ii) 75p

b) c � 20 pence3 a) 10 � a b) b � 4 c) d � c4 a) (i) 6 cm (ii) 10 cm

b) y � 6 cm5 a) (i) £110 (ii) £290

b) £P � 506 a) (i) 22 (ii) 19

b) 24 � s7 a) £65 � x b) £80 � x c) £y � x8 a) (i) 6 cm (ii) 8 cm

b) y 2 cm9 a) (i) 12 � 2r (ii) s � 12 b) 2s � t

10 £x d

12 Algebra 2Exercise 12.1H

1 3a 2 8b 3 6c 4 2d5 7c 6 4c 7 3a 8 5b9 c 10 7a 11 8x 12 6a

13 y 14 5b 15 3p 16 s17 3b 18 0 19 7b 20 7a

Exercise 12.2H1 5a � 3b 2 a � 2b3 5cd 4 5c � 3d5 5a � 3b 6 2p � 3q7 12ab 8 4x � 5y9 5a2 10 9a � 2b � 6c

11 4a 12 2ab � 4a2

13 3a � 2b 14 b2

15 s � 5 16 4b17 2ab2 18 x � 4y � 719 3a � b 20 12a2b2

13 Algebra 3Exercise 13.1H

1 21a � 42b 2 10c � 15d3 12e � 20f 4 21g � 6h5 12i � 6j � 9k 6 15m � 6n � 9p7 24r � 18s � 12t 8 32r � 16s � 8t9 12u � 20v 10 24w � 18x

11 10y � 2z 12 12y � 8z13 15v � 10 14 21 � 12w15 5 � 15a 16 24g � 15

Exercise 13.2H

1 a) 18a � 23 b) 26b � 18 c) 26 � 40c2 a) 23x � 4 b) 27y � 2 c) 18 � 11z3 a) 26s � 27t b) 18v � 19w

c) 24x � 36y d) 16v � 11w4 a) 18n � 5p b) 22q � 3r

c) 36d � 4e d) 27f � 4ge) 8h � 6j f) 14k � 9m

Exercise 13.3H1 a) 4(2x � 5) b) 3(x � 2)

c) 3(3x � 4) d) 5(x � 6)2 a) 8(2 � x) b) 3(3 � 5x)

c) 4(3 � 4x) d) 4(2 � 3x)3 a) 4x(x � 4) b) 6x(x � 5)

c) 4x(2x � 5) d) 3x(3x � 5)

Exercise 13.4H1 a) a2 � 8a � 15 b) b2 � 6b � 8

c) 12 � 7c � c2

2 a) 8d2 � 6d � 9 b) 15e2 � 2e � 8c) 6 � f � 40f 2

3 a) 15g2 � 28g � 12 b) 12h2 � 43h � 35c) 15j2 � 58j � 48

4 a) 12k2 � 13k � 35 b) 6 � 5m � 56m2

c) 8 � 14n � 15n2

5 a) 6 � p � 35p2 b) 10r2 � 37r � 30c) 12s2 � 35s � 18

Exercise 13.5H1 a) 75 b) 35 c) 26

2 a) d7 b) m6 c) t7

3 a) a4b2 b) c4d5 c) r3s2t4

4 a) 36xyz b) 24abc c) 120r2s2t

14 Formulae 1Exercise 14.1H

1 a) 400 b) 300 c) 340 d) 2702 a) 20 cm b) 52 cm c) 26 cm d) 32.8 cm3 a) 40p b) 35p c) 65p d) £1.184 a) 4 b) 11 c) 16 d) 25



5 a) 80 minutes b) 320 minutesc) 220 minutes d) 128 minutes

6 a) 12 m2 b) 49 m2 c) 15 m2 d) 27 m2

7 a) £80 b) £170 c) £830 d) £4008 a) 14 b) 31 c) 48 d) 879 a) £4 b) £100 c) £16 d) £7

10 a) 16 km b) 24 km c) 160 km d) 70.4 km

Exercise 14.2H1 s � 20r 2 p � 4l 3 c � �

a

2�

4 e � �5

s� 5 t � 40w 6 a � lw

7 c � 30 � 2m

In questions 8 to 10, the letters used in the formulae mayvary.8 e � 3w � d e stands for the number of points

earned.w stands for the number of matcheswon.d stands for the number of matchesdrawn.

9 p � �1

d

.5� p stands for the number of pounds.

d stands for the number of dollars.

10 k � �8

5

m� k stands for the number of kilometres.

m stands for the number of miles.

Exercise 14.3H1 a) 6 b) 2 c) 8 d) 28

e) 10 f) 16 g) 8 h) 16i) 24 j) 10 k) 10 l) 28m) 4 n) 20 o) 48 p) 24q) 32 r) 8 s) 2 t) 5u) �2 v) 1 w) 4 x) 0.5

2 a) C � 12 b) C � 42 c) C � 62d) C � 102 e) C � 4.5

3 a) P � 4 b) P � 1 c) P � 11d) P � �7

4 a) X � 3 b) X � 16 c) X � 12d) X � 350 e) X � 15.5

5 a) 5 b) 15 c) 6d) �1 e) 24

Review Exercise 14H1 £12 5002 a) £45.00 b) £32.003 a) £50.00 b) 13 hours4 a) £104.00 b) 15 hours5 a) £214.25 b) 8 hours

15 Formulae 2Exercise 15.1H

1 £212 a) (i) £140 (ii) £210

b) C � 60 � n

3 a) (i) £180 (ii) £240b) C � 80 � 20h

4 a) 17 cm b) P � 2(x � y)

5 a) V � 28 cm3 b) V � �A

3

h�

6 a) 7 minutes b) T � �w

r�

7 a) t � �d

s� b) 3.5 hours

8 C � 26.69 cm9 a) £2.50 b) A � 1 � 0.5n

10 a) A � 2.5 b) B � 7c) C � 8 d) D � 12e) E � 47 f) F � 0.5

Exercise 15.2H

1 a) b � a � c b) x � �a �

3

y�

c) t � �a �

c

b� d) q � �

F

2� � p

e) y � �x �

2

3z� f) n � �

5P

4

� 3�

2 d � �C

��

3 a) a � �2

3

n

b

A� b) n � �

3

2

a

A

b�

4 a � �P

2� � b

5 m � �y �

x

c�

6 r � ��4

A

��

7 a) V � 34.4 (to 1 d.p.)

b) (i) r � ��

4V

h�� (ii) r � 3.6 (to 1 d.p.)

8 h � �2

S

�r� � r

16 Sequences 1Exercise 16.1H

1 a) 3, 8, 13, 18 b) �5, �3, �1, 1c) 23, 18, 13, 8 d) 60, 35, 10, �15e) �17, �11, �5, 1 f) �1, ��

12�, 0, �

12�

2 a) 43, 50; rule �7 b) 43, 49; rule �6c) 57, 65; rule �8 d) 58, 67; rule �9e) 46, 51; rule �5 f) 65, 72; rule �7

3 a) 5, �1; rule �6 b) �3, �10; rule �7c) �4, �9; rule �5 d) �7, �13; rule �6e) �5, �13; rule �8 f) �10, �23; rule �13

4 a) 13, 31; rule �6 b) 23, 59; rule �12 c) 76, 58; rule �9 d) 91, 75; rule �4e) 37, 52; rule �15 f) 27, �1; rule �7



Exercise 16.2H1 a) b)

c) d)

2 a)

b)

c)

d)

Exercise 16.3H1 a) 28 b) subtract 92 a) 24 b)

3 a) 39, 46 b)

4 7, –35 �1, 2, 7

6 a) 23 b)

7

8 a) 3b) divide previous term by 2

17 Sequences 2Exercise 17.1H

1 a) 199b) Multiply the pattern number by 2 then

subtract 12 a)

b) They go up by 2 each time.c) 105

3 a)

b) 72. The rectangle will have 8 columns and 8 � 1 � 9 rows.

4 a) 7 � 1 � 10 � 7 � 10 � �3b) 4, 11, 18, 25

5 a) 10, 20, 30, 40 b) 10, 18, 26, 346 a) 1, 4, 9, 16, 25 b) 2, 8, 18, 32, 50

c) 5, 20, 45, 80, 1257 3, 9, 27, 81, 2438 12, 7, 2, �3

9 For example

and so on.

10 For example

and so on.

Exercise 17.2H1 a) 3n � 7 b) n � 1 c) 2n � 52 a) 30 � 5n b) 6 � 2n c) 4 � n3 a) Not linear b) Linear: 14, 17

c) Not linear d) Linear: �8, �12

rule�2

rule �5

rule �3rule�4

rule �3

rule �4

rule �6

rule �8

Pattern number 1 2 3 4 5

Number of matchsticks 7 9 11 13 15



4 a) 100, 200, 300, 400, 500b) 100n � 1

5 a)

b) 25n � 3c) 5

6 a) 1, 4, 9, 16, 25 b) n2 � 17 18308 a) 2, 4, 8, 16, 32 b) Powers of 29 a) 1, 8, 27, 64, 125

b) n3 � 2c) 1002

10 a) n(n � 1) b) n(2n � 1) c) 2n(2n � 1)

18 CoordinatesExercise 18.1H

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

2

Exercise 18.2H1 A(2, 4), B(4, �2), C(�4, �2), D(�4, 0),

E(�2, 2), F(3, �4), G(5, 1), H(�3, 4), I(0, �3), J(�1, �4)

2

Rectangle

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

A

B

D

C

0 1

1

2

3

4

5

6

7

8

y

x2 3 4 5 6 7 8

E

D

C

A

B

3

Right-angled triangle4

Parallelogram5

Trapezium6

D(�3, 3)

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

A

B

D

C

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

A

BC

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

A

B

D

C

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

A

B

D

C

Number of shirts 1 2 3

Cost in £ 28 53 78



7

C(1, �3)

8

D(�5, 2)

9

D is (�4, �3)

Exercise 18.3H1 a) y � 4 b) x � 3

c) y � �3 d) x � �12

3

4

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

A

BD

C

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

B

C

A

D

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

B

C

A

D

Graph for questions 2, 3 and 4

5 (4�12�, �

12�)

6

7

Graph for questions 6 and 7

8 (3, 3)

19 Solving equationsExercise 19.1H

1 x � 17 2 x � 8 3 y � 54 x � 11 5 p � 6 6 x � 17 x � 6 8 y � 8 9 x � �3

10 x � 8 11 x � 8 12 x � 0

Exercise 19.2 H1 x � 6 2 x � �3 3 x � 34 x � 4 5 x � 4 6 x � 147 x � 16 8 x � 4 9 x � 2

10 x � 1 11 x � 5 12 x � 1

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

x � y � 5

y � x � 2

y � x � 4

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

6

y

x2 3 4 5 6y � 6 � x

y � 6 � x

y � 2x � 3

x �3 �2 �1 0 1 2 3

y �1 �0 �1 2 3 4 5

x �3 �2 �1 �0 �1 �2 �3 4 5

y �7 �6 �5 �4 �3 �2 �1 0 1

x �1 0 1 2 3 4 5 �6

y �6 5 4 3 2 1 0 �1

x �2 �1 �0 �1 2 3 4 5

y �7 �5 �3 �1 1 3 5 7

x �2 �1 0 1 2 3 4 5 6 �7

y �8 �7 6 5 4 3 2 1 0 �1



Exercise 19.3H1 x � 28 2 a � 18 3 p � 494 y � 48 5 x � 36 6 x � 247 x � 21 8 x � 25 9 x � 6

10 x � 9 11 x � 27 12 x � 80

Exercise 19.4H1 x � 3 � 8, Robbie’s number is 52 3x � 15, Patsy’s number is 53 4c � 64, one chocolate biscuit costs 16p4 x � 16 � 34, Sonia has 18 CDs5 x � 6 � 7, Joy had 13 pens at the start

20 Equations and inequalitiesExercise 20.1H

1 x � 5 2 x � 3 3 x � 64 x � 3 5 x � 4 6 x � 57 x � 2 8 x � 1.5 9 x � 8.5

10 x � �1 11 x � �4 12 x � �313 y � �9 14 x � 3 15 x = �1.5

Exercise 20.2H1 x � 8 2 x � 3 3 x � 74 x � 2 5 x � 5 6 x � 27 x � 8 8 x � 3 9 x � 11

10 x � 1.5 11 x � 3 12 x � 313 x � 5.5 14 x � 4.5 15 x � 3.5


10 x � 3 11 x � 4.5 12 x � 513 x � 2 14 x � 2 15 x � �3


10 x � �4

Exercise 20.5H1 a) 10 b) 30 c) x � 18.1252 a) (i) 60 (ii) 120

(iii) 92.736 (iv) 99.123(v) 95.894 625

b) x � 4.63 x � 2.24 a) 23 � 3 � 2 � 14

33 � 3 � 3 � 36b) x � 2.8

5 a) 43 � 2 � 4 � 5653 � 2 � 5 � 115

b) x � 4.36 x � 4.47 x � 3.838 x � 3.79

9 a) x � x2 � 1000 b) x � 31.110 x � 8.47

Exercise 20.6H1 x 3

2 x � 2

3 x � 3

4 x 2.5

5 x � 2

6 x � 4 7 x � 3 8 x � 39 x � �4 10 x 5 11 x 6

12 x 2.5 13 x 5 14 x 315 x � 2

21 Further graphsExercise 21.1H

1 Three points plotted, e.g. (�3, �9), (0, 0), (3, 9),straight line drawn through them.

2 Three points plotted, e.g. (�4, �2), (0, 2), (2, 4),straight line drawn through them.

3 Three points plotted, e.g. (�3, �10), (0, 2), (3, 14), straight line drawn through them.

4 Three points plotted, e.g. (�1, �7), (0, �5), (5, 5), straight line drawn through them.

5 Three points plotted, e.g. (�4, 4) (0, �4), (2, �8), straight line drawn through them.

Exercise 21.2H1 Three points plotted, e.g. (�3, 0), (0, 2), (3, 4),

straight line drawn through them.2 Straight line joining (0, 2) and (5, 0).3 Straight line joining (0, 7.5) and (5, 0).4 Three points plotted, e.g. (�2, �9), (0, �4),

(4, 6), straight line drawn through them.5 Straight line joining (0, 6) and (8, 0).

Exercise 21.3H1 a) 16 gallons b) 20 minutes

c) 4 gallons/minute d) 8 gallons/minutee) Simon lets out 9 gallons of water over

1.5 minutes, then adds another 9 gallons over 2 minutes

f) 6 gallons/minute

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



2 a) £600b) £1.20c)

d) £3800e) £1.09 (to the nearest penny)

3 a) Accept 20–21 minutesb) 50 kilometresc) 22 kilometresd) Accept 2.5–3 minutese) Between about 16 and 18 minutes

4 a) E b) C c) B d) G5 a) £5

b) £57.50c)

d) 185 minutese) Plan A by £5

6

Exercise 21.4H1 a) Quadratic, �-shaped

b) Not quadraticc) Quadratic, �-shapedd) Quadratic �-shapede) Not quadraticf) Not quadraticg) Quadratic, �-shapedh) Quadratic �-shaped

2 a)

b)

c) (i) y � 6.5(ii) x � �2.5 or x � 2.5

�3 �2 �1 0

123456789

101112131415161718

y

y � 2x2

x1 2 3

0 50

10

20

30

40

50

60

100 150 200 250 300

Total number of minutes for calls per month

Plan APlan B

Tota

l cos

t (£)

0 1000

1000

2000

3000

4000

5000

6000

2000 3000 4000 5000 6000

Number of programmes

Cha

rge

in p

ound

s (£

)

Time after gates opened

Num

ber

of p

eopl

e in

the

grou

nd

0

100020003000400050006000700080009000

100001100012000130001400015000

30 60 90 120 150 180 210

x �3 �2 �1 0 1 2 3

x2 9 4 1 0 1 4 9

y � 2x2 18 8 2 0 2 8 18



3 a)

b)

c) (i) y � 4.2(ii) x � �3.4 or x � 2.4

4 a)

b)

c) (i) y � 1.8 (ii) x � �1.6 or x � 2.6

�3 �2 �1 0

123456789

1011121314

y

y � x2 � x � 2

x1 2 3 4

�3�4 �2 �1 0

1

�1

23456789

101112

y

y � x2 � x

x1 2 3

5 a)

b)

c) (i) y � �5.8(ii) x � �3.5 to �3.4 or x � 1.4 to 1.5

6 a)

b)

c) (i) y � 7.75(ii) x � �3.2 to �3.1 or x � 3.1 to 3.2

�3 �2 �1 0

1

�1

2345678y

y � 8 � x2

x1 2 3

x �4 �3 �2 �1 0 1 2 3

x2 16 9 4 1 0 1 4 9

y � x2 � x 12 6 2 0 0 2 6 12

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

2 2 2 2 2 2 2 2 2

y � x2 � x � 2 14 8 4 2 2 4 8 14

x �5 �4 �3 �2 �1 0 1 2 3

x2 25 16 9 4 1 0 1 4 9

2x �10 �8 �6 �4 �2 0 2 4 6

�5 �5 �5 �5 �5 �5 �5 �5 �5 �5

y � x2 � 2x � 5 10 3 �2 �5 �6 �5 �2 3 10

x �3 �2 �1 0 1 2 3

8 8 8 8 8 8 8 8

�x2 �9 �4 �1 0 �1 �4 �9

y � 8 � x2 �1 4 7 8 7 4 �1

�3�4�5 �2 �1 0

1

�1�2�3�4�5�6

23456789

1011

y

x1 2 3

y � x2 � 2x � 5



7 a)

b)

c) (i) y � �2.25 (ii) y � �1.7 or y � 2.7

8 a)

b)

c) (i) x � 0.4 or x � 2.6(ii) x � �1.7 or x � 4.7

22 Angles, points and linesExercise 22.1H

1 a) 168° b) 25° c) 90° d) 45° e) 295°2 a) Obtuse b) Acute c) Obtuse

d) Reflex e) Right angle f) Reflexg) Acute h) Obtuse

�3 �2 �1 0

1

�1�2

23456789

10y

y � (x � 2)(x � 1)

x1 2 3 4

�2 �1 0

1

�1

23456789

101112

y

y � x2 � 3x � 2

x1 2 3 4 5

3 a) Acute b) Obtuse c) Right angled) Reflex e) Acute f) Obtuseg) Reflex h) Obtuse i) Reflexj) Acute

Exercise 22.2Ha � 140° b � 105° c � 54° d � 85°e � 40° f � 72° g � 40° h � 35°i � 32° j � 35°

Exercise 22.3Ha � 345° b � 140° c � 125° d � 179°e � 133° f � 155° g � 63° h � 90°i � 134° j � 90°

Exercise 22.4H1 a � 125° Vertically opposite angles are equal.

b � 55° Vertically opposite angles are equal orAngles on a straight line add up to 180°or Angles around a point add up to360°.

2 c � 30° Vertically opposite angles are equal.d � 150° Vertically opposite angles are equal or

Angles on a straight line add up to 180°or Angles around a point add up to360°.

3 e � 137° Vertically opposite angles are equal.f � 43° Angles on a straight line add up to 180°.g � 43° Vertically opposite angles are equal or


4 h � 59° Vertically opposite angles are equal.i � 121° Angles on a straight line add up to 180°.j � 121° Vertically opposite angles are equal or


5 k � 82° Vertically opposite angles are equal.m � 98° Angles on a straight line add up to 180°.n � 98° Vertically opposite angles are equal or


6 p � 175° Angles on a straight line add up to 180°.q � 175° Vertically opposite angles are equal or

Angles on a straight line add up to 180°.r � 5° Vertically opposite angles are equal or


7 s � 31° Vertically opposite angles are equal andA right angle is 90°.

8 t � 90° Vertically opposite angles are equal.u � 53° Vertically opposite angles are equal or

Angles on a straight line add up to 180°.v � 37° Vertically opposite angles are equal or


x �3 �2 �1 0 1 2 3 4

x � 2 �5 �4 �3 �2 �1 0 1 2

x � 1 �2 �1 0 1 2 3 4 5

y � (x � 2)(x � 1) 10 4 0 �2 �2 0 4 10

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

�2 2 2 2 2 2 2 2 2

y � x2 � 3x � 2 12 6 2 0 0 2 6 12



9 w � 60° Vertically opposite angles are equal.x � 70° Vertically opposite angles are equal or

Angles on a straight line add up to 180°.y � 50° Vertically opposite angles are equal or


10 z � 120° Angles around a point add up to 360°.

Review Exercise 22H1 a) CE b) CF2 a) AB

b) e.g.

3

4

23 Triangles, quadrilaterals andcuboids

Exercise 23.1H1 a � 75°, b � 37°, c � 35°, d � 70°2 Check students’ sketches.

PRQ � 72°3 x � 111°4 a) Isosceles

b) x � 43°, y � 43°5 a � 40°, b � 115°

A

BC

O

CD

A

E

B

Q

R

P

Exercise 23.2H1 a) and b) are congruent2 B, F and H3 30°4 70°, 70°, 40°5

6 a) Equal (or the same size)b) Equal (or the same size)

Exercise 23.3H1

2 A � kite, B � square, C � rectangle, D � square, E � rectangle, F � kite, G � parallelogram

3 a) Kiteb) One pair of opposite angles are equal or

diagonals cross at right angles.4

5 Square, rectangle, parallelogram, rhombus

Exercise 23.4H1 B and D will not make an open box.2 A cuboid. The edges are different lengths.3

10 cm

10 cm

12 cm12 cm

15 cm

15 cm

10 cm

10 cm

15 cm

A B

D C

Shape All sides Opposite All anglesequal sides parallel right angles

A � � �

B � � �

C � � �

D � � �

E � � �

F � � �

G � � �



Exercise 23.5H1 2

3 4

5 6

24 Circles and polygonsExercise 24.1H

1 a) circumference b) diameterc) radius

2 a) pentagonb) (regular) hexagon c) rhombus or quadrilateral

3 60° 4 5.9 cm5 4.1 cm 6 E, F, A, G7 Check students’ diagrams8 Check students’ diagrams

25 Interpreting graphsExercise 25.1H

1 a) 183 cm b) 8.2 feet c) 30 cm2 a) 40 ha b) 112 acres c) 2.5 acres

Exercise 25.2H1 a) £15 000

b) (i) £9000 (ii) £1600c) Year 4 May

2 a) 03:00b) 38°Cc) Every 3 hoursd) Don’t know the temperatures in between.

3 a) 27 seconds b) 94°C c) 19°C

Exercise 25.3H1 Stage 1: Climbing hill

Stage 2: Resting

Stage 3: Walking on a levelStage 4: Walking down hill

2 a) Jasbir b) Jasbirc) Jasbir overtakes Robert.

3 a) 17:00b) B, 75 miles from St Pancrasc) 1737, 60 miles from St Pancras

4 a) 50 miles b) 66 minutesc) Before because the gradient is greater.d)

26 Properties of shapesExercise 26.1H

1 a � 60° Corresponding angles.2 b � 75° Allied angles.3 c � 65° Alternate angles.4 d � 49° Corresponding angles.

e � 49° Alternate or opposite angles.5 f � 60° Allied angles.

g � 120° Alternate angles or Angles on a straightline add up to 180°.

6 h � 100° Corresponding angles.i � 80° Allied angles or Angles on a straight line

add up to 180°.7 j � 60° Alternate angles.

k � 120° Angles on a straight line add up to 180°.8 l � 118° Corresponding angles.

m � 62° Allied angles.n � 118° Alternate angles.

9 o � 40° Alternate angles.p � 47° Allied angles.

10 q � 35° Corresponding angles.r � 55° Angles in a triangle add up to 180°.s � 55° Corresponding angles or Angles in a

triangle add up to 180°.

Exercise 26.2H1 a � 20° Angles in a triangle add up to 180°.2 b � 27° Angles in a triangle add up to 180°.3 c � 25° Angles in a triangle add up to 180°.4 d � 45° Angles in an isosceles triangle.5 e � 79° Exterior angle of a triangle equals the

sum of the opposite interior angles.

TimeD

ista

nce

(in

mile

s) fr

om S

wan

sea

0

20

40

60

80

100

120

10:00 11:00 12:00 13:00 14:00



6 f � 160° Exterior angle of a triangle equals thesum of the opposite interior angles.

7 g � 132° Exterior angle of a triangle equals thesum of the opposite interior angles.

h � 48° Angles on a straight line add up to 180°.

8 i � 75° Angles in a quadrilateral add up to 360°.

9 j � 115° Angles in a quadrilateral add up to 360°.

k � 65° Angles on a straight line add up to 180°.

10 l � 115° Angles on a straight line add up to 180°.

m � 136° Angles in a quadrilateral add up to 360°.

Exercise 26.3H1 A Parallelogram B Rectangle

C Trapezium (isosceles) D KiteE Trapezium F SquareG Parallelogram H SquareI Rhombus J Arrow head

2 a) Square, rectangleb) Rectangle, parallelogram, square,

rhombusc) Rectangle, square, isosceles trapeziumd) Rectangle, parallelogram, square, rhombus,

trapeziume) Square, rectangle, parallelogram,

rhombus

3 a)

Square

b)

Rectangle

0 1

1

2

3

4

y

x2 3 4 5

0 1

1

2

3

4

5

y

x2 3 4

c)

Parallelogram

d)

Trapezium (isosceles)4 All sides are equal length.5 Parallelogram

Exercise 26.4H1 1260°2 1980°3 a) 47.5°

b) 87°, 130°, 143°, 95°, 132.5°, 132.5°4 a) 58°

b) 10°, 100°, 23°, 105°, 122°5 e � 20°, i � 160°6 e � 15°, i � 165°7 308 45

27 Constructions 1Exercise 27.1H

1 a) 10 cm b) 2.5 cm c) 6.2 cmd) 3.8 cm e) 7.3 cm

2 a) 4.4 cm b) 5.7 cm3 a) 3 cm, 4 cm, 5 cm

b) 5.4 cm, 4.5 cm, 2.3 cm, 1.7 cm

80°

100° 80°

100°

0 1

1

2

3

4

5

y

x2 3 4 5 6 7 8

0 1

1

2

3

4

5

6

7

y

x2 3



Exercise 27.2Ha � 40°, b � 25°, c � 57°, d � 73°, e � 135°, f � 158°, g � 102°, h � 240°, i � 325°, j � 198°

Exercise 27.3HCheck students’ drawings.

Exercise 27.4HCheck students’ diagrams.

1 a) BC � 3.1 cm, angle ABC � 89°, angle BCA � 53°

b) LN � 11.2 cm, angle LNM � 18°, angle NLM � 15°

c) BC � 6.8 cm, angle BCA � 84°, angle ABC � 38°

2 a) Angle PRQ � 67°, QR � 5.6 cm, PR � 5.2 cm

b) Angle ACB � 53°, AC � 3.1 cm, BC � 6.7 cm

c) Angle YXZ � 70°, XY � 6.4 cm, XZ � 4.7 cm

Exercise 27.5H1 a) Angle QPR � 57°, angle PQR � 44°,

angle QRP � 78°b) Angle HGI � 104°, angle GHI � 29°,

angle GIH � 47°c) Angle BAC � 59°, angle ABC � 68°,

angle BCA � 53°2 a) LN � 5.7 cm, angle LNM � 51°,

angle LMN � 39°b) EF � 5.8 cm, angle EFD � 34°,

angle EDF � 46°c) XZ � 11.6 cm, angle XZY � 35°,

angle XYZ � 103°

Exercise 27.6H1 a) 30 m b) 80 km

c) 15 miles d) 14 m2 Lines of length

a) 6 cm b) 4 cmc) 9 cm d) 4.5 cm

3 a) 4 m by 3 mb)

c) 2 cm by 3.5 cm4 a) (i) 40 km (ii) 77 km

(iii) 51 km (iv) 106 km(v) 28 km (vi) 50 km

b) 66 cm

Exercise 27.7H1

2 Check students’ diagrams.3 a) Check students’ diagrams.

b) 1100 m or 1.1 kmc) 260°

28 Constructions 2Exercise 28.1HDiagrams are not full size. Measurements given arecorrect for the suggested scale.1

2 Scale 1 cm � 1 mile

3

4 Scale 1 cm � 1 m

5

3 cm

D 5 cm

5 cm

C

A B

5 cm

6 cm

8 cm

F

6 cm6 cm

B

6 cmA C

3 cm

Home

7 cmA B

Item Length (m) Width (m)

Bed 2 1

Wardrobe 1.5 0.75

Desk 1.5 0.5

Bookcase 0.75 0.25

Drawers 1.25 0.5

French Gym Maths Science English

055° 110° 195° 280° 330°

40 m 75 m 15 m 60 m 20 m



6

7

8



Exercise 28.2HDiagrams are not full size. Measurements given arecorrect for the suggested scale.

1

4 cmP

6 cm

Hedge

Zeke

4 cm

3 cm3.125 cm

4 cm

2.5 cm

2.5 cm

3 cm

40°

40°

S 7 cm

5 cm

R

P Q


3

4

5 Scale 1 cm � 5 km

6

7

5 cm

Locus

7 cm

P Q

3 cm

3 cm

6 cm

6 cm

3 cm

4 cmA B

2 cm

2 cm

P Q

R

X40° 35°

6 cm

5 cm

3 cm

BA

4 cm

3 cm

5 cm1 cm1 cm

1 cm1 cm



8 Scale 1 cm � 5 km


10

29 Transformations 1Exercise 29.1H

1 a)

b)

c)

2 a) 2b) 1c) 0

3

4 Equilateral

5

6 cm

8 cm7 cm

10 cm

LocusE F

G

D C

A B

2 cm

5 cm

1.5 cm

3 cm

D E

C5 cm

5 cm

4 cm

6

7 Check students’ diagrams.8 a)

b)

c)

Exercise 29.2H1 a) 2 b) 2 c) 4 d) 12 5, 53 Check students’ diagrams.4 5

6 Check students’ diagrams.7

8

9 Check students’ diagrams.



Exercise 29.3H1 a)

b)

c)

d)

e)

2 a)

b)

c)

3

4

5 a) 180° b) 90° anticlockwise6 a) 60° b) 240°7 a) B, D, F b) C, E

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

B A

C

�5 �4 �3 �2 �1 0 1

1

�1

�2

�3

�4

�5

2

3

4

5

y

x2 3 4 5

mirrorline

A

B

C



30 Transformations 2Exercise 30.1H

1

2

3 a)

b)

c)

4 a) A reflection in the line y � 2b) A reflection in the line y � xc) A reflection in the line x � 3.5

5 a) A reflection in the line y � 0.5b) A reflection in the line y � �xc) A reflection in the line y � 1.5

�3 �2 �1 0 1

1

�1

�2

�3

2

3

y

x2 3

D

A B

C

�2 0

�2

2

4

y

x2 4

A

DC

B

Exercise 30.2H1

2

3

4

5

6

7 a) A rotation of 180° about the originb) A rotation of 90° clockwise about (2, 1)c) A rotation of 90° clockwise about (1, 0)

150°A

O

C

�4 �2 0

�2

�4

2

4

y

x2 4

B

D

AC

�3 �2 �1 0

B

1

1

�1

�2

�3

2

3

y

x2 3D

C

A

�3 �2 �1 0 1

1

�1

�2

�3

2

3

4

y

x2 3 4

B

D

A

C



8 a) A rotation of 90° clockwise (�2, 2)b) A rotation of 90° (anticlockwise) about the

originc) A rotation of 180° about (0, 2)

9 A rotation of 120° about the point P10 a) A rotation of 90° (anticlockwise) about the

originb) A reflection in the line x � 2c) A rotation of 180° about (1, 0)d) A rotation of 90° clockwise about (1, �1)e) A reflection in the line y � �1

Exercise 30.3H1

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 reflection in the line x � �1c) A rotation of 90° (anticlockwise) about the

origin

d) A translation by vector � �e) A rotation of 180° about the point (1, 2)

2�3

1�2

�6�2

�1�2

3�3

50

�3 �2 �1 0 1

1

�1

�2

�3

2

3

4

5

y

x2 3 4 5

C

A

B

D

�2 0

�2

2

4

6

y

x2 4 6

D

A

B

C

f) A translation by vector � �g) A rotation of 180° about the point (3, 1)

h) A translation by vector � �31 EnlargementsExercise 31.1H

1 a)

b)

c)

d)

e)

2 a) 4 b) 3 c) 3 d) 23 a) No: the width of the smaller square has been

enlarged by scale factor 2, the length has not.b) No: the width of the shape has been enlarged by

scale factor 3, the length by scale factor 2.

03

�30



Exercise 31.2H1 a)

b)

c)

0 1

1

2

3

4

5

6

7

8

9

2 3 4 5 6 7 8 9 10 11 12

0 1

1

2

3

4

5

6

7

8

9

2 3 4 5 6 7 8 9 10 11 12

0 1

1

2

3

4

5

6

7

8

9

2 3 4 5 6 7 8 9 10 11 12

d)

e)

2 a) (i) 3 (ii) (1, 1)b) (i) 2 (ii) (�1, 4)c) (i) 2 (ii) (5, 5)d) (i) 3 (ii) (9, 5)e) (i) 4 (ii) (5, 8)

Exercise 31.3H1 a), b)

c) An enlargement with scale factor 3, centre theorigin

0 1

1

2

3

4

5

6

7

8

9

2 3 4 5 6 7 8 9 10 11 12

B

A

0

2

4

6

y

x2 4 6

0 1

1

2

3

4

5

6

7

8

9

2 3 4 5 6 7 8 9 10 11 12



2 a), b)

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

3 a), b)

c) An enlargement with scale factor �25�, centre the

origin4 a), b)

c) An enlargement with scale factor �13�, centre (1, 2)

5 a) An enlargement with scale factor 2, centre theorigin

b) An enlargement with scale factor �12�, centre the

originc) An enlargement with scale factor 3, centre

(0, 3)d) An enlargement scale factor �

13�, centre (0, 3)

6 a) An enlargement with scale factor �12�, centre the

originb) A reflection in the line y � xc) A reflection in the line x � 0d) A rotation of 180° about the origine) An enlargement with scale factor 3, centre

(0, �1)

A

B

0

2

4

6

y

x2 4 6

B

0

2

4

6

1

3

5

7

y

x2 4 61 3 5 7

A

B

0

2

4

6

8

1

3

5

7

y

x2 4 6 81 3 5 7

A

7

8

32 Measures 1Exercise 32.1H

1 a) 3 cm b) 7 cm c) 8.5 cm2 3.6 kg3 a) �8°C b) 23°C4 5.5 cm5 6.7 cm

Exercise 32.2H1 a) 200 cm b) 350 cm c) 2 cm

d) 1500 cm e) 4.5 cm2 a) 20 mm b) 55 mm c) 100 mm

d) 2000 mm e) 3500 mm3 a) 2000 g b) 5000 g c) 6350 g

d) 800 g e) 525 g4 500 ml, 1.2 litres, 2 litres, 2500 ml, 800 cl5 a) centimetres b) metres

c) centimetres or metresd) kilometres e) kilometres

6 160 g, 0.8 kg, 1.2 kg, 1500 g, 2000 g7 a) 2000 ml b) 3500 ml c) 20 ml

d) 150 ml e) 345 ml8 a) 85 mm, 45 cm, 1.2 m

b) (i) 1735 mm(ii) 173.5 cm(iii) 1.735 m

Exercise 32.3H1 a) 180 cm � 1.8 m b) 56 km

c) 6 kg d) 20 kge) 8 litres

�4 �2 0

�2

�4

2

4

y

x2 4

C

B

E

DA

�4 �2 0

�2

�4

2

4

y

x2 4

C

B

AD



2 a) 15 miles b) 200 inchesc) 11 lb d) 21 pintse) 8 inches

3 500 g4 50 cm

5 3�12� pints

6 160 cm7 a) 8.4 lb b) 32 litres8 48 km

Exercise 32.4H1 a) Check students’ answers.

b) 70 cm (accept 60–80 cm)c) 200 g (accept 150–300 g)d) 12 litres (accept 10–15 litres)e) 5 km (accept 3–8 km)

2 Approximately 5–6 m3 Approximately 4 m4 320 cm � 3.2 m5 a) It is too accurate. b) 1 km or 1.1 km

33 Measures 2Exercise 33.1H

1 a) 250 mm b) 2400 cm c) 13.6 mmd) 151 mm e) 235 mm

2 a) 20 000 cm2 b) 300 mm2 c) 11 200 cm2

d) 5 mm2 e) 2 000 000 mm2

3 a) 80 cm2 b) 840 cm2

c) 200 m2 d) 1800 m2

e) 6.4 m2

4 a) 32 000 mm3 b) 24 000 000 cm3

c) 5200 mm3 d) 420 000 cm3

e) 20 mm3

5 a) 5.2 m3 b) 270 cm3

c) 0.000 21 m3 d) 8 400 000 000 mm3

e) 0.17 cm3

6 a) 36 000 cm3 b) 6.3 litresc) 1400 ml d) 0.061 litrese) 5.4 litres

Exercise 33.2H1 a) 4.25 cm and 4.35 cm

b) 462.5 ml and 463.5 mlc) 10.45 seconds and 10.55 secondsd) 77.5 kg and 78.5 kge) 5.45 m2 and 5.55 m2

2 23 5003 141.5 cm and 142.5 cm4 74.95 cm and 75.05 cm5 7.825 mm and 7.835 mm6 a) 14.05 cm and 14.15 cm, 6.75 cm and 6.85 cm,

12.15 cm and 12.25 cmb) 32.95 cm and 33.25 cm

7 Shortest � 306 mm, longest � 308 mm8 a) 0.6 kg b) 0.8 kg

Exercise 33.3H1 a) 78 kg b) 16 minutes

c) 162 miles or 160 milesd) 5 m or 5.1 m e) 3 litres

2 a) 8, 9, 10 or 11 cm b) 45, 50, 55, 60 or 65°c) 10.4 cm2 d) 25 cme) 1.9 cm f) 206°g) About 2 hours or 2 hours 10 minutesh) £2.33

Exercise 33.4H1 8 km/h 2 65.7 mph3 8.75 km 4 5 hours 20 minutes5 558 g 6 3.6 g/cm3

7 4.4 km/h 8 350 g9 4.3 cm3 10 1.3 kg/m3

11 6.712 a) 48 km/h b) 1529

34 Perimeter, area and volumeExercise 34.1H

1 a) 32 cm b) 22 cm c) 20 cmd) 33 cm e) 17.2 cm f) 28.2 cm

2 14.8 cm 3 20 cm4 40 cm 5 2 m 10 cm or 210 cm

Exercise 34.2H1 10 cm2 2 4 cm2 3 12 cm2

4 24 cm2 5 24 cm2

Exercise 34.3H1 a) 15 cm2 b) 12 m2 c) 400 cm2

d) 36 cm2 e) 3.38 cm2 f) 5.76 cm2

g) 12.72 mm2 h) 5.04 cm2

2 13.78 cm2

3 12.96 cm2

4 3.09 cm2

5 560 m2

6 0.96 m2

7 a) 18.2 m2 b) £591.508 a) 5.25 m2 b) £131.25

Exercise 34.4H1 15 cm2 2 40 cm2 3 18 cm2 4 20 m2

5 60 cm2 6 160 cm2 7 96 mm2 8 10.5 cm2

9 38.5 m2 10 96 cm2

Exercise 34.5H1 28 cm2 2 54 cm2 3 25 cm2 4 56 m2

5 20 cm2 6 22 cm2 7 50 cm2 8 72 cm2

9 8 cm 10 11.25 cm

Exercise 34.6H1 a) 40 cm3 b) 126 cm3

2 120 cm3 3 64 cm3

4 121.5 cm3 5 1728 m3



6 2688 cm3 7 22 500 cm3

8 345 cm3 9 351 cm3

10 45 000 cm3 or 0.045 m3

35 Areas, volumes and 2-Drepresentation

Exercise 35.1HAnswers to 3 s.f. where appropriate.

1 25.1 cm 2 53.4 cm3 123 cm 4 364 mm5 16.0 m 6 19.9 m7 44.0 cm 8 72.3 cm9 245 mm 10 123 mm

11 13.8 m 12 8.64 m


1 a) 908 cm2 b) 1660 cm2

c) 14 100 cm2 d) 5810 mm2

e) 17 200 mm2 f) 3220 cm2

g) 10 600 cm2 h) 58.1 cm2

i) 238 cm2 j) 6940 m2

k) 11.3 m2 l) 20.9 m2

2 a) 254 cm2 b) 616 cm2

c) 3630 cm2 d) 1130 mm2

e) 4780 mm2 f) 2640 cm2

g) 1660 cm2 h) 32.2 cm2

i) 45.4 cm2 j) 804 m2

k) 9.08 m2 l) 14.7 m2


1 138 cm2 2 178 cm2

3 119 cm2 4 111 cm2

5 200 cm2 6 190 cm2


1 408 cm3 2 1330 cm3

3 423 cm3 4 798 cm3

5 1100 cm3 6 1100 cm3


1 915 cm3 2 815 cm3

3 1160 cm3 4 691 cm3

5 2240 cm3 6 4950 cm3

Exercise 35.6HAnswers to 3 s.f. where appropriate.1 4460 cm3 2 14 300 cm3

3 157 000 cm3 4 21 600 mm3

5 19 700 mm3 6 5.77 mm3

7 45.4 m3 8 72.2 m3

Exercise 35.7HAnswers to 3 s.f. where appropriate.1 a) 905 cm2 b) 1720 cm2

c) 2040 cm2 d) 3740 mm2

e) 452 mm2 f) 1460 mm2

g) 227 m2 h) 72.9 m2

2 a) 955 cm2 b) 4810 cm2

c) 8020 cm2 d) 8040 mm2

e) 10 300 mm2 f) 1200 mm2

g) 39.2 m2 h) 83.8 m2

Exercise 35.8H1 Plan

Side elevation

Front elevation



2 Plan

Side elevation Front elevation

3 Plan

Side elevation

Front elevation

4 Plan

Side elevation Front elevation

36 PythagorasExercise 36.1H

1 19 cm2 2 40 cm2

3 12 cm2 4 46 cm2

Exercise 36.2H1 a) 14.76 cm b) 15 m

c) 11.62 cm d) 9.38 cme) 14.81 cm f) 20.78 mg) 4.91 cm h) 19.14 cm

2 117 m (to the nearest metre)3 199 cm (to the nearest centimetre)4 10.4 cm5 110 cm3 (3 s.f.)

Exercise 36.3H1 Yes 152 � 202 � 252

(This is 5 � the 3, 4, 5 triangle)2 No 4.22 � 7.32 � 8.72

3 No 122 � 122 � 152

4 Yes 15.52 � 37.22 � 40.32

(This is 3.1 � the 5, 12, 13 triangle)5 No 72 � 82 � 112

6 No 6.52 � 11.12 � 12.82

7 Yes 8.42 � 28.82 � 302

(This is 1.2 � the 7, 24, 25 triangle)8 No 13.52 � 27.22 � 30.22

Exercise 36.4H1 a) (4, 5) b) (5, �0.5) c) (�2.5, 6)

d) (�3.5, 1) e) (�1.5, �5.5)2 a) (�1, 7) b) (5, 3) c) (5.5, 4.5)

d) (5, 4.5) e) (�2, 3.5) f) (�6, �4.5)

37 Solving problems 1Exercise 37.1H

1 a) 33 minutes b) 4 hoursc) 41 minutes d) 1 hour 34 minutese) 7 hours 44 minutes f) 6 hours 10 minutesg) 1 hour 45 minutes h) 3 hours 45 minutes

2 13:153 10:264 a) 2 hours 23 minutes b) 16:045 09:596 a) 08:45 b) 13:10

c) 19:05 d) 22:08e) Wednesday at 00:55

7 1 hour and 12 minutes8 a) 19:22 b) 1 hour 45 minutes9 48 seconds

10 14:54:11

Exercise 37.2H1 4 hours 30 minutes 2 17.5 km3 42 mph 4 218.4 km5 4 m/s 6 160 km7 746 km/h 8 4 hours 27 minutes



9 19.3 km/h10 a) 1 hour 26 minutes

b) 11 minutes

Exercise 37.3H1 7.5 miles 2 17.5 pints3 16 kg 4 9 m 60 cm5 16 ft 8 inches6 59.2 km (accept 59 or 60 km)7 46 litres 8 44 pounds

Exercise 37.4H1 a) (i) 55 mph

(ii) 56.25 mph (accept 56 mph)b) 40 km/h and 25 mph, 80 km/h and 50 mph,

120 km/h and 75 mph2 a) 14:18

b) 14:56c) 1830 arriving at 2141, 3 hours 11 minutes

3 a) 116 miles b) 228 miles4 a) 1045, 1441 and 1524

b) 46 minutes5 a) (i) 198 miles (ii) 279 miles

b) (i) 19 minutes (ii) 45 minutes

38 Solving problems 2Exercise 38.1H

1 2.77 2 9.48 3 4.03 4 9.665 7.8 6 7.84 7 0.69 8 2.919 15.26 10 0.33 11 2.34 12 0.05

Exercise 38.2H1 Check student’s answers. Possible answers include

the following.a) Positive negative � negativeb) Multiplying by number greater than

1 should make answer larger.c) 5 � 300 � 1500 and answer should be less

than this.d) 72 � 49 and answer should be more than this.

2 a) 9 � 60 � 540b) Negative � negative � positivec) 0.22 � 0.04d) 5 � 1 � 5 so last digit should be 5.

In questions 3 and 4, estimates may vary from thosegiven. Check the validity of other estimates.3 a) 90 � 100 � 9000

b) 0.62 � 0.36c) �20 � 5 � �15

4 a) 3 � £20 � £60b) 40 � £6 � £240c) 5 � £8 � 2 � £2 � £44

5 a) 83.7 � 235 � 19 669.5b) 71.22 � 5069.44c) 120.28 9.7 � 12.4 or 120.28 12.4 � 9.7d) 147.32 � 68.2 � 79.12, 79.12 4.6 � 17.2 or

79.12 17.2 � 4.6

6 a) 30.04b) 265.20

7 a) 0.862b) 233.558

8 a) 3.9b) 50

9 a) (i) 203 � 8000(ii) 200 � 0.3 � 60

(iii) �102 ��52� � �100 �� 25� � �75� � 9

(iv) �50

0

�

.02

40� � �

0

9

.0

0

2� � �

90

2

00� � 4500

b) (i) 9528.128 (ii) 58.59(iii) 10.0 (to 3 s.f.) (iv) 4140 (to 3 s.f.)

Exercise 38.3H1 a) 8.65 hours b) 5.35 hours

c) 0.55 hours d) 0.05 hours2 a) 4 hours and 48 minutes

b) 5 hours and 51 minutesc) 27 minutesd) 36 minutes

3 a) 3 mphb) 52.5 milesc) 4 minutes

4 23 hours and 40 minutes5 2.48 kg6 £31 5007 625 g or 0.625 kg8 1320 people/km2 (to 3 s.f.)9 £24.96

10 3.71%11 3100 g (to 3 s.f.)12 37.8 litres13 a) 36 minutes b) 63.3 mph (to 1 d.p.)

39 Probability 1Exercise 39.1H

1 a) Evensb) Certainc) Likely

2 a) at Likely or between Likely and Certainb) at Certainc) at Unlikely

3 a) Unlikely or very unlikelyb) Impossible c) Evens

Exercise 39.2H1 0 1

c) a) b)

12



2 a) likelyb)

3 a) �28� � �

14� b) �

38� c) 0

4 a) �36� � �

12� b) �

16�

5 a) 0.5 b) 0.2 c) 0.76 0 orange, 3 blue, 9 green7 a) Pink

b) 2 pink, or other answer with two more pinksweets than yellow taken.

8

9 �58�

10 a) �155� � �

13� b) �1

25� c) �

11

35�

Exercise 39.3H1 �

1320� � �

25� or 0.4

2 a) (i) �154020� � �2

7510� or 0.284

(ii) �55080� � �2

2590� or 0.116

b) (i) 0.2 (ii) 0.2c) No, the spinner does not seem to be fair. If it

were fair, it is unlikely that there would be somany 5s and so few 1s. More trials should bedone to check.

Review Exercise 39H1 a)

b) (i) �320� � (ii) �

c) (i) �360� � �

15� (ii) 30 (iii) £18.00

2 a)

b) (i) � (ii) c) �

d) (i) 240 (ii) £60.00

8––20

2–5

5––20

1–4

25––36

5

4

3

2

1

0

0

0

0

0

0

5

4

3

2

1

1

10

8

6

4

2

2Square spinner

15

12

9

6

3

3

Pen

tago

n sp

inne

r

1––15

28––30

14––15

8

7

6

4

3

1

9

8

7

5

4

2

1

10

9

8

6

5

3

2

12

11

10

8

7

5

4Red bag

Blu

e ba

g

14

13

12

10

9

7

6

15

14

13

11

10

8

7

0 10.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

a) b)

3

4 a)

b) (i) (ii)

c) �

d) (i) 200 (ii) £60

5 a)

b) (i) �1155� (ii) Only correct if there are

equal numbers of boys andgirls

6 a) �

b)

40 Probability 2Exercise 40.1H

1 0.82 �

56�

3 0.854 �1

70�

5 0.926 �

13

41�

Exercise 40.2H1 0.1 2 �1

79�

3 0.45 4 �341�

5 0.17 6 �220� � �1

10�

Exercise 40.3H1 82 43 124 8 or 95 a) 15

b) 456 240 yellow, 60 blue, 100 green

0 1

C A B

0 1

C B A

0 1

C AB

12

5–9

20––36

25––36

11––36

6

5

4

3

2

1

1

1

1

1

1

1

1

2

2

2

2

2

1

2

3

3

3

3

2

1

3Blue dice

Red

dic

e

4

4

4

3

2

1

4

5

5

4

3

2

1

5

6

5

4

3

2

1

6

0 10.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

G R B


Exercise 41.2H1 a)

b)

c)

2 a)

Type of tree

Freq

uenc

y

2

0

4

6

8

10

12

Oak

Beech

Pine

Sycam

oreLim

e

Oth

er

Type of vehicle

Freq

uenc

y

10

0

20

30

40

50

CarVan

Lorry Bus

Moto

rbik

e

Oth

er

Type of fast food

Freq

uenc

y

5

0

10

15

20

25

30

Pizza

Chines

e

Burger

Kebab

Fish &

chip

s

Oth

er


Exercise 40.4H1 a)

b) Yes. For a fair die each score should haveprobability �

16� � 0.166 ... or 1.67.

All the relative frequencies for Pete’s die areclose to this value.

2 a)

b) No. Only a small number of trials.3 a)

b) Large number of trials.4 a) 0.84

b) 0.165 a)

b) No. For a fair five-sided spinner, each scoreshould have a probability of �

15� � 0.2.

6 a)

b) The relative frequency values must have beenfound after a large number of trials.

41 Data collectionExercise 41.1H

1 Discrete: Number of peas in a pod, Day you wereborn, Price of an itemContinuous: Time of day, Weight of an egg,Amount of rain in a week

2 Check students’ answers.3 Check students’ data collection sheets.

Favourite colour

Freq

uenc

y

Blue

5

0

10

15

20

25

Red Green Yellow Pink Black Other

Score 1 2 3 4 5 6

Relative0.15 0.17 0.18 0.16 0.17 0.18

frequency

Result Win Lose Draw

Relative0.64 0.22 0.14

frequency

Score 1 2 3 4 5

Relative0.07 0.17 0.31 0.30 0.15

frequency

Flavour Relative frequency

Plain 0.28

Salt & Vinegar 0.22

Cheese & Onion 0.38

Other 0.13

Colour Yellow Green White Blue

Number 32 24 18 6



b)

c)

d)

e)

Number of sisters

Freq

uenc

y

00

5

10

15

1 2 3 4 ormore

f)

3

4

Car colour

Fre

quen

cy

Red0

4

2

8

12

6

10

Blue Green White Silver Other

School lunch rating

Freq

uenc

y

Excellent0

20

40

Good Fair Poor

Shoe size

Freq

uenc

y

39

2

0

4

6

8

10

12

14

16

40 41 42 43 44 45 Other

Type of bird

Freq

uenc

y

Sparro

w

Starli

ng

Pigeon

Finch

Dove

Oth

er

10

0

20

30

40

50

Drinks per day

Freq

uenc

y

Lessthan 4

5

0

10

15

20

25

30

4 5 6 7 8 ormore

Number of pets

Freq

uenc

y

0

10

0

20

30

40

50

1 2 3 4 5 ormore

Frequency

Excellent 27

Good 18

Fair 16

Poor 22

Replies Frequency

Red 9

Blue 4

Green 6

White 7

Silver 12

Other 6


5 a)

b) 66 c) 34 d) China e) 196

Exercise 41.4H1 a)

b)

c)

2 a)


5

Exercise 41.3H1

2 a)

b) 3 c) 89 d) 93 e) 120

3 a)

b) 26 c) 87 d) 124

4 a)

b) 21 c) 36 d) 99 e) 148

Eye colour

Freq

uenc

y

Blue0

4

2

8

12

6

10

14

16

Green Brown

Number of Tally Frequencylorries delivering

to a depot

0 to 19 6

20 to 39 14

40 to 59 24

60 to 79 14

80 to 99 2

Number of video games

Freq

uenc

y

1–5

10

0

20

30

40

6–10 11–15 16–20 21–25 26 ormore

Frequency

Blue 13

Green 7

Brown 15

Black Not black Total

German 18 49 67

Not German 23 64 87

Total 41 113 154

White Not white Total

Car 3 86 89

Not car 24 7 31

Total 27 93 120

Paperback Not paperback Total

Fiction 87 11 98

Non-fiction 9 17 26

Total 96 28 124

Right hand Left hand Neither Total

Maths 27 8 1 36

Not maths 99 13 0 112

Total 126 21 1 148

Marks out of 30 Tally Frequency

1 to 5 5

6 to 10 14

11 to 15 12

16 to 20 16

21 to 25 11

26 to 30 2

Gold Silver Bronze Total

Australia 34 27 13 74

China 16 20 27 63

USA 21 19 19 59

Total 71 66 59 196

Number of Tally Frequencyapples on

a tree

1 to 10 4

11 to 20 11

21 to 30 26

31 to 40 13

41 to 50 4

More than 50 2



b)

c)

d)

e)

f)

Number of eggs

Freq

uenc

y

1–5

10

0

20

5

15

25

6 –10 11–15 16 –20 21–25 26 ormore

Number of swimmers

Freq

uenc

y

0–49

4

0

8

12

2

6

10

50–99 100–149 150–199 200–249 250 ormore

Number of runners

Freq

uenc

y

1–5

5

0

10

15

20

6–10 11–15 16–20 21 ormore

42 Illustrating dataExercise 42.1H

1

2

3

4

Exercise 42.2H1 a)

Other

Softdrink

84°

24°

96°36°

120°

Milk

WaterJuice

January

February

March

April

May

June

July

August

September

October

November

December

represents 10 umbrellas

Black

Blue

Green

Red

Silver

Other

represents 10 cars

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

represents 4 swimmers

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

represents 4 fish

Number of balloons

Freq

uenc

y

0–90

10

20

30

40

10–19 20–29 30–39 40–49 50–59 60–69 70 ormore

Number of fish

Freq

uenc

y

1–100

10

20

30

11–20 21–30 31–40 41–50 51 ormore



b)

c)

2 a)

b)

c)

Comedy

Horror Romance

Action

Other

100°

56°128°

68°

8°

Satellite/cable

BBC

ITV

Five

Channel 4

75°

60°

150°

45°30°

Blue

Brown

Grey

Other

Green

114°

42°

138°

57°

9°

School

Sleeping Eating

Playing

TV

Other

90°

135°

45°

30°

30°

30°

Other

Soap

Comedy

Cartoon

Drama

63°

99°

72°

81°

45°

Exercise 42.3H1

2

3

4

M

26

28

30

32

34

36

38

T W Th F Sa Su M T W Th FDay

Tem

pera

ture

(°C

)

J

2

4

6

8

10

12

14

F M A M J J A S O N DMonth

Sale

s (t

onne

s)

M

50

100

150

200

250

T W Th F Sa SuDay

Tic

kets

J

5

10

15

20

25

30

35

40

F M A M J J A S O N DMonth

Sale

s (�

£100

0)



43 Measures of average andspread

Exercise 43.1H1 a) 7 b) 4 c) 7.5 d) 4 e) 62 £3063 424 a) (i) 8 (ii) 6.5

b) Sophie5 a) He has not put them in order.

b) 4

Exercise 43.2H 1 2 2 17 3 184 173 cm 5 18

Exercise 43.3H1 5 2 54 cm 3 74 19 5 £22 000

Exercise 43.4H1 7 2 45 cm 3 44 5 5 £10 000

Exercise 43.5H 1 50–54 kg2 £200–£249.993 60–694

Modal group is 61–70

Review Exercise 43H1 74.3 (3 s.f.)2 a) 22 b) 763 a) £106 b) £3514 a) 2 b) 155 a) 6 b) 7 c) 5 d) 5.86 a) 35 b) 347 a) 2 b) 68 a) 42 b) 469 a) 3 b) 4

44 Interpreting statisticsExercise 44.1H

1 a) 50 b) 135 c) 525 d) 752 a) Monday, Tuesday and Friday

b) 100 c) 840 d) 120

3 a) 3500 b) 6000 c) 5004 a) Sunday b) 20 c) 1455 a) 24 b) 36 c) 196 d) 286 a) 14 b) 10 (July)

c) 156 d) 13

Exercise 44.2H1 a) 21 b) 10 c) 122 a) 27 b) 213 a) 50 million

b) 5.33 million (to 2 d.p.)c) 1.67 million (to 2 d.p.)d) 3 million

4 a) 50 000 square milesb) 8000 square milesc) 6000 square milesd) 30 000 square miles

5 Fruit 1.5 kg, plain flour 0.23 kg (to 2 d.p.), butter 0.23 kg (to 2 d.p.), sugar 0.23 kg (to 2 d.p.), oats and nuts 0.2 kg

Exercise 44.3H1 a) 46°C

b) 25 minutesc) 15°Cd) The water was kept at boiling point.

2 a) 40 000 b) Game 4c) 12 000 d) 47 000e) The crowd size is likely to be between 40 000

and 60 000 for each team but it is not possibleto predict a precise figure.

3 a) 6 cm b) Januaryc) 11 cm d) 8.7 cm

4 a) February b) £1300c) £164 400 d) £13 700

5 a) 297 000b) 42 000 (to the nearest thousand)c) 14 000d) There are likely to be far fewer lorries and vans

using the bridge at the weekend.6 a) January and February

b) December, January and Februaryc) 24°C d) Marche) 9°C f) 11 cm

Exercise 44.4H1 a) 2009

b) Car sales was the largest proportion in 2007 butcar repairs was the greatest in 2009.

c) Parts sales and bike sales were the smallestproportion in each year.

2 a) 9 b) 4 c) 7 d) 7 e) 8f) Boys. More boys scored high marks, and the

mean for the boys (6.0) is higher than the meanfor the girls (5.7).

3 a) 5 b) 195 or 190 or 200c) About 100 d) 5e) About 195f) The developed countries

Mark Tally Total

41–50 8

51–60 10

61–70 12

71–80 9

81–90 10

91–100 1



g)

45 Statistical diagramsExercise 45.1H

1 a)

b) 4 a � 62 a)

b) 75 w � 80 c) 75 w � 803 a) 5 b) 40 c) 30%

d) 8 t � 9e)

6560

10

0

20

30

40

50

70 75 80 85 90Weight (kg)

Freq

uenc

y

20

5

0

10

15

20

25

4 6 8 10 12 14Age (years)

Freq

uenc

y

Exercise 45.2H1

2

3 a)

b) Answers should include the followingcomments.• In 1989 there were more younger

people / fewer older people.• In 2009 there were fewer younger people /

more middle-aged and older people.• For 1989 the modal group is 0 to 10, for 2009

it is 20 to 30.

Exercise 45.3H1 a), d), e)

b) Strong positive correlationc) 63.5 gf) About 87 kg

Wei

ght (

kg)

Amount of fertiliser (g/m3)100

40

30

50

60

70

80

90

20 30 40 50 60 70 80

100

10

0

20

30

40

50

60

70

80

90

20 30 40 50 60 70Age (years)

Fre

quen

cy

1989

2009

50

10

0

20

30

40

10 15 20 25 30Time (minutes)

Freq

uenc

y

43

5

0

10

15

5 6 7 8 9Height (cm)

Freq

uenc

y

Ango

laNige

r

Ethio

piaIn

dia

Turkey

USA

Taiwan U

K

Norway

Singa

pore

200

406080

100120140160180200

Country

IMR

(pe

r 10

00 b

irth

s)

Time (t mins) Frequency

5 t � 6 3

6 t � 7 9

7 t � 8 10

8 t � 9 13

9 t � 10 5



2 a), d), e)

b) Strong negative correlationc) 55 000f) (i) About £7900

(ii) 66 000 miles3 a), d), e)

b) Strong positive correlationc) 169.4 cmf) About 176 cm

46 Statistical calculationsExercise 46.1H

1 a) (i) 3 (ii) 3(iii) 5 (iv) 3.34

b) (i) 100 (ii) 101(iii) 6 (iv) 100.875

c) (i) 1 (ii) 1(iii) 6 (iv) 1.64

d) (i) 1 (ii) 2(iii) 7 (iv) 2.09

2 £8.203 1.3275

Exercise 46.2H1 a) (i) 20 (ii) 4.97

b) (i) 75 (ii) 17.4c) (i) 25 (ii) 72.2d) (i) 24 (ii) 7.42

2 a) 125 x � 150b) 150 x � 175c) 160.5

3 398.1

Hei

ght o

f dau

ghte

r (c

m)

Height of father (cm)

165160

165

160

170

175

180

170 175 180 185 190

Mile

age

(tho

usan

ds)

Price (£000s)10

10

0

20

30

40

50

60

70

80

90

100

2 3 4 5 6 7 8 9

Exercise 46.3H1 a) (i) 50 cm (ii) (131.3) 131 cm

b) (i) 25 g (ii) (36.4) 36 gc) (i) 80 mm (ii) (111.7) 112 mmd) (i) 10 min (ii) (59.56) 60 min

2 a) (i) 0.3 x � 0.6 (ii) (0.87) 0.9 mb) (i) 40 x � 50 (ii) (44.2) 44 gc) (i) 26 x � 28 (ii) (25.9) 26 mind) (i) 35 x � 40 (ii) (35.9) 36 mph

3 a) 1500 x � 2000b) 1500 x � 2000c) (£1562.50) £1560

4 (41.4 seconds) 41 seconds5 148 pence

47 Planning and collectingExercise 47.1H

1 a) Primary b) Secondaryc) Secondary d) Primary

2 a) There are not enough categories: for example,red and grey should be added.

b) Check students’ new questions.3 a) He has not stated whether 1 is ‘Not at all’ or

‘Very much’.b) Check students’ new questions.

4 a) Possible answers include the following.• The first 30 in the queue may be those

keenest on lunch.• The first 30 in the queue may all be from one

year group.b) For example, select two people at random from

each tutor group.5 a) This is a leading question.

b) Check students’ new question. A suitablequestion would beWhat is your opinion of the number of saladson the menu?� Too few� About right� Too many

6 Check students’ questions.


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ANSWERS TO THE HOMEWORK BOOK · PDF fileFoundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises219 1 Integers, powers and roots 1 Exercise