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Cambridge Essentials Mathematics Core 7 N1.1 Answers
Original Material © Cambridge University Press 2008 1
N1.1 Answers
1 a 107 b
10004 c
1008 d
109
2 a One hundredth b Eight hundredths
c Three tenths d Four thousandths
3 a Three tenths b Seven hundredths
c Forty-one thousandths d Thirty-eight hundredths
4 a 4.07 b 12.3 c 16.005 d 32.027
5 a 5.3 b 23.09 c 2.82 d 1.308 e 9.25
f 1.073 g 34.683 h 1.001 i 3.013
6 A = 0.3 B = 0.8 C = 1.6 D = 9.1 E = 10.2
F = 10.7 G = 6.6 H = 7.2 I = 7.8 J = 0.25
K = 0.75 L = 1.5 M = 15.5 N = 16.25 O = 16.75
P = 31.3 Q = 31.8 R = 32.4
7 A = 5.13 B = 5.15 C = 5.21 D = 9.38 E = 9.42
F = 9.48 G = 1.879 H = 1.883 I = 1.885 J = 2.452
K = 2.456 L = 2.468 M = 4.575 N = 4.625 O = 4.65
P = 3.9625 Q = 3.9725 R = 3.9775
8 a 3.65 b 2.15 c 3.95 d 0.05
e 7.8 f 5.365 g 8.99 h 0.005
9 a 27.1 b 0.36 c 2.09 d 0.45
e 0.037 f 28 g 3.7 h 67.3
10 a 120 b 342 c 0.67 d 57
e 0.0328 f 0.0027 g 2.86 h 2.39
Cambridge Essentials Mathematics Core 7 N1.1 Answers
Original Material © Cambridge University Press 2008 2
11 a 180 b 0.008 c 0.002 01 d 25
e 0.000 76 f 0.4 g 6.781 h 6
12 a 278 m b 2780 m
13 a 99 700p b £997
14 9.5 g
15 a 77.5 cm = 775 mm b 1.85 m = 1850 mm c 98 cm = 980 mm
d 2.4 m = 2400 mm e 1.2 m = 1200 mm f 53 cm = 530 mm
g 59 cm = 590 mm h 80 cm = 800 mm i 1.32 m = 1320 mm
16 a 10 b 1000 c 0.45
d 653 e 0.009 f 86
g 1000 h 160 i 10
17 a 375 mm b 49.5 cm c 0.786 m
d 1.27 m e 1.23 m f 3200 mm
18 a 300 cl b 2.7 litres c 70 cl
d 1.2 litres e 3200 ml f 85 cl
19 a 2 b 4
20 a 5.4999, 5.849, 5.85, 5.9, 6 b 11.06, 11.18, 11.29, 11.3, 11.56
c 0.249, 0.25, 0.278, 0.28, 0.3 d 7.12, 7.123, 7.127, 7.129, 7.192
e 0.0729, 0.073, 0.0732, 0.0738 f 19.09, 19.099, 19.1, 19.178, 19.18
21 a 0.19 b 0.309 c 0.092 d 0.138
22 b 0.18 > 0.179 c 2.409 < 2.413
d 12.23 > 12.229 e 32.001 < 32.01
f 26.047 > 26.0467 g 1000268
10037
>
h 1000
8910027
> i 1000
99101>
Cambridge Essentials Mathematics Core 7 N1.1 Answers
Original Material © Cambridge University Press 2008 3
23 A = 2.778 B = 2.784 C = 2.794
D = 2.798 E = 2.801 F = 2.816
24 a 27 mm > 2.5 cm b 9.8 cm < 9.7 m c 240 cm > 0.25 m
d 0.8 m > 760 mm e 58.2 cm < 590 mm f 3020 mm < 3.1 m
25 9.8, 9.7, 9.2, 8.9, 8.7, 8.2, 7.9, 7.8, 7.2, 2.9, 2.8, 2.7
26 a 5.031 b 5.002 c 4.991 d 5.015 e 5.007
27
28 a i 1620 ii 1640 iii 1640 iv 1600
v 1650 vi 1610 vii 1600 viii 1640
b 1605, 1615, 1625, 1635, 1645
c Yellow
d 1615 < x < 1625
e 1645 < y < 1655
29 a i 1010 ii 990 iii 980 iv 990
v 1000 vi 1010 vii 1020 viii 970
b 1005 < x < 1015
c 975 < y < 985
Cambridge Essentials Mathematics Core 7 N1.1 Answers
Original Material © Cambridge University Press 2008 4
30 a i Rob: £40 ii Tara: £60 iii Phil: £50
iv Ravi: £80 v Fran: £70 vi Kate: £70
vii Jack: £60 viii Salma: £80 ix Tim: £60
b 50p
c i £55 ii £64.99
31 a 500 b 500 c 800 d 500
e 100 f 0 g 100 h 100
i 1800 j 4700 k 21 400 l 17 400
32 a Real Madrid: 65 000 b Le Mans: 32 000 c Hamburg: 50 000
d Millwall: 10 000 e Luton town: 8000 f Stoke City: 9000
33 a 9 b 8 c 6 d 7
e 10 f 9 g 10 h 7
34 a 8.9 b 8.7 c 9.0 d 8.7
e 8.8 f 9.0 g 8.9 h 9.1
35 a £8 b £4 c £13 d £20
e £38 f £11 g £96 h £88
36 a £19.50 b £20.49 c £15 d £24.99
37 Each box could be 15.4 cm, for example, giving a total height of 154 cm = 1.54 m.
In addition, the height available could be as little as 1.45 m.
Cambridge Essentials Mathematics Core 7 N1.2 Answers
Original Material © Cambridge University Press 2008 1
N1.2 Answers
1 a −2, −4, −6 b −1, −3, −5 c −3, −6, −9
d 3, 5, 7 e 2, 4, 6 f 2, −1, −7
g 7, 1, −5 h −5, 3, 11 i −2.5, 2.5, 5
2 a Decreasing b Decreasing c Decreasing
d Increasing e Increasing f Decreasing
g Decreasing h Increasing i Increasing
3 a −5, −3, −2, 0, 4, 7 b −10, −5, −4, 0, 3, 6
c −9, −6, −3, −1, 0, 2 d −4.2, −3.8, −3, −1, 2.3
e −2, −1.2, −0.7, 0.1, 7.2 f −7.2, −3, −1.8, −1.75, 1
4 a −6 < −3 b 0 > −2 c −7 > −10 d −1 < 8
d −31 < −20 e −15 > −19 f −5.2 < −5 g −4.9 > −5
5 a 12 b 3 c −3 d 0
e −4 f 4 g −15 h −95
6 a 4 b −4 c −7 d −5
e −8 f −11 g −37 h −57
7 15 oC
8 a −9 oC b −7 oC c −12 oC d −25 oC
9 a −3 + 4 = 1 b −1 − 2 = −3 c −4 − 6 = −10 d −2 + 5 = 3
10 a −5 b −2 c −9 d −7
e 0 f 10 g 8 h 6
Cambridge Essentials Mathematics Core 7 N1.2 Answers
Original Material © Cambridge University Press 2008 2
11 a −3 b 3 c −8 d 4
12 a 8.5 b 5.5 c 2.5 d −1.5
13 a −0.5 b −2.5 c −6.5 d −9.5
14 a 4.5 b 6.5 c −0.5 d −2.5
e 5 f 2 g 0 h −2
15 a −2.4 b −2.8 c −1.9
d −0.7 e −3.1 f 1.6
16 a 9 b 10 c 7 d − 4
e + 8 f − 3 g − 4 h + 5
i −1 j 2 k −9 l −1
17
18 right 7, up 4, right −2, up −2, right −2, up 1, right −2, up 1, right −1, up −2,
right 2, up −1, right 2
19 a
b C
Cambridge Essentials Mathematics Core 7 N1.2 Answers
Original Material © Cambridge University Press 2008 3
20 a The ship travelled 50 miles south.
b In the evening, the temperature fell by 8oC.
c As the plane approached the airport, it lost 5000 ft in height.
d The car that Peter bought last year is now worth £3200 less.
e The population of the UK has risen by 10 million since 1950.
21 a Adding −4 is the same as subtracting 4.
b Subtracting −10 is the same as adding 10.
c 1 + −4 = 1 − 4 = −3
d 16 − −10 = 16 + 10 = 26
e Subtracting −9 is the same as adding 9.
f Adding −5 is the same as subtracting 5.
g −3 − −9 = −3 + 9 = 6
h 2 + −5 = 2 − 5 = −3
22 a −8 b 9 c 0 d 3
e −1 f 4 g −11 h 1
i −1 j −1 k 9.5 l 4
23 a −5 − −7 = −5 + 7 = 2 b 3 + − 10 = 3 − 10 = −7
c −8 − −9 = −8 + 9 = 1 d 5 + −11 = 5 − 11 = −6
e −4 + −3 = −4 − 3 = −7 f −2 + − 8 = −10
g −10 − −9 = −1 h −6 + −5 = −11
Cambridge Essentials Mathematics Core 7 N1.2 Answers
Original Material © Cambridge University Press 2008 4
25 a b
26 a b
27 a 7 and −3 b −3, −4 and −5 c x < 0
24
Cambridge Essentials Mathematics Core 7 N1.3 Answers
Original Material © Cambridge University Press 2008 1
N1.3 Answers
1 a 3 b 21, 24 c 30 d 300
2 a 5, 10, 15, 20, 25, 30 b 50 c 100 d 11 e 195
3 a 340 b 306
4 a 7 b 203, 210
5 a Multiples of 7, less than 50
b 5 c 44 d 8, 16, 24, 32, 40 and 48
6 33
7 a 15 b 24 c 10 d 28
e 9 f 24 g 56 h 60
i 8 j 30 k 24 l 60
8 a True b False; any number from the sequence 3, 9, 15, 21, ...
c True d True
e False; any pair of numbers whose only common factor is 1 e.g. 3 and 5.
9 1, 2, 3, 4, 6
10 a Less than 4 minutes.
b 12
c The cold tap alone could fill the bath 3 times in 12 minutes.
The hot tap alone could fill the bath 2 times in 12 minutes.
Both taps together could fill the bath 5 times in 12 minutes.
d 12 ÷ 5 minutes = 2 minutes 24 seconds
11 b True; 8 × 4 = 32 c True; 9 × 3 = 27 d False
e False f True; 16 × 3 = 48 g True; 25 × 4 = 100
h True; 12 × 6 = 72 i False j True; 21 × 5 = 105
Cambridge Essentials Mathematics Core 7 N1.3 Answers
Original Material © Cambridge University Press 2008 2
12
13 a
b
c
d
14 a 1, 2, 3, 5, 6, 10, 15, 30 b 1, 2, 4, 7, 14, 28
c 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 d 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
e 1, 5, 25, 125 f 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
g 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 h 1, 2, 4, 8, 16, 32, 64
15 36 is a factor of 3384.
3384 is a multiple of 36.
16 Only b and c must be true.
17 a 1, 2, 4 b 1, 3, 5, 15 c 1, 2, 3, 6
d 1, 2, 4, 8 e 1, 2, 4, 8, 16, 32 f 1
g 1, 3, 9 h 1, 3, 9, 27 i 1, 2, 3, 4, 6, 12
18 a 9
b The highest common factor of the numbers input to Machine A.
19 a 6 b 21 c 11 d 44
e 7 f 500 g 26 h 260
i 4 j 15 k 11 l 18
Cambridge Essentials Mathematics Core 7 N1.3 Answers
Original Material © Cambridge University Press 2008 3
20 a Any pair of numbers such that the first is a factor of the second.
b The larger number is the lowest common multiple of the pair.
21 a i 1, 2 ii 1 iii 1, 7 iv 1, 2, 11, 22
b 2 and 7
22 a 2, 3, 5, 7, 11, 13, 17, 19
b One
23 a i 5 + 7 ii 3 + 13 or 5 + 11
iii 5 + 19 or 7 + 17 or 11 + 13 iv 3 + 29 or 13 + 19
b 12
24 a i 3 × 7 ii 5 × 11 iii 2 × 13 iv 3 × 17
v 11 × 13 vi 2 × 19 vii 3 × 19 viii 5 × 19
b No
25 23, 29, 31, 37, 41, 43, 47
26 5 and 7, 11 and 13, 17 and 19, 29 and 31.
27 a 2 and 3
b 12 = 2 × 2 × 3
28 a 10 = 2 × 5 b 18 = 2 × 3 × 3 c 8 = 2 × 2 × 2
d 30 = 2 × 3 × 5 e 36 = 2 × 2 × 3 × 3 f 100 = 2 × 2 × 5 × 5
29 7883; both 7870 and 7864 are even, and 7795 is a multiple of 5.
Cambridge Essentials Mathematics Core 7 N1.4 Answers
Original Material © Cambridge University Press 2008 1
N1.4 Answers
1 a
b
2 a 16 b 25 c 64 d 81
e 121 f 225 g 196 h 64
3 a 50 b 25 c 80 d 51
e 11 f 18 g 32 h 9
4 a 32 + 42 = 52 b 132 − 122 = 52 c 102 − 82 = 62
5 b The answer is the square of the even number between the two odd numbers.
c The answer is the square of the odd number between the two even numbers.
6 a
b
c A square number has an odd number of factors.
The factors occur in pairs apart from the number that is squared.
Cambridge Essentials Mathematics Core 7 N1.4 Answers
Original Material © Cambridge University Press 2008 2
7 a 4 b 10 c 6 d 12
e 7 f 5 g 8 h 13
i 11 j 15 k 1 l 0
m 16 n 15 o 28 p 8
8 a √900 = √9 × √100 = 3 × 10 = 30
b i 20 ii 50 iii 40 iv 70
9 a √3 lies between 1 and 2 because 1 × 1 = 1 and 2 × 2 = 4.
b √20 lies between 4 and 5 because 4 × 4 = 16 and 5 × 5 = 25.
10 a
b i The sum of the first 5 odd numbers is 52.
ii The sum of the first 10 odd numbers is 102.
c The sum of the first 100 odd numbers is 1002 = 10 000.
11 a
1 3 6 10 15 21
b The sum of the 1st and 2nd triangle numbers = 22.
The sum of the 2nd and 3rd triangle numbers = 32 and so on...
c i The sum of the 9th and 10th triangular numbers is 102 = 100.
ii The sum of the 99th and 100th triangular numbers is 1002 = 10 000.
Cambridge Essentials Mathematics Core 7 N1.5 Answers
Original Material © Cambridge University Press 2008 1
N1.5 Answers
1 a 23.55 b 2.736 c 23.13
d 21.28 e 49.14 f 3.046
2 a £11.25 b £11.03 c £14.98
d £15.30 e £23.10 f £16.84
3 a 2.48 + 10.37 12.85
b 17.69 + 24.35 42.04
c 18.42 + 23.79 42.21
d 48.23 13.71 + 12.87 74.87
4
5 a
b The outermost numbers (0.25, 0.75, 1.25, 2, 1.75 and 0.5) add to give the magic total of 6.5
The remaining numbers add to 13, which is double the magic number.
The numbers on the vertices of each of the two large triangles sum to 3.25, which is half of the magic number (i.e. 0.5 + 0.75 + 2 = 0.25 + 1.75 + 1.25 = 3.25).
Cambridge Essentials Mathematics Core 7 N1.5 Answers
Original Material © Cambridge University Press 2008 2
6 a 30.7 b 7.813 c 67.149
d 388.17 e 1.4314 f 137.68
7 a £51.06 b £4.84 c £16.25
d £97.51 e £190.60 f £44.89
8 a 3.75 b 14.16 c 55.27
d 138.62 e 0.8007 f 24.346
g 91.42 h 0.625 i 1.0148
9 a 9.763 − 4.371 5.392
b 65.07 − 27.18 37.89
c 8.190 − 5.036 3.154
d 5.219 − 3.366 1.853
e 2.631 − 1.428 1.203
f 3.412 − 1.506 1.906
g 4.822 − 3.723 1.099
h 9.358 − 1.361 7.997
10 a 4.266 g b 5.273 g
11 a The Red team (28.63 s).
b The Green team.
c 57.48 s
d 0.08 s
e 0.94 s
Cambridge Essentials Mathematics Core 7 N2.1 Answers
Original Material © Cambridge University Press 2008 1
N2.1 Answers
1 a 29 b 2 c 120
d 2 e 10 f 300
2 a 8 b 70 c 46
d 22 e 16 f 3
3 a 4 × 3 × 2 = 24 b 120 ÷ 2 ÷ 5 = 12 c 7 × 100 ÷ 20 = 35
d 48 ÷ 4 × 3 = 36 e 427 − 1 − 99 = 327 f 1000 ÷ 25 ÷ 5 = 8
4 a 22 b 3 c 25
d 4 e 7 f 0
g 16 h 17 i 3
5 a 5 + 7 × 2 = 19 b 21 ÷ 3 + 11 = 18 c 18 + 6 ÷ 2 = 21
d 12 ÷ 2 + 4 × 5 = 26 e 45 − 15 × 2 − 11 = 4 f 24 ÷ 8 × 5 = 15
6 a 28 b 18 c 41
d 51 e 8 f 15
g 8 h 1 i 364
7 5 + 7 × 92 = 572
8 a 6 b 33 c 49
d 256 e 7 f 1
g 5 h 6 i 100
Cambridge Essentials Mathematics Core 7 N2.1 Answers
Original Material © Cambridge University Press 2008 2
9 a 5 × (4 + 3) = 35 b (98 + 10) ÷ 12 = 9
c 44 − 26 − (3 + 8) = 7 d 48 ÷ (16 − 4) = 4
e 7 + 24 ÷ (3 + 5) = 10 f (11 + 21) ÷ (7 + 9) = 2
g 18 ÷ (3 × 2) = 3 h √(17 − 8) +10 = 13
i √(25 + 5 × 3 − 4) = 6
10 b 12
4575 + c 53389657
++ d 1000 − 8 × (67.2 + 19.9)
e 28
1511 22 + f ( )9
38.79.4 2+
Cambridge Essentials Mathematics Core 7 N2.2 Answers
Original Material © Cambridge University Press 2008 1
N2.2 Answers
1 a 17 b 1 c 6
d 8 e 33 f 2
2 a 2.9 b 88 c 44.7
d 62.7 e 23.3 f 74.5
3 a 15.21 b 163.84 c 45.1584
d 3.76 e 112.81 f 70.55
4 a 8.4 b 12.3 c 19.4
d 26.2 e 11.11 f 58.7
5 a 0.16 b 11.06 c 73.5732
d 1.5481 e 0.3 f 0.13712
6 a 31.04 b 82.81 c 4.64
d 7.66 e 2.9 f 78.2
7 a 9.8 b 6.5 c 16.8
d 34.7 e 15.3 f 42.9
g 5 h 14
8 a 56 b 24 c 3
d 320 e 16 f 22
9 a £80 b £75 c £459
d £624 e £263 f £102
10 a 96 kg b 35 kg c 13 kg d 75 kg
11 a £73.95 b £14.09 c £44.77
d £31.69 e £93.06 f £48.29
Cambridge Essentials Mathematics Core 7 N2.2 Answers
Original Material © Cambridge University Press 2008 2
12 a £414.40 b £151.20 c £204.58
d £133.93 e £85.19 f £509.00
13 a 20.657 + 3.869 ≈ 21 + 4 = 25; less
b 9.8734 × 14.910 79 ≈ 10 × 15 = 150; less
c 8.192 432 ≈ 82 = 64; more
d √84.348 21 ≈ √81 = 9; more
14 a 47.565 568 c 19 066 d 6.927 264 97...
Cambridge Essentials Mathematics Core 7 N2.3 Answers
Original Material © Cambridge University Press 2008 1
N2.3 Answers
1 a i 87 ii
41 iii
94
iv 53 v
169 vi
83
b i 81 ii
43 iii
95
iv 52 v
167 vi
85
2 Shape B.
Fitting together two copies of shape B shows that the red section is 31 of the shape.
3 a 3023 b
2215 c
247 d
2925
4 a 2516 b
119 c
5342
d 9073 e
3017 f
1003
5 a 43 ,
86 b
32 ,
128 c
43 ,
129 d
65 ,
2420
Cambridge Essentials Mathematics Core 7 N2.3 Answers
Original Material © Cambridge University Press 2008 2
6 a 1510
32= b
2112
74= c
3212
83=
d 2520
108
54
== e 9027
309
103
== f 5445
4235
65
==
7 a 43
2821
= b 97
4535
= c 32
7550
=
d 21
4422
8844
== e 43
129
4836
== f 32
3020
9060
==
8 a 21 b
75 c
43
d 103 e
109 f
119
9 43
144108
=
10 a 72 <
31 b
53 >
74 c
32 <
87
d 83 <
52 e
54 <
76 f
65 >
32
11 a 31 ,
52 ,
21 b
74 ,
53 ,
85 c
75 ,
53 ,
65
d 43 ,
65 ,
76 ,
87 e
83 ,
52 ,
21 ,
74 f
74 ,
53 ,
85 ,
32
12 a 125;
6027,
6025 b
107;
3022,
3021 c
83;
2410,
249
d 2413;
4826,
4827 e
254;
7516,
7512 f
2725;
5451,
5450
13 a 312 b
432 c
544
d 873 e
1114 f
1099
Cambridge Essentials Mathematics Core 7 N2.3 Answers
Original Material © Cambridge University Press 2008 3
14 a 3
14 b 5
11 c 4
27
d 2
19 e 5
39 f 953
15 a 32 b
43 c
107 d
65
e 54 f
31 g
32 h
54
16 a 533 b
217 c
522 d
211
e 416 f
651 g
411 h
321
17 a 103 b
101 c
107 d
109
e 21 f
41 g
43 h
54
i 256 j
207 k
53 l
2011
18 a i 102
51= ii
104
52= iii
10035
207= iv
10044
2511
=
v 10045
209= vi
1006
503= vii
10098
5049
= viii 10024
256
7518
==
b i 0.2 ii 0.4 iii 0.35 iv 0.44
v 0.45 vi 0.06 vii 0.98 viii 0.24
19 a 0.95 b 0.28 c 0.45 d 0.63
20 a 21 , 0.59 , 0.7,
43 b
5027 , 0.575, 0.62,
43 c
107 , 0.72,
2015 , 0.8
21
Cambridge Essentials Mathematics Core 7 N2.4 Answers
Original Material © Cambridge University Press 2008 1
N2.4 Answers
1 a i 10017 ii 17% iii
10083 iv 83%
b i 10031 ii 31% iii
10069 iv 69%
c i 10048 ii 49% iii
10051 iv 51%
2 a 10032 = 32% b
10044 = 44% c
1009 = 9%
d 108 =
10080 = 80% e
207 =
10035 = 35% f
2511 =
10044 = 44%
g 5019 =
10038 = 38% h
200124 =
10062 = 62% i
30024 =
1008 = 8%
3 72%
4 19%
5 a i 106 ii 60%
b i 208 ii 40%
c i 2516 ii 64%
d i 2012 ii 60%
e i 6024 ii 40%
f i 5032 ii 64%
Cambridge Essentials Mathematics Core 7 N2.4 Answers
Original Material © Cambridge University Press 2008 2
6 a = d, b = e, c = f.
Diagrams d, e and f are made from copies of diagrams a, b and c, so the percentages are the same.
7 a i 50% ii 50%
b 50%
c 50%
The principle in this question is the same as in question 6. The larger patterns are repeated copies of the smaller pattern so the percentages are the same.
8 a 21 =
10050 = 50% b
41 =
10025 = 25% c
51 =
10020 = 20%
d 101 =
10010 = 10% e
43 =
10075 = 75% f
54 =
10080 = 80%
9 a 257 =
10028 = 28% b
2011 =
10055 = 55% c
5027 =
10054 = 54%
d 107 =
10070 = 70% e
200162 =
10081 = 81% f
400240 =
10060 = 60%
g %8410084
2521
7563
=== h %7510075
2015
6045
=== i %2410024
256
12530
===
10 a 53 b
10029 c
54
d 209 e
258 f
107
g 100
7 h 2521 i
81
11 Diagram with any 7 squares shaded.
Cambridge Essentials Mathematics Core 7 N2.4 Answers
Original Material © Cambridge University Press 2008 3
12
13 a 0.23 b 0.09 c 0.47
d 0.08 e 0.5 f 0.25
g 0.86 h 0.125 i 0.175
j 0.148 k 0.035 l 0.063
14 a 39% b 75% c 6%
d 1% e 27.5% f 37.5%
g 76.4% h 8.3% i 10.8%
15
16 0.085, 57.9%, 66%, 107 , 17
Cambridge Essentials Mathematics Core 7 N3.1 Answers
Original Material © Cambridge University Press 2008 1
N3.1 Answers
1 a
b
c
d
2 a 91 b 103 c 193
d 495 e 361 f 667
g 466 h 790 i 456
3 a
b
4 a 119 b 254 c 94
d 83 e 406 f 216
g 345 h 58 i 145
5 a 37 + 63 = 100 b 453 + 547 = 1000 c 8.9 + 1.1 = 10
d 4.36 + 5.64 = 10 e 87.4 + 12.6 = 100 f 41.8 + 58.2 = 100
g £7.80 + £2.20 = £10 h £4.68 + £5.32 = £10 i £34.80 + £65.20 = £100
6 a 32 b 5.9 c 6.35
d 90.73 e 42.1 f 80.62
g 73.6 h 10.79 i 9.22
7 a 30p b £3.60 c £6.68
d £5.53 e £8.04 f £9.42
Cambridge Essentials Mathematics Core 7 N3.1 Answers
Original Material © Cambridge University Press 2008 2
8 a b
c d
9 a 43 × 6 = (40 × 6) + (3 × 6) b 39 × 7 = (40 × 7) − (1 × 7)
= 240 + 18 = 280 − 7
= 258 = 273
c 3.7 × 11 = (3.7 × 10) + (3.7 × 1) d 5.8 × 9 = (5.8 × 10) − (5.8 × 1)
= 37 + 3.7 = 58 − 5.8
= 40.7 = 52.2
10 a 184 b 693 c 324
d 792 e 594 f 8019
11 a 74.8 b 38.7 c 51.3
d 363.6 e 475.2 f 456
12 a 25 × 36 = (25 × 4) × 9 b 2.5 × 24 = (2.5 × 4) × 6
= 100 × 9 = 10 × 6
= 900 = 60
c 125 × 12 = (125 × 4) × 3 d 12.5 × 16 = (12.5 × 2) × 8
= 500 × 3 = 25 × 8
= 1500 = 200
Cambridge Essentials Mathematics Core 7 N3.1 Answers
Original Material © Cambridge University Press 2008 3
12 e 6.4 × 30 = (6.4 × 10) × 3 f 0.92 × 400 = (0.92 × 100) × 4
= 64 × 3 = 92 × 4
= 192 = 368
13 a 400 b 425 c 350
d 1000 e 1125 f 4000
g 30 h 90 i 30
j 128 k 216 l 300
14 a 4.86 × 50 = 2.43 × 100 b 12.5 × 14 = 25 × 7
= 243 = 175
c £7.50 × 60 = £15 × 30 d £6.25 × 44 = £25 × 11
= £450 = £275
15 a £37.50 b £150 c £1875
16 a 36 b 138 c £36
d £40 e £108 f £720
g £70 h £52 i £105
17 a £72 b £156 c £204
18 a 3336 b 66720 c 2224
d 66.72 e 6.672 f 333.6
19 a 275 × 4 b 5.5 × 200 c 11 × 100
20 a 136 b 24 c 68
d 272 e 48 f 24
21 a 1467 and 6543
b No. 1467 and 6543 are both odd.
22 Any 6-figure number, ending in 0, such that the sum of its digits is divisible by 3.
Cambridge Essentials Mathematics Core 7 N3.1 Answers
Original Material © Cambridge University Press 2008 4
23 a Find a number ending in 5 or 0 and check if the sum of its digits is divisible by 3.
There are only two numbers ending in 5 or 0, so if it isn’t the first one checked
then it must be the other one.
b 97650
24 a Any 5-figure number with a digit sum divisible by 9.
b Any 5-figure even number with a digit sum divisible by 9.
c Any 5-figure number with a digit sum divisible by 9 ending in 5 or 0.
d Any 5-figure number with a digit sum divisible by 9 ending in 0.
25 a 1200 ÷ 24 = 1200/24 b 134 ÷ 50 = 134/50
= 100/2 = 268/100
= 50 = 2.68
26 a 24 b 55 c 14
27 a 8.46 b 12.84 c 2.88
Cambridge Essentials Mathematics Core 7 N3.2 Answers
Original Material © Cambridge University Press 2008 1
N3.2 Answers
1 a 144 b 160 c 328
d 1448 e 4563 f 5992
2 a 380.7 b 38.07 c 76.14
3 a i 2304 ii 4872 iii 1420
b i 23.04 ii 230.4 iii 487.2
iv 142 v 48.72 vi 14.2
4 a 14.4 b 58.4 c 0.78
d 3.55 e 26 f 5.31
5 a i 5144 ii 1729 iii 3429 iv 4404
b i 172.9 ii 51.44 iii 440.4 iv 34.29
c 558.44
6 a 12.15 b 494.4 c 15.48
d 14.6 e 48.24 f 71.52
7 a £46.35 b £7.04 c £74.88
8 a 6 × £3 + 3 × £10 = £18 + £30
= £48
£48 is an overestimate of the cost, so £54.70 is too much.
b £44.70
9 a 6 × £8 = £48 which is an over-estimate of the cost, so Steve has enough money.
b £2.30
Cambridge Essentials Mathematics Core 7 N3.2 Answers
Original Material © Cambridge University Press 2008 2
10 a 3″ > 3 × 2.5 cm = 7.5 cm (so 7.42 cm must be wrong).
10″ = 25.4 so 9″ < 24.86 cm which means this measurement is wrong.
b 3″ = 7.62 cm
9″ = 22.86 cm
11 a 384 b 1802 c 1820
d 1806 e 7708 f 3268
12 a 7657 b 24 024 c 8064
13 £19 552
14 a 96 b 45 c 104
d 1749 e 384 f 2233
15 a 4.2 b 1.81 c 4.9
d 87.4 e 17.89 f 354.8
16 Less; £0.97
17 £29.40
18 5.99
19 a 25 b 28 c 44
20
21 (551 ÷ 29) × (483 ÷ 23) = 399
Cambridge Essentials Mathematics Core 7 N3.3 Answers
Original Material © Cambridge University Press 2008 1
N3.3 Answers
1
2 a 78.84 b 138.71 c 24.6
d 262.44 e 519.14 f 8.36
3 8.24
4 a £1.90
b i £837.50 ii £494.20 iii £38.70 iv £250.40
c i £209.40 ii £32.70
5 a 7.63 b 153.036 c 76.440 049
d 6.45 e 139.932 f 50.74
6 a 2 b 6 c 18
d 46 e 52 f 13
7 a 185 b 5
8 a 35 b £6.60
9 a 12 b 16
10 a £65.95 b £80.02 c £63.42
d £15.37 e £43.15 f £1.79
Cambridge Essentials Mathematics Core 7 N3.3 Answers
Original Material © Cambridge University Press 2008 2
11 a £22.91 b £79.88 c £2792.15
d £898.68 e £6082.98 f £10250.11
12 a 12.4 m2 b 86.9 m2 c 19.7 m2 d 1.9 m2
Cambridge Essentials Mathematics Core 7 N4.1 Answers
Original Material © Cambridge University Press 2008 1
N4.1 Answers
1 a 51
b
c The number of blue squares in Diagram 2 is 51 of 20 =
520 = 4
d
e The number of shaded squares in Diagram 3 is 54 of 20 = 4 ×
51 of 20
= 4 × 4
= 16
2 a 46 b 96
3 a i 31 =
93 ii 126
b i 1 = 55 ii 305
4 26 years
Cambridge Essentials Mathematics Core 7 N4.1 Answers
Original Material © Cambridge University Press 2008 2
5 a i 8 ii 16 iii 24
b i 6 ii 18 iii 42
c i 3 ii 15 iii 33
d i 4 ii 8 iii 20
6 a 3 b 56 c 12
d 9 e 100 f 13
7 a 30 minutes b 15 minutes c 45 minutes
d 25 minutes e 10 minutes f 50 minutes
g 40 minutes h 42 minutes i 24 minutes
j 16 k 36 l 27
8 a 180° b 120° c 90°
d 270° e 240° f 108°
g 150° h 72° i 160°
9 a 12 b 48 c 18
d 14 e 22 f 9
10 a 322 b
433 c
317
d 525 e
4315 f
2127
11 a
11 b i 10% ii 60% iii 90% iv 40%
c i 51 ii
21 iii
107 iv
53
Cambridge Essentials Mathematics Core 7 N4.1 Answers
Original Material © Cambridge University Press 2008 3
12 a 30% of 40 = 103 of 40 b 80% of 30 =
54 of 30
= 12 = 24
13 a 12 b 43 c 9
d 300 e 105 f 1080
g 26 h 6 i 15
14 a 3.4 b 4.3 c 4.5
d 7.5 e 16.8 f 0.69
15 a £8 b £30 c £170 d £2500
e £9.20 f £0.70 g £23.40 h £6.75
i £0.94 j £2.78 k £0.07 l £0.15
16 a £6.40 b £3.20 c £9.60 d £19.20
17 a 4.6 kg b 9.2 kg c 13.8 kg d 6.9 kg
e £2.40 f £1.20 g £0.60 h £4.20
i 30 m j 3 m k 27 m l 33 m
m 42 g n 21 g o 10.5 g
18 a £14 b 4 cm c 35 mm
d £4.80 e 6 g f 18 litres
g 4.8 km h 9 people i 440 tonnes
19 a 31333× = 3(33 +
31 ) b
31
= 99 + 1
= 100
20 a 7 m b 30 oz
21 About 4 m/s
Cambridge Essentials Mathematics Core 7 N4.1 Answers
Original Material © Cambridge University Press 2008 4
22 a £62 b £30 c £18
d £24 e £38 f £17.20
23 a £51 b £93.60 c £405
d £12.69 e £16.86 f £14.85
24 £27 000
Cambridge Essentials Mathematics Core 7 N4.2 Answers
Original Material © Cambridge University Press 2008 1
N4.2 Answers
1
2 a i B ii A
b i A: 4/5, B: 7/10 ii A: 80%, B: 70%
3 a A: 68%; B: 66⅔% b Team A
4 a i 18% ii 20% iii 60% iv 45%
b The answers suggest that left-handers have some advantage over right-handers in these sports, particularly table-tennis. This may be because left-handers are used to playing right-handers, but right-handers are not so used to playing left-handers.
5 a No. Using brain weight alone would place humans as less intelligent than elephants and dolphins. At the other end of the scale, rats show greater intelligence than their relatively small brains would suggest.
b Dolphin: 100
1 Elephant: 1000
1 Horse: 2500
3
Human: 501 Rabbit:
2001 Rat:
801
c Dolphin: 1% Elephant: 0.1% Horse: 0.12%
Human: 2% Rabbit: 0.5% Rat: 1.25%
d Human, Rat, Dolphin, Rabbit, Horse, Elephant
e Opinion may vary on this, but using proportion is better than just using brain weight. However, the elephant is now at the bottom of the list, which seems odd, and the rabbit seems to be too high.
Cambridge Essentials Mathematics Core 7 N4.2 Answers
Original Material © Cambridge University Press 2008 2
6 a 2.5% b This result would place the tree shrew at the top of the list, ahead of humans, which shows that the method does not give a reliable method for comparing intelligence across species.
7 a 9 : 7 b 7 : 9 c 9 : 16 d 3 : 2 e 1
8 a 2 : 3 b 3 : 1 c 4 : 5 d 6 : 5
e 2 : 1 f 3 : 4 g 1 : 3 h 3 : 2
i 3 : 4 j 4 : 9 k 5 : 12 l 4 : 3
9 a 50 : 1 b 1 : 4 c 100 : 1
d 5 : 1 e 1 : 2 f 4 : 3
g 4 : 25 h 1 : 5 i 1 : 1000
10 a 50 p b 30 mm c 60 g
d 40 cm e 25 cm f 1600 m
11 11 : 9
12 1 : 19
13 2/9
14 7 : 1
15 a 35%
b i 39 litres ii 91 litres iii 6.5 litres
16 Asad £250; Sarah £150
17 a AP = 24 cm
b PB = 20 cm
c AP = 40 cm
18 a 16 litres blue, 14 litres red
b 40 litres blue, 35 litres red
c 4 litres blue, 3.5 litres red
Cambridge Essentials Mathematics Core 7 N4.2 Answers
Original Material © Cambridge University Press 2008 3
19 a 70 b 90 c 105
20 a 9 : 7
b i red number = 45, blue number = 35
ii red number = 540, blue number = 420
Cambridge Essentials Mathematics Core 7 N4.3 Answers
Original Material © Cambridge University Press 2008 1
N4.3 Answers
1 a 54
51
53 =+ b
1
55
53
52
=
=+
c 97
95
92
=+
d 75
74
71 =+ e
32
128
125
123
=
=+
f
21
84
83
81
=
=+
2 a
43
86
83
83
=
=+
(Any six squares shaded in the final diagram)
b
43
129
124
125
=
=+ (Any nine squares shaded in the final diagram)
3 a 97 b
32 c
54
d 54 e
43 f 1
4 a
531
58
54
54
=
=+
Cambridge Essentials Mathematics Core 7 N4.3 Answers
Original Material © Cambridge University Press 2008 2
4 b
751
712
76
76
=
=+
c
312
341
32
321
=
=+
d
212
461
43
431
=
=+
5 a 941 b
1211 c 1
d 411 e
211 f
411
6 a 541 b
512 c
832
d 212 e
523 f
214
7 a 31 b
43 c
32
d 52 e
103 f
851
g 1176 h
20178 i
251615
8 a 32 b
21 c
321
Cambridge Essentials Mathematics Core 7 N4.3 Answers
Original Material © Cambridge University Press 2008 3
9
107
103
104
103
52
=
+=+
10 a
151
1510
1511
32
1511
=
−=−
b
211
69
65
64
65
32
==
+=+
11 a 87 b
1631 c
43
d 20131 e
151 f
7513
12 a 211 b
811 c
5031
d 1072 e
413 f
658
g 20171 h
1211 i
25111
13 152
Cambridge Essentials Mathematics Core 7 N5.1 Answers
Original Material © Cambridge University Press 2008 1
N5.1 Answers
1 a 76
732 =× b
531
524 =× c
322
324 =×
2 a
76
732
732
=
×=×
b
531
58
524
524
=
=
×=×
c
98
942
942
=
×=×
d
871
815
853
853
=
=
×=×
3 a 311 b
751 c
871
d 922 e
533 f 3
g 1122 h
1072 i
1731
4 322 m
5 433 million
6 913 cm2
Cambridge Essentials Mathematics Core 7 N5.1 Answers
Original Material © Cambridge University Press 2008 2
7 a
b
8 a 2113 b
2116 c
533
d 528 e
214 f
326
9 a £10.50 b £3.50 c £4.20
d £1.40 e £5.25 f £8.75
10 a 15 kg b 2122 kg c
2137 kg
11 a F = 217 b F =
2117 c F = 40
12 a v = 21 b v = 2120 c v =
2113 d v =
213
Cambridge Essentials Mathematics Core 7 N5.2 Answers
Original Material © Cambridge University Press 2008 1
N5.2 Answers
1 a, c and e
2
3 160 cm2
4 a 6 litres b 30 litres
5 a 14 g b 56 g
6 a £5300 b £84 800 c £240 000
7 a Any example to show that the values of size and cost are not in the same ratio.
b
8 a £208
b i 3 m ii £624
9 40 minutes
b 540 g Sauce 90 g butter 180 g brown sugar 125 ml double cream
c 200 g
10 a Pudding 75 g dates 125 ml hot water 30 g butter 25 g caster sugar 1 egg 75 g self-raising flour
Cambridge Essentials Mathematics Core 7 N5.2 Answers
Original Material © Cambridge University Press 2008 2
t 0 2 4 11 a
s 0 4 8
b, c
d s = 2t
t 0 2 4 12 a
s 2 8 14
b No
c, d
e This line is steeper and doesn’t pass through (0, 0).
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