answers to the homework book · pdf filefoundation wjec gcse mathematics © 2010, hodder...
TRANSCRIPT
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 220
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 221
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 221
222 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
Exercise 7.6H1 a) �
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�
Exercise 8.2H1 a) �
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�
Exercise 8.3H1 a) �
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�
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 222
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.
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 223
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 223
224 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 224
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 225
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 225
226 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 226
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 227
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 227
228 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 228
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 229
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 229
230 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
Exercise 20.3H1 x � 3 2 x � 4 3 x � 24 x � 10 5 x � 3 6 x � 17 x � 1 8 x � 3 9 x � 3
10 x � 3 11 x � 4.5 12 x � 513 x � 2 14 x � 2 15 x � �3
Exercise 20.4H1 x � 14 2 x � 15 3 x � 124 x � 30 5 x � 6 6 x � 157 x � 96 8 x � 8 9 x � 7
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 230
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 231
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 231
232 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 232
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 233
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
Angles on a straight line add up to 180°or Angles around a point add up to360°.
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
Angles on a straight line add up to 180°or Angles around a point add up to360°.
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
Angles on a straight line add up to 180°or Angles around a point add up to360°.
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
Angles on a straight line add up to 180°or Angles around a point add up to360°.
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
Angles on a straight line add up to 180°or Angles around a point add up to360°.
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 233
234 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
Angles on a straight line add up to 180°or Angles around a point add up to360°.
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 � � �
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 234
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 235
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 235
236 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 236
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 237
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 237
238 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
6
7
8
9 Scale 1 cm � 4 m
10 Scale 1 cm � 4 m
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
2 Scale 1 cm � 4 m
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 238
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 239
8 Scale 1 cm � 5 km
9 Scale 1 cm � 1 m
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.
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:30 Page 239
240 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 240
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 241
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 241
242 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 242
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 243
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 243
244 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 244
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 245
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
50cAnswers.qxd:50cAnswers.qxd 13/5/11 17:24 Page 245
246 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
Exercise 35.2HAnswers to 3 s.f. where appropriate.
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
Exercise 35.3HAnswers to 3 s.f. where appropriate.
1 138 cm2 2 178 cm2
3 119 cm2 4 111 cm2
5 200 cm2 6 190 cm2
Exercise 35.4HAnswers to 3 s.f. where appropriate.
1 408 cm3 2 1330 cm3
3 423 cm3 4 798 cm3
5 1100 cm3 6 1100 cm3
Exercise 35.5HAnswers to 3 s.f. where appropriate.
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 246
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 247
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 247
248 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 248
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 249
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 249
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
250 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 250
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 251
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 251
5 a)
b) 66 c) 34 d) China e) 196
Exercise 41.4H1 a)
b)
c)
2 a)
252 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 252
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 253
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 253
254 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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)
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 254
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 255
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 255
256 Answers to the Homework Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
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
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 256
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Homework Book exercises 257
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.
50cAnswers.qxd:50cAnswers.qxd 22/9/10 08:31 Page 257