AnSWErS to tHE StudEnt'S Book ExErCiSES - Hodder Plus Home

AnSWErS to tHE StudEnt’SBook ExErCiSESChapter 1Exercise 1.1 (page 3)1 2 3 32 2 3 53 3 3 54 3 3 75 2 3 2 3 2 3 2 3 2 5 2 56 2 3 2 3 3 3 3 5 2 2 3 3 27 2 3 2 3 5 3 7 5 2 2 3 5 3 78 2 3 5 3 5 3 5 5 2 3 5 39 3 3 3 3 5 3 7 5 3 2 3 5 3 710 2 3 2 3 3 3 5 3 7 5 2 2 3 3 3 5 3 7Exercise 1.2 (page 7)1 4 5 2 2 ; 6 5 2 3 3; HCF 5 2;LCM 5 2 2 3 3 5 122 12 5 2 2 3 3; 16 5 2 4 ;HCF 5 2 2 5 4; LCM 5 3 3 2 4 5 483 10 5 2 3 5; 15 5 3 3 5; HCF 5 5;LCM 5 2 3 3 3 5 5 304 32 5 2 5 ; 40 5 2 3 3 5;HCF 5 2 3 5 8; LCM 5 2 5 3 5 5 1605 35 5 5 3 7; 45 5 3 2 3 5; HCF 5 5;LCM 5 3 2 3 5 3 7 5 3156 27 5 3 3 ; 63 5 3 2 3 7;HCF 5 3 2 5 9; LCM 5 3 3 3 7 5 1897 20 5 2 2 3 5; 50 5 2 3 5 2 ;HCF 5 2 3 5 5 10;LCM 5 2 2 3 5 2 5 1008 48 5 2 4 3 3; 84 5 2 2 3 3 3 7;HCF 5 2 2 3 3 5 12;LCM 5 2 4 3 3 3 7 5 3369 50 5 2 3 5 2 ; 64 5 2 6 ;HCF 5 2; LCM 5 2 6 3 5 2 5 160010 42 5 2 3 3 3 7; 49 5 7 2 ;HCF 5 7; LCM 5 2 3 3 3 7 2 5 294Exercise 1.3 (page 10)1 112 2 220 3 130 4 2545 228 6 216 7 118 8 249 15 10 28 11 13 12 1213 29 14 27 15 24 16 21217 221 18 26 19 29 20 220Exercise 1.4 (page 12)1 a) 49 b) 121 c) 66 d) 612e) 8 f) 1000 g) 4 h) 12 6 cm3 a) 625 b) 1600 c) 1225d) 1024 e) 1.444 a) 1728 b) 15.625 c) 226.981d) 27 000 e) 157.4645 a) 620 b) 623.98 c) 635.83d) 660.70 e) 61246 a) 8 b) 8.78 c) 20d) 21.15 e) 21.547 1 and 64. 0 is also a possible answer since0 2 1 0 3 5 0Exercise 1.5 (page 14)1 a) 3 5 b) 7 3 c) 3 4 3 5 22 a) 5 5 b) 10 7 c) 8 4d) 3 10 e) 2 63 a) 5 2 b) 10 3 c) 8 3d) 3 2 e) 2 0 5 14 a) 5 4 b) 10 11c) 8 2 d) 3 45 a) 2 5 b) 3 2 c) 5 4 d) 7 3Exercise 1.6 (page 17)1 a)1_3 b) 1_6 c) __ 1491d) ___100 e) ___ 16402 a) 16 b) 9 c) 52d) 67 e) 10003 a) 11_4 b) 2 2_3 c) 5_83d) __10 e) 12 1_24 a) 0.4 b) 2 c) 0.008d) 6.25 e) 0.3125Mixed exercise 1 (page 18)1 a) 3 3 5 2 b) 2 2 3 5 3 7c) 2 2 3 3 3 5 3 72 a) 24 5 2 3 3 3, 60 5 2 2 3 3 3 5, HCF 5 12,LCM 5 120b) 100 5 2 2 3 5 2 , 150 5 2 3 3 3 5 2 , HCF 5 50,LCM 5 300c) 81 5 3 4 , 135 5 3 3 3 5, HCF 5 27, LCM 5 4053 a) 212 b) 216 c) 8 d) 34 a) 16, 64 b) 36, 216 c) 100, 10005 a) 68 b) 6146 a) 5 b) 37 a) 21.16, 97.336 b) 441, 9261c) 8.41, 24.3898 a) 69.43, 4.46 b) 611.14, 4.99c) 631.40, 9.95Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 193

9 a) 5 7 b) 10 3 c) 8 2d) 2 6 e) 3 310 a)1_5b)1_8 c) 8d) 10 e) 0.625 or 5_8Chapter 2Exercise 2.1 (page 24)1 a) 9, 7_7_3_b) 24, c) 40,9 8 82 a)7_9 b) __ 711 c) 1_35d) __13 e) 5_6 f) 1 1_8g)1_3 h) 1 3_ i) 31_52j) 21_4 k) 4 1_9 l) 2 6_73 a)7_8 b) 7_9 c) __ 712d)1_4 e) 1 __ 310 f) 1 __ 132813g) __18 h) 1 1_2 i) 1 __ 131823j) __30 k) __ 1336 l) __ 394074 a) 5 __10 b) 3 1_8 c) 4 __ 11141d) 3 __12 e) 7 3_8 f) 4 __ 71211g) 7 __18 h) __ 126 i) 6 __ 12113j) 5 __20 k) 1 __ 1114 l) 5_6Exercise 2.2 (page 29)1 a)d)g)2 a) 22_5d) 43___ 194 b) __ 173 c) __ 132__ 218 e) __ 237 f) __ 1712__ 17__6 h) 6211b) 41_2 c) __ 2158 e) __ 521 f) 933 a) __16 b) __ 427 c) __ 524d) 13_8 e) 1 3_ f) __ 155284g) __27 h) 7_8 i) __ 2027j) 15_9 k) 5 1_3 l) __ 73274 a) 7 __10 b) 2 1_7 c) 1 4_717d) __40 e) 8 2_ f) 1 __ 9514g) 10 h) 31_3 i) 7 5_7j) 22_ k) 181_52 l) 1 __ 1039Exercise 2.3 (page 33)1 a)2 a)__ 1321 b) __ 720 c) __ 522__ 7e) 5 __ 131514 f) 1 __ 11127 h) 3 __ 9442_ b)5_58 c) __ 715__ 716 e) 1_9__ 1__ 11__d) 1g) 126_d)3 a) 2 b) 71517 c) 4 1315d) 44_ e) 8 __ 35134 a) 205_6 cm b) 24 3_4 cm2Exercise 2.4 (page 34)1 a) 0.8 b) 0.375 c) 0.182d) 0.111 e) 0.452 a) Terminating, 5 is a factor of 10b) Recurring, 3 is not a factor of 10c) Recurring, 9 is not a factor of 10d) Terminating, 16 has only factors which arefactors of 10e) Recurring, 7 is not a factor of 103 a) 0.714 285 7… b) SixExercise 2.5 (page 36)1 7.7 2 7.9 3 3.6 4 2.25 7.1 6 8.1 7 5.7 8 3.89 12.2 10 16.5 11 0.9 12 5.8Exercise 2.6 (page 39)1 a) 1.2 b) 3.5 c) 1.8d) 7.2 e) 0.24 f) 0.48g) 12 h) 35 i) 0.06j) 0.08 k) 0.49 l) 0.092 a) 40 b) 4 c) 4d) 9 e) 20 f) 20g) 30 h) 50 i) 80j) 30 k) 3.1 l) 1223 a) 6.3 b) 14.26 c) 35.99d) 19.44 e) 113.4 f) 388.8g) 49.84 h) 26.16 i) 5.08j) 1.872 k) 3.822 l) 9.9684 a) 49 b) 17 c) 24d) 32 e) 53 f) 78g) 5.7 h) 4.9 i) 2.9j) 2.7 k) 3.7 l) 4.5Exercise 2.7 (page 42)1 a) 1.13 b) 1.2(0) c) 1.68 d) 1.08e) 1.02 f) 1.175 g) 2(.00) h) 2.5(0)2 a) 0.86 b) 0.8(0) c) 0.55 d) 0.93e) 0.97 f) 0.77 g) 0.14 h) 0.8353 £4.78 4 £29.405 £2917 6 £34 6967 £8736 8 £159 6279 £2980.80Mixed exercise 2 (page 44)1 a) 30, 5_ b) 21,1_c) 40, 136 3 202 a) 12_ b) 1 __ 2521 c) __ 1124 d) 5_6 e) __ 13245f) 5 __12 g) 3 __ 720 h) 8 3_8 i) 6 __ 118 j) 1 __ 1320k)2_ l) __ 10521 m) __ 1516 n) 2 __ 110 o) __ 920p) 32_3 q) 1 __ 1321 r) 3 3_4 s) __ 1744 t) 9 3_73 a) 0.125 b) 0.222 c) 0.714 d) 0.2734 a) 9.7 b) 5.3 c) 8.7 d) 4.65 a) 2 b) 0.07 c) 0.72d) 10.8 e) 9.18 f) 18.726 a) 30 b) 8 c) 3d) 80 e) 79 f) 8.717 a) 1 __66 b) __ 1140 c) 3 1_7 d) 3 1_98 £52639 £29.52194Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

Chapter 3Exercise 3.1 (page 47)1 a) 2 : 1 b) 1 : 3 c) 5 : 1d) 1 : 3 : 5 e) 3 : 6 : 42 a) 1 : 20 b) 3 : 20 c) 4 : 1d) 16 : 3 e) 3 : 203 5 : 6 4 5 : 8 : 10 5 4 : 2 : 3Exercise 3.2 (page 48)1 a) 1 : 3 b) 1 : 5 c) 1 : 2.5d) 1 : 1.75 e) 1 : 7.5 f) 1 : 125g) 1 : 0.2 h) 1 : 500 0002 1 : 250 000 3 1 : 6Exercise 3.3 (page 52)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 £12010 a) 500 g b) 180 gExercise 3.4 (page 54)1 Dave £8, Sam £122 a) 15 litres b) 25 litres3 30 kg sand4 a) 50 ml b) 250 ml5 Amit £320, Bree £800, Chris £4806 15607 £2928 a) 400 g b) 80 gExercise 3.5 (page 57)In all these questions either cost per unit or numberof units per penny can be used. Both are given ineach answer. Where necessary, answers are roundedto 2 decimal places, unless otherwise indicated.1 Cost per gram: 420 g bag 5 0.38p,325 g bag 5 0.34pGrams per penny: 420 g bag 5 2.64 g,325 g bag 5 2.98 g325 g bag is better value2 Cost per litre: 2 litre bottle 5 42.5p,5 litre bottle 5 35.8pMillilitres per penny: 2 litre bottle 5 23.53 ml,5 litre bottle 5 27.93 ml5 litre bottle is better value3 Cost per gram: 680 g pack 5 0.47p,1.4 kg pack 5 0.39pGrams per penny: 680 g pack 5 2.125 g,1.4 kg pack 5 2.59 g1.4 kg pack is better value4 Cost per nail: 50 pack 5 2.5p,144 pack 5 2.64pNails per penny: 50 pack 5 0.4 nails,144 pack 5 0.38 nails50 pack is better value5 Cost per roll: 12 pack 5 14.92p, 50 pack 5 14.4pRolls per penny: 12 pack 5 0.067 rolls,50 pack 5 0.069 rolls (answers rounded to3 decimal places)50 pack is better value6 Cost per ml: 80 ml tube 5 3.49p,150 ml tube 5 3.33pMillilitres per penny: 80 ml tube 5 0.29 ml,150 ml tube 5 0.3 ml150 ml tube is better value7 Cost per litre: 3 litres 5 66.33p,2 litres 5 67.5p, 1 litre 5 57pLitres per pound: 3 litres 5 1.51 litres,2 litres 5 1.48 litres, 1 litre 5 1.75 litres1 litre bottle is the best value8 Cost per gram: 750 g 5 0.239p,1.4 kg 5 0.229p, 2 kg 5 0.245p (answers roundedto 3 decimal places)Grams per penny: 750 g 5 4.19 g, 1.4 kg 5 4.38 g,2 kg 5 4.09 g1.4 kg packet is the best valueMixed exercise 3 (page 58)1 a) 10 : 7 b) 5 : 12 c) 3 : 1d) 9 : 20 e) 3 : 52 a) 1 : 4 b) 1 : 2.4 c) 1 : 50d) 1 : 250 000 e) 1 : 0.43 a) 60 cm b) 5 cm4 250 g5 a) 60 g b) 250 g6 a) 500 ml b) 240 mlIn questions 7 and 8 either cost per unit or number ofunits per penny can be used. Both are given in eachanswer. Where necessary, answers are rounded to 2decimal places, unless otherwise indicated.7 Cost per litre: 5 litres 5 £3.70, 2 litres 5 £3.50Litres per pound: 5 litres 5 0.270 litres,2 litres 5 0.286 litres2 litres is better value8 Cost per millilitre: pint 5 0.076p, litre 5 0.075p(answers rounded to 3 decimal places)Millilitres per penny: pint 5 13.2 ml,litre 513.3 mlLitres are better valueChapter 4Exercise 4.1 (page 61)1 a) 26 b) 1.5 c) 58 d) 200e) 80.4 f) 20.1 g) 661 h) 10.1i) 283 j) 275Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 195

2 a) 16 b) 0.9 c) 87 d) 58e) 69.6 f) 65 g) 69 h) 277i) 85.7 j) 9963 a) 72 b) 52 c) 2.4 d) 160e) 800 f) 336 g) 185 h) 520i) 1000 j) 7754 a) 4 b) 80 c) 13 d) 16e) 13 f) 4 g) 0.08 h) 6i) 20 j) 35 a) 4 b) 24 c) 27 d) 6e) 22 f) 10 g) 26 h) 24i) 24 j) 06 a) 28 b) 212 c) 12 d) 235e) 40 f) 23 g) 24 h) 3i) 22 j) 167 a) 36 b) 25 c) 121 d) 100e) 169 f) 400 g) 90 000 h) 0.16i) 0.49 j) 0.098 a) 64 b) 63 c) 67 d) 613 e) 6159 a) 1 b) 125 c) 8d) 64 000 e) 0.02710 £9.20 11 8 cm12 £15.28 13 420 ml14 a) 17 cm b) 18 cm 215 8 and 5Exercise 4.2 (page 65)1 a) 8 b) 7 c) 20 d) 30e) 500 f) 7 g) 1000 h) 0.4i) 0.7 j) 4000 k) 4000 l) 32 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) 20003 a) 18 b) 180 c) 5700 d) 98 000e) 50 f) 0.17 g) 0.039 h) 0.0061i) 0.031 j) 0.994 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) 3.145 £180 or £200 6 37 54 cm 2 or 50 cm 2 8 21 cm or 20 cm9 £2000 or £3000 10 64 cm 3 or 60 cm 311 50 mph12 a) 4000 b) 9c) 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) 50 or 60Exercise 4.3 (page 67)1 a) 8p b) 64p c) 36pd) 26p e) 81p f) 7p2 a) 14p b) 80p c) 32pd) 50p e) 4 f) 16p3 5 : 2 4 225p cm 2 5 64 2 4p cm 2Exercise 4.4 (page 69)1 a) 4900 b) 0.036 c) 0.04d) 0.0016 e) 0.04 f) 30 000g) 560 000 h) 1120 i) 120 300j) 9040 k) 0.12 l) 0.062 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) 10003 a) 2160 b) 1.35 c) 16d) 0.002 16 e) 1600 f) 2164 a) 9880 b) 3.8 c) 260d) 38 e) 0.038 f) 265 a) 408.51 b) 40 851 c) 1530d) 4.0851 e) 26.7 f) 15 300Mixed exercise 4 (page 69)1 a) 92 b) 1.6 c) 141.9 d) 21.1e) 441 f) 7.2 g) 158 h) 8.1i) 383 j) 6.92 a) 153 b) 0.54 c) 710 d) 345e) 1025 f) 17 g) 0.35 h) 0.82i) 9 j) 123 a) 24 b) 6 c) 17 d) 29e) 1 f) 228 g) 30 h) 29i) 5 j) 234 a) 49 b) 0.81 c) 144d) 10 000 e) 1965 £15.416 a) 9 b) 4 c) 30d) 30 e) 600 f) 6g) 1000 h) 0.3 i) 0.6j) 50 0007 32 cm 2 or 30 cm 28 50 mph9 a) 4000 b) 10c) 200 d) 36 or 40e) 4200 or 4000 f) 0.1g) 30 h) 15 000 or 20 000i) 300 j) 21 or 2010 a) 9.2 b) 4.7 c) 0.014d) 160 000 e) 51011 a) 1480 b) 10.2 c) 0.0219d) 21.0 e) 0.005 6212 a) 10p b) 49p c) 22pd) 9p e) 85p f) 63p13 a) 15 000 b) 80 c) 48d) 0.09 e) 1539 f) 20g) 0.16 h) 70 i) 4500j) 12 00014 a) 4446 b) 2.34 c) 19d) 0.004 446 e) 1900 c) 4.44615 a) 38.682 b) 38 682 c) 1260d) 3.8682 e) 30.7 f) 1.26196Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

Chapter 5Exercise 5.1 (page 73)1 5 2 3.84 3 4.54 3.45 5 9.2 6 62.417 1.20 8 2.68 9 4.4810 2.65 11 1.78 12 1.85Exercise 5.2 (page 76)1 Check students’ answers. Possible answersinclude the following.a) positive 3 negative 5 negativeb) Multiplying by number less than 1 shouldmake answer smallerc) 3 3 60 5 180 and answer should be morethan thisd) √ ___64 5 8 and answer should be less than this2 Check students’ answers. Possible answersinclude the following.a) Answer is too large, since 0.9 is near 1b) negative 4 negative 5 positivec) 6 2 5 36 and answer should be less than thisd) 8 1 3 5 11 so last digit should be 13 a) 1000 3 20 5 20 000b) 0.4 3 0.4 5 0.16c) 220 4 5 5 244 a) 7 3 £9 5 £63b) 30 3 £15 5 £450 or 30 3 £10 5 £300c) 3 3 £6 1 3 3 £2 5 £245 a) 62 067.5 4 81.4 5 762.5or 62 067.5 4 762.5 5 81.4b) √ _______1466.89 5 38.3 c) 17.6 3 3.8 5 66.88d) 278.93 1 18.2 5 297.13, 297.13 4 4.3 5 69.1or 297.13 4 69.1 5 4.36 a) 468.38 b) 6.807 a) 12.647 b) 896.8748 a) 61.1 b) 4.89 a) (i) 40 3 5 64 000(ii) 20 3 0.2 5 4(iii) √ _______7 2 2 4 2 5 √ _______49 2 16 5 √ ___33 < 6(iv) _______ 10 1 30.5 ____ 400.08 0.08 5 _____ 4000 5 5008b) (i) 60 236.288(ii) 3.496(iii) 5.93 (to 2 d.p.)(iv) 516 (to nearest whole number)Exercise 5.3 (page 82)1 a) 2 hours and 51 minutesb) 9 minutes2 a) 1.45 hours b) 0.9 hours3 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 £191.1210 60 73611 200.8 (to 1 d.p.)12 2.2 g/cm 313 15.2 cmMixed exercise 5 (page 83)1 a) 3 b) 3.52 2.32 (to 2 d.p.)3 a) The answer should be more than 7 2 , whichis 49.b) Multiplying 2.4 by a number less than 1should give an answer less than 2.4.c) 120 3 49 < 120 3 50 5 6000, not nearly60 000 (or equivalent argument).d) The answer should be negative.4 a) 900 3 30 5 27 000b) 0.6 2 5 0.36c) 248 4 6 5 28 or 250 4 6 < 285 a) 1270.26 b) 2.886 a) (i) 20 3 5 8000 (ii) 30 3 0.3 5 9(iii) √ _______8 2 2 4 2 5 √ _______64 2 16 5 √ ___48 < 7(iv) _______ 30 1 505 ____ 800.04 0.04 5 2000b) (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 minutes d) 51 minutes9 34.3 mph (to 1 d.p.)10 66 834 people11 £96.91 or £96.9212 2.9 cm (to 1 d.p.)Chapter 6Exercise 6.1 (page 88)1 a) £696.73 b) £18 310.68c) £3124.132 a) £91.75 b) £399.19 c) £512.333 £18 5754 £17.785 2340 rabbitsExercise 6.2 (page 91)1 a) £92 b) £47 c) £192.40 d) £358.602 a) £696 b) £123 c) £221.33 d) £392.153 £813.954 £75.055 £12 5006 £759 or £760 or £758.977 £34 440 or £34 439 or £34 439.25Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 197

8 1540 votes9 £42510 a) 79p b) £1.2411 a) £56 b) £54.7512 £84Mixed exercise 6 (page 93)1 1679 bacteria2 331 people3 a) £724.50 b) £27.31 c) £346.75d) £903.23 e) £75.604 £5205 9216 copies6 234 seats7 a) £5705.83 b) £5824.56c) £6738.288 a) £2163.20 b) £2576.419 a) £112.50 b) £173.8010 40 miles per gallonChapter 7Exercise 7.1 (page 99)1 a) x 1_2b) x 24 c) x 5_22 a)1_ b) 2 c) 141d) __ e) 8 f) 100016g) 16 h)1_9 i) 1j) 16 k) 2 l)1_8m) 16 n) 8 o)1_23 a) 18 b) 243 c)1_5d) 18 e) 16 f) 7236g) __ 1_5 5h) 26Exercise 7.2 (page 101)1 a) 74.088 b) 0.073 116c) 65.944 d) 0.029 401e) 7 f) 1.5187g) 2.8439 h) 272 a) 225.10 b) 389.33c) 278.92 d) 2.8730e) 67.349 f) 0.18 303g) 768.20 h) 0Exercise 7.3 (page 102)1 a) 3 4 b) 3 21 c) 3 3_2d) 3 2e) 3 2n f) 3 9n g) 3 11n2 a) 5 21 b) 5 3c) 5 4 d) 5 5e) Cannot be simplifiedf) 5 7n3 a) 2 3 3 2 b) 2 3 3 3 2c) 2 1_33 3 2_3d) 2 2 3 3 22e) 3 3 3 2 214 a) 3 3 5 2 b) 2 5 3 3 2c) 2 2 3 5 3 d) 2 3 3 3 4 3 5Exercise 7.4 (page 104)1 a) 7 3 10 3 b) 8.4 3 10 4c) 5.63 3 10 2 d) 6.5 3 10 6e) 7.23 3 10 5 f) 2.7 3 10 1g) 8 3 10 6 h) 3.92 3 10 72 a) 3 3 10 23 b) 5.6 3 10 22c) 3.8 3 10 24 d) 6.3 3 10 26e) 8.2 3 10 25 f) 3.8 3 10 273 a) 50 000 b) 370 000c) 0.0007 d) 6 900 000e) 0.0061 f) 47 300g) 27 900 000 h) 0.000 048 3i) 0.0103 j) 989 000 000k) 0.000 002 61 l) 370Exercise 7.5 (page 106)1 a) 8 3 10 7 b) 1.2 3 10 11c) 5.6 3 10 6 d) 4 3 10 5e) 5.2 3 10 7 f) 5 3 10 4g) 6.4 3 10 4 h) 5.83 3 10 52 a) 2.356 3 10 13 b) 1.5 3 10 5c) 1.45 3 10 11 d) 1.073 3 10 26e) 3.25 3 10 4 f) 8.019 3 10 5g) 3.692 3 10 6 h) 5.202 3 10 23Mixed exercise 7 (page 108)1 a) 3 b) 9 c)1_9d)1_ e) 100 00042 a)2_b)3_54c) 109 d)7_6 or 1 1_63 a) 17.58 b) 2.074 c) 0.069 25d) 3.869 e) 13.574 a) 64.39 b) 0.028 97c) 3.166 d) 21.1585 a) 7 2 b) 5 22 c) 2 22d) 11 2_3e) 3 2 1_26 a) 2 6 3 3 3 b) 2 5 3 3 2 c) 2 3 3 3 24d) 5 3 3 2 –2 3 3 22 e) 3 1_33 5 1_37 a) 1.65 3 10 4 b) 8.69 3 10 24c) 5.3 3 10 7 d) 8.3 3 10 288 a) 530 000 b) 0.006 32c) 726 000 000 d) 0.000 001289 a) 8 3 10 8 b) 2.4 3 10 6 c) 2.25 3 10 4d) 2.5 3 10 9 e) 8 3 10 4 f) 2.1 3 10 27g) 4.6 3 10 4 h) 7.6 3 10 –4 i) 5.96 3 10 7j) 7.7 3 10 2410 a) 6.81 3 10 8 b) 2.88 3 10 210 c) 8.75 3 10 7d) 8.36 3 10 25 e) 7.26 3 10 5 f) 2.04 3 10 24Chapter 8Exercise 8.1 (page 112)1 a) 0.207 b) 0.429 c) 0.2112 a) 9.30 b) 4.68 3 10 24 c) 0.2933 a) 2.37 b) 0.977 c) 2.42198Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

4 a) 0.722 b) 1.26 c) 20.6495 a) 33.7° b) 65.5° c) 69.6°6 a) 4.67 3 10 8 b) 6.57 3 10 7c) 3.6 3 10 287 a) 37.8 b) 0.0308 c) 2.958 a) 0.070 b) 0.151 c) 0.7199 a) 1.51 b) 2.47 c) 31.1°10 a) 2.21 3 10 11 b) 0.08c) 4.06 3 10 17Exercise 8.2 (page 114)1 a) a 5 5000 3 1.03 tb) (i) £5627.54 (ii) £9030.562 a) v 5 9000 3 0.88 tb) (i) £6133.25 (ii) £3236.71c) 5 years3 a) 1 000 000b) (i) 31 250 (ii) 244c) 20 hours4 a) £2000b) 8%c) Number of years investedd) (i) £2938.66 (ii) £6344.345 a) P 5 60 000 000 3 1.05 tb) (i) 76 576 894 (ii) 6 182 080 587c) 14.2 years6 a) m 5 50 3 0.90 tb) (i) 36.5 g (ii) 17.43 gc) 6.6 yearsExercise 8.3 (page 117)1 a) UB 5 4.75 m, LB 5 4.65 mb) UB 5 37.5 kg, LB 5 36.5 kgc) UB 5 1.955 m, LB 5 1.945 md) UB 5 28.455 seconds, LB 5 28.445 secondse) UB 5 330.5 ml, LB 5 329.5 ml2 2.995 m < length , 3.005 m3 No. UB for card 5 12.55 cm,LB for envelope 5 12.5 cm4 a) UB 5 65 g, LB 5 55 gb) UB 5 210 m, LB 5 190 mc) UB 5 1365 seconds, LB 5 1355 secondsExercise 8.4 (page 119)1 UB 5 26.5 cm, LB 5 23.5 cm2 UB 5 536.25 cm 2 , LB 5 490.25 cm 23 UB 5 3 kg, LB 5 2.8 kg4 UB 5 1 cm, LB 5 0 cm5 a) UB 5 13.8, LB 5 13.6b) UB 5 3.6, LB 5 3.46 UB 5 7.88 m/s, LB 5 7.7 4 m/s7 UB 5 908 people/square mile,LB 5 892 people/square mile8 UB 5 84.5, LB 5 20.29 UB 5 0.405LB 5 0.38410 a) Least 5 14.5 kg, Greatest 5 15.5 kgb) (i) Least 5 1450 kg, Greatest 5 1550 kg(ii) 1550 2 3 3 15.5 5 1503.5 . 150097 blocks is too many.1550 2 4 3 15.5 5 1488 , 150096 blocks is under 1500 kg.At most 96 blocks.Mixed exercise 8 (page 120)1 a) 28.7 b) 1760 c) 3.232 a) 2.80 b) 55.6 c) 11.33 a) 2.59 b) 0.009 53 c) 1.474 a) 1.64 3 10 12b) 2.07 3 10 –45 a) £3000b) 5%c) Number of yearsd) (i) £3646.52(ii) £5387.576 a) v 5 12 000 3 0.87 tb) (i) £7902.04(ii) £3938.54c) 5 years7 a) UB 5 1.75 kg, LB 5 1.65 kgb) UB 5 255 kg, LB 5 245 kg8 UB 5 21.2 m, LB 5 20.8 m9 UB 5 64.3 km/h, LB 5 61.4 km/hChapter 9Exercise 9.1 (page 124)41 a) __ and c) __ 415 . 35. .2 a) 0.26b) 0.15 c) 0.114 285 7d) 0.072 e) 0.68753 a) 2_ , b) __ 17 , c) ___ 383_and e)5 20 125 84 a) 0.4.b) 0.85 c) 0.304d) 0.38e) 0.37535 a) __41b) _____6 a)7 a)8 a)25200 c) 3_8 d) 5164_9 b) 7_9 c) __ 1190 d) __ 4390__ 3599 b) __ 611 c) __ 433 d) __ 1799__ 437 b) ___ 41333 c) __ 799 d) ___ 31333Exercise 9.2 (page 128)1 a) 6 √ __3 b) 9 √ __5 c) 5 √ __5d) 12 e) 5 √ ___21 f) 122 a) 5 √ __2 b) 10 √ __5 c) 24 √ __2d) 15 √ __6 e) 3 √ ___10 f) 20 √ __53 a) 7 √ __3 b) 5 √ __5 c) 5 √ __2d) 12 √ __5 e) 24 f) 150 √ __24 a) 3 1 2 √ __3 b) 10 1 2 √ ___10c) 12 √ __7 1 28 √ __2 d) 20 1 10 √ __35 a) 32 1 9 √ __3 b) 13 2 2 √ __2 c) 8d) 12 1 5 √ __6 e) 10 f) 44 2 23 √ __76 a) 8 1 20 √ __3 b) 5 2 2 √ __3c) 29 √ __3 d) 299 1 √ __3Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 199

7 a) 9 2 15 √ __2 b) 10 1 3 √ __2 c) 6d) 241 e) 59 1 30 √ __2 f) 59 2 30 √ __28 379 a) 5 √ __√ ___102 b) ____2 √ ___c) _____ 10515d)7 √ ______ 2√ __e) ___ 612 √ ___f) ______ 101033510 a) 3 1 3 √ __1 1 3 √ __52 b) ________24 √ __3 1 √ __6c) _________5 √ __6 1 6 √ __d) __________ 226Mixed exercise 9 (page 130)1 a) 5_6 , c) __ 5 and e) __ 11. 18 15.2 a) 0.83b) 0.625 c) 0.27.d) 0.44 e) 0.73183 a) __ b) __ 132540 c) 5_8 d) ___ 241254 a)4_9 b) __ 4990 c) __ 611 d) ___ 561115 a) 4 √ __2 b) 10 √ __3 c) 15 √ __2d) 6 √ __3 e) 2 √ ___15 f) 15 √ __36 a) 7 √ __2 b) 4 √ __5 c) 7 √ __3d) 60 e) 8 √ __3 f) 12 √ __57 a) 5 √ __2 1 2 b) 3 √ ___15 1 30c) 2 √ ___11 1 22 √ __2 d) 9 √ __2 1 188 a) 17 1 11 √ __3 b) 2 1 3 √ __2 c) √ __5 2 11d) 17 1 7 √ __7 e) 4 f) 46 2 21 √ __39 a) 42 2 12 √ __3 b) 35 √ __3 1 30 c) 4 √ __3d) 37 e) 61 1 28 √ __10 a) 4 √ __2 b)d)2 √ __________ 5 1 55Chapter 102 √ ________ 155Exercise 10.1 (page 133)3 f) 61 2 28 √ __3c)√ _______ 1087 1 ___ √__ 33e) 4 √ __3 1 1 f) 2 √ __1 20a 1 30b 2 6c 1 21d3 15e 2 40f 4 28g 2 21h5 10u 1 15v 6 30w 1 18x7 21y 1 7z 8 16v 1 409 12 1 42w 10 12 2 32a11 8g 2 6 12 35 2 20b13 6i 1 8j 2 10k 14 20m 2 12n 1 8p15 12r 2 18s 2 24tExercise 10.2 (page 135)1 a) 20a 1 38 b) 27b 1 53c) 12 1 37c d) 32 1 22a2 a) 18s 1 43t b) 14v 1 49wc) 27x 1 77y d) 38v 1 27w3 a) 21x 1 8 b) 14y 1 1c) 22 1 3z d) 36 1 10x4 a) 16n 1 9p b) 21q 1 13rc) 23d 1 6e d) 14f 1 ge) 2h 1 11j f) 6k 1 3mExercise 10.3 (page 137)1 a) 5(2x 1 3) b) 2(x 1 3)c) 4(2x 2 3) d) 4(x 2 5)2 a) 7(2 1 x) b) 4(2 1 3x)c) 5(3 2 2x) d) 3(3 2 4x)3 a) x(3x 1 5) b) 5x(x 1 4)c) 4x(3x 2 2) d) 2x(3x 2 4)Exercise 10.4 (page 139)1 a) a 2 1 10a 1 21 b) b 2 1 11b 1 28c) 6 1 5c 1 c 22 a) 9d 2 1 3d 2 20 b) 8e 2 2 2e 2 15c) 6 1 5f 2 56f 23 a) 4g 2 2 20g 1 21 b) 4h 2 2 28h 1 49c) 6j 2 2 37j 1 564 a) 10k 2 1 23k 2 42 b) 6 2 11m 2 72m 2c) 6 2 n 2 15n 25 a) 4 2 4p 2 63p 2 b) 6r 2 2 37r 1 56c) 4s 2 2 20s 1 21Exercise 10.5 (page 141)1 a) 3 4 b) 7 3 c) 10 52 a) x 5 b) y 4 c) z 73 a) m 2 n 4 b) f 4 g 5 c) p 3 r 44 a) 56k 3 b) 120y 3 c) 8d 3Mixed exercise 10 (page 142)1 a) 24a 1 16b b) 20a 1 15bc) 36a 2 60b d) 9a 2 18be) 12x 1 15y f) 18x 2 12yg) 20x 2 12y h) 8x 1 2yi) 15f 2 20g j) 6j 1 15kk) 7r 1 14s l) 12v 2 4w2 a) 12x 1 11 b) 20x 1 27c) 7x 1 12 d) 16y 1 5e) 15y 1 7 f) 21y 1 4g) 3a 1 6 h) 6m 1 1i) 6p 1 18 j) 14t 1 24k) 2j 1 31 l) 463 a) 4(x 1 2) b) 6(x 1 2)c) 3(3x 2 2) d) 6(2x 2 3)e) 2(3 2 5x) f) 5(2 2 3x)g) 8(3 1 x) h) 4(4x 1 3)i) 2(3x 1 4) j) 4(8x 2 3)k) 4(5 2 4x) l) 5(3 1 4x)m) x(2 2 x) n) y(3 2 7y)o) z(5z 1 2)4 a) a 2 1 9a 1 20 b) a 2 1 5a 1 6c) 12 1 7a 1 a 2 d) x 2 1 7x 2 8e) x 2 1 4x 2 45 f) x 2 2 3x 1 2g) 3x 2 1 31x 1 36 h) 2y 2 1 y 2 21i) 14 2 25p 1 6p 2 j) 6p 2 1 8p 2 8k) 4t 2 2 23t 1 15 l) 6a 2 1 a 2 155 a) 4 6 b) 5 4 c) 2 5 d) a 7e) j 3 f) t 6 g) v 3 w 3 h) d 3 e 6i) x 3 y 5 j) 60p 3200Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

Chapter 11Exercise 11.1 (page 144)x 2 31 ______22x 2 1357______ 4 1 x3 2 2x______ 3x 2 12x 1 1_________3(3 2 2x)2(x 1 4)Exercise 11.2 (page 146)468________2(x 1 3)5(x 2 2)_________4(3 2 x)3(2 2 3x)______ x 2 23x 2 4________x(x 1 3)2x 2 11 a) (x 1 1)(x 1 2) b) (x 1 1)(x 1 5)c) (x 1 2)(x 1 6) d) (x 1 3)(x 1 5)e) (x 1 1)(x 1 9) f) (x 1 3)(x 1 3)g) (x 1 4)(x 1 5) h) (x 1 2)(x 1 12)2 a) (x 1 6)(x 2 1) b) (x 1 10)(x 2 1)c) (x 1 4)(x 2 2) d) (x 1 6)(x 2 2)e) (x 1 5)(x 2 3) f) (x 1 10)(x 2 2)g) (x 1 8)(x 2 3) h) (x 1 6)(x 2 4)3 a) (x 2 2)(x 2 5) b) (x 2 1)(x 2 8)c) (x 2 1)(x 2 2) d) (x 2 2)(x 2 7)e) (x 2 2)(x 2 8) f) (x 2 2)(x 2 12)g) (x 2 5)(x 2 6) h) (x 2 2)(x 2 3)Exercise 11.3 (page 148)1 a) (x 1 3)(x 2 3) b) (x 1 4)(x 2 4)c) (x 1 7)(x 2 7) d) (x 1 9)(x 2 9)e) (x 1 10)(x 2 10) f) (x 1 12)(x 2 12)2 a) 3(x 1 2)(x 2 2) b) 5(x 1 3)(x 2 3)c) 3(x 1 6)(x 2 6) d) 7(x 1 7)(x 2 7)e) 10(x 1 20)(x 2 20) f) 8(x 1 5)(x 2 5)Exercise 11.4 (page 149)1471013____ 4a 2 c3b 2 2_____ 6a 6 b 35c 3 5_____ 2a 2 d 2bc 2 e8_____8x 2 y 235z 2_____ 9t 3 w 24v 3 6______ ztv 2 x 3 y93e 2 _____8f 2 g 3 11 3x 3 126__x 2 1412 ___a 9______ a 2 b 2 c 35____3e 2 gf_____ 8a 2 c 29b 2 d 2____ 9a 5 b 415 20xExercise 11.5 (page 151)1 a) (3x 1 5)(x 1 4) b) (2x 1 3)(x 1 2)c) (3x 1 1)(x 1 4) d) (5x 1 3)(x 1 3)e) (4x 1 2)(x 1 1) f) (3x 1 5)(x 1 2)g) (2x 1 1)(x 1 2) h) (4x 1 5)(x 1 3)i) (5x 1 3)(x 1 1)2 a) (2x 1 5)(x 2 3) b) (3x 1 7)(x 2 2)c) (5x 1 3)(x 2 4) d) (3x 1 4)(x 2 3)e) (4x 1 5)(x 2 2) f) (2x 1 3)(x 2 5)g) (4x 1 1)(x 2 2) h) (3x 1 2)(x 2 6)i) (4x 2 3)(x 1 6)3 a) (3x 2 2)(x 2 4) b) (5x 2 4)(x 2 3)c) (3x 2 5)(x 2 7) d) (2x 2 5)(x 2 8)e) (2x 2 3)(x 2 4) f) (4x 2 3)(x 2 2)g) (2x 2 5)(x 2 8) h) (3x 2 2)(x 2 1)i) (3x 2 4)(x 2 1)Exercise 11.6 (page 152)1 (2x 1 3)(3x 1 2) 2 (4x 1 3)(5x 1 1)3 (9x 1 2)(3x 1 2) 4 (2x 2 3)(5x 1 2)5 (3x 2 2)(5x 1 1) 6 (5x 2 2)(10x 2 3)7 (10x 1 3)(2x 1 7) 8 3(10x 2 4)(x 2 1)9 (20x 1 3)(x 1 2) 10 (8x 2 3)(x 2 2)Exercise 11.7 (page 154)147103 _____x 2 2_____ x 2 4x 2 5______ 3x 1 22x 2 3________5(x 1 3)x 2 32586 _____x 1 2_____ x 1 1x 1 3______ 2x 2 3x 2 136911 x 1 2 12Mixed exercise 11 (page 155)1 a)d)g)x 1 2 _____3 2 x______ 2 2 3x3x 1 2______ 3b)e)h)_________2(2x 1 3)5 1 3x_________3(3 1 5x)5(x 2 2)5x ___4_____ x 2 2x 2 1________3(x 1 2)x 1 4______ 3x2x 2 1______ x 1 22x 2 3c)f)_________2(3x 2 2)5(2x 1 3)___ 43x2x 1 32 a) (x 1 1)(x 1 4) b) (x 1 3)(x 1 4)c) (x 1 2)(x 1 7) d) (x 1 1)(x 1 7)e) (x 1 2)(x 1 5) f) (x 1 1)(x 1 5)g) (x 1 2)(x 1 15) h) (x 1 2)(x 1 18)3 a) (x 1 9)(x 2 9) b) (x 1 8)(x 2 8)c) (x 1 13)(x 2 13) d) (x 1 15)(x 2 15)e) 3(x 1 4)(x 2 4) f) 5(x 1 3)(x 2 3)g) 7(x 1 7)(x 2 7) h) 10(x 1 10)(x 2 10)4 a)d)g)____ 4a 23bc 2 b)_____ 21v 210twe)8__x 7_2h)____ 5x 2c)3yz 2____ x 2 z 2f)6y 2____ 43a 23_____ 3q 3 s 210r 2___ 1ten5 a) (5x 1 2)(x 1 5) b) (3x 1 7)(x 1 3)c) (3x 2 4)(x 2 6) d) (4x 2 1)(x 2 3)e) (2x 1 7)(x 2 2) f) (6x 1 7)(x 2 1)g) (3x 1 8)(x 2 4) h) (5x 1 3)(x 2 3)i) (7x 1 2)(4x 1 3) j) (20x 2 3)(x 1 2)k) (6x 1 5)(5x 2 3) l) (8x 1 3)(3x 1 2)6 a)d)g)_____ 2x 2 3_____ x 2 3x 2 1________2(x 2 5)x 1 5b)e)h)________2(x 2 3)x(x 1 2)_____ 5xx 2 2_________2x(x 1 3)x 2 2c)f)_____ x 2 1x 1 2______ 3x 1 4x 1 3Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 201

Chapter 12Exercise 12.1 (page 158)1 x 5 7 2 x 5 0.5 3 x 5 74 x 5 7 5 x 5 1 6 x 5 77 x 5 5 8 x 5 4 9 x 5 1010 x 5 6 11 x 5 65 12 x 5 6713 y 5 68 14 m 5 69 15 m 5 6516 x 5 610 17 x 5 68 18 x 5 6419 x 5 62 20 x 5 610Exercise 12.2 (page 159)1 p 5 16 2 x 5 3 3 x 5 74 x 5 1 5 x 5 15 6 x 5 17 x 5 14 8 x 5 5 9 x 5 2410 x 5 10 11 x 5 10 12 a 5 113 x 5 51_ 14 x 5 3 15 x 5 2616 x 5 3 17 x 5 8 18 x 5 419 x 5 2 20 x 5 5.5Exercise 12.3 (page 160)1 x 5 3 2 x 5 3 3 x 5 24 x 5 10 5 x 5 3 6 x 5 27 x 5 10 8 x 5 22 9 x 5 310 x 5 2 11 x 5 2 12 x 5 113 x 5 3 14 x 5 4.5 15 x 5 416 x 5 6 17 x 5 1 18 x 5 219 x 5 23 20 x 5 7Exercise 12.4 (page 161)1 x 5 16 2 a 5 40 3 x 5 204 y 5 50 5 y 5 30 6 p 5 357 m 5 24 8 x 5 64 9 x 5 2710 y 5 33Exercise 12.5 (page 164)1 x . 132 x , 43 x , 134 x < 45 x > 36 x > 86 8 10 12 14 160 1 2 3 4 56 8 10 12 14 160 1 2 3 4 50 1 2 3 4 50 2 4 6 8 107 x , 2 8 x > 25 9 x , 2910 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 , 4Mixed exercise 12 (page 165)1 m 5 9 2 p 5 2 3 x 5 84 x 5 3 5 p 5 8 6 x 5 4 or 247 x 5 6 or 26 8 p 5 4 or 24 9 x 5 4 or 2410 a 5 5 or 25 11 x 5 25 12 x 5 3013 y 5 18 14 y 5 49 15 a 5 3616 x < 217 x > 318 x , 319 x . 420 x . 20 1 2 3 4 50 1 2 3 4 50 1 2 3 4 50 1 2 3 4 50 1 2 3 4 5Chapter 13Exercise 13.1 (page 169)1 x 5 20 2 x 5 4 3 x 5 22_34 x 5 4 5 x 5 3 6 x 5 27 x 5 3_4 8 x 5 4 9 x 5 2410 x 5 2_511 x 5 4 12 x 5 413 x 5 3 14 x 5 21 15 x 5 1Exercise 13.2 (page 171)1 x 5 4 2 x 5 1_33 x 5 12.5 4 x 5 325 x 5 1_2 6 x 5 2.747 x 5 4.81 8 x 5 9.189 x 5 3.2 10 x 5 0.283Exercise 13.3 (page 173)1 x . 3 2 x < 53 x . 4 4 x . 65 x .1.6 6 x < 87 x . 216 8 x < 129 x < 3 10 x < 3.85Exercise 13.4 (page 176)1y65432101Rx 2y 62 3 4 5 6 x202Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

2345y 3y4321R3 2 1 0 1 2 3 41y 2x 3234 3 2 1 0 11234y6543210y 3y543211 01x 21Ry4321x 4Ry 2xx2 3 42 3 4 5 6 xy x 1Ry 33x 4y 123x 5y 151 2 3 4 5 xMixed exercise 13 (page 177)1 x 5 32 x 5 53 x 5 44 x 5 225 x 5 26 x 5 2_37 x 5 2.58 x 5 1_69 x 5 7.510 x 5 2.4911 x 5 2.7812 x , 413 x > 1_414 x . 4.6x15y109876543211 012x 0RChapter 14y 3x 24x 3y 241 2 3 4 5 6 xExercise 14.1 (page 179)1 Three points plotted, e.g. (23, 212), (0, 0),(3, 12), straight line drawn through them.2 Three points plotted, e.g. (23, 0),(0, 3), (3, 6), straight line drawn through them.3 Three points plotted, e.g. (22, 210), (0, 24),(4, 8), straight line drawn through them.4 Three points plotted, e.g. (22, 210), (0, 22),(3, 10), straight line drawn through them.5 Three points plotted, e.g. (24, 8), (0, 24),(2, 210), straight line drawn through them.Exercise 14.2 (page 181)1 Three points plotted, e.g. (22, 24), (0, 21),(4, 5), straight line drawn through them.2 Points (0, 3) and (7.5, 0) plotted, straight linedrawn through them.3 Points (0, 7) and (2, 0) plotted, straight linedrawn through them.4 Three points plotted, e.g. (23, 26), (0, 11_2 ),(3, 9), straight line drawn through them.5 Points (0, 7) and (3.5, 0) plotted, straight linedrawn through them.Exercise 14.3 (page 184)1 a) She walked at 3 km/h for 20 minutes(distance 5 1 km), waited for 5 minutes,travelled in a bus (or car) at 45 km/h for12 minutes (distance 5 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/hHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 203

2 Description to include:• A winning, B second, C third• A ran at a steady speed, B started off quicklybut gradually slowed down, C ran in a seriesof sprints and rests.May also mention approximately whenovertaking took place.3 a) £2b) 80pc)30010 20 30 40 50Distance (km)d) £24e) 69p (to nearest penny)4 a) D b) Hc) F d) C5 a) £49.50b) £46.50c)606 a)Charge (£)Cost (£)Charge (£)25201510550403020100d)1 2 3 4 5 6 7 8 9 10 11 12Number of boxes180170160150140130 b)120110100908070605040302010020 60 100 14040 80 120 160Water used (cubic metres)b) Less than 91 cubic metresExercise 14.4 (page 192)Answers read from graphs may be approximate.1 a) x 23 22 21 0 1 2 3b)x 2 9 4 1 0 1 4 922 22 22 22 22 22 22 22y 5 x 2 2 2 7 2 21 22 21 2 7y x 2 2876543213 2 1 011 2 3234c) (i) 3.3(ii) 2.4 to 2.5 or 22.4 to 22.52 a) x 21 0 1 2 3 4 5x 2 1 0 1 4 9 16 2524x 4 0 24 28 212 216 220y 5 x 2 2 4x 5 0 23 24 23 0 5b)y5 y x 2 4x43211 011 2 3 4 5 x2345c) (i) 0.8 to 0.9 (ii) 0.6 or 3.43 a) x 24 23 22 21 0 1 2 3b)x 2 16 9 4 1 0 1 4 9x 24 23 22 21 0 1 2 323 23 23 23 23 23 23 23 23y 5 x 2 1 x 2 3 9 3 21 23 23 21 3 9y987654321y x 2 x 34 3 2 1 011 2 3 x234c) (i) 21.8 (ii) 22.3 or 1.3204Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

4 a) x 22 21 0 1 2 3 4 5x 2 4 1 0 1 4 9 16 2523x 6 3 0 23 26 29 212 2154 4 4 4 4 4 4 4 4y 5 x 2 2 3x 1 4 14 8 4 2 2 4 8 14b) y1413121110987654321y x 2 3x 42 1 0 1 2 3 4 5 xc) (i) 1.75 (ii) 21.4 or 4.45 a) x 22 21 0 1 2 3 4 53x 26 23 0 3 6 9 12 152x 2 24 21 0 21 24 29 216 225y 5 3x 2 x 2 210 24 0 2 2 0 24 210b) y3212 1 011 2 3 4 5 x2345678y 3x x 2910c) (i) 2.25 (ii) 20.5 to 20.6 or 3.5 to 3.66 a) x 23 22 21 0 1 2 3 4b)x 2 9 4 1 0 1 4 9 162x 3 2 1 0 21 22 23 2425 25 25 25 25 25 25 25 25y 5 x 2 2 x 2 5 7 1 23 25 25 23 1 7y x 2 x 5 y76543213 2 1 011 2 3 4 x23456c) (i) 21.8 or 2.8 (ii) 22.4 or 3.47 a) x 23 22 21 0 1 2 3b)2x 2 18 8 2 0 2 8 1825 25 25 25 25 25 25 25y 5 2x 2 2 5 13 3 23 25 23 3 13y 2x 2 5y131211109876543213 2 1 011 2 3 x23456c) (i) 21.6 or 1.6 (ii) 22.7 or 2.78 a) x 0 1 2 3 4 5b)A 5 6x 2 0 6 24 54 96 150A16014012010080604020A 6x 201 2 3 4 5 xc) (i) 1.8 (ii) 3.6 to 3.7Mixed exercise 14 (page 195)17654321y101 2 3 4123y 2x 1xHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 205

287654321y02x y 8 01 2 3 4x3 a) £39 b) £11 c) 8p4 a)50408 a)x 25 24 23 22 21 0 1 2x 2 25 16 9 4 1 0 1 43x 215 212 29 26 23 0 3 6y 5 x 2 1 3x 10 4 0 22 22 0 4 10b)y108642Cost (£)30205 4 3 2 1 0 1 2x1020200 400b) Gas by £205 a) db) d600 800 1000 1200 1400 1600Gas used (kWh)tc) (i) 22.25 (ii) x 5 23.8 or x 5 0.89 a)x 24 23 22 21 0 1 2 3(x 1 3) 21 0 1 2 3 4 5 6(x 2 2) 26 25 24 23 22 21 0 1y 5 (x 1 3)(x 2 2) 6 0 24 26 26 24 0 6b)y6543214t6 a) She stopped (e.g. waited for bus)b) 68 minutesc) 27 km/hd) (i) 1 km (ii) 10 km7 a) Quadratic, b) Not quadraticc) Quadratic, d) Quadratic, e) Not quadratic f) Not quadraticg) Quadratic, 4 3 2 1 0 1 2 312345678c) (i) 26.25(ii) x 5 22.5 to 22.6 or x 5 1.5 to 1.6x206Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

10 a)x 22 21 0 1 2 3 4x 2 4 1 0 1 4 9 1622x 4 2 0 22 24 26 2821 21 21 21 21 21 21 21y 5 x 2 2 2x 2 1 7 2 21 22 21 2 7b)87654321y2 1011 2 3 4234c) (i) x 5 20.4 or x 5 2.4(ii) x 5 21.4 to 21.5 or x 5 3.4 to 3.511 a)x 21 0 1 2 3 4 5 65x 25 0 5 10 15 20 25 302x 2 21 0 21 24 29 216 225 236y 5 5x 2 x 2 26 0 4 6 6 4 0 26b)654321y1 0 1 2 3 4 5 6123456c) (i) x 5 0.7 or x 5 4.3 (ii) 6.25Chapter 15Exercise 15.1 (page 200)1 a) 1.5 b) 22 c) 32 a) 6 b) 2 c) 25d) 1 e) 03 AB 5 0.4, AC 5 2.5, BC 5 214 a) 2 b) 1.25 c) 20.5xx5 a) Line drawn through (0, 3) and (3, 9),gradient 5 2b) Line drawn through (0, 22) and (3, 13),gradient 5 5c) Line drawn through (0, 1) and (3, 25),gradient 5 22d) Line drawn through (0, 0) and (3, 23),gradient 5 21e) Line drawn through (0, 6) and (4, 0),gradient 5 21.56 a) 4 km/h b) 212.5 m/sExercise 15.2 (page 203)1 a) y 5 3x 1 2 b) y 5 2x 1 4c) y 5 5x2 a) y 5 4x 1 2b) y 5 1_ x 1 4 or 3y 5 x 1 123c) y 5 2x 1 73 a) gradient 5 3, y-intercept 5 22b) gradient 5 2, y-intercept 5 4c) gradient 5 21, y-intercept 5 3d) gradient 5 23, y-intercept 5 2e) gradient 5 2.5, y-intercept 5 264 a) gradient 5 22, y-intercept 5 5b) gradient 5 22, y-intercept 5 4.5c) gradient 5 21.2, y-intercept 5 2.4d) gradient 5 1.5, y-intercept 5 23e) gradient 5 20.75, y-intercept 5 35 a) y 5 5x b) y 5 22x 1 8c) y 5 0.5x 2 5 or 2y 5 x 210Exercise 15.3 (page 204)1 Graph of y 5 x 1 1 drawn through (0, 1), (3, 4)and (5, 6)Graph of y 5 4x 2 5 drawn through (0, 25),(3, 7) and (5, 15)x 5 2, y 5 32 Graph of y 5 2x drawn through (22, 24), (0, 0)and (4, 8)Graph of y 5 8 2 2x drawn through (22, 12),(0, 8) and (4, 0)x 5 2, y 5 43 Graph of y 5 3x 1 5 drawn through (23, 24),(0, 5) and (2, 11)Graph of y 5 x 1 3 drawn through (23, 0), (0, 3)and (2, 5)x 5 21, y 5 24 Graph of y 5 2x 2 7 drawn through (21, 29),(0, 27) and (5, 3)Graph of y 5 5 2 x drawn through (21, 6), (0, 5)and (5, 0)x 5 4, y 5 15 Graph of 2y 5 2x 1 1 drawn through (0, 0.5),(3, 3.5) and (7, 7.5)Graph of x 1 2y 5 7 drawn through (0, 3.5),(3, 2) and (7, 0)x 5 2, y 5 2.5Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 207

Exercise 15.4 (page 206)1 x 5 4, y 5 12 x 5 2, y 5 33 x 51, y 5 34 x 5 2, y 5 35 x 5 5, y 5 16 x 5 2, y 5 17 x 5 3, y 5 28 x 5 4, y 5 39 x 5 3, y 5 110 x 5 3, y 5 21Exercise 15.5 (page 209)1 x 5 2, y 5 12 x 5 2, y 5 33 x 5 3, y 5 24 x 5 2, y 5 35 x 5 5, y 5 16 x 5 2, y 5 17 x 5 4, y 5 28 x 5 22, y 5 39 x 5 2.5, y 5 1.510 x 5 2, y 5 21Mixed exercise 15 (page 210 )1 a) 1.5 b) 212 a) 7.5 b) 253 a) Gradient 5 3, y-intercept 5 22b) Gradient 5 2.5, y-intercept 5 22c) Gradient 5 21.5, y-intercept 5 4d) Gradient 5 2, y-intercept 5 274 a) y 5 x 1 5 b) y 5 24x 1 8 or y 1 4x 5 85 a) yy 4x 313y 3x 11211109876543211 011 2 3 4234567x 5 2, y 5 5xb)11109876543213y102y 3x 72x 3y 121 2 3 4 5 64567x 5 3, y 5 26 a) x 5 4, y 5 2 b) x 5 4, y 5 1c) x 5 4, y 5 2 d) x 5 21, y 5 3e) x 5 3, y 5 2 f) x 5 2, y 5 21g) x 5 21, y 5 2 h) x 5 3, y 5 1Chapter 16Exercise 16.1 (page 217)1 a)Velocity (m/s)20181614121086420b) 1.8 m/s 22 a)6Velocity (m/s)420246b) 24.5 m/s2 4 6 8 10Time (seconds)2 4 68 10xTime(seconds)208Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

3 The velocity increases from 0 m/s to 8 m/s in2 seconds (acceleration 5 4 m/s 2 ).The velocity is constant at 8 m/s for 4 seconds.The velocity decreases from 8 m/s to 0 m/s in4 seconds (acceleration 5 22 m/s 2 ).4Velocity (m/s)5 a)6 a)420224 6 8 10Time (seconds)y20151052 1 051015203 4 5 6b) Gradient is approximately 21c) x 5 2.5y3530252015105120 0.5 1 1.5 2 2.5 3 3.5 4xb) 62 square units of areac) The answer in b) is slightly greater than theactual area as all the trapeziums are formedby going above the curve.7 a) Approximate acceleration is 20.075 m/s 2b) Approximate total distance in the first30 seconds is 93 metres.8 Velocity approximately 6 km/hExercise 16.2 (page 219)1 a)–b) y20151052 1 05y 9 2xy x 2 5x 51 2 3 4 5 6c) x 5 21, y 5 11 and x 5 4, y 5 1d) x 5 2.5, y 5 21.25xx2 a), b) y x 2 3x 1y420 2 4510c) x 5 23, y 5 17 and x 5 2, y 5 23d) x 5 1.5, y 5 23.253 a), b) y30y x 2 32201030252015105y 3x 7y 4x 50 2 4 6c) x 5 21, y 5 4 and x 5 4, y 5 194 a), b) y302010y 4x 1xxy x 2 2x 32 0 2 4 6xc) x 5 0.4, y 5 2.4 and x 5 5.6, y 5 24Exercise 16.3 (page 221)Answers are given to 1 decimal place.1 a) yy x52 2x 3y xy 220 2 45b) (i) x 5 21 or 3(ii) x 5 20.4 or 2.4(iii) x 5 20.8 or 3.8(iv) x 5 21.4 or 3.42 a) y1052 0 2 4b) (i) x 5 21.6 or 3.6(ii) x 5 21.3 or 2.3(iii) x 5 21.4 or 3.4xy 2y 8y 7y x 2 2x 2y 5 xxHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 209

3 a)42510y50y 2x 2 3x 9y 1y 5b) (i) x 5 22.9 or 1.4 (ii) x 5 22.4 or 0.94 a) y3025 y x 2 5x 320151052y 2x2 0 2 4 6 85xy 5b) (i) x 5 0.7 or 4.3 (ii) x 5 20.4 or 5.4(iii) x 5 0.5 or 6.55 y 5 246 y 5 2x 2 1 4x 2 3Exercise 16.4 (page 227)1 a)42604020204060yy x 3y 4x0 2 4b) x 5 22, 0 or 2c) yy x 3 4x15103 2 1 0 1 2 3510152 a) Year Number of birds (n)1970 50 0001980 40 0001990 32 0002000 25 6002010 20 4805xxxb)n50 00040 00030 00020 00010 000n 50 000 0.8 y01970 1980 1990 2000 2010Yearc) n 5 50 000 3 0.8 y where y is the number ofyears from the start (1970)3 a) The table of values is shown.x 24 23 22 21 0 1 2y 16 8 4 2 1 0.5 0.2520y 2 x 151054 2 0 2yb) (i) y 5 0.7(ii) x 5 23.324 a) n 5 2 3 3 y22005b) The missing values for n are 162 and 486.5 a) y35y 2 x302520151052 1 0 1 2 3 4 5b) (i) y 5 9.2(ii) x 5 3.36 a) The table of values is shown.x 24 23 22 21 0 1 2 3 4y 20.75 21 21.5 23 — 3 1.5 1 0.7542b) y 5 1.74224yy 3xx0 2 4xx210Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

7 a)y302826242220181614121086420y ax 2 b1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 x 2b) a 5 21 6 0.2, b 5 30 6 2Mixed exercise 16 (page 229)1 Velocity 5 m/s at start, slowing down. Stops att 5 4. (Negative acceleration until t 5 6, thenpositive acceleration.) Then moves in oppositedirection. Stops again when t 5 9.2 a), b) y x 2 5x 3y1614121086421 024681 2 3 4107x 2y 1112x4 a)y0246810121 2 3 4 5 6 7xy x 2 7xb) (i) x 5 1.7 and x 5 5.3(ii) x 5 0.2 and x 5 4.85 a) y363432302826242220181614121086426 a)2 1 02b) x 5 0.3 and x 5 3.7y30123y x 3 1y 9y 2x 1y x 2 4x 3y 24 5 6 7 8xc) (21, 9) and (2.5, 23.25)203 a) y87654y x 2 2xy x 1y 1103 2 1 010123y xx322011 0 1 2 3 4x1b) x 5 20.3 and x 5 3.330b) (i) x 5 1.3(ii) x 5 1.3Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 211

7 a) x 22.5 22 21.5 21 20.5 0 0.5 1b)y 32 16 8 4 2 1 0.5 0.25y 4 x21y3020100y 25c) (i) y 5 12.1 (ii) x 5 22.38 Gradient at x 5 21 should be around 11,gradient at x 5 2 should be around 38.9 (2)50 square units, the negative indicates thatthe area is below the x-axis.10 6.7 km/hr11 262.5 m12 Approximately y 5 10x 2 2 613 y 5 5 3 3 xChapter 17Exercise 17.1 (page 234)1 a)8_b) 440 metres3122 a) __ or4_b) 96 miles27 91753 a) ___ 7_or b) $31550 24 a)5_b) 20 rungs7155 a) __ 5_or b) 195 g27 96 a)7_b) 45.5 hours4407 a) __ 8_or b) 16 hours15 358 a) __b) £37.5012149 a) __ 7_or b) £34318 90.910 a) __ __b) 178.2 kgor 92.5 25Exercise 17.2 (page 236)481 a) __ 3_or b) 12 minutes32 2122 a) __ 3_or b) 4 weeks8 23 a)3_b) 24 hours4404 a) __ or4_b) 55 minutes50 5205 a) __ 5_or b) 9 days12 36 a)2_b) 9 hours37 a)3_4b) 16 kilometres per hour1x8 a)9 a)10 a)__ 14 7_or18 98_ or4_6 3__ 15 5_or9 3Exercise 17.3 (page 238)b) 27 weeksb) 13.5 hoursb) 12 days1 a) Direct b) y 5 340 x2 a) Direct b) y 5 7x c) 703 a) Direct b) y 5 4_3 x4 a) Direct b) y 5 2_ x5c) 605 a) Direct b) y 5 113 x6 a) Inverse b) y 5 ____ 240x7 a) Inverse b) y 5 ____ 150x8 a) Inverse b) y 5 _____ 1440x9 a) Inverse b) y 5 ____ 360x10 a) Inverse b) y 5 _____ 1800xExercise 17.4 (page 241)c) 16c) 7.2c) 11.251 a) y ~ x 2 b) y 5 x 22 a) y ~ x 2 b) y 5 2x 2 c) 1283 a) y ~ x 2 b) y 5 1_3 x24 a) y ~ x 2 b) y 5 0.4x 2 c) 4905 a) y ~ x 2 b) y 5 1.2x 26 a) y ~ __ 1 2xb) y 5 ____ 225x 2 c) 17 a) y ~ __ 1x 2 b) y 5 _____ 1250x 28 a) y ~ __ 1x 2 b) y 5 ___ 202xc) 0.29 a) y ~ __ 1x 2 b) y 5 ____ 800x 210 a) y ~ __ 1 2xb) y 5 ____ 256x 2 c) 1Mixed exercise 17 (page 244)1 a) 161 revolutions b) 988 metresc) 16 miles d) 25 gramse) 9.8 litres2 a) 10 hours b) 17.5 hoursc) 9 days d) 9 dayse) 10 days3 a) (i) y ~ x (ii) y 5 4xb) (i) y ~ x (ii) y 5 15 x (iii) 1204c) (i) y ~ x (ii) y 5 2_3 xd) (i) y ~ x (ii) y 5 1_ x5(iii) 55e) (i) y ~ __ 1 xf) (i) y ~ __ 1 x4 a) h 5 0.05 s 2b) 0.6125 mc) 9.5 m/s(ii) y 5 ___ 12x(ii) y 5 ___ 24x(iii) 2.4212Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

5 a) y 5 ___ 24xb) 486 a) d 5 ____ 250s 2b) (i) 2.5 m (ii) 31.6 m/sChapter 18Exercise 18.1 (page 248)1 2y 5 3x 1 4 2 y 5 3x 1 53 8x 1 3y 5 24 4 3x 1 8y 5 245 3y 5 2x 1 5 6 3x 1 4y 5 97 y 5 x 1 3 8 y 5 2x 2 19 3x 1 y 5 2 10 2x 1 3y 5 9Exercise 18.2 (page 253)1_2 b) 2 1_4 c) 4_51 a)2 y 5 3x 1 23 3x 1 2y 5 64 Check students’ answers.5 Check students’ graphs.a) 21_3 b) 36 x 1 3y 5 167 3y 5 2x 1 98 a) y 5 4x 1 3 and 4x 2 y 5 5b) 2y 2 3x 5 5 and 6y 1 4x 5 19 3y 5 x 1 410 a) y 5 2x 1 2b) x 1 2y 5 4c) (0, 2)Mixed exercise 18 (page 255)1 a) yb)54321012x 3y 92 3 4 5 xx 2 1 0125x 2y 10 0345y2 a) y 5 1_ x 1 2 or 2y 5 x 1 4215b) y 5 2 __ x 1 15 or 15x 1 8y 5 1208c) y 5 5_ x 2 1 or 3y 5 5x – 333 a) y 5 3x 1 2b) y 5 22x 1 6 or 2x 1 y 5 6c) y 5 1_ x 1 5 or 2y 5 x 1 1024 a) 4 b)2_ c) 22_ d) 26535 a) y 5 5_ x 2 10 or 2y 5 5x 2 202b) y 5 2_ x 1 8_ or 5y 5 2x 1 85 5c) 3x 1 y 5 96 AB: x 1 3y 5 14BC: y 5 2x – 7AC: 5x 1 y 5 147 a) y 5 7x – 34 b) 2y 5 5x – 20c) 5x 1 4y 5 68 a) x 1 2y 5 4 b) 3x 1 2y 5 2c) 2y 5 5x – 119 (i) y8765432101 2 3 4 5 6 7 8 xa) (ii) 4x 1 3y 5 24b) (ii) (4.5, 0)c) (ii) 3x 5 4y10 a) y 5 2x 1 4 b) (3, 10)Chapter 19Exercise 19.1 (page 258)1 x 5 22 or 0 2 x 5 1 or 53 x 5 23 or 4 4 x 5 22 or 275 x 5 0 or 3 6 x 5 647 x 5 210 or 6 8 x 5 11_2 or 79 x 5 24 or 1_2 10 x 5 2 1_3 or 2 1_211 x 5 221_3 or 4 1_2 12 x 5 2 1_4 or 0Exercise 19.2 (page 260)1 x 5 21 or 22 2 x 5 2 or 43 x 5 24 or 1 4 x 5 21 or 55 x 5 24 or 3 6 x 5 27 or 07 x 5 3 or 5 8 x 5 23 or 79 x 5 0 or 4 10 x 5 6611 x 5 28 or 22 12 x 5 23 or 813 x 5 26 or 1 14 x 5 2 or 915 x 5 621_16 x 5 210 or 2217 x 5 0 or 1_18 x 5 23 or 10319 x 5 25 or 0 20 x 5 4 or 521 x 5 21 or 21_ 22 x 51_3 2 or 323 x 5 221_2 or 1 24 x 5 22 or 2 1_325 x 5 211_ or 2 26 x 52_2 3 or 327 x 5 21_ or 5 28 x 5 2 2_ or1_5 3 229 x 5 5 (repeated) 30 x 5 21_331 x 5 210 or 10 32 x 5 241_33 x 5 22_ 3_or3 23_or52 or 4 1_2Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 213

Exercise 19.3 (page 262)1 x 5 23 or 4 2 x 5 22 or 53 x 5 22 or 7 4 x 5 1 or 65 x 5 0 or 6 6 x 5 25 or 17 x 5 22 or 4 8 x 5 22 or 1_29 x 5 23 or 5 10 x 5 24 or 1Exercise 19.4 (page 264)1 a) (i) (x 1 4) 2 2 16 (ii) (x 2 5) 2 2 25(iii) (x 1 6) 2 2 36 (iv) (x 1 0.5) 2 2 0.25b) (i) (x 1 4) 2 2 19 (ii) (x 2 5) 2 1 6(iii) (x 1 6) 2 2 41 (iv) (x 1 0.5) 2 1 1.752 a) (x 1 1) 2 2 4 b) (x 1 2) 2 2 5c) (x 2 3) 2 1 3 d) (x 1 5) 2 2 31e) (x 2 10) 2 2 150 f) (x 1 6) 2 2 37g) (x 1 4) 2 1 3 h) (x 2 1.5) 2 2 5.25i) (x 1 2.5) 2 1 3.75Exercise 19.5 (page 267)1 a) x 5 6.16 or 20.16b) x 5 0.41 or 22.41c) x 5 20.71 or 211.29d) x 5 0.12 or 28.122 a) (x 2 2) 2 2 14 5 0, x 5 5.74 or 21.74b) (x 1 4) 2 2 5 5 0, x 5 21.76 or 26.24c) (x 2 1) 2 2 8 5 0, x 5 3.83 or 21.83d) (x 2 5) 2 2 6 5 0, x 5 7.45 or 2.55e) (x 2 6) 2 2 15 5 0, x 5 9.87 or 2.13f) (x 1 2) 2 2 10 5 0, x 5 1.16 or 25.16g) (x 1 4) 2 2 3 5 0, x 5 22.27 or 25.73h) (x 1 10) 2 2 50 5 0, x 5 22.93 or 217.07i) (x 2 1.5) 2 2 13.25 5 0, x 5 5.14 or 22.14Exercise 19.6 (page 270)1 x 5 20.68 or 27.32 2 x 5 4.30 or 0.703 x 5 0.65 or 27.65 4 x 5 2.30 or 21.305 x 5 20.56 or 24.44 6 No real solutions7 x 5 1.12 or 23.12 8 x 5 20.13 or 22.549 x 5 2.53 or 20.53 10 x 5 3.28 or 1.2211 x 5 0.23 or 20.73 12 x 5 0.48 or 22.0813 x 5 2.21 or 0.79 14 No real solutions15 x 5 2.92 or 23.42 16 x 5 0.22 or 20.6517 x 5 11.05 or 29.05 18 x 5 20.32 or 21.8819 No real solutions 20 x 5 2.91 or 20.9121 x 5 21.26 or 28.74Mixed exercise 19 (page 271)1 a) x 5 0 or 6 b) x 5 23 or 7c) x 5 221_2 or 4 d) x 5 21 1_3 or 2 1_52 a) x 5 0 or 29 b) x 5 7 or 27c) x 5 24 or 21 d) x 5 28 or 1e) x 5 2 or 73 a) x 5 0 or 4 b) x 5 21_2 or 22 1_2c) x 5 21_ or 3 d) x 51_2 3 or 2e) x 5 211_3 or 34 a) x 5 0 or 7 b) x 5 1 or 24c) x 5 1 or 7 d) x 5 4 or 5e) x 5 1_3 or 2 1_25 a) (x 2 1) 2 1 6 b) (x 1 4) 2 2 26c) (x 2 2) 2 2 13 d) (x 2 2.5) 2 2 5.256 a) x 5 5.24 or 0.76 b) x 5 20.53 or 29.47c) x 5 4.65 or –0.65 d) x 5 0.30 or –3.307 a) x 5 3.41 or 0.59 b) x 5 20.59 or 28.41c) x 5 7.53 or 20.53 d) x 5 0.63 or 22.638 b) and c) have no solutions. For both, b 2 2 4ac isnegative (27 in each case).9 (x 1 1)(x 2 7) 5 33, x 5 10 or x 5 24 (reject),dimensions are 3 cm and 11 cm.10 x(2x 2 3) 5 77, x 5 25.5 or 711 a) 2x(x 1 3) 1 2x(x 1 2) 1 (x 1 3)(x 1 2) 2242 5 0Students assuming the cuboid is solid ratherthan open will end up with2x 2 1 6x 1 2x 2 1 4x 1 x 2 1 5x 1 6 2 242 →5x 2 1 15x 2 236 5 0b) 5.53, 28.53c) 5.53, 8.53, 7.53 cm12 a) h 2 5 x 2 1 (x 1 4) 25 x 2 1 x 2 1 8x 1 165 2x 2 1 8x 1 16b)1_ x(x 1 4) 5 45.62x 2 1 4x 2 91.2 5 07.8 cmChapter 20Exercise 20.1 (page 276)1 x 5 1, y 5 2 2 x 5 4, y 5 33 x 5 2, y 5 4 4 x 5 3, y 5 215 x 5 21, y 5 5 6 x 5 21_2 , y 5 37 x 5 22, y 5 23 8 x 5 4, y 5 19 x 5 5, y 5 3 10 x 5 3, y 5 2411 x 5 22, y 5 24 12 x 5 31_2 , y 5 4 1_213 x 5 4, y 5 2_3 14 x 5 2 1_2 , y 5 1_315 x 5 23, y 5 5 16 x 5 3, y 5 11_217 x 5 22, y 5 25 18 x 5 2, y 5 319 x 5 5, y 5 21 20 x 5 4, y 5 2321 x 5 21_2 , y 5 1 1_2Exercise 20.2 (page 279)1 x 5 2, y 5 1 2 x 5 3, y 5 213 x 5 22, y 5 5 4 x 5 2, y 5 235 x 5 2, y 5 4 6 x 5 3, y 5 24Mixed exercise 20 (page 280)1 a) x 5 3, y 5 21 b) x 5 11_2 , y 5 22c) x 5 23, y 5 1 d) x 5 4, y 5 32 a) x 5 21, y 5 2 b) x 5 24, y 5 2153 a) 3x 1 2y 5 155, 4x 1 y 5 140b) Pen 25p, exercise book 40p.214Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

Chapter 21Exercise 21.1 (page 283)1 a) Multiply the pattern number by 2b) 2002 a) Pattern number 1 2 3 4 5Number of matchsticks 4 6 8 10 12b) They go up by 2 each time; they are the 2times table plus 2.c) 1023 a)9 a) 1, 4, 9, 16, 25b) (i) Each term is 3 more than the equivalentterm in the sequence of square numbers.(ii) n 2 1 3c) 10 00310 a) Each term is 3 times the equivalent term inthe sequence of square numbers.b) 3n 2 c) 1200Mixed exercise 21 (page 289)1 a) 300 b) T n 5 3n2 a)b) 36You add 1 more each time, so T 4 5 10,T 5 5 15, T 6 5 21,T 7 5 28, T 8 5 364 a) 3 3 1 2 5 5 22b) 1, 4, 7, 105 a) 4, 10, 16, 22b) 5, 9, 13, 17c) 4, 2, 0, 226 a) 1, 4, 9, 16, 25b) 3, 6, 11, 18, 27c) 1, 8, 27, 64, 1257 2, 4, 8, 16, 328 5, 2, 21, 249 For exampleb) 64. This is the sequence of square numbers;the 8th pattern has 8 3 8 stars.3 a) T 1 5 1 3 6 2 2 5 4 b) 10, 16, 22, 284 a) 7, 12, 17, 22 b) 2, 5, 10, 17c) 88, 86, 84, 825 4, 8, 16, 32, 646 a) T n 5 3n 1 2 b) T n 5 6n 2 5c) T n 5 7 2 5n7 a) Linear: 24, 29 b) Not linearc) Not linear d) Linear: 212, 2188 a) 3, 9, 27, 81, 243 b) Powers of 39 A suitable answer is as follows.and so on.10 For exampleand so on.Exercise 21.2 (page 287)1 a) 2n 1 3 b) 3n 2 1c) n 1 62 a) 20 2 3n b) 10 2 5nc) 1 2 n3 a) Linear: 17, 20 b) Not linearc) Linear: 30, 36 d) Not linear4 a) 6, 0, 26, 212, 218 b) 14 2 6n5 a) Number of tickets 1 2 3 4Cost in £ 17 32 47 62b) 15n 1 2 c) 76 1, 3, 6, 10, 15, 21, 28, 36, 45, 557 2108 a) 10, 100, 1000, 10 000, 100 000b) Powers of 101 3 6 10 1510 a) 1, 4, 9, 16, 25 b) T n 5 n 2 1 4Chapter 22Exercise 22.1 (page 292)1 a) 90 minutes b) 210 minutes2 4°C3 £314 a) s 5 __ d tb) 60 km/h5 490 m6 187 a) 55 b) 208 a) 8x b) 3x 29 a) 2 hours 10 minutes b) 1.5 kg10 511 15 miles12 a) 12b) Number of posts, P 1 2 3 4 5 6Number of chains, C 0 3 6 9 12 15c) C 5 3P 2 3 or C 5 3(P 2 1)d) 8713 a) 24 cm 2 b) 22.5 cm 2Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 215

14 a) 120 cm 3 b) 216 cm 315 a) £45 b) 43 milesExercise 22.2 (page 296)1 a) b 5 a 1 cb) x 5 ______ 4a 2 ywc) t 5 _____ v 2 uad) t 5 _____ p 2 c3e) q 5 _______ A 2 pr or q 5 __ Ap p 2 rf) g 5 ______p 1 2f2g) n 5 _______ Ft 2 m42 u 5 ____ sbn3v3 h 5 ___ 2ab4 R 5 _____ 100IPT5 a) h 5 ___ 3Vb) 16.6 cmpr 26 a) 140°Fb) C 5 (F 1 40) 3 5_9 2 40___7 r 5 √___ 3Vph8 a) a 5 _______ v2 2 u 2b) u 5 √ ________v2s2 2 2asExercise 22.3 (page 298)1 x 5 1.72 a) 2 3 2 5 3 2 5 223 3 2 5 3 3 5 12b) x 5 2.83 a) 4 3 2 4 5 605 3 2 5 5 120b) x 5 4.64 a) 3.7 3 2 3.7 5 47.03.8 3 2 3.8 5 51.1b) x 5 3.775 x 5 2.36 x 5 4.337 228 31.69 a) x 2 1 x 5 10 b) 2.7 (or 23.7)10 a) x(x 2 4) 5 621, i.e. x 2 2 4x 5 621b) 27, 23 (or 227, 223)11 7.8Mixed exercise 22 (page 300)1 a) 104°F b) 32°F c) 23°F2 95p3 a) 12 cm 2 b) 21.6 cm 24 a) 34 minutes b) 47.8 minutes5 a) q 5 p 2 2r b) r 5 _____ x 2 s5c) r 5 ___ mspqd) y 5 ______ tx 2 A or y 5 __ x2t 2 2 __ A2t6 a) w 5 _______ T 2 40 b) w 5 2.4 kg457 a) 4 cm b) 8 cm8 a) 30 words b) 60 words9 a) 1 3 1 4 3 1 5 52 3 1 4 3 2 5 16b) x 5 1.710 a) 3 3 2 3 2 5 184 3 2 4 2 5 48b) x 5 3.411 a) x 3 1 x 5 100b) x 5 4.6Chapter 23Exercise 23.1 (page 303)1 r 5 _____ pq2 P 5s 1 t4y 1 153 x 5 ________3(1 1 y)5 r 5 _______ pq 1 pq 2 12s7 t 5 ______2u 1 asv9 u 5 _____v 2 s5g 2 3e11 f 5 _______2100A _________RT 1 1004 p 5 ______ rq 2 rq 1 16 x 5qy______q 1 pb 1 a8 x 5 _______3a 2 2bfu10 v 5 _____u 2 fc(5a 1 1)12 b 5 _________15a 2 2Exercise 23.2 (page 304)1 a) x 5 6 √ ___________ y 1 4b) l 5 ____ gt234p 2c) h 5 6 √ _____________(pr) A 2 2 r 2 d) u 5 6 √ ________v 2 2 2ase) r 5 6 √ ______ 3Vf) t 5 6ph√ ______________ 30 2 2sa___2 a) 9000 cm 3 b) r 5 √___ Vphc) 5.64 cm3 a) 5.39 b) 3.68 mc) x 5 √ ___________d 2 2 y 2 2 z 2 d) 0.71 mMixed exercise 23 (page 305)1 a) a 5 _____ 2rbb) g 5 ____ 4lp2r 2 1t 2c) u 5_____fvv 2 fe) a 5 ______ 2 1 b2b 2 1g) a 5 _____ 2bcb 1 11i) x 5 ______y 2 2 1d) x 5 b 2 ac ______c 2 1f) y 5 2xh) x 5 6 √ ____y3j) n 5 __________ p 2 2r 2 2p 2 2216Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

(x 2 np)2k) q 5 _________ l) x 5 6 √ ____________ Fnpy 2 F 1 1m) y 5 6 √ ________ns 2 2 x 2ax 2 amn) b 5 ________m 2 y2 a) 524 units 3 (to 3 s.f.)b) r 5 3 √ ______ 3V4pc) 9.42 m (to 3 s.f.)Chapter 24Exercise 24.1 (page 307)1 a) 4 b) 212 a) 22 b) 17 c) 13 a) x 5 6b) (i) 2x 2 9 (ii) 4x 2 54 a) x 5 2b) (i) 21 2 9x (ii) 23x 2 25 a) x 5 3_4b) (i) 4x 1 17 (ii) 4x 1 26 a) x 5 63b) (i) x 2 1 2x 2 1 (ii) x 2 2 17 a) 56b) (i) 3x 2 2 8x 1 5 (ii) 12x 2 2 4x8 a) x 5 4 or 21b) (i) 4x 2 2 6x (ii) x 2 2 x 2 2Exercise 24.2 (page 312)1 a)y2 a)y x 2 y (x 5) 21612844 20 2 4 6 8 10b) A translation of ( 5 0)42048y x 2121620y x 2 4b) A translation of0(24)3 a)yy (x 2) 2161284 y x 2y (x 2) 2 308 6 4 2 2 4x4b) A translation of ( 2223)yx2 4x4 a) y012390° 180° 270° 360° θy sin θ 1b) y 5 sin 2 15 a) y 5 x 2 2 5 b) y 5 (x 2 2) 26 y674224y f(x 2)y f(x)1 0 1 2 3y422y g(x 1)y f(x) 2xy g(x) 11 0 1 2 3 48 y 5 (x 2 1) 2 1 29 y 5 cos 1 210 a) y 5 (x 1 2) 2 1 3b) y 5 (x 1 2) 2 1 35 x 2 1 4x 1 4 1 35 x 2 1 4x 1 7Exercise 24.3 (page 317)1 a)101yy g(x)xy sin θ90° 180° 270° 360°b) A reflection in the x-axis2 a) y101y sin θy sinθ290° 180° 270° 360°y sin θθθHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 217

) A one-way stretch of scale factor 2, parallelto the x-axis3 a) A reflection in the x-axisb) A reflection in the y-axisc) A one-way stretch of scale factor 5 parallelto the y-axis4 y 5 cos 35 a) y 5 x 2 1 5 b) y 5 2x 2 2 56 a) y 5 3x 1 6 b) y 5 2x 1 27 a) A translation of ( 0 1)b) A one-way stretch parallel to the y-axis ofscale factor 3c) A one-way stretch parallel to the x-axis ofscale factor 0.5d) A one-way stretch parallel to the y-axis ofscale factor 5 and a one-way stretch parallelto the x-axis of scale factor 1_38 a) y 5 x 2 2 2xb) y 5 2x 2 2 2xc) y 5 2(x 2 3) 2 1 2(x 2 3) ory 5 2x 2 1 8x 2 159 a) y 5 1_4 x2 b) (2, 1) c)10 k 5 3Mixed exercise 24 (page 319)1_4d) (1,1_4 )1 a) x 5 1_2b) (i) 2x 1 9 (ii) 2x 1 42 a) x 5 ±1b) (i) x 2 1 2x 1 7 (ii) 4x 2 1 73 a) 24b) (i) x 2 2 6x 1 8 (ii) 4x 2 2 4x 1 34 a) yy x 24b) Translation by (024)5 y 5 2x 2 36 a) y12y x 2 40 90° 180° 270° 360°7 a) Translation by ( 21 0)xθy sin θ 1b) One-way stretch with scale factor 1_3 , parallelto the x-axisc) One-way stretch with scale factor 4, parallelto the y-axisd) Reflection in the y-axis8 a) y 5 cos 1 3 b) y 5 cos 49 a) y 5 2x 3 2 5 b) y 5 2x 3 1 510 a) y 5 2[(x 2 3) 2 1 1] or y 5 2x 2 2 12x 1 20b) (3, 2)11 y12 y(0, 1)Chapter 25Exercise 25.1 (page 323)1 ______ 5x 2 1623 _______ 7x 2 261245 __________ x 2 1 x 1 43(x 2 1)67 _____________2x 2 2 7x 2 213(x 2 5)89 _________ 17 1 14x4(2x 2 3)Exercise 25.2 (page 325)3x 1 51 _____________ 2(x 1 1)(x 1 2)35791134x 2 1 5x 1 6____________3x(x 1 3)x 2 7 _____________(x 2 1)(x 1 2)_____________x 2 2 2x 2 21(x 2 3)(x 2 5)_______________3(x 1 1)(2x 1 3)(2x 1 1)(x 1 2)x 2 2 33x 1 24_______________(3x 2 2)(5x 2 4)Exercise 25.3 (page 327)y (x 3) 2xy (x 3) 2y f(x) 2x46________ 23x 1 110________ 2x 1 124___________10 2 x 2 x 24(x 2 2)_________ 29x 1 127(4x 2 1)___________x 2 1 6x 1 3x(x 1 3)_____________2(x 2 1 12)(x 1 4)(x 2 4)2x 2 1 2_____________(x 2 2)(x 2 4)4x8 ______________2 2 9x 1 16(3x 2 4)(x 1 2)2(x 2 1 7x 2 3)10 _____________(x 1 3)(x 2 3)4(x 2 2 x 2 1)12 1 ______________(x 1 1)(5x 1 3)1 x 5 5 2 x 5 223 x 5 5 4 x 5 2 or x 5 65 x 5 5 or x 5 06 x 5 5.30 or x 5 1.707 x 5 20.86 or x 5 0.468 x 5 2.30 or x 5 21.309 x 5 20.21 or x 5 223.79218Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

Mixed exercise 25 (page 328)1 a)c)2 a)c)5x ___6_____________2x 2 1 8x 2 1510x_____________2(x 2 1)(x 1 4)(x 1 2)_________4(x 2 2 1)x(x 1 2)b)d)b)d)x 2 19 ______613x 1 5________________(4x 2 1)(3x 1 2)x 2 1 4x 2 2___________3(x 1 2)5x 2 1 4x 2 19______________(x 2 1)(3x 1 5)3 a) x 5 1 b) x 5 2c) x 5 8 d) x 5 2 or x 5 64 a) x 5 0.638 or x 5 21.305b) x 5 0.422 or x 5 21.422Chapter 26Exercise 26.1 (page 331)1 16 cm 2 2 50 cm 23 160 m 2 4 75 mm 25 64 cm 2 6 17.5 cm 27 55 cm 2 8 144 cm 29 150 m 2 10 120 m 2Exercise 26.2 (page 333)1 24 cm 2 2 72 cm 23 64 m 2 4 35 cm 25 14 cm 2 6 30 cm 27 42 cm 2 8 144 m 29 42 cm 2 10 16 cm 2Exercise 26.3 (page 337)1 a 5 74° (Alternate angles)2 b 5 65° (Allied angles)3 c 5 125° (Corresponding angles)4 d 5 65° (Alternate angles)e 5 65° (Corresponding or vertically oppositeangles)5 f 5 110° (Alternate angles)g 5 110° (Corresponding or vertically oppositeangles)6 h 5 55° (Allied angles)i 5 125° (Corresponding angles)j 5 125° (Alternate or vertically oppositeangles)7 k 5 65° (Corresponding angles)l 5 65° (Alternate or vertically oppositeangles)m 5 115° (Allied angles)n 5 115° (Vertically opposite angles)8 o 5 101° (Corresponding angles)p 5 101° (Corresponding angles)q 5 101° (Alternate angles)9 r 5 97° (Allied angles)s 5 83° (Corresponding angles)t 5 29° (Angles in a triangle add up to 180°)10 u 5 45° (Alternate angles)v 5 67° (Corresponding angles)w 5 68° (Angles on a straight line add up to180°)Exercise 26.4 (page 341)1 a 5 35° (Angles in a triangle add up to 180°)2 b 5 41° (Angles in a triangle add up to 180°)3 c 5 43° (Angles in a triangle add up to 180°)4 d 5 35° (Angles in an isosceles triangle)5 e 5 60° (Angles in an equilateral triangle)6 f 5 55° (The exterior angle of a triangle isequal to the sum of the oppositeinterior angles)7 g 5 141° (The exterior angle of a triangle isequal to the sum of the oppositeinterior angles)h 5 39° (Angles on a straight line add up to180°)8 i 5 115° (Angles in a quadrilateral add upto 360° or angle sum of a triangle 5180°)9 j 5 123° (Angles in a quadrilateral add up to360°)k 5 57° (Angles on a straight line add up to180°)10 l 5 100° (Angles on a straight line add up to180°)m 5 84° (Angles in a quadrilateral add up to360°)Exercise 26.5 (page 344)1 A: trapeziumB: rhombusC: squareD: kiteE: rectangleF: squareG: arrowheadH: parallelogramI: isosceles trapeziumJ: rhombusK: parallelogram2 a) Square, rhombusb) Rectangle, parallelogram, kite, arrowheadc) Rectangle, parallelogramd) Trapeziume) Square, rhombus, kite3 a) y86420 2 4 6 8RhombusxHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 219

)c)d)y420 2 4 6 8Trapeziumy420 2 4 6 8Parallelogramy420 24 6 8xxxKite4 All the angles are 90° and the diagonals areequal length.5 Isosceles trapezium, parallelogram or rhombus70°110°110°70°Isosceles trapezium70°110°110°Parallelogram70°110°110°Rhombus70°70°Exercise 26.6 (page 348)1 2340° 2 3240°3 a) 131° b) 86°, 130°, 95°, 49°4 a) 58°b) 90°, 100°, 123°, 105°, 122°5 e 5 30°; i 5 150°6 e 5 3.6°; i 5 176.4°7 15 8 20Mixed exercise 26 (page 349)1 a) 9 cm 2 b) 8 cm 2 c) 30 cm 22 a) 28 cm 2 b) 300 cm 2 c) 27 cm 23 a) a 5 110° Corresponding angles.b 5 70° Allied angles or Angles on astraight line.b) c 5 50° Alternate angles.d 5 50° Corresponding angles orOpposite angles.c) e 5 36° Alternate angles.f 5 72° Angles on a straight line.g 5 72° Corresponding angles or anglesin a triangle.4 a) a 5 19° Angles in a triangle add up to180°.b) b 5 47° Base angles in an isoscelestriangle are equal.c) c 5 31° Exterior angle of a triangle isequal to the sum of the opposite,interior angles.d 5 77° Angles on a straight line add upto 180° or Angles in a triangleadd up to 180°.5 a) a 5 126° Angles in a quadrilateral add upto 360°.b) b 5 129° Angles on a straight line add upto 180°.c 5 53° Angles in a quadrilateral add upto 360°.6 a) Rectangle, parallelogram, kite, arrowheadb) Rhombus, isosceles trapezium, parallelogramc) Square, rectangle, isosceles trapezium7 a) 900°b) Exterior angle 5 24°, interior angle 5 156°c) 36Chapter 27Exercise 27.1 (page 352)1 12 cm 2 2 85 cm 23 50 cm 2 4 28 cm 2Exercise 27.2 (page 354)1 a) 13 cm b) 5.83 m c) 6.24 cmd) 24 cm e) 7.64 cm f) 6.34 cmg) 30.50 m h) 9.35 m i) 8.30 cm2 4.53 m3 23.66 inchesExercise 27.3 (page 357)1 Yes 6 2 1 8 2 5 10 2 (This is 2 3 the 3, 4, 5 triangle)2 No 4 2 1 7 2 ? 8 23 No 8 2 1 8 2 ? 11 24 Yes 7.5 2 1 18 2 5 19.5 2 (This is 1.5 3 the 5, 12,13 triangle)5 Yes 3.5 2 1 12 2 5 12.5 2 (This is 0.5 3 the 7, 24,25 triangle)6 No 5 2 1 10 2 ? 11 27 No 4.5 2 1 9 2 ? 10 28 Yes 28.8 2 1 12 2 5 31.2 2 (This is 2.4 3 the 5, 12,13 triangle)Exercise 27.4 (page 360)1 a) (6.5, 3) b) (3, 5)c) (21.5, 6) d) (24.5, 0)e) (20.5, 25) f) (5.5, 24.5)2 a) (1, 6) b) (4, 4)c) (5, 4.5) d) (5.5, 4.5)e) (1, 2) f) (25, 27)220Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

Exercise 27.5 (page 362)1 a) (5, 3, 0) b) (5, 0, 2)c) (0, 3, 2) d) (5, 3, 2)2 a) (0, 6, 0) b) (6, 6, 0)c) (3, 3, 0) d) (3, 3, 5)3 a) (8, 6, 0) b) (8, 3, 0)c) (8, 3, 4) d) (4, 6, 4)Mixed exercise 27 (page 363)1 a) 20 cm 2 b) 23 cm 22 a) 11.40 cm b) 7.55 cmc) 6.27 cm d) 4.99 cm3 a) No 5 2 1 8 2 ? 9 2b) Yes 9 2 1 12 2 5 15 2(This is 3 3 the 3, 4, 5 triangle)c) Yes 17.5 2 1 60 2 5 62.5 2(This is 2.5 3 the 7, 24, 25 triangle)d) No 5.2 2 1 8.3 2 ? 9.7 24 a) (3, 4) b) (4, 51_2 ) c) (4 1_2 , 4 1_2 )5 1.93 m6 30.3 cm 27 15.66 m8 a) (i) (15, 0, 0) (ii) (0, 10, 6)(iii) (15, 10, 6)b) (11, 5, 6)Chapter 28Exercise 28.1 (page 368)12y 1y4321By x4 3 2 1 0 1 2 3 4x1A234yy x 43Ay 221B4 3 2 1 0 1 2 3 4x1C 2343 a) b)C4 a) A reflection in the line y 5 2b) A reflection in the line x 5 3c) A reflection in the line y 5 x5 a) A reflection in the line y 5 0b) A reflection in the line y 5 2xc) A reflection in the line y 5 xExercise 28.2 (page 373)12346y43214 3 2 1 01234y43B21C14 3 2 1 0 11234y876543AC214321 0 112B34CB90°AAABAA2BD3 4C2 3 4Dxx2 3 4 5 6 75Ox90°c)C120°BBAHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 221

7 a) A rotation of 90° anticlockwise about theoriginb) A rotation of 180° about (1, 0)c) A rotation of 90° clockwise about (1, 2)8 a) A rotation of 90° clockwise about theoriginb) 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 5 0b) A rotation of 90° anticlockwise about (2, 4)c) A reflection in the line y 5 xd) A rotation of 90° anticlockwise about theorigine) A reflection in the line y 5 2xExercise 28.3 (page 377)12y65B4A32C1D2 101 2 3 4 5 6x12Cy654D3212A2 10 1 2 3 4 5 6x13 a) A translation by vector (221)b) A translation by vector ( 2122)c) A translation by vector ( 22 1)d) A translation by vector ( 24 2)B4 a) A translation by vector ( 25 2)b) A rotation of 90° anticlockwise about theoriginc) A rotation of 90° clockwise about (2, 2)d) A translation by vector ( 2324)e) A reflection in the line y 5 0f) A reflection in the line y 5 xg) A translation by vector2(26)h) A rotation of 180° about (0, 2)Exercise 28.4 (page 381)1 a), b)y654321B0 1 2 3 4 5 6xc) An enlargement with scale factor 2, centrethe origin2 a), b) y87A654B32C10 1 2 3 4 5 6 7 8xc) An enlargement with scale factor 3, centre(1, 2)3 a), b) y87B6543A210 1 2 3 4 5 6 7 8xc) An enlargement with scale factor 1_4 , centrethe origin4 a), b) y87654321CAAB0 1 2 3 4 5 6 7 8c) An enlargement with scale factor 2_3 , centre(2, 1)5 a) An enlargement with scale factor 2, centre(0, 3)b) An enlargement with scale factor 1_2 , centre(0, 3)c) An enlargement with scale factor 11_2 , centrethe origind) An enlargement with scale factor 2_3 , centrethe originx222Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

6 a) A reflection in the line y 5 0b) An enlargement with scale factor 2, centre(0, 4)c) A translation by vector ( 2823)d) An enlargement with scale factor 21_2 , centrethe origine) A translation by vector ( 26 4)b)f) An enlargement with scale factor 1_3 , centre(5, 3)7 a) A reflection in the line x 5 1b) An enlargement with scale factor 2, centre(1, 0)c) A rotation of 90° anticlockwise about theorigind) A reflection in the line y 5 xe) An enlargement with scale factor 1_2 , centrethe originf) A translation by vector ( 1 4)8 a) A reflection in the line y 5 2b) A rotation of 90° clockwise or about theoriginc) A translation by vector (222)d) A reflection in the line y 5 0e) An enlargement with scale factor 1_2 , centre(0, 22)f) An enlargement with scale factor 1_3 , centre(2, 1)g) An enlargement with scale factor 3, centre(2, 1)Mixed exercise 28 (page 383)1 y4 3 2 112342 a)43211CB2 3 4Ax3456y43B2A14 3 2 1 0 1 2 3 4x123C4y4C3A214 3 2 1 0 1 2 3 4x1D23B4y987654A321B01 2 3 4 5 6 7 8 9y9x8765A432B1012 3 4 5 6 7 8 9xHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 223

7 a) A reflection in the line x 5 0b) A rotation of 90° clockwise about the originc) An enlargement with scale factor 3, centre(24, 3)d) A translation by vector0(23)e) An enlargement with scale factor 1_2 , centrethe originf) A translation by vector ( 23 2)g) A reflection in the line y 5 x8 a) A reflection in the line x 5 0b) A translation by vector1(23)c) An enlargement with scale factor 3, centre(0, 2)d) A rotation of 90° anticlockwise about(2, 22)e) An enlargement with scale factor 1_2 , centrethe originf) A rotation of 180° about the origing) A translation by vector ( 3 2)Chapter 29Exercise 29.1 (page 387)1 a) 2500 cm b) 420 mmc) 236 cm d) 5100 mm2 a) 30 000 cm 2 b) 230 mm 2c) 95 200 cm 2 d) 1.4 mm 23 a) 900 cm 2 b) 81.4 cm 2c) 720 m 2 d) 9.4 m 24 a) 3 200 000 cm 3 b) 0.000 042 m 3c) 0.005 m 3 d) 6 420 000 cm 35 a) 2610 cm 3 b) 9.5 litresc) 2400 ml d) 0.91 litre6 All the units need to be the same;change 50 cm to 0.5 m. 5 3 2 3 0.5 5 5 m 37 624 cm 3Exercise 29.2 (page 389)1 a) 56.5 m and 57.5 mb) 567.5 ml and 568.5 mlc) 23.925 seconds and 23.935 seconds2 a) 633.5 g and 634.5 gb) 233.5 ml and 234.5 mlc) 8.25 m and 8.35 m3 a) 28 to 32 m 2b) 15 cans (100 4 7 5 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 cmb) 1.95 cm and 2.05 cmc) 1.95 cm and 2.05 cm7 Maximum d: longest rod minus least depth 535.5 2 19.5 5 16 mmMinimum d: shortest rod minus greatest depth 534.5 2 20.5 5 14 mm8 2 3 (14.5 1 8.5) 5 46 cm and2 3 (15.5 1 9.5) 5 50 cmExercise 29.3 (page 391)1 a) 3.5 minutes b) 3 weeksc) 3 kg d) 2 m2 a) 5.5 m b) £16c) 665 km d) 0.1 cm 2Exercise 29.4 (page 392)1 62.5 m/s 2 43 mph 3 7.5 miles4 5 hours 5 278 cm 3 6 60 mph7 9 g/cm 3 8 100 km/h 9 7.8 g/cm 310 a) 8.9 g/cm 3 b) 151.3 g11 19.3 kg12 a) 58.5 kgb) (i) 0.7692 m 3 (ii) 769.2 m 313 a) 60 km/h b) 64.3 km/h14 10.6 g/cm 315 1156.3 people per square kilometreMixed exercise 29 (page 394)1 a) 120 000 cm 2 b) 371 mm 2c) 4200 cm 2 d) 5 mm 22 a) 3 000 000 mm 2 b) 41.25 m 2c) 94 cm 2 d) 600 cm 23 a) 2130 cm 3 b) 5.1 litresc) 421 000 ml d) 0.0917 litres4 a) 26.5 cm and 27.5 cmb) 5.55 cm and 5.65 cmc) 1.225 m and 1.235 m5 Greatest speed: greatest distance 4 least time5 100.05 4 5.5 5 18.19 m/s6 a) 33.5 mm and 34.5 mmb) Greatest perimeter: greatest length 3 35 34.5 3 3 5 103.5 mm7 a) 1 hour 15 minutes b) 8 km/h8 a) 60 mph b) 190 miles9 5394 m 2Chapter 30Exercise 30.1 (page 401)Diagrams are not full size. The measurements givenare correct for the suggested scale.15 cmA2 Scale 1 cm 5 20 m2.5 cm5 cm224Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

3 Scale 1 cm 5 10 mHedge2 Scale 1 cm 5 1 km5 cm6 cmPQTree4 cm45B5 cmC3 cm7 cm60° 30°5 cm3A5 cmB6 Scale 1 cm 5 1 m4 cmAD3 cm3 cm5 cm1 cm2 cmDC4 Scale 1 cm 5 1 mH 8 cmG7 NNWNET6 cm 5 cmWE5ECFSWSE7 cm9 cm8S7 cm3 cm3 cmLocusA 11 cm6 Scale 1 cm 5 1 mB9C3 cm5 cm7 cm 6 cm2 cmA 8 cm B10 Scale 1 cm 5 10 mNote: You could have used a different scale.7 1 cm 5 20 m2.5 cmLocus2 cm8 cmCastle 6 cm7 cmExercise 30.2 (page 404)Diagrams are not full size. The measurements givenare correct for the suggested scale.16 cm3 cmA8 Scale 1 cm 5 1 kmC5 cm9.5 cm5 cm5 cmA 7 cm BHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 225

9 Scale 1 cm 5 4 m5 cm6 Scale 1 cm 5 5 km2 cmHouse2.5 cm2 cm3.5 cm6 cm8 cm10 Scale 1 cm 5 5 miles6 cm3 cmH2 cmK7 Scale 1 cm 5 1 mDC4 cm3 cmMixed exercise 30 (page 406)Diagrams are not full size. Measurements given arecorrect for the suggested scale.18AG6 cm 5 cm5 cmB2100°E70°8 cm9 Scale 1 cm 5 1 m3 cmF8 cm5 cm33 cm 3 cm7 cm5 cm10 Scale 1 cm 5 1 m4C6 cm 8 cm5.2 cmA 9 cm BArea 5 23.4 cm 25 S5 cmRP8 cm5 cmQ3 cm3 cm10 cm3 cm3 cmChapter 313 cm3 cm 8 cmExercise 31.1 (page 409)These answers have been calculated using the pbutton on 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.)226Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

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 31.2 (page 410)These answers have been calculated using the pbutton on a calculator.1 a) 616 cm 2 (nearest whole number)b) 2463 cm 2 (nearest whole number)c) 20 106 cm 2 (nearest whole number)d) 3848 mm 2 (nearest whole number)e) 12 076 mm 2 (nearest whole number)f) 5809 cm 2 (nearest whole number)g) 9503 cm 2 (nearest whole number)h) 75.4 cm 2 (1 d.p.)i) 295.6 cm 2 (1 d.p.)j) 36.3 m 2 (1 d.p.)k) 21.2 m 2 (1 d.p.)l) 4.91 m 2 (2 d.p.)2 a) 201 cm 2 (nearest whole number)b) 452 cm 2 (nearest whole number)c) 3848 cm 2 (nearest whole number)d) 1018 mm 2 (nearest whole number)e) 5281 mm 2 (nearest whole number)f) 1810 cm 2 (nearest whole number)g) 2290 cm 2 (nearest whole number)h) 15.2 cm 2 (1 d.p.)i) 75.4 cm 2 (1 d.p.)j) 11.3 m 2 (1 d.p.)k) 6.2 m 2 (1 d.p.)l) 4.30 m 2 (2 d.p.)Exercise 31.3 (page 412)1 160 cm 22 126 cm 23 340 cm 24 227 cm 25 108 cm 26 212 cm 2Exercise 31.4 (page 414)1 a) 515 cm 3 b) 1376 cm 3c) 219.6 cm 3 d) 385.5 cm 3e) 192 cm 3 f) 780 cm 32 18 000 cm 3Exercise 31.5 (page 416)1 a) 1233 cm 3 b) 17 334 cm 3c) 2092.8 cm 3 d) 396.8 cm 3e) 2253.42 cm 3 f) 528.82 cm 32 119 000 mm 3Exercise 31.6 (page 418)These answers have been calculated using the pbutton on a calculator.1 a) 7037 cm 3 (nearest whole number)b) 25 862 cm 3 (nearest whole number)c) 113 097 cm 3 (nearest whole number)d) 24 881 mm 3 (nearest whole number)e) 11 781 mm 3 (nearest whole number)f) 115 mm 3 (nearest whole number)g) 707 m 3 (nearest whole number)h) 370 m 3 (nearest whole number)2 11 045 cm 3 (nearest whole number)Exercise 31.7 (page 420)These answers have been calculated using the pbutton on a calculator.1 a) 1810 cm 2 (nearest whole number)b) 2281 cm 2 (nearest whole number)c) 2827 cm 2 (nearest whole number)d) 3958 mm 2 (nearest whole number)e) 377 mm 2 (nearest whole number)f) 465.6 mm 2 (1 d.p.)g) 131.9 m 2 (1 d.p.)h) 77.0 m 2 (1 d.p.)2 152 cm 2 (nearest whole number)3 a) 2111 cm 2 (nearest whole number)b) 6993 cm 2 (nearest whole number)c) 10 336 cm 2 (nearest whole number)d) 3054 mm 2 (nearest whole number)e) 4869 mm 2 (nearest whole number)f) 1176.5 mm 2 (1 d.p.)g) 190.0 m 2 (1 d.p.)h) 59.7 m 2 (1 d.p.)Exercise 31.8 (page 424)1 PlanFront elevationSide elevation2 PlanFront elevationSide elevationHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 227

3 PlanFront elevationSide elevation4 PlanFront elevationSide elevation6 a) 20 308.2 cm 3 (1 d.p.) b) 1578.46 mm 3 (2 d.p.)c) 5617.5 cm 3 (1 d.p.) d) 0.8874 m 3 (4 d.p.)7 a) 2601 mm 3 (nearest whole number)b) 3268.5 mm 3 (1 d.p.)c) 106 437 cm 3 (nearest whole number)d) 181 cm 3 (nearest whole number)e) 23 091 m 3 (nearest whole number)f) 27.5 m 3 (1 d.p.)8 a) 1659 m 2 (nearest whole number)b) 2432 cm 2 (nearest whole number)c) 16.0 cm 2 (1 d.p.)d) 672 mm 2 (nearest whole number)9 a) 5202 mm 2 (nearest whole number)b) 113 m 2 (nearest whole number)c) 174 cm 2 (nearest whole number)d) 546 cm 2 (nearest whole number)10 a) Planb) Plan5 Plan6 PlanSide elevationSide elevationFront elevationFront elevationFront elevationFront elevationSide elevationSide elevationc) Pland) PlanMixed exercise 31 (page 425)Where necessary, the p button on a calculator hasbeen used to work out these answers, which are givento 3 s.f. (unless stated otherwise).1 a) 44.6 cm b) 93.3 cmc) 204 cm d) 101 mm2 a) 127 cm 2 b) 24.5 m 2c) 238 mm 2 d) 69.4 mm 2e) 125 cm 2 f) 72.1 m 23 Check students’ diagrams.4 a) 89.54 cm 2 (2 d.p.) b) 75 cm 2c) 176.5 cm 2 (1 d.p.) d) 178.23 cm 2 (2 d.p.)5 a) 208 cm 3 b) 156 cm 3c) 169.32 cm 3 (2 d.p.) d) 192 cm 3e) 257.544 cm 3 (3 d.p.) f) 655.2 cm 3 (1 d.p.)Side elevationFront elevationSide elevationFront elevation228Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

Chapter 32All answers are given correct to 3 significant figures.Exercise 32.1 (page 433)1 a 5 3.50 cm b 5 6.76 cmc 5 8.18 cm d 5 8.57 cme 5 2.01 cm f 5 1.33 cmg 5 3.41 m h 5 2.00 m2 2.05 m3 a) 6.88 cm b) 68.8 cm 2Exercise 32.2 (page 436)1 a 5 9.24 cm b 5 13.4 cmc 5 10.5 cm d 5 11.4 me 5 23.0 cm f 5 10.7 cmg 5 7.71 m h 5 26.7 m2 9.53 km3 a) 1.89 m b) 10.3 m 3Exercise 32.3 (page 440)1 a 5 47.2° b 5 9.46°c 5 45.6° d 5 69.2°e 5 52.8° f 5 42.7°g 5 39.6° h 5 56.7°2 69.8°3 36.9°4 32.3°Mixed exercise 32 (page 442)1 a 5 9.80 cm b 5 13.9 m c 5 9.79 md 5 14.5 cm e 5 5.57 m f 5 73.6 m2 a 5 52.0° b 5 39.4°3 a) 8.09 m b) 50.8°4 a) 75.7°, safe b) 6.09 m c) 3.39 m5 a) N2 a) 47° b) 70° c) 25°3 a) 31.6 cm b) 19.0 cmExercise 33.2 (page 451)1 a) a 5 7.1 cm b) angle C 5 51°c) angle B 5 39° d) r 5 16.1 cme) p 5 7.0 cm f) angle Y 5 33°2 a) angle R 5 56°, angle P 5 51°, QR 5 7.1 cmb) angle Y 5 20°, angle X 5 37°, YZ 5 16.8 cmc) angle B 5 38°, AB 5 6.9 cm, AC 5 4.3 cm (1 d.p)d) angle C 5 81°, AB 5 9.3 cm, BC 5 5.8 cm (1 d.p)e) angle A 5 49°, angle B 5 59°, AC 5 7.8 cm (1 d.p)f) angle Q 5 57°, PQ 5 15.0 cm, QR 5 11.5 cm (1 d.p)Exercise 33.3 (page 454)1 a) a 5 7.1 cm b) angle A 5 25°c) b 5 6.3 cm d) angle C 5 57°2 a) angle A 5 43°, angle B 5 54°, AB 5 7.3 cm (1 d.p)b) angle A 5 41°, angle B 5 61°, angle C 5 78°c) angle A 5 60°, angle C 5 74°, AC 5 5.4 cm (1 d.p)d) angle A 5 50°, angle B 5 69°, angle C 5 61°e) angle P 5 49°, angle R 5 33°, PR 5 10.2 cm (1 d.p)f) angle P 5 54°, angle Q 5 26°, angle R 5 100°g) angle P 5 66°, angle Q 5 61°, angle R 5 53°h) angle X 5 27°, angle Y 5 38°, XY 5 18.6 cm (1 d.p)i) angle X 5 49°, angle Y 5 82°, angle Z 5 49°j) angle X 5 16°, angle Y 5 45°, XY 5 16.9 cm (1 d.p)3 a) 19.5 cm b) 56°4 a) 54° b) 80° c) 46°Exercise 33.4 (page 460)1 a)y10.50y sin θ90° 180° 270° 360° 450° 540° θ70°120 kmb) (i) 113 km (ii) 41.0 km6 70.0°7 8.28 cm8 a) 51.3° b) 93.7 cm 29 35.3 m10 4.34 mChapter 33Exercise 33.1 (page 447)All lengths and areas are given correct to 3 s.f. and allangles to the nearest degree.1 a) 15.0 cm 2 b) 33.2 cm 2c) 16.7 cm 2 d) 50.0 cm 2e) 21.6 cm 2 f) 24.3 cm 2g) 59.7 cm 2 h) 53.1 cm 21b) 5 30°, 150°, 390° and 510°2 a)y1y cos θ180° 90° 0 90° 180° 270° 360°0.51b) 5 2120°, 120° and 240°θHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises229

3 a) y1y sin θ180° 90°0 90° 180° θb) 5 44° and 136° approximately4 a) y11y cos θ090° 180° 270° 360° 450° 540° θ1b) 5 114°, 246° and 474° approximately5 5 (53°), 127°, 413° and 487°6 a) y33y1y sin 2 θ21030° 60° 90° 120° 150° 180°θ0190° 180° 270° 360°θ41y2y tan θ1y cos 2 θ3b) 5 50° and 230° approximatelyExercise 33.5 (page 462)045° 90° 135° 180° 225° 270° 315° 360°θ1 a) 3, 360° b) 1, 72° c) 3, 90°d) 4, 720° e) 5, 120° f) 2, 450°2 y15 y332y 3 cos θ2y 2.5 sin θ110130° 60° 90° 120° 150° 180°θ0190° 180° 270° 360°θ2233230Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

6yd) (i)y1y cos 3 θ20130° 60° 90° 120° 150° 180°The solutions of cos 3 5 20.5 are 40°, 80° and160°Mixed exercise 33 (page 464)1 a) 17.1 cm 2 b) 30.9 cm 2c) 46.8 cm 2 d) 16.3 cm 22 a) 24° b) 31°c) 73°3 a) 7.95 cm b) 16.2 cm4 a) 8.1 cm b) 29°c) 53° d) 15.9 cm5 a) PR ∧ Q 5 52°, QP ∧ R 5 55°, QR 5 12.4 cmb) XY ∧ Z 5 53°, ZX ∧ Y 5 19°, YZ 5 9.7 cmc) AC ∧ B 5 49°, AC 5 8.8 cm, AB 5 6.7 cmd) PQ ∧ R 5 57°, QR 5 7.2 cm, PR 5 9.0 cm6 Side XY is longest at 8.7 cm7 a) 6.7 cm b) 9.2 cmc) 48° d) 51°8 a) CA ∧ B 5 36°, CB ∧ A 5 63°, AB 5 6.3 cmb) CA ∧ B 5 41°, AB ∧ C 5 51°, BC ∧ A 5 88°c) QP ∧ R 5 66°, PQ ∧ R 5 47°, PQ 5 5.6 cmd) YX ∧ Z 5 53°, XY ∧ Z 5 68°, XZ ∧ Y 5 59°9 82°, 60°, 38°10 a) 60° b) 67°11 a) (i) y1y sin θθ180° 120° 60° 0 60° 120° 180° θy tan θ11(ii) Approximately 2117° and 63°e) (i) 3, 360° (ii) 1, 72° (iii) 3, 90°(iv) 4, 720° (v) 5, 540° (vi) 2, 450°(vii) 5, 120° (viii) 2, 600°f) (i) y3y 3 sin θ(ii)210123y10130° 60° 90° 120° 150° 180° θy cos 4θ60° 120° 180° θ060° 120° 180° 240° 300° 360°θ(iii)y32y 3 cos 2θ1(ii) Approximately 44° and 136°b) (i)y1y cos θ101260° 120° 180° 240° 300° 360°θ3180° 120° 60° 0 60° 120° 180° θ1(ii) Approximately 2107° and 107°c) 233°, 487°, 593°Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 231

g)(iv)y101y 0.5 sin 3θ60° 120° 180° 240° 300° 360°y1180° 120° 60° 0 60° 120° 180°θ1y sin 5θValues of are approximately 2139°, 2113°,267°, 241°, 5°, 31°, 77°, 103°, 149° and 175°Chapter 34Unless stated otherwise, lengths are given correct to1 d.p. and areas and volumes to 3 s.f.Exercise 34.1 (page 469)1 a) and b)2 a) and c)3 b) and c)4 a) Length b) Volume c) Area5 a) Volume b) Areac) Nonsense d) LengthExercise 34.2 (page 472)1 a) 6.1 cm b) 12.9 cm c) 42.1 cm2 a) 16.5 cm 2 b) 40.5 cm 2 c) 221 cm 23 a) 52° b) 103° c) 91° d) 257°4 a) 9.1 cm b) 6.8 cm c) 8.6 cm5 a) 4.9 cm b) 5.7 cmc) 9.0 cm d) 6.5 cm6 187°, 62.6 cm 27 208 cm (to 3 s.f.)Exercise 34.3 (page 475)1 a) 47.1 cm 2 b) 107 cm 2 c) 51.1 cm 22 a) 37.7 cm 3 b) 126 cm 3 c) 39.3 cm 33 a) 32 cm 3 b) 240 cm 3 c) 106 cm 34 158 cm 25 12 cm6 a) 3.6 cm b) 3.1 cm c) 6.2 cm7 a) 2.6 cm b) 5.7 cm c) 9.9 cm8 a) 327 cm 2 b) 845 cm 2 c) 1260 cm 29 a) 556 cm 3 b) 2310 cm 3 c) 4190 cm 310 a) 8.5 cm b) 7.3 cmc) 6.6 cm d) 12.4 cmθExercise 34.4 (page 479)1 a) 2.39 cm 2 b) 28.4 cm 2 c) 46.6 cm 22 1390 m 33 a) 166 cm 2 b) 67.1 cm 2 c) 255 cm 24 990 cm 35 a) 7.3 cm, 224 cm 3 b) 4.5 cm, 61.7 cm 3c) 10.0 cm, 776 cm 36 a) 409 cm 3b) 10.7 cm, 382 cm 27 a) Check students’ answers.b) 2.56 litres8 1740 cm 39 4.8 cm, 174 cm 310 785 cm 3Mixed exercise 34 (page 481)1 a) √ ___6a 2 , b) ____ 4bc and d) ____ 2pad 52 a) Length b) Volume c) Noned) Area3 a) Arc length 6.7 cm, area 20.8 cm 2b) Arc length 34.9 cm, area 136 cm 24 a) 115° b) 302°5 439.5 cm 26 3.1 cm7 38 700 cm 3 (to 3 s.f.)8 8.4(69…) cmChapter 35Exercise 35.1 (page 484)1 A, B and C are similar. D and E are similar.2 XY 5 6 cm, YZ 5 9 cm3 AC 5 4.8 cm, AX 5 4.5 cm, XB 5 7.5 cm4 42 m5 x 5 2.7 cm, y 5 3 cm6 x 5 2.143 cm, y 5 10 cm7 27 cm8 a) Angle BAC 5 Angle CDE(Alternate angles)Angle ACB 5 Angle DCE(Vertically opposite angles)Angle ABC 5 Angle CED(Alternate angles)Corresponding angles are equal so triangleABC is similar to triangle CDE.b) AC 5 13.5 cm, BC 5 27 cmExercise 35.2 (page 488)1yCD 4B216 12 8 4 024A 68ADB4Cx232Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

2 a) (1, 8)b) 233 y1210CD8 A B64D C2BA02 4 6 8 10 12 14 16x4 a) (0, 3) b) 225 a) (2, 3) b) 20.5Exercise 35.3 (page 490)1 a) 1.6b) 6.4 cmc) 10 cm 2d) 25.6 cm 2e) The ratio of the areas is the square of theratio of the lengths.2 a) 4, 8 b) 25, 125c) 100, 1000 d) 0.25, 0.1253 a) 6, 216 b) 8, 512c) 7.07, 353.6 d) 0.316, 0.03164 422 ml5 a) 3.6 m b) 5.76 litres6 a) 15 b) 225 c) 4.52 m 37 15.1 cm8 0.0226 m 2 or 226 cm 29 3.30 : 2.08 : 3.7810 77.44 cm 2Mixed exercise 35 (page 492)1 a 5 3 cm b 5 4.5 cm c 5 10 cmd 5 7.5 cm e 5 2.5 cm2 a) 96 cm 2b) 16 cm3 y876543210ADBCA1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 xA9(14, 2.5) B9(6.5, 2.5)C9(6.5, 7) D9(14, 7)4 a) (0, 4)b) 225 10 cm 26 a) 650 m 2b) 0.5 litre or 500 ml7 a) 1.26 : 1.14 or 1.10 : 1b) 61.9 cm 2BCDChapter 36All answers which are not exact are given correct to1 decimal place.Exercise 36.1 (page 496)1 9.9 cm2 9.7 cm3 5.3 cm4 8.5 cm5 8.6 cm6 a) 12.0 cmb) (i) 26.6° (ii) 14.4°7 a) 11.0 cmb) 35.5°8 a) 10.9 m b) 68.9° c) 11.7 mMixed exercise 36 (page 498)1 9.6 cm2 9.9 cm3 a) 61.7° b) 13.7 cm4 a) 38.4 m b) 39.1 mc) 44.5°5 a) 30.3° b) 13 cmc) 14.8 cm d) 28.3°6 a) 4.3 m b) 79.2°7 a) 8.7 cm b) 30.7°8 a) 3.4 cm b) 47.0°Chapter 37Exercise 37.1 (page 502)1 CX 5 CY (Given.)Angle ACB is commonAC 5 BC (Given.)Therefore triangle CXB is congruent to triangleCYA (SAS).2 DZ 5 DV 1 VZVC 5 VZ 1 ZCDV 5 ZC (Given.)So DZ 5 VCTriangle DXC is isosceles.DX 5 XC (Given.)So angle BDZ 5 angle ACVAngle XAB 5 angle ACV(Alternate angles.)Angle XBA 5 angle BDZ(Alternate angles.)So triangle AXB is isosceles.So AX 5 XBSo DB 5 ACTherefore triangle DBZ is congruent to triangleCAV (SAS).3 a) a 5 20 cm, b 5 12 cmb) x 5 27°, y 5 23°Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 233

4 a) (i) Angle QPX 5 angle XRS(Alternate angles.)Angle PQX 5 angle RSX(Alternate angles.)PQ 5 SR (Given.)So triangle PQX is congruent to triangleRSX (ASA).(ii) Angle QRX 5 angle SPX(Alternate angles.)Angle RQX 5 angle PSX(Alternate angles.)QR 5 SP (Given.)So triangle RQX is congruent to triangleSPX (ASA).b) SX 5 XQ -(Since triangles PQX and RSX are congruent.)PX 5 XR(Since triangles RQX and SPX are congruent.)So X is the midpoint of SQ and PR.SR 5 RQ (PQRS is a rhombus.)Angle RSX 5 angle RQX(Triangle QSR is isosceles.)XR is common to both triangle SXR andtriangle QXR.So triangle SXR is congruent to triangleQXR (SAS).So angle SXR 5 angle QXR.Angle SXR 5 angle QXR 5 90°(Since SQ is a straight line.)5 A and B6 AP 5 PB 5 BQ 5 QC 5 CR 5 RD 5 DS 5 AS(Because P, Q, R and S are the midpoints of thesides of the square ABCD)So all the triangles are isosceles and congruentand all the marked angles are 45°.SAPBQD R CSo the interior angles of the quadrilateral PQRSare 90°(Angles on a straight line.)All the sides, PS, SR, RQ and QP, are equal.So PQRS is a square.7 Angle DCB 5 angle DCA(CD bisects angle ACB.)Angle DCA 5 angle CAE(Alternate angles.)Angle DCB 5 angle AEC(Corresponding angles.)So angle AEC 5 angle CAESo triangle ACE is isosceles and AC 5 CE.8 Angle ACB 5 angle ABC 5 70°(Base angles of an isosceles triangle are equal.)Angle ACD 5 40°(Alternate angles.)So angle BCD 5 110°So angle DBC 5 angle BDC 5 35°(Base angles of an isosceles triangle are equal.)9 Angle BCD 5 122°(Alternate angles.)Angle DCE 5 58°(Angles on a straight line add up to 180°.)Angle BCY 5 58°(Vertically opposite angles are equal.)Angle ABC 5 58°(Angles on a straight line add up to 180°.)Angle BAD 5 89°(Angle sum of triangle BAE.)10 Angle BDC 5 80°(Base angles of an isosceles triangle are equal.)So angle DBC 5 20°(Angles in a triangle add up to 180°.)So angle ABC 5 40°(BD bisects angle ABC.)So angle BAC 5 60°(Angle sum of triangle BAC.)11 Angle BRQ 5 125°(Angles in a quadrilateral add up to 360°.)Angle BRP 5 55°(Angles on straight line add up to 180°.)So a 5 145°(Exterior angle of triangle is equal to the sum ofthe opposite, interior angles.)Mixed exercise 37 (page 505)1 x 5 22° (Alternate angles.)y 5 26° (Base angles of an isosceles triangle(PRS) are equal and Angles in atriangle add up to 180°.)z 5 48° (Alternate angles.)2 x 5 70° (Angles in a triangle add up to 180°.)y 5 60° (Alternate angles.)z 5 130° (Vertically opposite angles.)3 Angle DCB 5 80°(Angles in a quadrilateral add up to 360°.)So angle ACB 5 angle ACD 5 40°(Given that CA bisects angle DCB.)Angle DAC 5 10°(Angles in a triangle add up to 180°.)So angle CAB 5 70°(80° – 10°.)Since CAB 5 ABC, triangle CAB is isosceles.4 a 5 87° (Allied angles.)b 5 74° (Alternate angles.)5 x 5 100°(Angles in a quadrilateral add up to 360°.)234Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

6 A7DCEBAD 5 AB, DE 5 DB and AE is common totriangles ADE and ABE.So triangles ADE and ABE are congruent (SSS).So angle DEA 5 angle BEAAngle DEA 5 angle BEA 5 90°.(Since DB is a straight line.)CD 5 CB, DE 5 EB and CE is common totriangles CDE and CBE.So triangles CDE and CBE are congruent (SSS).So angle CED 5 angle CEBAngle CED 5 angle CEB 5 90°(Since DB is a straight line.)This proves that the diagonals of a kite cross atright angles.ACEBCE 5 ED, angle CEA 5 angle DEA and EA iscommon to triangles AEC and AED.So triangles AEC and AED are congruent(SAS).So AC 5 DACE 5 ED, angle CEB 5 angle DEB and EB iscommon to triangles CEB and DEB.So triangles CEB and DEB are congruent (SAS).So CB 5 BDAE 5 EB, angle AED 5 angle BED and ED iscommon to triangles AED and BED.So triangles AED and BED are congruent(SAS).So DA 5 BDSo AC 5 CB 5 BD 5 DAChapter 38Exercise 38.1 (page 513)1 a 5 20° b 5 40° c 5 60°2 d 5 104° e 5 85°3 f 5 110° g 5 35°D4 h 5 66°5 i 5 50° j 5 56° k 5 34°6 m 5 49° n 5 41°7 p 5 45° q 5 60°8 r 5 20 cm9 s 5 40° t 5 80° u 5 50°10 v 5 95° w 5 126°11 x 5 42°12 y 5 30°13 z 5 57°14 a 5 44° b 5 46°15 c 5 30°16 d 5 90° e 5 40° f 5 32°17 g 5 120°18 h 5 10 cm19 i 5 98° j 5 120°20 k 5 18°Exercise 38.2 (page 517)1 a 5 142°2 b 5 70° c 5 50°3 d 5 50° e 5 50°4 f 5 90° g 5 35° h 5 55° i 5 35°5 j 5 36° k 5 108°6 m 5 74° n 5 32°7 p 5 70° q 5 40°8 r 5 45°9 s 5 61° t 5 61° u 5 58°10 v 5 85° w 5 71°Mixed exercise 38 (page 519)1 a 5 102° b 5 39°2 c 5 13°3 d 5 81° e 5 90°4 f 5 25° g 5 75°5 h 5 62° i 5 28° j 5 29°6 k 5 5.7 cm m 5 38.9°7 n 5 83° p 5 52°8 q 5 122° r 5 244°9 s 5 55° t 5 35° u 5 35°10 v 5 64° w 5 52°Chapter 39Exercise 39.1 (page 521)1Frequency2015105015 20 25 30 35 40 45 50Age (years)Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 235

2 a)Frequency050 70 90 110 130 150 170Rainfall (cm)b) 70 < r , 90c) 90 < r , 1103 a)30Frequency3020102010060 70 80 90 100 110Weight (kg)b) 80 < w , 90c) 80 < w , 904 Lifetime of lightbulb(h hours)Frequency300 < h , 400 3400 < h , 500 9500 < h , 600 12600 < h , 700 15700 < h , 800 13800 < h , 900 19900 < h , 1000 131000 < h , 1100 101100 < h , 1200 6Exercise 39.2 (page 525)12FrequencyFrequency201510501401201000 6 12 18 24 30Weight (kg)80604020015 30 45 60 75 90 105Time (minutes)3Frequency4 a)2520151050168 172 176 180 184 188 192Frequency30252015105Height (cm)Book 2Book 100 10 20 30 40 50 60 70No. of wordsb) Possible answers include:Book 1 has a wider variety of sentence lengths.Book 2 has more shorter sentences.Exercise 39.3 (page 529)1 a), e)Number of bad peaches6543210d)0 2 4 6 8 10 12 14 16 18Delivery time (hours)b) Strong positive correlationc) 10.4 hoursf) About 32 a), e)4030d)201000 10 20 30 40Paper 1b) Strong positive correlationc) 29.0 f) About 323 a), e)Paper 2Petrol consumption (mpg)5040d)30201000 1 2 3 4 5Engine size (litres)b) Strong negative correlationc) 32.9 mpg f) About 30 mpg236Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

4 a)Mark50403020100400 500 600Circumference of head (mm)b) No correlation c) Nod) Don’t know the ages of the people involved.Mixed exercise 39 (page 531)1 a)Time 0 < t , 5 5 < t , 10 10 < t , 15 15 < t , 20(t mins)Frequency 6 7 5 2b)2 a)Frequencyy86420 5 10 15 20xTime (minutes)c) 5 < t , 10 d) 5 < t , 10Frequency2015105y0304050 60 70 80 90Marksb) Suitable comments include the following.The marks range from 30 to 90.There are few low and high marks.Most of the marks are around 50 to 60.c) 50 < m , 60 d) 70 e)2_73 a), c)18001600140012001000800600400200Average weight (g)01 2 3 4 5 6 7 8 9Age of rabbit (months)b) Strong positive correlationd) (i) About 800 g (ii) About 1700 ge) No. A rabbit’s weight cannot keep increasing.xChapter 40Exercise 40.1 (page 536)1 a) (i) 3 (ii) 3 (iii) 5 (iv) 3.456b) (i) 50 (ii) 50 (iii) 5 (iv) 49.632c) (i) 1 (ii) 1 (iii) 5 (iv) 1.443d) (i) 2 (ii) 2 (iii) 4 (iv) 1.7282 a) 1.96 b) 1.04 c) 2.987 d) 4.4563 a) 4.51 b) 27.04 c) 12.75 d) 3.16254 £1.07 5 7.52Exercise 40.2 (page 542)1 a) (i) 50 (ii) 13.6b) (i) 20 (ii) 7.22c) (i) 40 (ii) 14.1d) (i) 20 (ii) 6.552 a) (i) 0–4 (ii) 20 (iii) 6.98b) (i) 0–9 (ii) 40 (iii) 15.5c) (i) 250–299 (ii) 250 (iii) 164.7d) (i) 30–44 (ii) 45 (iii) 31.53 a) (i) 3–5 (ii) 3.62b) (i) 4–7 (ii) 7.3c) (i) 30–39 (ii) 32.25d) (i) 75–99 (ii) 754 30.3 5 179.5Exercise 40.3 (page 546)1 a) (i) 50 cm (ii) 31.46 cmb) (i) 40 g (ii) 25.11 gc) (i) 16 cm (ii) 68.56 cmd) (i) 50 mm (ii) 16.04 mm2 a) (i) 0 < x , 3 (ii) 9.85 daysb) (i) 120 < x , 130 (ii) 121.36 gc) (i) 22 < x , 26 (ii) 21.2 cmd) (i) 50 < x , 55 (ii) 54.83 miniutes3 a) 250 < x , 300b) 250 < x , 300c) £270.004 18.3 g 5 165.71 penceMixed exercise 40 (page 548)1 a) (i) 6 (ii) 7 (iii) 4.488b) (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) 17.542 £11.363 2.71 (2 d.p.)4 a) (i) 20 cm (ii) 22.09 cmb) (i) 100 km/h (ii) 30.11 km/hc) (i) 50 seconds (ii) 59.33 secondsd) (i) 25 kg (ii) 55.8 kg5 a) 10 < x , 20 b) 10 < x , 20c) 19.31 minutes6 £24 888.89 (or £24.89 thousand)Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 237

Chapter 41Exercise 41.1 (page 552)1 0.9 23 0.15 45 0.57 6Exercise 41.2 (page 553)1 0.7 23 0.35 45 0.11 6Exercise 41.3 (page 556)5_6__ 310__ 1749__ 620 5 __ 310__ 411__ 1201 4 2 123 17 4 £3005 a) 50b) 1506 50 yellow, 75 blue, 125 greenExercise 41.4 (page 557)1 a) Score 1 2 3 4 5 6Relativefrequency0.14 0.09 0.17 0.22 0.11 0.27b)1_ or 0.17 (to 2 d.p.)6c) Yes, the dice is biased. The relative frequencyfor 2 seems too low and the relativefrequencies for 4 and 6 seem too high.2 Small number of trials. Cannot be predicted fromthese past events.3 a) Party RelativefrequencyLabour 0.3Conservative 0.47Lib. Dem. 0.17Other 0.06b) 0.3104 a) __ 5 0.5 which is the probability of tossing a20coin and getting a head.102b) ___ 5 0.34 which is very different from 0.5.300c) Emma. More trials give a more reliableindication.5 a) Score 1 2 3 4Relative frequency 0.27 0.23 0.26 0.24b) Yes. All values are approximately equal to0.25.c) Either 225, 225, 225, 225 (if the spinner isfair) orScore 1 2 3 4Relative frequency 240 204 237 2196 a) 200 is a large number of trials.b) Travel by … Bus Car Bike WalkEstimate ofprobability0.245 0.24 0.115 0.4Mixed exercise 41 (page 559)17_92 0.353 0.1374 a) __b) 5 red, 8 white, 7 blue205 12 days106 a) __20 5 1_ , which is the probability of getting2heads with a fair coin.b) She is not necessarily correct. She shouldcarry out more trials.7 a) About 6739b) (i) ___400 (ii) ___ 279(iii) ___ 121400 400Chapter 42Exercise 42.1 (page 564)151 a) __23 b) __ 18232 a) 0.85 b) 0.653 a) 0.53 b) 0.168 c) 0.412d) 0.83 e) 0.564 The events are not mutually exclusive: 3_ 5 2 . 1.51_416 ___1257 a) 0.12 b) 0.4218 a) ___121 b) ___ 9121 c) ___ 1612119 a) __16 b) __ 916 c) __ 616 5 3_810 a) 0.216 b) 0.064 c) 0.432238Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

Exercise 42.2 (page 568)1 a)First diceSecond diceOutcomeProbability16SixSS1616 13616Six56Not a sixSN1656 53656Not a six16SixNS5616 53656Not a sixNN5656 25362 a)b) (i)__ 136 (ii) __ 1036 5 __ 518First daySecond dayOutcomeProbability0.2LateLL0.2 0.2 0.04Late0.20.8Not lateLN0.2 0.8 0.160.8Not late0.2LateNL0.8 0.2 0.160.8Not lateb) (i) 0.64 (ii) 0.323 a)First discSecond discNNOutcome0.8 0.8 0.64Probability710BlackBB71071049100710Black310WhiteBW71031021100310White710BlackWB31071021100310WhiteWW31031091004 a)b) (i)___ 4910058(ii) ___First match100 5 __ 295051(iii) ___100Second matchOutcomeProbability0.5 WW0.30.2D0.5L0.50.3 0.3D0.2WDL0.20.5 WL0.30.2DLb) (i) 0.25 (ii) 0.50 (iii) 0.38WWWDWLDWDDDLLWLDLL0.5 0.5 0.250.5 0.3 0.150.5 0.2 0.100.3 0.5 0.150.3 0.3 0.090.3 0.2 0.060.2 0.5 0.100.2 0.3 0.060.2 0.2 0.04Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 239

5 a)First toss Second tossThird tossOutcomeProbability1212HT121212HTH121212121212HTHTHTHHHHHTHTHHTTTHHTHT1212 12121212181 81 1 1 1222 81 1 1 1222 81 1 1 1222 81 1 1 1222 8b) (i)1_81122HT(ii)3_8Exercise 42.3 (page 571)1 a)First ball12T(iii)4_8 5 1_2Second ballTTHTTTOutcome1 1 1 1222 81 1 1 1222 8Probability610YellowYY71161042110711Yellow410RedYR71141028110411Red710YellowRY4117102811042b) (i) ___110 5 __ 2155992 a) ___24953 a)First game310(ii)b)Red___ 56110 5 __ 2855___ 8992495Second gameRROutcome41131012110Probability0.7Judith winsJJ0.7 0.7 0.49Judith wins0.70.3Suki winsJS0.7 0.3 0.210.3Suki wins0.5Judith winsSJ0.3 0.5 0.15Mixed exercise 42 (page 573)1 a) 0.85 b) 0.40172 a) __b) __ 155 3_2525 53 a) 0.5 b) 0.914 a) __ b) __ 4c)252515 a) __42 b) __ 642 5 1_16 ___2160.57 c) 30Suki winsb) (i) 0.49 (ii) 0.15 (iii) 0.364 a) 0.42 b) 0.3412 1445 a) ____24 360 5 ____ 506 b) ____ 12 216101524 360 5 ____ 50910152160c) ____ ___24 360 5 18203__ 625__42 5 5_7SS0.3 0.5 0.15240Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

7 a)First discSecond discOutcomeProbability25BlackBB42525Black35WhiteBW62535White25BlackWB62535WhiteWW925b) (i)8 a)__ 425(ii) __ 1325First plant(iii) __ 1225Second plantOutcomeProbability0.7RedRR0.49Red0.70.3Not redRN0.210.3Not red0.7RedNR0.210.3Not redb) (i) 0.09 (ii) 0.42329 a) __72 5 4_9 b) __ 4072 5 5_910 a) 0.14 b) 0.14NN0.09Chapter 43Exercise 43.1 (page 579)1 a) Primaryb) Secondaryc) Primaryd) Secondary2 Possible answers include the following.a) Those not in the phone book have no chanceof being included.b) Those working on Saturday would not beincluded.3 Possible answers include the following.Make the categories exclusive(in Paul’s first draft, for example, 1 hour couldgo in two categories); have more categories,for example, split the groups into classes of 30minutes rather than 1 hour.4 Possible faults include the following.a) The person’s favourite sport might be onethat 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 answerswould be very difficult to analyse.b) Check students’ rewrites of Q1. It shouldhave better categories.6 Check students’ questions.Mixed exercise 43 (page 580)1 Secondary. Jan did not collect the data herself.2 a) Possible answers included the following.Ask people to draw a 70° angle without aprotractor.Show people three drawn angles and askthem to estimate what size the angles are.b) Possible answers include the following.Choose 30 students from Year 7, 30 fromYear 9 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-groupof the student as well as data on the angle(s)drawn/estimated.3 Check students’ answers.Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 241

Chapter 44Exercise 44.1 (page 585)1 Q 2 Q 1 Q 3 IQRGirls 156 cm 148 cm 163 cm 15 cmBoys 160 cm 150 cm 169 cm 19 cm2 a) Mass (m grams) Cumulative frequencym < 0 0m < 50 16m < 100 38m < 150 81m < 200 143m < 250 183m < 300 196m < 350 200b)Cumulative frequency200180160140120100806040200050100 150 200 250 300 350Mass (m grams)c) Median 5 165 g approx., IQR 5 95 g approx.3 a) Age (y years) Cumulative frequencyb)Cumulative frequency8070605040302010010y , 11 0y , 16 7y , 19 17y , 25 32y , 35 52y , 50 64y , 65 712030 40 50Age (y years)60 70c) 44d) 16e) Median 5 26 years, LQ 5 19.5 years,UQ 5 36.5 years4 Possible answersThe median shows that the boys’ heads are largerthan the girls’ heads, on average.The interquartile range shows that the girls’ headsizes are slightly more varied than the boys’.Boys and girls both have the same range of headsizes.5Cumulative frequency6 a)90807060504030201000Cumulative frequency50045040035030025020015010050200040 60 80Earnings (£w)100Key250500 750 12501000 1500Time (t hours)b) Both types have about the same averagelifetime but type B is more reliable since itsinterquartile range is smaller.Exercise 44.2 (page 592)1Frequency density10.5020 40 60 80 100 120 140 160Earnings (£w)AB242Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

2 a) You are aged 19 up until your 20th birthday,which is 20 years after you were born.b)Age(years)Under1010–19 20–29 30–49 50–89Frequency 24 46 81 252 288Frequencydensity2.4 4.6 8.1 12.6 7.2Frequency density(people per year)151050 20 40 60 80 100Age (years)3 a) Waiting time(w minutes)Frequency0 , w < 20 5020 , w < 40 8240 , w < 60 13060 , w < 90 15390 , w < 120 42120 , w < 180 24b) 60.2 minutes to 1 d.p.4 a) 5 girls and 18 boysb) Possible answers:In general, boys spent less time on thephone.The times for the girls were more evenlyspread than those for the boys.There were 50 girls and 50 boys represented.5 a) 100b) 81.2 kg to 1 d.p.Mixed exercise 44 (page 596)1 a) Height (h cm) Cumulativefrequencyh < 120 0h < 130 5h < 140 32h < 150 71h < 160 133h < 170 178h < 180 196h < 190 200b)Cumulative frequency200180160140120100806040200120 130 140 150 160 170 180 190Height (h cm)c) Median 5 155 cm, IQR 5 19 cm2 a) 12b) 35c) Approximately 9.5 km3 Age (years) Under 10 10–19 20–29 30–49 50–89Frequency 240 1460 2080 4950 6120Frequencydensity(people peryear)24 146 208 247.5 153Frequency density2502001501005000 10 20 30 40 50 60 70 80 90Age (years)4 Distance (km) Frequency0 , x < 10 610 , x < 15 715 , x < 20 920 , x < 25 1225 , x < 30 530 , x < 40 7Mean 5 20.2 km (to 1 d.p.)5 Suitable comments include the following.The second group did not run as far as the first,on average.The distances for the second group were not asspread out as those for the first (comparativelymore ran between 10 and 25 km).The estimate of the range is the same for bothgroups (both distributions go from 0 to 40 km).6 a) 21.1b) 75 and 85c) 16Higher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 243

Chapter 45 (page 600)1 a) 45b) Grass seed by £45.75c) (i) small box: 50 p/m² large box: 40 p/m²(ii) 2 large boxes and 1 small box2 a) £3.75 b) £13.753 a) £130b) No. The total amount collected on Sunday isnot known.4 a) e.g. no timescale; options are exhaustive.b) e.g. not a representative sample of thepopulation, rugby is probably playedon a Saturday afternoon and the peoplewho watch it are unlikely to be in thesupermarket at this time.5 a) Yes – it is better to change £300 straight intopesos. Converting £300 gives 6075 pesoscompared with 6075 pesos from changing$615.b) Mexican trip cheapest by £12.6 Any answer so long as it is justified.Travelling by bus is the cheapest at £32 in totalbut they would have to catch the bus at 07:50.Travelling by car costs £63 but they don’t have toleave until 11a.m.Travelling by train is the most expensive at atotal of £79, but they don’t have to catch the trainuntil 10:52.7 Hotel £1740 – the most expensive but includesuse of leisure facilities. Guest House £1140 –includes evening meal (but not flexible) andbreakfast. Cottage £880 – all meals must be paidfor and prepared.8 £10 0169 a) 1008 b) £95010 a) Electric superstore b) £6.8011 a) £16 and £64 b) 840 ml12 48 mph13 3456, £411.26, £424.82, £21.24, £446.05, £416.6814 15 days15 £258416 a) £975 b) £1372.9617 £195618 a) Player Mean RangeA 50 8B 33 106C 50 99b) Any, so long as reasoning is justified, e.g.Player A as the most consistent.19 a) 616, 15.52%b) Each dimension must be a multiple of 6and multiply together to give a volume of133 056 cm 3 , e.g. 66 cm 3 48 cm 3 42 cmc) 30 cm20 £11 53021 £700.56 (compared with £733.92)22 Cycling, by 3 minutes (walking 15 minutes,cycling 12 minutes)23 96%24 a) Cheapest option is to order meals for 51people:48 3 7.75 5 £372, 51 3 7.25 5 £369.75.b) Total cost 5 basic cost (44) 1 cost ofingredients (430) 5 £474.Total charge 5 £725. 53% profit.c) 625 a) £72, 111_4 hoursb) It would take Barbara 12 hours to earn £72so very similar in terms of time taken. Themoney she earns is guaranteed. Alan hasthe potential to collect more money if morepeople are in.26 £39127 £551.6928 a) 1: 36p 2: 90p 3: £5.70 4: £3.82b) Combine 4 parcels at 1.3 kg (4 3 5 5 £20 to1 parcel at 5.2 kg costing £11.02. Saving £8.98.29 a) 5700b) C – smallest volume of box with sufficientdimensionsc) Flour 450 g Fruit 1650 g Eggs 6 or 730 a) Diesel £983.99 Petrol £1297.76b) £300031 a) Various combinations are possible – G or Fto share with A, F to share with C or E and Bto share with Eb) £704.76c) 79%32 a) 108 b) 96 slabs or 99 slabsChapter 46 (page 614)1 6 2 9 1 8 1 7 1 6 1 5 1 43 1 21 (9 1 8 1 7 165 1 4 1 3 1 2 1 1 uses 7)2 Rachel, Jane, Kim, Shaun3 44 95 3 76 1 4 3 1 5 72245 Rounding of decimals6 123 and 1247 63 and 64 (Zen looks at 62 and 65 with 63 and 64missing.)81_89 90110 6511 1 hour 59 minutes12 201713 About 23p14 x 1 5 (2x 2 3, x 1 2, x 1 5, 2x 1 1, x 2 3)244Answers to the Student’s Book exercisesHigher WJEC GCSE Mathematics © 2010, Hodder Education

15 23 (because 0 is in the sequence and thenumbers decrease by three each time)161_4 1 __ 17217 £341018 3619 361.12 metres20 9 metres by 3 metres21 14 days22 28023 3024 99%25 Low energy bulb by £16.8026 a) ___ 6x 2or ___ 3x2b) y 5 3_16 84 x27 0.2 and 0.528 26 hens and 12 pigs29 Tile 135 mm, gap 35 mm30 Second column as they are all the multiples of 831 No, unless the 250 ml glass holds just a little morethan 250 ml32 12033 90 minutes (The wife takes 72 minutes, but has towait for her husband.)34 10 units35 2 days 16 hours or 22_3 days36 1 : 837 11.5 km/h38 59.48 m 239 Not possible as sum of angles 5 720°,3 3 140 5 420°, remaining 3 angles total 300°so 3 angles , 90° not possible40 72.8%41 (x 1 3)(x 1 5) m 2 or x 2 1 8x 1 15 m²42 a) x(y 2 2x) 2 b) ___ 4x 2y 3 10043 5.29 cm244 6.3 cm45 x 2 (1 1 √ __3 ) shown by working out perpendicularheight of triangle and adding the area of thesquare base to the area of 4 of these triangles464x 2 2 px 2 _________( 5 _________x2 (4 2 p))4 447 3.99 m48 4.8 m49 9 km50 ___ 2xtkm/h51 a) 21.21 cmb) Pencil or box has no thickness or accuracy ofmeasurement52 6.25 square units53 79.8 cm 254 1015.78 cm 3551_456 a) 1.154 cm b) 0.577 cm 257 4.7 cm 258 Bearing 115.8°59 5 people60 24.8 mm61 11, 44, 47, 50, 7362 3563 88%564 __65161_2, equal probability each time it is thrown66 a) 0.6 b) 0.2867 46.8 metres68 65 cm69 0.45Hard (page 627)1 54 kg wheat, 53 kg barley, 30 kg barley,62 kg wheat, 49 kg oats, 50 kg wheat2 183 69 cm 24 e.g. Terms 4a 1 7, 4a 1 8, 4a 1 9, 4a 1 10, 4a 1 11Sum 20a 1 45 5 5(4a 1 9)5 Yes6 AR 5 7.2 cm7 a) 16 sin y 1 8 sin 60b) (i) y 5 0 or equivalent in words, 4 √ __3 cm 2 orequivalent(ii) y 5 90° or equivalent in words,16 1 4 √ __3 cm 2 or equivalentHigher WJEC GCSE Mathematics © 2010, Hodder EducationAnswers to the Student’s Book exercises 245