Answers

1 Earnings What you need to know 1 a £342∙90

b £76∙65

c

£2331∙90

2 a £63∙70

b £84∙75

c

£25∙40

3 a Pay before any deductions are taken. Sometimes called ‘top-line pay’. b Pay after deductions are made. Sometimes called ‘take-home pay’. c When you are employed you are allowed some earnings free from taxation. Exercise 1.1A 1 a £50∙10

b £46∙32

c

£26∙10

d £62∙40

b £71∙40

c

i  £32∙64      ii  Time-and-a-third

b £823∙89

c

i  £11 193∙54    ii  £811∙53

2 £392∙80 3 £347∙10 4 £210∙25 5 £203∙17 6 Deal B Exercise 1.1B 1 £33∙60

2 a £350∙88 3 £392∙22 4 a £11 364 5 £8 per hour Exercise 1.2A 1 a £8105

b £8105

c

£15 925

2 a £9512∙50

b £1407∙50

c

£281∙50

3 a £2147

b £178∙91

4 a £19 586∙87

b £2296∙37

5 a 2∙5%

b £79∙44

d £9545

e

£3185

f

Exercise 1.2B 1 a £21 875

b £23 855

c

£16 915

d £12 795

2 a Calculates annual taxable income

b Calculates annual gross income

3 a £65 000

b £6874

c

£30 630

4 a £23 884

b £37 884

5 a £65 000

b £56 895

c

i  £6874    ii  £9010    iii  £15 884

d £12 252

c

15000

e

£19 126

Exercise 1.3A 1 a £1496∙16

b £3238∙56

c

£1246∙80

2 a £15 622∙88

b £963∙70

c

£18∙53

d £233∙88

3 a £2012∙16

b £2313∙98

c

£4326∙14

b £1320

c

i  £2640    ii  £3960    iii  £2112

4 £367∙34 5 a £11 000

1

£1909

Answers

Exercise 1.3B 1 £4557∙36

2 a £4402∙76

b £5030∙81

c

£9433∙57

1 a £1754

b £350∙44

c

£1403∙56

2 a £156∙31

b i  £1457    ii  £156∙31    iii  £255∙23    iv £1201∙77

3 a £232∙71

b £144∙76

c  i £232∙71    ii  £144∙76    iii  £377∙47    iv  £1461∙53

4 a £158∙31

b £100∙12

c

£258∙43

d £1208∙57

5 a £284∙90

b £25∙80

c

£16∙66

d £42∙46

3 £3570∙64 Exercise 1.4A

e

£242∙44

Exercise 1.4B 1 a £285∙76 e £38∙76

b £33∙84 f £24∙44

c £30∙08 g £63∙20

d £349∙68 h £286∙48

2 a £1290∙56 e £177∙09

b £130∙80 f £111∙38

c £139∙52 g £288∙47

d £1560·88 h £1272∙41

3 a £377∙79

b £208∙02

c

£585∙81

d £1622∙19

4 a £18 000

b £14 772∙04

Exercise 1.5A 1 a i  £39∙60    ii  £237∙60 c i  £7∙29     ii  £43∙74

2 a Option 2

b i  £1306∙80    ii  £7840∙80 d i  £295∙30     ii  £1771∙80

b £122

3 a  i £17∙92    ii  £1∙06    iii  £7∙80    iv  £133∙90    v  £26∙78

b £160∙68

4 a £21 f £42∙00

e

b £126 g £143∙35

5 a i  £75    ii  £37∙50    iii  £18∙75

c h

£0∙67 £28∙67

d £4∙02 j £172∙02

b £131∙25

c

£7

£881∙25

6 2011 by £9∙63 Exercise 1.5B 1 a £4∙42

b £442∙50

c

£88∙50

2 a i  £10∙62    ii  £91∙50    iii  £7672∙50    iv  £2∙12 3 a £4947∙50; £66∙72; £5∙10 3   ​ 4 a ​ __ 23

7 b ​ __   ​ 47

b £989∙50; £13∙34; £1∙02 1 c ​ __   ​ 21

b All one-sixth d 0

Preparation for assessment 1 £341∙04

2 a £4071∙60

b £339∙30

c

£1593

3 a £170∙91

b £107∙68

c

£278∙59

4 a £211∙20

b £27 025

c

£94∙08

5 £2406 6 £7672∙50

2

d £1251∙41

Answers

2 Measures What you need to know 1 a 31∙92 cm2

b 63 mm2

c

124∙7 cm2

c

864 cm2

2 106∙8 cm 3 a 77∙76 m3

b 77 760 litres

4 a 1728 cm3

b



5 a Cylinder, c Triangular prism, e Cuboid, f Triangular prism, g Hexagonal prism Exercise 2.1A 1 a i  255 ii  245

b Yes, 244

2 a i  1∙795 ii  1∙805

b 1∙195 to 1∙205

1 3 ​ __ 20  ​

4 a 36 mm 61 mm

b 230 g 65 g

c

2∙50 m 60∙05 m

5 69 mm, 63 mm Exercise 2.1B 1 a ​ _18 ​

1 b 87 ​ _2 ​%

2 a 171∙9 ml

b 180 ml 68∙1 ml

 

3 43∙75 hours, 43∙05 hours 4 546 cm 5 11∙4 mm 60∙1 mm or other, where maximum is 11∙5 mm 6 a 7∙56 hectares

b 32

Exercise 2.2A 1 a 1∙95 m3

b 532 cm3

c

473 cm3

b 332 cm3

c

142 cm3

5 a Triangular prism b 189 cm3

c

279 cm2

6 a 460 cm3

c

337 cm2

2 a 227 cm3 3

3 a 3174 cm

d 1980 mm3

b 1320 cm3

4 34∙9 cm3 b 22∙6 cm

7 689∙8 litres Exercise 2.2B 1 a 93 305 cm3

b 224 kg

2 a 148 cm3

b 1211 cm3

c

173 cm3

3 5∙86 cm 4 23∙4% 5 44 498 m3 6 a Lounge/kitchen 5569 BTU, bedroom 3434 BTU, bathroom 2686 BTU 2

7 a i  Student’s own sketch ii  4∙33 cm iii  64∙95 cm

1

b 12 624 BTU b 779∙4 cm3

e

61∙4 m3

Answers

Exercise 2.3A 1 24 b 281 250 cm3

2 a 32

c

4913 cm3

d 124 034 cm3 3

3 a 52 cm 3 32 cm 3 20 cm

b 33 280 cm

4 a Yes (total weight 392 kg) b    Many other ways are possible TD TD TD TD W

W W

Exercise 2.3B 1 a 30

b £1680

2 a Box 1: 33 4 8, 25 4 8, 11 4 5 5 4 3 3 3 2 5 24; box 2: 49 4 8, 33 4 8, 6 4 5 5 6 3 4 3 1 5 24 b First company’s box, by 627 cm2 3 a 108

b 95 g

4 a You wouldn’t be able to see the title of the book. b 264. Horizontally: 8 along 3 11 high 3 3 rows 5 264; vertically: 88 along 3 1 high 3 3 rows 5 264; same either way. 5 a Method 1 Edges of large container Match

Method 2

Method 3

Method 4

Method 5

Method 6

Packets

Match

Packets

Match

Packets

Match

Packets

Match

Packets

Match

Packets

29∙6 cm

5∙4 cm

5

5∙4 cm

5

6∙3 cm

4

6∙3 cm

4

9∙5 cm

3

9∙5 cm

3

21∙8 cm

9∙5 cm

2

6∙3 cm

3

9∙5 cm

2

5∙4 cm

4

5∙4 cm

4

6∙3 cm

3

26∙2 cm

6∙3 cm

4

9∙5 cm

2

5·4 cm

4

9∙5 cm

2

6∙3 cm

4

5∙4 cm

4

 

40

Total packets

30

32

32

48

b Methods 1 and 3 possible, so max. 40 small boxes by method 1 6 A, B, D, E, G, I, K, M at the sides and C, F, J in the middle (H, L, N don’t get on the first ferry) Exercise 2.4A 1 31 minutes

2

B

15 0

   60 minutes

45

Finish

A

15

Start 0

C

4

3

D 1

E

3 a 3∙5 hours d Empty room, paint woodwork

b Return furniture e 20∙5 hours

c

Paint walls

4 a 21 minutes

b 34 minutes

c

78 minutes

2

36

Answers

Exercise 2.4B 1 a

A B C D E

2 a, b  A B C D E F

3 a

Decide on plants Purchase plants Dig holes Put in plants Water plants Date and venue Book performers Make tickets Sell tickets Lighting and sound Refreshments

b

B A

Start

D

E

Stop

C

c

— A A A, C A, B A, D

Start

E

B

A

Stop F

C D

b Heat oven while assembling and mixing ingredients. Mix icing while cake is cooking

A B C D E F G H

— A — A, B A, B, C, D A, B, D, E A F, G

4 a

—      — Start B — A — D D D

A B C D E F G H I



— A A A, B, C A, B, C, D

or cooling. c

D

B A

1

5

3

Start

E

4

3

35

F 15

H

Stop

5

G

C

d 64 minutes

B 1

2

C 4

D

b Minimum time is 7 minutes



E

A

3 G

2 F

Stop H 5 2 I 3

4

Preparation for assessment 1 a 3∙25 mm, 3∙15 mm

b 5%

2 114 mm and 126 mm 3 a 792 cm3

b 5∙15 cm3 (to 3 s.f.)

4 a 59 648 mm3

b 342 000 mm3 3

5 a 180

b 329 cm

c

128 554 mm3

c

32%

d 106 029 mm3

6 Fitting 7∙5 cm along 85 cm side and 23 cm along 75 cm side and upright gives 11 3 3 3 2 5 66 boxes 7 a Having a shower 8 a

A B C D E F G

— — A A, B, C A, B, C, D B, C, D A, B, C, D, E

b Gets dressed     A Start

2 B 3

b Critical path is ACDEG c 24·5 hours

3

c

25 minutes

C

D

2

1.5

E G

18 F 1

1

Stop

Answers 9 42 days 9

12

9

foundations

walls

electrical/plumbing

17

3 [11]

7

2

drains

make doors

roof

ceiling

3 gutter 9

5

install doors 21 days

4

7 days

14 days

paint

Answers

3 Gradients and real-life linear functions What you need to know 1 1 ​ _3 ​

2 a 7 lb 5 3∙2 kg, so 3∙5 kg cat is heavier c Conversion factor between kg and lb, 1 kg 5 2∙2 lb a

n

0

5

10

15

20

C 5 6n 1 15

15

45

75

105

135



Advertisement cost

150 Cost (£)

3

b 2∙2 d 26∙4 lb b

c Because the cost is for whole numbers of lines only. d i  Cost per line    ii  The one-off charge

100 50 0

4 17 cm

0

5

10 15 Number of lines

20

25

Exercise 3.1A 1 b only

2 a 0∙3

b i  2∙61 m    ii  13∙57 m2



b 1306 cm

3 a 1300 cm

4 0∙003 km 5 42∙5 mph 6 a 25 litres/min

b 8∙8 min

Exercise 3.1B 1 a ​ _34 ​ 2 a 5

1 b 2 ​ _3 ​

c

0

b Rate per hour

c

Cost 5 15h

3 a 220

b Metres fallen per second

b 14 km 4 a 10.30 a.m. 5 BC and AD are parallel

c

1 d 2 ​ _2 ​

c

h 5 210t 1 1500

Shaun: 8 km/h; Ian: 12 km/h

Exercise 3.2A 1 a m 5 2, c 5 20 c £56

b c is the standing charge, m is the cost per mile d 2∙5 miles

2 a i  2880    ii  2720

b £120

c

The monthly payments

3 a A(x) 5 6·5x b Over 65 months the ‘cost so far’ for Plan C can be written as £199 when x is 60 or less and £398 when x is greater than 60. c Washing machine care plans

400

Cost (£)



Care Plan A

350

Care Plan B

300

Care Plan C

250 200 150 100 50 0

1

0

10

20

30 Months

40

50

60

Answers d i  36 and 60 months    ii  24236 months and 49265 months iii Plan A is cheapest for the first 24 months only. You would be paying more than the cost of the machine after 61 months. Plan B is cheapest between 24 and 36 months. Plan C is cheapest from 37 months to 60 months. You would only take it out for 5 years as after that you would be paying the same as the cost of the machine.

Amount of rainforest (hectares)

4 a m 5 24∙6, c 5 718∙3 b m 5 number of hectares of rainforest lost each year, c 5 number of hectares of rainforest in 1990 c Amount of rainforest 750 700 650 600 550 500 0

0

5

10 15 20 25 Number of years since 1990

30

d Just after the beginning of 2146

35 e

Student’s own investigation

Exercise 3.2B 1 a C 5 8x 1 48

b i 

c S 5 12x

d

x

0

5

10

15

20

C 5 8x 1 48

48

88

128

168

208

Motor bike hire costs

300

12 days

SpeedBikes Rent-a-Bike

250 Cost (£)

e

    ii  See graph below

200 150 100 50 0

0

5

10 15 Number of days

20

f i For less than 12 days’ hire choose SpeedBikes, for more than 12 days’ hire choose Rent-a-Bike, for 12 days’ hire it does not matter which company you choose. ii  SpeedBikes 2 a C(x) 5 30x

b £150

c

2 days

3 a T(x) 5 0∙085x 1 19∙50 b Y(x) 5 0∙07x 1 20 c Phone charges 25

Talk-a-lot Yellow

Cost (£)

23 21 19 17 15 0

0

10

20 30 40 Number of minutes

50

d Up to 33 minutes, Talk-a-lot is cheaper; more than 33 minutes, Yellow is cheaper.

2

d 13 days

Answers 4 a 3x 1 6y 5 3000 b i  y 5 2 ​ _12 ​ x 1 500     ii 

School concert ticket sales

800

3x � 6y � 3000 x � y � 750

Number of adults

700 600 500 400 300 200 100 0

0

200 400 600 Number of students

800

c 0 students and 500 adults, 100 students and 450 adults, 400 students and 300 adults (or others from the graph) d x 1 y 5 750

e

See graph above

f When the x- and y-values for each equation are the same; 500 students and 250 adults Exercise 3.3A 1 a Domain 5 {​  x : x ∈ , 0 , x < 10 000 }​

b Range 5 {​  5·90, 6·35, 7·55, 9·75, 24·50 }​

c 26 24 22 20 18 Cost (£)

16 14 12 10 8 6 4 0

0

50 0 10 00 15 00 20 00 25 00 30 00 35 00 40 00 45 00 50 00 55 00 60 00 65 00 70 00 75 00 80 00

2

Weight (g) 2 a Domain 5 {​  h : h ∈ , 0 < h < 24 }​ ;   range 5 {1∙00, 1∙50, 2∙00, 2∙50,3∙00}

b 4·0

Cost of parking

3·5 3·0 2·5 2·0 1·5 1·0 0·5 0

3

0

2

4

6

8 10 12 14 16 18 20 22 24 26 Number of hours

Answers

{

  5·75h if 0 < h < 40 3 a P(h) 5 11·5h 2 230    if   h . 40

c   £287∙50

b 350 300 Pay (£)

250 200 150 100 50 0

{

0·2203x if 0 < x < 900 4 a C(x) 5 b 87.57 1 0·123x  if  x . 900

0

5 10 15 20 25 30 35 40 45 50 55 60 Number of hours worked

c £505∙77

600 550 500 450

Cost (£)

400 350 300 250 200 150 100 50 0

50 0 10 00 15 00 20 00 25 00 30 00 35 00 40 00

0

{

5 S(m) 5 200 1 50m if 0 < m < 12 70m 2 40    if  m . 12

Amount of electricity used (kW h) b £2060

Exercise 3.3B 1 a

550 500 450

Cost (£)

400 350 300 250 200 150 100 0

0

50 10 0 15 0 20 0 25 0 30 0 35 0 40 0 45 0 50 0 55 0 60 0

50

Number of copies

4

b Best to get 201 copies

Answers

{

10 1 5x    if   0 < x < 50 2 a T(x) 5 10 1 3·5x    if   x > 51 c Best to buy 51 t-shirts

b

400 350

Cost (£)

300 250 200 150 100 50 0

{

F(x) 5   0·21x        if 0 , x < 730 0·15x 1 43·8x   if   x . 730 e If you use less than 2433 kW h you should go with Fusion; if you use more Fusion than 2433 kW h you should go with Bright Sparks Bright Sparks

3 a C(x) 5 0∙26 3 365 1 0∙129x 5 0∙129x 1 94∙9

c

b and d   700 600 500 Cost (£)

0 10 20 30 40 50 60 70 80 90 100 Number of t-shirts

400 300 200 100 0

0

1000 2000 3000 4000 Amount of electricity used (kW h)

Preparation for assessment 1 a 2∙5 m

b 10∙3 m

2 a 43 km/h

b 10 p.m.

b P(t) 5 2300t 1 209 000 3 a 2300 people per year d It does not take account of other factors, e.g. housing or land availability. b

{

if if if

0,h<2 2,h<4 4 , h < 24

Luxury Limos Party Cars

150 100 50 0

5·2 5 a G(h) 5 6·9 8·5

252 700

Limo hire

200 Cost (£)

4 a L(x) 5 20 1 2x  P(x) 5 3·6x c i  Party Cars   ii  Luxury Limos d 12∙5 miles

c

0

20 40 Number of miles

60

b 9 8 7 Cost (£)

6 5 4 3 2 1 0

5

0

2

4

6

8 10 12 14 16 18 20 22 24 Number of hours parked

Answers

{

6 a P(h) 5    8h     if   0 < h < 35   b   12h 2 140   if 35 , h < 45



450

c

£364

400 350

Pay (£)

300 250 200 150 100 50 0

{

0

5 10 15 20 25 30 35 40 45 50 Number of hours worked

12x 1 20 if 0 , x < 50 7 School Hoodies Company S(x) 5 10x 1 20 if 51 < x < 100   8·5x 1 20   if   x > 101

{

13x Personal Screen Printers P(x) 5   9x   8·5x  

1700

if 0 , x < 40 if 41 < x < 120 if     x > 121

School Hoodies Company Personal Screen Printers

1600 1500 1400 1300 1200 1100 Cost (£)

1000 900 800 700 600 500 400 300 200 100 0

0 20 40 60 80 100 120 140 160 180 200 220 240 260 Number of hoodies

Personal Screen Printers are cheaper for 0 to 19 hoodies, for 41 to 100 hoodies and for 121 or more hoodies. School Hoodies Company is cheaper for 21 to 40 hoodies and for 100 to 119 hoodies.

6

Answers

4 Savings and spending What you need to know 1 a 6∙74

b 72∙99

c

15∙71

d 99∙70

2 a 0∙04

b 0∙13

c

0∙062

d 1∙25

3 a £1∙33

b £9∙37

c

42p

d 35p

4 a 14 413

b 8∙1%

c

27 376 shillings

d 29 200 yen

c

£43∙48

c

1629∙63 CHF

Exercise 4.1A 1 a €230

b 9354 baht

2 a 54 750 yen

b 2092∙50 dollars

3 a £600

b £40∙32

4 a €105

b €10

5 a £572∙99

b €2070

6 a Germany £1752∙61, USA £1745∙38

b USA (cheaper by £7∙23)

7 a Americana Clubs £272∙47, Tiger Clubs £209∙14 8 a 75 pesos

b 11 672∙25 rubles

9 a £3184∙71

b €2081∙17

d £103∙47

c

£1070∙58

c

€45∙67

b Tiger Clubs, cheaper by £63∙33 d $131∙22

Exercise 4.1B 1 a 279 624 dong

b 113∙57 baht

2 a 25 926 baht

b €554∙33

3 a 7∙90 pesos

b £1012∙66

4 a i  3940 real   ii  3540 lira 5 a €402∙50

b €1∙19

6 a $1∙57

b £10

b i  1 real 5 $0∙51   ii  1 lira 5 $0∙56

c

7 3∙7% 8 2∙5% 9 Student’s own investigation Exercise 4.2A 1 a £15

b £45

c

£21∙25

d £179∙55

2 a £25∙84

b £51∙68

c

£12∙92

d £17∙23

3 a £336

b £88∙20

c

£1023∙83

b £121∙20 4 a A 5 60, B 5 3060, C 5 61∙20, D 5 3121∙20 c i  Interest after 1 year    ii  Total amount in account    iii  C65C5*0∙02, C75C51C6 iv  Total interest earned    v  Amount needs to be rounded to 2 decimal places

5 a £958∙70

b £33∙70

6 a £24∙48

b £56∙03

c

£308∙59

d £472∙21

7 £22 497∙28 8 a £88∙81

b £2∙81

Exercise 4.2B 1 a 1∙04

b 1∙02

c

1∙015

d 1∙125

2 a £809∙22

b £149∙72

c

£1205∙85

d £402∙64

1

3593∙91 lira

Answers 3 16 years 4 36 months or 3 years 5 £5116∙67 6 45 years 7 €2596 8 £1 996 500 9 a i  Frank £2, Faith £1∙01    ii  Frank £6, Faith £1∙05    iii  Frank £26, Faith £1∙28 b 652 years c Frank 999 999 years, Faith 1389 years 10 238 years 11 a i  8 years    ii  12 years    iii  6 years    iv 18 years b i 

Doubling time

Time to double, T (years)

80 70 60 50 40 30 20 10 0



0

1

2

3

4

5

6

ii 

7 Rate (%)

8

9

10

11

12

13

9

10

11

12

Doubling time

0.20 0.18 0.16 0.14

1 T

0.12 0.10 0.08 0.06 0.04 0.02 0

0

1

2

3

4

5

6

7 Rate (%)

8

13

c Student’s own investigation Exercise 4.3A 1 a i  £43∙90     ii  £1053∙60    iii  £53∙60 c i  £118∙20    ii  £2127∙60    iii  £127∙60 e i  £293∙55    ii  £10 567∙80     iii  £1067∙80

2 a £165

b £5940

c

£415∙80

3 a £321∙20

b £7708∙80

c

£1008∙80

4 a £242∙05

b £11 618∙40

c

£1318∙40

5 £5000

2

b i  £86∙50 d i  £141

ii  £1038 ii  £6768

iii  £38 iii  £768

Answers

Exercise 4.3B 1 a £623

b £7476

c

£952

2 a 12 months: £1274∙79, 24 months: £670∙63

b £1935∙12

3 a i  £3800    ii  £2528    iii  £1179∙68

b £1250∙46

4 Yes, if Daisy borrows £2950 she will pay back £348∙10 in interest after one year, but if she borrows £3000 she will only pay back £321 in interest after one year. 5 £472∙70 6 29% 7

a b c d e f

i  £91    ii  £81∙91    iii  £72∙73

(Setting up spreadsheet) i  £63∙46    ii  11th month    iii  £5∙90 Student’s own investigation The debt remains at £100 Student’s own investigation

Exercise 4.4A 1 a £6∙15

b £416∙15

2 a £16∙79

b £1415∙79

3 a £17∙81

b £801∙84

c

£215∙45

4 £1206∙02 5 £380∙24 Exercise 4.4B 1 a 28∙3%

b 18∙2%

c

6∙2%

2 a £5

b £6∙84

c

17∙9%

3 a 16∙1%

b £2434∙04

d 24∙3%

4 4 months 5 a £4725∙47

b 15 months

c

His balance would increase every month.

6 a £49

b £331∙50

c

£326∙20

d 28∙8%

Exercise 4.5A 1 10 oranges for £3∙40

2 Packet B 3 a 22-pack

b No, unit cost of three 6-packs is 22p, but unit cost of 22-pack is 21∙3p

4 a 8 3 330 ml cans b 4 3 2-litre bottles 5 REAL Light, because Clint can get 50 texts and 10∙5 minutes per £1 Exercise 4.5B 1 Heart Broadband; Heart Broadband offers 10 GB for £11 and 1 MB speed for £2·20 per month; Brill Broadband offers

10 GB for £19∙98 and 1 MB speed for £1∙25 per month 2 a Supreme

b Supreme 2 buy 3 packs for £6

3 a Softly

b Softly

c

Fresh

d Softly

4 Student’s own choice. Some reasons could include: Elm Light 2 best value per £ for calls, Oak Green 2 best value for data per £, Sycamore T6 2 shorter contract.

3

Answers

Preparation for assessment 1 a €374∙40

b £20∙25

2 a Euro Tyres £139∙53, Sam’s Tyres £146∙50 3 a 246∙99 naira

b £80∙97

4 a £24∙75

b £74∙25

5 a £48∙72

b £101∙40

c

72 cents

b Euro Tyres, by £6∙97 c

£18∙56

6 35 years 7 a £2634∙93

b £1154∙79

8 a £1327∙50

b £8827∙50

c

£245∙21

9 a £4∙75

b £400∙74

c

£60∙98

10 21% 11 a B 12 10 months

4

b C

d £10∙31

Answers

5 Summary statistics What you need to know 1 a i  £31 062·50    ii  £23 200

2 a 4

b £32 600

c

There is no mode

b Sixties

Exercise 5.1A 1 a i  54    ii  75    iii  63·5    iv  58 and 69

b

50

52

54

56

58

60

62 64 Age

66

68

70

72

74

76

c 21 2 a L 5 22·5 °C, Q1 5 20·3 °C, median, Q2 5 0·7 °C, Q3 5 1·25 °C, H 5 1·9 °C

�3

�2

0

�1

1

2

b i  4·4 °C    ii  629% to nearest whole number    iii  Fairly consistent 3 a Median, Q2 5 50, Q1 5 38, Q3 5 56 b i There are many more teachers towards the older end of the age-range. ii There will probably be a lot of teachers retiring about the same time possibly leading to staffing problems.

Exercise 5.1B 1

a b c d

i  £562 (nearest £)    ii  £556    iii  £395

2

a b c d

i  £219    ii  £78

£480, £516, £522, £524, £606, £633, £677, £677, £875 i  £612 (nearest £)    ii  £606    iii  £395 When £50 is added to each fare, the mean and median are increased by £50, but the range stays the same. L 5 £172, Q1 5 £219, median, Q2 5 £223·50, Q3 5 £239, H 5 £250 i  £249    ii  £78 L 5 £202, Q1 5 £249, median, Q2 5 £253·50, Q3 5 £269, H 5 £280

3 a Median, Q2 5 50%, Q1 5 37%, Q3 5 63% b 30 4 Men’s: L 5 77·15 m, Q1 5 80·09 m, median, Q2 5 82·27 m, Q3 5 83·73 m, H 5 84·58 m Women’s: L 5 58·78 m, Q1 5 59·40 m, median, Q2 5 62·26 m, Q3 5 64·72 m, H 5 69·55 m Olympic javelin finals Women’s Men’s 55

5 a b c

1

60

65

70 Metres

75

80

85

Section 1: L 5 13, Q1 5 27·5, median, Q2 5 35·5, Q3 5 52, H 5 66 Section 2: L 5 28, Q1 5 51·5, median, Q2 5 63, Q3 5 80, H 5 97 Section 2 has generally much higher marks and the marks are more spread out. Section 2 may have more ability in maths; Section 1 may not have worked so hard, etc.

Answers 6 a It doesn’t seem justified as half the boxes have fewer than 50 matches. b In general, the second sample shows more matches per box and a smaller spread of matches per box. c We would be more confident of the results from a sample of size 100 rather than a sample of 10. In the second sample, only a quarter of the boxes had fewer than 50 matches and the smallest number was 48, so we would be a bit more likely to accept the manufacturer’s claim.

Exercise 5.2A 1 a 57·5 ml b 3 ml

2 a Median, Q2 5 55 kg, Q1 5 51 kg, Q3 5 59 kg b IQR 5 8 kg, SIQR 5 4 kg 3 a Cheapest quotes: median, Q2 5 £18·41, IQR 5 £5·26; more cover quotes: median, Q2 5 £44·18, IQR 5 £29·19 b Student’s own answers should include comments on second set of quotes being much more expensive and much more variable. Comment could also be made on the desirability of better cover, etc. 4 a Archie’s: L 5 4 months, Q1 5 5 months, median, Q2 5 9 months, Q3 5 14 months, H 5 17 months; Carla’s: L 5 4 months, Q1 5 5 months, median, Q2 5 10 months, Q3 5 12 months, H 5 13 months b Archie’s: IQR 5 9 months, Carla’s: IQR 5 7 months c Both showrooms have similar medians of car age at 9 and 10 months. The ages of Archie’s Autos’ cars are more variable. d Carla’s Cars because more of them ( ​ _34 ​ ) are 12 months old or less e Student’s own answers to possibly include price, mileage, condition of car, etc.

Exercise 5.2B 1 a If a box plot is drawn, we can see that the RPI is generally higher than the CPI and also more variable. Inflation indices over 18 month RPI CPI 3

4

Index

5

6

b As the CPI is generally smaller, it would cost the government less every year when the annual pension rise comes in. As it is slightly less variable it might make it easier for planning ahead. 2 a b c

Median, Q2 5 £27 250, IQR 5 £4000 £27 000, £27 000, £28 500, £30 000, £31 000, £34 000; new median, Q2 5 £29 250, new IQR 5 £4000 i Same amount added to the median ii IQR stays the same

3 a Median, Q2 5 £60, IQR 5 £14 b Discounted prices: £36, £45, £52·20, £53·10, £53·10, £54, £54, £63, £63, £63·90, £66·60, £67·50, £69·30; new median, Q2 5 £54, new IQR 5 £12·60 c i Decreases by 10% ii Decreases by 10% 4 a Median (Q2) 5 £499, SIQR 5 £42·50 b Median, Q2 5 £628·80, SIQR 5 £51 5 a IQR 5 £7000 b New median, Q2 5 £29 400, new IQR 5 £7350

2

Answers

Exercise 5.3A 1 a 3·05 absentees 2

a

b 7·9 passengers

52·92 cm

Journey time, t (min)

Frequency, f

Mid-value, x

f   3 x

0,t<5

 1

  2·5

   2·5

  5 , t < 10

 2

  7·5

  15

10 , t < 15

 4

12·5

  50

15 , t < 20

 9

17·5

157·5

20 , t < 25

 8

22·5

180

25 , t < 30

 3

27·5

  82·5

30 , t < 35

 2

32·5

  65

35 , t < 40

 1

37·5

  37·5

S

30

b 19·7 min (to 1 d.p.)



c

590 3 d ​ __   ​ 10

15 , t < 20

c

Exercise 5.3B 1

a

i

Price, P (£)

Frequency, f

Cumulative frequency

     0 < P , 25 000

 0

 0

25 000 < P , 50 000

 1

 1

50 000 < P , 75 000

 7

 8

  75 000 < P , 100 000

20

28

100 000 < P , 125 000

20

48

125 000 < P , 150 000

 9

57

150 000 < P , 175 000

16

73

80

House prices

Cumulative frequency

70 60 50 40 30 20 10 0

0 25 50 75 100 125 150 175 200 Price (£ thousands)

ii  Median, Q2 5 £110 000 (approx.), Q1 5 £88 000 (approx.), Q3 5 £142 000 (approx.) b 24 2

a

3

Pulse rate, P (beats per minute)

Frequency, f

Cumulative frequency    4

30 < P , 40

 4

40 < P , 50

12

  16

50 < P , 60

16

  32

60 < P , 70

19

  51

70 < P , 80

21

  72

80 < P , 90

12

  84

  90 < P , 100

12

  96

100 < P , 110

 6

102

110 < P , 120

 4

106

Answers

b

Pulse rates of sports centre members

110 100

Cumulative frequency

90 80 70 60 50 40 30 20 10 0

30 40 50 60 70 80 90 100 110 120 Pulse rate (beats per minute)

c Median, Q2 5 71 beats per minute (approx.), Q1 5 56 beats per minute (approx.), Q3 5 86 beats per minute (approx.) d Approx. 28 people Exercise 5.4A 1 2·68 cm (to 2 d.p.) b 3·7 hours (1 d.p) 2 a 3·7 hours (1 d.p) c Student’s own answers, e.g. basic formula: involves working to 2 d.p. throughout, alternative form of the formula: have to be careful to work out the whole numerator before dividing by (n 2 1) _

_

​  5 61·4 goals, s 5 16·7 goals (1 d.p.) b x​ ​  5 37·2 goals, s 5 3·1 goals (1 d.p.) 3 a x​ c Top 5 teams had scored on average many more goals than the bottom 5 teams. Number of goals scored by top 5 teams was much more variable than the number scored by the bottom 5 teams. _

4 ​x​ 5 31·2 min (1 d.p.), s 5 1·8 min (1 d.p.) __

5 a ​x​ 5 £57·82, s 5 £17·20 (to nearest 1p) __ b ​x​ 5 £60·82, s 5 £17·20 __ c ​x​ 5 £63·60 (to nearest 1p), s 5 £18·92 Exercise 5.4B 1

a

Number of missed appointments, x

Number of days, f

x2

Working to find Ʃx

Working to find Ʃx2

0

10

 0

   0

   0

1

16

 1

  16

  16

2

22

 4

  44

  88

3

 8

 9

  24

  72

4

 4

16

  16

  64

Ʃ

60

100

240

b i  ∑ f 5 60    ii  ∑ x 5 100    iii  ∑ x2 5 240 _ c x​ ​  5 1·67 missed appointments/day (to 2 d.p.), s 5 1·11 missed appointments/day (to 2 d.p.) _

​  5 148·1 hours, s 5 38·8 hours (to 1 d.p.) 2 a x​ b South-east England has on average nearly 60 more hours of sunshine in June than the north of Scotland. South-east England has slightly more variable hours of sunshine than the north of Scotland. c The north of Scotland would have more hours of daylight in June than south-east England. _

​  5 £310, s 5 £91·29 3 a x​

b 6 days

4 a Means: Africa 5 56·6 years, Europe 5 78·4 years; standard deviations: Africa 5 6·7 years, Europe 5 4·1 years. So life expectancy is on average over 20 years more in European regions than African regions. The life expectancy in African regions is slightly more variable than in European regions. b Student’s own answers to include, for example, health care, drought, wars, poverty, etc.

4

Answers

Preparation for assessment 1 a Median, Q2 5 349 kilowatt-hours, range 5 16 kilowatt-hours b Q1 5 341 kilowatt-hours, Q3 5 353 kilowatt-hours, IQR 5 12 kilowatt-hours c i  351 kilowatt-hours    ii  12 kilowatt-hours

2 a 6 < d , 8 b



Distance, d (km)

Number of days

Cumulative frequency

0
 2

 2

2
 5

 7

4
 6

13

6
11

24

8 < d , 10

 9

33

10 < d , 12

 2

35

c

Running distances

Cumulative frequency

35

  i  6·8 km    ii  4·5 km    iii  8·4 km

30 25 20 15 10 5 0

0

2

4 6 8 10 12 Distance (km)

d

0

1

2

3

4

5 6 7 8 kilometres

e ​ _15 ​



Running distances

9 10 11 12

3 a Mean 5 25·4 cars (to 1 d.p.), standard deviation 5 6·6 cars (to 1 d.p.) b There is little difference in the average number of cars that drive straight through the two streets. However, it is more variable in Catriona’s street. 4 a

_

Number of seals, x

Frequency, f

x2

Working to find Σx

Working to find Σx2

 8

 4

  64

  32

  256

 9

 7

  81

  63

  567

10

 5

100

  50

  500

11

 8

121

  88

  968

12

 6

144

  72

  864

Σ

30

305

3155

​x​ 5 10·2 seals (to 1 d.p.), s 5 1·4 seals (to 1 d.p.)

b 20%

5 Students could choose to look at mean and standard deviation. _ _ 197021982: x​ ​  5 213·7 mm, s 5 47·4 mm; 200022012: x​ ​  5 267·5 mm, s 5 65·4 mm OR 5-figure summary. 197021982: L 5 104·6 mm, Q1 5 185·5 mm, median, Q2 5 217·7 mm, Q3 5 240·5 mm, H 5 303·3 mm; IQR 5 55 mm 200022012: L 5 176·5 mm, Q1 5 207·1 mm, median, Q2 5 259·3 mm, Q3 5 321·6 mm, H 5 374·4  mm; IQR 5 114·5  mm Either way, the conclusion would be that summers have got wetter in the early 21st century compared to the seventies/ early eighties. The results also show that the amount of rain is more variable in the early 21st century than in the seventies/early eighties.

5

Answers

6 Tables, graphs and charts What you need to know 1 17·5% 2 ​ _3 ​ 8

3 150 4 a° 5 60°, b° 5 30°, c° 5 45°, d° 5 75°, e° 5 150°; a°: 16·7%, b°: 8·3%; c°: 12·5%; d°: 20·8%; e°: 41·7% 5 No. Because the vertical scale starts at £100 000, sales seem to be rising faster than they actually are. The rise is in fact only 4%. 6 Because length and breadth have both doubled it makes the second amount appear four times the size of the first amount when it is actually only twice the amount. 7

a b c d

The graph should have equal intervals on both axes. It suggests a steady fall in cases of the disease. It falls slowly to start with then falls very fast, leading to very few cases towards the end of the time period. 1941; during the Second World War statistics may not have been available.

8 a 6 days

b median 5 42 miles; range 5 57 miles

Exercise 6.1A 1 a Mathsville b Probably Circletown because the most common houses are either detached or semi-detached.

2 a

Annual days of air frost Scotland England 2 7 3 1 3 3 5 6 7 9 9 6 4 3 5 5 6 7 8 9 8 8 5 4 4 2 1 5 2 4 8 8 5 5 4 1 0 6 0 7 0 2 1 1 8 2 9 3 10 n 5 20       2 | 7 5 27 days       n 5 20

b Annual number of days of air frost in Scotland is generally much more than in England. The number of days is similarly spread out in both countries. 3 a In general students in 4H used more minutes for phoning that month than students in 4T. b Probably 4H; they made more longer calls probably for phoning home. c Stem-and-leaf diagram has retained all the actual data whereas the frequency table has grouped the data, so we couldn’t identify median and range for example from the table. 4 a Distribution of cars in the 2 schools is very similar apart from double the amount of Fords in Noeleen’s school. b Noeleen’s is clearer and easier to read. c Volumes of the cuboids in Roisin’s 3-D diagram give a false impression of the numbers, e.g. Toyota and Ford have the same number of cars but Toyota looks much more; similarly with Volkswagen and Fiat. 5 a She should probably choose the home nursing as the hours are more consistent. The lowest amount she has been offered is 56. Although this is less than she would like, she has been offered fewer than 30 hours at the hospice on 8 of the months. b Home nursing may involve more travelling and be more lonely. The hospice will have more staff and it might lead to more permanent hours. Personal preference for which type of nursing would also be a consideration.

1

Answers

Exercise 6.1B 1 a

b 4%



Weight of workers

20

Frequency

15 10 5 0

60

70

2

80 90 100 Weight (kg)

110

Women’s heights

Frequency

50 40 30 20 10 0 140

3 a

150

160 170 180 Height (cm)



Inverness rents

20

Frequency

190 b Student’s own answers, e.g. more expensive flat might

be ‘all inclusive’ of bills ... phone, electricity, gas, council tax, etc. It may be better decorated or it might have a bit of garden.

15 10 5 0 400

450

4

500

550 600 Rent (£)

650

700

7

8

750

Loch Ness marathon 1200

Frequency

1000 800 600 400 200 0

2

3

4 5 6 Time (hours)

5 The areas of the rectangles for 0 < t , 60 and 120 < t , 180 are too big for the frequencies they represent giving a false

impression of the number of students in each of these categories. The areas should be proportional to the frequencies.

2

Answers

Exercise 6.2A 1 a

Baby’s weight

Weight (kg)

10 8 6 4 2 0



0

1

2

3

4

5 6 7 8 Age (months)

9 10 11 12

b The baby’s weight has been rising quite steadily over the year, slightly faster at the start.

2 a Both cars depreciated fast in the first 2–3 years and then they depreciated more slowly. Both cars depreciated in a similar way for the first 2 years. Then the new car depreciated a bit faster for about 3 years. They both have the same value after 6 years. b Possibly the secondhand car as its depreciation is mostly slightly slower. c Student’s own answer, e.g. secondhand car may have more repair and maintenance costs. It may also have a bigger engine, which would make it heavier on fuel and insurance. 3 a Both graphs have the same information but different scales have been used on the vertical axis. b Sharon’s graph because the scale on Gerry’s graph suggests there is a bigger difference in the average temperatures over the two periods. c For most of the period 2000–12 the mean annual temperature is a bit higher (about 1°C) than the corresponding years in 1910–22. 4 It depends on the length of hire: less than 3 days, use Environmental Enterprises; 3 days, either Lazy Gardener or Environmental Enterprises; between 3 and 5 days, use Lazy Gardener; 5 days, either Lazy Gardener or Green Hire; more than 5 days, use Green Hire. Exercise 6.2B 1

It depends on how long the journey is: less than 4 km, use Charlie’s Cabs; more than 4 km, use Tom’s Taxis; for a 4 km trip, use either.



Cost of taxis

8

Charlie’s Cabs

7

Tom’s Taxis

Cost (£)

6 5 4 3 2 1 0

0

1

2 3 4 5 6 7 Number of kilometres

8

2 a y 120



100

b Student’s own line c Student’s own answer (perhaps about 86) d No, we don’t know that the variables will

continue to behave in the same way as they get bigger.

80 60 40 20 0

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14

x

3 a No, we can’t assume lines of best fit will go through the origin. The red one because it follows the general direction of the points. b About 36

3

Answers

Exercise 6.3A 1

a

Blood group

Percentage of population

Angle at centre

O

51

184°

A

35

126°

B

11

40°

AB

3

11°

b Blood groupsininScotland Scotland Blood groups

(Note that with rounding, the angles add up to 361°. One of the sectors can be adjusted to fit ... probably the biggest one.)

A bar chart       d  Blood groupsininSpain Spain Blood groups

c

AB

AB B

B

O

O A

A

Scottish people have O as the most common blood group and Spanish people have A as the most common blood group. In both countries, B and AB are much less common. 2

a

Day

Mon

Tues

Wed

Thurs

Fri

Sat

Sun

Angle

40°

40°

40°

40°

80°

60°

60°

b No, although the pie charts are identical, they only give the proportion of time spent on Facebook each day. We don’t know the number of hours Lorraine spends. c Neil spends 6 times as much time on Facebook as Lorraine.

3

Number of people

Angle (nearest °)

Lung, trachea and bronchial cancer

  28 044

  40

Other cancers

  37 776

  54

Chronic obstructive lung disease

  22 346

  32

Pneumonia

  23 565

  34

Heart and vascular disease

138 436

197

Stomach and duodenal ulcer

   2 340

   3

Cause of death

4 a 3 hours

Neil’s Facebook time Sun

Mon Tue

Sat

Wed Fri

Thu

Deaths attributed to smoking

Lung, trachea and bronchial cancer Other cancers Chronic obstructive lung disease Pneumonia Heart and vascular disease Stomach and duodenal ulcer

b 1 hour

Exercise 6.3B 1 Because the pie chart is 3-D, the sections representing week 2 and week 3 appear larger

Hours worked

than they are, giving a false impression of the hours worked for those weeks. The correct pie chart is shown. 2 It would depend on what was most important to them. Newcastle would provide the cheaper and faster option ... shortest distance and journey time and cheapest parking for the week. However, they may prefer to go to Manchester as it has more choice of flights. 3 a Length of call, t (min) Percentage of Una’s calls Percentage of Irene’s calls

4

0
 6

 5

2
28

30

4
34

35

6
20

20

t>8

12

10

Week 4 (50) Week 1 (55)

Week 3 (55) Week 2 (40)

Answers b No. We don’t have enough information. The proportion of calls in each interval is similar but we don’t know how

many calls Irene made. c Irene made only 20 calls in total so her usage is much less than Una’s unless the 2 calls she made > 8 minutes were very long calls. d Stem-and-leaf diagram 2 it gives more information e Back-to-back stem-and-leaf diagram Preparation for assessment 1 a 83

c ​ _14 ​

b 7th

2 The pulse rates after exercise are quite a bit higher. The pulse rates after exercise are slightly more variable. 3

a b c d e

Between 40 000 and 41 000 About 5​ _12 ​% (answers will vary depending on estimates) The age intervals are all different. Student’s own answers, e.g. to help authorities plan for pre-school, school age, working age, pensioners, elderly. There has been a decline in the number of younger people and an increase in the number of older people.

b $0·08 or 8 cents 4 a Label on the vertical axis c As the scale on the vertical axis doesn’t start at 0, the rate appears to have varied much more than it actually did.

5

Floor sander options

500

Buy

450 400

Easy Hire

Cost (£)

350 300

Best Hire

250 200

Joiner

150 100 50 0

0

1

2

3

4 5 6 7 8 Number of days

9 10 11 12

If the job is likely to take 1 or 2 days, hire with Easy Hire. If it is likely to take 328 days, hire with Best Hire. If it will take 9 or more days, hire a joiner. It will never be cheaper to buy the sander but students may consider that buying is the best option because the machine may be needed in the future. Alternatively, the cost might be shared between a few friends who could all use it. Students may also consider that getting a joiner to do it may save time and effort as they have expertise in the work.

5

Answers

7 Related quantities What you need to know 1 48 minutes

2 a 66 g

b 210 cal

3 8 days 4 a 210

b 54

Exercise 7.1A 1 a His pay will double      b   Nothing      c   k 5 6      d   £126      e   33 hours

2 a C 5 2∙1t

b i  £2·10    ii  £0·35

c

i  3·333…    ii  7∙00

3 a °R 5 1·8K

b 671·67 °R

c

273·15 K

4 a i  k 5 230 c i  5 A

ii  P 5 230C b i  1380 W    ii  11·5 W    iii  40·02 W ii  3·48 A    iii  1·30 A

Exercise 7.1B 1 a £17·70 (D 5 0∙03P)

b £597

b i  7·52 MB    ii  6·58 MB    iii  11·656 MB 2 a S 5 1·88t c i  3 min    ii  4 min 30 s    iii  3 min 15 s

3 a 0·433 c i  3·90 cm2    ii  140·29 cm2    iii  270·63 cm2

b A 5 0·433x2 d 15·20 cm

4 a i  1·720    ii  A 5 1·720x2    iii  172 cm2 c i  3·633    ii  A 5 3·633x2    iii  363·3 cm2

b i  2·598    ii  A 5 2·598x2    iii  259·8 cm2 d i  4·828    ii  A 5 4·828x2    iii  482·8 cm2



5 Student’s own investigation. As the number of sides gets larger the shape gets closer and closer to a circle. Using the method shown you can calculate the area of the ‘circle’. The perimeter is almost a circle. It’s easy to work out: side length 3 number of sides. By comparing the area and perimeter you are able to calculate the radius and then figure out p. The more sides you add the closer you get to p.

Exercise 7.2A 1 a £16·80

b £11·20

c

£14

2 a 600 strides

b 1200 strides

c

400 m

3 a 282·24 km/h

b 185·22 km/h

c

1·7 s

1 a 4·9 m

b 148·23 m

c

3.5 s

2 a 2·56 cm2

b 11·56 cm2

d £5·60

4 280 km

Exercise 7.2B



3 a 12 000 N b 333 N c No, at 35 mph, centripetal force is 9187∙5 N (.9000 N), so car will skid. b 19·8 miles 4 a 7 miles c Yes, at 50 ft, horizon is 9·9 miles away (.9 miles) so ship is visible.

5 a 1·2 s

b 0·6 s 3

3

c 3

100 cm

6 a i  5793 cm     ii  40·64 cm     iii  8015 cm b Yes, circumference must be between 68·5 cm and 69·5 cm ⇒ volume is between 5429 cm3 and 5670 cm3 ⇒ football is an acceptable volume at 5500 cm3

1

Answers

Exercise 7.3A 480 1 a i  St 5 480    ii  S 5 ____ ​   ​   

b 15 mph c 10 mph t 57·6 ​   ​  b 16 folders c 42 DVDs 2 a i  NW 5 57·6   ii  N 5 ____ W 1000 ​   ​     b 200 kPa c 83·3 kPa 3 a i  VP 5 1000     ii  P 5 _____ V e If the volume is made very small, the pressure will become very high.

d 40 min

4 a lf 5 300 000

c

b i  500 THz    ii  600 THz    iii  461 THz

5 a i  0·01 s    ii  0·00667 s    iii  0·00133 s

d 7 box files

e

57·6 cm

d 4 cm3

698 nm

b 5 Hz

Exercise 7.3B 128 d 8 __ 2 2 a i  Rd 5 8   ii  R 5 ​  2  ​  d

1 a i  Id2 5 128   ii  I 5 ____ ​  2 ​ 

3 a 6 cm

b 9·375 cm

b 8 units

c

0·5 unit

d 3·58 km

b 1·28 ohms

c

3∙56 ohms

d 2 mm

c



d 428 cm2

9·375 8 9·375

8

8

4 a 4·37 cm

b

3·99 cm

c

r � 3·99



d

401 cm2

12 25·07 __ 3 6·2 5 a i  R​√  d ​ 5 6·2   ii  ___ ​ 3 __  ​ ​√  d ​  b i  3·12 cm   ii  2·76 cm   iii  2·31 cm   iv  4·45 cm   v  62 cm   vi  10·73 cm      c   0·030 g/cm3

Exercise 7.4A 1 a P 5 0·05LT

b £150

c

15 m

d 272 microns

2 a A 5 0·785ab

b 58·9 m2

c

23 022 m2

d 3646 m2

3 a i  1.8 mm    ii  0·6 mm    iii  18 mm

b 22·5 mm

4 a 13 m 7·5 s

d 1 h 34 m 44 s

b 6 m

c

51 m 26 s

e

Price quadruples (34)

Exercise 7.4B 0·318V b 19·83 cm R kH2 ​   ​    b i  300 kg    ii  600 kg 2 a L 5 ____ d c Suggested changes give a safe load of 1815 kg; no, it isn’t enough as this is below the 2000 kg required.

1 a H 5 ______ ​  2 ​   

W 2 3 a R 5 ___ ​   ​  b 1·4 A 4 a i  5 N    ii  20 N 5 26·67 m 6 250 ml

2

c

1·44

b 114·3 N

d 2

Answers

Preparation for assessment 1 a C 5 0·004W c i  £4·70    ii  £28·20    iii  £6·27

b i  750 g    ii  £1 d i  £2·63    ii  £2∙45    iii  £6∙30

2 a D 5 0·75M

b 135 mm

c

11·25 mm

3 a i  6·60 m    ii  9·62 m    iii  13·2 m

b C (9·62 m)

c

1·42 s

150 4 a i  R 5 150    ii  I 5 ____ ​   ​  R

b Decreases to 10 ohms

c i  4·29 amps    ii  10·71 amps    iii  15 amps 112 5 a i  Fd2 5 112    ii  F 5 ____ ​  2 ​   b 12·4 N c 10·6 cm d 3 6 a P 5 0·000333 Av b Area swept by 1st turbine 5 254·5 m2; area swept by 2nd turbine 5 314·2 m2. If the constant and wind speed are the same for both turbines then the 2nd turbine will produce about 23% more power than the 1st. 7 No, the new bottle has half the volume, i.e. 5 ml not 10 ml.

3

Answers

8 Using Pythagoras’ theorem What you need to know 1 a a 5 11·5 cm

b b 5 24 cm

2 8·25 m (to 2 d.p.) 3 173·2 m 4 a 2

b 17

c

1·74

Exercise 8.1A 1 a 20 cm

b 29 cm

2 a 13 cm

b 186 cm

3 a 1447∙8 m (to 1 d.p.)

b 1527∙7 m (to 1 d.p.)   c   PQS is shorter by 82·2 m

4 a Stall 2, 3 m more

b Stall 2 is 1 m further from source

5 a i  AC1B 5 791·4 m   ii  AC2B 5 698·6 m

b i  640·3 m   ii  250 m

Exercise 8.1B 1 a 24 cm cut in ratio 1 : 3 5 6 : 18; shorter side 5 13·416… longer side 5 21·63330…, so perimeter 5 59·0 m (to 1 d.p.) b Yes, perimeter 5 60·0 m (to 1 d.p.)

2 a i  4·68   ii  2·07 units

b 11·15 m

3 a i  2·8 m   ii  3·25 m   iii  3·6 m   iv  4·85 m

b 30·65 m     c   £1072·75

2

4 a 31·25 m

b i  473·625 m    ii  No

5 a 17·8 m

b R uses 25·6 m wire; S uses 22·4 m; S better

6 a 58 cm

b 1465·0 cm2 (to 1 d.p.)

Exercise 8.2A ____

1 a √ ​  117 ​  cm

b 8·25 cm (to 2 d.p.)

2 a 16·6 m

b 30·2 m

3 QP 5 3·49 units, SQ 5 2·3 units (to 1 d.p.). D

4 a 3



b 4·24 cm

c

11·8 cm

3

A

C

E

12

12

D

Exercise 8.2B 1 a Angles subtended by a diameter on the circumference of a circle are right angles. b 14·46 (to 2 d.p.)

2 a 111·8 m (to 1 d.p.)

b 190·2 m (to 1 d.p.)

3 a 7·42 km (to 2 d.p.)

b 5·48 km (to 2 d.p.)

4 a i  13·9 m (to 1 d.p.)   ii  43·9 m (to 1 d.p.)

b 41·7 m (to 1 d.p.)

1

Answers

Exercise 8.3A ______

______

1 a 20 cm, √ ​  472·36 ​   cm, √ ​  809·64 ​   cm

b 29 cm

2 a 125 cm

c

b 159 cm

145·5 cm

3 8·66 cm (to 2 d.p.) 4 a i  115 m    ii  185·9 m (to 1 d.p.)    iii  218·6 m (to 1 d.p.) 5 a 3·9 m (to 1 d.p.)

2

b 93·7 m (to 1 d.p.)

c

b 1·5 m (to 1 d.p.)

12·6 m (to 1 d.p.)

d 7·2 m (to 1 d.p.)

Exercise 8.3B 1 a 2·45 units (to 2 d.p.)

b 5·92 units (to 2 d.p.)

2 a i  5·66 units (to 2 d.p.)    ii  7 units

b 7·55 units (to 2 d.p.)

3 a 0∙075 km

b 3·83 km

4 a i  10·58 cm    ii  7·75 cm    iii  9·17 cm

b Length 5 √ ​  S 2 2 L2 ​; breadth 5 √ ​  S 2 2 F 2 ​; height 5 √ ​  S 2 2 B 2 ​ 

_______

c

7·28 units (to 2 d.p.) _______

_______

Preparation for assessment 1 a 8·60 cm (to 2 d.p.)

b 9·49 cm (to 2 d.p.)

2 a 9·85 m (to 2 d.p.)

b 5·20 m (to 2 d.p.)

3 a 18·33 cm (to 2 d.p.)

b 23·75 cm (to 2 d.p.)

c

6·75 cm (to 2 d.p.)

4 a 5 cm

b 14·14 cm

c

5 cm 3 2·14 cm

5 a 4·19 cm

b QR 5 1·82 cm, so PR 5 4·57 cm

6 a 15·62 m

b 15·91 m

7 a 27·73 m

b 26·55 m

8 a 13 units

b 6 units

9 21·0 m (to 1 d.p.)

2

c

d 19·53 cm (to 2 d.p.)

i  Height 5 1·3 cm   ii  Width 5 5·02 cm

Answers

9 Budgeting and finance What you need to know 1 £871∙25

2 1∙80 (to 2 d.p.) 3 39∙6% (to 1 d.p.) Exercise 9.1A 1 £233

2 a £674∙80

b £144∙60

c

£54∙23

3 a £55∙70

b £675

c

£441

d £385∙30

e

692%

4 a For cakes: 550 g butter, 550 g caster sugar, 10 eggs, 5 tsp vanilla extract, 550 g self-raising flour, 200 ml milk; for buttercream icing: 700 g butter, 1400 g icing sugar, 200 ml milk b Butter £8, caster sugar £1∙05, eggs £2, vanilla extract 84p, self-raising flour £1∙69, milk 79p, icing sugar £3∙76, food colouring 84p, paper cases 58p c £19∙55 d 39p 5 a £15 750

b £11 919

6 a £227∙50

b 23∙7%

7 a 2 months

b 66∙7%

c

£3831

c

Months 5 and 6

d £600

Exercise 9.1B 1 a One possible solution (others are possible): accommodation: 2 3 41 3 4 5 £328, 2 3 33 3 4 5 £264; trips:

2 full-day 5 2 3 25 3 4 5 £200, 1 half-day 5 1 3 15 3 4 5 £60; total cost 5 £328 1 £264 1 £200 1 £60 5 £852 b For solution in a, they would save £160 c Plan 1: accommodation for 3 nights: 2 3 36 3 3 5 £216, 3 3 24 3 3 5 £216; trips: 2 full-day 5 2 3 21 3 5 5 £210; total cost 5 £216 1 £216 1 £210 5 £642. Plan 2: accommodation for 4 nights: 2 3 36 3 4 5 £288, 3 3 24 3 4 5 £288; trips: 2 half-day 5 2 3 11 3 5 5 £110; total cost 5 £288 1 £288 1 £110 5 £686. 2 50% Exercise 9.2A 1 a £16 644∙22

b £4644∙42

2 a i  £11 560   ii  £11 440

b i  £1610   ii  £1490

3 a £9024

b 22∙1%

4 Option B 5 11∙6% 6 a £99∙45

b £1806∙05

c

18∙0%

7 £3673 to the nearest pound Exercise 9.2B 1 a £2080

b £2163∙20

c

£2530∙64

d 60∙1%

2 a 26∙8%

b 42∙6%

c

12∙7%

d 90∙1%

3 a 12∙7%

b £1915∙60

4 a 1∙5%

b 2∙5%

c

1∙2%

d 3∙4%

1

e

2∙9%

Answers

Exercise 9.3A 1 a £129 812∙50

b £507∙18

c

£2∙27

2 £11∙41 3 £254∙05 4 a £1623∙51

b His increase is above the inflation rate

5 a £1524∙88

b 7∙4%

6 a i  £12∙31    ii  £12∙50

b 12p

Exercise 9.3B 1 £339∙81

2 £44 499∙02 3 £14 581∙38 4 £199∙50 5 10% b 4∙4 3 108% 6 a 22 400% c i  6677 marks to nearest mark    ii  7 442 740 marks to nearest mark    iii  248 485 160 marks to nearest mark d 124 242 480%

Exercise 9.4A 1 A 5 £126 450, B 5 £200 560, C 5 £308 782∙50, D 5 £295 600

2 a Plan C

b £31 750

3 a £561(to the nearest pound)

b i  £117 950    ii  £7961∙63

4 a i  £3750    ii  £146 250

b £638∙40

c

25 years; £9120

5 a £22 599

b £858∙88

c

£247 471∙80

6 a £153 010

b £111∙06

c

17∙49%

Exercise 9.4B 1 a £25∙20

b £18∙90

2 a £19∙38

b Second company (£19)

c

£38∙38

d £38∙93

e

3 £325 000 Preparation for assessment 1 £205

2 a £248

b Decreases by £4∙29

3 £361∙67 4 a £92∙50

b £2067∙50

5 18∙2% 6 £51∙02 7 a £977∙28 per month

b 0∙15%

8 £17 089∙84 9 a £23 575

b 88∙5%

c

10 £28∙89 11 Yes, savings are £589 per month, which covers £558 monthly mortgage repayment.

2

£181 425

£38∙17

Answers

10 Scale drawing What you need to know 1 a 3·6 cm f 230 cm

b 5 cm g 1280 cm

c h

18·7 cm 516 cm

d 600 cm i 100 000 cm

2 a 1 : 100

b 1 : 600

c

1 : 100 000

d 1 : 500 000

3 a 90°

b 45°

c

90°

4 a 135° f 245°

b 050°

c

220°

5 a Student’s own scale drawing

e j

5000 cm 160 000 cm

d 135°

e

135°

d 305°

e

236°

b 14·5 km

Exercise 10.1A ​___›

​___›

( 24 27 )

( 245)

1 a i ​QR​  5 ​    ​  ​  ​    ii ​RP​  5 ​    ​ ​    ​

(  )

( 

(  )

)

16 28 ​  ​    iii ​    b i ​   ​ ​   ​    ii ​    ​  28  ​  ​  ​

4 214 10 c Students’ own enlargement ____ ____› ​____› ​_____› 6 ​ › 6 ​  ​, ​E9F9​ 26  26 ​   ​   ​, D9E9​ ​   5 ​    ​ 23 ​   5 ​    ​ 212 ​  ​, F9C9​ ​   5 ​    ​ 12​   ​ 2 a ​C9D9​  5 ​     3 ​____› ​____› ​_____› ​____› ​____› ​____› 6 6 ​  ​, L9M9​ 26 26 12 212 b ​J9K9​  5 ​   ​ 0​   ​, K9L9​ ​   5 ​    ​ 29 ​   5 ​    ​29 ​  ​, M9N9​ ​   5 ​    ​ 0​   ​, N9O9​ ​   5 ​    ​ 9​    ​, O9J  ​ 9  ​5 ​     ​   ​   ​ 9 ​____› ​____› ​____› ​____› ​____› 5 10 0  25 210 c ​R9S9​  5 ​   ​ 5​   ​, S9T  ​ 9  ​5 ​     ​   ​   ​, T  ​ 9U9​  5 ​    ​ 220 ​  ​, U  ​ 9V 9  ​5 ​    ​ 5​    ​, V  ​ 9R9​  5 ​    ​ 5​   ​ 5 x 2x 10 20 3 Each displacement ​     ​   ​   ​becomes ​       ​   ​   ​, e.g. width at hem goes from ​   ​ 0​   ​to ​   ​ 0​   ​. y 2y

(  )

(  ) (  )

(  )

(  ) (  ) (  )

(  ) (  ) (  )

(  )

(  ) (  )

(  ) (  ) (  )

(  ) (  ) (  ) (  )

(  )

_ ____› ​____› ​___› ​___› ​ 12 ​ x x 6 3 4 ​  ​becomes ​E9F9​ 2 ​  ​, etc. 4 a Each displacement ​     ​   ​   ​becomes ​    ​_1  ​  ​, e.g. DE​ ​   5 ​     ​   ​   ​, becomes D9E9​ ​   5 ​     ​   ​   ​and EF​ ​   5 ​    ​ 28 ​   5 ​    ​ 24 y 0 0 ​ 2 ​ y

(  )

(  )

(  )

(  )

_ ​____› ​___› ​ 23 ​ x x 6 ​   ​   ​becomes ​    ​_2  ​  ​, e.g. RS​ ​   5 ​         ​    ​  ​becomes R9S9​ ​   5 ​         ​  4 ​   ​, etc. b Each displacement ​     y 29 26 ​ 3 ​ y

(  )

(  )

(  )

(  )

(  )

x    ​   ​   ​becomes ​ 2·5x ​2·5y ​  ​. 5 Each displacement ​     y 6 a A(8, 9), B(13, 7), C(15, 5), D(13, 3), E(8, 1), F(6, 3), G(4, 4), H(2, 3), I(2, 7), J(4, 6), K(6, 7) b B9(25, 11), C9(29, 7), D9(25, 3), E9(15, 21), F9(11, 3), G9(7, 5), H9(3, 3), I9(3, 11), J9(7, 9), K9(11, 11) c Student’s own scale drawing Exercise 10.1B 1 a Student’s own diagram; B9(9, 8), C9(11, 6), D9(9, 4) c Area of kite ABCD 5 56 square units

b Area of kite A9B9C9D9 5 14 square units d 4 times greater

b 6 units 2 a 3 units c i  Width 5 units, height 7 units, radius of quarter-circles 1·5 units, diameter of pocket 3 units ii  Width 15 units, height 21 units, radius of quarter-circles 4·5 units, diameter of pocket 9 units

3 a 60 cm 3 40 cm

b 3 cm 3 2 cm

4 a Student’s own drawing c Student’s own diagram e ​ _49 ​

b L9(12, 23), M9(4, 23), N9(0, 3) d i  48 square units    ii  108 square units

1

(  )

Answers

Exercise 10.2A 1 a 5 c, b 5 g, d 5 f, e 5 h

2 a 40 m

b 100 m

c

200 m

d 32 m

e

70 m

3 a 2·8 km

b 7 km

c

2·1 km

d 140 km

e

9·8 km

4 a 32 cm

b 12·8 cm

c

2·1 cm

d 42·7 cm

5 a 1 cm representing 5 m (1 : 500) c 1 cm representing 2·5 m (1 : 250) e 1 cm representing 30 m (1 : 3000)

b 1 cm representing 2 m (1 : 200) d 1 cm representing 20 m (1 : 2000)

6 a Student’s own scale drawing with dimensions from top clockwise: 6·2 cm, 5·0 cm, 7·9 cm, 5·3 cm b 10·6 m c Trapezium d 141 m2 7 8 9

a Student’s own scale drawing b 4·2 cm c 12·6 m a Student’s own scale drawing with suitable scale of 1 : 200 000 (1 cm : 2 km) b 36 km from starting point (18 cm on the scale drawing)

Suitable scale is 1 : 200 (1 cm : 2 m) or 1 : 300 (1 cm : 3 m)

Exercise 10.2B 1 a Student’s own scale drawing with scale: 1 cm representing 3 cm or 1 : 3; measurements on scale drawing (top to

bottom) are 5 cm, 13 cm and 14 cm _4 b i  Enlargement factor is __ ​ 52 39 ​5 ​ 3 ​, so the other measurements are 20 cm and 56 cm ii Student’s own scale drawing with scale 1 : 3 (or 1 : 4); measurements on scale drawing (top to bottom) are 6·7 cm (5 cm using 1 : 4 scale), 17·3 cm (13 cm) and 18·7 cm (14 cm) 1 2 a Student’s own scale drawing: length 5 11 cm (​ __ 20  ​of 220 cm), breadth 5 9·5 cm, width of door 5 4 cm b i  Bath 8·5 cm 3 3·5 cm    ii  Wash-hand basin 3·1 cm 3 2·5 cm    iii  Toilet 3 cm 3 2·3 cm c Student’s own scale drawing

3 Student’s own scale drawing with scale is 1 cm : 50 yards, hole 1: 10·1 cm, hole 2: 7·9 cm, hole 3: 8·5 cm, hole 4: 3·2 cm, hole 5: 7·3 cm 4 a Student’s own scale drawing with scale 1 cm : 5 yards; length of pitch 5 24 cm, breadth 5 16 cm, 10 yd  2 cm, 18 yd  3·6 cm, 12 yd  2·4 cm, 8 yd  1·6 cm, 6 yd  1·2 cm, 20 yd  4 cm, 44 yd  8·8 cm, 1 yd  0·2 cm b i  AB 5 84 yd (16·8 cm)    ii  CD 5 144 yd (28·8 cm) Exercise 10.3A 1 a 3·3 cm

b 6·6 km

2 a i  5 km    ii  6·4 km    iii  9 km

b i  036°    ii  112°    iii  260°

3 a i  112°    ii  205°    iii  6·4 cm    iv 16 km    v 3·1  cm    vi  7·75 km b 6·25 km shorter 4

From

To

Distance on map (cm)

Actual distance (km)

Bearing (°)

Kirkcaldy

Musselburgh

10·0

19·00

163

Musselburgh

Leith

  3·9

  7·41

296

Leith

Burntisland

  5·3

10·07

335

5 a 1 cm : 2 km b Wind farm 1: 7 km; wind farm 2: 11·6 km c Ayrmouth to wind farm 1: 033°; wind farm 1 to wind farm 2: 254°; wind farm 2 to Ayrmouth: 097°

2

Answers

Exercise 10.3B 1 a

N

Birlin 65 km

45° Peerie 100° 40 km Chirnside



b Student’s own scale drawing (scale 1 cm : 10 km or 1 : 1 000 000)

2 a 1140 km, 130°

b 2318 km, 236°

c

c

2280 km, 028°

3 a Greenbank 3·8 km, Whiteside 1·8 km, Roselea 2·2 km b Yes, Whiteside is less than 2 km away from landfill site c Whiteside 4 a

i  82 km    ii  196°

d 180°

Ardrossan Brodick Ayr



(The distances on the map depend on the scale. The scale used here to answer the question was 1 : 190 000.) From

To

Distance on map (cm)

Actual distance (km)

Bearing (°)

Ayr

Ardrossan

11·7

22·23

330

Ardrossan

Brodick

11·5

21·85

253

Brodick

Ayr

18·5

35·15

115

Preparation for assessment ___› ​___› ​___› ​___› ​__› ​___› 3 ​___› 0 ​__› 3 ​___› 3 0 ​  ​, ​DE​ 23 23 23 23 1 a ​BC​  5 ​     ​   ​   ​, CD​ ​   5 ​    ​ 26 ​   5 ​    ​ 0​    ​, EF​ ​   5 ​    ​23 ​  ​, FG​ ​   5 ​    ​ 3​    ​, GH​ ​   5 ​    ​ 0​    ​, HJ​ ​   5 ​     ​   ​   ​, JK​ ​   5 ​     ​   ​   ​, KA​ ​   5 ​     ​   ​   ​ 0 6 0 3 ____ ​____› ​____› ​____› ​____› ​____› ​____› ​____› 5 ​ › 5 0  25 25 25 25 0​   ​, J  b ​B9C9​  5 ​     ​   ​   ​, C9D9​ ​   5 ​    ​ 210 ​   5 ​    ​ 0​    ​, E9F  ​ 9  ​5 ​    ​25 ​  ​, F  ​ 9G9​  5 ​    ​ 5​    ​, G9H9​ ​   5 ​    ​ 0​    ​, H9J  ​ 9  ​5 ​   ​ 10 ​ 9K9​  5 ​     ​   ​   ​, ​  ​, D9E9​ 0 0 ​____› 5 ​K9A9​  5 ​     ​   ​   ​

(  ) (  ) ( 5 )

(  ) (  ) (  ) (  ) (  ) (  ) (  )

(  ) (  )

(  ) (  )

(  ) (  ) (  ) (  )

c Students’ own drawing _ _ _ ____› _​ ___› _ _​ ____› _ ​ ___› ​ ___› ​ ___› ​ ___› ​ ___› 0 0 ​  ​, ​D  22 22 22 22       ​5 ​ 22 ​  2 ​  ​, B  ​ 0C 0  ​5 ​     ​ 2 ​   ​, C  ​ 0D 0  ​5 ​    ​ 24 ​ 0E 0  ​5 ​    ​ 0​    ​, E  ​ 0F 0  ​5 ​ 22 ​  ​  ​, F  ​ 0G0​  5 ​    ​ 2​    ​, G  ​ 0H0​  5 ​    ​ 0​    ​, H 0J 0​ ​   5 ​     ​   ​   ​, d ​A0B 0   0 4 _ ___ _ ____ ​ ​ › › ​J 0K 0​  5 ​     ​ 2 ​   ​, K 0A0​ ​   5 ​     ​ 2 ​   ​ 0 2 0 ​  ​, ​ 18 12  212         ​  ​, ​ 212 ​  ​, ​ 218 ​ 212 ​   ​ 6​   ​, ​   ​ 12 ​ 6​   ​; inner sides, starting at top and 2 a Outer sides, starting at top and moving clockwise: ​    6 26 212 12       ​   ​  ​, ​ 26 ​  ​  ​, ​    ​ 6​   ​, ​   ​ 6​   ​ moving clockwise: ​ 26 0 6 26 4 ​  ​, ​    24 ​ 24 ​24 ​  ​, ​    ​ 2​    ​, ​     ​   ​   ​, ​     ​   ​   ​; inner sides, starting at top and moving b Outer sides, starting at top and moving clockwise: ​    4 2 4 24 2 22              ​   ​  ​, ​ 22 ​  ​  ​, ​ ​ 2​    ​, ​ ​   ​   ​ sideways: ​ 22 2 3 Cube B: 16 cm 3 16 cm 3 16 cm, cube C: 12·8 cm 3 12·8 cm312·8 cm, cube D: 10·2 cm 3 10·2 cm 3 10·2 cm, cube E: 8·2 cm 3 8·2 cm 3 8·2 cm, cube F: 6·6 cm 3 6·6 cm 3 6·6 cm

(  )

(  )

(  ) (  )

(  )

(  ) (  ) ( 

(  ) (  ) (  ) (  )

4 a 60 m

b 300 m

) (  )

(  ) ( 

(  )

) ( 

) ( 

(  )

(  )

) (  ) (  )

(  ) (  ) (  ) (  ) (  )

c

5·4 km

d 15 km

5 a Student’s own scale drawing with scale 1 cm : 1 m (1 : 100)

b 13·6 m

6 a Student’s own scale drawing (bedroom is 7 cm 3 6 cm on drawing) b i  4 cm 3 2 cm    ii  5 cm 3 1 cm    iii  3 cm 3 1·5 cm

c

7 a i  40 m    ii  35 m    iii  37 m

3

(  )

Student’s own drawing

b i  038°    ii  290°    iii  126°

Answers

8

From

To

Distance on map (cm)

Actual distance (km)

Bearing (°)

Glasgow

Stockholm

4·1

1230

083

Stockholm

Rome

5·9

1770

193

Rome

Glasgow

5·8

1710

332

9 Student’s own answers

4

Answers

11 Scatter graphs and probability What you need to know 3 1 a ​ _5 ​

b

2 ​ _34 ​

2 The red line is the best of the lines given but you will see later how to get a more accurate line. y

3 a, b



c

2

c

9

d 1 or (0, 1)

9 8 7 6 5 4 3 2 1 0

0

1

2

3

4

5

x

6

4 a, b Student’s own answers e y

d 5

8 7 6 5 4 3 2 1 0

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 x

f Student’s own answer 5

x

24

22

0

2

4

y 5 3x 1 2

210

24

2

8

14

Any 3 of (24, 210), (22, 24), (0, 2), (2, 8), (4, 14) 6 (2, 0), (0, 210), (3, 5), (7, 25) y

7

6 5 4 3 2 1 �2 �1 0 �1 �2

8 ​ _12 ​

9 ​ __ 10  ​ 7

1

1

2

3

4

5

6

7

8

9 10 11 12 13 x

Answers

Exercise 11.1A 2 1 a ​ _3 ​

b 25

5 c ​ _2 ​

2 a y 5 x 1 1

b y 5 22x 1 14

c

y 5 2x 2 9

3 a y 5 1·2x 1 2

b 6·8

c

10

b y 5 6·2

c

x53

d

10 2 ​ __ 3  ​

d y 5 25x 1 11

4 (8, 22·4), (12, 21·6), (20, 0) 5 a y 5 21·8x 1 15·2 Exercise 11.1B 1 a Student’s own line of best fit, something like the one drawn q 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 p b Student’s own answer, something like q 5 20·5p 1 8 c Student’s own answer, something like q 5 4·5

Petrol in tank (litres)

2 a, b Student’s own graph and line, similar to ones shown 50 40 30 20 10 0

0 50 100 150 200 250

Distance travelled (km) c Student’s own answer, something like y 5 20·13x 1 50 d Student’s own answer, something like 22 litres. There is not enough fuel to travel 400 km. e As Yousef ’s speed varied and he probably had stops and starts, the petrol will not go down at a completely steady rate.

3





90

90

90

80

80

80

70 60

70 60

50

50

0

0

0 50 60 70 80 90 100 English

French

100

Maths

100

French

100

70 60 50

0 50 60 70 80 90 100 English

0

0 50 60 70 80 90 100 Maths

b Student’s own line for the first graph only. The others don’t lend themselves to a linear relationship. c The English/French graph because it shows a strong relationship

2

Answers 4 a, c Student’s own curve and ‘curve of best fit’, similar to that shown P 50 40 30 20 10 0

M

0 10 20 30 40 50 b Yes d Student’s own answer, approximately P 5 13

Exercise 11.2A 1 a

Cost of flights by distance

Cost (£)

200 150 100 50 0

0

500 1000 1500 2000 Distance from Glasgow (km)

2500

b Positive correlation, not very strong c Student’s own answer, e.g. popularity of destination Life expectancy (years)

2

GDP and life expectancy

100 80 60 40 20 0

0

10 000 20 000 30 000 40 000 50 000 60 000 GDP per capita ($US)

a No clear correlation. At the lower end of GDP there is a weak positive correlation. b Student’s own answer, e.g. drought, war, etc. 3

GDP and birth rate

Births per 1000 population

50 40 30 20 10 0

0

10 000 20 000 30 000 40 000 50 000 60 000 GDP per capita ($US)

No clear correlation but possibly slightly negative

3

Answers

4

UK summer rainfall and temperature

Maximum Temperature

21 20.5 20 19.5 19 18.5 18 17.5

0

50

100

150 200 250 Rainfall (mm)

300

350

400

Weak negative correlation 5 Student’s own investigation Exercise 11.2B 1 a Positive d Positive

b Negative e Negative

c f

No correlation Positive

2 a Distance on ruler, d (mm)

150 140 130 120 110 100 90 0

0

1 2 3 4 5 Bottles of beer, b

6

b (3, 113) c Student’s own line, approximately d 5 9b 1 86 d No, because 10 beers is outside the range of the data. Also, this relationship might not be linear, a curve might be a better possibility. 3 a Cholesterol, c (mmol/l)

8 7 6 5 0



0

1

2

3 4 5 Month, m

6

7

8

b (4, 6·8) c Student’s own line, approximately c 5 20·13m 1 7·2 d Student’s own answer, approximately 6·7 e Student’s own answer, approximately another 9 months f We cannot know how her progress will continue over the next months. Some people have a level which is correct for

them so they might never reach 5.

4

Answers 4 a Negative b

SPL goals 2011-12

90 80 Goals against, A

70 60 50 40 30 20 10 0

0 10 20 30 40 50 60 70 80 90 Goals for, F

Student’s own answer c (50, 50) to nearest whole number d Student’s own line, possibly A 5 2F 1 100 Exercise 11.3A 1 f and g are student’s own answers



d

c

a

g possibly

e

b 0

1

2 80% or _​ 45 ​

3 ​ _38 ​

13 4 a ​ __ 30 ​

1 b ​ _2 ​

8 5 _1 __ ​ 20   ​, B: P(spade) 5 ​ 4 ​5 ​ 20  ​; by comparing fractions with a common denominator, A is more likely 5 A: P(girl) 5 _​ 25 ​5 __

1 6 ​ __ 10  ​

7 HH, HT, TH, TT; _​ 14 ​

3 8 ​ __ 20  ​

Exercise 11.3B 1 1 a ​ __ 12  ​ 1 __ 2 ​    ​

1 b ​ __ 12  ​

4 3 a ​ __ 99  ​

4 2 __ b ​ __ 98  ​5 ​ 49  ​

72

364 4 ​ ___ 365  ​ 9 ___ 5 ​      ​ 100

5

Answers

Preparation for assessment 1 y 5 3x 2 1

2 a 10 9 General knowledge, g

8 7 6 5 4 3 2 1 0

0

1

2

3 4 5 6 7 Specialist subject, s

8

9 10

b Quite strong positive correlation d Student’s own answer, approximately g 5 _​ 12 ​ s 1 2 e Student’s own answer, approximately 6 or 7

c

3 a Strong negative correlation

b C 5 25t 1 90

4 a ​ _38 ​ 7 5 a ​ __ 50  ​

b 15 green, 9 blue

(7, 5·5)

b 0

China – exports/imports

2500 2000 1500 1000 500 0

0

500

1000 1500 2000 Exports (US$ billions)

2500

Imports (US$ billions)

Imports (US$ billions)

6 Scatter graphs of imports v. exports show a strong correlation between the two for each country. Over the period, USA imports/exports have been higher than China, in general. USA – exports/imports

3000 2500 2000 1500 1000 500 0

0

500

1000 1500 2000 Exports (US$ billions)

2500

Students may also wish to plot imports and or exports against year to spot trends in the variables over the decade and compare these for both countries.

6

Answers

Preparation for assessment Exercise Test A 1 a £68·94

b £8·96

2 a £23·78

b i  £1·17   ii  £149·70

3 a i  750   ii  495    iii  702·6   iv 1415·7 b i  18    ii  1·73   iii  4·017   iv 4·767 4 a 1350 e 0·3297

b 1650 f 0·12682

5 a i  9·79 s   ii  9·8 s

b i  76·163 s   ii  76·16 s

6 a £360

b £419·30

c

Track shoes £20·01, football boots £11·05

c

i  72 m   ii  £510

c

6136

d 0·4281

7 a Area of ABCD 5 12 cm2, required area 5 8 cm2, rectangles 4 cm 3 2 cm (8 boxes 3 4 boxes) or 8 cm 3 1 cm (16 boxes 3 2 boxes) would be suitable b Required area 5 9 cm2, rectangles 3 cm 3 3 cm (6 boxes 3 6 boxes) or rectangle 9 cm 3 1 cm (18 boxes 3 2 boxes) would be suitable 8 a 51·75 miles/gallon

b 35 000 miles

9 a 13 ​ _12 ​miles 10 a ​ _13 ​

b 1

b £630 1 c ​ _8 ​

2 d ​ _3 ​

11 14 12 17 13 a i  £15   ii  £30·45

b £530·45

14 £2210 15 5% 16

Common fraction

Decimal fraction

Percentage

_ ​ 12 ​

0·5

50%

​ _14 ​

0·25

25%

​ _15 ​

0·2

20%

_ ​ 34 ​

0·75

75%

__ ​ 3  ​  20

0·15

15%

​ _35 ​

0·6

60%

3   ​  ​ __

0·3

30%

10

17 a 656 km/h

b 2840 km

c

i  2 h 30 min   ii  13 30

19 a 15 min

b 20 min

c

60 min (1 hour)

20 a 57

b 133

21 a 750 m

b 20 cm

18 £140

22 a A: 48 m, B: 48 m, same amount of skirting board

b A, 32 m2

23 a Triangular prism

b 142·8 cm2

c

58·5 cm3

24 a 1·4 kg d 6·3 litres

b 6·5 cm e 125 g

c

36 ​ _34 ​ °C or 36·75 °C

25 a i  376·1 kg   ii  62·7 kg   iii  55·6 kg to 69·1 kg, or 13·5 kg b i  363·8 kg   ii  60·6 kg   iii  53·7 kg to 68·7 kg, or 15 kg d It increased from 13·5 kg to 15 kg

c

12·3 kg

26 a Oranges £3·54, red grapes £2·70, cherries £1·96, clementines £2·25, potatoes £3·90, fillet steak £9·15, black pudding £1·76, turnip £0·90, jellies £3·54, orange juice £2·76, eggs £2·58 b £35·04

1

Answers

Exercise Test B 1 A 5 £1023·16, B 5 £94·47, C 5 £928·69

2 a £516

b £371·16

c

£9797·84

3 a 937·95 euros

b 4386·81 kroner

c

£252·97

4 a Loan C

b Loan A

c

£498·24

5 a In-Touch at £12 [cheaper than Easi-com (£13) and Tok-n-Text (£12·80)] b Easi-com at £12 [cheaper than Tok-n-Text (£14·50) and In-Touch (£13·20)] 6 a

Obesity rates

Imports (US$ billions)

35% 30% 25% 20% 15% 10% 5% 0%

Italy

Japan

b 0·23

Spain UK c 230

USA

7 a 921 m2

b 92·1 kg

8 a 31 ​ _12 ​232 ​ _12 ​ in

b i  16·02 m    ii  15·98 m

c

4

d £150

9 a Adamson 17·8%, Baillie 20·6%, Campsie 23·8%, Donald 32·4%, White 5·4% b Share of the vote at the local election White 5·4%

Donald 32·4%

Adamson 17.8% Baillie 20·6%

Campsie 23·8% 10 a Northern Building Society

b £8·80

11 a Set A: i  L 5 21    ii  Q1 5 28     iii  Q2 5 35    iv  Q3 5 41    v  H 5 47; Set B: i  L 5 26    ii  Q1 5 34·5    iii  Q2 5 39    iv  Q3 5 44    v  H 5 49 b i  Set A: number of press-ups

28 35    21 ii  Set B: number of press-ups

41

47

26 34·5 39 44 49    c Set A, mean 5 34·5 press-ups; set B, mean 5 38·95 press-ups d Very effective at improving the number of press-ups. The lowest value increased by 5, the highest value only improved by 2. Set B’s lower quartile is almost equal to Set A’s median value. 12 a 0·072 1 13 a ​ _ ​

b 42 b 8 m

c

4·47 m

14 a 5 hours

b 11 03

c

5 h 50 min

2

15 a AB 5 126·9 m

2

2

b 5854 m

Answers 16 16 tins on bottom layer (4 tins 3 4 tins) and 3 layers. Dimensions of box: 32 cm 3 32 cm 3 12 cm, giving a surface area of 3584 cm2. Two layers of 24 tins (6 tins 3 4 tins) require a box with surface area 4352 cm2. Box with dimensions 32 cm 3 32 cm 3 12 cm uses the least cardboard. 17 a Student’s own drawing

b AB 5 82·5 ft

c

82·5 ft (to 3 s.f.)

18 a i  0·35    ii  0·26    iii  0·17 c About 3630

b i  230 000    ii  126 000    iii  138 000

19 a 4 km

c

b 075°

i  330°    ii  3·5 km

d 2·9 km

20 0·6 cmHg 21 a i  62·8 ft2    ii  37·7 ft2    iii  11·8 ft2    iv 0·785 ft2 2

22 679 km

23 a 5 km

3

b 180°

b 55·5%