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Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 1
ANSWERS TO fOuNdATiON GCSE MATHEMATiCS fOR CCEA PRACTiCE BOOK
Chapter 1 1 a 46 392
b 52 035 c 8 065 017
2 a Twenty-seven thousand four hundred and thirty-eight
b One hundred and fifteen thousand nine hundred and one
c Thirteen million six hundred and twenty thousand and twenty-four
d Two million and five hundred thousand
e Six hundred and one thousand
3 a 3 hundredsb 3 tensc 3 thousandsd 3 unitse 3 tens of thousandsf 3 millions
4 sum = 52 difference = 16 product = 612
5 a 193b 2341
6 a 1363b 7749
7 a 163b 1545
8 a 256 b 4038
9 a 230b 7100c 1230d 45 000
e 1300 f 3770 g 36 200 h 4800 i 60 j 1500 k 24 000 l 1200
10 a 23 b 71 c 73 d 45 e 13 f 38 g 590 h 860 i 2030 j 654 k 349 l 800 000
11 a 32 b 8600 c 12 000 d 59 e 320 f 6500
12 a 53 and 27 b 25 and 5 c 2 and 14 d 27 and 68 e 5 and 14 f 68 and 37
13 a < b = c < d = e > f < g =
h < i >
14 300 pencils
15 200 students
16 154 boxes
17 576 light bulbs
18 49
19 21 years
20 947 000
21 1 315 750
22 No. It is only true when you multiply a whole number by 10. It is not true when you multiply a decimal number by 10, e.g. 2.8 × 10 = 28
23 2
24 £18
25 372 g
26 26 km
27 79 446
Chapter 2 1 a Tens
b Thousands
c Tenths
d Hundreds
e Thousandths
f Tens
g Hundredths
h Units
i Tens of thousands
j Millions
2 a 7.003, 7.06, 7.1, 7.13, 7.3
b 1.118, 1.25, 1.291, 1.3, 1.8
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 2
3 a 63.4
b 97
c 218.3
d 745
e 8053
f 960
g 4
h 50
i 6100
j 30.6
k 81.3
l 94
4 a 8.37
b 3.159
c 0.64
d 0.289
e 0.6473
f 0.8
g 1.3
h 0.04
i 0.006 17
j 0.05
k 0.002 1
l 0.002 49
5 a 100
b 10
c 1000
d 1000
e 10
f 100
g 1000
h 100
6 a 35
b 1750
c 920
d 325
e 18
f 225
g 1720
h 81200
i 13100
j 7125
k 1250
l 3
10000
m 3
20
n 25
o 1531000
p 103500
q 1171000
r 21500
7 a 0.1
b 0.25
c 0.2
d 0.7
e 0.75
f 0.6
g 0.15
h 0.48
i 0.11
j 0.375
k 0.175
l 0.007
m 0.85
n 0.015
o 0.625
p 0.4
q 0.29
r 0.9
s 0.34
t 0.145
u 0.011
8 a 15
, 0.23, 14
, 0.3
b 25
, 0.403, 0.45, 12
c 0.3, 0.32, 38
, 39100
9 £4.65
10 48 km
11 5.46 seconds
12 28
13 a 15.04
b 5.67
c 1.4
d 0.78
e 27.19
f 4.96
g 31.2
h 2.43
i 4.8
j 2.292
k 0.134
l 8.0549
m 10.389
n 4.791
o 0.169 344
p 34.8
14 Yes. 58
= 0.625 which is
greater than 0.6
15 125
16 £441.25
17 £5.75
18 a £2.80 b £6.12 c £1.50 d £2.40 e £0.70 f £3 g £0.85 h £0.02
19 a 0.03 seconds b 0.2 seconds
20 3.54 km
21 7 apples
Chapter 3 1 7, 33, 89, 661, 921
2 6, 98, 302, 442, 1002
3 a 7652 b 2576 c 7625
4 a 1, 5, 7, 35 b 1, 2, 4, 5, 10, 20
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 3
c 1, 13 d 1, 2, 4, 7, 14, 28 e 1, 2, 4, 11, 22, 44 f 1, 2, 3, 4, 5, 6, 10, 12, 15,
20, 30, 60 g 1, 2, 3, 4, 6, 7, 12, 14, 21,
28, 42, 84 h 1, 7, 13, 91 i 1, 2, 4, 8, 16, 32, 64 j 1, 2, 3, 5, 6, 9, 10, 15, 18,
27, 30, 45, 54, 90, 135, 270 k 1, 2, 5, 10, 25, 50, 125, 250 l 1, 2, 3, 5, 6, 10, 11, 15, 22,
30, 33, 55, 66, 110, 165, 330
5 a 9, 18, 27, 36, 45 b 7, 14, 21, 28, 35 c 50, 100, 150, 200, 250 d 200, 400, 600, 800, 1000 e 0.2, 0.4, 0.6, 0.8, 1 f 105, 210, 315, 420, 525
g 12
, 1,1 12
, 2,2 12
h 13, 26, 39, 52, 65 i 12, 24, 36, 48, 60 j 15, 30, 45, 60, 75 k 35, 70, 105, 140, 175 l 60, 120, 180, 240, 300
6 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
7 31, 37
8 a 1, 3, 5, 15 b 1, 3, 9 c 1, 7 d 1, 2, 4 e 12 or 24 f 30 or 60 g 24 or 48 h 30 or 60
9 a 35
b 48
c 64
d 117 e 51
f 24 × 53
10 a 256 b 343 c 14 641 d 1 048 576 e 9 765 625
f 65 536 g 4096 h 1 i 729 j 625 k 18 l 1
11 a 36 b 27 c 12 d 5 e 1 f 15 g 9 h 121 i 4 j 8 k 25 l 32
12 9, 643 , 23, 42
13 a 8 b 6 c 16 d 8
14 a 12, 36 b 15, 125, 1000 c 41, 19 d 36, 121 e 1000, 125
15 a −47, −34, 9, 15, 56 b −15, −14, −1, 8, 10 c –20, –15, –12, –7, –6 d –600, –420, –112, –90, –84
16 a −4 oCb 7 oC
c −13 oC d −8 oC e −29 oC f −25 oC g 13 oC h −25 oC
17 −£285 or £285dr
18 15 oC
19 −4 oC
20 No, factors of 49 are 1, 7, 49 (A prime number has exactly two factors)
21 1 has only one factor
22 64
23 Yes. Because 8 is a factor of 16, the factors of 8 will also divide into 16
Chapter 4
Exercise A 1 a 1, 2, 3, 4, 6, 12
b 1, 2, 3, 6, 9, 18c 6
2 a 1, 2, 4, 5, 10, 20b 1, 2, 3, 5, 6, 10, 15, 30c 10
3 a 9b 8c 12d 18e 1f 15g 14h 17i 18j 42k 21l 36
4 a 3, 6, 9, 12, 15, 18b 5, 10, 15, 20, 25, 30c 15
5 a 4, 8, 12, 16, 20, 24b 6, 12, 18, 24, 30, 36c 12
6 a 24b 35c 30d 36e 24f 18g 60h 120i 160j 180k 120l 240
7 2, 3, 5, 7, 11, 13, 17, 19
8 a 23 × 3
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 4
b 2 × 32 × 5c 22 × 3 × 52
d 3 × 72
e 3 × 52 × 11f 22 × 3 × 5 × 7g 2 × 3 × 5 × 7 × 11h 23 × 32 × 52
i 22 × 32 × 17j 24 × 32 × 52
k 2 × 53 × 7l 23 × 3 × 37
9 16
10 120
11 24
12 882
13 a Falseb Truec Trued Falsee Truef Falseg Falseh False
14 a 15 bagsb 11 oranges, 14 lemons
15 6th September
16 a It does not equal 60. It should be 22 × 3 × 5
b It does not equal 80. It should be 24 × 5.
c 1 is not prime. It should be 34.
d 6 is not prime. It should be 22 × 3 × 52.
e 25 is not prime. It should be 2 × 53.
f It does not equal 315. It should be 32 × 5 × 7.
Exercise B 1 a 32
b 74
c 103
d 45
e 112
f 63
g 24
h 53
i 37
j 85
k 2 × 73
l 52 × 94
m 34 × 63
n 42 × 84
o 23 × 32 × 5 × 62
p 73 × 84 × 9
2 a 25b 125 c 10000d 64e 64f 128 g 196h 343i 32j 1k 81l 216m 256n 161 051o 1024p 1q 39.304r –32s 36t 81u 16v –27w 28x 1y 530.8416z 1
3 a 36
b 79
c 25
d 58
e 87
f 910
g 411
h 312
i 64
4 a 32
b 44
c 85
d 53
e 76
f 63
g 25
h 33
i 96
j 85
k 46
l 79
m 38
n 72
o 20 or 1
5 a 38
b 76
c 98
d 59
e 228
f 412
g 88
h 610
i 330
6 a 29
b 85
c 107
d 59
e 84
f 311
g 56
h 98
i 26
j 6k 34
l 46
m 612
n 514
o 215
p 420
q 810
r 324
s 89
t 710
u 127
7 a 48
b 86
c 52
d 35
e 66
f 1111
g 320
h 716
i 36
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 5
8 a 3b 4c 9d 5e 5f 6g 7h 11i 7
Chapter 5
1 a 34
b 38
c 45
d 58
e 510
or 12
f 915
or 35
2 a 5b 12c 20d 18e 72f 24g 45h 88i 90j 84k 2l 7m 9n 7o 32p 135
3 a 12
b 35
c 34
d 23
e 78
f 34
g 45
h 45
i 34
j 47
k 79
l 45
m 23
n 34
o 23
p 1013
4 a 16
, 14
, 13
, 38
b 310
,
720
, 25
,
12
c 512
,
715
,
35
, 1320
d 716
,
920
,
35
,
58
5 a 35
b 2127
c 6070
d 416
6 a 15 kg
b £13
c 12
d £12
e 3.4
f £58
g 28 cm
h 27
i £2800
j 21.6 m
k 210 mm
l £660
7 13
8 a 59
b 3 boys
9 29
10 5
12
11 36 km
12 49
= 52117
613
= 54117
Finn has read most as 54117
is greater than 52117
13 5
14 Dan by 4 minutes
Chapter 61 a 1
25
b 214
c 147
d 612
e 523
f 356
g 59
10
h 338
i 813
j 429
k 4411
l 735
m 516
n 934
o 847
p 1412
q 579
r 513
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 6
2 a 72
b 114
c 256
d 149
e 198
f 145
g 223
h 2910
i 236
j 192
k 237
l 254
m 438
n 416
o 499
p 317
q 414
r 809
3 a 5710
b 235
c 125
d 1212
e 314
f 89
100
g 513
100
h 6725
i 334
j 11125
k 621
200
l 91320
4 a 7.5b 3.25c 8.9d 6.4e 2.333…f 4.125g 2.15h 5.07i 4.6363…j 7.65k 23.75l 35.1666…
5 a 57
b 118
c 815
d 1112
e 4170
f 1324
g 710
h 1712
i 1635
j 1815
k 17190
l 4144
6 a 35
b 1324
c 940
d 221
e 815
f 2360
g 712
h 740
i 1033
j 1330
k 940
l 552
7 a 115
b 512
c 335
d 25
e 18
f 14
g 118
h 718
i 12
j 12
k 37
l 1
8 a 38
b 16
c 120
d 332
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 7
e 115
f 340
g 12
h 115
i 310
j 215
k 1549
l 110
9 a 25
b 516
c 23
d 115
e 258
f 34
g 114
h 115
i 1
j 121
k 24
l 13
10 a 328
m2
b 15
14 metres
11 3 packets
12 5 pints13 4
15
14 720
15 a 2536
cm2
b 313
cm
Chapter 7
Exercise A1 a 8
b 312
c 535
d 256
e 61115
f 635
g 103
10
h 151130
i 512
j 618
k 41724
l 121120
m 5335
n 15340
o 42355
p 1214
2 a 312
b 335
c 537
d 23
10
e 3720
f 2940
g 4536
h 35
24
i 51970
j 51720
k 11730
l 178
m 13144
n 2330
o 23740
p 31718
3 a 1516
b 1118
c 1120
d 58
e 1720
f 416
g 438
h 579
i 61
20
j 415
k 712
l 6m 5
12
n 21
32
o 21112
p 3715
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 8
4 a 423
b 114
c 814
d 1112
e 2740
f 2544
g 935
h 2845
i 1033
j 11
12
k 515
l 2910
m 216
n 1114
o 3521
p 11125
5 51920
km
6 241
10 tonnes
7 Yes. 23
× 7 = 423
kg,
434
− 423
= 112
kg left
8 a 4415
kg
b 11115 kg
9 113
43
÷
10 a 35
12
b 2732
c 214
d 1627
Exercise B1 a 0.4̇
b 0.3̇4̇
c 0.1̇43̇
d 4.3̇7̇
e 0.71̇2̇
f 5.0̇12̇
g 0.03̇19̇
h 3.1̇749̇
i 0.93̇
j 0.93̇6̇
k 0.09̇34̇
l 1.9̇
2 a 0.333…
b 0.777…
c 0.3999…
d 0.203 203 203…
e 0.421 212 1…
f 3.282 828…
g 9.172 172 172…
h 0.093 209 320 932…
i 0.174 444…
j 0.291 061 06…
k 0.314 231 42…
l 8.190 216 161 6…
3 a 0.3̇
b 0.4̇
c 0.6̇
d 0.7̇
e 0.83̇
f 0.083̇
g 0.26̇
h 0.5̇71 428̇
i 0.8̇
j 0.583̇
k 0.38̇
l 0.8̇1̇
4 59
and 16
5 0.03̇
6 Joy. 23
is 66.6̇% which is bigger
than 66%
7 a >b <
c >d <e <f <g <h >i =j <k >l <
Chapter 81 a 2
b 6c 12d 12e 35f 7g 24h 3i 3j 31k 9l 20m 342n 49o 28p 207q 22r 1s −5t −3u 0v −4w −12x −9
2
Nearest 10
Nearest 100
Nearest 1000
a 6870 6900 7000
b 1240 1200 1000
c 9370 9400 9000
d 1930 1900 2000
e 780 800 1000
f 12 370 12 400 12 000
g 28 770 28 800 29 000
h 74 500 74 500 75 000
i 370 400 0
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 9
Nearest 10
Nearest 100
Nearest 1000
j 1110 1100 1000
k 20 090 20 100 20 000
l 19 320 19 300 19 000
m 789 270 789 300 789 000
n 499 690 499 700 500 000
o 999 670 999 700 1 000 000
3 a 3.2b 8.8c 31.1d 11.3e 9.5f 6.2g 21.9h 133.0i 9.5j 2.1k 8.9l 6.0m 58.0n 4.0o 21.1p 0.5q 3.7r 314.9s 90.0t 129.9u 1999.0v 47.0w 0.0x 200.0
4 a 9.83 b 12.64c 2.04d 98.58e 9.02f 8.95g 12.90h 1.01i 3.96j 92.78k 9.89l 9.90m 172.34n 18.91o 3.23p 78.86q 20.00
r 1.90s 50.00t 0.60u 1.85v 0.00w 2.50x 1.24
5 a 2.884b 83.448c 7.909d 1.827e 9.857f 3.885g 0.815h 1.804i 9.990j 12.004k 1.773l 34.293m 8.772n 1.237o 2.337p 0.896q 9.126r 8.040s 0.690t 29.999u 99.400v 1.004w 2.598x 3.000
6 a 2000b 4000c 50 000d 8e 20f 0.01g 0.008h 0.02i 0.9j 1k 500 000l 8000m 20 000n 7o 2p 10q 7r 0.001s 0.06
t 8u 10v 30w 1x 1
7 a 2400b 3900c 54 000d 8.5e 16f 0.014g 0.0079h 0.018i 0.94j 0.99k 540 000l 8000m 16 000n 7.0o 2.0p 13q 7.0r 0.0014s 0.060t 8.0u 14v 27w 1.0x 1.0
8 a 2370b 3870c 53 700d 8.49e 16.3f 0.0143g 0.007 92h 0.0184i 0.942j 0.995k 539 000l 8050m 16 000n 7.05o 2.01p 13.0q 7.00r 0.001 40s 0.0604t 7.99u 14.0
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 10
v 27.0w 0.996x 1.00
9 a £2.08b £89.34c £128.48d £3.50e £0.70f £7.00
10 a 7.7b 5.2c 2.80d 4.31e 7.416f 24g 16h 154i 2.65j 1.71
11 1.1
12 36 849
13 a 95 b 104 c 475 d 624
14 a 750 b 849
Chapter 9
Exercise AAccept appropriate alternative estimates throughout
1 a 90b 400c 2100d 2e 37f 27g 19.2h 0.14i 16j 40k 360 000l 766m 0.7n 1040
o 8000p 400q 0.64r 570s 600t 160u 1600v 2020w 40x 270
2 a 70b 30c 10d 50e 700f 30g 400h 200i 240j 500k 6l 80
3 £50 000
4 2400 litres
5 80 000 light bulbs
6 £1400
7 5 boxes
8 60 miles per gallon
9 £1400
10 a £56b £240c £3200
11 4400
12 a 40 000 m2
b 800 m
13 Accept appropriate estimates.a 5.1b 6.9c 5.5d 10.2e 4.2f 12.4g 7.3
h 11.2i 8.8j 14.1
Exercise B 1 a 149 − 56 = 93
b 97 + 186 = 283c 1495 ÷ 23 = 65d 25 × 64 = 1600e 62.23 ÷ 6.35 = 9.8f 812 25. = 28.5g 84 × 28.5 = 2394
2 a 125b 195c 76d 275e 512f 428g 1728h 37 736i 146j 174k 109.5l 121.4m 2081n 457o 142 450p 15.75
3 a 150b 2000c 4d 76e 890f 800g 61h 8.2i 0.53j 2.6k 0.79l 81m 0.9n 60.8o 5100p 70
4 a 8.1b 16.4c 27.5
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 11
d 8.61e 4.4f 3.5g 5.28h 5.55i 33.99j 4.56k 8.58l 8.75m £38.94n £16.73o £9.19p £4.18
5 a 1.2
b 3.5
c 4.8
d 1.8
e 16.1
f 34.4
g 38.4
h 25.2
i 21.6
j 9.52
k 26.7
l 165.6 m 11.1 n 10.8 o 63.72 p 32.76
6 a 0.6
b 0.8
c 0.53
d 7.4
e 0.56
f 1.28
g 7.83
h 1.77
i 2.4
j 19.25
k 0.652
l 5.24 m 0.128 n 0.02 o 2.606̇ p 2.895
7 a 0.32 b 0.18
c 0.3 d 0.06 e 0.04 f 2.4 g 6.3 h 6.6 i 11.5 j 9.1 k 55.8 l 48 m 28.8 n 34.8 o 4.41 p 86.4
8 a 60 b 50 c 170 d 90 e 400 f 500 g 6 h 250 i 540 j 145 k 3640 l 482 m 187.6 n 10.5 o 10.85 p 35.8
9 a 6b 8c 24d 48e 5f 4.2g 0.9h 21i 23.8j 14.4k 5.1l 4.2m 35 kgn 4.5 mlo £3.50p 3.75 mg
10 a 9b 0.7
c 0.8 mld £0.80e 0.85f 1.6g 4.35h £0.30i 10.5j 10.2k 6.3l £28.60m 5.4n 20.46o £16.56p £9.36
11 a 14b 26c 13d 135e 21f 47g £126h £19.20i £4.95j £2.20k £3.12l £3.50m £1.80n £1.50o £1.89p £0.14
12 a =b >c <d >
13 a > b < c = d <
14 a 10 320b 120c 10.32d 860
15 a 399 b 142.5 c 28 d 3.99
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 12
16 a 3.375b 202 500c 2.025d 600
17 32.4 km
18 £17.61
19 4
20 7
21 5
22 12
Chapter 10
Exercise A 1 a subtract 4
b add 3
c divide by 2
d multiply by 5
e subtract 10
f divide by 8
g multiply by 0.5
h add –8
2 a 15, 18, 22b 2, 7, 10
3 a 6, 10, 13 b 4, 0, −4 c 28, 105, 224 d 6, 10, 19
4 a 32
b 5
c 18
d 110
e 54
f 34
g 49
h 314
i 52
j 57
k 423
l 100301
5 0
6 a 16
b 83
c 56
d 1041
e 2067
f −5
Exercise B 1 a 13
b 14c 11d 3e 15f 6g 15h 10i 23j 20k 12l 10m 11n 52o 48p 13q 10r 8s 0t 46u 8v 40w 30x 14
2 a 18b 9c 6d 5e 30f 35g 7
h 20i 7j 7k 4l 18m 14n 6o −12p −5q −21r 17s 17t 32u 11v 5w 14x 112
3 a 25b 64c 46d 44e 54f 32g 33h 23i 100j 64k 162l 32m 100n 48o 25p 5q 36r 31s 5t 75u 324v 12w −7x 16
4 a 27b 16c 20d 8e 7f 12
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 13
g 23h 12i 3j 9k 27l 225m 21n 32o 137p 28q 37r −3s −15t 33u 23v 13w −77x 0
5 a 8 × (7 − 4) = 24b 20 ÷ (2 + 3) = 4c (3 + 4) × 2 = 14d (10 − 4) × 3 = 18e 10 − (3 + 7) = 0f 6 × (1 + 4) = 30g (2 + 3) × (6 − 1) = 25h 3 × (2 + 1) × 2 = 18i 6 + 8 × (7 − 4) = 30j (12 + 6) ÷ (5 − 2) = 6k (11 − 4) × (3 + 2) = 35l (6 − 2)2 × 3 = 48
6 a 2b 3c 6d 21e 4f 4g 24h 1i 7j 4k 3l 3
Chapter 11 1 a 1
2
b 710
c 920
d 225
e 825
f 17100
g 625
h 1920
i 150
j 34
k 3350
l 2125
m 13200
n 13
o 157500
p 3500
q 1 15
r 172000
2 a 0.83
b 0.14
c 0.27
d 0.4
e 0.09
f 0.085
g 0.65
h 0.03
i 0.1
j 0.99
k 0.098
l 0.063
m 0.121
n 3.3
o 0.002
p 1.4
q 0.0005
r 0.0394
3 a 71%
b 20%
c 90%
d 75%
e 3%
f 55%
g 52%
h 94%
i 60%
j 65%
k 8.7%
l 37.5%
m 95%
n 84%
o 17%
p 7.5%
q 81.25%
r 1.6%
4 a 75%
b 64%
c 12%
d 40%
e 8%
f 3.6%
g 94%
h 83%
i 90%
j 11.4%
k 7%
l 2.1%
m 21.3%
n 72.25%
o 3.75%
p 120%
q 105%
r 2.01%
5
Fraction Decimal Percentage
a310
0.3 30%
b710
0.7 70%
c35
0.6 60%
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 14
Fraction Decimal Percentage
d925
0.36 36%
e18
0.125 12.5%
f81
2000.405 40.5%
g11
4000.0275 2.75%
h25
0.4 40%
i625
0.24 24%
j1725
0.68 68%
k1720
0.85 85%
l1920
0.95 95%
m 125
1.4 140%
n 3 12
3.5 350%
6 a 0.4, 41%, 44100
b 57%, 35
, 0.63
c 0.7, 34
, 77%
d 320
, 0.18, 19.5%
7 70%
8 82.5%
9 60%
10 85%
11 86%
12 60%
13 25%
14 a £5
b 72 g
c 60 m
d £840
e 17.5 km
f 130 litres
g £45
h £112 i 183.6 m
j £19.88
k 31.72 cm
l £204.18
m 146.2 g
n 346.48 ml
o 165.36
p £106.25
15 a £2.84
b £0.62
c £0.06
d £62.67
e £5.99
f £0.34
g £0.07
h £2.57
i £10.43
j £3.49
k £37.96
l £56.30
m £1.61
n £29.93
o £28.62
p £4.82
16 6 boys
17 £96
18 63
Chapter 12
Exercise A 1 a 45
b 84c 384d 224e 2.1f 96.6g 0.95h 444i 16.15j 7.2k 0.24l £26.03
m 300 gn 87o £4p 1125
2 a £33b £64c 114d £75.52e £412.50f 27.6 gg 149.04 kgh 698.64 mi £2.37
3 £42
4 £99.20
5 £1512
6 5 light bulbs
7 £54.60
8 38 684
9 a £7.60
b £45.60
10 £37.80
11 a £482
b £102
12 £1432
13 £1140
14 a 1345 unitsb £175.93c £8.80d £184.73
15 £96
16 £150
17 £1456
18 £4611.20
19 £14.40
20 £9033.50
Exercise B1 a 24%
b 55%c 75%
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 15
d 6%e 2%f 13.5%g 12.5%h 20%i 6.4%j 14%k 80%l 5.7%
2 85%
3 60%
4 54.8%
5 44%
6 7.5%
7 13.5%
8 7.0%
9 28.3%
10 20%
11 27.8%
Exercise C 1 a £18.81
b –£29.19c –£487.54d £970.80e £2470.80
2 a £16b –£40c –£72.50d –£2.50e –£243.45f £1136.55
3 a £307b £207c £76.50d £116.75e £39.05f £2037.40g £170
4 £136
5 6 hours
Chapter 13 1 a £6000
b £24 000
2 £21 600
3 £23 800
4 £138.60
5 £9.24
6 399 miles
7 a £2484b £684
8 2096
9 5.13 g
10 £194 616
11 a £5848b £2752c No, if it fell by 35% it
would be £5590
12 £330.75
13 a £594.88b £44.88
14 a £5306.04b £306.04
15 £62
16 Bank A. She will get £10.91 more interest
Chapter 14 1 a −2
b −4c 0d −6e 6f −8g −9h −23i 5j −18k 11l −1m −9n −12o 1
p 26q −8r −8s −12t −5u −45v −27w −4x 6
2 a 3b −6c −6d −2e −28f 12g 4h −12I −14j 4k −13l 4
3 a −12b −30c −28d −18e 24f −20g −35h −55i 35j 56k −48l 16m 24n −30o −8p −18
4 a −5b −6c 6d 7e −32f −12g −4h −5i 6j −7
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 16
k −7l –0.3m −9n −32o −4p –2.5
5 a −5b −4c −5d −7e −1f −40g −21h −100i 8j –3.8k −3l −0.5
6 a 6 and –6b 10 and –10c 13 and –13d 1 and –1
7 A negative number multiplied by 10 will give a smaller number, e.g. –5 × 10 = –50
8 No. A negative number divided by 2 will give a larger number, e.g. –8 ÷ 2 = –4
Chapter 15 1 a 5:3 b 3:5 c 4:5 d 5:3:4 e 4:3:5
2 a 1:2 b 3:2 c 3:4 d 3:2 e 5:6 f 7:10 g 4:5 h 4:5 i 6:1 j 40:43 k 4:7 l 3:6:5
m 3:4:6 n 1:6:10 o 6:8:9 p 1:3:4
3 a 1:15 b 1:9 c 5:1 d 3:20 e 25:4 f 2:3 g 3:7 h 24:5 i 30:1 j 4:3 k 5:3 l 50:1 m 5:1 n 3:50 o 3:1 p 14:3
4 a 8:20 b 30:48 c 42:49 d 54:60 e 16:24:56 f 15:35:40 g 2:7:9 and 18:63:81 h 1:5:12 and 6:30:72 i 31.5 j 28.8 k 19.25 l 28.6
5 16 males
6 160 g
7 2304 cm2
8 a 40 ml b 180 ml
9 £136
10 390 ml
11 24 sweets
12 a 59
b 49
13 a 18
b
78
14 a 512
b 13
15 1:3
16 3:2
17 3:4
Exercise 16 1 a £4, £16
b £15, £3 c £8, £20 d £27, £63 e £70, £50 f £800, £2200 g £6, £12, £24 h £40, £60, £140
2 £51, £34
3 £36
4 £60
5 £24
6 108º
7 12 sweets
8 45º, 90º, 90º, 135º
9 54p
10 £5.85
11 48 minutes
12 21 minutes
13 375 g plain flour, 5 eggs, 50 g sugar, 600 ml buttermilk
14 1000 g mince steak, 750 g tinned tomatoes, 2 1
2onions,
1500 ml cheese sauce
15 a 8 oranges (38 p per orange) b 3 litres of milk (57 p per litre) c 60 minutes (2.6 p per minute) d 500 g of butter (0.44 p per gram)
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 17
16 a €14.16b €354c €80.83d £200e £35f £52.54g £83.05
17 a $1825.68b $684.63c $179.53d £5000e £45 000f £354.94g £36.99
18 a €27.36b £263.16c $317.50d €982.68e $608.08f £884.10g £1381.41. Yes, they can
afford the painting
Chapter 17 1 a 6
b 3c 11d 14e 16f 19g 24h 26i 31j 30
2 a 01000b 01001c 00111d 00101e 01010f 01100g 10001h 10100i 10111j 11001
3 a 100b 1101c 1111d 10010
e 10110f 11011g 100000h 101000i 110111j 111100k 1000001l 1001010m 1010000
4 a 21b 28c 33d 36e 41f 45g 82h 50i 63j 66k 72l 83m 100
5 a >b <c <d >
6 It ends with 1
Chapter 181 a x + 10
b 10 − yc 8cd d − 4
e w5
f 4m
g 20e
h w2
i xyj 30 + xk 5x
l n3
m 2 − d
2 a 9 m + 4 6 e − 4
b 7 c − 3 12 d + 3
c 15 3h 7
w3
d 6
t2
16 2x
e 4n 4w 8c 3p 5e
f m3
a 45k 6e
g5
3
3 a x + 5b x − 4c 3xd 3x + 2
4 a n − 3 b 4n c 4n − 1 d 4n + 5
5 a 9xb 4yc 6xd 11y e 6xf 9x + 8yg 3x + 10yh 7x + 3yi 9x2 j 5x + 8y k 11x + 5yl 2x + 6ym 4yn 5x − 3y
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 18
o 9x2 + 3xp –3xq 15x − 2yr −3x − 4y − 2y2
6 a 9b 19c 21d 2e 6f 30g 80h 27i 18j 10k 65l 53m 13n 43o 2p 6q 18r 15s 10t 25u 10v 3.5w 51x 50y 36
7 a 8pb 4mc 15yd 2cte 7w2
f 24d2
g 63efh 60g2
i 16gj h3
k 3hl 6e2f 2
m 22cd2
n 7jo 24x2y2
8 a 10x + 4b 10
9 5n + 2
10 4x + 13y
11 a 26x + 10b 50x + 12x2
12 a x7
12
b x7
10
c x6
d x
20
e x14
15
f x17
40
g x17
30
h x29
30
i x17
18
j x7
8
k x19
40
l x
55
13 a 2xyb 5cdc 6abd 10nme 2abf 4xyg 9fgh 8pq
Chapter 191 a x = 3
b x = 8c x = 5d x = 13e x = 8f x = 19g x = 4h x = 1i x = 8j x = 12k x = 20l x = 9m x = 8
n x = 4o x = 18p x = 50q x = 14r x = 4s x = 4t x = 3.5u x = 0v x = 3 1
3
w x = 2 15
x x = 123
2 a x = 4b x = 3c x = 1d x = 2e x = 6f x = 7g x = 3h x = 4i x = 7j x = 0k x = 7l x = 4m x = 7n x = 4
o x = 7 45
p x = 5.5
q x = 4 23
r x = 14
s x = 2 25
t x = 8.5
u x = 56
v x = 3.5w x = 2.5x x = 0.85
3 a x = 4b x = 5c x = 7 d x = 12e x = 3f x = 10
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 19
g x = 5h x = 8i x = 21j x = 50k x = 4l x = 5m x = 6n x = 2o x = 0p x = 7q x = 2r x = 6s x = 8t x = 11u x = 8v x = 6w x = 4.5x x = 7.5
4 a x = 7b x = 4c x = 5d x = 16e x = 3f x = 5g x = 6h x = 6i x = 1j x = 8k x = 11l x = 4m x = 5n x = 13o x = 9p x = 9q x = 7r x = 15s x = 6t x = 7u x = 0v x = –6w x = –3x x = –1
5 a x = −3b x = −1c x = −4d x = −2e x = −3f x = −4
g x = −6h x = −1i x = −3j x = −4k x = −2l x = −9m x = −3.5
n x = −1 13
o x = −5
p x = − 14
q x = −2 15
r x = 15
s x = −1 14
t x = − 13
u x = −2 15
v x = −0.5
w x = − 45
x x = − 45
6 a 3 + 6 = 9 incorrectb 17 − 5 = 12 correctc 2(7) + 3 = 17 incorrectd 4(2.5) − 5 = 5 correcte 7 − 10 = –3 incorrect
7 a 2x = 24b x − 8 = 30c x + 7 = 12d
3x = 8
e 4x = 24f 3x + 4 = 25g
2x − 3 = 8
h 2x = 80i 5x = 400j 2x + 10 = 66k 7x + 5 = 24.60l 11n + 10 = 230m 5x + 2 = 10.75
8 a x = 12b x = 38c x = 5d x = 24e x = 6
f x = 7g x = 22h x = 40i x = 80j x = 28k x = 2.80l x = 20m x = 1.75
Chapter 201 a 3x + 6
b 5y + 20c 2t + 10d 30 + 6pe 12 + 4xf 27 + 9vg 12x + 20h 10 + 10ni 4e + 8fj 20x + 30wk 15g + 10hl 21a + 35b
2 a 4x − 12b 5d − 10c 3y − 9d 30 − 5te 18 − 9xf 55 − 11pg 6x − 4h 8g − 4i 28v − 63j 18 − 12xk 48x − 42yl 10w − 15e
3 a −2x − 6b –4y − 8c –5m − 5cd −3t − 6ye –16f − 24gf −30x − 36yg –2t + 8h –9a + 27i –3v + 21j –20 + 15wk –77x + 88yl –12m + 54n
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 20
4 a 5x + 6b 4y + 17c 8m − 10d 6x − 6e 8e − 2f 7c + 17g 7x + 17h 11x + 13i 6x − 16j 4x + 29k 3x + 21l –2x + 8
5 a 2(w + 5)b 3(m + 4)c 5(y − 4)d 2(e − 7)e 3(2m + 1)f 5(3d + 4)g 6(5g − 2)h 4(4i − 5)i 9(2n + 3)j 6(1 − 4c)k 10(2i + 3f)l 7(x + 3y)m 9(m − 4n)n 6(2e +3g)o 4(10j +9k)p 8(p − 2q)q 7(3h − 4e)r 4(t + 8k)s 12(5i − m)t 15(2w + e)u 15(3x − 2y)
6 a x + 10b 5x c 5 (x + 10) or 5x + 50
7 a n – 5b n + 8c 3(n – 5) or 3n – 15d 4(n + 8) or 4n + 32e 7n + 17
Chapter 211 a x2 + 4x
b y2 + 5yc m2 + 3md 3e − e2
e t2 − 4tf a2 − 5ag xy + x2
h 9m − m2
i c2 + cdj 5d − d2
k x3 + 4xl w2 − 2nw
2 a 8x + 10b 9x + 12c 3x + 7d 7y + 6e 7y + 10f 5y + 16g 7c + 4h 7di 6m + 6j 8e − 19k 10x + 19l 23a − 39m 3x + 6n –2x − 10o 10x + 7yp 11x − 13yq 2x − 8yr 7ts m2 –3m − 4t 2xu 13y − 2y2
v 7x + 7yw 4x − y − cx ab + 4ac + 3b
3 a 12x + 20b 10a2 − 6a
4 a 30b 170
5 55 cm2
6 a x(5 + y)b e(4 − t)c g(2 − n)d i(10 + m)e h(1 + x)f w(3 − c)g y(y + 1)h e(e + 3)i h(1 − h)j x(1 + 5x)
k w(1 + 2n)l c(5 − c)m m(1 + m2)n d(7d − 3)o e(5e − 4h)p f(6g − 5)q x(3y + 5e)r x(8x − 5t)s k(2m − 3k)t b(7c − 4b)u c(ab + de)
7 a 3x(e + 2y)b 5w(3c − d)c 4e(2y + 3)d 2m(3c + 5)e 5y(2e + 5)f 3h(3y − 4)g 10i(2x − 3)h 4x(2y + 1)i 5c(4d − 1)j 7e(1 − 2y)k 3d(d + 3y)l 2y(3x + y)m 6m(2f − m)n 5x(3x + 2y)o 8n(2n − e)p 10i(3y − 4i)q 4e(e2 − n)r 3x(2y − x2)s 2w(5c + 4w − 3)t 5x(2x + y − 3x2)u 4b(2a + 3b − c)
Chapter 22
Exercise A1 a x = 3
b y = 12c d = 4d x = 16e c = 6f m = 5g g = 3h h = 4i x = 8j c = 3k y = −5l d = −3
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 21
m x = −7n e = −10o x = 3
12
p h = 59
q w = −3
r t = 323
s m = −123
t x = − 45
u y = −312
v x = 37
w x = 0
x p = 25
2 a x = 8b m = 35c c = 32d w = 24e d = 100f y = 16g x = 30h e = 24i h = 12j x = 6k t = 28l c = −30m n = −12n r = −8o t = −24p x = −15q y = −32r d = −14s t = 21t b = −45u c = 12v x = 120w x = 0x p = −45
3 a x = 3b x = −2c x = −3d x = 3e x = 1f x = 2g x = 7
h x = 3i x = 4j x = 15k x = −10l x = 4m x = −40n x = 40o x = −2p x = 3q x = 24r x = 3s x = 35t x = 6u x = 30v x = 5w x = 12x x = −1
4 a x = 3b y = 7c w = 10d m = 1e e = 2f g = 3g x = 7.5h d = 3
23
i n = 115
j t = 1
38
k c = 14
l y = 13
m x = −1n m = −3o w = −4p p = 0
q y = − 12
r x = −2s t = 10t x = 3u x = 2v x = 6w x = 1x x = 3
5 a x = 6b y = 8c m = 5d e = 4
e t = 10f d = 3g f = 2h w = 2i t = 4j y = 3k c = 4l x = 3m h = −7n y = −6o a = −2p x = 2q y = 1r c = 4s d = 2t x = 10u t = −1v y = 2w b = −2x g = 4
136 a x = 5
b x = 2c y = 10d d = 2e h = 10f w = 3g x = 2h t = 3i d = 1
j c = 112
k m = 30l y = −22m m = −30n y =
1
14
o t = 4p p = 4q g = 1r x = 3
s x = 13
t x = −323
u x = −125
v x = 1w x = 1
x x = 112
7 a always trueb sometimes truec never true
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 22
d sometimes truee never truef sometimes trueg always trueh sometimes true
Exercise B1 a 2x + 40 = 180 x = 70º
b 4x + 140 = 360 x = 55ºc 5x + 15 = 180 x = 33ºd 3x − 12 = x + 6 x = 9ºe 4x + 100 = 360 x = 65ºf 2x + 38 = 180 x = 71º
2 4x + 8 = 56 x = 12
3 3x + 3.20 = 15.20 x = 4
4 2x − 10 = 130 Cost of drink is 70 pence
5 2(x + 4) = 15, x = 3.5
6 5x − 3 = 27 Biggest field is 12 acres
7 3x + 6 = 201 Kyle’s mass is 73 kg
8 3x + 5 = 350 100 drinks were sold on Wednesday
9 75 cm2
Chapter 23
Exercise A1 a i £2.40 ii £6 iii £12 iv £8.40
b 11 ice-creams
2 a i £105 ii £255 iii £90
b 6 hours
3 a £70b £40
c £60d £65
4 a £204.20b £254.60c £179
5 a i 2 hours 45 minutes ii 6 hours 30 minutes iii 4 hours 15 minutes iv 3 hours 52 minutes
30 secondsb 4 pounds
Exercise B 1 a C = 3n
b T = 2y
c y = e + 10d N = 4xe H = 10ef m =
3w
g T = 5 (x + y)h P = 3abi C =
8a + b
j Y = a2
2 T = x + 12
3 T = x + 50
4 N = 30 − x
5 C = 75x
6 C = 3.5y
7 C = 25x + 30y
8 W = 4m + 6n
9 a P = 6.8H + 0.4Mb i £63.20
ii £40.80c 35 hours
Exercise C 1 T = 12
2 W = 13
3 D = 34
4 H = 24
5 L = 22
6 A = 27
7 C = 28
8 Y = 3
9 E = 10
10 y = 4
11 A = 9
12 T = 12
13 C = −20
14 W = 1
15 B = 13
16 F = −8
17 M = 40
18 A = −6
19 N = −4
20 C = 4
21 a equationb expressionc formulad expressione equationf formulag equationh formulai expressionj formulak expressionl equation
Chapter 24 1 A (10, 2)
B (2, 8)C (6, 4)D (0, 5)E (3, 2)F (9, 6)G (5, 7)H (8, 0)I (12, 10)
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 23
2
00
1
2
3
4
5A
IG
D K
B
L
F
C
H J
E6
7
8
9
10
1 2 3 4 5 6 7 8 9 10 x
y
3 O (−4, 0) P (2, −2) Q (−2, 2) R (−2, −3) S (−5, −6) T (3, −4) U (0, 6) V (0, −7) W (−4, 6) X (4, 5) Y (5, 0) Z (5, −7)
4
–1–1
1
2
3
4
5
6
O
X
Q
PS
VU
Y W
R T
Z
0
–2
–3
–4
–5
–6
1 2 3 4 5 6–2–3–4–5–6
y
x
5
–1–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–2–3
(d)
(b)(f )
(a)
(e)
(c)(g)
–4–5–6 654321
y
x
a squareb parallelogramc trapezium
d kitee right-angled trianglef isosceles triangleg rectangle
6 a MAKE HAY WHILE THE SUN SHINES b EARLY BIRD CATCHES THE WORM
Chapter 25
Exercise A1 a A x = −4
B y = −7
C x = −2
D y = 2
E x = 1
F y = 5
G x = 4
H y = −5
b i (1, 5)ii (4, 2)iii (−2, 2)iv (−2, −7)
2 a – j
–10–1–2–3–4–5–6 2 3 4 5 6
–2
–3
–4
–5
–6
–7
–8
1
2
3
4
5
7
8
x
y
y = 8x = 4x = 1
x = 0
x = –2x = –5
y = 6
y = 3
y = –5
y = –7
1
6
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 24
3 a
x 0 1 2 3 4
y 5 6 7 8 9
b
x 0 1 2 3 4
y 3 7 11 15 19
c
x 0 1 2 3 4
y −4 1 6 11 16
d
x 0 1 2 3 4
y 7 10 13 16 19
e
x 0 1 2 3 4
y −6 −4 −2 0 2
f
x 0 1 2 3 4
y 5 3 1 −1 −3
g
x 0 1 2 3 4
y 12 7 2 −3 −8
h
x 0 1 2 3 4
y 0 −1 −2 −3 −4
4a
x −3 −2 −1 0 1 2 3
y 0 1 2 3 4 5 6
b
x −3 −2 −1 0 1 2 3
y −2 0 2 4 6 8 10
c
x −3 −2 −1 0 1 2 3
y −11 −8 −5 −2 1 4 7
d
x −3 −2 −1 0 1 2 3
y −10 −6 −2 2 6 10 14
e
x −3 −2 −1 0 1 2 3
y 14 11 8 5 2 −1 −4
f
x −3 −2 −1 0 1 2 3
y 9 8 7 6 5 4 3
5 a – c
−1−1−2−3−4−5−6−7
−8
1
1
0
2345678
2 3 4 5 x
y
y = 5 − x
y = 2 x + 1
y = 3 − 2 x
−2−3−4−5
Exercise B1 a 3
b 5c 6d 4e 1f −2g −3h −1
2 a y = 8xb y = 3xc y = 4x − 1d y = 2 + 6x
3 a 2b 6c 1d −4e −3f ½
4 a i 0ii 3iii 6iv 2v −3
b i 3ii ½ iii −2iv 1½ v 1
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 25
5 a
Number of duck eggs 1 2 3 4 5
Cost (pence) 30 60 90 120 150
b
0
20
60
100
Pric
e (p
ence
)
Number of duck eggs
Cost of duck eggs
140
1 2 3 4 5
40
80
120
160
c 540 pence or £5.40d 30e The cost per egg
6 a Number of days 1 2 3 4 5
Cost (£) 75 100 125 150 175
b
1
25
50
75
Cos
t in
(£)
Number of days
Cost of hiring a car
100
2 3 4 5 6
125
150
175
7 8
7 a Number of hours 1 2 3 4 5
Cost (£) 55 80 105 130 155
b
10
30
50
70
20
40
60
Cos
t (£
)
8090
100110120130140150160170180
2 4 510 3Number of hours
c i 30 ii fixed charged i 25 ii pay for every hour
8 a £60b £12c £16d call-out feee rate per hour
Chapter 261 a (2, 4)
b (5, 6)c (2, 8)d (2, 7)
e (7, 7 12
)
f (1, 2)g (−2, 3)h (−1, −1)i (−6, 0)
j ( 5 12
, 3 12
)
k (2, −2 12
)
l ( 2 12 , −2 1
2)
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 26
2 a (2, 2)b (1, 0)c (3, −1)d (3, −1)e (1, 4)f (0, 6)g (1, −4)h (−1, −6)
3 a 10b 5c 13d 9.22e 8.06f 9.49g 7.81h 12.81i 18.38j 7.21k 14.87l 7.81
4 a ( 12
, 5 12
)
b 7.616
5 a (7, − 12
)b 6.4
6 LN = 8.94
Chapter 27 1 a
b 1, 3, 6, 10 and 15 c Triangle numbers
2 a
b 1, 4, 9, 16 and 25 c Square numbers
3 1, 8, 27, 64, 125, 216
4 a
b
Pattern number 1 2 3 4 5 6
Number of matchsticks 3 5 7 9 11 13
5 a
b
Pattern number 1 2 3 4 5 6
Number of matchsticks 5 9 13 17 21 25
6 a
b
Pattern number 1 2 3 4 5 6
Number of matchsticks 4 7 10 13 16 19
7 a i 19, 22 ii Add 3b i 80, 160 ii Multiply by 2
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 27
c i 6, 0 ii Subtract 6d i 64, 75 ii Add 11e i 5, 0.5 ii Divide by 10f i 22, 17 ii Subtract 5g i 480 000, 9 600 000 ii Multiply by 20h i 1, 1.2 ii Add 0.2
8 a i 29 and 21 ii Subtract 4b i 27 and 43 ii Add 8c i 1 and 27 ii Multiply by 3d i 6, 48 and 192 ii Multiply by 2e i 45, 30 and 0 ii Subtract 15f i 0.8 and 8 ii Multiply by 10g i 0.8 and 1.04 ii Add 0.08h i 1000 and 62.5 ii Divide by 2
9 a 6, 16, 26, 36, 46 b 40, 34, 28, 22, 16c 11, 22, 44, 88, 176d 1200, 600, 300, 150, 75e 3.6, 3.8, 4, 4.2, 4.4f 3, 7, 15, 31, 63 g 2, 10, 26, 58, 122h 10, 15, 30, 75, 210i 40, 24, 16, 12, 10j 1, 8, 50, 302, 1814
10 a 22b 7c 42
11 a 18b 9c 102
Chapter 28 1 a 23, 28 (add 5)
b 64, 128 (multiply by 2)c 28, 25 (subtract 3)d 34, 40 (add 6)e 7000, 70 000 (multiply by 10)f 2, −3 (subtract 5)g 7.6, 8 (add 0.4)h 6, 3 (divide by 2)
2 a 3, 6, 9, 12, 15b 3, 5, 7, 9, 11c 2, 6, 10, 14, 18d 4, 9, 14, 19, 24e –2, −4, −6, −8, −10f −2, −5, −8, −11, −14g 5, 4, 3, 2, 1h 17, 14, 11, 8, 5i 1, 4, 9, 16, 25j 4, 7, 12, 19, 28k 1, 8, 27, 64, 125l 60, 30, 20, 15, 12
m 12
, 1, 1 12
, 2, 2 12
n 12
, 23
, 34
, 45
, 56
o 1, 12
, 13
, 14
, 15
3 a i 10th term = 20 ii 50th term = 100b i 10th term = 20 ii 50th term = 140c i 10th term = 41 ii 50th term = 201d i 10th term = 10 ii 50th term = −30e i 10th term = −30 ii 50th term = −150f i 10th term = −5 ii 50th term = −85g i 10th term = 100 ii 50th term = 2500h i 10th term = 1
10
ii 50th term = 12
i i 10th term = 10 ii 50th term = 2
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 28
4 a 5nb 2n + 3c 4n +1d 3n − 1e 5n − 2f 10n + 3g n + 5h 6n + 2i 4n − 3j 2n + 5k –3nl –10nm 10 − 2nn 9 − 3no 2 − 5np –1 − 2nq 6 − nr n − 8
5 a
Pattern 4 Pattern 5
b Pattern number 1 2 3 4 5
Number of matchsticks 4 7 10 13 16
c 31d 16e No. 3n + 1 = 80 3n = 79 n = 79
3 79 does not divide exactly by 3 and n must be
a whole number
6 a
b
Pattern number 1 2 3 4
Number of black tiles 1 1 1 1
Number of white tiles 4 8 12 16
Total number of tiles 5 9 13 17
c i 4n ii 4n + 1d 11e 13f 24
7 a
b
Pattern number 1 2 3 4
Number of tables 1 2 3 4
Numbers of chairs 6 10 14 18
c 4t + 2d 7e 12
Chapter 29
Exercise A1 x = 3.2
2 a x = 9.6b x = 5.2c x = 5.4d x = 4.3e x = 1.8f x = 4.7g x = 5.7h x = 2.7i x = 3.6j x = 7.7k x = 4.7l x = 16.5
Exercise B1 a x6
b x14
c x6
d w13
e k16
f h23
g x8
h m5
i e12
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 29
2 a y6
b y9
c y5
d g7
e x9
f x−3 g e8
h m10
i y0 = 1j x8
k x6
l x8
m t7
n t–1
o t–2
3 a y12 b y14 c y25 d x18 e m55 f t0 = 1g x9
h c40
i e56
4 a x16
b y−3
c y7
d n56
e x9
f y7
g m6
h m8
i m−2
j m8
k m9
l m7
m y4
n y15
o m3
5 a 12x5
b 35x6
c 32x3
d 3x8
e 6m3
f 7m9
g 20y2
h 15y6
i 10yj 1k 2yl 4y10
m 9x5
n 5m3
o x5y3
p m3p7
q 4x3y8
r 9y5
Chapter 30
Exercise A1 a x < 4
b y > 2c m 8d t > −5e w < −6f c 10
2 a x = 1, 2, 3, 4b x = 0, 1, 2, 3c x = 3, 4d x = 2, 3e x = 3, 4, 5, 6f x = −2, −1, 0, 1g x = −5, −4, −3, −2, −1h x = −7, −6i x = −3, −2j x = −5k x = 4, 5l x = 5
3 a x = 1, 2b x = 2, 3, 4, 5c x = −3, −2, −1d x = −6, −5, −4, −3e x = 4, 5f x = 2, 3, 4, 5, 6g x = −2, −1, 0, 1h x = −2i x = −4, −3, −2, −1, 0, 1, 2
4 a x > 0b x 10
c x < 0d x > 10e x −4f x −5g x > 5h x < 4i x 4j x > 18k x 16l x −40m x > 4n x 5o x 5p x < 2 2
3
q x > 2 23
r x 1 15
s x > 8 12
t x 4u x < 7v x 4w x > 3x x < 1y x > 9z x − 3
4
5 a 2 < x < 6b 2 x 8c 1 < x 3d 3 < x < 5 1
2e − 1
4 < x 2
f 23
< x < 3 13
g 1 25
x < 4
h 56
x 2
i − 34
x < 0
Exercise B1 a x > 3
b x < 1c x > −2d x −2e 1 x 4f 2 < x < 5g −1 x < 3h −2 < x 2
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 30
2 a −3−4 −2 −1 0 1 2 3 4
b −3−4 −2 −1 0 1 2 3 4
c −3−4 −2 −1 0 1 2 3 4
d −3−4 −2 −1 0 1 2 3 4
e −3−4 −2 −1 0 1 2 3 4
f −3−4 −2 −1 0 1 2 3 4
3 a x 4 −3−4 −2 −1 0 1 2 3 4 5 6
b x < 1 −3−4 −2 −1 0 1 2 3 4 5 6
c −2 x < 4 −3−4 −2 −1 0 1 2 3 4 5 6
d −3 < x 2 −3−4 −2 −1 0 1 2 3 4 5 6
e x 4 −3−4 −2 −1 0 1 2 3 4
f x > −2 −3−4 −2 −1 0 1 2 3 4 5 6
4 a x = 0, 1, 2, 3, 4 −1 0 1 2 3 4 5
b x = −2, −1 −3 −2 −1 0 1 2 3
c x = 1, 2, 3 −2 −1 0 1 2 3 4
d x = 0, 1, 2 −2 −1 0 1 2 3 4
e x = 2, 3, 4, 5 −1 0 1 2 3 4 5 6
f x = 3, 4 −1 0 1 2 3 4 5
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 31
Exercise C1 a x = y − 4
b x = w − tc x = 12y + 4d x = m + 2pe x = 2y − 3f x = 2t − 9c
g x = q3
h x = 47m
i x = 34y
j x = yw
k x = zy
l x = 3wt
m x = 4wn x = pqo x = 3mwp x = 6wtq x = 2d − 7c
r x = 118
g
s x = 7k − 8h
t x = e fab
2 a x = ghb x = 3 + hc x = c − h
d x = wh
e x = w − 5f x = gh + d
g x = p3
h x = 7cdi x = ef + cj x = jk − t
k x = fgk
l x = 8mym x = kp − t − d
n x = w ka+
2
o x = a − 2b − 3w
p x = dm
y3
3 a x = w y−2
b x = m −12
c x = t + 23
d x = e −54
e x = n + 410
f x = c y−2
g x = m d+4
h x = w k−6
i x = 25
t g+
j x = 43e
k x = 132m
l x = n7
m x = 54y
n x = g tn−
o x = m ye+ 2
p x = 4e − dq x = 5d + c
r x = 32
h y+
s x = 4I n
k−
t x = 2(m − 3)u x = 3(e + n)v x = 5(c − t)w x = w(d + 5)x x = gh(D − y)
4 a x = 3 − yb x = c − yc x = 8 − 3pd x = t − ghe x = 5 − tf x = n − 4g x = 5y − wh x = 9wi x = 3 − dj x = m2 − y
k x = 2
m t−
l x = 4
e d−
m x = 3
L k−
n x = −35y
o x = 4(m − 3)p c = 5(d − C)q x = h − 4gr x = n − cI
s x = 3 52
− ed
t x = h tyg−
5 a x = e n−3
3
b x = c + 10
5
c x = d −124
d x = m j−217
e x = i hh
−2
f x = t mm
+ 3
g x = 33
n y−
h x = 105− g
i x = 44
t w−
j x = 3i fi−
k x = km Lk−
l x = m t+ 36
m x = wy dw−3
n x = 3 53
f t−
o x = 3 23
p −
p x = 2 32
y d−
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 32
Chapter 311 a
Pounds (£) 1 2 3 4 5
Thai baht (THB) 40 80 120 160 200
b
0
40
80
120
Tha
i bah
t (T
HB
)
Pounds (£)
Conversion graph for£ and THB
160
1 2 3 4 5
200
240
6 7
c i £2.50 ii 440 THB iii 2800 THB
2 a
100 125 150 1757550Speed (mph)
Conversion graph for mph and km/h
Spee
d (k
m/h
)
250
40
80
120
160
200
240
280
b 96 km/hc 87–88 mphd 750 mphe 400 km/h
3 a
Metres 3 6 9 12 15
Feet 10 20 30 40 50
b
6 9 12 153Metres
Conversion graph for metres and feet
Feet
0
10
20
30
40
50
60
70
c approx. 17 feetd approx. 12.6 me approx. 667 feet
4 a 840 gramsb £25 000c £500 000
5 a 26 kmb 17 minutesc 72 km/h
6 a 8 milesb 5 minutesc 2 milesd 36 mph
7 a 0840b i 20 minutes ii 40 minutes iii 10 km
c 1010 and 1040d 15 km/h
8 a i 10 km ii 20 minutes iii 30 minutes iv 60 km/h
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 33
b
0900 0910 0920 09300850Time
Distance time graph for Neil’s motherD
istan
ce fr
om h
ome
(km
)
08400
2
4
6
8
10
12
9 a 50 minutesb 1 kmc 8 minutesd 1543e approx. 4.3 kmf 14.4 km/hg 10 minutes
Chapter 32
Exercise A1 y = x2 + 5, y = 3x − x2, y = x2 + 6x + 3
2 a
x −3 −2 −1 0 1 2 3
y 9 4 1 0 1 4 9
b
x −3 −2 −1 0 1 2 3
y 13 8 5 4 5 8 13
c
x −3 −2 −1 0 1 2 3
y 6 2 0 0 2 6 12
d
x −3 −2 −1 0 1 2 3
y 0 −2 −2 0 4 10 18
e
x −3 −2 −1 0 1 2 3
y 4 1 0 1 4 9 16
f
x −3 −2 −1 0 1 2 3
y 15 8 3 0 −1 0 3
g
x −3 −2 −1 0 1 2 3
y 1 −3 −5 −5 −3 1 7
h
x −3 −2 −1 0 1 2 3
y 1 6 9 10 9 6 1
i
x −3 −2 −1 0 1 2 3
y −15 −8 −3 0 1 0 −3
3 a
x −3 −2 −1 0 1 2 3
y 12 7 4 3 4 7 12
b
–3 –2 –1 0 1
1
2
3
4
5
6
7
8
9
10
11
12
2 3 x
y
c accept y = 9.2 or 9.3d x = 2.2 and x = −2.2
4 a
x −4 −3 −2 −1 0 1 2 3
y 3 −2 −5 −6 −5 −2 3 10
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 34
b
–3 –2 –1 0 1
1
2
3
4
5
6
7
8
9
10
11
12
2 3 x
y
–4 –1
–2
–3
–4
–5
–6
c x = 1.4 and x = −3.4 d y = −3.75 (accept −3.7 or −3.8) e x = 1.2 and x = −3.2
5 a
x −2 −1 0 1 2 3 4 5
y 6 0 −4 −6 −6 −4 0 6
b
–1 0 1
1
2
3
4
5
6
7
2 3 x
y
–2 –1 4 5
–2
–3
–4
–5
–6
–7
c x = 4 and x = −1d accept x = −6.2 or x = −6.3e x = 4.5 and x = −1.5
Exercise B1 a x = 1, y = 2
b x = 2, y = 1c x = –2, y = –1d x = –4, y = –2
2 a x 0 1 2 3
y 2 3 4 5
b x 0 1 2 3
y –2 1 4 7
c
–1–10
1
2
3
4
5
6
7
8y = 3x – 2
y = x + 2
–2
1 2 3 4 5 x
y
–2–3–4–5
d (2, 4)
3 a x 0 1 2 3
y 1 0 –1 –2
b x 0 1 2 3
y –2 0 2 4
c
−1−1−2−3−4
1
1
0
234
2 3 4 x
y
y = 2x − 2
y =1− x
−2−3−4
d (1, 0)
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 35
4
–1–10
12
3
4
5
6
7
8
9
10
11
12
–2
1 2 3 4 5x
y
–2–3–4–5
y = 4 – x
y = 4x – 1
(1, 3) is the point of intersection
5 a
–1–1–2–3–4–5–6 10 2 3 4 5 6
–2–3–4–5–6–7–8
1
2
3
4
5
6
7
8
x
y
y = –3x
y = x – 2
y = 4 – x y = 2x + 1
b i (−3, −5) ii (3, 1) iii (1, 3) iv (−2, 6)
Chapter 331 a 4 cm b DC c AB or DC d AD and BC e AB and DC f 42 mm
2 a ML or PQ b LQ c ML and PQ
d LQ and ML or LQ and PQ e 14.2 cm
3 square or rectangle
4 rhombus or parallelogram
5 right-angled triangle
6 b N c SW d SW e NW f SE g S h E i SW
7 a acute b obtuse c right angle d obtuse e reflex f full turn g obtuse h obtuse i straight line j acute k obtuse l obtuse m reflex n reflex o obtuse p acute q acute r reflex
8 i correct estimates ii a = 52º b = 130º c = 43º d = 293º
9 Angles drawn and labelled
10 a = 124º
11 b = 65º
12 c = 230º
13 d = 43º
14 e = 134º
15 f = 159º
16 g = 39º
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 36
17 h = 57º i = 123º j = 123º
18 k = 47º
19 l = 158º
20 m = 69º
21 n = 73º
22 p = 54º q = 126º
23 r = 140º
24 s = 61º t = 119º u = 79º
25 No. 150º + 40º = 190º (a straight line is 180º)
26 a False b False c True d True e False27 a 90º b 45º c 90º d 45º28 a 90º b 28º c 90º
Chapter 34
Exercise A1 1 − B
2 − A 3 − D 4 − C
2 1 − B 2 − C 3 − D 4 − A5 − F 6 − E
3 A − right-angled triangleB − parallelogramC − rectangle D − isosceles triangleE − rhombusF − trapeziumG − square H − trapezium I − right-angled triangle
4 X − hexagonY − pentagonZ − octagon
5 circle, semicircle, crescent
6 Circle correctly drawn and labelled
7 Circle correctly drawn and labelled
8 Circle correctly drawn and labelled
9 a 1 line, none b 3 lines, order 3 c 0 lines, none d 4 lines, order 4 e 2 lines, order 2 f 2 lines, order 2 g 0 lines, order 2 h 1 line, none i 6 lines, order 6 j 10 lines, order 10 k 9 lines, order 9
10 a equilateral triangleb rectangle, rhombusc regular pentagond parallelograme regular octagon
Exercise B1 Name Number of faces Number of edges Number of vertices
Cube 6 12 8
Cuboid 6 12 8
Triangular prism 5 9 6
Sphere 1 0 0
Cone 2 1 1
Square-based pyramid 5 8 5
Hexagonal prism 8 18 12
Hemisphere 2 1 0
Cylinder 3 2 0
Triangular pyramid or tetrahedron 4 6 4
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 37
2 a i F ii D
b correct nets drawn
3 correct net drawn
4 a square-based pyramidb octagonal prism
5 a Correct net drawnb Correct net drawn
c Correct net drawnd Correct net drawn
6 a i side ii front iii plan
b i side ii front iii plan
c i side ii front iii plan
d i side ii front iii plan
e i side ii front iii plan
Chapter 35
Exercise A 1 a = 53º
2 b = 120º
3 c = 60º
4 d = 38º, e = 104º
5 f = 69.5º, g = 69.5º
6 h = 39º, i = 141º
7 x = 123º
8 m = 300º
9 w = 129º
10 74º
11 34º, isosceles triangle
12 a x = 15º b 30º, 105º, 45º
13 a y = 33º b 66º
14 46°, 46° and 88° or 46°, 67° and 67°
Exercise B 1 a = 67º
2 b = 55º
3 c = 145º
4 143º
5 100º
6 a PMO = 36º, angle PMN is a right-angle b MOP = 54º, angles in a triangle add up to 180°
7 a ABC = 72º b DAB = 108º
8 QRS = 81º
9 a EFG = 127º b GIF = 90º
10 square, rhombus, kite
11 a False b False c True d False
12 a x = 40º b 120º
13 a y = 50º b 95º, 110º, 35º, 120º
14 70°, 110°, 70°, 110°
Chapter 361 a hexagon b decagon c quadrilateral
2 a a = 149º, b = 67º b c = 43º, d = 65º, e = 108º
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 38
3 a 72º b 108º
4 a 45° b 135° c 1080°
5 a AOB = 60º b FED = 120º c 720º d 30º
6 10 sides
7 15 sides
8 72 sides
9 150º
10 18º
11 No. 180º − 155º = 25º. 360 does not divide evenly by 25
12 Can be divided into 2 triangles. 180º + 180º = 360º
13 It is made up of 3 triangles. 3 × 180° = 540°
14 (6 − 2) × 180° = 4 × 180° = 720°
15 (10 − 2) × 180° = 8 × 180° = 1440°
16 1260º
17 6120º
18 157º
19 x = 99°
20 y = 113°
21 15 sides
22 43 sides
Chapter 37 1 a corresponding b vertically opposite c alternate d interior
2 a k b m c p d m e o
f l g n h i i i j o
3 a = 124º (alternate)
4 b = 113º (corresponding)
5 c = 95º (vertically opposite) d = 95º (corresponding)
6 e = 45º (straight line) f = 135º (corresponding) g = 135º (vertically opposite)
7 h = 79° (vertically opposite) i = 101° (vertically opposite j) j = 101° (interior angles)
8 k = 81° (vertically opposite) m = 81° (corresponding) n = 99° (straight line) p = 81° (vertically opposite)
9 a u = 38º v = 38º t = 142º b w = 108º x = 90º y = 108º c q = 63º d x = 127º
Chapter 381 a 9th April 2011
b 4th May 2011c Sunday
2 a 180 secondsb 120 minutesc 30 minutesd 900 secondse 210 minutesf 270 seconds g 48 hoursh 56 daysi 168 hours
3 a 3.00 p.m.b 11.00 p.m.c 7.30 a.m.d 4.20 p.m.e 1.10 p.m.f 8.05 p.m.g 12.00 p.m. (12 noon) h 10.45 a.m.i 5.40 a.m.
j 10.07 p.m.k 7.04 p.m.l 8.45 a.m.
4 a 0800b 1120c 0351d 1345e 1830f 2359g 1005h 1647i 0205j 1218k 0001l 2338
5 a 10.21 a.m.b 6.10 a.m.c 11.05 a.m.d 1.15 p.m.e 8.44 p.m.f 12.25 p.m.g 3.11 a.m.h 11.57 p.m.i 12.03 a.m.j 5.38 p.m.k 9.41 a.m.l 7.15 p.m.
6 9.50 p.m.
7 2055
8 1425
9 1 hour 5 minutes
10 a i 0745ii 50 minutes
b 1500 (3.00 p.m.)
11 a 0915b 42 minutesc 0726 (7.26 a.m.)d 0928 (9.28 a.m.)e No
12 45 minutes
Chapter 39 1 a centimetres
b metresc kilometres
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 39
d metrese millimetresf centimetres
2 a gramsb tonnesc kilogramsd gramse tonnesf milligrams
3 a millilitresb litresc litresd millilitrese litresf millilitres
4 a 300 cmb 6000 mc 70 mmd 5 kme 9 mf 4 cmg 8200 mh 3.5 cmi 1.2 mj 0.6 kmk 24 mml 740 mmm 6070 mn 0.7 cmo 4080 mmp 23.8 mmq 0.77 mr 190 000 cms 2.8 kmt 7520 mm
5 a 5000 gb 4000 kgc 7 gd 4 kge 2900 kgf 0.4 kgg 4700 mgh 5.9 kgi 0.608 tonnesj 3.935 gk 0.57 kgl 3040 gm 13 000 kg
n 0.605 kgo 300 kgp 0.325 gq 0.06 kgr 300 000 mgs 115 000 gt 0.000 065 kg
6 a 6000 mlb 2900 mlc 8 litresd 4300 mle 7.2 litresf 10 000 mlg 1.1 litresh 300 mli 1300 mlj 2430 litresk 0.904 litresl 0.055 litresm 12 800 mln 0.321 mlo 0.015 litresp 0.08 litresq 7.63 litresr 35 000 mls 72.5 mlt 0.002 litres
7 2.39 m (239 cm)
8 15
9 a 3.5 cm, 82 mm, 0.3 m, 45 cmb 0.75 kg, 840 g, 1050 g, 1.3 kgc 270 ml, 45 cl, 0.48 litres,
705 mld 1.99 km, 2098 m, 2.4 km,
3360 m
10 6.85 m (6850 mm)
11 20
12 6
13 2350 g (2.35 kg)
14 a 600 mm2
b 350 mm2
c 50 000 cm2
d 24 000 cm2
e 8 cm2
f 0.7 cm2
g 6 m2
h 4 750 000 mm2
i 30 mm2
j 90 m2
k 100 cm2
l 2 500 000 m2
15 a 1000 mm3
b 2700 mm3
c 6 000 000 cm3
d 800 000 cm3
e 90 cm3
f 1.385 m3
g 40 mm3
h 17 200 000 cm3
i 7 cm3
j 30 000 cm3
k 0.5 m3
l 3400 litres
16 a 60 ml, 12
litre, 800 cm3, 1 m3
b 11 000 mm2, 120 cm2, 0.1 m2, 1 m2
Chapter 401 a Correct rectangle 12 cm by 3 cm
b 62 m
2 a Correct triangle base = 6.5 cm and height = 5 cm
b 82 m
3 a Correct trapezium drawnb AB = 20.3 m AD = 18.3 m
4 Correct triangle with scale perimeter = 94 m
5 a 1 : 600b 1 : 150c 1 : 3000d 1 : 300 000e 1 : 40 000f 1 : 1 200 000g 1 : 500h 1 : 40i 1 : 2500j 1 : 25 000k 1 : 30 000l 1 : 240 000
6 a 0.4 kmb 1.2 kmc 0.35 km
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 40
d 2.3 kme 0.21 kmf 0.05 km
7 a 60 kmb 140 kmc 170 kmd 220 kme 44 kmf 66 km
8 Distance on map
Actual distance
a 5.cm 500 m
b 8.cm 800 m
c 7. cm 14 km
d 2.cm 4 km
e 2.5 cm 25 km
f 2..cm 20 km
g 15.cm 7.5 km
h 4.cm 500 m
i 3.4 cm 510 m
j 14.5 cm 290 m
9 a 35 mb 9 kmc 240 md 400 kme 76 kmf 156 mg 420 miles
Chapter 41 1 a 7
b 13c 19
2 a 22b 28c 36
3 a 25b 75c 105
4 a 6.5b 7.25c 8.75
5 a 11.4b 12.6c 13.2
6 a 83b 96c 115
7 a 13.3b 14.7c 15.9
8 a 45b 57.5c 72.5
9 a 675b 850c 1025
10 a 220b 250c 290
11 a 506b 512c 516
12 a 30.2b 30.4c 31.2
13 a 8.43b 8.45c 8.49
14 a 6.84b 6.96c 7.02
15 a 9.15b 9.375c 9.525
16 a 0.253b 0.255c 0.258
17 a 3.465b 3.4875c 3.5025
18 a 8.016b 8.022c 8.028
19 a −7.5b −5.75c −4.25
20 a 9.625b 9.65c 9.6875
Chapter 42 1 a b2 = a2 + c2
b r2 = p2 + q2
c x2 = y2 + z2
d e2 = d2 + f 2
2 a 13 cmb 5 mc 10 mmd 7.81 cme 20.12 cmf 8.06 mg 14.87 mmh 26.57 cmi 5.64 cmj 5.67 kmk 1.53 ml 1.50 km
3 a 12 cmb 15 mc 13.08 cmd 14.66 me 17.66 mmf 2.83 cmg 2.42 mh 33.09 cmi 8.49 kmj 3.82 mk 1.08 ml 60.10 cm
4 a 13.4 cmb 8.1 mc 21 mmd 4.5 me 56.9 cmf 35.4 cm
5 85.96 m
6 No. 52 + 122 = 169 and 169 = 13
7 6.5 m
8 25 cm
9 155.52 cm2
10 16 m
11 50 cm
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 41
Chapter 43 1 a 054º
b 150ºc 200ºd 165ºe 124ºf 320ºg 100ºh 072ºi 346º
2 a 234ºb 330ºc 020ºd 345ºe 304ºf 140ºg 280ºh 252ºi 166º
3 223º
4 341º
5 055º
6 a Correct constructionb Correct constructionc Correct constructiond Correct construction
7 a 068º (±2º)b 225º (±2º)c 334º (±2º)d 045° (±2°)e 154° (±2°)f 248° (±2°)
8 a Correct diagramb 4.7 cm
9 a Correct diagramb i 4.8 km ii 321º
Chapter 44Exercise A1 a 26 cm
b 36 mc 24 mmd 66 cme 160 mm
f 24 mg 17 mh 7.3 cmi 14.4 cmj 44 mm (4.4 cm)k 13.9 ml 38 m
2 5 cm
3 7 cm
4 16 cm
5 12 cm, 12 cm and 18 cm
6 21 cm and 21 cm or 30 cm and 12 cm
7 a 40 cm2
b 54 m2
c 144 cm2
d 77 mm2
e 442 m2
f 7.68 cm2
8 121 cm2
9 24 mm2
10 400 m2
11 25.2 mm2
12 12.6 cm2 (1260 mm2)
13 a 30 cm2
b 42 m2
c 18 m2
d 12 mm2
e 6.4 m2
f 270 cm2
g 58.5 cm2
h 30 mm2
i 165 cm2
14 48 cm2
15 85 m2
16 7.5 cm2
17 380 mm2
18 7.2 cm2
19 5 cm
20 Correct rectangles, e.g. (18 × 1) or (9 × 2) or (6 × 3) or (4.5 × 4) or (36 × 0.5)
21 8 cm
22 24 m
23 5 cm
24 49 cm2
25 14 cm, 16 cm, 26 cm
26 a 52 cm2
b 43 cm2
27 112 cm or 80 cm
Exercise B1 a 36 cm b 62 cm
2 a 38 cm2
b 70 cm2
c 74 cm2
d 82 cm2
e 108 cm2
f 66.5 cm2
3 i a Perimeter = 40 cm b Area = 63 cm2
ii a Perimeter = 52 cm b Area = 81 cm2
iii a Perimeter = 64 cm b Area = 119 cm2
iv a Perimeter = 54 cm b Area = 94 cm2
Exercise C1 a 400 cm3
b 729 m3
c 360 cm3
d 84 mm3
2 a 120 cm3
b 240 mm3
c 45 m3
d 96 cm3 (96 000 mm3)e 0.27 m3 (270 000 cm3)
3 8 cm3
4 1728 mm3
5 32.768 m3
6 10 cm
7 5 cm
8 24 m
9 4 cm
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 42
10 Correct cuboids e.g.
(2×3×10), (1×3×20), (3×4×5),
(1×5×12), (2×2×15),
(1×1×60)
11 4 cm
12 a 24 cm2
b 104 cm2
c 122 cm2
d 224 cm2
13 a 96 cm2
b 124 cm2
c 68 cm2
d 39 600 cm2 (3.96 m2)
14 150 cm2
Chapter 45
Exercise A1 a − f
(a)
(c)
(e) (f )
(d)
(b)
2 a − g(a)
(c)
(e)
(g)
(f )
(d)
(b)
3 a − c (a)
(c)
(b)
4 a rotational symmetry order 4b rotational symmetry order 2c rotational symmetry order 4
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 43
d rotational symmetry order 2e does not have rotational symmetryf rotational symmetry order 2g does not have rotational symmetryh rotational symmetry order 2i rotational symmetry order 2j rotational symmetry order 3k rotational symmetry order 2l does not have rotational symmetrym rotational symmetry order 2n rotational symmetry order 4
5 a − b (a) (b)
Exercise B1
–1–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–2–3
A
C
B
–4–5–6 654321
y
x
2
–1–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–2–3
D
E
F
–4–5–6 6
y = 1
x = –1
54321
y
x
3
–1–1–2–3–4–5–6 10 2 3 4 5 6
–2
–3
–4
–6
–7
–8
1
2
3
4
5
6
7
8
x
y
IG
H
y = –2
x = –1
–5
4 a reflection in y = 4b reflection in the x-axisc reflection in x = 2d reflection in y = 5e reflection in x = −2f reflection in the x-axisg reflection in x = −3h reflection in x = 1i reflection in y = 4½
Exercise C1
–1–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–2–3
A
B
C
–4–5–6 654321
y
x
a − b
a − b
a − c
a − b
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 44
2
–1–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–2–3
D
E
F
–4–5–6 654321
y
x
3
–1–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–2–3
G
H
I
–4–5–6 654321
y
x
4 a rotation 90° clockwise about (0, 0)b rotation 90° anticlockwise about (0, 0)c rotation 90° clockwise about (2, 1)d rotation 180° about (0, 0)e rotation 180° about (1, 0)f rotation 90° anticlockwise about (0, 2)g rotation 90° anticlockwise about (0, −2)h rotation 90° clockwise about (3, 3)
Exercise D1 a 2 right and 3 up
b 5 right and 4 downc 6 upd 5 left and 2 upe 5 rightf 3 left and 1 down
2 a 3
5
b −−
4
4
c 15−
d 9
0
e 06−
f 1510−
g 1311
−
h 0
7
i 240
−
3
–1–1–2–3–4–5–6 1 2 3 4 5 6
–2
–3
–4
–5
–6
–7
1
2
3
4
5
6
7
y
7 x–7
D
F
H
B
G
C
T
A
E
4 A to B, 3 right and 1 up, 3
1
A to C, 6 left and 5 down, −−
6
5
A to D, 6 left and 4 up, 64
−
A to E, 2 right and 5 down, 25−
A to F, 3 up, 0
3
A to G, 7 left and 1 down, −−
7
1
A to H, 1 left and 6 down, −−
1
6
A to I, 4 left, 40
−
A to J, 3 right and 2 down, 32−
a − b
a − b
a − h
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 45
Exercise E1
–1–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–2–3
A
B
C
–4–5–6 654321
y
x
D
2
–1–1–2–3–4–5–6 1 2 3 4 5 6
–2
–3
–4
–5
–6
–7
1
2
3
4
5
6
7
y
7 x–7
C
B
A
3
–1–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–2–3
F
G
E
–4–5–6 654321
y
x
4 a enlargement, scale factor of 2, centre of enlargement (−6, 2)
b enlargement, scale factor of 3, centre of enlargement (−5, 0)
c enlargement, scale factor of 4, centre of enlargement (−4, 3)
d enlargement, scale factor of 2, centre of enlargement (0, 5)
Exercise F1 a translation
12
b rotation 90° clockwise about (0, 0)c reflection in y-axisd enlargement, scale factor of 2, centre (−4, 5)e reflection in y = 2
f translation 50
−
g rotation 180° about (0, 0)
h translation 16
−
i rotation 90° anticlockwise about (2, 2)j enlargement, scale factor of 2, centre (−4, 0)
2 a translation 42
b reflection in x-axisc rotation 90° clockwise about (−4, 0)d reflection in x = 1e enlargement, scale factor of 2, centre (−1, −6)f reflection in y = −3g rotation 180° about (0, −1)
h translation 62
−
Chapter 46
Exercise A1 a 18.8 cm
b 88.0 cmc 23.6 md 71.6 m
2 a 65. 97 cmb 54.04 mmc 135.09 cmd 270.18 cm
3 a 12 cmb 37.7 cm
4 a 5.5 cmb 34.6 cm
5 12.73 cm
6 10.35 cm
a − b
a − b
a − b
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 46
7 a 61.7 cmb 57.1 cmc 55.1 cmd 107.4 cm
8 1.885 km
9 63 complete revolutions
Exercise B1 a 113.1 cm2
b 19.6 m2
c 153.9 cm2
d 102.1 m2
2 a 254.47 cm2
b 10.18 mm2
c 176.71 cm2
d 10.64 m2
3 201.06 cm2
4 132.73 m2
5 4.3 cm
6 8.56 cm
7 6.6 cm
8 a 508.9 cm2
b 153.9 cm2
c 131.5 m2
d 169.3 cm2
e 147.1 cm2
9 a 69.5 cm2
b 45.9 cm2
c 100.5 cm2
d 293.0 cm2
e 113.1 cm2
Exercise C1 a 16 cm b 50.3 cm c 201.1 cm2
2 a 12.5 cm b 78.5 cm c 490.9 cm2
3 20.4 cm2
4 34 cm
5 24.3 cm
6 44.1 m
7 336.2 cm2
8 a 226.2 cm3
b 235.6 cm3
c 2799.2 cm3
d 28.3 m3
9 404.1 cm3
10 a 6.9 litres b 12.7 litres c 74.3 litres
11 7.96 cm
12 9.92 cm
13 3.24 cm
14 29.84 cm
15 9.26 cm
16 5.6 times bigger (1 d.p.)
17 80 full tanker loads
Chapter 47
Exercise A1 a 18 cm2
b 210 cm2
c 60 cm2
d 54 m2
e 98 cm2
f 115 cm2
g 90 cm2
h 63 cm2
i 0.6 m2 (6000 cm2)j 105 mm2 (1.05 cm2)
2 a 120 cm2
b 60 mm2 (0.6 cm2)c 128 cm2
d 60 cm2
3 a i Perimeter = 82 cm ii Area = 360 cm2
b i Perimeter = 56 cm ii Area = 84 cm2
c i Perimeter = 46 cm ii Area = 112 cm2
d i Perimeter = 30 cm ii Area = 60 cm2
4 a h = 7 cmb h = 3 cm
c h = 4 md h = 3.6 m
5 Area = 330 cm2
Exercise B 1 a 360 cm3
b 280 m3
c 120 cm3
d 336 cm3
2 a 432 cm3
b 13 818 mm3
3 1125 cm3
4 13 000 cm3
5 4760 mm3 (4.76 cm3)
6 a 420 cm3
b 216 cm3
c 61.2 cm3
d 1296 mm3
7 a 2520 cm3
b 1500 cm3
8 a 360 cm3
b 512 cm3
9 12.5 cm
10 24 mm2
Chapter 48 1 metres, centimetres
2 yards, inches
3 grams, tonnes
4 stones, pounds
5 litres, millilitres
6 pints, gallons
7 a metres b kilograms c millilitres d grams e millimetres f litres
8 a milesb poundsc gallonsd yards or feet
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 47
e gallonsf stones or pounds
9 a 1.6b 3.2c 8d 12.8e 16f 40g 20h 56.25i 45j 70k 160l 120m 40n 93.75o 400p 125q 0.8r 0.625
10 a 2.2b 4.4c 11d 44e 5f 40g 100h 45i 154j 14.3k 184.8l 46m 17.6n 1.1o 0.55p 45.5q 1.76r 3.1
11 27 litres
12 10 cm
13 2.4 oz
14 160 km
15 64 km/h
16 31.25 mph
17 152 km
18 Yes. He drove at 80 km/h
19 196.875 gallons
20 44.875 kg
Chapter 49
Exercise A 1 a Correct construction b AB and BC are the same
length (5.4 cm)
2 a Correct construction b DE is 6.2 cm and EF is
8.3 cm c 65 º
3 a
C
A B5 cm
40°
6 cm
b 3.9 cm
4 a
7 cm
5 cm
60°P Q
R
b 6.2 cm
5 a N
L M6 cm
70° 60°
b 6.8 cm
6 a
F
D E65° 50°
b 4 cm c 3.4 cm
7 a I
G H6 cm
7 cm 7 cm
b 65º
8 a
X Y5 cm
8 cm
Z
6 cm
b 39º
9 a A B
C6 cm
4 cm
D
b 56º
10 a P Q
S R8 cm
5 cm
40°
b 7.8 cm
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 48
11 a
5 cm
5 cm
b 9.2 cm
12 a
6 cm
6 cm
b 6.6 cm
Exercise B
1 a
A B
b 3.5 cm
2
3
DC T
4
R
P
Q
5 P
X Y
6
7
8
9
A3 cm
10
A B4 cm 2 c
m
11 3.5 cm
12
2 cm
3 cm
A D
B C
6 cm
13
5 cm
6 cm
3 cm
B
A C
14 a – b
4 cm
W X
Z Y5 cm
15
7 m4 m
8 m
3 mA
D
B
C
Shed
Chapter 50 1 a 10 cm, 8 cm
b 18 cmc 36 cmd twice as bige 20 cm2
f 80 cm2
g 4 times bigger
2 a 8 cmb 24 cmc 3 times biggerd 4 cm2
e 36 cm2
f 9 times bigger
3 a 88 cmb 320 cm2
4 3
5 4
6 a 28 cmb 40 cm2
7 99 cm2
8 250 cm
9 160 cm2
10 12 cm
11 108 cm2
12 112 cm2
13 22 cm2
14 2304 cm2
a − b
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 49
Chapter 51
Exercise A 1 78 beats/minute
2 81 beats/minute
3 75 beats/minute
4 69 beats/minute
5 a Mrs A 88 beats/min, Mrs B 71 beats/min, Mr C 72 beats/min, Miss D 68 beats/min, Mr E 74 beats/min, Mr F 80 beats/min
b Mrs A
c Miss D
6 41 mpg
7 17 mpg
8 4.8 mpg
9 672 miles
10 No, a tank will only do 384 miles
11 He did 2176 miles. The salesman said the car would do 2100 miles
Exercise B 1 a 120 minutes
b 210 minutesc 15 minutesd 36 minutese 72 minutesf 96 minutesg 168 minutesh 18 minutes
2 a 14
hour
b 16
hour
c 25
hour
d 1112
hour
e 120
hour
f 160
hour
g 310
hour
h 1120
hour
3 a 40 mphb 30 mphc 46 mphd 56 mphe 60 mphf 64 mphg 51 mphh 72 mph
4 a 50 km/hb 38 km/hc 66 km/hd 65 km/he 37.5 km/hf 96 km/hg 60 km/hh 84 km/h
5 45 mph
6 112 mph
7 1 hour and 40 minutes
8 105 km
9 50 km/h
10 a 27.5 milesb 62.5 milesc 2
12
hours
d 114
hours
e 80 km/hf 54 mphg 3 kmh 15 minutes ( 1
4hour)
Exercise C 1 a 5 g/cm 3
b 2 g/cm 3
c 0.25 g/cm 3
d 0.3 g/cm 3
e 2.4 g/cm 3
f 1 g/cm 3
2 a 0.03 kg/cm3
b 30 g/cm3
3 1200 g
4 a 2080 gb 2.08 kg
5 80 cm3
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 50
6 400 cm3
7 a 5 g/cm3
b 3.5 g/cm3 c 4.6875 g/cm3
d 2.5 g/cm3 e 1.49 g/cm3
f 9.43 g/cm3
8 0.781 25 g/cm3
9 0.6 g/cm3
10 a 336 gb 4896 g
11 6 cm
Chapter 52
Exercise A 1 a quantitative
b qualitativec quantitatived quantitativee quantitativef qualitative
2 a discreteb continuousc discreted discretee continuousf continuous
3 a Number of cups of tea
0123456
Tally Total
25
106432
b Freya asked only 32 people. She needs to ask more people before she can decide.
4 a Number of times
0–3
4–7
8–11
12–15
Tally Total
15
17
12
4
b 48
c No. Karli asked only 48 people. Someone may go more than 14 times a month who she didn’t ask.
5
Exercise B1 a Does not include a given time frame, e.g. per week
b Does not allow for zero. Overlap with the numbers
c Suitable question and response sectiond No
2 a Question too long. Leading question.b No response for ‘don’t know’c Suitable question and response section
3 a Asked adults only. People at the library are more likely to read more.
b Suitable question and response sectionc Example of a more neutral venue. Bigger
sample size, at least 30
4 a Leading questionb Doesn’t include response ‘disagree’ c Suitable question and response section
5 a Question too generalb Doesn’t include ‘other’c Suitable question and response sectiond A mixture of young and old people and a
mixture of male and female.
6 a Suitable question that is easy to interpret and not leading
b Suitable question that is easy to interpret and not leading
c Suitable question that is easy to interpret and not leading
d Suitable question that is easy to interpret and not leading
Time, t, minutes
0 < t ≤ 10
10 < t ≤ 20
20 < t ≤ 30
40 < t ≤ 50
50 < t ≤ 60
30 < t ≤ 40
Tally Frequency
3
7
6
3
4
3
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 51
Exercise C1 a
70
120
50
male
female
notuse gym
not usegym
use gym
use gym
15
55
36
14
b 91c 29d 55e 14
2 a
95
35
20
150
90
5
8
27
2
18not late
train
bus
car
not late
not late
late
late
late
b 35c 15
d =35150
730
e =220
110
f 94.7%g 90%
3
30
1716
1
5
8
13
girls
boys
do notget bus
do notget bus
get bus
get bus
4
women
85
62
23
17
45
19
4
men
did notuse card
did notuse card
used card
used card
5
45
39
28
84
boys
girls
not a tongueroller
not a tonguerollertongue roller
tongue roller
17
24
15
6 a French Spanish German Total
Female 12 43 13 68
Male 18 22 12 52
Total 30 65 25 120
b
female
French
Spanish
Spanish
German
German
Frenchmale
120
68
12
43
13
18
22
12
52
Exercise Da 26b 7c 18
2 a 76b 23c 29d No, they could play a different instrument, for
example, the violin. It means 31 do not play the piano or the guitar.
3 Tea Coffee
12 13
5
4 German Spanish
14 20
9
7
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 52
5 Juice Tea
21 30
6
8
6 a 245b 16c 91d 138e 166f 24g Asia
7 Swimming Cycling
Horse-riding
65 34
2217
20
15
12
25
8 40 (Hint: draw a Venn diagram.)
Eiffel Tower Disneyland Paris
Notre Dame Cathedral
34 74
1362
14
15
28
40
Chapter 53 1 mean = 14
2 mode = 6
3 median = 7
4 median = 11.5
5 mean = 51.25 cm
6 a mean = 74.85%b median = 80%c mode = 72%d range = 84%
7 x = 12
8 range = 13
9 mean height = 162.4 cm
10 a e.g. 6, 8, 8, 8, 9b e.g. 5, 6, 10, 12, 14c e.g. 2, 3, 4, 5, 6d e.g. 5, 5, 6, 7, 8
11 a mode = 2b mean = 3.43c median = 3
12 a mode = 9b mean = 7.48c median = 8
13 a mode = 2b mean = 2.55c median = 2
14 3, 5, 7
15 5, 5, 6, 9, 10
16 a £39 024 b £27 750 c Median − no mode and mean distorted by
large salary
17 mode with explanation
18 a i 40 < m ≤ 50ii 20 < m ≤ 30iii 28.2
b i 60 < V ≤ 70ii 60 < V ≤ 70iii 59.1
c i 0 − 1ii 4 − 5iii 4.03
19 9A because 9B has a higher mean than 9A, but only by 5%.
9B has a much bigger range than 9A; 9A is more consistent
Chapter 54
Exercise A 1 a 13
b 11
c
d 65
2 Correct pictogram with key
3 No key, different sizes of objects, no title
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 53
4 a 8b 5c 22
5
6 Bars are different widthsNo numbers on the vertical axisNo labels on the horizontal and vertical axesNo title
7 Number of days Tally Frequency
0 / / / / / / / 8
1 / / / / / / / / 10
2 / / / / / 6
3 / / / 3
4 / / 2
5 / 1
30
8 a Number of DVDs Tally Frequency
0−4 / / / / / / / 8
5−9 / / / / / / 7
10−14 / / / / / / 7
15−19 / / 2
24
b
Exercise B1 Pie chart drawn and labelled Water = 72° Orange juice = 108° Milk = 60° Tea = 90° Coffee = 30°
2 Pie chart drawn and labelled Walk = 32° Bicycle = 60° Car = 84° Bus = 160° Train = 24°
3 Pie chart drawn and labelled Swimming = 48° Running = 88° Walking = 120° Cycling = 64° Other = 40°
4 Pie chart drawn and labelled Cow = 120° Sheep = 70° Horse = 10° Pig = 100° Hen = 60°
5 a 60360
= 16
b 16 studentsc 6 students
6 a 36360
= 110
b £30
Exercise C1 a 38 marks
b 52 marksc 51.68̇1̇ marksd 7
2 No keyN umbers in the leaf are not in order7 is missing from the stem
3 3 2 2 4 5 74 0 1 1 1 85 1 1 2 66 0 5 5 6 97 2 8 98 3 6
Key8 3 = 8.3
50
40
30
20
10
Toast PizzaSnack
Number of snacks eaten at break time
Freq
uenc
y
Fruit Scones0
8
7
6
5
4
3
2
1
00–4 5–9
Number of DVDs
Number of DVDs owned by students in Class 10A
Freq
uenc
y
10–14 15–19
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 54
4 a 26.5%b 34%c 31 pupilsd 41%
5 10X 10Y
4 8
9 9 8 8 5 0 1 1 3 7 8 8 9
9 8 8 7 7 6 0 2 4 4 5 6 8
7 7 6 5 2 2 0 7 1 3 3 3 4 4 9
9 8 8 6 6 8 2
9 8 4 1 9
Key8 2 = 82
Chapter 55
Exercise A1 a 16 °C
b April and Mayc November
2 a i 1800 ii 0900 and 1000b No, we can only tell how many customers
were at the service station at 1000 and 1100. We cannot use the graph for times between 1000 and 1100.
3 a
109876543Age (weeks)
Mas
s (k
g)
2100
10
20
30
40
50
60
70
Mass of a calf
80
90
b 75 kg
4
FriThurWedTueDay of the week
Students absent from school in one week
Num
ber
of s
tude
nts
abse
nt
Mon
10
20
5 a
50 60 70 80 904030Number of days
Height of sunflower
Hei
ght
(cm
)
20100
20
40
60
80
100
120
140
160
180
200
220
b 126 cm c Between 40 and 50 days. There is the greatest
increase in height between 40 and 50.
6 a i 192 km ii 208 km iii 217 km iv 313 kmb 373 kmc 119 km
7 a i 36.8 miles ii 26.6 miles iii 60.7 miles iv 40.0 milesb 144.4 miles
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 55
8 a 3 boysb 12 girlsc 14 boys
d 2330
9 a 12 childrenb Channel 4c ITVd BBC 1 because it has the highest number for
both adults and children combined.
10 a
iPhone Nokia Blackberry Samsung Total
Men 5 11 8 16 40
Women 9 8 12 11 40
Total 14 19 20 27 80
b 12 womenc 11 mend 80 people
11 Other pets may be chosen
Cat Dog Rabbit Horse Other
Boys
Girls
12 a 2005b 1990c 44º Cd 230 mm
13 a Fendt 714 Variob Massey Ferguson 6480c 797 kgd John Deere 6930 − it has the highest power
and is lighter than the New Holland 6080
Exercise B 1 a positive correlation
b no correlationc negative correlation
2 a positive correlationb negative correlationc positive correlationd no correlatione positive correlationf no correlationg positive correlation
3 a – c
60 70 80 905040Maths result
Scie
nce
resu
lt
30
30
40
50
60
70
80
90
100
b positive correlationc line of best fit drawnd approx. 70e interpolationf approx. 100g extrapolation
4
20 1Engine size (litre)
Ave
rage
fuel
con
sum
ptio
n (m
pg)
10
20
30
40
50
60
b negative correlationc line of best fit drawnd approx. 40 mpge approx. 1.7 litresf this point lies furthest away from the trend
line of the rest of the data
a , c and f
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 56
5 a, c
170 180 190160150Height (cm)
Arm
spa
n (c
m)
140
140
150
160
170
180
190
b positive correlationc line of best fit drawnd approx. 165 cme approx. 175 cmf interpolation
6 a, c and e
4 5 6 7 8 932Number of books
Hou
rs w
atch
ing
TV
100
2
4
6
8
10
12
14
16
b negative correlationc line of best fit drawnd approx. 7 bookse Adult has a lot of free time, is unemployed, or adult’s employment involves reading booksf No
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 57
Exercise C1 a Value of x Value of T
1 8
2 13
3 18
4 23
b 4
2 a Value of x Value of A
1 5
2 8
3 13
4 20
5 29
6 40
b 63 a
Value of x Value of y Value of P
1 1 2
2 2 12
3 3 36
b 36
4 a
Value of x Value of y Value of C Value of D
2 2 4 10
3 3 6 18
4 4 8 28
5 5 10 40
b x = 5 and y = 5
5 a
0130 135 140 145
Height (cm)
Heights of students in a Year 8 class
Freq
uenc
y
150 155 160
1
2
3
4
5
6
7
b 23 students
6 a
02 4 6 8
Weight (kg)
Weights of turkeys
Freq
uenc
y
10 12 14
5
10
15
20
25
b 64 turkeys
7 a
030 40 50 60
Time (minutes)
Time to complete Maths challengeFr
eque
ncy
70 80 90
5
10
15
20
25
b 70 peoplec 30 minutes
Chapter 56
Exercise A1
impossible unlikely evens likely certain
2 a impossibleb certainc evensd likelye unlikely
3 a 29
b 39
or 13
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 58
c 0
d 69
or 23
4 a 16
b 36
or 12
c 16
d 26
or 13
5 1022
or 511
6 a 213
b 313
c 0
d 513
7 a 35
b 25
c 0
8 a 720
b 520
or
14
c 1520
or
34
d 0
9 a 16
b 36
or
12
c 26
or 13
d 26
or 13
e 46
or 23
10 a 126
b 1326
or 12
c 1226
or
613
d 1626
or 813
11 a 12
b 30200
or 320
c 79200
d 1
12 No. Each outcome is not equally likely (e.g. Melissa may be a better tennis player)
13 Winning, losing and drawing a match are not 3 equally likely outcomes
Exercise B 1 a 30%
b 88%c 2
9
d 415
e 0.35f 0.2g 0.96
h 1930
i 63%
2 0.7
3 0.58
4 36%
5 0.15
6 a 0.15b 0.7
7 a H1 H2 H3 H4 H5 H6
T1 T2 T3 T4 T5 T6
b i 312
or 14
ii 112
8 a + 2 2 3 3 3
1 3 3 4 4 4
2 4 4 5 5 5
3 5 5 6 6 6
4 6 6 7 7 7
5 7 7 8 8 8
6 8 8 9 9 9
b i 530
or 16
ii 1530
or 12
iii 0
Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2017 59
9 a
Y Y Y B B
R RY RY RY RB RB
R RY RY RY RB RB
B BY BY BY BB BB
B BY BY BY BB BB
Y YY YY YY YB YB
Y YY YY YY YB YB
b i 430
or 215
ii 2230
or 1115
iii 1030
or 13
iv 1230
or 25
10 a 1 2 3 4 5 6
A A1 A2 A3 A4 A5 A6
B B1 B2 B3 B4 B5 B6
C C1 C2 C3 C4 C5 C6
b i 118
ii 318
or 16
iii 818
or 49
iv 318
or 16
11 Tea Beef, Tea Turkey, Coffee Beef, Coffee Turkey
12 a Art German, Art French, Technology German, Technology French, ICT German, ICT French
b Art Technology German, Art Technology French, Art ICT German, Art ICT French, Technology ICT German, Technology ICT French
13 8 options
Exercise C 1 a 9
20b 42
2 a 0.13b 160
3 a 36%b 60 sheep
4 a 0.38b 18
5 a 495b 360c 162
6 a 320b 140c 52
7 a i 730
ii 1230
or 25
iii 2430
or 45
b i Yes. You would expect the relative frequency of each number to be around 1
6 ii Increase the number of trials
8 a 510
, 3050
, 62100
, 125200
b No. 125200
is a more accurate relative frequency
9 a Yes, if it was fair you would expect to get close to the same number of Heads and Tails
b 30
12014
=
c 14
of 200 = 50 Heads.