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Rates and Ratios

Rates and Ratios

Curriculum Ready

Copyright © 2009 3P Learning. All rights reserved.

First edition printed 2009 in Australia.

A catalogue record for this book is available from 3P Learning Ltd.

ISBN 978-1-925202-69-4

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Rates and Ratios Solutions Mathletics © 3P Learning

1SERIES TOPIC

11I

questions

Ratios

How does it work? Solutions Rates & Ratios

Shaded to Non-shaded parts = 7 : 9. Shaded to Non-shaded parts = 9 : 5.

1

2

a

b

(i) Theratioofgirlstoboysis: : .

(i) Theratioofbasketballplayerstorugbyplayers: : .

(ii) Theratioofsoccerplayerstoswimmers: : .

(iii) Theratioofrugbyplayerstosoccerplayers: : .

(iv) Theratiooftennisplayerstonetballers: : .

(v) Theratioofsportplayerstonon-players: : .

(ii) Theratioofboystogirlsis: : .

(iii) Theratioofallstudentsintheclassroomtothenumberofboysis: : .

(iv) Theratioofthenumberofgirlsintheclassroomtothetotalnumberofstudentsis:

: .

17

12

29

17

41

61

23

17

214

12

17

12

29

61

23

29

31

8


2SERIES TOPIC

11I


questions

3

4

:

:

:

:

:

:

:

:

(ii)

(i)

a b c

Ratios

5

5

4

4

7

7

12

12

4

9

(ii) :

(i) : 10

7

7

17(ii) :

(i) : 5

4

4

9

5

9

5

12

7

19

(ii) :

:

(i) :

:

3

6

1

2

6

9

2

3

or

or


3SERIES TOPIC

11I


= :

= :

= : = : = :

: : :

: : :

: : :

or or or

or or or

or or or

14 10 6

2

10 15 9

8 25 15

6 20 12

12 30 18

5 3

simplestform

= : simplestform

= :

= : simplestform

= :

= : = : = : = :

= : = : = : = :

Page 6 questions

Equivalent ratios

2 8 4

1

7 6 8

1

5 9 12

4 15 20

3 12 16

6 18 24

3 4

4 2

2 4 2

1 2 1

1

3

2

(i)

(ii)

(i)

(ii)

a b c

6

2

3

1


4SERIES TOPIC

11I


÷ 7

14 : 35

2 : 5

÷ 7 ÷ 2

70 : 36

35 : 18

÷ 2 ÷ 9

18 : 81

2 : 9

÷ 9

Page 7 questions

Equivalent ratios

4 2 : 10a 12 : 48c

70 : 36e

10 : 30b

14 : 35d 18 : 81f

5

1 9 1053 72 1164 8

3

5

2 7

10

1

6

94

8

E

E

E

R

D

S

S

T

TM

RL

L

A

A

T

O

W

11

180 : 150 48 : 36

90 : 20 24 : 9

64 : 16 9 : 180

12 : 9 17 : 15

95 : 20 5 : 10

8 : 3 19 : 4

123 : 123 4 : 1

85 : 75 6 : 5

21 : 35 18 : 4

45 : 51 15 : 17

1 : 20 1 : 1

1 : 3 23 : 69

1 : 2 3 : 5

L SW T MO T RE E S

÷ 2

2 : 10

1 : 5

÷ 2 ÷ 10

10 : 30

1 : 3

÷ 10 ÷ 12

12 : 48

1 : 4

÷ 12


5SERIES TOPIC

11I


` 9 : 27

=

1 : 3 ` 30 : 5

=

6 : 1 ` 5 : 25

=

1 : 5

Page 9 questions

Using fractions to reduce ratios in lowest terms

1

2

3 : 27a 12 : 30b

Rabbits to carrots Lettuce to slugs Spikey puffer fish ( ) to all fish

a b c

8 : 8c 20 : 100d

21 : 70e 200 : 512f

3 27 =

12 30 =

8 8 =

20 100 =

200 512 =

21 70 =

9 27

=

1 3 30

5

=

6 1 5

25

=

1 5

` 3 : 27 = : ` 12 : 30 = :

` 8 : 8 = : ` 20 : 100 = :

` 200 : 512 = : ` 21 : 70 = :

1

1

3 25

1

2

9

1

10 64

5

5

1

1

3 25

1

29

1

10 64

5

5


6SERIES TOPIC

11I


0.008 : 0.018

= 8 : 18

= 4 : 9

2.400 : 1.840

= 2400 : 1840

= 30 : 23

1.240 : 4.480

= 1240 : 4480

= 31 : 112

6.420 : 0.600

= 6420 : 600

= 107 : 10

0.0220 : 0.400

= 22 : 400

= 11 : 200

Page 11 questions

Ratios with decimals

1

2

3

1.5 : 4.5

0.08 : 0.60

0.008 : 0.018 0.025 : 0.100

1.2 : 7.2

2.8 : 0.21

2.40 : 1.84 6.42 : 0.60

9.2 : 2.4

2 : 3.52

1.24 : 4.48 0.022 : 0.40

a

a

a b

b

b

c d

c

c

e f

1.5 : 4.5 = 15 : 45

= 1 : 3

1.2 : 7.2 = 12 : 72

= 1 : 6

9.2 : 2.4 = 92 : 24

= 23 : 6

0.08 : 0.60 = 8 : 60

= 2 : 15

2.8 : 0.21 = 280 : 21

= 40 : 3

2 : 3.52 = 2.00 : 3.52

= 200 : 352

= 25 : 44

0.025 : 0.100

= 25 : 100

= 1 : 4

(Greatestcommonfactor= 15)







7SERIES TOPIC

11I


Page 13 questions

Ratios with fractions

b

d

2 7 : 1

14 = 2 × 14 : ×

= :

= :

2 1 5 : 2 2

3

1

2

a

a

c

c

b

d

1 5 : 4

5 = :

4 7 : 2

5

1 2 : 1

7 = 14 :

14

= :

3 16 : 1 = 3

16 :

= × : ×

= :

1

7

28

4

7

7

3 16

4

2

7

1 3 16

2

1

1 1

1 1

4 7 : 2

5 = 4 × 5 : 7 × 2

= 20 : 14

= 10 : 7

5 1 4 : 4 2

3

5 1 4 : 4 2

3 = 21 4 : 14

3

= 21 × 3 : 4 × 14

= 63 : 56 = 9 : 8

2 1 5 : 2 2

3 = 11 5 : 8

3

= 11 × 3 : 5 × 8

= 33 : 40

2 5 : 3 1

4

2 5 : 3 1

4 = 2 5 : 13

4

= 2 × 4 : 5 × 13

= 8 : 65


8SERIES TOPIC

11I


Page 15 questions

Best buys and the unitary method

4kgoffishfor$24.00 or

8kgoffishfor$50?

(4kgfor$24.00) × 2 = 8kgfor$48.00

` 4kgoffishfor$24.00 isthebestbuy.

(5setsfor$78.75) × 7 = 35setsfor$551.25

(7setsfor$110.75) × 5 = 35setsfor$553.75

` 5setsfor$78.75 isthebestbuy.

(8for$41.60) × 25 = 200for$1040

(25for$131.25) × 8 = 200for$1050

` 8loavesfor$41.60 isthebestbuy.

(3 sacksfor$14.00) × 4 = 12 sacksfor$56.00

(4 sacksfor$17.00) × 3 = 12 sacksfor$51.00

3sacksofpotatoesfor$14 or

4sacksofpotatoesfor$17?

3 a b

` 4 sacksfor$17.00 isthebestbuy.

12applescost$6.60

7avocadoscost$15.75

150gofcheesecosts$4.50

200mofwirecosts$356

1 apple=

1 avocado=

1gcheese=

1m wire=

5 setsofguitarstringsfor$78.75 or7 setsofguitarstringsfor$110.95?

8loavesofsourdoughbreadfor$41.60 or 25loavesofsourdoughbreadfor$131.25?

1

2

a

d

c

c

b

b

d

c d

Halfapacketofpegscost$2.10 1packetofpegs= a

$0.55

$4.20

$2.25

0.7cmofgoldcosts$251 1cmofgold= $358.57 (to 2 d. p.)

$0.03

0.4kgofpastacosts$1.55 1kgpasta= $3.88 (to 2 d. p.)

$1.78

1 4 watermeloncost$6.60 1 watermelon= $26.40


9SERIES TOPIC

11I


120min13 seconds÷ 13 ÷ 13

= 9.23min1second

8videogamesfor$62.80÷ 8 ÷ 8

= 1videogamefor$7.85

162kmin2.7 hours (162 ÷ 2.7)kmin1hour= 60kmin1hour (or 60km/h)

215kmin3.32 hours (215 ÷ 3.32)kmin1hour= 64.759kmin1hour (or ~ 64.8km/h)` trainhasthefastestspeedbetweentwohours.

13videogamesfor$100.23÷ 13 ÷ 13

= 1videogamefor$7.71

220min22 seconds÷ 22 ÷ 22

= 10min1second

` amanwhcanrun220min22 secondsisthefasterrunner.

` 8videogamesfor$62.80 ismoreexpensive.

Page 16 questions


• amanwhocanrun120min13secondsor• amanwhocanrun220min22seconds.

• 8videogamesfor$62.80 or• 13videogamesfor$100.23

a

b

Findthemodeoftransportthattravelsatthefastestspeedbetweentwotownsif:

• bybusyoutravel162kmin2.7 hoursor• bytrainyoutravel215kmin3.32 hours.

4

c

25gofflourcosts$0.20

2000mLofmilkcosts$4.85

75mLoflavenderoilcosts$7.65

10 800minutesofmachinehirecosts$175.00

`100g =

`100mL =

`100mL =

`100mL =

5 a

c

b

d

1g = $0.008

1mL = $0.102

1mL = $0.002425

1min = $0.0162

$0.80

$10.20

$0.2425

$1.62


10SERIES TOPIC

11I


54goffishfor$2.60 or 75goffishfor$3.70

750gofricefor$5.60 or 600gofricefor$4.68

6

7

a

a

b

b

Page 17 questions


` 54gfor$2.60 isthebestbuy.

` 100gCoriander(B)mustbe1 $7.00tobethebetterbuy

` 250kgSoil(Y)2 $650tobethemoreexpensivebuy

54gfor$2.60

` 1gfor$0.0481` 100gfor$4.81 (to 2 d. p.)

60gCoriander(A)= $4.20100gCoriander(B)1?tobethebetterbuy

60gCoriander(A)= $4.20 ` 1g= $0.07 ` 100g= $7.00

222kgSoil(X)= $577.20250kgSoil(Y)2?tobethemoreexpensivebuy

222kgSoil(X)= $577.20 ` 1kg= $2.60 ` 250kg= $650

750gfor$5.60

` 1gfor$0.00746` 100gfor$0.746 ~ $0.75 (to 2 d. p.)

600gfor$4.68

` 1gfor$0.0078` 100gfor$0.78

75gfor$3.70

` 1gfor$0.0493` 100gfor$4.93 (to 2 d. p.)

` 750gfor$5.60 isthebestbuy.


11SERIES TOPIC

11I


Page 19 questions

Dividing a quantity in a given ratio

1

2

$1200intotheratio1 : 2.

700kgintotheratio3 : 11.

360⁰intotheratio5 : 4.

Totalnumberofpartsis + = .

` parts is $1200.

` 1 part is $ ÷ = $ .

` 2 parts is $ .

` $1200isdividedintotheamounts$ and $ .

a

b

c

1

3

3 400

400 800

1200

800

2 3

Totalnumberofparts= 3 + 11 = 14.

` 14 parts = 700kg 1 part = 700 ÷ 14 = 50kg

` 3 parts = 150kg 11 parts = 550kg

Totalparts= 5 + 4 = 9 parts.

` 9 parts = 360o` 1 part = 360o ÷ 9 = 40o

Harry= 3 partsSally= 1 part

` 4 parts = 36 cookies` 1 part = 36 ÷ 4 = 9 cookies

` 3 parts = 27 cookies

` 5 parts = 200o` 4 part = 160o

` 360oinratio5 : 4 = 200o: 160o

` 700kginratio3 : 11 = 150kg : 550kg

`Harrygets27cookies. Sallygets9cookies.

parts


12SERIES TOPIC

11I


Page 20 questions

Page 21 questions

3

4 5

(i)

6 2 : 2 : 4

4 : 4 : 4

10 : 5 : 35 : 20

3 : 6 : 12

2 : 2 : 4 : 8

6 : 15 : 9 : 27 : 81

a

c

e

b

d

f


Dividing a quantity in a given Ratio

Totalamountshared= $450 + $650

= $1100

(ii) 450 : 650 = 450 650

= 9 13

`moneywasdividedintheratio9 : 13.

÷ 20 ÷ 20

180 : 20

9 : 1

` 9 : 1 = x : 5

` x = 9 × 5 = 45

Fiona = x - 10Joan = x

x + (x - 10) = $400

2x - 10 = $400

2x = $410

x = $205

` x - 10 = $195

`Fionagets$195

Joangets$205

Greatestcommonfactor = 2

` 2 : 2 : 4 = 2 2

: 2 2

: 2 4

= 1 : 1 : 2


` 4 : 4 : 4 = 4 4 : 4

4 : 4 4

= 1 : 1 : 1


` 3 : 6 : 12 = 3 3

: 6 3

: 12 3

= 1 : 2 : 4


` 2 : 2 : 4 : 8 = 2 2 : 2

2 : 4 2 : 8

2

= 1 : 1 : 2 : 4


` 10 : 5 : 35 : 20 = 10 5 : 5

5 : 35 5 : 20

5

= 2 : 1 : 7 : 4


` 6 : 15 : 9 : 27 : 81 = 6 3 : 15

3 : 9 3 : 27

3 : 81 3

= 2 : 5 : 3 : 9 : 27


13SERIES TOPIC

11I


Page 21 questions

Page 22 questions

7 a b


Dividing a quantity in a given Ratio

` $2 000 000 ÷ 20 = $100 000

` Liamwins13 × $100 000 = $1 300 000

Everybodyelsewins$100 000.

ratio = 1 : 1 : 1 : 1 : 1 : 1 : 1 : 13 1 + 1 + 1 + 1 + 1 + 1 + 1 + 13 = 20 parts

8 a

b

c

d

e

1 2 : 2

3 : 5 6 = 1

2 × 3 3 : 2

3 × 2 2 : 5

6 × 1

= 3 6 : 4

6 : 5 6

`Totalnumberofparts= 3 + 4 + 5

= 12

1partofwheatseed= 2000kg ÷ 12

= 166.6kg

`Eachfarmergets= 166.6 × 3 : 166.6 × 4 : 166.6 × 5

= 500kg : 666.6kg : 833.3kg

= 500kg : 667kg : 833kgroundedtothenearestkg.

50 seeds = 1.6g

` 2000kg÷ 1.6g= 2 000 000g÷ 1.6g

= 1 250 000

` 1 250 000squaremetresoflandarerequiredtosowalltheseeds.


14SERIES TOPIC

11I

SolutionsWhere does it work? Rates & Ratios

Page 24 questions

1

3

2

4

Equivalent ratios with missing terms

x:6 = 2:3

=

6:5 = x:30

=

x

3

6

5

2

x

3

30

(togetcommon denominators)



(usecrossmultiplication)

method1: x 6 × 1

1 = 2 3 × 2

2

x 6 = 4

6

` x = 4

6 5 × 6

6 = x 30 × 1

1

36 30 = x

30

36 = x

` x = 36

3x 4 × 1

1 = 30 1 × 4

4

3x 4 = 120

4

3x = 120

` x = 40

x 6 = 2

3

x × 3 = 6 × 2

3x = 12

x = 4

÷ 3 ÷ 3

3x 4 = 30

1

3x × 1 = 4 × 30

3x = 120

` x = 40

÷ 3 ÷ 3

6 5 = x

30

6 × 30 = 5 × x

180 = 5x

36 = x

` x = 36

÷ 5 ÷ 5

method1:

method1:

method2:

method2:

method2:

3x:4 = 30:1

3:2x = 1:3

÷ 3 ÷ 3

3 2x = 1

3

3 × 3 = 2x × 1

9 = 2x

` x = 4.5 or 4 1 2

÷ 2 ÷ 2


15SERIES TOPIC

11I


Page 25 questions

5





(usecrossmultiplication)

15y 20 = 1

2

3y 4 = 1

2

3y 4 × 1

1 = 1 2 × 2

2

3y 4 = 2

4

3y = 2

` y = 2 3

5a 2 × 4

4 = 25 8 × 1

1

20a 8 = 25

8

20a = 25

a = 25 20

` a = 5 4

= 1 1 4

15y 20 = 1

2

3y 4 = 1

2

3y × 2 = 4 × 1

6y = 4

y = 4 6

` y = 2 3

÷ 6÷ 6

5a 2 = 25

8

5a × 8 = 2 × 25

40a = 50

a = 50 40

` a = 5 4 = 1 1

4

÷ 40 ÷ 40

3x 5 = 6

6

18x = 30

x = 30 18

` x = 5 3 = 1 2

3

÷ 18 ÷ 18

method1:

method1:

method1:

method2:

method2:

method2:

6

7

8

15y:20 = 1:2

3x:5 = 6:6

5a:2 = 25:8

y:6 = 6:y

÷ 3

÷ 20

÷ 3

÷ 20

3x 5 × 6

6 = 6 6 × 5

5

18x 30 = 30

30

18x = 30

x = 30 18

` x = 5 3 = 1 2

3

÷ 18 ÷ 18

(since(-6)2 and 62bothequal36)

` y 6 = 6

y

` y2 = 36

` y = 36

` y = !6


16SERIES TOPIC

11I


Page 27 questions

Scale drawings

1

2

4.5cm

a

b

c

d

e

1cm : 2m = 1cm : 200cm(2m= 200cm)

= 1 : 200

1m : 4cm = 100cm : 4cm

= 25 : 1

2cm : 1m = 2cm : 100cm(1m= 100cm)

= 1 : 50

20cm : 1km = 20cm : 100 000cm(1km= 100 000cm)

= 1cm : 5000cm

= 1 : 5000

1250mm : 250km = 1250mm : 250 000 000mm(1km= 1 000 000mm)

= 1mm : 200 000mm

= 1 : 200 000

12 : 1 = 4.5 : x

` 12 1 = 4.5

x

12x= 4.5

x= 0.375

`Inreallife,theantis0.375 cmlong.


17SERIES TOPIC

11I


Page 28 questions

Scale drawings

4

5

44 : 1

13 : 11 : 35

1 : 9

5 : 16

3 : 40a

a b

c

ba

b

c

c

3

Scale:1 : 100

Kitchen

Bathroom

Combinedlounge/bedroom3cm

5cm

7cm

5cm

1cm

1 : 35 = 6.5 : x

1 35 = 6.5

x

x= 227.5

`Reallifelength= 227.5 cm

44 : 1 = x : 4

44 1 = x

4

176= x

`Scaledrawing= 176 m

1 : 100 = 10 : x

1 100 = 10

x

x= 1000 cm

`Studioinreallifeis10 mlong.

length= 3 cm+ 7 cm

= 10 cm

Area= 7 m× 5 m

= 35 m2

13 : 1 = 6.5 : x

13 1 = 6.5

x

13x= 6.5

x= 0.5


3 : 40 = x : 4

3 40 = x

4

12= 40x

` x= 0.3

`Scaledrawing= 0.3 m

5 : 16 = 6.5 : x

5 16 = 6.5

x

5x= 104

x= 20.8


1 : 9 = x : 4

1 9 = x

4

4= 9x

` x= 0.4

`Scaledrawing= 0.4 m


18SERIES TOPIC

11I


Page 30 questions

Maps

1

2

(i) (ii)

1cm

1cm

P R

Q

`Reallifedistance= 1 140 000 cm

= 11.4 km

1 : 95 000 = 12 : x

1 95 000 = 12

x

x= 1 140 000

` 6 cm= 8 km

` 6 cm : 8 km

= 6 cm : 800 000 cm

` 1 cm : 133 333.3 cm

`Scaleofmap= 1 :133 333 1 3

PR = 4gridsapart

` 4 × 133 333 1 3 cm

= 533 333 1 3 cm

= 5.3 km


19SERIES TOPIC

11I


Page 32 questions

Rates

a b

c

1

2

3

Weeklyincome = 35 h × $17.50/h

= $612.50

Binspicked = 2.5 × 12

= 30

1920 cars/day

= 1920 cars/24 hours

= 80 cars/hour

224 bins/30 days

= 224 30 bins/day

= 7.46 bins/day

, 7 bins/day(tonearestbin)

1 year = 52 weeks

`workdays = 52 weeks× 5

= 260 days

`Totalworkdays = 260

` $82 420/260 days

= $82 420 ÷ 260/day

= $317/day


20SERIES TOPIC

11I


Page 34 questions

Rates involving flow of liquids

a

b

1

2

3

50 L/min

`After45 min = 45 × 50 L

= 2250 L in 45 min

30 000 L÷50 L/min = Totalminutestoempty

= 600 min

` 600 min÷60 min = 10 hours

94 000 Latrateof12 000 L/hour

= 12 000 L/60 min

= 12 000 L/3600 sec

= 3.3 L/s

= 3.3 L/s(to1 d.p.)

432 km/35 L

` 432 35 km/L = 12.342 857 14 km/L

` 100 km÷12.342 857 14 km = 8.101 851 82 L

` 100 km/8.1 L (to 1 d.p.)


21SERIES TOPIC

11I


4

Page 35 questions

Page 36 questions

Page 37 questions

Rates involving flow of liquids

Rates involving currency conversions


ba

5

6

24 L/100 km = 648 L/x km

24 100 = 648

x

24x= 64 800

` x= 2700 km

12 000 L @ 8.5 L/s

`Timetoempty=12 000 8.5

= 1411.76 s

`Thefirsttankemptiesintheshortesttime.

20 000 L @ 11.5 L/s

`Timetoempty= 20 000 11.5

= 1739.13 s

0.96 USD/1 AUD= $ xUSD/$5000 AUD

` 0.96 1

= x 5000

$4800= x

` $5000 AUD= $4800 USD

0.96

1 = $980 USD x

0.96x= $980 USD

x= $980 0.96 USD

x= $1020.83 (to2d.p.)AUD

Y1 GBP= 18.51ZAR

` Y25 000GBP= 25 000 # 8.51ZAR

= R462 500

Y1 GBP= 18.51ZAR

`1ZAR= 1 18.51GBP

1ZAR, 0.054GBP

`2 000 000ZAR, 2 000 000 # 0.054GBP

= Y108 000 GBP

ba7


22SERIES TOPIC

11I


Page 37 questions

Page 38 questions



1 Rupee= 0.0157 USD

` 40 000 (INR) , 40 000 # 0.0157 USD

= $628 USD

$1 USD = ¥123.630JPY

` $200 USD , 200 # 123.630JPY

= ¥24 726JPY

$1 NewZealanddollar= 0.716 USD

`$260 NZD , 260 # 0.716 USD

= $186.16 USD

$1 USD = $1.347 SGD

`$3600 USD , 3600 # 1.347 SGD

= $4849.20 SGD

$349 000 (NZD) $1 NZD = $0.716 USD`$349 000 NZD = 349 000 # 0.716 USD = $249 884 USD

Y163 500(GBP) Y1 GBP= $1.533 USD`Y163 500GBP= 136 500 # 1.533 USD = $250 645.50 USD

)229 000 (EUR) )1 EUR = $1.096 USD`)229 000 EUR = 229 000 # 1.096 USD = $250 984 USD

$325 000(AUD) $1 AUD= $0.767 USD`$325 000AUD= 325 000 # 0.767 USD = $249 275 USD

$336 800 (SGD) $1 SGD = $0.742 USD`$336 800 SGD = 336 800 # 0.742 USD = $249 905.60 USD

`)229 000(EUR)willexchangeforthelargestamountinUSDattheratescurrentlygiven.

b

d

a

c

e

8

8


23SERIES TOPIC

11I

SolutionsWhat else can you do? Rates & Ratios

Page 40 questions

Speed

1

3

2

a

a

b

c

d

e

b

c

Averagespeed = 50 km/2 h

= 25 km/h

Averagespeed = 400 km/0.5 h

= 800 km/h

Averagespeed = 876 km/9 h

= 97 1 3 km/h

Distance = 100 km/h × 3.5 hours

= 350 km

Distanceinfirst4hours = 80 km/h × 4 hours

= 320 km

Distanceinlast4hours = 110 km/h × 4 hours

= 440 km

Totaldistance = 320 km + 440 km

= 760 km

` 760 km/8 h = Averagespeedfor8 hours

= 95 km/h = Averagespeed

Totaltimeperiod = 8 hours


24SERIES TOPIC

11I


Page 41 questions

Speed

4

6

5 Totaldistanceran = (6 m × 15) × 2 forback&forth

= 180 m

Timeran = 3minutes,15seconds

= 195 sec

` 180 m/195 sec

= 0.92 m/s (to 2 d.p.)

6 m/sfor4 min30 sec= 6 m/sfor270 sec

D = ST

= 6 m/s × 270 sec

= 1620 m

T = D S

= 7000 km 900 km/h

= 7.7 hours

= 7 hours46 min40 sec

= 7 hours47 min (tonearestminute)


25SERIES TOPIC

11I


Page 43 question

Speed and different units

1

3

2

4

840 km/hin10 min= 840 km/hin 1 6 hour

` D = 840 km/h× 1 6 h

= 140 km

8 km/h= 8000 m/h

= 8000 m/60 min

= 8000 m/3600 sec

= 2.2 m/s

12 km/h= 12 000 m/h

= 12 000 m/3600 sec

= 3.3 m/s

`Cyclisttravellingat4 m/sisfaster.

2 410 000 km/27.3days

= 2 410 000 000 m/27.3days

= 2 410 000 000 m/655.2 h

= 2 410 000 000 m/39 312 min

= 2 410 000 000 m/2 358 720 sec

= 2 410 000 000 2 358 720 m/s= 1021.74 m/s

, 1022 m/s


26SERIES TOPIC

11I


Page 45 questions

Population growth rate

1 ChangeinPopulation=Populationin2013 -Populationin1990

PopulationGrowthRate,

= -

=

PGR =

× 100%

% (1 dp)

22 262 501

5 093 501

5 093 501

17 169 000

17 169 000

29.7

2

Find 37%ofthisandaddintofindthenewpopulation:

`Populationin2020:

` 120 000 000 + =

Populationatbeginningoftimeperiod= .

37% of = 0.37

×

=

120 000 000

120 000 000 120 000 000

44 400 000

44 400 000 164 400 000


27SERIES TOPIC

11I


3

a

Country Population in 2000 Population in 2013 Change in Population Population Growth Rate PGR (%)

Australia 19 000 000 22 262 501 326 250 17.2%

Indonesia 206 264 595 251 160 124 21.8%

Japan 127 000 000 127 253 075 253 075 0.2%

China 1 242 612 226 75 299 292 6.1%

Vietnam 70 000 000 92 477 857 22 477 857 32.1%

United States 281 421 923 316 668 567 35 246 644 12.5%

India 1 040 000 000 1 220 800 359 180 800 359

Papua New Guinea 6 431 902 544 902 9.3%

Afghanistan 29 863 000 31 108 077 1 245 077 4.2%

North Korea 22 488 000 24 720 407 2 232 407 9.9%

South Korea 47 817 000 48 955 203 113 820 2.4%

Pakistan 140 000 000 193 238 868 53 238 868 38%

a

b

c

d

b

c

d

Page 46 questions

Population growth rate

Population(2000) = 6 431 902 - 544 902

= 5 887 000

Population(2013) = 1 242 612 226 + 75 299 292

= 1 317 911 518

Change = 251160124 - 206 264 595

= 44 895 529

180 800 359 1 040 000 000 × 100% = 17.4 % (to 1 d.p.)

PapuaNewGuinea–Populationin2000:

China–Populationin2013:

Indonesia–ChangeinPopulation:

India–PopulationGrowthRate:


28SERIES TOPIC

11I

SolutionsNotes Rates & Ratios

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