cambridge essentials mathematics core 7 n1.1 answers - cambridge ocr advanced...

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



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>



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



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.



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



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



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



25 a b

26 a b

27 a 7 and −3 b −3, −4 and −5 c x < 0

24



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



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



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.



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.



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.



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).



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



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



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+



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



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...



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



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



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



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%



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.



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



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



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



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.



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



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



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



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



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



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



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



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



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



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.



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



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



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

=

=+



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



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



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



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



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



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).

cambridge essentials mathematics core 7 n1.1 answers - cambridge ocr advanced...

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