N1.1 Homework Answers - Cambridge Essentialsessentials.cambridge.org/media/CEMKS3_C8_N1_1_WS_HANS3.pdf · Cambridge Essentials Mathematics Core 8 N2.2 Homework 2 Answers Original

Cambridge Essentials Mathematics Core 8 N1.1 Homework Answers

Original material © Cambridge University Press 2009 1

N1.1 Homework Answers

1 a i – 6 ii 1

b 11

c i –10 ii 3

2 Any pairs of numbers which satisfy the calculation. For example

a –1 – –4 = 3

b –6 – –3 = –3

3

4 a

b

5 a –8 and +3 b –10 and –2

6 a 2 + –7 = –5 b –3 – –8 = 5

c –8 × –2 = 16 d –20 ÷ –4 = 5

7

× −1 4 −6

2 −2 8 −12

−3 3 −12 18

−5 5 −20 30




1 a 49 b 52 c 96 d 256

2 a 8 b 13 c 26 d 54

3 a 196 = 4× 49 = 2 × 7 = 14

b 484 = 4× 121 = 2 × 11 = 22

c 8100 = 81× 100 = 9 × 10 = 90

4 a 9 cm b 81 cm2

5 a 3 cubed equals 27 b 8 is the cube of 2

c 1 is the cube root of 1 d 64 is the cube of 4

e The cube root of 125 is 5 f 1000 is the cube of 10

6 64

7 a 99 b 875 c 8

8 a 5 b 3 c 6

9 36 = 6 and 49 = 7

42 lies between 36 and 49 so 42 must lie between 6 and 7.

10 a 361 b 1024 c 7.29

d 1331 e 79.51 f 3.16

g 9.22 h 12.73 i 13.67




1 a 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

b 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

c 12, 24

d 12

2 a 28 b 36 c 60

3 a 72

b All multiples of 6 are even numbers and numbers ending in ‘5’ are odd.

4 a 1, 2, 3, 4, 6, 8, 12, 24

b 1, 2, 4, 5, 8, 10, 20, 40

c 1, 2, 4, 8

d 8

5 a 6 b 42 c 12

6 a 11 is a prime number.

b

1 is the only number with just one factor.

Numbers with just two factors are prime numbers.

Square numbers have an odd numbers of factors.

Number Factors Number

of factors

1 1 1 2 1, 2 2 3 1, 3 2 4 1, 2, 4 3 5 1, 5 2 6 1, 2, 3, 6 4 7 1, 7 2 8 1, 2, 4, 8 4 9 1, 3, 9 3 10 1, 2, 5, 10 4

Number Factors Number

of factors

11 1, 11 2 12 1, 2, 3, 4, 6, 12 6 13 1, 13 2 14 1, 2, 7, 14 4 15 1, 3, 5, 15 4 16 1, 2, 4, 8, 16 5 17 1, 17 2 18 1, 2, 3, 6, 9, 18 6 19 1, 19 2 20 1, 2, 4, 5, 10, 20 6



7 a 9, 72 b 3, 6 c 9, 25 d 8, 125 e 3, 43

8 a b 90 = 2 × 3 × 3 × 5 = 2 × 32 × 5

9 126 = 2 × 3 × 3 × 7 = 2 × 32 × 7

10 a b 264 = 2 × 2 × 2 × 3 × 11 = 23 × 3 × 11

11 1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7 = 24 × 32 × 7




1 a 35

b 14

c 1120

d 1625

e 2325

f 38

g 43200

h 58125

2 a 415

b 9920

c 1134

d 15399500

e 63791125

3 a 0.8 b 0.25 c 0.7 d 0.375 e 1.125

f 2.2 g 4.75 h 2.5 i 5.8 j 5.375

4 a 0.03125 b 0.6875 c 2.4 d 4.45 e 2.1875

5 a 60 boys b 14

c 0.25 d 16

e 0.166666…

6 a i 0.142857… ii 0.285714… iii 0.428571…

b Recurring decimals

c The recurring decimals contain the same repeating sequence of six digits, but start at

different points in the sequence.

d 87

= 1.142857… 97

= 1.285714… 107

= 1.428571…

7 a i 0.25

ii 0.555555…

iii 0.857142…

iv 0.666666…

v 0.75

vi 0.727272…

b 14

and 912

are terminating decimals. 59

, 67

, 1015

and 811

are recurring decimals.



8 a i 18

= 45360

19

= 40360

110

= 36360

ii 718

= 718

49

= 818

13

= 618

iii 4 288 7 280 7 315 = = = 5 360 9 360 8 360

b i 18

, 19

, 110

ii 4 7 1, , 9 18 3

iii 7 4 7, ,8 5 9

c i 18

= 0.125 19

= 0.111111… 110

= 0.1

ii 187 = 0.388888…

94 = 0.444444…

31 = 0.333333…

iii 45

= 0.8 79

= 0.777777… 78

= 0.875

9 a 58

is greater than 0.6.

b 516

is greater than 0.3.

c 0.59 is greater than 59

.

10 a i 63 and 5

6 ii

156 and 14

15 iii

128 and

129

b i 46

= 32 ii 10

15 =

32 iii 17

24

Cambridge Essentials Mathematics Core 8 N2.2 Homework 1 Answers


N2.2 Homework 1 Answers

1 a 79

b 17

c 8 212 3

= d 14 716 8

=

e 5 125 5

= f 14 221 3

= g 12 230 5

= h 10 215 3

=

i 10 120 2

= j 24 430 5

= k 18 324 4

= l 3 115 5

=

2 3 1 15 4 15 4 194 5 20 20 20 20

++ = + = =

3 a 43 b

107 c

1211 d

2019 e

1615

f 97 g

65 h

158 i

1413

4 a 1511 b

1211 c

2417 d

2219

e 3529 f

9067 g

5033 h

7553

5 a 127 b

103 c

61 d

2219

e 103 f

2413 g

91 h

203

6 a 101 b

4019 c

3611 d

207

e 4229 f

6011 g

3316 h

352

7 a 611 b

4091 c

30111 d

3611

e 1252 f

40113 g

2854 h

3075

8 a 118 b

4021 c

2017 d

158

e 65 f

4017 g

2013 h

3613




1 a 15 b £8 c 120 g d 40 cm e 12 miles

f 20 g £27 h 2131 g i

2128 cm

2 a 9 white chocolates b 15 plain chocolates

c 12 milk chocolates; 12 136 3

= d 16 436 9

=

3 a 21 b 35 c 35 d 465

e 193

f 164

g 285

h 26

4 a 15 g b 27 m c 28 mm

d £56 e 25 kg f 38 cm

5 a 5 fifths; 1 ÷ 51 = 5 b 6 sixths; 1 ÷

61 = 6 c 24 sixths; 4 ÷

61 = 24

6 Dividing by 18

is the same as multiplying by 8.

7 a 45 b 48 c 21 d 64 e 50 f 20

8 a 40 × 18

= 5 therefore 5 ÷ 18

= 40

b 10 × 35


= 10

c 12 × 34


= 12

d 21 × 57


= 21




1 a 20 1100 5

= b 32 8100 25

= c 55 11100 20

=

d 84 21100 25

= e 7100

f 2.5 5 1100 200 40

= =

2 a 75% b 13% c 4%

d 23.5% e 1.8% f 246%

3 Apple Pear Strawberry Melon Banana

12 7 10 5 6

a 103

407

41

81

203

b 30% 17.5% 25% 12.5% 15%

4 Dan should work out 2 ÷ 7 × 100% = 28.57…%, so 27

= 29% to nearest percent.

5 a 9 b 9 c 14.3 d 8.4 e 32 f 5.04

6 a £28.50 b 6.3 m c 67.5 km d 21.7 kg

e 97.5 g f 57.46 m g £390.50 h 33 mm

7 Yes, she is correct.

40% of £60 = 0.4 × 60 = £24

60% of £40 = 0.6 × 40 = £24

8 a 600 m2 b 90 m2

9 a 48% b 20% c 37.5%

10 a 1350

b 26%

11 a 5% b 4.8% c 7.5% d 8% e 32.5%




1 a £54 b £62.72 c £167.28 d £15 e £18.72 f £153.09

2 1028 × 1.13 = £1161.64

3 a The number of barrels of oil produced daily in 2008 will be 105% of the number

produced in 2000. As a fraction, this percentage is equivalent to 2011

100105

= .

b 9602250 barrels

4 a 3100 × 1.07 = £3317 b 3100 × 0.29 = £899

5 a £138 b £1440 c £1578 d £1476

e Option B is cheaper by £102.

6 Original value = £210 000

After an increase of 5%, the value is 1.05 × £210 000 = £220 500.

After a further decrease of 5%, the value is 0.95 × 220 500 = £209 475.

The house is worth less than when he bought it, not the same.




1 a 0.6 b 0.25 c 0.7 d 0.625 e 0.36 f 0.65

2 a 60% b 25% c 70% d 62.5% e 36% f 65%

3 a 0.23 b 0.16 c 0.35 d 0.48 e 0.075

4 a 23100

b 16 4100 25

= c 35 7100 20

=

d 48 12100 25

= e 7.5 15 3100 200 40

= =

5 a 5.6 b 11.2 c 2.8 d 19.6

e 7.8 f 3.9 g 19.5 h 50.7

6 a £6.60

b 17.48 kg

c 0.76 litres

d 23.4 hours = 23 hours 24 minutes

e 5.95 cm

f £148.50

7 a Find 10%. Then halve it to find 5%. Then halve it it again to find 122

%.

Add all three numbers together to find 1172

%.

Or multiply by 7 then divide by 4 then divide by 10 (or equivalent).

b £73.50

c £493.50

8 The trainers cost £59.50 in the sale, so Charlie does have enough money.

9 a 4.8 b 48 c 0.48 d 4800

e 4.8 f 0.48 g 0.48 h 4.8

10 a 0.5 b 0.05 c 0.005




1 a 300 000 b 8000 c 36 000 d 2 950 000

2 a 4 × 103 b 9 × 102 c 5 × 106 d 7 × 104

3 a 1.4 b 0.03 c 7.2 d 0.049

4 a 40 b 500 c 1700 d 3000

5 a 0.18 b 0.004 c 0.3

d 60 e 12 f 40

6 a 0.01 × 0.2 = 0.002 b 0.2 ÷ 0.01 = 20

7 a 0.1 × 0.2 = 0.02 b 10 ÷ 0.5 = 20 or 2 ÷ 0.1 = 20




1 a 80 b 460 c 300 d 820

2 a 400 b 500 c 300 d 4600

3 a 7000 b 2000 c 23 000 d 137 000

4 hundred pounds

5 a 35 608 b 36 000

6 250 km ≤ length < 255 km. Any length in this range is correct.

7 a 14.8 b 6.4 c 11.5 d 18.7

8 a 1.68 b 9.06 c 37.81 d 4.01

9 a 1.4 b 1.43 c 1.64

10 a 31.5 cm2 b 24.3 cm2 c 25.8 cm2




1 a 293 b 216 c 383 d 94

2 £11.25

3 a 5.2 b 25.2 c 6.5 d 33

4 £34.65

5 £5.76

6 a 27 b 122.4 c 351 d 211.2

7 £29.90

8 24.96 kg

9 a 308 b 893 c 1672 d 7644

10 414

11 a 23 b 68 c 189 d 47

12 13

13 a 5 b 600 c 600 d 7000

14 25




1 To find 50% of a number divide the number by 5

To find 41

of a number divide the number by 3

To find 0.333 … of a number divide the number by 2

To find 20% of a number divide the number by 10

To find 0.1 of a number divide the number by 4

2 a 63 b 30 c 7 d 48

e 68 f 6.9 g 28 h 52

3 0.36 kg

4 £2.55 less

5 £245

6 Sam claimed £2.25, Kate claimed £1.50 and Sharon claimed £1.25.

7 126 cm

8 a 2.8 b 4.1 c 6.5 d 8.4

9 Answers may vary – check pupil’s rounding.

a 2100 b 8 c 10

d 25 e 24 f 8000




1 a 26.08 b 283.16 c 237.02

d 34.7 e 15.48 f 62.67

2 a 8.18 kg b 23.48 kg c Less by 1.52 kg

3 a i 35 × 4 = 140 ii 151.2

b i 150 × 5 = 750 ii 725.2

c i 18 × 0.1 = 1.8 ii 1.424

4 US $ 553

5 £3.98

6 £20.76

7 a 4.2 b 6.4 c 12.8




1 a 11 b 4 c 4

d 34 e 15 f 2.3

2 a 4410 b 2.5

3 a Question 3 b Question 2

4 a 10 500 rand b i 2178 rand ii £220

5 110 gallons

6 a £65.21 b 17p

7 £125.80

8 83

of £12.56 is £4.71

72 % of £6.75 is £4.86

So 72% of £6.75 is greater

9 a 6 hours b 9 hours c 36 minutes

d 39 seconds e 7.2 hours f 42 minutes

10 a 360º b 36025

or 725

c 4 minutes 10 seconds




1 a 52 b 100 c 58 d 2 e 48

f 16 g 0 h 10 i 19 j 5

k 2.5 l 5.33 m 7 n 1 o 7

2 a 2 b 10 c 29 d 11 e 14

f 84 g 12 h 64 i 0

3 a (8 + 12) ÷ 4 + 2 = 7 b 8 + 12 ÷ 4 + 2 = 13

c (8 + 12) ÷ (4 + 2) = 3.33 d 8 + 12 ÷ (4 + 2) = 10

e 26 + 15 × 8 − 5 = 141 f (26 + 15) × 8 − 5 = 323

g 26 + 15 × (8 − 5) = 71 h (26 + 15) × (8 − 5) = 123

4 Sharmi worked out 12 + 48 ÷ 16 + 4 = 12 + 3 + 4 = 19

She should have found the answer to 12 + 48 first then divided by 16 + 4.

She could think of it as having brackets like this (12 48)(16 4)

++

.

5 a P = 3 (4m + 2n) b P = 78 cm

6 a P = 4d cm b A = d2 cm 2 c (d + 3) cm

d Yes because the edge lengths are all equal.

e Q = 4 (d + 3) cm f B = (d + 3)2 cm 2

g i W = d2 cm 2 ii X = 3d cm 2 iii Y = 3d cm 2

iv Z = 9 cm2 v Area = (d2 + 3d + 3d + 9) cm 2 = (d2 + 6d + 9) cm 2

h Perimeter = 4 (5 + 3) = 32 cm

Area = (5 + 3)2 = 64 cm2 or 52 + 30 + 9 = 25 + 30 + 9 = 64 cm2




1 a 11 − 5 × 2 = 12 is incorrect. Multiplication must be done before subtraction

so it is 11 − 10 = 1.

b (16 − 4)2 − 8 ÷ 2 = 68 is incorrect division must be done before subtraction

so it is 144 − 4 = 140.

c 3 × 2.82 = 81 is incorrect 3 × 32 would only be 27 and it must be less than this.

d 214 3 8.71

2.5÷

= is incorrect 14 ÷ 32 = 14 ÷ 9 which is less than 2.

So when it is divided by 2.5, the answer must be less than 1.

2 a 78 × 30 = 2340 80 × 30 = 2400 so 78 × 30 must be a bit smaller than 2400.

b 6.95 ÷ 0.2 = 34.75 ÷ by 0.2 makes the answer bigger so it must be bigger

c 418 ÷ 1.1 = 380 418 ÷ 1 = 418 so the answer must be a bit smaller than 418.

d 94 9− × 0.5 = 4.61 85 is about 9. Multiplying by 0.5 is the same as dividing

3 a x = 44 ÷ 4 − 8 (i) b x = 3 729 (iii) c x = 20 ÷ 5 + 6 (ii)

4 If you add the lengths together the total length cut is 7 m which can not be correct as

there was only 6 m of ribbon.

1.9 + 2.4 + 1.4 + 1.3 = 7.0

5 Mode means the most frequently occurring value. In this case it is 4. 142

is not a possible

mode as it does not appear in the list of shoe sizes.

than 6.95.

by 2 so the answer must be about 4.




1 a 820

= 25

b 612

= 12

c 515

= 13

2 a 8 : 12 = 2 : 3 b 6 : 6 = 1 : 1 c 5 : 10 = 1 : 2

3 a 1036

= 518

b 1836

= 12

c 10 : 26 = 5 : 13 d 18 : 18 = 1 : 1

4 a 2 : 1 b 1 : 3 c 1 : 4

d 3 : 5 e 5 : 3 f 12 : 7

g 3 : 2 h 2 : 1 i 1 : 5

j 2 : 11 k 7 : 2 l 3 : 4

5 a x = 12 b p = 6 c n = 3

d y = 8 e q = 5 f g = 9, h = 18




1 a 4 : 30 = 2 : 15 b 8 : 200 = 1 : 25 c 10 : 1000 = 1 : 100

d 15 : 120 = 1 : 8 e 300 : 2000 = 3 : 20 f 5 : 1000 = 1 : 200

g 25 : 600 = 1 : 24 h 35 : 2000 = 7 : 400 i 6 : 48 = 1 : 8

2 a 9.6 m b 5.25 cm

3 a i 10 000 m ii 10 km

b 3.2 cm

4 a Smaller part = 10 cm, larger part = 50 cm.

b Smaller part = 24 cm, larger part = 36 cm.

c Smaller part = 12 cm, larger part = 48 cm.

d Smaller part = 27 cm, larger part = 33 cm.

e Smallest part = 15 cm, middle-sized part = 20 cm, largest part = 25 cm.

5 9

6 a i 800 ml ii 1 litre

b 40 ml

c No it is not correct, a ratio of 1 : 4 means there are 5 parts, so it is 15

not 14

.

7 a 16 : 10 = 8 : 5 b 21 : 15 = 7 : 5

c 42 : 36 = 7 : 6 d No, it would mean they were the same age.




1 a Pounds (£) 0 5 10 15 20

Yen (¥) 0 1000 2000 3000 4000

b

2 a Time (hours) 0 2.5 5 7.5 10

Distance (km) 0 1125 2250 3375 4500

b Speed of aeroplane is 450 km/hour

c

d 2800 km (see graph)



3 a 1 : 5.5 b 1 : 1.25 c 1 : 0.7 d 1 : 0.45 e 1 : 0.8

4 a The two variables are directly proportional because it is a linear graph (it is a straight

line which passes through the origin).

b (approximately) 220 pounds c 110 pounds

d 2.2 pounds e 1 : 2.2

f (approximately) 154 pounds g 0.45 kg

h 1 : 0.45 i 2200 pounds

Documents

N1.1 Homework Answers - Cambridge Essentialsessentials.cambridge.org/media/CEMKS3_C8_N1_1_WS_HANS3.pdf · Cambridge Essentials Mathematics Core 8 N2.2 Homework 2 Answers Original