ANSWERS TO THE STUDENT’S BOOK EXERCISES... 2, 3, 6 ANSWERS TO THE STUDENT’S BOOK EXERCISES ......
Transcript of ANSWERS TO THE STUDENT’S BOOK EXERCISES... 2, 3, 6 ANSWERS TO THE STUDENT’S BOOK EXERCISES ......
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 165
Chapter 1Exercise 1.1 (page 3)
1 a) 99 b) 91 c) 124d) 181 e) 418 f) 453
2 a) 41 b) 37 c) 47d) 94 e) 107 f) 276
3 a) 69 b) 76 c) 180d) 476 e) 738 f) 1048
4 a) 21 b) 24 c) 15d) 13 e) 24 f) 46
5 £696 £277 276p, £2.768 26
Exercise 1.2 (page 7)1 a) 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78,
84, 90, 96b) 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
2 24, 48, 72, 963 a) 2, 6, 18, 30 b) 6, 15, 18, 30, 33
c) 15, 304 a) 12, 24, 36, 48, 60, 72, 84, 96
b) 15, 30, 45, 60, 75, 905 606 a) 1, 2, 3, 6, 9, 18 b) 1, 2, 3, 4, 6, 8, 12, 247 1, 2, 3, 68 a) 1, 2, 4, 5, 8, 10, 20, 40
b) 1, 2, 3, 4, 6, 9, 12, 18, 369 1, 2, 4
10 a) 23 000 b) 197 000 c) 8000d) 148 000 e) 5 732 000
11 a) 7700 b) 17 600 c) 800d) 654 300 e) 5000
12 a) 70 000 or 68 000 b) £5 000 000c) 8000 or 7900 d) £700 000 or £690 000
Exercise 1.3 (page 11)1 a) 520 b) 6300 c) 54 000
d) 36 100 e) 560 000 f) 6000g) 549 000 h) 810 000 i) 530 000j) 470 000 k) 92 300 000 l) 62 000 000
2 a) 53 b) 140 c) 532d) 640 e) 6400 f) 53 600g) 6754 h) 73 000 i) 5800
3 a) 1500 b) 5600 c) 14 000d) 60 000 e) 24 000 f) 2000g) 1 800 000 h) 300 000 i) 5 600 000j) 12 000 000 k) 2 800 000 l) 72 000 000
4 a) 1920 b) 4320 c) 7020d) 11 200 e) 25 200 f) 23 400g) 259 200 h) 232 000
5 a) 1728 b) 2356 c) 4674d) 1764 e) 1914 f) 6216g) 3321 h) 9240 i) 34 776j) 29 713 k) 43 902 l) 20 768
6 a) 63 200p b) £567 47 000 metres8 £2409 156 000 metres or 156 kilometres
10 952p
Exercise 1.4 (page 14)1 a) 49 b) 81 c) 121
d) 144 e) 900 f) 2500g) 3600 h) 40 000 i) 160 000j) 640 000
2 a) 196 b) 484 c) 961d) 2209 e) 7921 f) 3136g) 1156 h) 32 400 i) 69 169j) 555 025
3 a) 216 b) 729 c) 1331d) 2744 e) 15 625 f) 50 653g) 79 507 h) 3 176 523
4 a) 15 b) 14 c) 19d) 23 e) 39 f) 87g) 68 h) 54
5 a) 20 b) 30 c) 50d) 80 e) 200
Exercise 1.5 (page 16)1 a) 3 b) �3 c) �32 a) �1°C b) 4°C c) �8°C3 a) 16°C b) 26°C c) 14°C4 a) �8, �3, 1, 7
b) �6, �4, 0, 5c) �6, �4, �3, 1, 2, 5
5 �3
Mixed exercise 1 (page 18)1 a) 132 b) 44 c) 269
d) 348 e) 1016 f) 632 271p3 a) 20, 40, 60, 80, 100, 120
b) 12, 24, 36, 48, 60, 72, 84, 96, 108, 120c) 60, 120
4 a) 1, 2, 3, 4, 6, 12 b) 1, 2, 3, 6, 9, 18 c) 1, 2, 3, 5, 6, 10, 15, 30d) 1, 2, 3, 6
ANSWERS TO THE STUDENT’SBOOK EXERCISES
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166 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
5 a) 5600 b) 18 000 c) 273 000d) 273 500 e) 6 000 000 f) 3500
6 a) 9300 b) 63 000 c) 572 000d) 78 e) 6300 f) 4000g) 21 000 h) 1410 i) 34 800j) 140 000 k) 31 920 l) 292 800
7 a) 1764 b) 4731 c) 97288 8370 km9 a) 64 b) 1600 c) 250 000
d) 100 000 e) 800010 a) 841 b) 1728 c) 2809
d) 22 e) 7211
Chapter 2Exercise 2.1 (page 22)
1 a) �12� b) �
13� c) �
49� d) �
25�
e) �23� f) �
15� g) �
19� h) �1
36�
2 a) �12� � �
24� � �
36� � �1
62� � �
12
00� � �12
00
00�
b) �15� � �1
20� � �1
35� � �2
40� � �3
60� � �
15
00�
3 a) �34� � �1
92� b) �
11
06� � �
58� c) �
12� � �1
98� d) �
3500� � �
35�
e) �11
28� � �
69� f) �
27� � �
13
05� g) �
45� � �
23
40� h) �2
31� � �
17�
i) �29� � �2
67� j) �1
31� � �
14
24� k) �
13
55� � �
37� l) �
2780� � �1
40�
4 a) �45� b) �
16� c) �
57� d) �
34�
e) �23� f) �
56� g) �
12� h) �
35�
i) �23� j) �
12� k) �
16� l) �
12�
m) �45� n) �
89� o) �
57� p) �
23�
Exercise 2.2 (page 23)1 a) 5 b) 9 c) 17
d) £25 e) £2.502 a) 6 b) 9 c) 16
d) £24 e) 5.2 m3 a) 18 b) 36 c) 150
d) £42 e) £1054 a) 25 b) 40 c) 100
d) 35 cm e) £755 £1.606 a) £3 b) £97 56 m8 729 210
10 �58� of £120 � £75, �
34� of £96 � £72;
�58� of £120 is the larger.
Exercise 2.3 (page 26)1 a) �
35� b) �
47� c) �
35� d) �
89� e) �
14�
2 a) 2�15� b) 1�
37� c) 3�
13� d) 6�
12� e) 4�
23�
f) 1�56� g) 2�
38� h) 2�
67� i) 5�
34� j) 3�1
30�
3 a) 3�12� b) 1�
15� c) 1�
12� d) 1�
37� e) 2�
25�
f) 2�12� g) 2�
29� h) 2�
12� i) 5�
14� j) 3�
37�
k) 4�45� l) 2�1
10� m) 7�
12� n) 2�1
81� o) 1�
12�
Mixed exercise 2 (page 27)1 a) �
34� � �
12
50� b) �
12
51� � �
57�
c) �12� � �
12
12� d) �
16
80� � �1
30�
e) �11
68� � �
89� f) �
37� � �
1228�
g) �49� � �
49
00� h) �2
84� � �
13�
2 a) �23� b) �
45� c) �1
41� d) �
35� e) �
25�
f) �131� g) �
34� h) �
56� i) �
45� j) �
12�
3 a) 8 b) 11 c) 45 d) 1604 40 metres5 10 8006 28 km7 �
34� of 180 � 135, �1
70� of 200 � 140
�170� of 200 is the larger.
8 a) �59� b) �
13� c) �
35� d) �
11
27� e) �
23�
9 a) 3�34� b) 2�
45� c) 2�
47� d) 6�
23� e) 1�
35�
10 4�45� metres
Chapter 3Exercise 3.1 (page 32)
1 a) 4 tens b) 4 tenthsc) 4 ten thousands d) 4 hundredthse) 4 thousandths
2 a) 0.3 b) 4.7 c) 0.09d) 52.79 e) 0.021
3 a) �35� b) 4�1
30� c) 14�1
10�
d) �34� e) 9�1
300�
4 £0.05, £0.07, £0.92, £1.42, £6.07, £8.60
5 9.207, 7.29, 0.927, 0.209, 0.0726 a) 0.468 kg b) 1.645 kg c) 0.072 kg
d) 0.006 kg e) 2.45 kg7 a) 0.12 m b) 0.874 m c) 0.218 m
d) 0.056 m e) 1.38 m
8 6.4 cm, 78 mm, 47.6 cm, 0.58 m, 1.07 m
9 1745 g, 1.54 kg, 785 g, 0.75 kg, 486 g10 a) 0.1 b) 0.5 c) 0.4
d) 0.25 e) 0.03
Exercise 3.2 (page 36)1 a) 13.91 b) 42.09 c) 111.15
d) 14.63 e) 60.71 f) 113.372 a) 9.65 b) 14.91 c) 54.84
d) 8.31 e) 20.77 f) 221.843 a) £16.62 b) £24.90 c) £114.47
d) £97.104 £57.905 1.76 m6 2.96 seconds7 a) 1.2(00) kg b) £11.978 £5.90
Temperature (°C) 15 �3 �4 �10
10° warmer 15 �7 �6 �10
5° colder 10 �8 �9 �15
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Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 167
9 a) 16.32 m b) 11.15 m c) 5.55 md) 7.88 m e) 6.8 cm f) 7.3 cm
10 a) 4.572 kg b) 1.96 kg c) 1.614 kgd) 1.475 litres e) 1.872 litres f) 0.7 litre
11 £14.1112 £4.8913 a) 3.5 b) 1.8 c) 2.4 d) 6.3
e) 0.03 f) 0.54 g) 15 h) 42i) 0.08 j) 0.15 k) 0.25 l) 0.01
Mixed exercise 3 (page 38)1 a) 6 thousands b) 6 tenths
c) 6 tens d) 6 hundredthse) 6 units
2 0.068, 0.215, 0.4, 0.532, 0.713 8p, 26p, 87p, 156p4 a) 0.9 b) 2.1 c) 0.07
d) 16.23 e) 0.0195 a) 0.3 b) 0.2 c) 0.75
d) 0.7 e) 0.66 a) 236 cm b) 8.3 cm c) 57 cm
d) 580 cm e) 47 cm7 a) 9.31 b) 45.46 c) 118.84
d) 16.88 e) 51.51 f) 128.298 a) 13.61 b) 24.08 c) 46.54
d) 5.43 e) 6.83 f) 196.079 £60.13
10 3.1 m11 £2.9212 a) 1.2 b) 0.05 c) 0.56 d) 0.48
Chapter 4Exercise 4.1 (page 42)
1 a) �270� b) �
12
30� c) �2
25� d) 1�
15�
2 a) 0.16 b) 0.27 c) 0.83
d) 0.07 e) 0.31 f) 0.04
g) 0.17 h) 0.02 i) 1.5
j) 2.5 k) 0.09 l) 0.1253 a) 62% b) 56% c) 4%
d) 16.5% e) 132%4 a) 70% b) 60% c) 35%
d) 40% e) 34%
Exercise 4.2 (page 44)1 a) £16 b) £10 c) £212 £6 3 240 4 £12605 a) £8.16 b) £86.406 £18 7 38.4 m 8 21 280 9 £83.60
Exercise 4.3 (page 46)1 a) £480 b) £580 c) £424 d) £7202 a) £168 b) £204 c) £232.80 d) £963 £12 480 4 £34.20 5 £129.60
6
7 a) £76.16 b) £85.68c) £72.76 d) £111.52
8 a) £255.84 b) £212.16c) £283.92 d) £68.64
9 £739510 80 96011 £399.50 (using a VAT rate of 17.5%)12 £71.44
Exercise 4.4 (page 49)1 10% 2 25% 3 40%4 5% 5 20% 6 13%7 7.5% 8 53% 9 82.5%
10 17%
Mixed exercise 4 (page 50)1 a) 0.27 b) 0.96 c) 0.02
d) 0.165 e) 3.5(0)2 a) 8% b) 70% c) 72%
d) 40% e) 123%3 £8.40 4 £7.505 £2.10 6 £16 4807 £29.75 8 £2169 4.2% 10 28%
Chapter 5Exercise 5.1 (page 53)
1 70 2 31 3 74 4 895 136 6 37 7 57 8 609 73 10 72 11 91 12 73
13 92 14 99 15 73 16 11617 117 18 122 19 105 20 183
Exercise 5.2 (page 54)1 70 2 25 3 41 4 235 72 6 22 7 41 8 169 65 10 21 11 69 12 46
13 37 14 19 15 35 16 6717 7 18 69 19 82 20 17
Exercise 5.3 (page 55)1 56 2 42 3 73 4 425 14 6 43 7 57 8 499 27 10 39
Item Original Reduction Saleprice (£) (£) price (£)
Television 150 30 120
Washing 360 72 288
machine
DVD player 40 8 32
Computer 550 110 440
system
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168 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
Exercise 5.4 (page 56)1 12 2 12 3 45 4 455 35 6 12 7 48 8 279 36 10 15 11 28 12 40
13 18 14 36 15 50 16 5617 49 18 18 19 54 20 63
Exercise 5.5 (page 57)1 6 2 4 3 3 4 45 5 6 7 7 5 8 99 3 10 9 11 8 12 7
13 7 14 9 15 4 16 817 7 18 6 19 7 20 4
Exercise 5.6 (page 58)1 3.5, 3.6 or 3.7 2 4.8 or 4.93 9.2, 9.3 or 9.4 4 7.7, 7.8 or 7.95 5.5, 5.6 or 5.7 6 6.8 or 6.97 6.1, 6.2 or 6.3 8 7.3, 7.4 or 7.59 9.4, 9.5 or 9.6 10 8.7, 8.8 or 8.9
Exercise 5.7 (page 63)1 a) 14 b) 17 c) 581
d) 205 e) 9 f) 28g) 320 h) 924 i) 1j) 35
2 a) 5.2 b) 48.1 c) 0.9d) 7.7 e) 9.9
3 a) 5.24 b) 48.12 c) 0.89d) 7.67 e) 9.89
4 a) 1000 b) 3000 c) 60 000d) 40 e) 600 000 f) 9 000 000g) 300 h) 4000 i) 600
5 20 000
Exercise 5.8 (page 65)1 �1 2 4 3 2 4 �35 2 6 8 7 1 8 �19 5 10 �1 11 �1 12 1
13 �3 14 �1 15 �5 16 117 2 18 �3 19 1 20 3
Exercise 5.9 (page 66)1 4 2 2 3 4 4 65 1 6 �4 7 �4 8 �79 6 10 �4
Mixed exercise 5 (page 67)1 a) 58 b) 94 c) 82 d) 133 e) 622 a) 35 b) 36 c) 37 d) 24 e) 83 a) 21 � 45 � 66, 66 � 21 � 45, 66 � 45 � 21
b) 39 � 14 � 53, 53 � 14 � 39, 53 � 39 � 14c) 15 � 52 � 67, 67 � 15 � 52, 67 � 52 � 15d) 37 � 18 � 55, 55 � 18 � 37, 55 � 37 � 18e) 36 � 54 � 90, 90 � 36 � 54, 90 � 54 � 36
4 a) 43 b) 14 c) 16 d) 45 a) 15 b) 28 c) 48 d) 32 e) 636 a) 8 b) 8 c) 7 d) 2 e) 77 a) 6 � 7 � 42, 42 � 6 � 7, 42 � 7 � 6
b) 8 � 7 � 56, 56 � 8 � 7, 56 � 7 � 8c) 8 � 5 � 40, 40 � 8 � 5, 40 � 5 � 8d) 6 � 4 � 24, 24 � 6 � 4, 24 � 4 � 6e) 6 � 9 � 54, 54 � 9 � 6, 54 � 6 � 9
8 a) 1 b) 25 c) 49 d) 64e) 8 f) 125 g) 4 h) 6
9 a) �4.2 b) �9.4 c) �8.5d) �6.7 e) �7.5
10 a) 47 b) 2 c) 98d) 105 e) 7
11 a) 9.1 b) 1.6 c) 68.7d) 1.4 e) 3.9 f) 16.4
12 a) 1.39 b) 3.88 c) 16.38d) 43.95 e) 1.33 f) 2.67
13 a) 40 b) 30 000 c) 8000d) 800 000 e) 10 000
14 20 00015 a) �6 b) 2 c) �4
d) 2 e) 516 a) 6 b) �1 c) 6
d) 1
Chapter 6Exercise 6.1 (page 71)
1 a) 7.29 b) 22.09 c) 1444d) 107 584 e) 0.3844 f) 0.0361g) 0.0049 h) 3.24 i) 4.6656j) 998.56
2 a) 4.1 b) 7.7 c) 1.6d) 17.2 e) 36 f) 0.31g) 0.49 h) 0.86 i) 3.75j) 0.047
3 a) 4.16 b) 5.46 c) 9.38d) 23.81 e) 48.46 f) 0.59g) 0.95 h) 154.24 i) 1.37j) 0.28
4 21.9 cm
Exercise 6.2 (page 73)1 2.419 2 3.84 3 34.24 3.450 5 12.606 6 62.417 41.33 8 0.417 9 4.48
10 26 11 6.983 12 2.545
Mixed exercise 6 (page 74)1 a) 50.41 b) 40.96 c) 1444
d) 271 441 e) 0.21162 a) 4.8 b) 8.3 c) 24.3
d) 0.33 e) 0.0633 a) 6.11 b) 23.17 c) 201.70
d) 0.624 e) 0.284 98.2 m5 a) 7.529 b) 10.536 c) 19.36
d) 91.2 e) 23.810 f) 2.494
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Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 169
Chapter 7Exercise 7.1 (page 77)
1 2 � 3 2 2 � 53 3 � 5 4 3 � 75 2 � 2 � 2 � 2 � 2 � 25
6 2 � 2 � 3 � 3 � 22 � 32
7 2 � 2 � 5 � 7 � 22 � 5 � 78 2 � 5 � 5 � 5 � 2 � 53
9 3 � 3 � 5 � 7 � 32 � 5 � 710 2 � 2 � 3 � 5 � 7 � 22 � 3 � 5 � 7
Exercise 7.2 (page 81)1 4 � 22; 6 � 2 � 3; HCF � 2;
LCM � 22 � 3 � 122 12 � 22 � 3; 16 � 24; HCF � 22 � 4;
LCM � 3 � 24 � 48 3 10 � 2 � 5; 15 � 3 � 5; HCF � 5;
LCM � 2 � 3 � 5 � 304 32 � 25; 40 � 23 � 5; HCF � 23 or 8;
LCM � 25 � 5 � 1605 35 � 5 � 7; 45 � 9 � 5; HCF � 5;
LCM � 32 � 5 � 7 � 3156 27 � 33; 63 � 32 � 7; HCF � 32 � 9;
LCM � 33 � 7 � 1897 20 � 22 � 5; 50 � 2 � 52; HCF � 2 � 5 � 10;
LCM � 22 � 52 � 1008 48 � 24 � 3; 84 � 22 � 3 � 7;
HCF � 22 � 3 � 12; LCM � 24 � 3 � 7 � 336 9 50 � 2 � 52; 64 � 26; HCF � 2;
LCM � 26 � 52 � 160010 42 � 2 � 3 � 7; 49 � 72; HCF � 7;
LCM � 2 � 3 � 72 � 294
Exercise 7.3 (page 84)1 �12 2 �20 3 �30 4 �545 �28 6 �16 7 �18 8 �49 �5 10 �8 11 �3 12 �2
13 �9 14 �7 15 �4 16 �1217 �21 18 �6 19 �9 20 �20
Exercise 7.4 (page 86)1 a) 49 b) 121 c) �6 d) �12
e) 8 f) 1000 g) 4 h) 12 6 cm3 a) 625 b) 1600 c) 1225
d) 1024 e) 1.444 a) 1728 b) 15.625 c) 226.981
d) 27 000 e) 157.4645 a) �20 b) �23.98 c) �35.83
d) �60.70 e) �1246 a) 8 b) 8.78 c) 20
d) 21.15 e) 21.547 1 and 64
Exercise 7.5 (page 87)1 a) 35 b) 73 c) 34 � 52
2 a) 55 b) 107 c) 84
d) 310 e) 26
3 a) 52 b) 103 c) 83
d) 32 e) 20 � 1
4 a) 54 b) 1011 c) 82 d) 34
5 a) 25 b) 32 c) 54 d) 73
Exercise 7.6 (page 90)1 a) �
13� b) �
16� c) �4
19�
d) �1100� e) �6
140�
2 a) 16 b) 9 c) 52
d) 67 e) 1000
3 a) 1�14� b) 2�
23� c) �
58�
d) �130� e) 12�
12�
4 a) 0.4 b) 2 c) 0.008d) 6.25 e) 0.3125
Mixed exercise 7 (page 91)1 a) 3 � 52 b) 22 � 5 � 7
c) 22 � 3 � 5 � 72 a) 24 � 23 � 3, 60 � 22 � 3 � 5, HCF � 12,
LCM � 120b) 100 � 22 � 52, 150 � 2 � 3 � 52, HCF � 50,
LCM � 300c) 81 � 34, 135 � 33 � 5, HCF � 27, LCM � 405
3 a) �12 b) �16 c) 8 d) 34 a) 16, 64 b) 36, 216 c) 100, 10005 a) �8 b) �146 a) 5 b) 37 a) 21.16, 97.336 b) 441, 9261
c) 8.41, 24.3898 a) �9.43, 4.46 b) �11.14, 4.99
c) �31.40, 9.95
9 a) 57 b) 103 c) 82 d) 26 e) 33
10 a) �15� b) �
18� c) 8
d) 10 e) �58� or 0.625
Chapter 8Exercise 8.1 (page 97)
1 a) 9, �79� b) 24, �
78� c) 40, �
38�
2 a) �79� b) �1
71� c) �
13�
d) �153� e) �
56� f) 1�
18�
g) �13� h) 1�
35� i) 3�
12�
j) 2�14� k) 4�
19� l) 2�
67�
3 a) �78� b) �
79� c) �1
72�
d) �14� e) 1�1
30� f) 1�
1238�
g) �1138� h) 1�
12� i) 1�
1138�
j) �2330� k) �
1336� l) �
3490�
4 a) 5�170� b) 3�
18� c) 4�
1114�
d) 3�112� e) 7�
38� f) 4�1
72�
g) 7�1118� h) �2
16� i) 6�2
11�
j) 5�1230� k) 1�
1114� l) �
56�
Exercise 8.2 (page 102)1 a) �
149� b) �
137� c) �
123�
d) �281� e) �
273� f) �
1172�
g) �167� h) �
6121�
2 a) 2�25� b) 4�
12� c) �1
25�
d) 4�38� e) �2
51� f) 9
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170 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
3 a) �136� b) �2
47� c) �2
54�
d) 1�38� e) 1�
35� f) �
1258�
g) �247� h) �
78� i) �
2207�
j) 1�59� k) 5�
13� l) �3
72�
4 a) 7�170� b) 2�
17� c) 1�
47�
d) �14
70� e) 8�
25� f) 1�1
94�
g) 10 h) 3�13� i) 7�
57�
j) 2�25� k) 18�
12� l) 1�
1309�
Exercise 8.3 (page 106)1 a) �
12
31� b) �2
70� c) �2
52�
d) 1�175� e) 5�
11
34� f) 1�
1112�
g) 12�67� h) 3�4
94�
2 a) �25� b) �
58� c) �1
75�
d) �176� e) �
19�
3 a) 2�115� b) 7�
11
17� c) 4�
1135�
d) 4�45� e) 8�1
33�
4 a) 20�56� cm b) 24�
34� cm2
Exercise 8.4 (page 108)1 a) 0.8 b) 0.375 c) 0.182
d) 0.111 e) 0.452 a) Terminating, 5 is a factor of 10
b) Recurring, 3 is not a factor of 10c) Recurring, 9 is not a factor of 10d) Terminating, 16 has only factors which are
factors of 10e) Recurring, 7 is not a factor of 10
3 a) 0.714 285 7…b) Six
Exercise 8.5 (page 109)1 7.7 2 7.9 3 3.64 2.2 5 7.1 6 8.17 5.7 8 3.8 9 12.2
10 16.5 11 0.9 12 5.8
Exercise 8.6 (page 113)1 a) 1.2 b) 3.5 c) 1.8 d) 7.2
e) 0.24 f) 0.48 g) 12 h) 35i) 0.06 j) 0.08 k) 0.49 l) 0.09
2 a) 40 b) 4 c) 4 d) 9e) 20 f) 20 g) 30 h) 50i) 80 j) 30 k) 3.1 l) 122
3 a) 6.3 b) 14.26 c) 35.99 d) 19.44e) 113.4 f) 388.8 g) 49.84 h) 26.16i) 5.08 j) 1.872 k) 3.822 l) 9.968
4 a) 49 b) 17 c) 24 d) 32e) 53 f) 78 g) 5.7 h) 4.9i) 2.9 j) 2.7 k) 3.7 l) 4.5
Exercise 8.7 (page 116)1 a) 1.13 b) 1.2(0) c) 1.68 d) 1.08
e) 1.02 f) 1.175 g) 2(.00) h) 2.5(0)2 a) 0.86 b) 0.8(0) c) 0.55 d) 0.93
e) 0.97 f) 0.77 g) 0.14 h) 0.8353 £4.78
4 £29.405 £29176 £34 6967 £87368 £159 6279 £2980.80
Mixed exercise 8 (page 118)1 a) 30, �
56� b) 21, �
13� c) 40, �
12
30�
2 a) 1�25� b) 1�2
21� c) �
12
14� d) �
56� e) �
12
34�
3 a) 5�152� b) 3�2
70� c) 8�
38� d) 6�1
18� e) 1�
12
30�
4 a) �25� b) �
12
01� c) �
11
56� d) 2�1
10� e) �2
90�
5 a) 3�23� b) 1�
12
31� c) 3�
34� d) �
14
74� e) 9�
37�
6 a) 0.125 b) 0.222 c) 0.714 d) 0.2737 a) 9.7 b) 5.3 c) 8.7 d) 4.68 a) 2 b) 0.07 c) 0.72
d) 10.8 e) 9.18 f) 18.729 a) 30 b) 8 c) 3
d) 80 e) 79 f) 8.7
10 a) 1�616� b) �
14
10� c) 3�
17� d) 3�
19�
11 £526312 £29.52
Chapter 9Exercise 9.1 (page 121)
1 a) 2 : 1 b) 1 : 3 c) 5 : 1d) 1 : 3 : 5 e) 3 : 6 : 4
2 a) 1 : 20 b) 3 : 20 c) 4 : 1d) 16 : 3 e) 3 : 20
3 5 : 64 5 : 8 : 105 4 : 2 : 3
Exercise 9.2 (page 122)1 a) 1 : 3 b) 1 : 5 c) 1 : 2.5
d) 1 : 1.75 e) 1 : 7.5 f) 1 : 125g) 1 : 0.2 h) 1 : 500 000
2 1 : 250 0003 1 : 6
Exercise 9.3 (page 126)1 a) 12 cm b) 3.5 cm2 a) 24 babies b) 9 helpers3 a) 6 litres b) 4 litres4 140 mm or 14 cm5 a) 28 miles b) 10 inches6 a) 30 ml b) 10 teaspoons7 a) 100 ml b) 36 ml8 a) 150 g b) 48 g9 £120
10 a) 500 g b) 180 g
Exercise 9.4 (page 128)1 Dave £8, Sam £122 a) 15 litres b) 25 litres3 30 kg sand
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 170
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 171
4 a) 50 ml b) 250 ml5 Amit £320, Bree £800, Chris £4806 15607 £2928 a) 400 g b) 80 g
Exercise 9.5 (page 131)In all these questions either cost per unit or number of unitsper penny can be used. Both are given in each answer.Where necessary, answers are rounded to 2 decimal places,unless otherwise indicated.
1 Cost per gram: 420 g bag � 0.38p, 325 g bag � 0.34pGrams per penny: 420 g bag � 2.64 g, 325 g bag � 2.98 g325 g bag is better value.
2 Cost per litre: 2 litre bottle � 42.5p, 5 litre bottle � 35.8pMillilitres per penny: 2 litre bottle � 23.53 ml, 5 litre bottle � 27.93 ml5 litre bottle is better value.
3 Cost per gram: 680 g pack � 0.47p, 1.4 kg pack � 0.39pGrams per penny: 680 g pack � 2.125 g, 1.4 kg pack � 2.59 g1.4 kg pack is better value.
4 Cost per nail: 50 pack � 2.5p, 144 pack � 2.64pNails per penny: 50 pack � 0.4 nails, 144 pack � 0.38 nails50 pack is better value.
5 Cost per roll: 12 pack � 14.92p, 50 pack � 14.4pRolls per penny: 12 pack � 0.067 rolls, 50 pack � 0.069 rolls (answers rounded to 3 decimal places)50 pack is better value.
6 Cost per ml: 80 ml tube � 3.49p, 150 ml tube � 3.33pMillilitres per penny: 80 ml tube � 0.29 ml, 150 ml tube � 0.3 ml150 ml tube is better value.
7 Cost per litre: 3 litres � 66.33p, 2 litres � 67.5p, 1 litre � 57pLitres per pound: 3 litre � 1.51 litres, 2 litre � 1.48 litres, 1 litre � 1.75 litres1 litre bottle is the best value.
8 Cost per gram: 750 g � 0.239p, 1.4 kg � 0.229p, 2 kg � 0.245p (answers rounded to 3 decimal places)Grams per penny: 750 g � 4.19 g, 1.4 kg � 4.38 g, 2 kg � 4.09 g1.4 kg packet is the best value.
Mixed exercise 9 (page 132)1 a) 10 : 7 b) 5 : 12 c) 3 : 1
d) 9 : 20 e) 3 : 52 a) 1 : 4 b) 1 : 2.4 c) 1 : 50
d) 1 : 250 000 e) 1 : 0.43 a) 60 cm b) 5 cm
4 250 g5 a) 60 g b) 250 g6 a) 500 ml b) 240 ml
In questions 7 and 8 either cost per unit or number ofunits per pound or per penny can be used. Both aregiven in each answer.
7 Cost per litre: 5 litres � £3.70, 2 litres � £3.50Litres per pound: 5 litres � 0.270 litre, 2 litres � 0.286 litre (answers rounded to 3 decimal places)2 litres is better value.
8 Cost per millilitre: pint � 0.076p, litre � 0.075p(answers rounded to 3 decimal places)Millilitres per penny: pint � 13.2 ml, litre �13.3 ml(answers rounded to 1 decimal place)Litres are better value.
Chapter 10Exercise 10.1 (page 135)
1 a) 26 b) 1.5 c) 58 d) 200e) 80.4 f) 20.1 g) 661 h) 10.1i) 283 j) 275
2 a) 16 b) 0.9 c) 87 d) 58e) 69.6 f) 65 g) 69 h) 277i) 85.7 j) 996
3 a) 72 b) 52 c) 2.4 d) 160e) 800 f) 336 g) 185 h) 520i) 1000 j) 775
4 a) 4 b) 80 c) 13 d) 16e) 13 f) 4 g) 0.08 h) 6i) 20 j) 3
5 a) 4 b) �4 c) �7 d) 6e) �2 f) 10 g) �6 h) �4i) 24 j) 0
6 a) �8 b) �12 c) 12 d) �35e) 40 f) �3 g) �4 h) 3i) �2 j) 16
7 a) 36 b) 25 c) 121 d) 100e) 169 f) 400 g) 90 000 h) 0.16i) 0.49 j) 0.09
8 a) 4 b) 3 c) 7 d) 13e) 15
9 a) 1 b) 125 c) 8 d) 64 000e) 0.027
10 £9.2011 8 cm12 £15.2813 420 ml14 a) 17 cm b) 18 cm2
15 8 and 5
Exercise 10.2 (page 140)1 a) 8 b) 7 c) 20 d) 30
e) 500 f) 7 g) 1000 h) 0.4i) 0.7 j) 4000 k) 4000 l) 3
2 a) 10 b) 200 c) 20 d) 800e) 6000 f) 0.01 g) 0.6 h) 0.04i) 1 j) 20 000 k) 0.07 l) 2000
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172 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
3 a) 18 b) 180 c) 5700 d) 98 000e) 50 f) 0.17 g) 0.039 h) 0.0061i) 0.031 j) 0.99
4 a) 8.26 b) 69.8 c) 16 300 d) 208e) 12 500 f) 7.10 g) 50.9 h) 0.416i) 0.0386 j) 3.14
5 £180 or £2006 37 54 cm2 or 50 cm2
8 21 cm or 20 cm9 £2000
10 64 cm3 or 60 cm3
11 50 mph12 a) 4000 b) 9
c) 125 or 100 d) 49 or 50e) 24 000 or 20 000 f) 0.1g) 0.75 or 0.8 h) 36 000 or 40 000i) 43 or 40 j) 60k) 3.5 or 3 or 4 l) 60
Exercise 10.3 (page 142)1 a) 8 b) 64 c) 36
d) 26 e) 81 f) 72 a) 14 b) 80 c) 32
d) 50 e) 4 f) 163 5 : 24 225 cm2
5 (64 � 4) cm2
Exercise 10.4 (page 144)1 a) 4900 b) 0.036 c) 0.04
d) 0.0016 e) 0.04 f) 30 000g) 560 000 h) 1120 i) 120 300j) 9040 k) 0.12 l) 0.06
2 a) 25 b) 0.05 c) 0.13d) 70 e) 0.006 f) 90g) 30 h) 35 i) 15 000j) 4000 k) 0.013 l) 1000
3 a) 2160 b) 1.35 c) 16d) 0.002 16 e) 1600 f) 216
4 a) 9880 b) 3.8 c) 260d) 38 e) 0.038 f) 26
5 a) 408.51 b) 40 851 c) 1530d) 4.0851 e) 26.7 f) 15 300
Mixed exercise 10 (page 145)1 a) 92 b) 1.6 c) 141.9
d) 21.1 e) 441 f) 7.2g) 158 h) 8.1 i) 383j) 6.9
2 a) 153 b) 0.54 c) 710d) 345 e) 1025 f) 17g) 0.35 h) 0.82 i) 9j) 12
3 a) �4 b) 6 c) 17d) �9 e) 1 f) �28g) 30 h) �9 i) 5j) �3
4 a) 49 b) 0.81 c) 144d) 10 000 e) 196
5 £15.416 a) 9 b) 4 c) 30
d) 30 e) 600 f) 6g) 1000 h) 0.3 i) 0.6j) 50 000
7 32 cm2 or 30 cm2
8 50 mph9 a) 4000 b) 10
c) 200 d) 36 or 40e) 4200 or 4000 f) 0.1g) 30 h) 15 000 or 20 000i) 300 j) 21 or 20
10 a) 9.2 b) 4.7 c) 0.014d) 160 000 e) 510
11 a) 1480 b) 10.2 c) 0.0219d) 21 000 e) 0.005 62
12 a) 10 b) 49 c) 22d) 9 e) 85 f) 63
13 a) 15 000 b) 80 c) 48d) 0.09 e) 1539 f) 20g) 0.16 h) 70 i) 4500j) 12 000
14 a) 4446 b) 2.34 c) 19d) 0.004 446 e) 1900 f) 4.446
15 a) 38.682 b) 38 682 c) 1260d) 3.8682 e) 30.7 f) 1.26
Chapter 11Exercise 11.1 (page 150)
1 a) 6 b) x � 2 c) b � r2 a) 5 b) 2 � p c) q � r3 a) 5 b) x � 3 c) 2 � x4 a) 13 b) p � 9 c) 4 � q5 a) x � 5 b) x � 8 c) x � 2 � y
d) 2x � 46 a) 4 � x b) x � y c) 2x7 a) 10 b) 14 c) x � 68 a) 75p b) £1.50 c) 25x9 a) 2x b) 5x c) 7x
10 a) 2m b) m � 6
Exercise 11.2 (page 153)1 a) (i) 8 (ii) 3
b) g � 72 a) (i) 2 (ii) 7
b) p � 33 a) 12 � r b) s � 8 c) v � t4 a) (i) 6 cm (ii) 11 cm
b) p � 35 a) (i) 155 cm (ii) 184 cm
b) h � 56 a) x � 14 b) x � 21 c) x � p7 a) 12p b) a � 68 a) y � 10 b) y � 15 c) y � g9 a) 25 � a b) 15 � a c) b � a
10 b � 5
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 172
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 173
Mixed exercise 11 (page 155)1 a) 35 � f b) 60 � f c) c � f2 a) 15 � r b) x � 5 c) z � y3 a) (i) 9 (ii) 15 b) 3h4 a) p � 29 b) p � 53 c) p � e5 4x6 a) (i) £1.60 (ii) £2.40 b) 20x (pence)7 a � 8 (£)8 a) t � 4 b) t � 2 c) 2t9 a) x � 6 b) x � 3 c) 3x
10 a) p � 2 b) p � 3 � q c) p � r � s
Chapter 12Exercise 12.1 (page 158)
1 5p 2 7a 3 5x 4 4c5 7p 6 6b 7 3p 8 4s9 2a 10 5c 11 7x 12 4m
13 8a 14 2c 15 0 16 p17 2b 18 9x 19 9a 20 5a
Exercise 12.2 (page 160)1 a � 3b 2 x � 3y 3 4ab4 3p � q 5 6a � 6b 6 2a � 3c7 8pq 8 6x � 4y 9 3p2
10 6a � 4b � 4 11 3ab � 2bc 12 a2
13 a � 3c 14 4ab � 2a2 15 3s16 2a � 4 17 a2b 18 x � 3y19 10a � 2b 20 3a2b2
Mixed exercise 12 (page 161)1 4a 2 2a 3 abc4 y2 5 2c 6 4a � b7 2y � 3s 8 6a � b 9 2p2
10 3x � 2y 11 3x 12 6ab13 3ab � 3ac 14 3x � 2y 15 6a � 3b16 3 � 5x � 2y 17 3ab2 18 6 � a � b � c19 8pq 20 2a � 3b � 7
Chapter 13Exercise 13.1 (page 163)
1 20a � 30b 2 6c � 21d3 15e � 40f 4 28g � 21h5 10u � 15v 6 30w � 18x7 21y � 7z 8 16v � 409 12 � 42w 10 12 � 32a
11 8g � 6 12 35 � 20b13 6i � 8j � 10k 14 20m � 12n � 8p15 12r � 18s � 24t
Exercise 13.2 (page 166)1 a) 20a � 38 b) 27b � 53
c) 12 � 37c d) 32 � 22a2 a) 18s � 43t b) 14v � 49w
c) 27x � 77y d) 38v � 27w
3 a) 21x � 8 b) 14y � 4c) 22 � 3z d) 36 � 10x
4 a) 16n � 9p b) 21q � 13rc) 23d � 6e d) 14f � ge) �h � 11j f) 6k � 3m
Exercise 13.3 (page 167)1 a) 5(2x � 3) b) 2(x � 3)
c) 4(2x � 3) d) 4(x � 5)2 a) 7(2 � x) b) 4(2 � 3x)
c) 5(3 � 2x) d) 3(3 � 4x)3 a) x(3x � 5) b) 5x(x � 4)
c) 4x(3x � 2) d) 2x(3x � 4)
Exercise 13.4 (page 169)1 a) a2 � 10a � 21 b) b2 � 11b � 28
c) 6 � 5c � c2
2 a) 9d2 � 3d � 20 b) 8e2 � 2e � 15c) 6 � 5f � 56f 2
3 a) 4g2 � 20g � 21 b) 4h2 � 28h � 49c) 6j2 � 37j � 56
4 a) 10k2 � 23k � 42 b) 6 � 11m � 72m2
c) 6 � n � 15n2
5 a) 4 � 4p � 63p2 b) 6r2 � 37r � 56c) 4s2 � 20s � 21
Exercise 13.5 (page 170)1 a) 34 b) 73 c) 105
2 a) x5 b) y4 c) z7
3 a) m2n4 b) f 4g5 c) p3r4
4 a) 56k3 b) 120y3 c) 8d3
Mixed exercise 13 (page 171)1 a) 24a � 16b b) 20a � 15b
c) 36a � 60b d) 9a � 18be) 12x � 15y f) 18x � 12yg) 20x � 12y h) 8x � 2yi) 15f � 20g j) 6j � 15kk) 7r � 14s l) 12v � 4w
2 a) 12x � 11 b) 20x � 27c) 7x � 12 d) 16y � 5e) 15y � 7 f) 21y � 4g) 3a � 6 h) 6m � 1i) 6p � 18 j) 14t � 24k) �j � 31 l) 46
3 a) 4(x � 2) b) 6(x � 2)c) 3(3x � 2) d) 6(2x � 3)e) 2(3 � 5x) f) 5(2 � 3x)g) 8(3 � x) h) 4(4x � 3)i) 2(3x � 4) j) 4(8x � 3)k) 4(5 � 4x) l) 5(3 � 4x)m) x(2 � x) n) y(3 � 7y)o) z(5z � 2)
4 a) a2 � 9a � 20 b) a2 � 5a � 6c) 12 � 7a � a2 d) x2 � 7x � 8e) x2 � 4x � 45 f) x2 � 3x � 2g) 3x2 � 31x � 36 h) 2y2 � y � 21i) 14 � 25p � 6p2 j) 6p2 � 8p � 8k) 4t2 � 23t � 15 l) 6a2 � a � 15
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 173
174 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
5 a) 46 b) 54 c) 25 d) a7
e) j3 f) t6 g) v3w3 h) d3e6
i) x3y5 j) 60p3
Chapter 14Exercise 14.1 (page 174)
1 a) £45 b) £100 c) £60 d) £752 a) 3 b) 32 c) 16 d) 373 a) £24 b) £60 c) £14 d) £924 a) £25 b) £12 c) £280 d) £18.505 a) £90 b) £150 c) £105 d) £2906 a) 9 cm2 b) 75 cm2 c) 5 m2 d) 12.3 mm2
7 a) 40 mph b) 80 km/h c) 8 m/s d) 230 mph8 a) £17 b) £28 c) £50.50 d) £37.509 a) £35 b) £55 c) £80
10 a) £60 b) £400 c) £10 d) £48
Exercise 14.2 (page 177)1 c � 5a 2 B � J � 14
3 r � 4m 4 a � �m
n�
5 c � 50 � 10h 6 a � �b
2
h�
7 s � �d
t� 8 t � 6a � 2.5c
9 v � lwh 10 t � 0.2w
Note that in questions 11 to 15, different letters could beused.
11 t � 4.5wt stands for the total amount savedw stands for the amount saved each week
12 n � �3
r�
n stands for the number of strips of paperr stands for the length of a roll of paper
13 s � n � ds stands for the sale pricen stands for the normal priced stands for the discount
14 f � �d
5� � 3
f stands for the fared stands for the distance covered
15 c � 100 � 7sc stands for the total costs stands for the number of students
Exercise 14.3 (page 179)1 a) 9 b) 6 c) 3 d) 11
e) 10 f) 12 g) 10 h) 19i) 2 j) 17 k) 28 l) 14m) 1 n) 8 o) 8 p) 40q) 40 r) 18 s) 2 t) 25u) 3 v) 10 w) 20 x) 12y) 100 z) 8
2 a) 5 b) �1 c) 15 d) 5e) 11 f) 4 g) 9 h) 90i) 15 j) 27
3 a) 19 b) 39 c) 4 d) 6�12�
e) 14.54 a) 10 b) 10 c) 2325 a) 4 b) 6 c) 8.5 d) 8
Mixed exercise 14 (page 182)1 a) 15 m b) 42 m c) 75 m d) 10.5 m2 a) 50 °F b) 32 °F c) 86 °F d) 53.6 °F3 a) 2 hours b) 4.5 hours
c) 14 hours d) 80 seconds4 a) C � 3d b) F � 1.8C � 32
c) t � �d
s�
5 a) 9 b) 3 c) 30 d) 27e) 15 f) 24 g) 37 h) 26i) 16 j) 4 k) 5 l) 7.7m) 25 n) 13 o) 8 p) 107
Chapter 15Exercise 15.1 (page 184)
1 a) 90 minutes b) 210 minutes2 4°C3 £31
4 a) s � �d
t� b) 60 km/h
5 4906 187 a) 55 b) 208 a) 8x b) 3x2
9 a) 2 hours 10 minutes b) 1.5 kg10 511 15 miles12 a) 12
b)
c) C � 3P � 3 or C � 3(P � 1)d) 87
13 a) 24 cm2 b) 22.5 cm2
14 a) 120 cm3 b) 216 cm3
15 a) £45 b) 43 miles
Exercise 15.2 (page 188)
1 a) b � a � c b) x � �4a
w
� y�
c) t � �v �
a
u� d) t � �
p �
3
c�
e) q � �A �
p
pr� or q � �
A
p� � r
f) g � �p �
2
2f� g) n � �
Ft �
4
m�
Number of posts, P 1 2 3 4 5 6
Number of chains, C 0 3 6 9 12 15
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 174
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 175
2 u � �s
3
b
v
n�
3 h � �2
b
a�
4 R �
5 a) h � �
3V
r2� b) 16.6 cm
6 a) 140°F b) C � (F � 40) � �59� � 40
7 r � ��8 a) a � �
v2
2
�
s
u2
� b) u � �v2 � 2�as�
Mixed exercise 15 (page 189)1 a) 104°F b) 32°F c) 23°F2 95p3 a) 12 cm2 b) 21.6 cm2
4 a) 34 minutes b) 47.8 minutes
5 a) q � p � 2r b) r � �x �
5
s�
c) r ��m
pq
s� d) y � �
tx �
2t
A� or y � �
x
2� � �
A
2t�
6 a) w � �T �
45
40� b) w � 2.4 kg
7 a) 4 cm b) 8 cm8 a) 30 words b) 60 words
Chapter 16Exercise 16.1 (page 193)
1 a) 1, 5, 9, 13, 17 b) �4, �1, 2, 5, 8c) 21, 18, 15, 12, 9 d) 5, 10, 15, 20, 25e) 100, 60, 20, �20, �60 f) 1, 1�
12�, 2, 2�
12�, 3
2 a) 25, 29; �4 b) 39, 45; �6c) 47, 54; �7 d) 25, 28; �3e) 38, 43; �5 f) 77, 86; �9
3 a) 7, 5; �2 b) 9, 5; �4c) 9, 3; �6 d) 4, 0; �4e) �1, �5; �4 f) �2, �7; �5
4 a) 15, 36; Add 7 b) 17, 35; Add 6c) 65, 21; Subtract 11 d) 66, 30; Subtract 9e) 22, 30; Add 8 f) 18, �2; Subtract 5
Exercise 16.2 (page 194)1 a) rule �3 b) rule �2
c) rule �5 d) rule �4
3V�h
100I�PT
2 a) b)
rule �4 rule �3
c) d)
rule �4 rule �5
Exercise 16.3 (page 196)1 a) 11, 15, 19, 23, 27 b) 13, 21, 29, 37, 45
c) 12, 19, 26, 33, 40 d) 2, 5, 8, 11, 14e) 13, 18, 23, 28, 33 f) 16, 25, 34, 43, 52
2 a) 603 b) 799 c) 2194d) 1202 e) 2413 f) 1795
Mixed exercise 16 (page 196)1 a) 1, 6, 11, 16, 21 b) 50, 46, 42, 38, 34
c) �6, �4, �2, 0, 22 a) 26; rule �4 b) 51; rule �8
c) 34; rule �53 a) 9, 5; rule �4 b) 5, 2; rule �3
c) �2, �15; rule �134 a) 22, 27, 37; rule �5 b) 22, 13, 7; rule �3
c) 26, 37, 70; rule �115 a) rule �3 b) rule �3
6 a) rule �6
b) rule �7
7 a) 5, 9, 13, 17; 601 b) 4, 13, 22, 31; 697c) 10, 18, 26, 34; 738
Chapter 17Exercise 17.1 (page 200)
1 a) Multiply the pattern number by 2b) 200
2 a)
b) They go up by 2 each time; they are the 2 timestable plus 2.
c) 1023 a)
b) 36You add 1 more to the difference each time, soT4 � 10, T5 � 15, T6 � 21, T7 � 28, T8 � 36
Pattern number 1 2 3 4 5
Number of matchsticks 4 6 8 10 12
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 175
176 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
4 a) 3 � 1 � 5 � �2 b) 1, 4, 7, 105 a) 4, 10, 16, 22 b) 5, 9, 13, 17
c) 4, 2, 0, �26 a) 1, 4, 9, 16, 25 b) 3, 6, 11, 18, 27
c) 1, 8, 27, 64, 1257 2, 4, 8, 16, 328 5, 2, �1, �49 For example
and so on.10 For example
and so on.
Exercise 17.2 (page 205)1 a) 2n � 3 b) 3n � 1 c) n � 62 a) 20 � 3n b) 10 � 5n c) 1 � n3 a) Linear: 17, 20 b) Not linear
c) Linear: 30, 36 d) Not linear4 a) 6, 0, �6, �12, �18 b) 14 � 6n5 a)
b) 15n � 2 c) 76 1, 3, 6, 10, 15, 21, 28, 36, 45, 557 2108 a) 10, 100, 1000, 10 000, 100 000
b) Powers of 109 a) 1, 4, 9, 16, 25
b) (i) Each term is 3 more than the equivalentterm in the sequence of square numbers.
(ii) n2 � 3(iii) 10 003
10 a) Each term is 3 times the equivalent term in thesequence of square numbers.
b) 3n2 c) 1200
Mixed exercise 17 (page 207)1 a) 300
b) Multiply the term number by 3 or start with 3and add 3 each time.
2 a)
b) 64. This is the sequence of square numbers; the8th pattern has 8 � 8 stars.
3 a) T1 � 1 � 6 � 2 � 4 b) 10, 16, 22, 284 a) 7, 12, 17, 22 b) 2, 5, 10, 17
c) 88, 86, 84, 825 4, 8, 16, 32, 64
6 a) Tn � 3n � 2 b) Tn � 6n � 5c) Tn � 7 � 5n
7 a) Linear: 24, 29 b) Not linearc) Not linear d) Linear: �12, �18
8 a) 3, 9, 27, 81, 243 b) Powers of 39 A suitable answer is as follows.
10 a) 1, 4, 9, 16, 25 b) Tn � n2 � 4
Chapter 18Exercise 18.1 (page 209)
1 A(2, 1) B(4, 6) C(7, 7) D(1, 8)E (7, 2) F(6, 0) G(0, 4) H(9, 4)I(5, 3) J(10, 1)
2
Exercise 18.2 (page 214)1 A(1, 2) B(3, �1) C(�2, 4) D(0, �2)
E(�3, �1) F(2, �3) G(3, 3) H(�4, 2)I(0, 3) J(�2, �3)
2
Square
3
Isosceles triangle
�5�4�3�2�10 1
1C
B
A
�1�2�3�4�5
2345y
x2 3 4 5
�5�4�3�2�10 1
1
C B
D A
�1�2�3�4�5
2345y
x2 3 4 5
0
1
2
3
4
5
6
7
8y
x1 2 3 4 5 6 7
E
C
A
B
D
8
1 3 6 10 15
Number of tickets 1 2 3 4
Cost in £ 17 32 47 62
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 176
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 177
4
Trapezium
5
Rhombus
6
D(�2, 3)
7
C(�3, �1)
8
C(�3, �4)
�5�4�3�2�10 1
1
C
B
D
A
�1�2�3�4�5
2345y
x2 3 4 5
�5 �4 �3 �2 �10 1
1
C B
D A
�1�2
�3
�4
�5
2
3
4
5y
x2 3 4 5
�5 �4 �3 �2 �10 1
1
C B
D A
�1�2
�3
�4
�5
2
3
4
5y
x2 3 4 5
�5�4�3�2�10 1
1C
B
D
A
�1�2�3�4�5
2345y
x2 3 4 5
�5�4�3�2�10 1
1
C
B
DA
�1�2�3
�4�5
2345y
x2 3 4 5
Exercise 18.3 (page 219)
1 a) x � 3 b) y � 2
c) x � �4 d) y � �12
For graph, see question 4.3
For graph, see question 4.
4
5
For graph, see question 6.
6
7 (1, 4)
x
y
y � 5 � x
y � 3x � 1
�7�6�5�4�3�2�1
10
234567
�7 �5 �3 3 5 7�1 1
x
y
y � x � 4
y � x � 2
x � y � 6
�7�6�5�4�3�2�1
10
234567
�7 �5 �3 1 3 5 7�1
x �3 �2 �1 0 1 2 3
y � x � 4 1 2 3 4 5 6 7
x �3 �2 �1 0 1 2 3
y � x � 2 �5 �4 �3 �2 �1 0 1
x �1 0 1 2 3 4 5 6
x � y � 6 7 6 5 4 3 2 1 0
x �2 �1 0 1 2
y � 3x � 1 �5 �2 1 4 7
x �2 �1 0 1 2 3 4 5
y � 5 � x 7 6 5 4 3 2 1 0
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 177
178 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
Mixed exercise 18 (page 220)1 A(5, 1), B(2, �1), C(�2, 1), D(�4, 0),
E(�1, �3), F(0, �2), G(2, 4)2
3
Parallelogram4
Trapezium5
D(�1, �3)
�5 �4 �3 �2 �1 0 1
D
1
�1
�2
�3
�4
�5
2
3
4
5
y
x2 3 4 5
A
B
C
�5 �4 �3 �2 �1 0 1
A
1
�1
�2
�3
�4
�5
2
3
4
5
y
x2 3 4 5
B
C
D
�5 �4 �3 �2 �1 0 1
A
D
1
�1
�2
�3
�4
�5
2
3
4
5
y
x2 3 4 5
C
B
�5 �4 �3 �2 �1 0 1
F
D
G
A
C
E
B
1
�1
�2
�3
�4
�5
2
3
4
5
y
x2 3 4 5
6 There are two possible answers to this question.
(5, 4), (�1, 4) or (2, 1), (2, �5)7 y � x � 1
For graph, see question 9.8 x � y � 2
For graph, see question 9.9 y � 2x � 1
10 a) (2, 3) b) (1, 1) c) (�12�, 1�
12�)
�7 �4�5�6 �3 �2 �1 0 1
1
�1
�2
�3
�4
�5
�6
�7
2
3
4
5
6
7 C
A
B
y
x2 3 4 5 6 7
�5 �4 �3 �2 �1 0 1
1
�1
�2
�3
�4
�5
2
3
4
5
y
x2 3 4 5
x �3 �2 �1 0 1 2 3
y �2 �1 0 1 2 3 4
x �3 �2 �1 0 1 2 3 4
y 5 4 3 2 1 0 �1 �2
x �2 �1 0 1 2 3 4
y �5 �3 �1 1 3 5 7
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 178
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 179
Chapter 19Exercise 19.1 (page 223)
1 a � 5 2 p � 5 3 x � 84 m � 2 5 a � 7 6 x � 37 n � 12 8 h � 3 9 r � 11
10 n � 4 11 x � 28 12 m � 1313 b � 16 14 p � 36 15 x � 416 x � �5 17 x � �4 18 x � �819 x � �4 20 x � �14
Exercise 19.2 (page 224)1 x � 6 2 m � 11 3 b � 84 p � 8 5 x � 3 6 x � 47 x � 7 8 x � 5 9 x � 2
10 x � 4 11 x � 5 12 x � 913 x � 14 14 x � 8 15 x � 816 x � �1
Exercise 19.3 (page 225)1 x � 6 2 p � 12 3 p � 254 x � 18 5 a � 6 6 m � 487 t � 4 8 b � 128 9 d � 18
10 y � 1000 11 x � 54 12 x � 1813 x � 4 14 x � 21 15 x � 7216 x � 24 17 x � 80 18 x � 3019 x � �10 20 x � �16
Exercise 19.4 (page 226)1 a � 59° b � 92° c � 149° d � 98°2 x � 2 � 16, x � 183 8x � 72, x � 94 2x � 5 � 13, x � 45 3x � 6 � 18, x � 86 3x � 5 � 10, x � 5
Mixed exercise 19 (page 227)1 x � 4 2 x � 63 x � 7 4 x � 65 x � 23 6 x � �267 x � 14 8 x � �19 x � 7 10 x � 5
11 m � 3 12 p � 213 y � 8 14 x � 415 x � 5 16 x � 617 x � 2 18 x � 1619 x � 75 20 x � �1621 10x � 5 � 95; x � 9
Chapter 20Exercise 20.1 (page 229)
1 x � 7 2 x � 0.53 x � 7 4 x � 75 x � 1 6 x � 77 x � 5 8 x � 49 x � 10 10 x � 6
11 x � 5 or x � �5 12 x � 7 or x � �713 y � 8 or y � �8 14 m � 9 or m � �915 m � 5 or m � �5 16 x � 10 or x � �1017 x � 8 or x � �8 18 x � 4 or x � �419 x � 2 or x � �2 20 x � 10 or x � �10
Exercise 20.2 (page 229)1 p � 16 2 x � 3 3 x � 74 x � 1 5 x � 15 6 x � 17 x � 14 8 x � 5 9 x � �4
10 x � 10 11 x � 10 12 a � 113 x � 1 14 x � 3 15 x � 216 x � 3 17 x � 8 18 x � 419 x � 2 20 x � 5.5
Exercise 20.3 (page 231)1 x � 3 2 x � 3 3 x � 24 x � 10 5 x � 3 6 x � 27 x � 10 8 x � �2 9 x � 3
10 x � 2 11 x � 2 12 x � 113 x � 3 14 x � 4.5 15 x � 416 x � 6 17 x � 1 18 x � 219 x � �3 20 x � 7
Exercise 20.4 (page 232)1 x � 16 2 a � 40 3 x � 204 y � 50 5 y � 30 6 p � 357 m � 24 8 x � 64 9 x � 27
10 y � 33
Exercise 20.5 (page 234)1 x � 1.72 a) 23 � 5 × 2 � �2
33 � 5 × 3 � 12b) x � 2.8
3 a) 43 � 4 � 6053 � 5 � 120
b) x � 4.64 a) 3.73 � 3.7 � 47 (nearest whole number)
3.83 � 3.8 � 51.1 (1 d.p.)b) x � 3.77
5 x � 2.66 x � 4.337 228 31.69 a) x(x � 4) � 621, i.e. x2 � 4x � 621
b) 27, 2310 7.8
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 179
180 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
Exercise 20.6 (page 237)1 x 13
2 x � 4
3 x � 13
4 x � 4
5 x 3
6 x 8
7 x � 2 8 x �5 9 x � �910 x 1 11 x 5 12 x � 913 x � 2 14 x 6 15 x 516 x � 0.25 17 x 2 18 x 319 x � 4 20 x � 4
Mixed exercise 20 (page 238)1 a) m � 9 b) p � 2
c) x � 8 d) x � 3e) p � 8 f) x � 4 or �4g) x � 6 or �6 h) p � 4 or �4i) x � 4 or �4 j) a � 5 or �5k) x � 25 l) x � 30m) y � 18 n) y � 49o) a � 36
2 a) 13 � 4 � 1 � 5, 23 � 4 � 2 � 16b) x � 1.7
3 a) 33 � 32 � 18, 43 � 42 � 48b) x � 3.4
4 a) x3 � x � 100 b) x � 4.65 a) x � 2
b) x 3
c) x � 3
d) x 4
e) x 2
0 1 2 3 4 5
0 1 2 3 4 5
0 1 2 3 4 5
0 1 2 3 4 5
0 1 2 3 4 5
Chapter 21Exercise 21.1 (page 240)
1 Three points plotted, e.g. (�3, �12), (0, 0), (3, 12), straight line drawn through them.
2 Three points plotted, e.g. (�3, 0), (0, 3), (3, 6), straight line drawn through them.
3 Three points plotted, e.g. (�2, �10), (0, �4), (4, 8), straight line drawn through them.
4 Three points plotted, e.g. (�2, �10), (0, �2), (3, 10), straight line drawn through them.
5 Three points plotted, e.g. (�4, 8), (0, �4), (2, �10), straight line drawn through them.
Exercise 21.2 (page 242)1 Three points plotted, e.g. (�2, �4), (0, �1),
(4, 5), straight line drawn through them.2 Points (0, 3) and (7.5, 0) plotted, straight line drawn
through them.3 Points (0, 7) and (2, 0) plotted, straight line drawn
through them.4 Three points plotted, e.g. (�3, �6), (0, 1�
12�),
(3, 9), straight line drawn through them.5 Points (0, 7) and (3.5, 0) plotted, straight line drawn
through them.
Exercise 21.3 (page 245)1 a) She walked at 3 km/h for 20 minutes (distance
� 1 km), waited for 5 minutes, travelled in abus (or car) at 45 km/h for 12 minutes (distance� 9 km).
b) Approximately 35 minutesc) (i) 0.25 km/minute
(ii) 15 km/hd) (i) Approximately 0.75 km/minute
(ii) Approximately 45 km/h2 Description to include:
● A winning, B second, C third● A ran at a steady speed, B started off quickly but
gradually slowed down, C ran in a series ofsprints and rests.
May also mention approximately when overtakingtook place.
3 a) £2 b) 80pc)
d) £24e) 69p (to nearest penny)
100 20 30Distance (km)
Ch
arg
e (
£)
40 50
5
10
15
20
25
30
d)
6 8 10 12 14 16
0 1 2 3 4 5
6 8 10 12 14 16
0 1 2 3 4 5
0 1 2 3 4 5
0 2 4 6 8 10
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 180
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 181
4 a) D b) H c) F d) C5 a) £49.50 b) £46.50
c)
6 a)
b) Less than 91 cubic metres
Exercise 21.4 (page 253)Answers read from graphs may be approximate.
1 a)
b)
c) (i) 3.3(ii) 2.4 to 2.5 or �2.4 to �2.5
�3 �2 �1 0 1 2 3
1
�1�2�3�4
2345678y � x2 �2
y
x
40
0
80 120Water used (cubic metres)
Cha
rge
(£)
16020 60 100 140
2010
40
60
80
100
120
30
50
70
90
110
130140150160170180
b)
20
4 6Number of boxes
Cos
t (£)
8 10 121 3 5 7 9 11
10
20
30
40
50
60
2 a)
b)
c) (i) 0.8 to 0.9 (ii) 0.6 or 3.4
3 a)
b)
c) (i) �1.8 (ii) �2.3 or 1.3
�3�4 �2 �1 0 1 2 3 x
y
1
�1�2�3�4
23456789
y � x2 � x � 3
�1 1 30 2 4 5 x
y
�2�3�4�5
�1
12345 y � x2 �4x
x �3 �2 �1 0 1 2 3
x2 9 4 1 0 1 4 9
�2 �2 �2 �2 �2 �2 �2 �2
y � x2 � 2 7 2 �1 �2 �1 2 7
x �1 0 1 2 3 4 5
x2 1 0 1 4 9 16 25
�4x 4 0 �4 �8 �12 �16 �20
y � x2 � 4x 5 0 �3 �4 �3 0 5
x �4 �3 �2 �1 0 1 2 3
x2 16 9 4 1 0 1 4 9
x �4 �3 �2 �1 0 1 2 3
�3 �3 �3 �3 �3 �3 �3 �3 �3
y � x2 � x � 2 9 3 �1 �3 �3 �1 3 9
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182 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
4 a)
b)
c) (i) 1.75 (ii) �1.4 or 4.4
5 a)
b)
c) (i) 2.25(ii) �0.5 to �0.6 or 3.5 to 3.6
6 a)
y
�10�9�8�7�6�5�4�3�2�1
123
y � 3x � x2
�2 �1 10 2 3 4 5 x
y
123456789
1011121314
y � x2 �3x � 4
�2 �1 10 2 3 4 5 x
b)
c) (i) �1.8 or 2.8 (ii) �2.4 or 3.47 a)
b)
c) (i) �1.6 or 1.6 (ii) �2.7 or 2.78 a)
b)
c) (i) 1.8 (ii) 3.6 to 3.7
x
A
A � 6x2
10 2 3 4 5
20
40
60
80
100
120
140
160
�3 �2 �1 0 1 2 3 x
y
1
�1�2�3�4�5�6
23456789
10111213
y � 2x2 � 5
�3 �2 �1 0 1 2 3 4 x
y
1
�1�2�3�4�5�6
234567
y � x2 � x � 5
x �2 �1 0 1 2 3 4 5
x2 4 1 0 1 4 9 16 25
�3x 6 3 0 �3 �6 �9 �12 �15
4 4 4 4 4 4 4 4 4
y � x2 � 3x � 4 14 8 4 2 2 4 8 14
x �2 �1 0 1 2 3 4 5
3x �6 �3 0 3 6 9 12 15
�x2 �4 �1 0 �1 �4 �9 �16 �25
y � 3x � x2 �10 �4 0 2 2 0 �4 �10
x �3 �2 �1 0 1 2 3 4
x2 9 4 1 0 1 4 9 16
�x 3 2 1 0 �1 �2 �3 �4
�5 �5 �5 �5 �5 �5 �5 �5 �5
y � x2 � x � 5 7 1 �3 �5 �5 �3 1 7
x �3 �2 �1 0 1 2 3
2x2 18 8 2 0 2 8 18
�5 �5 �5 �5 �5 �5 �5 �5
y � 2x2 � 5 13 3 �3 �5 �3 3 13
x 0 1 2 3 4 5
A � 6x2 0 6 24 54 96 150
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 182
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 183
Mixed exercise 21 (page 256)1
2
3 a) £39 b) (i) £11 (ii) 8p4 a)
b) Gas by £205 a)
b) d
t
d
t
1200 1400 1600600 800
Gas used (kWh)
Cos
t (£)
10000
200 400
10
20
30
40
50
2x � y � 8 � 0
x
y
2 41 3
1
0
3
5
2
4
6
7
8
x
yy � 2x � 1
�1 2 41 3
�3
�1
1
0
3
5
�2
2
4
6
7
6 a) She stopped (e.g. waited for bus)b) 68 minutes c) 27 km/hd) (i) 1 km (ii) 10 km
7 a) Quadratic, � b) Not quadraticc) Quadratic, � d) Quadratic, �e) Not quadratic f) Not quadraticg) Quadratic, �
8 a)
b)
c) (i) �2.25 (ii) x � �3.8 or x � 0.89 a)
b)
c) (i) �6.25(ii) x � �2.5 to �2.6 or x � 1.5 to 1.6
x
y
�1�2�3�4 1 2 3
�3
�1
1
0
3
5
�4
�5
�6
�7
�8
�2
2
4
6
x
y
�1�2�3�4�5 1 20
�4
�2
2
4
6
8
10
x �5 �4 �3 �2 �1 0 1 2
x2 25 16 9 4 1 0 1 4
3x �15 �12 �9 �6 �3 0 3 6
y � x2 � 3x 10 4 0 �2 �2 0 4 10
x �4 �3 �2 �1 0 1 2 3
(x � 3) �1 0 1 2 3 4 5 6
(x � 2) �6 �5 �4 �3 �2 �1 0 1
y � (x � 3)(x � 2) 6 0 �4 �6 �6 �4 0 6
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 183
184 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
10 a)
b)
c) (i) x � �0.4 or x � 2.4(ii) x � �1.4 to �1.5 or x � 3.4 to 3.5
11 a)
b)
c) (i) x � 0.7 or x � 4.3 (ii) 6.25
Chapter 22Exercise 22.1 (page 262)
1 e, c, b, d, a2 a) right angle b) obtuse c) acute
d) reflex e) acute f) reflexg) obtuse h) right angle
x
y
�1 1 2 3 4 5 6
�3
�1
1
0
3
5
�4
�5
�6
�2
2
4
6
x�1�2 1 2 3 4
�3
�1
1
0
3
5
�4
�2
2
4
6
7
8
y
3 a) obtuse b) acute c) reflexd) reflex e) obtuse f) reflexg) right angle h) acute i) reflexj) obtuse
Exercise 22.2 (page 265)a � 55° b � 110° c � 132° d � 81°e � 70° f � 35° g � 17° h � 37°i � 39° j � 45°
Exercise 22.3 (page 266)a � 50° b � 110° c � 120° d � 100°e � 105° f � 122° g � 135° h � 57°i � 87° j � 60°
Exercise 22.4 (page 268)1 a � 60° b � 120° c � 120°2 d � 20° e � 160° f � 160°3 g � 135° h � 45° i � 45°4 j � 47° k � 133° m � 133°5 n � 114° p � 66° q � 66°6 r � 28° s � 152° t � 152°7 w � 143° x � 37° y � 37°8 z � 47°9 a � 40° b � 90° c � 50° d � 50°
10 e � 40° f � 40° g � 140°
Mixed exercise 22 (page 269)1 a) right angle b) obtuse
c) right angle d) reflex2 a � 140° b � 95° c � 54° d � 91°3 a � 90° b � 44° c � 77° d � 120°4 a � 100° Vertically opposite angles are equal.
b � 80° Angles on a straight line add up to180°.
c � 80° Angles on a straight line add up to180° or Vertically opposite angles areequal or Angles around a point add upto 360°.
d � 138° Vertically opposite angles are equal.e � 42° Angles on a straight line add up to
180°.f � 42° Angles on a straight line add up to
180° or Vertically opposite angles areequal or Angles around a point add upto 360°.
g � 70° Vertically opposite angles are equal.h � 110° Angles on a straight line add up to
180°.i � 110° Angles on a straight line add up to
180° or Vertically opposite angles areequal or Angles around a point add upto 360°.
j � 52° Vertically opposite angles are equal.k � 128° Angles on a straight line add up to
180°.l � 128° Angles on a straight line add up to
180° or Vertically opposite angles areequal or Angles around a point add upto 360°.
x �2 �1 0 1 2 3 4
x2 4 1 0 1 4 9 16
�2x 4 2 0 �2 �4 �6 �8
�1 �1 �1 �1 �1 �1 �1 �1
y � x2 � 2x � 1 7 2 �1 �2 �1 2 7
x �1 0 1 2 3 4 5 6
5x �5 0 5 10 15 20 25 30
�x2 �1 0 �1 �4 �9 �16 �25 �36
y � 5x � x2 �6 0 4 6 6 4 0 �6
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Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 185
Exercise 23.5 (page 280)1 2
3 4
5 6
Sides Diagonals Parallel sides
Quadrilateral 4 equal sides 2 different pairs Equal 2 pairs of Only one pair of equal sides diagonals parallel sides of parallel sides
Square � � �
Rectangle � � �
Rhombus � �
Parallelogram � �
Trapezium �
Kite �
Chapter 23Exercise 23.1 (page 272)
1 a � 51° b � 113° c � 60° d � 114°2 a � 50° b � 130° c � 20° d � 130°
e � 137° f � 25° g � 68° h � 128°i � 64°
3 a � 74° b � 41° c � 56° d � 76.5°4 a) (i) a � 54° (ii) b � 45° (iii) c � 36°
b) It is an isosceles triangle.
Exercise 23.2 (page 274)1 C, F and G 2 triangles a, b, d and f
Exercise 23.3 (page 276)1 A � right-angled triangle
B � isosceles triangleC � parallelogramD � rhombusE � trapezium
2 a) A, B, F and G b) C and D or H and Ic) F, G, H and I
Exercise 23.4 (page 278)1 a) F b) CB c) LK2 Note: this diagram is not full-size.
3 a) 4b) A � 4 � 1 � 1, B � 3 � 2 � 1,
C � 2 � 2 � 1, D � 5 � 1 � 1
Mixed exercise 23 (page 281)1 a � 55° b � 80° c � 37° d � 65°2 x � 115° Base angles of an isosceles triangle are
equal; angles on a straight line add upto 180°
y � 50° The sum of the angles in a triangle is180°
3 a) cuboid b) 2 cm � 2 cm � 4 cm4
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186 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
5 a) Trapezium b) Square, rhombus, kitec) Square, rectangle d) Rhombus, kite
6 7
Chapter 24Exercise 24.1 (page 285)
1 a) Radius b) Centre c) Diameter2 a) Hexagon
b) (Regular) octagonc) (Isosceles) triangle
3 5For example
4 20For example
5 36°6 40°7 Check student’s hexagons. 5 cm8 Check student’s hexagons. 4.6 cm
Mixed exercise 24 (page 287)1 a) Radius b) Circumference
c) Diameter2 Check students’ diagrams.
10 cm3 It does not have eight equal angles.4 Square5 Rhombus6 67 45° 8 a) Isosceles triangle
b) Pentagon9 Check student’s diagrams.
10 Check student’s diagrams.
Chapter 25Exercise 25.1 (page 291)
1 a) $53 b) £46 c) $1.522 a) 22.5 litres b) 8.8 gallons c) 4.5 litres3 a) 25 miles b) 24 km c) 1.6 km
Exercise 25.2 (page 293)1 a) 45 seconds b) 160°2 a) £20 000 b) 6.2 years c) £13 5003 a) 06:00 b) 21°C c) 21:00 (20°)4 a) 7.3 years b) £1400
Exercise 25.3 (page 296)1 During stage 1, from 08:00 to 08:45, the car travels
10 miles. It is travelling slowly as it leaves London.During stage 2, from 08:45 to 09:45, the car travels60 miles. It is travelling quickly on a motorway ormajor road.During stage 3, from 09:45 to 10:00, the car isstationary. The driver could have stopped for petrolor a break.During stage 4, from 10:00 to 11:30, the car travels100 miles. It is travelling quickly on a motorway ormajor road.
2 The tortoise travels steadily without stopping. It covers 100 m in 100 minutes.The hare covers the first 50 m in 10 minutes. It then stops for 20 minutes. It then covers another40 m in 10 minutes but then stops for 60 minutes.The tortoise wins the race.
3 a) The bicycle travels from Hereford toBirmingham steadily without stopping. Itcovers 60 miles in 4 hours.The car travels from Birmingham to Hereford.It leaves Birmingham at 14:30 and travels 20 miles in �
12� hour. It then stops for �
34� hour,
between 15:00 and 15:45, before continuing fora further 40 miles and arriving in Hereford after1 hour at 16:45.
b) They pass going in opposite directions.
Mixed exercise 25 (page 297)1 a) €30 b) $46.50 c) $1.352 a) July b) Moscow
c) (i) March to April (ii) April to May3 Ian leaves home at 7:30 a.m. and walks �
12� km to the
bus stop. It takes 10 minutes.He waits 5 minutes for the bus.The bus travels 6 km and arrives at 8:05 a.m.Ian then walks 1 km in 15 minutes.
4 a) 23°C b) �6.5°Cc) November d) May
5 a) 0.7 second b) 1 hourc) After the first hour, reaction time gets longer
(slower).
Chapter 26Exercise 26.1 (page 302)
1 a � 74° (Alternate angles)2 b � 65° (Allied angles)3 c � 125° (Corresponding angles)4 d � 65° (Alternate angles)
e � 65° (Corresponding or vertically oppositeangles)
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Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 187
5 f � 110° (Alternate angles)g � 110° (Corresponding or vertically opposite
angles)6 h � 55° (Allied angles)
i � 125° (Corresponding angles)j � 125° (Alternate or vertically opposite angles)
7 k � 65° (Corresponding angles)l � 65° (Alternate or vertically opposite angles)m � 115° (Allied angles)n � 115° (Vertically opposite angles)
8 o � 101° (Corresponding angles)p � 101° (Corresponding angles)q � 101° (Alternate angles)
9 r � 97° (Allied angles)s � 83° (Corresponding angles)t � 29° (Angles in a triangle add up to 180°)
10 u � 45° (Alternate angles)v � 67° (Corresponding angles)w � 68° (Angles on a straight line add up to 180°
or angles in a triangle add up to 180°)
Exercise 26.2 (page 305)1 a � 35° (Angles in a triangle add up to 180°)2 b � 41° (Angles in a triangle add up to 180°)3 c � 43° (Angles in a triangle add up to 180°)4 d � 35° (Angles in an isosceles triangle)5 e � 60° (Angles in an equilateral triangle)6 f � 55° (The exterior angle of a triangle is equal
to the sum of the opposite interiorangles)
7 g � 141° (The exterior angle of a triangle is equalto the sum of the opposite interiorangles)
h � 39° (Angles on a straight line add up to180°)
8 i � 115° (Angles in a quadrilateral add up to360°)
9 j � 123° (Angles in a quadrilateral add up to360°)
k � 57° (Angles on a straight line add up to180°)
10 l � 100° (Angles on a straight line add up to180°)
m � 84° (Angles in a quadrilateral add up to360°)
Exercise 26.3 (page 308)1 A: trapezium
B: rhombusC: squareD: kiteE: rectangleF: squareG: arrowheadH: parallelogramI: trapeziumJ: rhombusK: parallelogram
2 a) Square, rhombusb) Rectangle, parallelogram, kite, arrowheadc) Rectangle, parallelogramd) Trapeziume) Square, rhombus, kite
3 a)
Rhombusb)
Trapeziumc)
Parallelogramd)
Kite4 All the angles are 90° and the diagonals are equal
length.5 Isosceles trapezium, parallelogram or rhombus
Exercise 26.4 (page 312)1 2340°2 3240°3 a) 131° b) 86°, 130°, 95°, 49°4 a) 58° b) 90°, 100°, 123°, 105°, 122°5 e � 30°; i � 150°6 e � 3.6°; i � 176.4°7 158 20
Rhombus
110°
110°
70°
70°
110°
110°
70°
70°
Parallelogram
Isosceles trapezium
110°110°
70°70°
0 2
2
4
y
x4 6 8
0 2
2
4
y
x4 6 8
0 2
2
4
y
x4 6 8
0 2
2
4
6
8
y
x4 6 8
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188 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
Mixed exercise 26 (page 313)1 a) a � 110° Corresponding angles.
b � 70° Allied angles or Angles on astraight line.
b) c � 50° Alternate angles.d � 50° Corresponding angles or vertically
opposite angles.c) e � 36° Alternate angles.
f � 72° Angles on a straight line.g � 72° Corresponding angles or angles in
a triangle.2 a) a � 19° Angles in a triangle add up to 180°.
b) b � 47° Base angles in an isosceles triangleare equal.
c) c � 31° Exterior angle of a triangle is equalto the sum of the opposite, interiorangles.
d � 77° Angles on a straight line add up to180° or Angles in a triangle add upto 180°.
3 a) a � 126° Angles in a quadrilateral add up to360°.
b) b � 129° Angles on a straight line add up to180°.
c � 53° Angles in a quadrilateral add up to360°.
4 a) Rectangle, parallelogram, kite, arrowheadb) Rhombus, isosceles trapezium, parallelogramc) Square, rectangle, isosceles trapezium
5 a) 900°b) Exterior angle � 24°, interior angle � 156°c) 36
Chapter 27Exercise 27.1 (page 315)
1 a) 6 cm b) 4.5 cm c) 9 cmd) 3.4 cm e) 7.8 cm f) 10.2 cmg) 2.9 cm h) 1.3 cm i) 5.6 cmj) 8.7 cm
2 a) 7 cm b) 3.5 cm c) 2.2 cmd) 6.8 cm
3 a) 4 cm � 3 cm b) 2 cm � 2.4 cmc) 3.4 cm � 3.4 cm
Exercise 27.2 (page 320)a � 30° b � 64° c � 50° d � 61° e � 125° f � 73° g � 90° h � 310°i � 127° j � 136° k � 40° l � 300°m � 109° n � 119° o � 29° p � 302°q � 67° r � 270° s � 128° t � 218°
Exercise 27.3 (page 324)Check students’ drawings.
Exercise 27.4 (page 327)Check students’ drawings.1 a) BC � 7.6 cm B � 67° C � 23°
b) BC � 6.7 cm B � 43° C � 72°c) AB � 9.1 cm A � 20° B � 30°d) AB � 4.6 cm A � 65° B � 32°e) BC � 9.6 cm B � 22° C � 40°
2 a) Y � 70° YZ � 4.9 cm XY � 5.5 cmb) Y � 45° YZ � 5 cm XY � 7.1 cmc) Y � 33° XY � 7.2 cm YZ � 3.8 cmd) Y � 60° XY � 7.2 cm YZ � 4.5 cme) Y � 65° XY � 6 cm XZ � 3.4 cm
Exercise 27.5 (page 330)Check students’ drawings.1 a) A � 65° B � 65° C � 49°
b) A � B � C � 60°c) A � 35° B � 84° C � 60°d) A � 78° B � 57° C � 44°e) A � 59° B � 35° C � 86°
2 a) X � 65° Y � 43° YZ � 6.7 cmb) Y � 38° Z � 91° XY � 6.4 cmc) Y � 41° Z � 21° XY � 3.2 cmd) Y � 81° X � 64° YZ � 6.7 cme) X � 52° Y � 56° XZ � 6.1 cm
Exercise 27.6 (page 333)1 a) 12 m b) 20 m c) 26 m d) 10 m2 a) 40 km b) 100 km c) 55 km d) 27 km3 Check students’ drawings.
The lines should be the lengths given below.a) 5 cm b) 5 cm c) 12 cm d) 7.5 cm
4 a) 11 mb) Living room: 10 m � 5 m
Dining room: 6 m � 4 mBedroom 1: 5 m � 5 mBedroom 2: 3 m � 4 mBathroom: 3 m � 3 mKitchen: 4 m � 3 m
c) 13 cm � 7.5 cm5 a) (i) 90 km (ii) 270 km
(iii) 110 km (iv) 66 km(v) 126 km (vi) 272 km
b) 16 cm
Exercise 27.7 (page 337)Diagrams are not full size. The measurements given arecorrect for the suggested scale.
1 A: 005° B: 050° C: 090° D: 145°E: 240° F: 300° G: 345°
2 Park: 3 km, 035°Swimming pool: 6 km, 060°Youth club: 4.5 km, 100°Shop: 7 km, 127°Hairdresser: 3 km, 188°Church: 4.5 km, 231°School: 6.5 km, 266°Cinema: 3.5 km, 315°
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Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 189
3 Check students’ drawings.
4 a) Check students’ drawings.
b) 1.24 km c) 029°
5 Check students’ drawings.
Mixed exercise 27 (page 339)1 7.5 cm, 4.7 cm, 4.3 cm, 3.4 cm2 a � 52°, b � 37°, c � 125°, d � 98°, e � 217°,
f � 296°3 Check students’ diagrams.4 Check student’s diagrams.
a) BC � 2.9 cm, B � 53°, C � 92°b) E � 50°, ED � 6.8 cm, EF � 7.4 cmc) HI � 4 cm, H � 125°, I � 55°
5 Check student’s diagrams.a) K � L � M � 60°b) OP � 4.3 cm, O � 48°, N � 32°c) QR � 3.9 cm or 10 cm
6 a) 2 m b) 14 mc) Study 8 m � 4 m, lounge 8 m � 10 m,
dining room 8 m � 7 m, kitchen 8 m � 7 md) 113 cm � 52.5 cm
7 a) 450 m, 105° b) 400 m, 329°c) 325 m, 225°
8 a) Check students’ diagrams.b) 106 miles, 335°
4 cm
6 cm
5.5 cm
6.5 cm
Coastguard
5 cm
E
D
C
B
A
N
125°
250°
5 cm
7.5 cm
C
P
L
N
N
N
085°
150°
5 cm
4 cm
Ashton Bradbury
Charlton
Chapter 28Exercise 28.1 (page 351)Diagrams are not full size. The measurements given arecorrect for the suggested scale.1
2 Scale 1 cm � 20 m
3 Scale 1 cm � 10 m
4
5
6 Scale 1 cm � 1 m
7 N
S
NW NE
SW
W E
SE
1 cm
4 cm
2 cm
A
B
5 cm
5 cm
3 cm
D
C
60° 30°
6 cm
Hedge
Tree
5 cm
2.5 cm
A5 cm
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190 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
8
9
10 Scale 1 cm � 10 m(Note: other scales are also acceptable.)
Exercise 28.2 (page 354)Diagrams are not full size. The measurements given arecorrect for the suggested scale.
1
2 Scale 1 cm � 1 km
3
4 Scale 1 cm � 1 m
8 cm
6 cm 5 cm
E F
H G
T
7 cm
3 cm
3 cm
3 cm
3 cm
5 cm
5 cmA
D
B
C
7 cm
5 cm
4 cm
P Q
6 cm
3 cmA
6 cm2 cm
8 cm
Castle
7 cm 6 cm
8 cmA B
C
5
6 Scale 1 cm � 1 m
7 1 cm � 20 m
8 Scale 1 cm � 1 km
9 Scale 1 cm � 4 m
10 Scale 1 cm � 5 miles
9 cm7 cm
11 cmA B
C
Locus
H K2 cm
3 cm
4 cm
5 cm
3.5 cm
2 cm
2.5 cm
Hou
se
2 cm
B
C
A 7 cm
9.5 cm
5 cm
5 cm
5 cm
2.5 cm
7 cm
Locus
3 cm
2 cm
5 cm
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Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 191
Mixed exercise 28 (page 355)Diagrams are not full size. Measurements given arecorrect for the suggested scale.
1
2
3
4
Area � 23.4 cm2
5
6 Scale 1 cm � 5 km
7 Scale 1 cm � 1 m
100°
D C
A B5 cm
3 cm
8 cm
6 cm
6 cm
S R
P Q
5 cm
8 cm
9 cmA B
C
5.2 cm6 cm 8 cm
7 cm
3 cm 3 cm
8 cm
8
9 Scale 1 cm � 1 m
10 Scale 1 cm � 1 m
Chap ter 29Exercise 29.1 (page 359)
1
2 a) 1 b) 0 c) 2
70°
5 cm
8 cmE F
G
6 cm
10 cm
3 cm
3 cm8 cm
3 cm
3 cm
3 cm
3 cm
3 cm
5 cm
5 cm
a)
b)
c)
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192 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
3
4 Isosceles triangle5 Other answers with more squares shaded are
possible.
6 Other answers with more squares shaded arepossible.
7 Check students’ patterns.8 a)
b)
c)
Exercise 29.2 (page 363)1 a) 2 b) 1 c) 4
d) 4 e) 1 f) 82 6, 63 Equilateral triangle
4
Purple
Orange
Pink
G G � greenB � blueY � yellowR � red
G
BR
R Y
B
5
6 Check students’ patterns.
7
8
9 Check students’ patterns.
Exercise 29.3 (page 369)1 a) b)
c) d)
e)
2 a) b)
c)
3
�5�6�7�8 �4�3�2�1 0 1
1
�1�2�3�4�5
2345y
x2 3 4 5
A
C
B
mirrorline
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Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 193
4
5 a) 90° anticlockwise b) 180°6 a) 120° b) 240°7 a) 180° (or �
12� a turn)
b) 90° anticlockwise (or �14� of a turn)
8 a) B, E, F b) C, D
Mixed exercise 29 (page 372)1 a) 1 b) 4 c) 02 a) 1 b) 4 c) 13
4
5 a) b)
6 a) 90° clockwise b) 90° anticlockwise7 B, E, F8 a)–b)
c) 90° anticlockwise
�5 �4 �3 �2 �1 0 1
1
�1
�2
�3
�4
�5
2
3
4
5
y
x2 3 4 5
A
B
C
D
mirrorline
�5 �4 �3 �2 �10 1
1
C
AB
�1�2
�3
�4
�5
2
3
4
5y
x2 3 4 5
9
Chapter 30Exercise 30.1 (page 377)
1
2
3 a) b)
c)
4 a) A reflection in the line y � 2b) A reflection in the line x � 3c) A reflection in the line y � x
5 a) A reflection in the line y � 0b) A reflection in the line y � �xc) A reflection in the line y � x
�4 �3 �2 �10 1
1
�1
�2
�3
�4
2
A
C
B3
4y
y � 1
y � x
x2 3 4
�5 �4 �3 �2 �1 0 1
1
�1
�2
�3
�4
�5
2
3
4
5
y
x2
C
AB
3 4 5
�4 �3 �2 �10 1
1
�1
�2
�3
�4
2
3
4y
y � �x
y � 2
x2 3 4
A
B
C
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194 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
Exercise 30.2 (page 382)
1
2
3
4
�4 �3 �2 �10 1
A
C
D
B1
�1
�2
�3
�4
2
3
4y
x2 3 4
�4 �3 �2 �10
A
C
1
1
�1
�2
�3
�4
2
3
4y
x2
B
3 4
C B90°
A
B� A�
�4�3�2�10 1
CA
D
B
1
�1�2�3�4
2345678y
x2 3 4 5 6 7
5
6
7 a) A rotation of 90° (anticlockwise) about the originb) A rotation of 180° about (1, 0)c) A rotation of 90° clockwise or �90° about
(1, 2)8 a) A rotation of 90° clockwise or �90° about the
originb) A rotation of 180° about (2, 1)c) A rotation of 90° (anticlockwise) about (1, 1)
9 A rotation of 150° clockwise about O10 a) A reflection in the line x � 0
b) A rotation of 90° (anticlockwise) about (2, 4)c) A reflection in the line y � xd) A rotation of 90° (anticlockwise) about the origine) A reflection in the line y � �x
Exercise 30.3 (page 386)1
C
B�
B120°
A�
A
90°O
�2 �1 1
D0
A
B
C
2 3 4 5 6
�2
�1
1
2
3
4
5
6y
x
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Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 195
2
3 a) A translation by vector � �b) A translation by vector � �c) A translation by vector � �d) A translation by vector � �
4 a) A translation by vector � �b) A rotation of 90° (anticlockwise) about the
originc) A rotation of 90° clockwise or �90° about
(2, 2)
d) A translation by vector � �e) A reflection in the line y � 0f) A reflection in the line y � x
g) A translation by vector � �h) A rotation of 180° about (0, 2)
Mixed exercise 30 (page 388)1
2�6
�3�4
�52
�42
�21
�1�2
2�1
�2 �1 1 2 3 4 5 6
�2
�1
1
2
3D
C
0
A
B4
5
6y
x
y
x1
C
A
B
2 3 4�4 �3 �2 1
�4
�3
�2
�1
1
2
3
4
2 a)
b)
3
4
�4 �3 �2 �1 0 1
1
�1
�2
�3
�4
2
3
4
y
x2 3 4
A
B
C
D
�4 �3 �2 �1 0 1
1
�1
�2
�3
�4
2
3
4
y
x2
C
B
3 4
A
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Chapter 31Exercise 31.1 (page 394)Note: Diagrams not full-size.1 a)
b)
c)
d)
e)
2 a) 2 b) 3 c) 4 d) 33 a) No: for an enlargement, all the lengths must be
enlarged by the same scale factor. AC � 4 andDF � 8 so DF is twice as long as AC but AB � 4 and DE � 10 so DE is more than twiceas long as AB.
b) No: for an enlargement, all the lengths must beenlarged by the same scale factor. AB � 2 andDE � 8 so DE is four times as long as AB butthe height of the triangle ABC, from side ABto C, is 4 and the height of triangle DEF, fromside DE to F, is 15, which is less than fourtimes as long.
Exercise 31.2 (page 398)1 a)
b)
c)
d)
e)
2 a) (i) 3 (ii) (0, 0)b) (i) 4 (ii) (0, 1)c) (i) 2 (ii) (�2, 6)d) (i) 3 (ii) (5, 4)e) (i) 2 (ii) (5, �3)
Exercise 31.3 (page 402)1 a), b)
c) An enlargement with scale factor 2, centre theorigin
10 2 3 4 5
B
A
6
1
2
3
4
5
6y
x
0 1
12345678y
x2 3 4 5 6 7 8 9 10 11 12
0 1
12345678y
x2 3 4 5 6 7 8 9 10 11 12
0 1
12345678y
x2 3 4 5 6 7 8 9 10 11 12
0 1
12345678y
x2 3 4 5 6 7 8 9 10 11 12
0 1
12345678y
x2 3 4 5 6 7 8 9 10 11 12
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 196
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 197
2 a), b)
c) An enlargement with scale factor 3, centre (1, 2)
3 a), b)
c) An enlargement with scale factor �14�, centre the
origin
4 a), b)
c) An enlargement with scale factor �23�, centre (2, 1)
5 a) An enlargement with scale factor 2, centre (0, 3)
b) An enlargement with scale factor �12�, centre (0, 3)
c) An enlargement with scale factor 1�12�, centre the
origind) An enlargement with scale factor �
23�, centre
the origin6 a) A reflection in the line y � 0
b) An enlargement with scale factor 2, centre (0, 4)
c) A translation by vector � �d) An enlargement with scale factor 2�
12�, centre
the origin
e) A translation by vector � �f) An enlargement with scale factor �
13�, centre (5, 3)
�64
10 2 3 4 5
A
6 7 8
1
2
3
4
5
6
7
8y
x
B
C
�8�3
10 2
C
A
B
3 4 5 6 7 8
1
2
3
4
5
6
7
8y
x
10 2
A
B
3 4 5 6 7 8
1
2
3
4
5
6
7
8y
x
7 a) A reflection in the line x � 1b) An enlargement with scale factor 2, centre
(1, 0)c) A rotation of 90° (anticlockwise) about the
origind) A reflection in the line y � xe) An enlargement with scale factor �
12�, centre the
origin
f) A translation by vector � �8 a) A reflection in the line y � 2
b) A rotation of 90° clockwise or �90° about theorigin
c) A translation by vector � �d) A reflection in the line y � 0e) An enlargement with scale factor �
12�, centre
(0, �2)f) An enlargement with scale factor �
13�, centre (2, 1)
g) An enlargement with scale factor 3, centre (2, 1)
Mixed exercise 31 (page 405)1 a)
b)
2 a)
14
0 1
12345678y
x2 3 4 5 6 7 8
2�2
0 1
123456789
10y
x2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
b)
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 197
198 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
3 a) (i) 3 (ii) (0, 0)b) (i) 2 (ii) (8, 9)
4
5
6 a) A reflection in the line x � 0b) A rotation of 90° clockwise about the origin.c) An enlargement with scale factor 3, centre
(�4, 3)
d) A translation by vector � �e) An enlargement with scale factor �
12�, centre the
origin
f) A translation by vector � �g) A reflection in the line y � x
7 a) A reflection in the line x � 0
b) A translation by vector � �c) An enlargement with scale factor 3, centre
(0, 2)d) A rotation of 90° (anticlockwise) about
(2, �2)e) An enlargement with scale factor �
12�, centre the
originf) A rotation of 180° about the origin
g) A translation by vector � �
Chapter 32Exercise 32.1 (page 410)
1 7.8 cm2 1150 g or 1.15 kg3 0.7 litre or 700 ml
32
1�3
�32
0�3
10
1
2
3
4
5
6
7
8
9
y
x2 3 4 5 6 7 8 9
A
B
10
1
2
3
4
5
6
7
8
9
y
x2 3 4 5 6 7 8 9
B
A
4 a) 2.4 kg b) 400 g or 0.4 kg5 a) A: �4°C, B: 18°C b) 22°C
Exercise 32.2 (page 413)1 100 ml, 0.75 litre, 1500 ml, 1.6 litres, 2 litres2 a) centimetres b) metres
c) metres d) kilometrese) metres f) metresg) centimetres or millimetres
3 1.1 m4 0.725 �
34� kg, 1500 g, 1.6 kg, 2 kg, 10 000 g
6 a) 140 ml b) 25 mlc) 5000 ml d) 5230 ml
7 3.627 kg
Exercise 32.3 (page 415)1 a) 900 g or 0.9 kg
b) 2250 g or 2.25 kgc) 10 800 g or 10.8 kgd) 225 g or 0.225 kg
2 a) 48 km b) 22 poundsc) 264 pounds d) 40 milese) 20 kg
3 200 miles
Exercise 32.4 (page 417)The answers may vary a little from those given.1 a) 3 m b) 25 cm c) 30 g
d) 2 litres e) 70 kg f) 50 cm2 a) 2.5 m b) 7 m3 16 m4 7 m
Mixed exercise 32 (page 418)1 a) 60 mm b) 350 mm c) 4500 mm
d) 620 mm e) 37.2 mm2 a) 5000 m b) 4320 m
c) 46 700 m d) 1234 m3 a) 5 km b) 6.7 km
c) 12.345 km d) 0.543 21 km4 31.04 cm, 1623 mm, 2.42 m, 284 cm, 9.044 m5 a) m b) m
c) cm or mm d) cm6 a) 9000 g b) 1129 g c) 3100 g d) 300 g7 a) 90 cm b) 40 km c) 0.5 kg d) 8 kg8 55 miles � 88 km9 9 m
10 3.75 kg
Chapter 33Exercise 33.1 (page 421)
1 a) 2500 cm b) 420 mmc) 236 cm d) 5100 mm
2 a) 30 000 cm2 b) 230 mm2
c) 95 200 cm2 d) 1.4 mm2
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Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 199
3 a) 900 cm2 b) 81.4 cm2
c) 720 m2 d) 9.4 m2
4 a) 3 200 000 cm3 b) 0.000 042 m3
c) 0.005 m3 d) 6 420 000 cm3
5 a) 2610 cm3 b) 9.5 litresc) 2400 ml d) 0.91 litre
6 All the units need to be the same; change 50 cm to0.5 m. 5 � 2 � 0.5 � 5 m3
Exercise 33.2 (page 423)1 a) 56.5 m and 57.5 m
b) 567.5 ml and 568.5 mlc) 23.925 seconds and 23.935 seconds
2 a) 633.5 g and 634.5 gb) 233.5 ml and 234.5 mlc) 8.25 m and 8.35 m
3 a) 28 to 32 m2
b) 15 cans (100 � 7 � 14.2)4 a) 4.965 mm
b) 4.975 mm5 No; 595.5 mm is greater than 59.5 cm.6 a) 14.9 cm and 15.1 cm
b) 1.95 cm and 2.05 cmc) 1.95 cm and 2.05 cm
7 Maximum d: longest rod minus leastdepth � 35.5 � 19.5 � 16 mmMinimum d: shortest rod minus greatestdepth � 34.5 � 20.5 � 14 mm
8 2 � (14.5 � 8.5) � 46 cm and 2 � (15.5 � 9.5) � 50 cm
Exercise 33.3 (page 425)1 a) 3.5 minutes b) 3 weeks
c) 3 kg d) 2 m2 a) 5.7 m (or 5�
34� m) b) £16
c) 665 km d) 0.1 cm2
Exercise 33.4 (page 426)1 62.5 m/s 2 43 mph3 7.5 miles 4 5 hours5 278 cm3 6 60 mph7 9 g/cm3 8 100 km/h9 7.8 g/cm3
10 a) 8.9 g/cm3 b) 151.3 g11 19.3 kg12 a) 58.5 kg
b) (i) 0.7692 m3 (ii) 769.2 m3
13 a) 60 km/h b) 64.3 km/h14 10.6 g/cm3
15 1156 people per square kilometre
Mixed exercise 33 (page 428)1 a) 120 000 cm2 b) 371 mm2
c) 4200 cm2 d) 5 mm2
2 a) 3 000 000 mm2 b) 41.25 m2
c) 94 cm2 d) 600 cm2
3 a) 2130 ml b) 5.1 litresc) 421 000 ml d) 0.0917 litre
4 a) 26.5 cm and 27.5 cmb) 5.55 cm and 5.65 cmc) 1.225 m and 1.235 m
5 Greatest speed: greatest distance � least time� 100.05 � 5.5 � 18.19 m/s
6 a) 33.5 mm and 34.5 mmb) Greatest perimeter: greatest length � 3
� 34.5 � 3 � 103.5 mm7 a) 1 hour 15 minutes b) 8 km/h8 a) 60 mph b) 190 miles9 5394 m2
Chapter 34Exercise 34.1 (page 430)
1 a) 22 cm b) 8 cm c) 18.4 cmd) 14.9 cm e) 17.6 cm f) 33 cm
2 16.8 m 3 18.8 cm4 15 m 5 83.3 m
Exercise 34.2 (page 431)1 a) 12 cm2 b) 8 cm2 c) 15 cm2
d) 9 cm2 e) 5 cm2 f) 25 cm2
Exercise 34.3 (page 433)1 a) 24 m2 b) 36 cm2 c) 80 cm2
d) 75 m2 e) 8 cm2 f) 17.6 m2
g) 30.66 m2 h) 10.24 m2 i) 9.66 cm2
2 16.92 cm2
3 6.76 m2
4 15.023 cm2
5 15.68 m2
6 36 m2
7 a) 14 m2 b) £3438 a) 15 m2 b) £375
Exercise 34.4 (page 435)1 16 cm2 2 50 cm2
3 160 m2 4 75 mm2
5 64 cm2 6 17.5 cm2
7 55 cm2 8 144 cm2
9 150 m2 10 120 m2
Exercise 34.5 (page 437)1 24 cm2 2 72 cm2
3 64 m2 4 35 cm2
5 14 cm2 6 30 cm2
7 42 cm2 8 144 m2
9 42 cm2 10 16 cm2
Exercise 34.6 (page 440)1 a) 60 cm3 b) 128 cm3
2 150 m3 3 125 cm3
4 4500 cm3 5 72 m3
6 42.875 cm3 7 252 cm3
8 189 000 cm3 9 1800 cm3
10 750 cm3
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200 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
Mixed exercise 34 (page 441)1 a) 20.6 cm b) 16.9 cm
c) 28 cm d) 15.4 cm2 perimeter � 17.4 cm, area � 18.02 cm2
3 perimeter � 54 m, area � 180 m2
4 perimeter � 18.4 cm, area � 21.16 cm2
5 perimeter � 13 m, area � 10 m2
6 a) 4.41 m2 b) 23.68 m2
c) 28.09 m2 d) £21.07 (to the nearest penny)7 a) 9 cm2 b) 8 cm2 c) 30 cm2
8 a) 28 cm2 b) 300 cm2 c) 18 cm2
9 120 cm3
10 19.683 cm3
11 3000 cm3
12 360 000 cm3 or 0.36 m3
Chapter 35Exercise 35.1 (page 445)These answers have been calculated using the buttonon a calculator.
1 37.7 cm (1 d.p.)2 78.5 cm (1 d.p.)3 282.7 cm (1 d.p.)4 116.2 mm (1 d.p.)5 207 mm (nearest whole number)6 84.8 cm (1 d.p.)7 163.4 cm (1 d.p.)8 14.8 cm (1 d.p.)9 28.9 cm (1 d.p.)
10 22.9 m (1 d.p.)11 9.1 m (1 d.p.)12 3.86 m (2 d.p.)
Exercise 35.2 (page 446)These answers have been calculated using the buttonon a calculator.
1 a) 616 cm2 (nearest whole number)b) 2463 cm2 (nearest whole number)c) 20 106 cm2 (nearest whole number)d) 3848 mm2 (nearest whole number)e) 12 076 mm2 (nearest whole number)f) 5809 cm2 (nearest whole number)g) 9503 cm2 (nearest whole number)h) 75.4 cm2 (1 d.p.)i) 295.6 cm2 (1 d.p.)j) 36.3 m2 (1 d.p.)k) 21.2 m2 (1 d.p.)l) 4.91 m2 (2 d.p.)
2 a) 201 cm2 (nearest whole number)b) 452 cm2 (nearest whole number)c) 3848 cm2 (nearest whole number)d) 1018 mm2 (nearest whole number)e) 5281 mm2 (nearest whole number)f) 1810 cm2 (nearest whole number)
g) 2290 cm2 (nearest whole number)h) 15.2 cm2 (1 d.p.)i) 75.4 cm2 (1 d.p.)j) 11.3 m2 (1 d.p.)k) 6.2 m2 (1 d.p.)l) 4.30 m2 (2 d.p.)
Exercise 35.3 (page 448)1 160 cm2
2 126 cm2
3 340 cm2
4 227 cm2
5 108 cm2
6 212 cm2
Exercise 35.4 (page 450)1 a) 515 cm3 b) 1376 cm3 c) 219.6 cm3
d) 385.5 cm3 e) 192 cm3 f) 780 cm3
2 18 000 cm3
Exercise 35.5 (page 452)1 a) 1233 cm3 b) 17 334 cm3 c) 2092.8 cm3
d) 396.8 cm3 e) 2253.42 cm3 f) 528.82 cm3
2 119 000 mm3
Exercise 35.6 (page 453)These answers have been calculated using the buttonon a calculator.
1 a) 7037 cm3 (nearest whole number)b) 25 862 cm3 (nearest whole number)c) 113 097 cm3 (nearest whole number)d) 24 881 mm3 (nearest whole number)e) 11 781 mm3 (nearest whole number)f) 115 mm3 (nearest whole number)g) 707 m3 (nearest whole number)h) 370 m3 (nearest whole number)
2 11 045 cm3
Exercise 35.7 (page 456)These answers have been calculated using the buttonon a calculator.
1 a) 1810 cm2 (nearest whole number)b) 2281 cm2 (nearest whole number)c) 2827 cm2 (nearest whole number)d) 3958 mm2 (nearest whole number)e) 377 mm2 (nearest whole number)f) 465.6 mm2 (1 d.p.)g) 131.9 m2 (1 d.p.)h) 77.0 m2 (1 d.p.)
2 a) 2111 cm2 (nearest whole number)b) 6993 cm2 (nearest whole number)c) 10 336 cm2 (nearest whole number)d) 3054 mm2 (nearest whole number)e) 4869 mm2 (nearest whole number)f) 1176.5 mm2 (1 d.p.)g) 190.0 m2 (1 d.p.)h) 59.7 m2 (1 d.p.)
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 200
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 201
Exercise 35.8 (page 459)1 2
3 4Plan
Front elevation
Side elevation
Plan
Front elevation
Side elevation
Plan
Front elevation
Side elevation
Plan
Front elevation
Side elevation
5 6
Mixed exercise 35 (page 461)Where necessary, the button on a calculator has beenused to work out these answers.
1 a) 44.6 cm b) 93.3 cmc) 204 cm d) 100.8 mm
2 a) 127.08 cm2 b) 24.45 m2
c) 237.79 mm2 d) 69.40 mm2
e) 124.69 cm2 f) 72.08 m2
3 Check students’ diagrams.4 a) 89.54 cm2 b) 75 cm2
c) 176.5 cm2 d) 178.23 cm2
5 a) 208 cm3 b) 156 cm3
c) 169.32 cm3 d) 192 cm3
e) 257.544 cm3 f) 655.2 cm3
6 a) 20 308.2 cm3 b) 1578.46 mm3
c) 5617.5 cm3 d) 0.8874 m3
7 a) 2601 mm3 (nearest whole number)b) 3268.5 mm3 (1 d.p.)c) 106 437 cm3 (nearest whole number)d) 181 cm3 (nearest whole number)e) 23 091 m3 (nearest whole number)f) 27.5 m3 (1 d.p.)
8 a) 1659 m2 (nearest whole number)b) 2432 cm2 (nearest whole number)c) 16.0 cm2 (1 d.p.)d) 672 mm2 (nearest whole number)
9 a) 5202 mm2 (nearest whole number)b) 113 m2 (nearest whole number)c) 174 cm2 (nearest whole number)d) 546 cm2 (nearest whole number)
Plan
Front elevation
Side elevation
Plan
Front elevation
Side elevation
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 201
202 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
10 a) b)
c) d)
Chapter 36Exercise 36.1 (page 465)
1 12 cm2 2 85 cm2
3 50 cm2 4 28 cm2
Exercise 36.2 (page 467)1 a) 13 cm b) 5.83 m c) 6.24 cm
d) 24 cm e) 7.64 cm f) 6.34 cmg) 30.50 m h) 9.35 m i) 6.57 cm
2 4.53 m3 23.66 inches
Exercise 36.3 (page 470)1 Yes 62 � 82 � 102 (This is 2 � the 3, 4, 5 triangle)2 No 42 � 72 � 82
3 No 82 � 82 � 112
Plan
Side elevation
Front elevation
Plan
Side elevation
Front elevation
Plan
Side elevation
Front elevation
Plan
Side elevation
Front elevation
4 Yes 7.52 � 182 � 19.52
(This is 1.5 � the 5, 12, 13 triangle)5 Yes 3.52 � 122 � 12.52
(This is 0.5 � the 7, 24, 25 triangle)6 No 52 � 102 � 112
7 No 4.52 � 92 � 102
8 Yes 28.82 � 122 � 31.22
(This is 2.4 � the 5, 12, 13 triangle)
Exercise 36.4 (page 473)1 a) (6.5, 3) b) (3, 5)
c) (�1.5, 6) d) (�4.5, 0)e) (�0.5, �5) f) (5.5, �4.5)
2 a) (1, 6) b) (4, 4)c) (5, 4.5) d) (5.5, 4.5)e) (1, 2) f) (�5, �7)
Mixed exercise 36 (page 474)1 a) 20 cm2 b) 23 cm2
2 a) 11.40 cm b) 7.55 cmc) 6.27 cm d) 4.99 cm
3 a) No 52 � 82 � 92
b) Yes 92 � 122 � 152
(This is 3 � the 3, 4, 5 triangle)c) Yes 17.52 � 602 � 62.52
(This is 2.5 � the 7, 24, 25 triangle)d) No 5.22 � 8.32 � 9.72
4 a) (3, 4) b) (4, 5�12�) c) (4�
12�, 4�
12�)
5 1.93 m6 30.3 cm2
7 15.66 m
Chapter 37Exercise 37.1 (page 478)
1 14:252 a) 09:35 b) 00:133 1 hour and 20 minutes4 5 minutes to 65 a) 33 minutes b) 20 minutes
c) 39 minutes d) 40 minutese) 45 minutes f) 33 minutes
6 a) 3:35 b) 3:05c) 13:10 d) 13:23e) 5 past 10 f) 25 past 5
7 08:218 9:209 16:35
10 11:1511 1 hour and 35 minutes
Exercise 37.2 (page 482)1 54 km 2 2.8 mph3 3 hours 4 12 km/h5 1470 m 6 4.5 hours7 10.44 m/s8 a) �
14� hour b) 52 km/h, yes
9 a) 150 seconds b) 1.2 m/s10 162.5 km
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 202
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 203
Exercise 37.3 (page 484)1 14 ounces2 1.5 pounds3 a)
b)
Exercise 37.4 (page 486)1 a) 17.5 pence
b) A 7-minute call to Jamaica, by 0.5 pencec) 3
2 a) 509 km b) 15 km
Mixed exercise 37 (page 487)1 23:50 and 01:502 a) £9 b) £6 c) £5.113 a) £69.65 b) £3.95 c) £2.524 50 m/s5 30 mph6 10.5 miles7 7.5 hours8 a) �2
15� second b) 40 seconds
9 a) 13 b) 810 a) 48 km/h b) 50 mph11 a) 31.5 litres b) 225 litres c) 1350 litres
Chapter 38Exercise 38.1 (page 491)
1 5 2 3.84 3 4.54 3.45 5 9.2 6 62.417 1.20 8 2.68 9 4.48
10 2.65 11 1.78 12 1.85
Exercise 38.2 (page 494)1 Check students’ answers. Possible answers include
the following.a) positive � negative � negativeb) Multiplying by number less than 1 should make
answer smaller.c) 3 � 60 � 180 and answer should be more than
this.d) �64� � 8 and answer should be less than this.
2 Check students’ answers. Possible answers includethe following.a) Answer is too large, since 0.9 is near 1.b) negative � negative � positivec) 62 � 36 and answer should be less than this.d) 8 � 3 � 11 so last digit should be 1.
3 a) 1000 � 20 � 20 000b) 0.4 � 0.4 � 0.16c) �20 � 5 � �4
4 a) 7 � £9 � £63b) 30 � £15 � £450 or 30 � £10 � £300c) 3 � £6 � 3 � £2 � £24
5 a) 62 067.5 � 81.4 � 762.5 or 62 067.5 � 762.5 � 81.4
b) �1466.8�9� � 38.3c) 17.6 � 3.8 � 66.88d) 278.93 � 18.2 � 297.13, 297.13 � 4.3 � 69.1
6 a) 468.38 b) 6.807 a) 12.647 b) 896.8748 a) 61.1 b) 4.89 a) (i) 403 � 64 000
(ii) 20 � 0.2 � 4
(iii) �72 � 4�2� � �49 � 1�6� � �33� 6
(iv) �10
0
�
.08
30� � �
0
4
.0
0
8� � �
40
8
00� � 500
b) (i) 60 236.288 (ii) 3.496(iii) 5.93 (to 2 d.p.)(iv) 516 (to nearest whole number)
Exercise 38.3 (page 500)1 a) 2 hours and 51 minutes
b) 9 minutes2 a) 1.45 hours b) 0.9 hour3 3 hours and 15 minutes4 1 hour and 48 minutes5 56 £31.32 and £20.887 700 ml or 0.7 litre8 54 mph9 £191.11 or £191.12
10 66 83411 200.812 2.2 g/cm3
13 15.2 cm
Mixed exercise 38 (page 502)1 a) 3 b) 3.52 2.32 (to 2 d.p.)3 a) The answer should be more than 72, which
is 49.b) Multiplying 2.4 by a number less than 1 should
give an answer less than 2.4.c) 120 � 49 120 � 50 � 6000, not nearly
60 000 (or equivalent argument).d) The answer should be negative.
4 a) 900 � 30 � 27 000b) 0.62 � 0.36c) �48 � 6 � �8 or �50 � 6 �8
Imperial Metric
5 feet 1.5 m or 150 cm
12 pounds 6 kg
5 pints 2.9 litres
Metric Imperial
20 km 12.5 miles
3 m 10 feet
10 litres 17.5 pints
15 kg 30 pounds
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:29 Page 203
204 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
5 a) 1270.26 b) 2.886 a) (i) 203 � 8000 (ii) 30 � 0.3 � 9
(iii) �82 � 4�2� � �64 � 1�6� � �48� 7
(iv) �30
0
�
.04
50� � �
0
8
.0
0
4� � 2000
b) (i) 9800.344 (ii) 7.743(iii) 6.93 (to 2 d.p.)(iv) 2054 (to nearest integer)
7 38 a) 3 hours 42 minutes
b) 2 hours 45 minutesc) 48 minutesd) 51 minutes
9 34.3 mph (to 1 d.p.)10 48.75 cm3
11 £96.91 or £96.92
Chapter 39Exercise 39.1 (page 506)
1 a) Unlikely (or Impossible)b) Evensc) Likely
2 a) Arrow at Certainb) Arrow at Very unlikelyc) Arrow at Likely (if answering this at school)
3 a) Unlikelyb) Evensc) Impossible
4 a) All 1sb) All not 1c) Two 1s and three othersd) Four 1s and one other
Exercise 39.2 (page 511)1 a) Arrow at 0.5
b) Arrow at 1c) Arrow at �
13� (3rd tick mark from the left)
2 a) Unlikelyb) R at 0.5, G at 0.3, B at 0
3 a) �15� or 0.2 b) �
25� or 0.4
4 a) �16� b) �
46� � �
23� c) 0
5 a) 0.1 b) 0.7 c) 0.3
6 a) �28� � �
14� b) �
18� c) 0
7 a) 6 b) 128 5 orange, 3 blue, 2 red, no green9 a) Red b) 3 red and 1 purple
10 a) Arrow at 0.4b) Arrow at 0.6
11 �78�
12 a) �156� b) �1
76� c) �1
96�
13 a)
b) 10 c) 24 d) �224� � �1
12�
14 a) (Order can be different)
b) �29�
Exercise 39.3 (page 514)1 �
2644� � �
38� or 0.375
2 a) �123000� � �
1230� or 0.65
b) About 100c) Do many more tosses.
3 a) (i) �35070� or 0.19 (ii) �3
3090� or 0.13
b) (i) 0.167 (ii) 0.167c) They could do although the experimental
probabilities are different from the theoreticalprobabilities, but more throws are needed tocheck.
Mixed exercise 39 (page 516)1 a) Impossible b) Evens
c) Likely (this depends on the local climate)2
3 a) 5 b) 04 a) �
15� b) �
35� c) �
25�
5 a) �18� b) �
28� or �
14� c) 0
6 a) �16� b) 0.7
7 48 0.659 �2
7020� � 0.36
10 a)
b) �16�
0 10.5
c) a) b)
Dice
1 2 3 4 5 6
1 2 3 4 5 6 7
Spinner2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
First scoop C C C V V V S S S
Second scoop C V S C V S C V S
T-shirt Jeans
Red Blue
Red Black
White Blue
White Black
Yellow Blue
Yellow Black
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 204
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 205
Chapter 40Exercise 40.1 (page 519)
1 0.9 2 �56� 3 0.15
4 �130� 5 0.57 6 �
1479�
Exercise 40.2 (page 521)1 0.7 2 �2
60� or �1
30� 3 0.35
4 �141� 5 0.11 6 �2
10�
Exercise 40.3 (page 523)1 4 2 123 17 4 £3005 a) 50
b) 1506 50 yellow, 75 blue, 125 green
Exercise 40.4 (page 525)1 a)
b) �16� or 0.17 (to 2 d.p.)
c) Yes, the dice is biased. The relative frequency for2 seems too low and the relative frequencies for 4and 6 seem too high.
2 Small number of trials. Cannot be predicted fromthese past events.
3 a)
b) 0.34 a) �
12
00� � 0.5, which is the probability of tossing a
fair coin and getting a head.b) �
13
00
20� � 0.34, which is very different from 0.5.
c) Emma. More trials give a more reliableindication.
5 a)
b) Yes. All values are approximately equal to0.25.
c) Either 225, 225, 225, 225 (if the spinner is fair)or
6 a) 200 is a large number of trials.b)
Mixed exercise 40 (page 527)1 �
79�
2 0.353 0.134 a) �2
70� b) 5 red, 8 white, 7 blue
5 12 days
6 a) �12
00� � �
12�, which is the probability of getting heads
with a fair coin.b) She is not necessarily correct. She should carry
out more trials.7 a) About 67
b) (i) �43090� (ii) �
24
70
90� (iii) �
14
20
10�
Chapter 41Exercise 41.1 (page 530)
1 Discrete: Number of pets, Money, Age in yearsContinuous: Weight, Distance, Temperature
2 Check students’ answers.3 a)
b)
c)–e) Check students’ answers.4 Check students’ answers.
Score 1 2 3 4 5 6
Relative0.14 0.09 0.17 0.22 0.11 0.27
frequency
Party Relative frequency
Labour 0.30
Conservative 0.47
Lib. Dem. 0.17
Other 0.06
Score 1 2 3 4
Relative0.27 0.23 0.26 0.24
frequency
Score 1 2 3 4
Relative240 204 237 219
frequency
Method of travel Bus Car Bike Walk
Estimate of0.245 0.24 0.115 0.4
probability
Day of birth Tally Frequency
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Month of Tally Frequencybirth
January
February
March
April
May
June
July
August
September
October
November
December
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 205
206 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
Exercise 41.2 (page 532)1 a)
b)
c)
2 a)
b)
2
0
468
1012
0 1 2 3 Morethan 3
Number of brothers
Freq
uenc
y
2
0
468
1012
Bir
d
Type of pet
Freq
uenc
y
Cat
Dog
Fish
Hor
seR
abbi
tO
ther
2
0
468
1012
1
Number of bedrooms
Freq
uenc
y
2 3 4 5 Morethan 5
2
0
468
1012
0
Number of cars
Freq
uenc
y
1 2 3 4 Morethan 4
2
0
468
1012
1p
Type of coin
Freq
uenc
y
2p5p
10p20p
50p£1
£2
c)
d)
e)
Exercise 41.3 (page 534)1 a)
b) 610 c) 107 d) 72 e) 1002 a)
b) 1850 c) 550
3
10
0
2030405060
Plain
Beef
Chicken
C&O
S&V
Favourite crisps
Freq
uenc
y
Oth
er
2
0
468
10121416
0 1 2 3 Morethan 3
Number of fillings
Freq
uenc
y
2
0
468
1012
Blue
Brown
Gre
enG
rey
Oth
er
Eye colour
Freq
uenc
y
Japanese Not Japanese Total
Red 35 65 100
Not red 72 438 510
Total 107 503 610
Existing New Totaldrug drug
Symptoms eased 700 550 1250
No change in350 250 600
symptoms
Total 1050 800 1850
Riding Sport Total
Boys 8 18 26
Girls 15 7 22
Total 23 25 48
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 206
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 207
4 a)
b) 15
5 a)
b) The USA c) China
Exercise 41.4 (page 536)1 a)
b)
c)
2 a)
b)
c)
d)
e)
f)
0
10
20
30
40
50
Apples per box
Freq
uenc
y
140–149
150–159
160–169
170–179
180–189
190–199
200or
more
10
0
20304050
0–19
20–39
40–59
60–79
80–99
100or
moreGreenfly per plant
Freq
uenc
y
10
0
203040
1–25
26–50
51–75
76–100
101or
moreLeaves per branch
Fre
quen
cy
10
0
20304050
30–49
50–69
70–89
90–109
110or
moreGrapes per bunch
Freq
uenc
y
20
0
406080
100
0–9 10–19
20–29
30–39
40or
moreEggs per day
Freq
uenc
y
10
0
20304050
Lessthan30
30–49
50–69
70–89
90or
moreNumber of ants
Fre
quen
cy
Hockey Not hockey Total
Badminton 33 13 46
Not badminton 24 15 39
Total 57 28 85
Gold Silver Bronze Total
USA 31 18 10 59
Germany 18 16 9 43
China 22 9 11 42
Total 71 43 30 144
Number Tally Frequencyof birds
1 to 5 � � 12
6 to 10 � � � � � 25
11 to 15 � � 13
16 to 20 � 5
21 to 25 3
26 to 30 2
Number Tally Frequencyof stamps
1 to 10 � 7
11 to 20 � � � 16
21 to 30 � � � 18
31 to 40 � � 13
41 to 50 � 5
51 to 60 0
61 to 70 1
Number Tally Frequencyof cars
1 to 20 4
21 to 40 � � � 15
41 to 60 � � � � � 25
61 to 80 � � 13
81 to 100 3
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 207
208 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
Mixed exercise 41 (page 538)1 Discrete: Hair colour, Vehicle type, Number of
sisters, Crowd size, Score on a diceContinuous: Height, Length
2 Check students’ data collection sheets.3 a)
b)
c)
d)
10
0
20304050
Pla
ysta
tion
Games console owned
Fre
quen
cy
X-b
ox
Gam
ecub
e
PC
Oth
er
1
2
0
4
6
8
10
12
14
16
2 3 4 5 Morethan 5
Number of goals
Freq
uenc
y
1
2
0
4
6
8
10
12
14
2 3 4 5 6
Score
Freq
uenc
y
Brown
5
0
10
15
20
25
30
Black Blonde Red Grey Other
Hair colour
Freq
uenc
y
4 a)
b)
c)
5
0 1 2 3 Morethan 3
2
0
4
6
8
10
12
14
16
Number of pets
Freq
uenc
y
Mot
orol
a
Sam
sung
Nok
ia
Eri
csso
n
Siem
ens
Oth
er
0
5
10
15
20
Make of phone
Fre
quen
cyF
ord
5
0
10
15
20
25
30
35
Vau
xhal
l
Toy
ota
Nis
san
Vol
ksw
agen
Oth
er
Vol
vo
Make of car
Fre
quen
cy
Alton Legoland Thorpe TotalTowers Park
Girls 31 25 27 83
Boys 43 11 21 75
Total 74 36 48 158
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 208
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 209
6 a)
b)
7 a)
b)
0
5
1–5 6–10 11–15 16–20 Morethan 20
10
15
20
Number of flowerson a plant
Freq
uenc
y
c)
Chapter 42Exercise 42.1 (page 543)
1 represents 10 kilos of apples.
2 represents two pairs of spectacles.
3 represents four people.
0
10
1–5 6–10 11–15 16–20 21–25
20
30
5
15
25
Number of mice in a nest
Freq
uenc
y
M
Tu
W
Th
F
Sa
Su
M
Tu
W
Th
F
Sa
Su
M
Tu
W
Th
F
Sa
Su
Number of Tally FrequencyCDs owned
11 to 10 � � � � 14
11 to 20 � � � � � � � � � 11
21 to 30 � � � � � � � 18
31 to 40 � � � � � � � � 10
41 to 50 � � � � � � � 18
51 to 60 � � � � � 16
61 to 70 � � � � 13
Number of Tally Frequencyflowers per
plant
11 to 20 � � 12
21 to 40 � � � � � � � � � � � � � � � � 22� �
41 to 60 � � � � � � � � � � � � � � � � 28� � � � � � �
61 to 80 � � � � � � � 18
0
10
0–9 10–19 20–29 30–39 40–49
20
30
40
Number of passengers on a bus
Freq
uenc
y
50–59
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 209
4 � represents 20 boxes of bananas.
5 You can use any symbol to represent ten ice creams.Here is used.
Exercise 42.2 (page 545)1 a)
b)
c)
Jan
Feb
March
April
May
June
July
Aug
Sep
Oct
Nov
Dec
M
Tu
W
Th
F
Sa
Su
No cars
1 car
2 cars
3 cars
More than 3 cars
No pets
1 pet
2 pets
3 pets
More than3 pets
1 bedroomMore than4 bedrooms
2bedrooms
3 bedrooms
4bedrooms
210 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
2 a)
b)
c)
3 a)
b)
Exercise 42.3 (page 547)1
Black
BlondeBrown
RedOther
OtherBlue
Brown
Green
Grey
Cheeseand onion
Beef
ChickenSalt andvineger
Other
England
Wales
Scotland NorthernIreland
FruitFlour
Butter
Sugar
Oatsand nuts
12
14
16
18
Tem
pera
ture
(°C
)
Day
20
22
24
M Tu W Th F Sa Su
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 210
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 211
2
3
4
5
12
10
J F M A M J JMonth
A S O N D
14
16
18
Sale
s (�
£10
00) 20
22
24
5 10 15Time (minutes)
20 25 30
50
60
70
80
90
100
Tem
pera
ture
(°C
)
0
12
34
56
78
910
1112
1314
Day
20
40
60
80
100
120
Sale
s (£
)
140
0
300
400
500
600
Num
ber
of v
isit
ors
700
800
900
M Tu W ThDay
F Sa Su
Mixed exercise 42 (page 548)1 Represents 4 skips
2 Represents 100 tickets
3
4
Rent
Food
Clothes
Entertainment
Savings
Carbohydrate
OtherProtein
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 211
212 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
5
6
Chap ter 43Exercise 43.1 (page 551)
1 a) 6 b) 7 c) 4d) 4 e) 8 f) 7.5
2 483 a) 5 or more b) 6
Exercise 43.2 (page 552)1 182 73 kg3 194 There are two modes: 47 and 50.
Exercise 43.3 (page 553)1 a) 6 b) 9 c) 6.52 a) 5 b) 7.2 c) 63 11.1 minutes
Exercise 43.4 (page 554)1 a) 19 b) 3.2 c) 7562 a) £32 b) £92
Exercise 43.5 (page 555)1 121–130 cm2 £8–£11.993 11–15 words
4
Modal class � 40 � s � 45 mph
Mixed exercise 43 (page 556)1 a) Tom: mode � 7, median � 7, mean � 6,
range � 5Freya: mode � 3, median � 3, mean � 5, range � 9
b) Possible answers include: Tom’s scores aremore consistent (the range of his scores issmaller). Tom’s scores are higher on average(higher mode, median and mean).
2 a) 4 b) 45 mm c) 200.3 mm3 a) Football team: mean � 12.9 seconds,
median � 13 seconds, range � 4 secondsHockey team: mean � 13.1 seconds, median � 13 seconds, range � 4 seconds
b) Mean � 12.4 seconds, median � 12 seconds, range � 4 seconds
c) PE staff: lower mean and lower median times4 a) Data set A: range � 6, mean � 3.6,
median � 3, mode � 3Data set B: range � 6, mean � 3.6, median � 3, mode � 3Data set C: range � 12, mean � 7.2, median � 6, mode � 6
b) The range, mean, median and mode for datasets A and B are the same. The results for dataset C are double those of data sets A and B.
5 a) (i) Mean � 3, median � 3, mode � 3(ii) Mean � 30, median � 20, mode � 20(iii) Mean � 130, median � 120, mode � 120(iv) Mean � 13, median � 13, no mode
b) The values for set (iii) are 100 more than thecorresponding values in set (ii) so the values ofthe mean, median and mode are also 100 more.
6 a) Boys: mean � 14.7 hours, median � 15 hours,mode � 13 hours and 15 hours, range � 23 hoursGirls: mean � 12.1 hours, median � 12 hours,mode � 9 hours, 12 hours and 15 hours, range � 9 hours
b) Yes, the boys watch more television than thegirls.
7 a) Median � 7, no modeb) Median � 36 kg, no mode
8 Median � 124 cm, mode � 123 cm
0 Mon
Tem
pera
ture
(°C
)
4
8
12
16
20
24
28
Tues Wed Thurs
Day
Fri Sat Sun
0 J F M A M J J A S O N D
14
16Sale
s (¥
mill
ion)
18
20
22
24
26
Month
Speed (mph) Tally Total
30 � s < 35 2
35 � s < 40 � 9
40 � s < 45 � � 10
45 � s < 50 � 8
50 � s < 55 1
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 212
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 213
9
The modal class is 380� m � 400
Chapter 44Exercise 44.1 (page 559)
1 a) 630 b) 45 c) Monday2 a) Saturday b) Wednesday
c) 21 d) 1503 a) 60 b) 45 c) 2754 a) 70 b) 105 c) 4155 a) Wednesday
b) 75c) 195
6 a) 325 (June)b) 500 (January)c) 5150d) Approximately 429
Exercise 44.2 (page 564)1 a) �
12� b) About �
13�
2 a) The Mailb) The Sun, magazines, and other newspapers
3 a) 36 b) 64 a) 28 b) 165 a) 14 b) 10 c) 186 a) 44 b) 16 c) 24
Exercise 44.3 (page 568)1 a) 75°C b) 5 minutes
c) 21°C d) 19°C2 a) 44 b) Friday
c) 115 d) 1623 a) 22°C b) 18°C (Monday)
c) 23� 18� 5°C d) 147� 7� 21°C
4 a) Novemberb) £22 000� £15 000� £7000c) £223 000d) 223 000� 12� £18 583.33
5 a) 10 500b) 1500c) 1850� 1300� 550
6 a) The café is closed.b) £100c) The second Monday (£40)d) 540� 8� £67.50
Exercise 44.4 (page 572)1 a) England
b) Walesc) Scotland is a relatively large country with a
relatively small population.2 a) 8 b) 0 c) 7
d) 10� 1� 9e) The girls did better in the test. The shape of the
charts show that there are more girls gettinghigher scores. The mean for the boys is 5.6 andthe mean for the girls is 6.2.
3 a) $38 000b) $35 000c) $31 000 > $31 200d) 2003 range � $15 000, 2009 range � $63 000e) Student’s own answerf) Check students’ bar charts.
Mixed exercise 44 (page 574)1 a) 60 b) 75 c) 270 d) 452 a) 240 b) 1760
c) 251 (to nearest whole number)d) 300
3 a) County councilb) (i) Any answer from £275 to £285
(ii) Any answer from £157.50 to £167.50(iii) Any answer from £75 to £85
4 a) Spainb) Spain: any answer from 41 to 43,
USA: any answer from 23 to 25,France: any answer from 15 to 17,Asia: any answer from 11 to 13,Italy: any answer from 5 to 7,Other: any answer from 19 to 21
5 a) Week 7 b) 28 c) 250d) 28 (to the nearest whole number)
6 a) July and August b) 14 cmc) 5°C d) 113 cm
7 a) (Just over) halfb) North America. The ‘Forest’ sector is larger in
the pie chart for North America.c) The total areas are differentd) A greater proportion of land is used for pasture
and grazing and for farming (arable) in NorthAmerica than in Australia, and a smallerproportion is non-productive.
Mass (grams) Tally Frequency
200� m � 220 � � 2
220� m � 240 � 1
240� m � 260 � 1
260� m � 280 � 1
280� m � 300 � � � 3
300� m � 320 � � 2
320� m � 340 � � 2
340� m � 360 � 1
360� m � 380 � � 2
380� m � 400 � � � � 5
400� m � 420 � � � � 4
50bAnswers-157-208.qxd:48Answers-157-208.qxd 16/5/11 12:42 Page 213
214 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
8 a) Germany, $23 billionb) USA, $15 billionc) France and Italyd)
Chapter 45Exercise 45.1 (page 579)
1
2 a)
b) 70 � r � 90 c) 90 � r � 110
3 a)
b) 80 � w � 90 c) 80 � w � 90
0
10
60 70 80 90 100 110
20
30
Weight (kg)
Freq
uenc
y
France
Ger
man
yIta
lyU
KU
SA
5
0
10
15 Spending
Earnings
20
Tourist Spending and Earnings
25
$ (b
illio
n)
0
10
50 70 90 110 130 150 170
20
30
Rainfall (cm)
Freq
uenc
y
0
5
15 20 25 30 35 40 45 50
10
15
20
Age (years)
Freq
uenc
y
4
Exercise 45.2 (page 583)1
2
3
4 a)
5
0
10Freq
uenc
y
15
20
100 20 30No. of words
40 50 60 70
25
30
Book 1
Book 2
5
0
10
Freq
uenc
y
15
20
172168 176 180
Height (cm)
184 188 192
25
20
0
40
Freq
uenc
y
60
80
3015 45 60Time (minutes)
75 90 105
100
120
140
5
0
10Fr
eque
ncy
15
20
60 12 18Weight (kg)
24 30
Lifetime of lightbulb Frequency(h hours)
300 � h � 400 3
400 � h � 500 9
500 � h � 600 12
600 � h � 700 15
700 � h � 800 13
800 � h � 900 19
900 � h � 1000 13
1000 � h � 1100 10
1100 � h � 1200 6
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 214
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 215
b) Possible answers include:Book 1 has a wider variety of sentence length.Book 2 has more shorter sentences.
Exercise 45.3 (page 587)1 a), d), e)
b) Strong positive correlationc) 10.4 f) About 3
2 a), d), e)
b) Strong positive correlationc) 29 > 29.1f) About 32
3 a), e)
b) Strong negative correlationc) 32.9d) About 32 mpg
4 a), d)
b) No correlationc) 34.1e) Nof) Don’t know the ages of the people involved.
10
0
20Mar
k 30
40
400 500
Circumference of head (cm)
50
600
10
0
20
Pet
rolc
onsu
mpt
ion
(mpg
)
30
40
10 2 3Engine size (litres)
4
50
5
10
0
20
Pape
r2 30
40
100 20 30
Paper 1
40
1
0
2
Num
ber
ofba
dpe
ache
s
3
4
20 4 6
Delivery time (hours)
8 10 12 14 16 18
5
6
Mixed exercise 45 (page 589)1 a)
b)
c) 5 � t � 10d) 5 � t � 10
2 a)
b) Suitable comments include the following.The marks range from 30 to 90.There are few low and high marks.Most of the marks are around 50 to 60.
c) 50 � m � 60d) 70
e) �27�
3 a), c)
b) Strong positive correlationd) (i) About 800 g (ii) About 1700 ge) No. A rabbit’s weight cannot keep increasing.
04030
5
10
Fre
quen
cy 15
20
50 60Mark
70 80 90
0 5
2
4
Freq
uenc
y
6
8
10 15Time (minutes)
20
0 1 2 3 4 5
Age of rabbit (months)
6 7 8 9
200
400
600
800
1000
1200
1400
Ave
rage
wei
ght(
g)
1600
1800
Time (t mins) Frequency
0 � t � 5 6
5 � t � 10 7
10 � t � 15 5
15 � t � 20 2
50bAnswers-157-208.qxd:48Answers-157-208.qxd 13/5/11 17:23 Page 215
216 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
Chapter 46Exercise 46.1 (page 594)
1 a) (i) 3 (ii) 3(iii) 5 (iv) 3.456
b) (i) 50 (ii) 50(iii) 5 (iv) 49.632
c) (i) 1 (ii) 1(iii) 5 (iv) 1.443
d) (i) 2 (ii) 2(iii) 4 (iv) 1.728
2 a) 1.96 b) 1.04 c) 2.987 d) 4.4563 a) 4.51 b) 27.04 c) 12.75 d) 3.16254 £1.075 7.52
Exercise 46.2 (page 599)1 a) (i) 50 (ii) 13.6
b) (i) 20 (ii) 7.22c) (i) 40 (ii) 14.1d) (i) 20 (ii) 6.55
2 a) (i) 0–4 (ii) 20 (iii) 6.98b) (i) 0–9 (ii) 40 (iii) 15.5c) (i) 250–299
(ii) 250(iii) 164.7
d) (i) 30–44(ii) 45(iii) 31.5
3 a) (i) 3–5 (ii) 3.62b) (i) 4–7 (ii) 7.3c) (i) 30–39 (ii) 32.25d) (i) 75–99 (ii) 75
4 30.35 179.5
Exercise 46.3 (page 603)1 a) (i) 50 (ii) 31.46
b) (i) 40 (ii) 25.11c) (i) 16 (ii) 68.56d) (i) 50 (ii) 16.04
2 a) (i) 0 � x � 3 (ii) 9.85b) (i) 120 � x � 130 (ii) 121.36c) (i) 22 � x � 26 (ii) 21.2d) (i) 50 � x � 55 (ii) 54.83
3 a) 250 � x � 300 b) 250 � x � 300c) £270.00
4 18.3 g5 166 (165.71) pence
Mixed exercise 46 (page 606)1 a) (i) 6 (ii) 7 (iii) 4.488
b) (i) 50 (ii) 7 (iii) 50.27c) (i) 1 (ii) 6 (iii) 1.42d) (i) 6 (ii) 5 (iii) 6.36e) (i) 2 (ii) 5 (iii) 3.47f) (i) 18 (ii) 5 (iii) 17.54
2 £11.363 2.71 (2 d.p.)4 a) (i) 20 (ii) 22.09
b) (i) 100 (ii) 30.11c) (i) 50 (ii) 59.33d) (i) 25 (ii) 55.8
5 a) 10 � x � 20 b) 10 � x � 20c) 19.31
6 £24 888.89 (or £24.89 thousand)
Chapter 47Exercise 47.1 (page 613)
1 a) Primary b) Secondaryc) Primary d) Secondary
2 Possible answers include the following.a) Those not in the phone book have no chance of
being included.b) Those working on Saturday would not be
included.3 Possible answers include the following.
Make the categories exclusive (in Paul’s first draft,for example, 1 hour could go in two categories). Have more categories, for example, split the groupsinto classes of 30 minutes rather than 1 hour.
4 Possible faults include the following.a) The person’s favourite sport might be one that
isn’t listed.b) This question is vague: it needs categories, such
as hours spent.c) This is a leading question.Check students’ new questions.
5 a) Possible answers include the following.Q1 is too vague.Q2 is an open question and the answers wouldbe very difficult to analyse.
b) Check students’ rewrites of Q1. It should havebetter categories.
6 Check students’ questions.
Mixed exercise 47 (page 615)1 Secondary. Jan did not collect the data herself.2 a) Possible answers include the following.
Ask people to draw a 70° angle without aprotractor.Show people three drawn angles and ask themto estimate what size the angles are.
b) Possible answers include the following.Choose 30 students from Year 7, 30 from Year9 and 30 from Year 11.Choose a random sample of students from amixed-age group.
c) Check students’ data collection sheets. Thesheets should include the age or year-group ofthe student as well as data on the angle(s)drawn/estimated.
3 Check students’ answers.
50bAnswers-157-208.qxd:48Answers-157-208.qxd 22/9/10 08:30 Page 216
Foundation WJEC GCSE Mathematics © 2010, Hodder Education Answers to the Student’s Book exercises 217
Chapter 481 a) 8th, 6th, 3rd, 4th
b) 18c) Wong and Selby
2 a) 47 b) 145 c) 153 Any answer so long as it is justified, e.g. taxi is thequickest but most expensive at £32.50, cycling isthe cheapest but the longest at 2 hours.
4 a) 120 m2 b) 108 m2 c) £425 a) Starters £16.25
Main course £45.00Dessert £18.50Tea or coffee £5.25Total £85.00
b) £1.506 a) 9, 8, 16:30, 7 �
12� , 08:00, �
12� , 1 �
12�
b) £360c) Yes: 360� 2.5� 24� £420
7 SOS: ABC £75 for 20, ET £70 for 20, SOS £70 for 218 Expected income £1250, expected cost £900,expected profit £350
9 a) 74 b) 132c) (i) 6 (ii) 14
10 a) �1°C b) Stockholmc) Friday d) 13°C
11 a) 45 m2 b) Grass seed by £45.75c) (i) Small box: 50p/m² Large box: 40p/m²
(ii) 2 large boxes and 1 small box12 a) £3.75 b) £13.7513 a) (i) £130 (ii) No. The total amount
collected on Sunday is not known.b) (i) Possible answers include: no timescale,
categories overlap, options are exhaustive.(ii) Possible answers include: not a
representative sample of the population,rugby is probably played on a Saturdayafternoon and the people who watch itare unlikely to be in the supermarket atthis time.
14 Any answer so long as it is justified, e.g. bus ischeapest at £32 in total but have to catch the bus at07:50, car costs £63 but don’t have to leave until 11a.m.
15 a) $1008 b) £95016 Hotel £1740 � the most expensive but includes use
of leisure facilities. Guest house £1140 � includesevening meal (but not flexible) and breakfast.Cottage £880 � all meals must be paid for andprepared.
17 a)
b) Any answer, so long as reasoning is justified,e.g. player A as they are the most consistent.
18 a) (i) £3025(ii) Six hundred and five pounds > six hundred
and twenty-five poundsb) 6541
19 a) 102 b) 31720 a) £33 b) £12.5521 a) 10 miles
b) �12� litre milk, 2 kg potatoes
22 Possible answers include: Ann £12, Gareth £6,Lucy £2.
23 a) €456 b) £53
Chapter 49Number (page 627)1 a) 1248 b) 82 113 Yes: water 52� 18� 936, lunches 45� 20� 9004 a) 54.81 b) 548.1 c) 0.635 a) $1780 b) £1202.706 a) 1200, 1200, 30, 1950, 2100, 30
b) 700 (grams)c) No: 2� 80� 160 grams are needed but
5 ounces� 125 grams7 a) 97, 99, 101, (103), 105, 98, 100, 102, 104, 106
b) 9, 11, 13, 15, 17 � strategy: must be oddnumbered, 65 ÷ 5 or algebraic method
c) 9 and 108 a) 6 p.m.
b) Between 12:30 p.m. and 2 p.m. UK time and8:30 p.m. and 10 p.m. HK time
c) Hotel Bear and reason, e.g. four dinners for £1.Hotel Gelton 4� 80� £320,Hotel Bear 3� 107� £321.
9 a) False: counter example, e.g. 10 ÷ 5� 2b) False: counter example, e.g. 14 ÷ 2� 7c) True: one or other must be even, and
even� odd� even10 a) 1000 (ml), 1000 (ml), 460 (g), 60 (ml)
b) 4411 The 4 m roll � rectangle is 280 cm by 350 cm so
either 350 cm of 3 m roll (3.5� 3� 10.5 m2) or 280cm of 4 m roll (2.8� 4� 11.2 m2) � both must beseen. Area from 3 m roll� 6� £63.Area from 4 m roll� 5� £56.
12 a) 26 cm b) 9 c) 39
Algebra (page 631)1 a) n � 4m
b) y � x � 3c) (i) 50 (ii) 20d) 20°
2 a) (4, 2) b) D marked at (�2, 2)c) E(4, �4), F(�2, �4)
3 a) A(�3, 4), B(�3, �2)b) C marked at (�3, 1)c) E marked at (�3, �1)
4 a) 15 b) 20, 33, 46, 595 a) A(12, 10) b) B(�12, 5)
c) C(7, −12)6 a � 3, b � 6, c � 7, d � 57 A(12, 4), B(0, 8), C(16, 16)8 a) (i) X marked at 2 cm above sea level
(ii) Y marked at 1 cm below sea levelb) 300 mc) �220 m
Player Mean Range
A 50 8
B 33 106
C 50 99
50bAnswers-157-208.qxd:48Answers-157-208.qxd 13/5/11 17:23 Page 217
218 Answers to the Student’s Book exercises Foundation WJEC GCSE Mathematics © 2010, Hodder Education
9 a) (4, 2) b) T marked at (�3, 2)c) (�1, 1)
10 a) x � x � 2� x � 3� x � 7b) (i) 4x � 12� 40 (ii) x � 7c) 7 cm, 9 cm, 10 cm, 14 cm
Geometry and measure (page 636)1 a) 60° b) 40° c) 50°2 a) 36 cm b) 56 cm2
3 a) 62° b) 75°4 S, P, Q, R5 14 cm3
6 a) (i) 26 cm (ii) 6.5 cmb) (i) 36 cm2 (ii) 6 cm
7 �DCB� 40°, �DBC� 100°, �DBA� 80°, x � 20°8 Check students’ diagrams.AB� 6 cm, AC� 7 cm, BC� 9 cm
9 a)
b) (i) square-based pyramid(ii) triangular prism
10 General explanation, e.g. decimals are not accurateenough � not rounded correctly. Specificexplanation, e.g.
13 � 0.33…,
23 � 0.66... .
11 Not possible: angle sum of polygon� 720°,sum of remaining angles � 720 – 3� 140� 300°,3� 89 < 300°
12 Arc centre X, radius DX � 2 mm; arc centre cornerof building, correct radius � 2 mm
13 Use of a 90° angle from the rectangle. Angles in atriangle: angle AGD� 70°, angle BFC� 70°.BFC�AGD, so triangle EFG is isosceles.
14 a)
b) 3 + 5 < 10 c) 100°15 AD� 11.2 cm (AC� 10 cm)16 a) AB� 4.5 cm b) 22.1 > 22.05
Statistics (page 643)1 a) £40.09 b) £22
c) 10 a.m. next day2 a) Louise b) 1 hour 45 minutes
c) Nell d) Betweeen 5:45 and 6:00 p.m.3 a) 138 b) 20 c) 284 a) 25% b) No: you need to know the
total numbers of boys and girls.5 4, 6, 10, 12, 166 5, 6, 9, 10, 10
Statement Rectangle Parallelogram Rhombus
The diagonals are not equal in length � �
All angles are equal �
The sum of the interior angles is 360° � � �
Statement Square Parallelogram Trapezium
The diagonals are equal in length � �
Opposite angles are equal � �
Only one pair of opposite sides �are parallel
The diagonals are lines of symmetry �
50bAnswers-157-208.qxd:48Answers-157-208.qxd 13/5/11 17:23 Page 218