Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 2014
ANSWERS TO HigHER gCSE MATHEMATiCS FOR CCEA PRACTiCE BOOK
Chapter 1 1 a 18, 24, 60
b 25, 60c 24, 60 d 24e 60
2 a 4, 12 b 35c 12, 21 d 17
3 a 2, 18 b 1, 2, 5c 15, 18 d 2, 5, 17
4 a 36 b 1c 100 d 25e 121f 64g 1h 1000i 0.49j 8
5 a 7 b 3c 9d 10e 6f 1g 10h 1i 2j 0.6
6 a 28b 65
c 117d 290
7 a 43 b 74
c 39 d 96
e 27
f 42 × 53
g 32 × 84
h 23 × 64
8 a 16 b 1c 1024 d 2401e 256
9 30
10 273
11 4, 12, 20, 60
12 15 and 16
13 a 2 × 7b 2 × 2 × 2 × 2 = 24
c 2 × 2 × 7 = 22 × 7d 5 × 7e 2 × 3 × 7f 7 × 7 = 72
g 2 × 2 × 3 × 3 × 3 = 22 × 33
h 2 × 2 × 3 × 13 = 22 × 3 × 13i 3 × 3 × 5 × 5 = 32 × 52
j 2 × 2 × 2 × 53 = 23 × 53k 2 × 2 × 2 × 2 × 2 × 3 × 3 ×
3 = 25 × 33
l 2 × 3 × 3 × 5 × 7 × 11 = 2 × 32 × 5 × 7 × 11
14 a a = 2 b = 3 c = 2b x = 4 y = 1 z = 2
c m = 5 n = 2 p = 3d d = 4 e = 3
15 a 7b 2c 1d 3e 2f 3g 20h 26
16 a 336b 140c 1404d 95 400
e 3150f 39 690g 9900h 40 018
17 a 84 = 22 × 3 × 7; 154 = 2 × 7 × 11; HCF = 14; LCM = 924
b 75 = 3 × 52; 135 = 33 × 5; HCF = 15; LCM = 675
c 150 = 2 × 3 × 52 95 = 5 × 19 HCF = 5; LCM = 2850
d 645 = 3 × 5 × 43 225 = 32 × 52 HCF = 15; LCM = 9675
18 a HCF = 1; LCM = 680 b HCF = 13; LCM = 884 c HCF = 7; LCM = 1078
19 a 28b 44
20 231
21 1pm
1
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 20142
Chapter 2 1 a 717
b 829c 5972 d 62 201e 4881f 16 457g 494 886h 8818
2 a 147b 626c 769d 1311e 1253f 1802g 54 166h 11 378
3 530
4 It is not possible to make exactly 1000
5 54 kilometres
6 a 3179b 6628c 3182d 9807
7 a 3600b 240c 5200d 124e 9000
8 a 18 000b 36 000c 400d 20e 2520
9 a 3854 b 4266c 33 540 d 188 448e 3 716 601
10 360
11 a 51.529 (3dp)b 27c 35
d 325e 690.95
12 8
13 23
14 200 g
15 82 miles
16 95p
17 a 83b 26
18 a 169 600b 169 600
19 a 2165b 3554
20 a 150b 135
21 a 9158b 174 900
22 a 140b 9600
Chapter 3 1 a 57.74
b 87.71c 77.356d 22.355e 21.096f 63.1784
2 a 4.8b 7.2c 112.2d 53.6e 5.04f 15.08g 34.992h 21.0273i 125.8j 2.432
3 a 2.4b 1.7c 12.5d 13.5e 30f 50
g 26h 52i 1.39j 56.38
4 6.25 m
5 £53.65
6 60 cm or 0.6 m
7 535.5 cm
8 119.2 m
9 23.5 mm or 2.35 cm
10 13.9 g
11 a 24.91 b 24 910 c 0.2491 d 2.491
12 £80.04
13 a 1.35 kgb £2.97
14 5
15 41.6 miles
16 45p
Chapter 4 1 The differences for each
country are:Northern Ireland 48.3°CEngland 64.6°CWales 56.9°CScotland 60.1°C England has the biggest difference
2 a –2 b –3 c –8 d –56 e –8 f 17 g 9 h 0 i –23j –9 k –72 l –80
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 20143
m –31 n 54 o –8 p –33 q –28 r –63 s –24 t 49 u –85 v –78 w –22 x –61 y –52
3 a –4°Cb 3°C
4 a 0 b –40c 12d –24e –35f –21g 20h –4 i –5 j –5 k 16 l 5m –5 n –8 o –3p –2q –24 r –3s 6t –15
5 a –26 b 10 c 1 d 24 e –3 f –9 g 4 h 1 i –21 j –1 k 13
l 32 m 13 n 8 o –15 p –31 q 64r –64
Chapter 5
Exercise A 1 a = 3
41520
b 1521
57
=
c 12
1122
=
d 1860
310
=
e 1618
89
=
2 a 45
b 56
c 34
d 12
e 35
f 13
g 58
h 34
i 411
j 25
k 35
l 13
3 a 14
27100
310
720
b 512
35
1320
23
4 a 3 12
b 3 13
c 2 18
d 1 59
e 3 45
f 1 37
g 1 57
h 5 12
I 3 14
J 3 23
5 a 97
b 138
c 152
d 114
e 175
f 145
g 299
h 296
i 418
j 133
6 a 1 45
b 123
c 116
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 20144
d 14
e 1 12
f 5
14
g 123
h 1 13
i 1 211
j 1 13
Exercise B 1 a 13
18
b 14
c 118
d 45
e 2360
2 a 7 712
b 8 59
c 5 18
d 3 916
e 8 128
f 3 712
g 4 49
h 1212
3 6 38
inches
4 a 4 718
b 7 15
c 5 2140
5 1334
m
6 5 1320
cut off, 4 720
left, not enough
7 a 34
b 4
c 10 15
d 8 14
e 1 910
f 5 110
8 a 2 89
b 2 1112
c 12
d 2 1720
e 12
f 4877
9 a 9 34
b 16 12
c 9 15
d 2 25
e 8
f 1641
g 9 13
h 3 922
i 5 58
j 2 67
k 3 717
l 14
m 6985
n 8 710
o 81155
10 a 2 13
b 2 2655
c 5 13
d 5 13
e 4 120
f 6 16
Exercise C 1 a 84
b £168c 141 milesd £204.20
2 They are the same, £90.
3 415
4 150
5 241500
6 £15
7 p = 1 q = 20 (or any pq = 20)
Exercise D 1 8
15x
2 m6
3 3340
w
4 730
e
5 5 420
c d+
6 2 14 535
( )m e−
7 10 3
12x y+
8 y x+ 4
12
9 56
2xy
10 x x( )3 212+
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 20145
11 23
12 x15
13 1 14
14 310
cd
15 x32
16 ny2
17 2342
x
18 215x
19 w2
6
20 xm
2
2
Chapter 6 1 a i 80.9 ii 80.93
b i 5.1 ii 5.12c i 4.4 ii 4.40d i 0.0 ii 0.03e i 649.0 ii 649.00f i 17.0 ii 16.98
2 a 10b 40 c 7 d 300 e 1000 f 0.8 g 0.6 h 0.05 i 2000 j 0.01 k 8 l 20 m 700 n 8000 o 100 p 0.7 q 0.005 r 0.02 s 400 t 20 000
3 600 people
4 a 3 mb 300 cm
5 a 900 b 600 000c 7 d 0.0004e 19f 0.99g 7.39 h 2.72i 8.0
6 a 200 + 400 = 600b 800 ÷ 80 = 10c 20 × 50 = 1000d 7002 = 490 000
e 90
40 20980×
=
f 60 × 6 = 360g 4 × 9 = 36h 20 × 30 = 600i 70 × 50 = 3500
j 20 640
3 × =
k 10 10 100 10× = =l 0.8 × 30 = 24
m 0 6 70
67. × =
n 203 = 8000o 200 × 0.3 = 60
p 10 5 100 25 75 8 72 2− = − = ≈ .
q 50 400 02
900 02
90002
4500. .+ = = =
r 70 × 60 = 4200
s 6000 5
1200.
=
t 60005
= 1200
u 202 = 400v 60 × 8000 = 480 000
w 620
= 0.3
x 3050
= 0.6
y 8000 × 40 = 320 000
z 900 409 × = 4000
7 a 6 × 7 = 42 b 30 ÷ 6 = 5c 50 × 30 = 1500 d 8000 ÷ 200 = 40e 300 × 0.3 = 90
f 20 × 20 = 400g 900 ÷ 200 = 4.5 h 5 × 6 × 10 = 300
i 700 0 84 2
70.×× =
j 9 60 5 0 3
270. .×− =
8 20 × 40p = 800p = £8
9 £20 × 4000 = £80 000
10 4 × 8 = 32 cm²
11 a 30 ÷ 5 = 6 cmb Estimate is smaller than
the actual length because the numerator is reduced and the denominator is increased.
12 3 ÷ 0.2 = 15
13 Number of tiles = 5 × 6 ÷ 0.3 = 100
14 £600 ÷ 5 = £120
15 6000 77≈
16 3 × 4² = 48 cm²
Chapter 7
Exercise A 1 18
2 10
3 27
4 11
5 19
6 30
7 10
8 2.11
9 20
10 3 5
12
11 2
12 20
13 26 ÷ 2 + 4 = 17
14 6 × 2 + 3 = 15
15 18 + 6 ÷ 2 = 21
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 20146
16 19 – 2 × 3 = 13
17 5 × 3 + 4 × 5 = 35
18 6 + 5 – 1 × 2 = 9
19 3 × 8 ÷ 2 – 1 = 11
20 10 – 2 – 6 + 3 = 5
Exercise B 1 7.75
2 32.768
3 10
4 1.65
5 1.6
6 5.1975
7 100
8 12
9 6 1324
10 3403
Exercise C 1 –1.7
2 –21.24
3 0.5625
4 –1.67
5 1.37
6 2.45
7 41.67
8 0.39
9 7.03
10 39.54
11 104.8576
12 0.872
13 49.215
14 5.840
15 7.963
16 22.09
17 46.53
18 490.912
19 4.347
20 2.626
21 3.21
22 11.6
23 8.33
24 12.5
25 0.510
26 26.88 or 26.9 cm2
27 38.8129 or 38.8 cm2
28 £78.98
Chapter 8
Exercise A 1 a 4 : 3
b 2 : 5 c 7 : 11 d 1 : 3 : 4 e 3 : 5 : 4
2 a 2 : 5 b 1 : 5 c 12 : 5 d 5 : 2 e 1 : 6f 2 : 3g 6 : 7h 63 : 44
3 a 1 : 5 b 1 : 6 c 1 : 4.5 d 1 : 2.25 e 1 : 0.6 f 1 : 20 g 1 : 24 h 1 : 0.35 i 1 : 25 000
4 4 : 7 : 9
5 1 : 2 : 5
6 Paula £15, Tom £25
7 £520 : £650 : £780
8 Sue £14 000, Jane £21 000, Christine £35 000
9 1.5 litres
10 Copper 150 g, iron 200 g, nickel 100 g
11 £2.50
12 a 6000 votes b 3000 votes
13 £12 800
Exercise B 1 1 : 250 000
2 a 2.5 kg b 900 g
3 a 72 b 40
4 a 600 m b 38 cm
5 a 12 cm
b 6.3 cm
6 a 6 cm b 180 cm
7 a 150 gb 13 people
8 a 2.6 kmb 12.5 cm
9 24
10 780
Chapter 9
Exercise A
1 a 920
0.45
b 34
0.75
c 325
0.12
d 1110
1.1
e 9100
0.09
f 740
0.175
2 a 47% 47100
b 82% 4150
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 20147
c 4% 125
d 42 12
1740
%
e 135% 2720
f 33 13
13
%
3 a 0.19 19%b 0.18 18%c 0.65 65% d 0.03 3%e 1.75 175%
f 0. 2̇ 7̇ 27.2̇ 7̇ %
4 a 29100
, 0.3, 31%, 0.32, 13
b 0.25, 0.27, 28%, 310
, 0.35
c 920
, 0.46, 56%, 64100
, 0.65
d 23
, 1725
, 710
, 72%, 0.84
e 16.9%, 725
, 0.29, 30%, 13
f 0.605, 66%, 23
, 0.67, 79
5 Man. Utd. by 5%
6 0.344
7 62 12
%
8 3200 000
9 a £2.16 b £6 c £108
10 294
11 In the first week of the sale, the price would be £360. In the second week of the sale, the price would be £324. In the third week of the sale, the price would be £291.60. So the selling price of the television was £291.60.
12 a 2.52 mb £1071 c £3.24
13 a £660 b £690 c £612 d £657
14 a £300
b £328 c £376 d £356
15 £52.80
16 £15 525
17 £23.76
18 583.6996mm
Exercise B 1 a 2
25
b 1925
c 28%d 12%e 65%f 24%
2 a 14% b 12% c 60% d 27% e 24% f 16.7% g 17.1% h 22.2% i 30% j 39.2%
3 39.7%
4 57.4%
5 12.9%
6 1623
%
7 4%
8 10.25%
Exercise C 1 £24 520
2 £45
3 £1440
4 £13 500
5 28 million
6 £6
7 £42
8 £75
9 £72 000
10 £90
Exercise D 1 a Cheaper Sounds by £88.80
b Cheaper Sounds by £62
2 380
3 S.I. by £328.76
4 £6959
5 6 years
6 4.5%: £2604.525%: £2552.56 4.5% for 6 years is better.
7 Anglo Bank: £5692.15Bonus Bank: £5705.83Bonus Bank pays more.by £13.68
8 6 years
9 £6400
10 20%
Chapter 10 1 a 1
3
b 16
c 1640
d − 110
e − 1317
2 a 18b 52c 1000d 2 1
2e −2
3 a 114
b 2 23
c 58
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 20148
d 310
e 1212
4 a 0.4b 5c 4
5d 6.25e 5
16
5 a ba
b 1y
c p2
d − 32x
e nn2 1+
6 59
7 a 58
b 85
c 481
d 0.0723e 500
8 a 0
b 415
c false e.g. 5 > 3 but 15
< 13
d 2e 5
8
Chapter 11
Exercise A 1 a 4 × 104
b 4.8 × 103
c 7.37 × 105
d 2.5 × 10e 8 × 106
f 1.234 × 104
g 6 × 106
h 7.89 × 107
I 3.6 × 106
J 9.3 × 107
k 5 × 105
l 2 × 1012
2 a 7 × 10–3
b 2.04 × 10–1
c 4.5 × 10–5
d 7.07 × 10–3
e 1 × 10–7
f 7.936 × 10–2
g 1.0008 × 10–1
h 6.47 × 10–4
i 3 × 10–3
j 2.9 × 10–3
k 5.2 × 10–11
l 7.3 × 10–5
3 a 30 000b 5 700 000c 0.875d 0.00402e 773f 0.0000012g 80 300 000 000h 548 000i 0.0999j 0.000386
4 1 × 1012
5 19
6 1.26 × 10–3, 1.62 × 10−1, 6.12 × 100, 216 × 10−1, 2.16 × 102
Exercise B 1 3.400412 × 106
2 5.47 × 10−2
3 8.2825 × 105
4 6.087 × 10−2
5 6.66 × 106
6 4.12 × 10−2
7 3.2 × 1011
8 2 × 105
9 3 × 10−5
10 3 × 103
11 3.4 × 10−3
12 3.0256 × 104
13 3.2 × 1012
14 48 mm or 4.8 cm
15 2.48 × 10−17 g
16 4.88 × 103 mm
Exercise C 1 a 4.32 × 108
b 2.1 × 102
c 2.924 × 10–1
d 5.785 × 10–5
e 7.3 × 106
f 9.2 × 10–11
g 2.89 × 10–4
h 7.744 × 1013
i 3.1884 × 10–2
j 7.3081 × 108
k 1.815 × 10–5
l −4.44 × 10–3
2 a 6.48 × 1011
b 3.46 × 104
c 1.73 × 10–7
d 3.39 or 3.39 × 100
e 3.20 × 1010 f 2.28 × 106
3 a 1.472 × 1011
b 3.9 × 107
c 1.08 × 10–6
d 2.3 × 102
e 1.312 × 101
f 5.4756 × 1010
4 a 3.16 × 109
b 3.17 × 10–10
5 1.67 × 10−24g
6 5.9 × 1012 miles
Chapter 12 1 a Rational, terminating
decimalb Rational, terminating
decimalc Not rational (irrational),
π is irrationald Rational, terminating
decimale Rational, 144 = 12f Not rational (irrational),
66 = 3.899 538 434… (non-recurring, non-terminating)
g Not rational (irrational), 3 is irrational
h Rational, fractioni Rational, recurring decimal
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 20149
2 a Rational 1425
b Rational 5699
c Rational 311
d Irrational
e Rational 5
f Rational 491
g Rational 11
h Irrational
i Rational 103999
j Irrational k Irrational
3 a 7299 = 8
11
b 2245
c 34111
d 41333
e 1 311
f 1 718
g 606990
101165
=
h 5190
1730
=
i 31599990
117370
=
4 a π, , , ...2 3 5b e.g. 2 5and 2 +( )
5 a 3
b 1π
c 1
7 or 12 7
6 For example, 3 12 36 6× = =
7 For example, 6 62( ) =
8 a irrationalb irrationalc rational
9 Any root between 36 and 49
10 4 or 16( )Chapter 13 1 2 7
2 3 7
3 5 5
4 10 6
5 6 10
6 20 2
7 12 6
8 12 7
9 2 3
10 2
11 a 20b 5
3c 16d 9 5
e 5
3f 2 2
12 a 9 2
b 6 3
c 29 2
d 3 5
e 8 3
f 7 2
13 a 10b 2 2c 23
14 a 12 3−
b 2 3 3+
c 52 14 3+
d 29 9 3−
15 a 28 + 10 3
b 1
c 48 – 24 3d 32 + 11 12 7
16 2 6
17 a 4 cm
b 8 2 cmc 8 cm2
18 a 33
b 3 55
c 7 1010
d 2 5
e 5 36
f 26
g 66
h 355
19 13 630
20 9 22
21 a falseb truec trued truee false
Chapter 14
Exercise A 1 4a
2 2a
3 abc
4 y2
5 3p + 4r
6 2c
7 5x + 4y
8 7a + 2b
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201410
9 4a + b
10 2y + 3s
11 a3b2
12 12xy
13 10x
14 3ab + 3ac
15 6ab
16 3x + 2y
17 6a + 3b
18 a + 2b
19 2a2 + 9a
20 4p – 3q + 4
21 5p + q
22 5x2 – 3x
23 5x3 – 3x2 + 2x
24 2ab + 3ac
25 7x – 3y + 6z
26 3a2 – 5ab + 4b2
27 6a + 3b
28 a – b + c + 6
29 9ab + 6ac
30 –2a2 + ab
31 10a pence
32 7a2 + 3ab
33 3x – 6
34 a a + 3bb −3a – 3bc 3a – 6
Exercise B 1 a 6
b 2c 8d 28e 10f 16g 8h 16
i 24j 10k 10l 28m 4n 12o 48p 24q 32r 8s 2t 5u −2v 1w 4x 0.5y 32z 64
2 a 12b 42c –58d 102e 4.5
3 a 4b 11c –13d –7
4 a 3b –8c 12d 350e –6.5
5 a 16b –11c –18d –12e 97
6 a 38b 7.6c 52d –2e 438
7 3
8 –4
Chapter 15
Exercise A 1 a 24
b 22 × 32× 53
c a5
2 a 211
b 38
c 45
d 57
3 a 53
b 76
c 22
d 34
4 a 26
b 30 or 1c 54
d 71 or 7e 5–2
f 33
5 a 2a6
b a2
c 12a5
d 3a
e 14p
or p−4
f y
g k−310
h t2
i lj 6
2y or 6y−2
k 64a6
l 36p4q6
6 a 6a5
b 18x6
c 20a3b4
d Cannot be simplified e 2a4b5
f 14c3
g 16y10
h 2p2qi 4p–3
j 2p–2
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201411
k 32mn
l 43
2pq
m 2p13
n 36a5b5
o 12b4
7 a x12
b x6
c x 2
4
d 4n32
e mnf 36k4
g 13p or p–3
h 7ti 9p–4 or 9
4pj 6m3n2
8 a 26
b 23
c 2–3
d 20
e 272
f 22n+1
9 29a–6b–3
10 a 48b 64c 216
d 113
e 36f 512
Exercise B 1 a 1
5b 1c 5d 25e 32
f 12
2 a 243b 100c 16d 1
64
e 32f 1000
3 a 16
b 6c 32d 27e 1
25f 1
4 a 36
b 175
c 1 920
d 8e 61 1
2 5 a 7776
b 27
6 211
7 a − 12
b 23
c –10
Exercise C 1 4
2 4
3 2
4 2
5 −1
6 −32
7 −2
8 1
9 2
10 −16
11 −18
12 −23
13 −1
14 4
15 38
Chapter 16
Exercise A 1 21a + 42b
2 −10c − 15d
3 −12e – 20f
4 21g – 6h
5 12i + 6j – 9k
6 −15m + 6n − 9p
7 24r – 18s – 12t
8 32r + 16s + 8t
9 12u + 20v
10 −24w − 18x
11 10y + 2z
12 12y + 8z
13 −15v − 10
14 21 + 12w
15 −5 + 15a
16 24g – 15
17 2x2 + xy
18 10p2 −5p
19 a2b – ab3
20 −10k +6k2
21 2a + 1
22 5p −4
23 7x −7
24 4t2 – 10t
25 15 – 5y
26 5x2 + 2x
27 −3b −3
28 –t + 4r −6
29 21x + 29
30 i 5x + 2ii 4 1
2 x −3 or 9 6
2x −
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201412
Exercise B 1 x2 + 3x + 2
2 x2 + 7x + 12
3 x2 + x – 2
4 x2 + 2x – 15
5 x2 – 3x + 2
6 x2 – 4x – 5
7 x2 – 9
8 x2 + 4x + 4
9 x2 – 14x + 49
10 x2 – 21x + 108
11 x2 – 9x + 20
12 x2 – 4x – 21
13 4x2 – 33x + 8
14 6x2 + 16x + 8
15 3x2 – x – 10
16 8x2 – 10x – 12
17 14x2 – 53x + 14
18 6x2 – x – 15
19 9x2 + 42x + 49
20 15a2 + 26ab + 8b2
21 6m2 – 5mn –6n2
22 10p2 – 11pq +3q2
23 3a2 + 7ab –6b2
24 6x2 + xy –12y2
25 25a2 – 4b2
26 a2 – ab – 2b2
27 18p2 + 15p – 12
28 2x2 + 8
29 27y3 – 27y2 + 9y – 1
30 1 – 4x2 – 12x
31 2x2 + 4x – 6
32 a = 16 b = −4
33 4x2 = > multiple of 4
35 c = 6
36 d = 4 or −4
Chapter 17
Exercise A 1 x = 7
2 x = 6
3 x = 2
4 x = −45
5 x = 1.5
6 x = −2
7 x = 5
8 x = −2.25
9 p = −7.5
10 y = 2.5
11 a = −0.25
12 k = 0.5
13 y = 2
14 d = −3
15 x = 2.5
16 x = 1.75
Exercise B 1 x = 3
2 x = 4
3 x = 2
4 x = 10
5 x = 3
6 x = 1
7 x = 1
8 x = 3
9 x = 3
10 x = 3
11 x = 4.5
12 x = 5
13 x = 2
14 x = 2
15 x = −3
16 y = 1
17 p = − 15
18 a = 710
19 t = −4
20 y = 1.5
Exercise C 1 x = 8
2 x = 1
3 x = 7
4 x = 0
5 x = 3
6 y = 1 711
7 a = −1 18
8 t = −2
9 p = 58
10 h = 0.5
11 x = 6
12 x = 5
13 y = 13
14 x = 3 12
15 x = −20
16 x = 3
Exercise D 1 x = 4
2 x = 20
3 x = 6
4 x = 27
5 x = 35
6 x = 8
7 x = 50
8 x = 3 13
9 x = 9
10 x = −2
11 x = 1 12
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201413
12 x = 715
13 x = 15
14 x = 12
15 x = 17
16 x = 11
Exercise E 1 x = 1 4
11
2 x = −5
3 x = 2 47
4 x = − 811
5 x = 81
6 x = 9
7 x = 13
8 x = 7
9 x = 19
10 x = 1 517
11 x = − 58
12 x = 1 811
Exercise F 1 1
2 b × 7 = 21, base = 6 cm
2 n n n3 4
2 24= + =,
3 a x x− =7 34
b x = 28; he had 28m of rope.
4 a 80 13
− =x x
b x = 60, she has spent £60
5 a 13
15
50 180x x x+ + − =
b x = ° ° ° °150 100 30 50; , ,
6 a x x x
x
− + + + −
+ − =
15 3 27
3 68
14
12
b x = 40; 25cm, 13cm, 13cm, 17cm
7 125, 127, 129
8 336 + 24k + 44 = 500; k = 5
9 24
Chapter 18 1 a 19, 22, 25
b 59, 52, 45c 1.0, 1.2, 1.4 d 43, 50, 57e 22, 28, 35 f 57, 65, 73g 1, 7, 0 h 46, 51, 56i 0, −10, −22j 6.25, 3.125, 1.5625
2 a 3, 6, 9, 12b 26, 24, 22, 20c 1, 10, 100, 1000d x, x + 4, x + 8, x + 12e 1000, 100, 10, 1f n n n n,
2, ,
4 8
3 a Half the previous term 1 1
234
38
, ,
b Subtract 1; 96, 95, 94c Multiply by 2; 16, 32, 64d Subtract 0.5; 4, 3.5, 3e Subtract 6; 5, −1, −7f Subtract 7; −3, −10, −17g Subtract 5; −4, −9, −14h double the previous term
64, 128, 256i Subtract 8; −5, −13, −21j Subtract 13; −10, −23, −36k Add the two previous
terms 8, 13, 21l Subtract 5; 2, −3, −8
4 a 13, 31; Add 6b 23, 59; Add 12c 76, 58; Subtract 9d 91, 75; Subtract 4e 37, 52; Add 15f 27, −1; Subtract 7
5 a 25, 36, 49b 84, 119, 160c 57, 74, 93
6 a 2n b 3n + 1 c 3n – 3 d n + 20
e 4n – 3 f 3n + 7 g 2n – 5 h 30 – 5n or −5n + 30 i 6 – 2n or −2n + 6 j 4 – n or −n + 4k – 3n
l n
n + 5
7 a 7, 8, 9, 10 b 6, 12, 18, 24 c −1, 0, 1, 2 d 5, 8, 11, 14 e −5, −3, −1, 1 f 1, 4, 7, 10g 8, 12, 16, 20 h −1, −2, −3, −4i 7, 12, 17, 22 j −1, −3, −5, −7k 2, −1, −6, −13l 7, 13, 23, 37
8 9n – 6
9 3n – 4 100th term = 296
10 14th term
11 a 51b s = 5p +1c 76d 16
12 a T = 3n + 1b K = 4r – 1 c P = 5m – 7d w = 2d + 5
13 a Squares 1, 5, 9, 13, 17, 4n – 3b 15th
14 a 4, 6, 8, 10, 12, 2n + 2b 38c 38d No nth = 25.5 not possible
15 (n + 2) (n + 3) – n(n+5) Expand brackets n² + 5n +6 − n² – 5n = 6
16 15 terms
17 1st, 3rd
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201414
Chapter 19
Exercise A 1 4(2x + 5)
2 3(x + 2)
3 3(3x – 4)
4 5(x – 6)
5 8(2 + x)
6 3(3 + 5x)
7 4(3 – 4x)
8 4(2 – 3x)
9 4x(x + 4)
10 6x(x + 5)
11 4x(2x – 5)
12 3x(3x – 5)
13 3(2x + y)
14 2(2a – 5b)
15 a(5 + 7a)
16 2x(3x – 2)
17 a(3a – b + c)
18 y(4x + 2y – 1)
19 2y(1 + 4x)
20 3a(3a + b)
21 4ab(2 – b)
22 a2(a + b)
23 x2(2 – y)
24 3x(2x2 – 5y)
25 5ab(a + 3b)
26 3a(4bc + 5b2 – ac)
27 4xyz(2x + y + 3)
28 2πr(h + r)
29 x2(3 – x2)
30 2pq(3p + 5q² + 4q)
Exercise B 1 (k + m) (a + b)
2 (p² – 2) (p + 3)
3 (a + c²) (b – c)
4 (x – z) (x + 1)
5 (2a² – t) (3a + t)
6 (m – t) (m + n)
7 (r² + 1) (r + 1)
8 (a – 8) (c + 1)
9 (c – 8) (6c – d)
10 (2a + 3d) (6c – b)
Exercise C 1 (x + 3)(x – 3)
2 (x + 8)(x – 8)
3 (x + 14)(x – 14)
4 (x + y)(x – y)
5 (5 + y)(5 – y)
6 (4 + c)(4 – c)
7 (a + 100)(a – 100)
8 (9 + s)(9 – s)
9 (x – 6)(x + 6)
10 (7 – y)(7 + y)
11 (3x – 5)(3x + 5)
12 (2y – 3)(2y + 3)
13 (1 – 8t)(1 + 8t)
14 (x – 11y)(x + 11y)
15 (9a – 4b)(9a + 4b)
16 (6a – 5b)(6a + 5b)
17 (10 – 7y)(10 + 7y)
18 2(x – 5y)(x + 5y)
19 p p+
−
1
101
10
20 (0.5a + 0.6b) (0.5a – 0.6b)
21 a 117
b 14
c 80 000
22 7x² + 6x or x(7x + 6)
Exercise D 1 (x + 3)(x + 1)
2 (x + 4)(x + 3)
3 (x – 1)(x – 4)
4 (x + 20)(x + 1)
5 (x + 9)(x + 1)
6 (x + 5)(x + 4)
7 (a – 8)(a – 1)
8 (a – 2)(a – 8)
9 (y – 6)(y – 5)
10 (x – 16)(x – 1)
11 (x + 5)(x – 3)
12 (x + 7)(x – 1)
13 (x – 7)(x + 2)
14 (x + 9)(x – 4)
15 (x + 10)(x – 1)
16 (a + 6)(a – 2)
17 (b + 8)(b – 3)
18 (c – 9)(c + 4)
19 (x + 14)(x – 1)
20 (a – 7)(a + 3)
21 (x + 2)(x + 6)
22 (2x – 1)(x – 2)
23 (2x – 3)(2x – 1)
24 (4x + 1)(x + 5)
25 (x – 3)(5x – 1)
26 (x – 4)(x + 3)
27 (2x + 3)(x – 4)
28 (3x – 1)(2x + 1)
29 (4x – 3)(2x + 1)
30 (6x + 5)(x – 2)
Exercise E 1 p(p – 1) (p + 1)
2 2(2x + 7) (x – 3)
3 4xy²(3xy + 5)
4 10(b – 1)(b +1)
5 3 (x + 1) (y +2)
6 2(4 + k) (5 – 2k)
7 cannot be factorised
8 (3c + d)(2c – d)
9 (2m + 5n)(4m + 3n)
10 (5w – 3e)(2w + 5e)
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201415
Chapter 20
Exercise A 1 F = 1.19
2 C = 26.85
3 a 140°b 162°
4 a 30 °Cb 248 °F
5 12.7
6 54.1
7 9 1027 cubic units
8 k = 2xp + mk = 850
Exercise B 1 a b = 180 – a – c
b y x c= −5
c t p c= −3
d g p f= + 22
2 hh
= −S ππ
rr
2
2
3 a ut
= −v
4 r C=2π
5 x f ed
= −
6 t p r= − − 18
7 a hb
= 2A
b n a= + 360180
c q A prp
= −
d n Ft m= −4
8 x = 4y
9 xy
= +8
3
10 m Ev
= 22
11 h Vr
= 32π
12 RP
= 100
13 a r Ah
=2π
b a P= −( )1
c c a b= −2 2
d x y= + 43
14 v as u= +( )2 2
15 t Sa
= −30 2
16 x = t2 v2
17 x p q y= + +( )2 2 2
18 v r= 43
3π
19 a u fvf v
= −
b r p qq
= +−
( )11
c x qyp q
= +
d t su a
= +2
2
e r pqt s
= +f x y
y= +
−3 4
1
g y KK
= −3
2
h vf u
u= +( )2 1
20 a equationb identityc expressiond formulae equationf identity
Chapter 21 1 16 days
2 £1.85
3 250 g butter, 350g flour
4 5 hours 20 mins
5 4560
6 30
7 a y = 4wb y = 32c w = 1.5
8 a m = 16h
b m = 0.8c h = 0.16
9 81.25
10 18G
11 64
12 a 921.6 gb 3.5 mm
13 a t is 8 times biggerb t is 27 times smaller
14 p ∝ r2
15 a P = 1000V
b P = 2
16 0.8
17 a It is 19
of its value at the Earth’s surface.
b 6400 km
18 p = 6, r = 16
19 distance needs to be halved
20 1600 m
Chapter 22 1 0 is between –2 and 3 so one
solution is between 1 and 2. x = 1.6
2 0 is between –3 and 3 so one solution is between 0 and 1. x = 0.6
3 0 is between –10 and 4 so one solution is between –3 and –2. x = –2.4
4 0 is between 2 and –2 so another solution is between 0 and 1. x = 0.4
5 1.77
6 5.8
7 4.8
8 2.69
9 2.5
10 19.6
11 3.29
Chapter 23 1 a 4
5b 3
7c 3
5 2 a pq
3
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201416
b 1y
c 35qp
3 a 5x
b x4
c 12x
d 45x
4 a p−1b 3
2
2xyx y−
c 13a
d 43
e xx + 3
f t − 1
5 a 75x −
b 22
xx +
c xx−+
15
d xx+ 4
2
e xx−+
43
f xx2 1−
g 3 12
xx−+
h 3 21
xx
−−
i x bx a
++
j k rk r+−
36
6 a 5 26
a +
b 9 1310
x +
c 8 2115
x −
d 3 11
bb b
++( )
e 8 92 3x
x x+
− +( )( )
f 7 2
12p +
g 1 212− p
h –( )x + 1121
i 7 82
xx x
−−( )
j 4 111 2
mm m
++ +( )( )
k 2 6 51 2
2x xx x
+ ++ +( )( )
l x xx x x
2 2 11 1− −+ −( )( )
m 7 312
aa a
−−( )
n 3 212
pp
+−
o 4 32 6xx+−
7 a 2 6ab
b 2 14
2x yx−
c 16
d 23pq
e m qm q
2
3−+( )
f −23
g −54
h 1i ( )( )
( )( )a aa a+ −− +
3 43 4
j −2p
k xx− 64
l a3
6
m 2 2 12
( )xx
−+
Chapter 24
Exercise A 1 a x = 0, x = 3
b x = 2 x = –6
c x = − 14
d p p= =,12
13
1
e y y= =0 13
,
f x x= = −,12
23
2 a x = –3, x = −1b x = –5, x = 6
c x x= − =,1 213
d x x= =,35
4
e x x= = −,56
4
f x x= = −,12
53
3 a x = 0, x = –4b x = 7, x = –7
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201417
c y = 3, y = –3
d p = 0, p = −16
e h h= = −,16
16
f x x= = −,53
53
4 a x = 0, x = 3b x = 0, x = 4c x = 5, x = –7d x = 0, x = 8e x = −1, x = 4
f x x= − = −,13
3
5 a x = 18, x = 1b x = 0, x = 5
c x x= = −,34
2
d x x= = −,25
3
e p p= =0 112
,
f m m= − = −1 13
,
6 a x = −0.46, x = −6.54b x = −0.10, x = −2.10c x = 1.81, x = −1.47d x = 1.16, x = −1.82e x = 0.85, x = −3.52f x = 0.74, x = 0.15
7 a x =− ±2 14
b x = ±3 372
c x =− ±9 2 29
d x = − ±1 2 53
e x = ±2 22
f x = ±2 2 115
8 a x = −12.4, x = 0.403b x = 0.586, x = 3.41c x = 0.551, t = 5.45d x = −2.58, x = 6.58e x = 0.172, x = 5.83f x = −1.72, x = 0.387
Exercise B 1 x = 2
2 x = 4 or x = −2
3 x = 115
4 x = −0.78 or x = 1.28
5 x = −3 or x = 6
6 x = 4 or x = −3
7 n = −4 or n = 7
8 x = − 34
or x = 2
9 x = − 57
or x = 6
10 p = −0.72 or p = 1.39
11 x = −0.48 or x = 1.19
12 x = −0.19 or x = 0.11
Exercise C 1 10 m
2 17, 19
3 12 cm
4 50 km/hr
5 10p
6 25
7 48.28
8 3.2, 0.3125 (3 15 and 5
16 )
Chapter 25
Exercise A 1
x –3 –2 –1 0 1 2 3
y = 6x + 1 –17 –11 –5 1 7 13 19
2
x –2 –1 0 1 2 3 4
y = 3x – 5 –11 –8 –5 –2 1 4 7
3
x –3 –2 –1 0 1 2 3
y = 4 – 5x 19 14 9 4 –1 –6 –11
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201418
4
a x –2 0 4
y = 3x – 3 –9 –3 9
b
2
0–2
–1 1 2 3 4 x–2–3
–4–6
–8
–10
4
6
8
10
y = 3x – 3
y
c x = 2.3
5
�4 �3 �2 �1 0 1 2
3x + 4y = 12
3 4
y
x
�3
�2
�1
1
2
3
4
5
6
6
�3 �2 �1 0 1 2
2y – 5x = 15
3
y
x
�2
�1
1
2
3
4
5
6
7
8
7 a nob yesc nod yes
8 k = 5
9 a (4,5)
b 5 12
, −
c −2 61
2,
d −3 11
2,
e − −
1 51
212
,
10 a (−1, 7)b (5, 3)
c 5 412
12
,
d 5 4 12
,
e −2 3 1
2,
f − −
6 4 1
2,
11 A(−3, 7)
12 a 7.21b 6.40c 7.28d 8.06e 7.62
13 a 5.39b 8.60c 9.06d 5e 13f 18.79
14 AB = 5 20 BC = 5, AC = 5 20 BC2 = AB 2 + AC 2, 25 = 5 + 20, therefore ABC is a right-angled triangle
Exercise B 1 a 3
b 12
c −2
d 1 12
e 1
2 a 3b 2c 1
5d –4 e − 1
4f 1
6
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201419
3 a 7b – 4c 1d – 1e 2f – 4g 31
2
h − 13
4 a y = 4x + 3 y = 4x + 5b y = 3x – 2 y = 5 + 3xc y = 6 – x y = –x + 3d y = x + 4 2y = 2x + 3e 3x + y = 2 y = 5 – 3x
5 – 4
6 – 12
7 14
8 a (0, 5)b (0, 6)c (0, 0)d (0, 2)e (0, –2)
f 0 14
,−
9 a y = 5x + 1b y = 3x – 8c y = x + 2d y = 10x + 4
10 a A; y = 3x – 5b B; y = 7 – xc C; y = 2x + 3d D; y = 2
11 y = 3x + 7
12 y = 2x – 4
13 a 2y = 3x + 4b y = 3x + 5c 8x + 3y = 24d x + 3y = 9
14 y = 4x + 1
15 y = 3x – 5
16 a y = 4x + 2b y = 4x – 4c y = –3x + 5d y = 2x – 1e y = –2x + 9f y x= −4
525
5
17 y = − 14
x + 10
18 y = 3x + 8
19 y = − 25
x + 2
20 y = –2x + 6
Chapter 26
Exercise A 1
x –2 –1 0 1 2 3 4 5
x2 4 1 0 1 4 9 16 25
+3x –6 –3 0 3 6 9 12 15
–5 –5 –5 –5 –5 –5 –5 –5 –5
y = x2 + 3x – 5 –7 –7 –5 –1 5 13 23 35
1−1
2
−2−4−6−8
468
1012141618202224262830323436
−2−3 2 3 4 5 x
y
y = x2 + 3x – 5
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201420
2
0–1
–5
–10
1
5
2 3 x
y
–2–3
y = 2 + x – x2
3
–2 –1
–5
0
5
10
15y
1 2 3 x
y = 2x2 – 3x – 1
4
1−1
2
4
6
8
10
12
14
16
18
−2 2 3 4 x
y = (3 – 2x)(1 – x)
y
20
5 a
x –3 –2 –1 0 1 2 3
x3 –27 –8 –1 0 1 8 27
–5x 15 10 5 0 –5 –10 –15
x –12 2 4 0 –4 –2 12
b
–2–3 –1
–5
–10
–15
0 1 2 3 x
y15
10
5
y = x3 – 5x
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201421
6 a
x –4 –3 –2 –1 0 1 2
x3 –64 –27 –8 –1 0 1 8
4x2 64 36 16 4 0 4 16
–6 –6 –6 –6 –6 –6 –6 –6
y –6 3 2 –3 –6 –1 18
b
x
y
•
••
•
•
•
•
–3–4 –2 –1 0 1 2
2
4
6
8
10
12
14
16
18
–2
–4
–6
y = x3 + 4x2 – 6
7
x
y
•
•
•
•
•
•
–3 –2 –1 1 20
14
16
18
20
12
10
8
6
4
2
y = 3
y = x3 + 3x2
8
6
4
2
8
10
12y
y = 5x – x3
0 1 2 3 x–1
–2
–4
–6
–8
–10
–12
–2–3
Exercise B 1
1−1
1
−1
−2
−3
−4
−5
−6
−7
−8
−9
−10
2
3
4
5
6
7
8
9
10
11
12
−2−3 2 3 x
y
y = 3x
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201422
2
1−1
−2
−4
−6
−8
−10
2
4
6
8
10
−2−3−4−5 2 3 4 5 x
y
y = −10x
3
1−1
−2
−4
−6
−8
−10
2
4
6
8
10
−2−3−4 2 3 4 x
y
y = 12x
4
1−1
−2
−4
−6
−8
−10
−12
−14
2
4
6
8
10
−2−3−4 2 3 4 x
y
y = 82−x
5
–2 –1 0
5
10
15
20
25
30
35
40
1 32 4 x
y
y = 2.5x
b i 22.5 ii 2.6
6 a x y
–8 5.96–6 3.81–4 2.44–2 1.560 12 0.644 0.416 0.268 0.17
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201423
b
–8 –6 –4 –2 0 2 4 6 8 x
1
2
3
4
5
6y
y = 0.8x
c i x = 3.1 ii x = −7.2
7
10−1
2
4
6
8
10
12
14
16
18
20
22
24
26
27
y
y = 3–x
−2−3 2 3 x
8
−1
2
4
6
8
−2−3 1 32 x
y
10
y = 1
y = 2x + 1
Asymptote y = 1
Exercise C 1 a
30
1
–1
x
y
60 90 120150180210240270300330360
y = cos x
b 60°, 300°
2 a
1
–1
x
y
90 180 270 360
b 45º, 135º
3 140º, 220º
4 a 150°b 60°c 135°d 340°
5 a 240°b 330°c 150°d 270
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201424
6 a x = 5.7° 174.3°b x = 60° 300°c 108.4° x = 288.4°d x = 60° 120°e x = 135° 315°
Chapter 27 1 a £60
b £12c £16
2 a AB and CD b 11:50 c 16 milesd BCe 12 mph
3 a Imran walked 1 kilometre in 20 minutes. He stopped for 5 minutes and then travelled the remaining 9 kilometres in 9 minutes. (Perhaps he got a lift or caught a bus.)
b 32 minutes c 6 minutes d 15 km/hr
4 a
2
1
3
4
5
6
7
1200 1210 1220 1230 1240
Time
Dis
tanc
e fr
om h
ome
(km
)
1250 1300 1310 1320
• •
• •
•
b 15 km/h
5 a t 0 1 2 3 4
H 0 3 4 3 0
b
2
1
3
4
Hei
ght
(met
res)
H
10 2 3 4t
H = 4t– t2
c 4 metresd 1 second, 3 seconds
6 a x 0 1 2 3 4 5 6 7 8
T –16 –15 –12 –7 0 9 20 33 48
b
–10
–20
(Tem
pera
ture
°C
)
10
20
30
40
50
y
x1 2 3 4 5 6 7 8
T = x2 – 16
c –16 °Cd 7.5 minutes
7 a
40
20
(Year)
Mas
s (g
)
60
80
100
120
y
x0 10(2010)
20 30 40 50 60
140
160
b 2030
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201425
8 a
10
20
10
40
60
80
100
(Pop
ulat
ion
Rob
bits
)
120
140
160
2 3 4 5 6 7
(Months)
8 9 10 11 12 x
y
b 32 rabbitsc 7 months
Chapter 28
Exercise A 1 a i x = 1; y = 2
ii x = 2; y = 1 iii x = −2; y = −1 iv x = −4; y = −2b They are parallel so they will never intersect
2
x
y
–2
2
0
6
4
14
12
10
8y = x + 2
y = 3x – 2
1 2 3 4 5
(2, 4)
3
y
x4321 5
y = 4x − 1
x +y = 4
20
18
16
14
12
10
8
6
4
2
0
–2
x = 1y = 3
4 y7
6
5
4
3
2
1
0
–1
–2
–3
x54321
2x + y = 7
2y = x + 3
x = 2.2, y = 2.6
5 (−2, 5) (4, 2) (6, 3)
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201426
Exercise B 1 x = −1, y = 10
2 x = 5, y = −2
3 x = 4, y = 3
4 x = −2, y = −3
5 x = 2 17 , y = −5
7
6 x = 4, y = 3
7 x = 6, y = −2
8 x = 4, y = 3
9 x = −2, y = −3
10 x = −1, y = 31 12
11 x = 5, y = 3
12 x = 1 12
, y = 3
13 x = 8, y = 41 12
14 x = −2, y = 5
15 x = −3, y = −7
16 x = 21 12 , y = −8
Exercise C 1 x + y = 40, x – y = 14,
x = 27, y = 13
2 2 = –2m + c, 1 = 4m + c,
c m
y x
= = −
= − +
1 23
16
16
1 23
,
3 2a + 4c = 27, a + 3c = 17, adult £6.50, child £3.50
4 3p + 2r = 135, 4p + 3r = 190, pen 25p, ruler 30p
5 a = 2c, 2a + 3c = 84, adult £24, child £12
6 a x + y = 46b y + 1 = 3(x + 1) y – 3x = 2c Lan 11 years old, mother 35 years old
7 4.5 hours
8 £24
Exercise D 1 a, b
y8
6
4
2
0
–2
–4
–6
x654321
y = x2 − 6x + 8
x + 2y = 8
y = 2x − 5
c (2.3, –0.5) and (5.7, 6.5)
2 (4.6, 1.7) and (0.9, 3.6)
3 a x = 1, y = 2 or x = –2 , y = 5b x = – 1 1
2, y = –2 1
4 or x = –2, y = –3
c x = 9, y = –6 or x = 1, y = 2
d x = 2.56, y = 7.56 or x = –1.56, y = 3.44
e x = 1, y = 5 or x = –3 1 12
, y = –4
f x = 2.62, y = –1.43 or x = 0.104, y = 2.34
g x = 4, y = 2 or x = –3, y = – 2 23
h x = 2.39, y = 0.706 or x = –0.218, y = 2.66
i x = 10 15
, y = 1 − 25
or x = –1, y = –1
j x = –3, y = –2 or x = 32
, y = 52
Chapter 29 1 a
–2
–4
–6
–8
2
4
6
–2–4 2 4
y = x2 – 2x – 8
x
y
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201427
b i x = 4, x = –2 ii x = 4.7, x = –2.7 iii x = 3.4, x = –1.4
2 a
1
10
20
30
–1–2–3 2 3 4
y = 3x2 – 2x
y
x
b i – 13
ii x = 2.2, x = –1.5
3 a
1
2
4
6
8
10
–1–2–3 2 3 4 5 6–4
12
y = x2 – 2x + 512
y
x0
2
b i x = 5.5, x = –1.5 ii x = 3.4, x = 0.6
4 a
2
–2
–4
–6
–8
–10
–12
–14
–16
–18
–20
4
6
8
10
–1–2–3 1 2 3 4 x
y
y = 5x – 2x2
b i y = 3.1 when x = 1.25 ii x = 2.5, x = 0 iii x = 0, x = 1.5 5 a
1
–1
–2
2
3
4
5
6
10 2 3 4 5
y = x2 – 5x + 6
x
y
–1
b i x = 2, x = 3 ii x = 0.7, x = 4.3
6 a
–1
–2
–3
–4
1
–1–2 10 2 3
2
y = x2 – x – 4
y
x
b i x = 2.6, x = –1.6 ii x = 1.8, x = –0.8
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201428
7 a
2
4
8
10
–1–2–3 1 2 3
6
y = 5 – 12
x
y = x2
y
x
b x2 + 12
x – 5 = 0 c x = 2, x = –2 1
2
8 a
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
2
1
4
3
–1–2–3 1 2 3
5
y = 2x2 + 3x – 9
y
x
b i x = 1.4, x = –2.9 ii x = 0.9, x = –2.4
9 a, b
2
–2–4–6
468
10
14161820
–1–2–3 1 2 3 4
12
y = x2 – 4x
22
y = x – 3
y
x5
c x = 0.7, x = 4.3
10 a
2
–2
–4
–6
4
6
8
10
14
16
18
20
24
26
28
–1–2–3 1 2 3 4 5 6 7
12 y = x2 – 5x + 3
22
8 x
y
b i x = 4.3, x = 0.7 ii x = 5.4, x = –0.4 iii x = 6.5, x = 0.5
11 a
–2
2
6
8
10
–1–2 1 2 3 4 5
4
y = x2 – 3x
x
y
b i x = 3.6, x = –0.6 ii x = 3.7, x = 0.3
12 y = x + 2
13 x2 – 1 = 0
14 a y = 2x – 8
b y = –4x – 2
c y = –x – 1
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201429
Chapter 30
Exercise A 1 a 3, 4
b 3, 4, 5, 6c –2, –1, 0, 1,d –7, –6e –3, –2f –5
2 a –3, –2, –1b 4, 5c 2, 3, 4, 5, 6d –2, –1, 0, 1e –2f –4, –3, –2, –1, 0, 1, 2
3 3
4 –3
5 a x 2b x –3c 1 x 4d –1 x 3
6 a 543210–1–2–3–4
b 543210–1–2–3–4
c 543210–1–2–3–4–5
d 543210–1–2–3–4–5
7 a x 2.5b x 2c x 4d x 3e x 3f x –4g x 5h x 6i x 2.5j x 5k x 3l x 2m x –1
n x 2o x –1 3
8p –1 x 7q 0 x 3
r 12
x 3
s − 25
x 0
t 6 x 10
Exercise B 1
x = –3
y5
x
4
3
2
1
–5 –4 –3 –2 –1–1–2
–3
–4
–5
10 2 3 4 5
R
2
y = x
x
y
–2
–3
–4
–5
–1
1
2
3
4
5
–1 1
0
32 4 5–2–3–4–5
3
x + y = 3
x
y5
4
3
2R 1
0–1–5 1 2 3 4 5–4 –3 –2 –1
–2
–3
–4
–5
4 y = 2x – 1
y
–3 –2 –1 x3210–1–2
–3
–4
–5
5
4
3
2
1
R
5 y
–2 –1 10 2 3 4 5 6 x–1
–2
4x + 3y = 12
6
5
4
3
2
1R
6
x76543210–3 –2–1
y = 2x + 1
y
7
6
5
4
3
2
1
–3
–2–1
y = 4
x = –2
R
7 y5
4
3
2
1
x–5 –4 –3 –2 –1 10 2 3 4 5–1–2
–3
–4
–5
x = 4
y = 3
y = –x
R
8 y7
6
5
4
3
2
1
0 x7654321
3x + y = 6
R
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201430
9
x542
y5
4
3
2
1
–1–2
–3
x = –1
x + 2y = 4
–3 –2 –1 10 3
R
10
x876543210
y8
7
6
5
4
3
2
1
–1–1–2
–2
x = 1
x + y = 5
y = 2x + 1R
11 a y 3b x –1c y x – 3d 5x + 2y 10
12 a x 2 y 1b y x + 1 y –2c y x x 3 d y 2x + 1 y 3 – x y –1
Exercise C 1 a (4, 1)
b (−1, 1)
2 a (5, –1)b (−1, −1)
Chapter 31
Exercise A 1 ABD = ACD, angles in the
same segment are the same size when they touch the circumference.
2 MCO = 90°; the angle between a tangent and a radius is a right angle.
3 PQR + PSR = 180°; opposite angles in a cyclic quadrilateral add up to 180°
4 FPG = 90°; the angle at the circumference of a semicircle is a right angle.
5 Let PQO = x then POQ = 180 – 2x (isosceles triangle) Let RQO = y then ROQ = 180 – 2y (isosceles triangle) POR = 360 – (180 –2x) – (180 – 2y) = 2x + 2y = 2PQR
6 a = 150° (angle at centre = 2 × angle at circumference)
7 b = 65° (angle at centre = 2 × angle at circumference)
c = 25° (angle sum of a triangle = 180° and base angles of an isosceles triangle are equal)
8 d = 35° (base angles of an isosceles triangle are equal)
e = 70° (angle at centre = 2 × angle at circumference or exterior angle of a triangle
= sum of interior opposite angles)
9 f = 128° (angle at centre = 2 × angle at circumference)
10 g = 44° (angles in the same segment)
11 h = 90° (angle in a semicircle)i = 38° (angles in the same segment)j = 52° (angle sum of a triangle)
12 k = 26° (angle at centre = 2 × angle at circumference and angles in the same segment)
13 l = 31° (angles in the same segment)
m = 59° (angle at centre = 2 × angle at circumference and isosceles triangle)
Exercise B 1 b = a = 110° (angles at centre
= 2 × angle at circumference and angles in the same segment)c = 70° (opposite angles of a cyclic quadrilateral)
2 d = 106° (opposite angles of a cyclic quadrilateral)e = 98° (opposite angles of a cyclic quadrilateral)
3 f = 62° (angles in the same segment) g = 32° (angle BAC = angle BDC = 48°, angles in the same segment; angle sum of a triangle)
4 h = 43° (angle in a semicircle and angle sum of a triangle)i = 137° (opposite angles of a cyclic quadrilateral)
5 j = 36°, k = 72°
6 L = 123°, m = 62°
Exercise C 1 a = 55° (angle between radius
and tangent and angle sum of a triangle)
2 b = 40° (perpendicular from centre to chord and angle sum of a triangle)
c = 50° (angle between radius and tangent and angle sum of a triangle)
3 d = 53° (isosceles triangle and angle between radius and tangent)
e = 53° (angle in a semicircle and angle sum of a triangle)
4 f = 24° (angle at centre = 2 × angle at circumference)g = 66° (angle between radius and tangent)
5 n = 9 cm (perpendicular from chord to centre and Pythagoras)
6 OM = 12 cm (perpendicular from chord to centre and Pythagoras)
ON = 5 cm (perpendicular from chord to centre and Pythagoras)k = 17 cm
7 180° – 2x
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201431
Exercise D 1 a = 50° (alternate segment
theorem)b = 80° (alternate segment theorem)
2 c = 65° (alternate segment theorem)d = 55° (alternate segment theorem)
3 e = 25° (angle between radius and tangent)f = 65° (alternate segment theorem)
4 g = 63° (alternate segment theorem)h = 42° (alternate segment theorem)
5 j = 77° (opposite angles of a cyclic quadrilateral)k = 42° (alternate segment theorem)i = 61° (angles on a straight line)
6 l = 51° (alternate segment theorem)m = 66° (angles on a straight line)
Exercise E 1 a = 40° (angle in a semicircle
and exterior angle of a triangle)
2 b = 151° (angle at centre = 2 × angle at circumference and angles on a straight line)
3 c = 55° (angle sum of a triangle and base angles of an isosceles triangles give angle at centre as 110°; angle at centre = 2 × angle at circumference)
4 d = 152° (angle at the centre = 2 × angle at circumference)e = 208° (angles at a point)
f = 104° (angle at the centre = 2 × angle at circumference
5 g = 132° (angles at a point)
6 h = 28° (exterior angle of a triangle and isosceles triangle)
i = 112° (angle at centre = 2 × angle at circumference)
7 j = 22 12
° (3j + j = 90°, angle in a semicircle and
angle sum of a triangle)
8 k = 43° (isosceles triangle and angles in the same segment)
9 L = 65º, m = 65º, n = 50° (alternate segment theroem, angles, in a triangle)
10 p = 80°, q = 65°, r = 35° (opposite angles in cyclic quadrilateral, alternate segment theorem, angles on a straight line)
11 (i) 90°(ii) 2x(iii) 180 − x(iv) 180 − 2x
Chapter 32 1 a = 94 º, b = 68 º c = 111º
d = 54 º e = 75 º
2 w = 112 º, x = 113 º, y = 77 º, z = 67 º
3 p = 34 º, q = 126 º, r = 141 º, s = 146 º
4 e = 20 º, i = 160 º
5 e = 15 º, i = 165 º
6 30
7 45
8 nonagon
9 36º
10 1260º
11 1980º
12 a 47.5 ºb 87 º, 130 º, 143 º, 95 º,
132.5 º, 132.5 º
13 a 58 ºb 10 º, 100 º, 23 º, 105 º, 122 º
14 x = 59º
15 16 sides
16 2340º
17 ext = 16º, 360/16 ≠ integer number of sides ; no
18 A = 30º, D = 60º, C = 90º
19 360x
20 a 13 sidesb 79º
21 octagons 360 902– = 135º
so ext = 45º. 36045
8= sides
Chapter 33
Exercise A 1 p2 = q2 + r2
2 b2 = a2 + c2
3 52 = 32 + 42
4 19 cm2
5 12 cm2
6 6.71 cm
7 8.80 cm
8 9.48 cm
9 14.76 cm
10 15 cm
11 11.62 cm
12 9.38 cm
13 20.78 m
14 14.20 cm
15 6.51 cm
16 117 m (to the nearest metre)
17 199 cm (to the nearest centimetre)
18 9.54 m
19 7.81 cm
20 170 km
21 a Yes 15² + 20² = 25²b No 12² + 12² ≠ 15²
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201432
Exercise B 1
O
O
A
A
1
2
θ
θH
H
2
O
O
A
A
1
2
θ
θH
H
3 sinθ = ab
4 tanθ = dc
5 cosθ = ef
6 sinθ = hg
7 a = 6.34 cm
8 b = 5.60 cm
9 c = 11.8 cm
10 d = 25.0 cm
11 35.2 m
12 19.1 m
13 24.3 cm
14 31.3 cm
15 a = 34.5°
16 b = 32.6°
17 c = 8.58°
18 d = 61.5°
19 a = 2.60 cm
20 b = 99.7 cm
21 c = 10.1 m
22 d = 9.20 m
23 e = 46.7°
24 f = 53.4°
25 42.7 cm
26 32.5°
Exercise C 1 a w = 30.3 cm
b h = 62.5 cm
2 a a = 14 cmb b = 24.25 cmc c = 12.61 cmd 258 cm²
3 a 180 kmb 126 km
4 145.3 cm³
5 l = 2.32 m
6 a a = 21.06 cmb 84.24 cm²
7 16.8 km
8 13.1 cm
9 33.7°
10 120°
11 x = 108.7°
12 34.7 miles north, 197.0 miles east
Exercise D 1 a 7.21 cm
b 33.7°c 7.81 cm d 22.6°
2 a 17.0 cm b 55.6°c 13.7 cm d 64.1°
3 a 4.47 cm b 48.2°c 9.22 cm d 29.0°
4 64.4°
5 5.29 cm
6 15.3°
7 a 23.4° b 49.3°
8 62.1°
9 a 8.22 cm b 10.1 cm
10 a 22.9 cmb i 12.6° ii 60.8°
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201433
Chapter 34
Exercise A 1 Angles are the same but 6 ÷ 4 = 1.5 and
10 ÷ 7 = 1.43 or equivalent explanation
2 In first triangle, 3rd angle = 180 – (72 + 66) = 42° So both triangles have angles 42°, 66° and 72°, so the triangles are similar.
3 A and B; length is 1 12
× width or equivalent statement
(scale factor = 1.25) C and E; length is 1 1
3 × width or equivalent statement
(scale factor = 0.75)
4 equilateral triangles, regular polygons, circles
5 x = 4.8 cm
6 x = 4.2 cm
7 ST = 4.8 cm, SU = 4.2 cm
8 AB = 3 cm, EF = 8.75 cm
9 a PSR = 85°b AB = 10.5 cm, SR = 10 cm
10 a similar, angles are 50°, 60° and 70° in each triangle
b not similar, angles are 65°, 40° and 75° in first triangle angles are 65°, 50° and 65° in second triangle
c not similar, Corresponding sides are not in the same ratio:
35
412
513
≠ ≠
d similar, they are equilateral trianglese not similar, corresponding sides are not in the
same ratio:5
12615
≠
Exercise B 1 BAC and DAE are the same in each triangle
ABC = ADE since they are corresponding ACB = AED since they are corresponding The triangles ABC and ADE are similar since all the angles in each triangle are equal.
2 MON = POQ since they are vertically opposite NMO = OQP since they are alternate ONM = OPQ since they are alternate The triangles MON and POQ are similar since all the angles in each triangle are equal.
3 Using Pythagoras’ theorem, GH = 18cm Using Pythagoras’ theorem, HI = 24cm
GFGH
= =10 818
35
.
FHHI
= =14 824
35
.
GHGI
= =1 83 0
35
The triangles FGH and GHI are similar since all the corresponding sides are in the same ratio
4 KT = 8 cm TL = 8 cm Using Pythagoras’ Theorem KL = = ( )128 8 2cm cm
Using Pythagoras’ Theorem JK = = ( )128 8 2cm cm
KTTL
JKKL
KLKT
JLJK
KLTL
= =
= = = =
=
1 1
2 28 28
168 2
8 228
168 2
2 2= = =JLKL
The triangles JKL and KTL are similar since all the corresponding sides are in the same ratio.
5 x = 7.5 cm
6 y = 7.2 cm
7 p = 11.2 cm q = 15 cm
8 m = 5.6 cm n = 5.25 cm
9 c = 5.25 cm d = 17.6 cm
10 364.5 cm2
11 172.8 cm2
12 0.4 m3
13 11.7 cm
14 a 75 cm b 1.25 litresc 24 000 kg
15 a 4.75 cm b 256 cm²c 2432 cm³
16 a 3.2 cm b 3.73 cm²c 14.18 cm³
17 3024 cm²
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201434
Chapter 35
Exercise A 1 10.9 cm
2 4.79 cm
3 8.36 cm
4 17.0 cm
5 55.4°
6 21.9°
7 22.8°
8 24.0°
9 2.96 cm
10 25.2 cm
11 12.2 cm
12 20.7 cm
13 86.6°
14 101.6°
15 44.6°
16 109.5°
17 a 13.1 cm²b 163.8 cm²
18 59.1 cm²
19 4.9 cm
20 66.0°
Exercise B 1 a 63.6°
b 55.4°c 3.95 cm
2 a 6.18 cmb 50°c 6.09 cm
3 a BC = 250.4 mb BT = 29.4 m
4 a 4.37 cmb 82.8°
5 A = 134.4° B = 29.0° C = 16.6°
6 a 15.7 cmb 5.64 cmc 121.6 cm2
7 4.52 km
8 50.74 cm²
9 a 54.0°b 87.0°c 11.1 cm
10 AC = 3.44 m, BC = 3.18 m
11 5 385 40 55.
sin sin sin,
°=
°=
°PR PQ
PR = 3.42km, PQRR = 5.3km, PQ = 4.36km,
total = 13.08km
12 a 6.84 cmb 12.1 cm
13 Area = 16 800 m², perimeter = 533 m
14 79.9°
Chapter 36
Exercise A 1 a 12 cm
b 8 cm²
2 a 36 cmb 66 cm²
3 a 30xb 36x²
4 a 10x + 10b 5x2 − 3x + 15
5 a 10x + 12yb 2x2 + 18 xy
6 a 23.41 cmb 23.5 cm²
7 320 m²
8 26 cm²
9 1.4 m
10 4.5 m
11 1−57
m
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201435
Exercise B 1 a 12π cm
b 50π m
2 a 42 cm b 0.8 m
3 a 2.5 cmb 8 m
4 a 25.1 cm b 53.4 cm c 123.2 cm
5 a 490.1 mmb 245.0 mm c 27.6 m
6 a 4.46 cm b 0.51 m
7 a 1.34 mb 1.59 cm
8 30.8 cm
9 6.17 cm
10 4.46 m
11 21.4 cm
12 9.06 m
13 a 908 cm2
b 58.1 cm2
14 a 254 cm2
b 10.4 m2
c 3 530 000 mm2
15 3.09 cm
16 7.57 m
17 38.8 cm
18 30.2 m2
19 101 cm2
20 4.52 cm2
21 35.0 cm
22 a 42.8 m2
b 28.6 m
23 9.05 litres
24 76.4 cm2
Exercise C 1 125 cm3
2 a 48.36 m3
b 182.5 m3
3 a 43 200 cm3
b 0.0432 m3
4 4 cm
5 12 500
6 190 cm2
7 324 cm2
8 144 cm3
9 384 m2
10 108 m3
11 408 m3
12 1330 cm3
13 422.55 cm3
14 798 cm3
15 1099 cm3
16 1098.24 cm3
17 a 160 000 cm3
b 25 155 cm2
18 1.285 m
Exercise D 1 62.8 cm3
2 3.18 cm
3 2.54 cm
4 180.96 cm2
5 314.16 cm2
6 50 cm
7 34.14 cm2
8 3.20 cm
9 6.30 cm
10 3451 litres
Chapter 37
Exercise A 1
a i 51.1 cm² ii 70.7 cm² iii 39.3 cm³b i 65.9 cm² ii 108.9 cm² iii 61.6 cm³c i 106.0 cm² ii 169.6 cm² iii 127.2 cm³d i 357.6 cm² ii 704.0 cm² iii 311.7 cm³e i 549.8 cm² ii 703.7 cm² iii 1231.5 cm³
2 8.95 cm
3 677.72 cm2
4 816.74 cm2
5 2412.74 cm3
6 a 980.18 cm3b 1060.98 cm³c 770.15 cm³
7 a 659.73 cm²b 682.44 cm²c 502.86 cm²
8 a 314.16 cm²b 523.60 cm³
9 a 190.85 cm²b 190.85 cm²
10 46.69 cm²
11 94.03 cm3
12 888.30 cm3
13 579.46 cm3
14 a 12 cm³b 57 cm³c 48 cm³
15 6.45 × 6.45 × 6.45
16 2.02 mm
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201436
17 3.39 cm
18 a 805.86 cm3
b 440.33 cm2
19 1.5 cm
20 a 1490 cm³b 503 cm2
Exercise B 1 a 6.03 cm
b 41.4 cmc 25.9 cm d 13.7 cme 47.6 cm
2 a 14.5 cm2
b 161 cm2
c 123 cm2 d 55.5 cm2
e 295 cm2
3 a 19.5 cm b 19.3 cmc 58.8 cm
4 a 57° b 244°c 74° d 65°e 108° f 213°
5 a 10.7 cm b 6.2 cmc 8.3 cm d 3.6 cm
6 a 49.75 cm2
b 34.44 cm
7 a 3.49 cm2
b 11.48 cm
8 a 5.29 cm2
b 11.41 cm
Exercise C 1 length
2 area
3 area
4 area
5 none
6 area
7 none
8 length
9 none
10 volume
11 length
12 area
13 none
14 area
15 none
16 none
17 area
18 volume
Chapter 38
Exercise A 1 a B
A B
40º
7 cm
5 cm
b 4.5 cm
2 a
40° 50°
6 cm
B
A B
b 4.6 cm
3
A C5 cm
3 cm 4.5 cm
B
b <ABC = 81° <BAC = 63° <ACB = 36°
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201437
4 a
6.5 cm
7.4 cm
52 °
BA
C
b 6.1 cm
5 a E
FD 7.7 cm
48° 55°
b 6.5 cm
6
7.2 cm
5.8 cm 6.3 cm
R T
S
b 57°
7 a
5 cm BA
46° 71°
C
b i 4 cm ii 20 m
8
105°
Y
X
5 cm Z
7cm
b 44°
9
5.8 cm
A C
8.3 cm
D
B
4.6 cm
b 13.3 cmc 30.59 cm2
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201438
10
B7.2 cm
A
11
X Y
P
6 cm
2 cm
4 cm
12
110˚
13
8 cm
9 cm
6 cm
point P
b The angle bisectors all meet at one point.
14
A
3.6 cm
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201439
15
X
8 cm
Y
2 cm
16
5 cm
A
C
C
10 cm
8 cm
B
17
3 cm
4 cm
4 cm
10 cm BA
OC D
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201440
18
11 cm
7 cm
A
C
B
9 cm
19
7 cm
A B
C D10 cm
6 cm
Exercise B 1 FrontPlan Side
FrontPlan Side
Front SidePlan
FrontPlan
Side
5Plan Font side
6 sideFontPlan
2
3
4
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201441
Chapter 39
Exercise A 1 a 35 mph
b 62 mphc 50 mphd 64 mphe 54 mphf 69 mphg 115 mphh 45 mphi 45 mphj 1440 mph
2 a 48 km/hb 66 km/hc 62 km/hd 36 km/he 85 1
3 km/h
f 112.8 km/hg 60 km/hh 95 km/hi 2.4 km/hj 0.0864 km/h
3 48 mph
4 112 mph
5 1 hour 40 minutes
6 105 km
7 50 km/h
8Average speed Time taken Length of journey
a) 45 mph 30 minutes 22.5 miles
b) 74 mph 114
hours 92.5 miles
c) 50 km/h 3 hours 36 minutes 180 km
d) 60 km/h 54 minutes 54 km
e) 100 km/h 45 minutes 75 km
f) 90 mph 8 minutes 12 miles
g) 36.4 km/h 6 minutes 3.64 km
h) 48 km/h 1 12
minutes 1200 m
9 56 mph
10 42 mph
11 0800
12 a 60 km/hb 64.3 km/h
13 138.6 km
14 6 minutes 15 seconds
15 a 10 m/sb 18.3
. m/s
c 0.015 m/sd 2.3 m/se 0.25 m/s
16 a 72 km/hb 172.8 km/hc 0.72 km/hd 0.432 km/he 1.2 km/h
Exercise B 1 2 g/cm³
2 a 0.003 kg/cm³b 3 g/cm³
3 1250 g
4 a 3780 gb 3.78 kg
5 80 cm³
6 400 cm³
7 a 5.71 g/cm³b 19.29 g/cm³c 1.07 g/cm³d 1.74 g/cm³
8 0.78125 g/cm³
9 0.06 kg/cm³
10 a 1226.88 gb 59.86008 kg
11 6 cm
12 Density of cone = 1.55 g/cm³ Therefore it will not float.
13 7.33 cm
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201442
Chapter 40 1
Measurement Accuracy Lower Bound
Upper Bound
1 15 cm nearest cm 14.5 cm 15.5 cm
2 5.9 cm nearest mm 5.85 cm 5.95 cm
3 200 cm nearest 10 cm 195 cm 205 cm
4 23.80 s nearest hundredth of asecond
23.795 s 23.805 s
5 464 ml nearest ml 463.5 ml 464.5 ml
6 5.5 m2 1 decimal place 5.45 m2 5.55 m2
7 75.0 cm 1 decimal place 74.95 cm 75.05 cm
8 6000 g nearest 100 g 5950 g 6050 g
2 a 43.25 cm + 81.75 cm = 125 cmb 10.315 seconds + 19.175 seconds = 29.49
seconds
3 a 124.8 cm
b 29.47 seconds
4 a 38 m
b 0.299 kg
5 a 36 m b 0.297 kg
6 greatest 5 hours 1 minute, least 4 hours 59 minutes
7 greatest = 155.5 mm, least = 144.5 mm
8 4.2 m
9 Yes upper bound of sum of weights = 500 g
10 a 27.1875 m2
b 26.697375 m2
11 a 26.1375 m2
b 26.592275 m2
12 a 64.29 km/hb 7.733 cm/second
13 a 61.37 km/hb 7.731 cm/second
14 a minimum width = 25.77 cm, maximum width = 27.62 cm
b minimum width = 4.252 cm, maximum width = 4.345 cm
15 a maximum height = 9.368 cm, minimum height = 6.918 cm
b maximum height = 3.677 cm, minimum height = 3.471 cm
16 a 28.5 cm b 330.75 cm2
17 100 seconds
18 a i 15.8 ii 60.0075 iii 1.512 b i 3 ii 87.4225 iii 2.5
19 a i 1275 ii 435 iii 2.04819277 b i 562500 ii 1165 iii 20.37154879
20 a 3.265 b 3.230623819
Chapter 41
Exercise A 1
1
–1–1 1 2 3 4 x–2–3
–2–3
–4
2D A
C
B
E
3
4
y = 1
x = 3
5–4–5
y
2
1
–1–1 1 2 3 x
x = 1/2
–2–3
–2–3
2B
D
A
C
3
y
y = x
3 a reflect in line y = 12
b reflect in the line y = −xc reflect in the line y = 11
2
4 a Reflect A in the line y = 2 to get Bb Reflect A in the line y = x to get Cc Reflect B in the line x = 31
2 to get D
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201443
5
1
–1–1 1 2 3 x–2–3
–2–3
2C
B
3
4
y
A
D
6 a
1
–1–1 1 2 3 4 x–2–3
–2–3
–4
2B
T
A3
4
5
6
7
5 6 7 8–4–5–6
y
b Rotation 90° clockwise about (5, 5)d Rotation 180° about (0, 3)
7 a Rotation 90° clockwise about the origin (0, 0) b Rotation 90° anticlockwise about (4, 5)c Rotation 180° about (0, 3) d Rotation 90° anticlockwise about the origin (0, 0)
8 a Rotation 180° about originb Rotation 90° clockwise about (2, 1) c Rotation 90° clockwise about (1, 0)
9
1
–1–1 1 2 3 4 x–2–3
–2–3–4
2
DC
A
EB
345678
–5–6
5 6 7 8 9 10–4–5–6
y
10
1
–1–1 1 2 3 4 x–2–3
–2–3
2
C
B
A
D
3
4
5
5
y
11 a Translation 5
0
b Translation 3
3−
c Translation −−
1
2
d Translation −−
6
2
Exercise B 1 a
1
10 2 3 4 x
2
B
A3
4
5
6
7
5 6 7
y
c Enlarge B by a scale factor 13 centre of
enlargement (1, 2)
2 a
1
10 2 3 4 x
2
A
B
3
4
5
6
5 6
y
c Enlarge B by a scale factor of 3, centre of enlargement (0, 0)
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201444
3
1
10
2 3 4 x
2 A
B
3
4
5
6
7
8
5 6 7 8
y
c Enlarge B by a scale factor 25
centre of enlargement (0, 0)
4 a Enlargement scale factor 2 centre of enlargement (0, 0)
b Enlargement scale factor 12 centre of
enlargement (0, 0)c Enlargement scale factor 3 centre of
enlargement (0, 3)d Enlargement scale factor 1
3 centre of enlargement (0, 3)
5
1
–1–1 1 2 3 4 x–2–3
–2–3
–4
2
3
4
5
6
–5
–6
5 6–4–5–6
y
6
1
–1–1 1 2
A B
C
3 4 x–2–3
–2–3–4
23456
–5–6–7–8–9
5 6–4–5–6–7–8–9–10
y
B’
A’C’
7 a enlargement scale factor –2 centre (0, 0) b enlargement scale factor –3 centre (0, 2) c enlargement scale factor –4 centre (4, 2)
d enlargement scale factor – 13 centre (0, –1)
e enlargement scale factor –12 centre (0, –21
2 )
f enlargement scale factor – 13 centre (0, 2)
Exercise C 1 a Translation 1
2−
b Reflection in the line x = –1c Rotation 90° anticlockwise about (0, 0)
d Translation 23−
e Rotation 180°about (1, 2)
f Translation 03
g Rotation 180°about (3, 1)
h Translation −
30
2 a Rotation 90° anticlockwise about (0, 0) b Reflection in the line x = 2 c Rotation 180° about (1, 0) d Rotation 90° clockwise about (1, –1) e Reflection in the line y = –1
3
1
–11 2 3 4 x
–2–3
2
3
4
5
5 6 7 8 9 10C
BA
y
c Rotation 180° about (5, 1)
4
1
–11 2
D
E
F
3 4 x
–2–3
2
3
4
5 6 7 8 9 10
y
c Rotation 90° anticlockwise about (7, 3)
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201445
5
1
–1–1 1 2
A
C
B
3 4 x–2–3
2
3
4
5
5–4–5
y
c Translation 12
6
1
F
D
E
–1–1 1 2 3 4 x–2–3
–2–3
–4
2
3
4
5
6
–5
–6
5 6–4–5–6
y
c Enlargement scale factor –2, centre of enlargement (0, 0)
7
1
–1–1 1 2 3 4 x
A
B
–2–3
–2–3
–4
2
3
4
5
6y = –x
–5
–6
5 6–4–5–6
y
8 Translation −
52 , reflection in the line x = 4
9 a Translation 47−
followed by a rotation 90°
anticlockwise about (1,–5) b Enlargement scale factor 2
7 about (–2, 3)
c Reflection in the line y = x followed by rotation 90º clockwise about (–3, 0)
d Translation −−
45
e Translation 74−
followed by reflection in y = 3
Chapter 42 1 What do you eat for breakfast?
Toast Cereal Porridge Fruit Other Nothing
2 a It is a leading question.b The response section only has Yes and No. It
needs to have Unsure.
3 a It needs to include a time e.g. How often do you eat fruit and vegetables in a day? or How often do you eat fruit and vegetables in a week?
b 4 and 8 are included twice (1–4 and 4–8, 4–8 and 8–12) There is nowhere to record 0 times.
4 a It is a personal question.b What age group do you belong to?A 20−29B 30−39C 40−49D 50−59E 60−69
5 a It is too general, it is not related to the caravan park.
b It does not include an option for other. It does not include an option for none.
c Which of these activities would you like to do while staying at the caravan park? Tennis ? Swimming ? Crazy Golf ? Football ? Other ? None ?
If other, please specify…………………….
6 Do you go to the cinema? ? Yes ? No If yes, how often do you go in a month?
? 1-2 ? 3-4 ? 5-6 ? more than 7 times ? less than once a month
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201446
7 a What type of programme on the radio do you like most?
b When do you listen to the radio? ? morning ? afternoon ? evening ? never
c Do you like competitions and phone-ins on the radio?
? Yes ? Nod Question is too personal and not needed for
this questionnaire
8 a Do you live in the countryside or in the town? ? countryside ? town
How often do your children go to the park |in a week? ? 1-2 times ? 3-4 times ? 5 or more times ? 0 times
b How many texts do you send a day? ? 0 ? 1-10 ? 11-20 ? 21-30 ? more than 30 What were your most recent exam results?c Do you wear glasses or contact lenses? ? Yes ? No How often do you eat carrots in a week? ? 0 times ? 1-2 times ? 3-4 times ? 5 or more timesd Would you describe yourself as musical? Yes ? No ?
Would you say you are good at Maths? Yes ? No ?
Chapter 43
Exercise A 1 a Mark Frequency
0–9 210–19 520–29 1030–39 940–49 4
b
1
2
Freq
uenc
y
3
4
5
7
8
9
10
Mark in test0−9 10−19 20−29 30−39 40−49
6
2 a Height (cm) frequency155 h 160 2160 h 165 6165 h 170 8170 h 175 10175 h 180 11180 h 185 7185 h 190 4190 h 195 2
b
12
Freq
uenc
y
345
789
1011
155 160 165 170 175Height (cm)
180 185 190 195
6
3 a 8 t 9b 40c 30%d 7.7 minutes
4
1
2
Freq
uenc
y
3
4
5
7
8
9
10
11
12
3 4 5 6 7
Height (cm)
8 9
6
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201447
5
5
10
Freq
uenc
y
15
20
25
35
40
50 10 15 20 25Time minutes
30 x
y
30
6 a, b
5
10
Freq
uenc
y
15
20
25
3.63.4 3.8 4.0 4.2Vital lung capacity (litres)
4.4 4.6 x
30
c 124 pupilsd There are more boys than girls with larger
vital lung capacities.
7 a
1 4 7 8
2 1 2 5 8 9 9
3 0 1 1 2 2 5 7 8 9 9 9 9
4 0 1 2 3 5 6 7 7
5 0
Key 3|2 = 32 yearsb i 36 ii 39 iii 36
8 a
Women Men
3 2 1 7
7 3 3 7 9
9 4 2 1 0 4 7 7 7 8
4 3 2 2 2 1 5 1 2 7 8
7 4 4 3 2 1 1 6 1 1 2 2 4 5 9
7 1 7 3 4 6 7
4 2 8 1 2
Key 8|1 = 81 yearsb 8 years
9 a 3.8 cmb 5.2 cmc 5.168̇1̇ cmd 10
10 a 27%b 34%c 32d 41%e 39%f 26%
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201448
Exercise B 1 a negative correlation
b no correlationc positive correlation
2 a
10
Rai
nfal
l (m
m)
20
40
50
60
70
80
90
0 10 20Temperature (˚c)
30
30
b no correlationc nothing can be deduced
3 a b
10
Wei
ght
of T
omat
oes
(kg)
20
40
50
60
70
80
90
100
0 20 3010 40 50Amount of fertiliser (g/m2)
60 70 80
30
b positived reading from pupil's line of best fit
4 a c
10
0
Mile
age
(Tho
usan
ds o
f m
iles)
20
40
50
60
70
80
90
100
0 2 31 4 5Price (Thousands of £)
6 7 8 9
30
b negatived reading from pupil's line of best fit
Exercise C 1 T = 24
2 C = 10
3 T = 107
Chapter 44
Exercise A 1 a 5
b 9c 4.16d 4
2 a 100b 6c 100.875d 101
3 a 1b 6c 1.636d 1
4 a 1b 7c 2.092d 2
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201449
5 a 0–4b 0–4c 5.065
6 a 4–7b 4–7c 7.417
7 a 120 x 130b 130 x 140c 131.273
8 a 58 x 60b 58 x 60c 59.56
9 a 0.3 x 0.6b 0.6 x 0.9c 0.875d 0.25m
Exercise B 1 3
2 7
3 27
4 7
5 151 cm
6 71.6%
7 60%
8 35.1 g
9 £1.80
10 7 marbles
11 Tim, mean = 194 g, range = 220 g Zoe, mean = 208 g, range = 180 g Zoe's potatoes bigger as she had higher mean. Less variation with her potatoes as range was smaller.
12 Aóife; Range = 15, No modal group, Mean = 7.526, Median group 8-9
Clare; Range = 9, Modal group 8-9, Mean = 8.756, Median group 8-9
13 Exposed site: Mean = 10.2, Modal group = 9 ı 10, Median group = 10 ı 11, Range = 8
Sheltered site: Mean = 11.64, Modal group = 11 ı 12, Median group = 11 ı 12, Range = 7
14 a Mean = £26625b Median = £18,095c Median
15 a mode – suitable reasonb mean/median – suitable reasonc median– suitable reasond mean/median – suitable reasone mean/median – suitable reasonf mode – suitable reasong mean/median – suitable reasonh mode – suitable reason
Chapter 45
Exercise A 1 a 190
b 80c 11.6%
2 a Mass (m grams) Cumulative frequencym 40 7m 50 19m 60 43m 70 75m 80 93m 90 98
m 100 100
b
0
20
40
60
80
100
20 40 60
Cum
ulat
ive
freq
uenc
y
Mass (g)
UQ
M
LQ
80 100
c Median = 62, interquartile range = 17
3 a
Height (cm) Frequency Cumulative frequency 10 15 15 20 23 38 30 36 74 40 42 116 50 24 140 60 10 150
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201450
100
20
40
60
80
100
120
140
160
UQ
Cum
ulat
ive
freq
uenc
y
M
Height (cm)
LQ
20 30 40 50 60
b Median = 30.5, interquartile range = 18.5c 150 – 103 = 47
Exercise B 1 a 24
b 19.5c 24 – 14 = 10d 420e 480 – 260 = 220
2 a 46b 62 – 30 = 32c 5d 29 – 10 = 19e 40 – 35 = 5
Exercise C 1
0 2 4 6 8 10 12 14
2
0 2 4 6 8 10 12 14 16 17
3
20 22 24 26 28 30 32 34
4
32 34 36 38 40 42 4430
5
0 2 4 6 8 10 12 14 16
6
2 4 6 8 10 12 14 16 18
Exercise D 1
a i £320 ii £300 iii £150b i £200 ii £200 iii £100e.g.c Men have a higher median wage than women.
Men have a bigger range than women.
2 Girls spend longer on average (girls’ median = 64 seconds, boys’ median = 36 seconds); the spread of times for the boys is very slightly less than the spread for the girls (girls’ interquartile range = 35 seconds; boys’ interquartile range = 34 seconds).
3 a
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
Alice
Ronnie
30
b
c Ronnie has a bigger range than Alice. Alice has a bigger interquartile range than
Ronnie. Medians very similar but Alice’s median is
slightly higher than Ronnie’s.
4 a i 156 cm ii 15 cm iii 60 cm
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201451
b i 160 cm ii 19 cm iii 60 cmc The boys have a higher median than the girls
The boys have a larger IQ range than the girls. d i ii
120 130 140 150 160 170 180 190
Boys
Girls
5 Kevin if you want the chance of a really fast time, as his mean time is faster, so Kevin is generally faster but is not as consistent (higher IQ range). Dermot if you want to rely on his time, as he is more consistent (lower IQ range).
6 a Make B – if you are buying one battery you need it to be a reliable one.
b Make A – if you are buying a large quantity the spread is less important and the higher average life is more important.
Chapter 46
Exercise A 1
20
1
0
Freq
uenc
y D
ensi
ty
2
40 60 80 100 120 140Height (h cm)
160 180 x
y
2
0.1
0.2
0.3
Freq
uenc
y D
ensi
ty
0.4
0.5
1000 300200 400 500Amount raised (£)
600 700 800 9001000
3
0.2
0.4
0.6
Freq
uenc
y D
ensi
ty
0.8
1.0
1.2
1000 300200 400 500Amount earned (£)
600 700 800 9001000
4 a 10b 47c 72
5 a Money Raised (£) Frequency
0 < m 50 15
50 < m 100 25
100 < m 200 30
200 < m 500 45
500 < m 800 18
b £257.14
6 a 24b 262c 60.1̇7 6715̇ minutes
7 They have the same range Most people leaving on the 10.00 are older, than people leaving on the 0800
Exercise B 1 a Not everyone is represented in the telephone
book. Young people are not included. b Only people who use the train will be
included.c Only people who eat out are included.
2 a Roisin needs 3 pupils from each class. She should use random numbers to obtain 3 pupils from each class or pick names from a hat.
b Roisin needs 6 boys and 9 girls to make up her sample.
3 a To ensure each of the 4 departments are represented fairly.
b A 17, B 5, C 25, D 13 or A 18, B 5, C 25, D 12c Use random numbers or pick names from a hat.
4 a The method is not suitable, the people being sampled were all at the football match.
b The method is suitable.c The method is not suitable, nothing is
sampled from in between.
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201452
5 a Not suitable. These people will own a car (or some may be passengers).
b Not suitable. Not everyone is registered to vote.c Not suitable. People who do not use the bus
are excluded.
6 a 24 b 6
7 a 23 males 27 females b 38 adults 12 children
8 a 25b 15c 80
9 a 60 b 60
10 a 2 b 10
11 84
12 250
13 200
14 a 500 b Time period too big
Chapter 47
Exercise A 1 a score Relative frequency
1 0.152 0.173 0.184 0.165 0.176 0.18
b Yes, For a fair dice each score should have probability 1
6 = 0.166... or 0.17.
All the relative frequencies for Pete's dice are close to this value.
2 a Flavour Relative frequencyPlain 0.28Salt and vinegar 0.22Cheese and onion 0.38Other 0.13
b There is large number of trials.
3 a 0.84 b 0.16
4 a score Relative frequency1 0.072 0.173 0.314 0.305 0.15
b No. For a fair five-sided spinner, each score should have a probability of 1
5 = 0.2
5 0.15
6 27
7 0.25
8 0.21
9 0.27
10 a 0.17b 0.47c 0.32d 0.27e 0.46
11 a 0.85b 0.65
12 a 0.003b i 0.15 ii 0.01 iii 0.91 iv 0.18c i 0.0081 ii 0.0009
13 a 710
b 12
c 45
14a i 0.09 ii 0.3 iii 0.15b i 0.19 ii 0.49 iii 0.61 iv 0.45
Exercise B 1 1
12
2 0.42
3 14
Higher GCSE Mathematics for CCEa Practice Book © Hodder & Stoughton Ltd 201453
4 a 0.21 b 0.09
5 a 0.42b 0.46
6 a 0.225 b 0.775 c 0.275
7 a 715
b 115
c 815
d 715
8 a 0
b 121
c 27
d −57
9 a 31105
b 1021
10 a 16169
b 1169
c 8169
Exercise C 1 a
Tea
Coffee
Muesli
Muesli
Toast
Toast
Grapefruit
Grapefruit
b 16
c 13
2 a
R
W
R
W
11
15
11
15 415
R
W
1115
415
415
b i 16225
ii 88225
3 a
cycles
bus
0.3
0.1
0.4
0.2
0.5 Shopping
car
0.5
canteen
gym
0.1
0.4
0.5 Shopping
canteen
gym
0.10.4
0.5Shopping
canteen
gym
b i 0.15 ii 0.1
4 a
Gazette
News
13
23
water
orange
cola
15 2
5
25
water
orange
cola
15 2
5
25
b i 115
ii 25
5 a
boy
girl1220
820
boy
girl
719
1219
boy
girl
819
11 19
b i 3395
ii 4895
6 a
red
black
613
red
black
612
612
red
black
512
712
713
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