NELSON SENIOR MATHS ESSENTIALS 12

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Sue THOMSON Judy BINNS

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�-•# NELSON

lait CENGAGE Learning·

Nelson Senior Maths for the Australian Curriculum Essentials 12 1st Edition

Sue Thomson Judy Binns

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National Library of Australia Cataloguing-in-Publication Data National Library of Australia Cataloguing-in-Publication entry Thomson, S. (Susan), 1953- author.

Nelson senior maths for the Australian curriculum essentials 12 / Sue Thomson, Judy Binns.

Includes index.

ISBN 9780 17 026411 2 (paperback) For secondary school age

Mathematics--Australia--Textbooks.

510

Cengage Learning Australia Level 7, 80 Dorcas Street

South Melbourne, Victoria Australia 3205

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For learning solutions, visit cengage.com.au Printed in China by China Translation & Printing Services. 234S672019 181716

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About this book vii 3.02 Two-dimensional shapes

About the series ix 3.03 Three-dimensional solids 45

About the authors X Investigation: Stacking and

1 It's about time! 3 packaging 48

1.01 World time zones 4 3.04 Drawing solids 49

Investigation: How did we get time 3.05 From 30 to 20 51

zones? 7 3.06 House plans and elevations 56

Investigation: The International Investigation: SketchUp I 59

Date Line 8 3.07 Perspective drawings 60

1.02 Daylight saving 8 Investigation: Perspective drawing

Investigation: When do we have in art 62

daylight saving? 10 Keyword activity 62

1.03 Happy New Year! 11 Solution to the chapter problem 63

Investigation: How many New Years 4 Taking a chance 65

can you celebrate? 13 4.01 Gavin's spinner

1.04 International sport 13 Investigation: Is Gavin's

Investigation: Choose your spinner fair? 67

special event 16 Investigation: What's in the bag? 68

Investigation: Where? 16 4.02 The language of chance 69

Keyword activity 16 Investigation: Making designer

Solution to the chapter problem 17 spinners 71

2 According to my sources 19 4.03 Experimental probability 72

2.01 Statistical inquiry 20 Investigation: Beat the dealer 72

2.02 Sample vs Census 22 4.04 Theoretical probability 75

Investigation: The Australian census 24 4.05 Writing probabilities 78

2.03 Types of samples 25 4.06 What's more likely? 80

Investigation: Sample sizes in polls 28 4.07 How often will it happen? 83

2.04 Questionnaires 28 4.08 The range of probabilities 85

Investigation: Travelling to school 30 4.09 Complementary events 85 2.05 Bias and misrepresentation 31 4.10 Using tables to count outcomes 88

Keyword activity 34 4.11 Using tree diagrams 91

Solution to the chapter problem 35 4.12 Probability tree diagrams 94

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How much money? 107 7.02 The sides of a right-angled triangle

5.01 Simple interest 108 7.03 The tangent ratio 163

Investigation: Is my investment safe? 112 7.04 Using the tan ratio to calculate

5.02 Compound interest 113 an angle 165

Investigation: Is it a scam? 116 7.05 Angles of elevation and depression 167 5.03 The future value of an investment 116 7.06 The sine and cosine ratios 169

Investigation: Different 7.07 Remembering the ratios 171

compounding periods 119 7.08 Calculating the hypotenuse 174

Investigation: Is compound interest 7.09 Compass directions 176

always better than simple interest? 120 7.10 Bearings 181

Investigation: Which is better: Investigation: How far and in what

Simple or compound interest? 120 direction is Mecca? 187

5.04 Interest rates and savings 121 Keyword activity 188

Investigation: Avoiding the monthly Solution to the chapter problem 189

service f,ee 124 8 Across then up 191

5.05 Investing in shares 124 8.01 The Cartesian plane 192

Investigation: Investment scams 126 Investigation: Points of view 195

5.06 Share tables and graphs 127 8.02 From rules to graphs 196

Investigation: Practical activity: 8.03 Using linear functions 199 Create a share portfolio 129

Keyword activity 130 8.04 Intersecting lines and break-even points 203

Solution to the chapter problem 131 Investigation: Nonlinear graphs 208

Health issues 133

Keyword activity 208

6.01 Medical measurements 134 Solution to the chapter problem 209

Investigation: Measuring baby's 9 Scattering the data 211

temperature 138

6.02 Grams, milligrams and millilitres 139 9.01 Bivariate data and scatter plots 212

6.03 Medical graphs 141 Investigation: My body parts 215

Investigation: How did you 9.02 Is there a relationship? 215

measure up as a baby? 145 Investigation: My body parts 2 219

6.04 Formulas used in hospitals 146 9.03 What does it mean? 219

6.05 Medical data 148 Investigation: Association or not? 220

Investigation: Recognising the 9.04 Putting it all together 221

signs of lung cancer 151 Keyword activity 222

Keyword activity 152 Solution to the chapter problem 223

Solution to the chapter problem 153 10 Changing populations 225

7 So, you've got a right angle ... 155 10.01 Feral camels 226

7.01 Pythagoras· theorem 156 Investigation: How many feral

Investigation: Cutting rectangles 160 camels? 227

Investigation: Will it become extinct? 228

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Australia and world populations 230 13.05 Surface area and curved surfaces

Investigation: Australia and world Investigation: Christmas

populations 230 bauble boxes 323

10.03 Inflation and the value of money 231 13.06 Surface area and pyramids 324

10.04 Doubling time 235 Investigation: Finding pyramids 329

Investigation: The relationship 13.07 Surface area and irregular solids .329

between growth rate and doubling Keyword activity 330

time 235 Solution to the chapter problem 331

10.05 Exponential functions: a model 14 Repaying our debts 333

for growth 239

14.01 Hire purchase loans 334

Investigation: Counting ancestors 245

Keyword activity 246 free loan? Investigation: A cheap, interest

Solution to the chapter problem 247 14.02 Reducible interest loans 341

11 Paper to reality 249 14.03 Spreadsheets and reducible loans

11.01 How long is that? 250 Investigation: Which loan?

11.02 Scale diagrams 254 14.04 Online calculators and reducible

11.03 House plans 258 loans 348

Investigation: My home 264 Investigation: Making smart

11.04 Building and decorating 264 repayments

11.05 Producing scale drawings 268 14.05 It's my money and my life! Investigation: Make my own scale Investigation: Can you afford to

drawing 272 buy a home? 359

Keyword activity 272 Keyword activity 360

Solution to the chapter problem 273 Solution to the chapter problem 361

12 Fitting the data 275 15 Sailing the World 363

12.01 Drawing a line of best fit 276 15.01 Locating positions on the Earth's

12.02 What does it mean? 282 surface 364

12.03 Correlation 286 Investigation: Australian position

Investigation: Changing correlations 291 coordinates

12.04 Predictions 292 Investigation: Where are you?

Keyword activity 298 15.02 Distances on the Earth's surface

Solution to the chapter problem 299 Investigation: How accurate is it? 371

13 Surfacearea.com.au 301 15.03 Longitude and time differences 371

13.01 What is area? 302 Investigation: Time zones in

Asia and the Pacific 373

13.02 All the shapes 306

15.04 Crossing the ocean 13.03 Areas of composite shapes 310

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Building our world 383 18.03 Allocated pensions

16.01 What is volume? 384 Investigation: Is funeral insurance

16.02 Volume and capacity 387 a good investment? 434

16.03 Volume: cubes and rectangular 18.04 How long do allocated

prisms 389 pensions last? 435

lnvestigatioh: The volume of my Investigation: It's your retirement! 438

school 394 Keyword activity 440

16.04 Volume: triangular prisms and Solution to the chapter problem 441

cylinders 394 Answers 442

Investigation: Designing a Glossary 471

smaller can 397 Index 474

Investigation: SketchUp Ill 397 16.05 Volume: pyramids, cones and

spheres 398

16.06 Volume and composite solids 403

Keyword activity 406

Solution to the chapter problem 407

17 Playing games 409

17.01 How lucky are you? 410

Investigation: How lucky are you? 410 Investigation: Will you be lucky in

the surgery? 411

Investigation: Guessing numbers

from 1 to 20 412

17.02 Gambling games and systems 412

17.03 Coins and dice 416

17.04 Financial expectation 418

Keyword activity 420

Solution to the chapter problem 421

18 Looking after Grandma 423

18.01 Life expectancy 424

Investigation: How long can you

expect to live? 427

Investigation: Life expectancy in

Australia 428

18.02 Inflation and expenses 429

Investigation: How have prices

changed during your lifetime? 431

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ABOUT THIS BOOK

A clear outline of chapter contents is provided. Links to curriculum content descriptions are included.

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The practical applications of each chapter are highlighted with a chapter opening problem which shows students how the learning links to their life.

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Example 2

Fourteen million people live in Zimbabwe and this number is increasing by 4.4% p.a. If the growth rate stays at 4.4% p.a., in approximately how many years will there be 28 million people living in Zimbabwe?

Solution

28 million is double 14 million. Amounts double in approximately (72 + growth rate) years.

Divide 72 by the annual growth rate. Write the answer.

Approximate time= 72 + 4.4

= 16 to the nearest whole number

It will take approximately 16 years for Zimbabwe's population to grow to 28 million.

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There are generally one or two examples leading to an exercise. Websites, spreadsheets and basic calculators are used.

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Exercise questions include those involving concepts and techniques as well as reasoning and communication.

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Each chapter concludes with one of a variety of styles oflanguage activities and the solution to the chapter problem.

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ABOUT THIS SERIES

There are 8 books in this series. These cover the subjects General Mathematics, Mathematical

Methods and Specialist Mathematics as well as Essential Mathematics.

These books have all been written specifically by a national author team for the Senior Australian Curriculum.

Accompanying each printed textbook is a digital textbook called the NelsonNetBook and a NelsonNet website.

Go to www.nelsonnet.com.au to log in.

For each chapter, the resources are listed. Simply click on the required resource. This is a web-based eBook that can be customised to suit your own learning needs.

The icons with the blue NelsonNet logo are 'hotspots'. Click on the icon and the resource will open. The tools on the vertical tool bar allow you to personalise pages in a variety of ways, including voice recordings, drawings and links to favourite websites. You are also able to zoom in and out.

The tools on the horizontal toolbar allow you to navigate around your eBook and change settings. Please note that complimentary access to NelsonNet and the NelsonNetBook is only available to Teachers who use the accompanying student textbook as a core educational resource in their classroom. Contact your sales representative information about access codes and conditions.

ICONS IN THE TEXTBOOK

·i·inHII

Worksheels

Link from question to worked example

Worksheet

Web icons

Interactive spreadsheet Spreadsheet

Weblink Webl;nk

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ABOUT THE AUTHORS

Sue Thomson

Sue Thomson was Head of Mathematics at De La Salle College Cronulla, Director of Teaching and Learning at Hunter Valley Grammar School, an examination writer and assessor for the NSW Board of Studies and a Senior Higher School Certificate marker. An active presenter of the Mathematical Association ofNSW and beyond, Sue's interests are in language development, financial literacy and making mathematics accessible to all. Sue co-wrote the successful User Friendly Maths in Practice, Access to General Mathematics, Workable and Access to Pre-vocational maths series.

Judy Binns

Judy Binns is Head Teacher of Mathematics at Mulwaree High School in Goulburn. She has co-written the New Century Maths 7-8 series for over 20 years and has recently written with Sue Thomson for the new senior syllabus in NSW She has an interest in motivating and teaching students with learning difficulties or who do not see the relevance of mathematics to their lives. She presents workshops for the Mathematical Association ofNSW and in her local area.

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is equal to -le is not equal to

"" is approximately equal to square root

< is less than > is greater than

� is less than or equal to

� is greater than or equal to therefore

ABBREVIATIONS

AND SYMBOLS

LHS left-hand side RHS right-hand side

Q3 3rd quartile

x

mean of x values

sx or ax standard deviation

TT pi (approximately 3.14159 ... )

Ill

is similar to

L angle

6 triangle

1: 650 000 at a scale of 1 to 650 000 36° 27' 36 degrees and 27 minutes 5:8 ratio of 5 to 8

% I A, B,

r,

�, E,

z,

H, 0, percentage per

GREEK ALPHABET

a alpha I,

p

beta K,

y gamma A,

0 delta M,

f epsilon N,

s

zeta �,

l] eta 0,

e

theta

n,

t K 'A, µ V

s

0 1t:

053° a true bearing

N 53° E a compass bearing

iota P, p rho

kappa

r,

CT sigma

lambda T, 't tau

mu Y, 'l) upsilon

nu <l>, <1> phi

xi X, X chi

omicron '¥, \fl psi

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CHAPTER PROBLEM

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f

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EARTH GEOMETRY AND TIME

ZONES

IT'S ABOUT

TIME!

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Solve problems involving time zones in Australia and in neighbouring nations, making any necessary allowances for daylight saving (ACMEM163)

Solve problems involving Greenwich Mean Time and the International Date Line (ACMEMI64) Ill Find time differences between two places on Earth (ACMEM165)

Solve problems associated with time zones; for example, internet and phone usage (ACMEM166) Solve problems relating to travelling east and west, incorporating time zone changes (ACMEM167)

@

How are we ever going to use this?

• When making overseas phone calls or contacting people in other countries via the internet • When planning an overseas trip

• When planning to watch sport in other countries

1111

WORLD TIME ZONES

Different parts of the world operate on different time zones. The time zones are related to Greenwich Mean Time - GMT, also sometimes referred to as Coordinated Universal Time -UTC. In precise scientific terms, there are small differences between these two systems of time but for our

purposes they are interchangeable.

STANDARD TIME ZONES OF THE WORLD

lllll

Does not observe Daylight Saving time

We measure time from Greenwich, which is near London, England.

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0

Example 1

For each country, state whether it is ahead or behind Greenwich Mean Time *(GMT). a Australia

b USA

c Chile d China

Solution

a On the map, Australia is to the right of Australia is ahead of GMT. England.

b On the map, the USA is in North America, to USA is behind GMT. the left of England.

c On the map Chile is in South America, to the Chile is behind GMT.

left of England.

d On the map China is in Asia, to the right of China is ahead of GMT. England.

Times for cities around the world are given in relation to Greenwich Mean Time. Cities to the west of London are behind GMT and cities to the east of London are ahead of GMT.

West(-) GMT East(+)

The table shows us the time in various cities in relation to GMT.

Cities

Honolulu Anchorage

I

Las Vegas, Vancouver, Los Angeles, Seattle Banff, La Paz Chicago, Mexico City

Atlanta, New York,

Lima

Bridgetown, Santiago

Rio de Janeiro, Buenos Aires

South Sandwich Islands Azores

Hours from GMT Cities

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

Florence, Algiers, Paris, Berlin

Helsinki, Cairo Nairobi, Mecca

Baku, Port Louis, Dubai, Moscow

Islamabad Astana, Dhaka Jakarta, Phnom Penh

Perth, Denpasar, Hong Kong, Singapore

Tokyo, Ambon

Brisbane, Melbourne, Hobart, Cairns, Sydney

Port Vila

Hours from GMT

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��jzones i,,i::

limo zones mop

®

Example 2

a What is the time difference between Rio de Janeiro and Christchurch? b When it is 2 a.m. in Rio de Janeiro, what time is it in Christchurch? c What time is it in Rio de Janeiro when it is 7 a.m. in Christchurch?

Solution

a Rio de Janeiro is -3 from GMT.

Christchurch is+ 12 from GMT. = Time difference is 3 + 12 hours 15 hours

MINUS PLUS

-3 Rio de Janeiro

0 Greenwich

12 Christchurch

b Christchurch is 15 hours later. c Rio de Janeiro is 15 hours behind.

2 a.m. + 15 hours= 5 p.m. the same day 7 a.m. -15 hours= 4 p.m. the day before

Remember to include which day it is in your answer.

EXERCISE 1.01

World time zones

Use the map of time zones and the table of time differences from GMT to complete this exercise.

•iH,iiiiiiJI

For each country, state whether it is ahead or behind Greenwich Mean Time.

a USA (Alaska) b Japan c India

1 d Argentina ' e Canada f Saudi Arabia

2

•Mniiii:I

What is the time difference bet�een the following cities? Remember that a line diagram can help you work it out!

a Mecca and Las Vegas c Honolulu and Buenos Aires e Banff and Florence

b Lima and Brisbane d Helsinki and Suva

3 Use your answers to question 2 to answer the following. a When it is 9 a.m. in Las Vegas, what time is it in Mecca? b When it is 4 p.m. in Mecca, what time is it in Las Vegas? c What time is it in Brisbane when it is 3 a.m. in Lima? d When it is 10 a.m. in Brisbane, what time is it in Lima? e What time is it in Honolulu when it is 2 p.m. in Buenos Aires?

What time is it in Buenos Aires when it is 10 p.m. in Honolulu? g When it is 10 a.m. in Suva, what time is it in Helsinki?

h When it is 10 p.m. in Helsinki, what time is it in Suva? When it is 8 p.m. in Florence, what time is it in Banff? What time is it in Florence when it is 11 a.m. in Banff?

Remember to include which day it is in your answer.

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4 a When it is 5 a.m. in Mexico City, what time is it in Helsinki? b When it is 4 p.m. in Hong Kong, what time is it in Vancouver? c What time is it in Algiers when it is 10 a.m. in Honolulu? d When it is 1 p.m. in La Paz, what time is it in Reykjavik? e If it is 9 p.m. in Atlanta, what time is it in Dhaka?

When it is 11 a.m. in Chicago, what time is it in Port Vila?

5 At 9:00 a.m. in Bridgetown, Wesley phones his cousin in Cairo. What time is it in Cairo? 6 James joins a chat room on the internet at 10 p.m. in Perth. He is exchanging views with Juan

in Santiago. What time is it in Santiago?

7 Michelle caught a flight from Melbourne to Christchurch. This flight left Melbourne at 1030 (Melbourne time).

a What time was it in Christchurch when Michelle's flight left Melbourne?

b The flight arrived in Christchurch at 1800 (New Zealand time). How long did Michelle's flight take?

8 Carol flew from New York to Honolulu. Her flight left New York at 1520 on Saturday and took 11 hours to get to Honolulu. At what local time did she arrive in Honolulu?

9 Simon flies from Brisbane to Los Angeles. He leaves Brisbane at 1030 on Saturday 7 April. He arrives in Los Angeles at 0900, also on Saturday 7 April.

a How is this possible?

b How long is the flight from Brisbane to Los Angeles?

I

INVESTIGATION

How did we get time zones?

Use the Internet to research the history of time zones. You should include answers to the following:

• how people kept time before clocks were widely used and why this worked

• why Greenwich was established as 'zero' time

• what developments led to the need for common time zones • what people were involved in the development of time zones • when time zones became established

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INVESTIGATION

The International Date Line

Use the Internet to answer the following questions. • What is the International Date Line?

• How is it related to the Prime Meridian through Greenwich?

• What happens when you cross the International Date Line when you are travelling west, for example when flying from the USA to Australia?

• What happens when you cross the International Date Line when you are travelling east, for example when flying from Australia to the USA?

• Name an island on each side of the International Date Line.

• Two countries have recently changed where they are in relation to the International Date Line. What are they and why did they make the change?

• Find and copy a map showing the International Date Line.

111..1

DAYLIGHT SAVING

During summer, daylight saving time is adopted by many countries or parts of countries. Clocks are advanced by one hour near the start of spring and put back by one hour near the start of autumn ('spring' advance, 'fall'

put back"). Countries which use daylight saving are shown on the map on page 4.

In Australia, New South Wales, ACT, Victoria, Tasmania and South Australia usually use daylight saving from the first Sunday in October through to the first Sunday in April. During this time of year, these states are an extra hour ahead of GMT. Queensland, the Northern Territory and Western Australia do not use daylight saving. Daylight saving time changes the time differences between countries and cities.

8 I NELSON SENIOR MATHS Essentials 12

+10

+8

+10.5

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0

Example 3

When it is 10:20 a.m. in December in Adelaide, what time is it in Perth?

Solution

In December, Adelaide is on daylight saving time. This means that it is 2½ hours ahead of

Perth instead of the usual 1 ½ hours.

Time in Perth = 10:20 a.m. -2½ hours

= 7:50 a.m.

Countries in the northern hemisphere have daylight saving in their summer, which is our winter. This means that London, for example, is GMT+ 1 during summer. Because of daylight saving, the east coast of Australia is 11 hours ahead of London in our summer ( except for Queensland) and only 9 hours ahead in winter.

0

Example 4

Jackie in Cairns wants to chat on the internet with her best friend Alice who is visiting New York. Daylight saving is operating in New York. When should Jackie log on in Cairns to reach Alice at 4 p.m. Friday in New York?

Solution

Look up the table to see the time zones for Cairns and New York.

Adjust for daylight saving in New York. Calculate the time difference.

NewYork-4

Calculate the time in Cairns.

Cairns is GMT +10. New York is GMT -5.

Add 1 hour: New York is GMT -4. Time difference= 4 + 10 hours

= 14 hours

Greenwich Cairns +10

Log on time = 4 p.m. Friday+ 14 hours = 6 a.m. Saturday

(21)

World clock

EXERCISE 1.02

Daylight saving

•#HuHiid

Use the map of Australia to answer these questions. Assume that daylight saving is • I •

m operat10n.

a When it is 8:30 p.m. in Darwin, what time is it in Hobart? b What time is it in Adelaide when it is 11:45 a.m. in Melbourne? c When it is 1:05 p.m. in Sydney, what time is it in Perth? d What time is it in Brisbane when it is 8:20 a.m. in Darwin?

2 Ben, working in the mines in Western Australia, wants to ring his wife in Victoria during summer. He knows she will have the children in bed by 8 p.m. After what time in Western Australia can he ring her so that he can talk to her after the children are in bed?

3 Janine, who lives in Queensland, wants to ring her daughter Alexis in Adelaide before she goes to work to start a new job. She knows Alexis intends to leave for work at 7:45 a.m., so wants to talk to her at 7:15 a.m. What time in Queensland should Janine ring her?

4 ■

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Michael is conducting business in Melbourne with a company in Jakarta, Indonesia. Melbourne is on daylight saving, while Indonesia is not. Michael needs to organise a video conference for 2 p.m. Indonesian time. What time will it be in Melbourne?

5 Joe is visiting Ouagadougou in Burkina Faso in West Africa. This city does not observe daylight saving. He wants to connect to his friend Steve in Sydney via the internet. He logs on at 6 p.m. local time.

a What time will it be in Sydney?

b Is this a good time for Joe to try to talk to his friend? Why or why not?

6 Alyda's brother is working in Baku in the former Eastern Russian region of Azerbaijan. Alycia is studying in Adelaide. It is February and daylight saving is operating in Adelaide. Between what times in Adelaide can Alycia ring him so that she rings between 6 p.m. and 10 p.m. in Baku?

7 The Sanders family from Hobart is visiting New Zealand in January. Both countries are on daylight saving. Amy wants to talk to her best friend Sue and she knows that she can catch Sue at 11 :30 a.m. Hobart time. At what time in New Zealand should she ring her?

8 Frances and Sally have been travelling around the world together. Frances stayed in Paris while Sally flew on to Vancouver. Both countries are operating on daylight saving. Frances texts Sally at 4 p.m. Paris time. What time is this in Vancouver?

INVE

S

TIGATION

When do we have daylight saving?

Using the map given on page 4, choose a country or a state that observes daylight saving from each continent.

Using the Internet, find out at what time of year each place observes daylight saving. One possible website to use has a world clock.

(22)

l1J1

HAPPY NEW YEAR!

Each city in the world celebrates the arrival of the New Year but we don't all do it together. In January, some countries in the southern hemisphere are on daylight saving time but countries in the northern hemisphere are not.

0

Example 5

What time is it in London when the residents of Hobart are celebrating midnight on New Year's Eve?

Solution

Using the information on time zones and daylight saving, find the difference between London time (GMT) and Hobart time in January.

0

Example 6

At this time of the year, Hobart is 11 hours ahead of GMT.

Midnight - 11 hours = 1 p.m.

The time in London is 1 p.m. on 31 December.

How many hours later than the New Year in Perth is the New Year in Las Vegas?

Solution

Find the time difference between Perth and Las Vegas. There is no daylight saving in Western Australia and none in Las Vegas as it

Perth is GMT +8. Las Vegas is GMT -8. 8 + 8 = 16

(23)

EXERCISE 1.03

Happy New Year!

•4H,H4

What time is it in Dubai when the residents of Perth are celebrating midnight on New Year's Eve?

2 What time is it in Honolulu when people in Darwin are celebrating the arrival of the New Year? 3 The pyramids in Egypt have a special light show at the start of the New Year. At what time in

Melbourne should Jack switch on the TV to see the light show on the pyramids?

4 Kit and Jennifer want to watch the spectacular fireworks at the Space Needle in Seattle online. At what time should they log on in Broome (WA) to watch the fireworks, which start at 11:45 p.m. in Seattle?

5 ■

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How many hours are there between the New Year in Brisbane and the New Year in Berlin, Germany?

6 How many hours earlier is the New Year in New Zealand than the New Year in Moscow? 7 Use the information in the table on page 5 to answer the following questions.

a Which listed city is the first to celebrate New Year? b Which listed city is the last to celebrate New Year?

c How many hours are there between these two celebrations? 8 Use the information in the table on page 5 to answer this question.

a Choose a city that you would like to visit for the New Year's celebration.

b Your parents want to ring you when it is the New Year in the city you have chosen. At what time should your parents ring you from home?

(24)

INVESTIGATION

How many New Years can you celebrate?

Is it possible to celebrate the New Year in the capital city of your state and celebrate it again in another city? Is it possible to do this more than once?

In this investigation, we will assume that you are at the airport and that a plane will take off as soon as midnight passes.

You will need to find the flight times between your capital city and other cities in the world that have a large time difference with your capital city.

• Make a list of possible cities.

• Calculate the time difference between your capital city and each city.

• Use the Internet to find the flight times from your capital city to each city.

• By comparing the times, decide if it's possible to celebrate the New Year in more than one city.

l1J1

INTERNATIONAL SPORT

Major sporting events, for example, Wimbledon, the World Cup, Super Rugby and Formula 1 motor races are watched by millions of people in many different countries. We can use time zones to work out when different events will be shown on TV in Australia.

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(25)

EXERCISE 1.04

International sport

Use the information on time zones at the beginning of this chapter to answer the questions in this exercise. If you need to, look up the Internet to find time zones that you don't know.

Formula 1 Grand Prix races are held all over the world, 19 races in all. All races are broadcast live on Australian television. Work out the time at which you need to turn on the TV to see the start of each of these races.

a at Sakhir in Bahrain in April, starting at 6 p.m. local time

b the Chinese April race in Shanghai that starts at 3 p.m. Shanghai time

c at Monza in Italy in September, starting at 2 p.m. local time

Remember to check whether daylight saving is operating and, if necessary, take it into account.

d the United States race at Austin in November, starting at 2 p.m. local time

2 Wimbledon, one of the four Grand Slam tennis tournaments, takes place in London at the end ofJune and the start ofJuly.

a Each day, matches start at 11 a.m. local time. What time is this where you live?

b The semi-finals start at 2 p.m. local time. At what time will you need to switch on the TV to watch the semi-finals?

c The Men's Final starts at 2.30 p.m. local time. One final lasted 3 hours and 35 minutes. At what time, in your location, did this final finish?

3 In 2014, the FIFA World Cup was held in Brazil in June and July. Australia had to play three other countries in the Group rounds.

a The Australia vs. Chile match was scheduled for 6 p.m. local time. What time was this where you are?

b Australia's other two matches against the Netherlands and Spain were scheduled for 1 p.m. local time. What time was this where you are?

c The final was played at 4 p.m. local time. The broadcast lasted 2 hours and 45 minutes. What time did it finish where you are?

(26)

4 There are 15 teams in the Super Rugby competition: 5 from Australia, 5 from New Zealand and 5 from South Africa. For the Australian teams, some games are played in Australia and some are played in the other countries. New Zealand is GMT+ 12 and South Africa is GMT +2. a The Queensland Reds will play the South African Sharks in Brisbane, with kick-off at 1605

local time. What time is this for fans in South Africa?

b The Western Force play the New Zealand Highlanders in Dunedin New Zealand. Kick-off is at 1935 local time. What time is this in Perth for fans who want to watch the game?

c The South African Bulls play the Melbourne Rebels in Pretoria, South Africa, with kick-off at 1910 local time. At what time in Melbourne does the game start?

5 Every four years in July the Australian Cricket team plays the Ashes Series against England in England. At this time of year, England is on daylight saving time and Australia isn't. The daily schedule is as follows:

6

Start of play: 10.30 a.m. Lunch: 12.30 p.m. to 1.10 p.m. Tea: 3.10 p.m. to 3.30 p.m. Close of play: 5.30 p.m.

List the daily schedule in the time zone where you live.

The US Masters Golf Tournament is played in April each ye;u at Augusta in the United States. Augusta is GMT-5. In April, parts of the United States, including Augusta, are on daylight saving time and Australian states are not. a Practice rounds are

broadcast from 12 noon to 7 p.m. local time. Peter lives in Hobart and wants to watch

practice. Between what times should he be watching?

b Each of the four days of competition are broadcast from 3 p.m. to 7 p.m. Between what times can you watch the daily rounds?

i

1

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e

c Play finishes at 7 p.m. each day but if there is a tie at the end of the competition, extra play-off holes have to be played on the last day. The play-off takes an extra 45 minutes. What time will the play-off finish on the last day in your time zone?

7 The Tour de France is a cycling race that takes place in July each year. It lasts three weeks, covers about 3700 km and is raced mostly in France. There are twenty racing days and two rest days. The race on each day is called a stage. In July, France is on daylight saving and Australia is not. a Stage 10 starts at approximately 10 a.m. local time. What time is this where you are? b Live broadcast on Australian television starts at 10.30 p.m. in the Eastern states.

i What time is this where you are?

(27)

World dock

INVESTIGATION

Choose your special event

Many special events around the world

are broadcast live on Australian television or on the internet. These events include the Olympics, the Commonwealth Games, the Oscars, religious festivals, weddings and funerals of famous people, ANZAC Day services, Remembrance Day services and other sporting events. • Choose one event that you are

interested in that takes place in our summer and one event that takes place in our winter.

• For each of your chosen events, work out the times that you will be able to watch it at home onTV

For one of the events you have chosen:

• find out how long it would take you to fly from your state's capital city to the event

• imagine that you are able to fly to see the event live and that you wish to arrive at least

2 hours before the event commences. By what time must you leave your state's capital city?

INVESTIGATION

Where?

In this investigation, use the world clock website to answer the following questions. • Find three locations that have the same time as you.

• Find three locations that are 5 hours behind you.

• Find three locations that are 2 hours ahead of you. • What town or city is as far behind you as possible?

• What town or city is as far ahead of you as possible?

• Choose three places that you would like to visit and find the time in those places when it is 12 noon where you are.

KEYWORD ACTIVITY

Greenwich Mean Time Time zone

International Date Line Daylight saving

For each of the above phrases, write a short paragraph to explain its meaning and importance. Then write a single paragraph including all four terms.

(28)

CHAPTER PROBLEM

The FA Cup final is played at Wembley Stadium in London in May each year. At this time of the year, England is on daylight saving time and Australia is not. The match starts at 1700 local time. At what time should fans around Australia tune in to watch the final?

SOLUTION TO THE CHAPTER PROBLEM

In London: In Australia:

In May, daylight saving is operating, so the time is GMT+ 1 Western Australia is GMT +8. The time difference is 7 hours.

South Australia and Northern Territory are GMT +9.5. The time difference is 8.5 hours.

Queensland, NSW and the ACT, Victoria and Tasmania are GMT+ 10. The time difference is 9 hours.

Western Australia: 1700 + 7 hours= Midnight

South Australia and Northern Territory: 1700 + 8.5 hours= 1:30 a.m. next day

(29)

?

CHAPTER PROBLEM

Andrew is a market researcher. The United Club has asked him to evaluate the facilities and services it provides for members. Should he survey all 14 100 members or take a sample? Ifhe chooses to use a sample, how should he select participants to ensure that he gets a representative range of views?

, .

(30)

DATA COLLECTION

ACCORDING TO

MY SOURCES

2.01 Statistical inquiry

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CENSUS

Investigate the procedure for conducting a census (ACMEM127)

Investigate the advantages and.disadvantages of conducting a census (ACMEM128)

SURVEYS

Understand the purpose of sampling to provide an estimate of population values when a census is not used (ACMEM129)

Investigate the different kinds of samples: for example, systematic samples, self-selected samples, simple random samples (ACMEM130)

Investigate the advantages and disadvantages of these kinds of samples: for example, comparing simple random samples with self-selected samples (ACMEM131)

SIMPLE SURVEY PROCEDURE

Identify the target population to be surveyed (ACMEMl32)

Investigate questionnaire design principles: for example, simple language, unambiguous questions, consideration of number of choices, issues of privacy and ethics, and freedom from bias (ACM EM 133)

SOURCES OF BIAS

Describe the faults in the collection of data process (ACMEM 134)

Describe sources of error in surveys: for example, sampling error and measurement error (ACMEMl35)

Investigate the possible misrepresentation of the results of a survey due to misunderstanding the procedure,

or misunderstanding the reliability of generalising the survey findings to the entire population (ACMEM136)

Investigate errors and misrepresentation in surveys, including media misrepresentations of surveys

(ACMEM137)@

How are we ever going to use this?

• When we read or consider information in the media • When we evaluate the results of surveys

• When we undertake a survey

tJ111

STATISTICAL INQU

.

IRY

A variety of people collect information to enable others to make informed decisions. This process is called statistical inquiry and it involves the following steps.

Posing questions - deciding what information is needed and in what form.

Collecting data - choosing to use a census or a sample of the population. We have to decide how we will collect information and then collect the information.

Organising data - after we collect the data we need to organise it. We could use a frequency table, with either grouped or ungrouped data.

Summarising and displaying data - in this step we present the information in a way that makes it easy to follow and understand. Often we do this graphically.

Analysing data and drawing conclusions - this step involves the calculation of summary

statistics and then analysing the assembled information.

Writing a report - this step involves presenting the data in an understandable way with the conclusions supported by the statistics.

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EXERCISE 2

.

01

Statistical inquiry

1 In your own words, summarise the steps in the process of statistical inquiry.

2 Classify each of the following activities according to which step they are part of - posing questions (PQ), collecting data (CD), organising data (OD), summarising and displaying data (SDD), analysing data and drawing conclusions (ADDC), or writing a report (WR).

3

Q 0

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.Q @

a / eter asks fellow students in Year 12 how they travel to school b � ane draws a frequency histogram of her data

E 8 '-�

1

j

c

j

nna finds the mean house price for her suburb d

/j anaging Director Theo decides he needs to know customers' favourite car colour e ieran makes recommendations in his final report

1i

n puts her information about favourite holiday destinations into a frequency table arian concludes that coffee is her friends' favourite daytime drink

110n visits the houses in Smith Street to collect their Census forms deline decides to research the drinking habits of 18-year-olds

m displays data about pocket money received by Year 12 students in a sector graph oebe writes a report on her data about popular sports

m goes through a pile of surveys and records the responses to question 4

se a topic to research and describe how you would implement each of the six steps of a ·ical inquiry.

4 Different organisations collect information on a large scale. Visit the website of each organisation below and write down at least five things they collect information about. a the Australian Bureau of Statistics (ABS) b the United Nations (UN) c the World Health Organization (WHO)

-5 The privacy of collected information can be important. Visit the Australian Bureau of Statistics website. Go to the Census page and click on 'About the Census'. Scroll down and click on Privacy and Confidentiality. Describe in your own words how the ABS ensures the privacy of

(33)

tl•�A

SAMPLE VS CENSUS

To collect information, we usually survey a representative group. This process is called taking a sample.

To collect information about a whole population, all people or items must be surveyed. This is called taking a census. People who are members of small groups can be missed in a sample. We always use a census when we want to make sure that the views of small groups are included. The Australian Bureau of Statistics conducts a national census every five years. The census occurs in each year ending in a 1 or a 6.

Sample

Census 100 years 1911-2011

9Aucllllt2011

Why a Census? The Census is the only practical way to get information on how many people there are in each part of Australia, what they do and how they live.

Collection authority The Information asked for is collected under the authority of the Census and Statistics Act

1905. Your co-operation is sought in completing this form.

Household Form

WHAT YOU NEED TO DO

Census Form Number c, .. , Ch"' Lettu L,tter

□□□□□□□-□-□□□□

-

• Use this form to record the details of all people (including visilors) who spend the night in your dwelling on Census Night, Tuesday, 9 August 2011.

• Your Colleclor will relurn between 10 August and 28 August to collect your form. • On one form you can record details of six people. If you need more forms, refer to the

'Help available' section below.

• If someone in your household wants a separate Census form for privacy reasons, just ask the Collector for a Personal Form and a Privacy Envelope or phone the Census Inquiry Service. Refer to the 'Help available' section below.

HOW TO WRITE YOUR ANSWERS • Use a black or blue pen. • Mark boxes like this: • Start numbers in the first box.

Census

• Surveys a selected group of people or items • Surveys all people or items in the population • Gives approximate information about the

population

• Simple and inexpensive

• Can be done quickly

0

Example 1

• Gives exact information about the population

• Complex and expensive

• Takes a tot of time to collect and process the informa�ion

The United Club asked Andrew to evaluate the facilities and services it provides to its 14 100 members. Should he use a census or a sample to gather information?

Solution

A census would be expensive and it would take a long time to process the information.

22 I NELSON SENIOR MATHS Essentials 12

A sample should be used in this situation.

(34)

0

Example 2

From what population should you take a sample to investigate the reputation of the United Club in the local community?

Solution

He would need to ask people who live close

enough to use the club. The population would be the residents of the town or suburb where the United Club is located.

EXERCISE 2.02

Sample vs Census

1 Write a paragraph in your own words describing the advantages and disadvantages of using a census to collect information.

2

•4H,Hd

Should a census or a sample be used for each investigation? Give a reason for your answer.

a The most popular car colour in Australia b The number of retired people living in Darwin

c The number of Australians who watch the AFL Grand Final d The use of soap versus bodywash

e Testing coffee for taste

Finding the population of Alice Springs

g The number of people using the emergency department at a large city hospital on Saturday night

(35)

Australian Bureau of Statistics

3 0j,j,,i,j

What is the population for each investigation?

a Are girls better than boys at Maths? b Voting intentions for the next State election c The best song of the last decade

d Student attitudes to school uniform at your school e Favourite make of car in Western Australia

How much people are prepared to spend on going to the gym each week g Which venue Year 12 should use for their formal

h Giving to charities by rich people

What factors influence the choice of supermarket The batting performance of the Australian cricket team

INVESTIGATION

The Australian census

The Australian census is conducted by the Australian Bureau of Statistics. Visit their website and click on 'Census' to find the answers to these questions.

When was the first national census conducted? 2 When was the last census?

3 List five questions that were asked in the last census.

4 Find three questions that have been asked in the past but were not asked in the most recent

census.

5 Were there any questions in the most recent census that have not been asked before? If so, what were they?

6 Are all questions in the census compulsory?

7 Give three examples of how census information is used.

(36)

W,,1111

TYPES OF SAMPLES

If we decide to use a sample for a survey or questionnaire, there are four types of samples we can use. Random sample

In a random sample, every member of the population has an equal chance of being included. For example, when a computer selects a customer at random to be surveyed about a mobile phone company, every customer of that company has an equal chance of being selected.

Stratified sample

In a stratified sample, different categories in a population are represented according to the size of each category and then members of each category are selected randomly.

For example, a school's population may be made up of72% junior students and 28% senior students. A stratified sample of school students must also be made up of 72% junior students and 28% senior students.

Systematic sample

In a systematic sample, selections are made on a regular basis. For example, testing every 500th battery manufactured to check that the machines producing the batteries are working properly.

Self-selected sample

In a self-selected sample, whoever wishes to participate answers the questions asked. For example, when a television show asks people to ring in and answer a Yes/No question, anyone can participate.

0

Example 3

The United Club has 14 100 members. This table

gives a breakdown of members by age group. Less than 30 years Andrew is considering four different of ways of 30 to 39 years choosing a sample of the members for his market 40 to 49 years research. Which type of sample is each one? 50 years and over a Every 100th member on the alphabetical membership list

b Names selected randomly by the computer

Number of members 2100 2700 5100 4200

c Putting up a sign at the entrance of the club asking members to volunteer

d 21 members less than 30 years old, 27 members 30 to 39 years old, 51 members 40 to 49 years old and 42 members aged 50 years or more.

Solution

a Selections are made on a regular basis, in this case every 100th member.

b Every member of the population has an equal chance of being included and the computer chooses randomly.

c Any member who volunteers can participate.

Systematic sample

Random sample

(37)

When we use a stratified sample, we need to calculate how many people from each category should be included in the sample.

0

Example 4

Jason decided to use a stratified sample to survey members at his local gym. There are 970 gym members, 590 are female and 380 are male. He plans to survey 10% of the members.

a How many members will Jason survey? b How many female members should he survey? c How many male members should he survey?

Solution

a Calculate 10% of the membership. 10% of 970 = 10 lO0 X 970

=97

Jason should survey 97 members. 590

- x97=59 970

b Female members make up 590 out of 970 members. Find the fraction of the

number of members surveyed. Jason should survey 59 female members.

c Males are 380 out of 970 members.

OR

380

- X 97=38 970

Calculate the total to be surveyed minus the number of females.

97 members -59 females = 38 males Jason should survey 38 males.

EXERCISE 2.03

Types of samples

ii\,i,,i,,M Which type of sampling is described in each case? a Selecting every 105th name from the phone book.

b The names of all prefects are placed in a hat and 2 are drawn out to represent the school at a council function.

c A television program asks viewers to respond to a Yes/No question.

d Selecting an appropriate number of students from each year at your local high school. e Door prizes drawn out of a barrel.

f The audience at a concert finds prize tickets under every 5th seat in each row. g A company sends out an email to customers asking for their opinions.

h Employees are sorted from tallest to shortest and every 5th employee completes a questionnaire.

20 females and 28 males were surveyed out of a group of athletes with 100 females and 140 males in it.

j A customs officer searching every 10th person walking through customs.

k A medical researcher advertises for people to participate in a health survey. 5 cards are selected from a pack of cards without looking.

m An import/export business employs i25 women and 250 men. 17 women and 34 men are surveyed about their work hours.

(38)

2 Children from 400 families attend the local infants/primary school. The P&C has raised money for new play equipment in the playground and wants to interview parents about their ideas. The committee would like to survey 40 families. Suggest how they might select the 40 families using a:

a random sample b stratified sample

c systematic sample d self-selected sample.

3

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Amanda is going to use a stratified sample to survey the parents of her local netball club. There are 540 children playing netball. There are 380 primary students and 160 high school students. Amanda is going to survey 15% of parents.

a How many parents should complete the survey?

b How many parents of primary students should complete the survey? c How many parents of high school students should complete the survey?

4 Kieran wishes to survey Year 8 students about their opinions of the school. There are 96 boys and 69 girls in Year 8. He aims to survey 20% of students.

a How many students should complete the survey?

b How many boys should complete the survey?

5 Joanna is going to ask a sample of her Facebook friends about their favourite sport. She has 376 single friends and 416 friends in a relationship. She is going to survey 12.5% of her friends. a How many friends will she survey?

b How many single friends will be in the survey?

c How many friends in a relationship will be in the survey?

6 Global Communications employs 750 people, 479 males and 271 females. The company intends to survey 75 employees about their working conditions.

a How many males should be surveyed?

(39)

Roy Morgon Research

Gciloxy Research

INVESTIGATION

Sample sizes in polls

In this investigation we will look at the sizes of samples used by polling organisations. Visit the Roy Morgan Research website.

2 Click on the Findings tab and select one of the polls in Australia that interests you. 3 Write down what the poll is about and the size of the sample.

4 Use the Internet to find the population of Australia. 5 What percentage is the sample of Australia's population?

sample

Hint: Percentage=--�- x 100% population 6 Visit the Galaxy Research website.

7 Select a recent national or state poll and write down the sample size used.

8 Use the Internet to find the population of Australia or the state in the poll you have chosen. 9 What percentage of the population is the sample?

10 Write two or three sentences describing what you have found.

11 How well do you think the samples reflect the opinions of the population?

tl•J1

QUESTIONNAIRES

Using questionnaires is one of the most common ways to collect information. A good questionnaire has the following features.

• It uses simple language

• Questions are written so that the meaning is clear • It meets privacy requirements. Unauthorised people

cannot access your information • It is free from bias

The style of answers and any provided alternatives are another important consideration.

(40)

EXERCISE 2.04

Questionnaires

Andrew has designed the first draft of a questionnaire to survey club members about entertainment the United Club provides, including trips away. Andrew's draft is given below. Read the

questionnaire and answer the questions that follow.

United Club Help us help you!

Please complete this short questionnaire to help the United Club better serve you.

1. How old are you? 2. Are you male or female?

D Less than 30 years D Male

D Between 31 and 40 years D Female

D From 41 to 50 years

Over 50 years

3. Which of the Club's entertainments do you attend?

4. How often do you attend the following Club activities? D Concerts

D Films D Dance nights

Trips away

5. Do you think the entertainment offered is reasonably priced?

6. Should the club offer more types of entertainment, and if so, what should it offer?

7. Are there any other comments that you would like to make about the Club's entertainment program?

Thank you for taking the time to complete this questionnaire. Please hand it in at the bar.

Open-ended questions require the person answering to write their own answer. How many questions in the questionnaire are open-ended?

2 Closed questions give options to choose for the answer. How many questions in the questionnaire are closed?

3 The first question about age has a problem with the options given. What error has Andrew made? (Hint: where would a 30-year-old tick?). Rewrite the options to this question to fix this error. 4 When Andrew asks 'Which of the Club's entertainments do you attend?' it is not clear exactly

what he means. Club members may be unsure about which of the Club's activities is classed as entertainment. Rewrite the question to make it clear what activities Andrew means.

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8 There is a risk that answers won't remain private if the questionnaires are handed in at the bar. Suggest a more secure way to collect the questionnaire forms.

9 Do you think Andrew has missed anything in his questionnaire? (Hint: how would people who don't attend entertainment activities express their views?) Write three additional questions that Andrew could ask.

INVESTIGATION

Travelling to school

You are going to conduct a survey of how students in your school travel to school. Before you start you will need to make some decisions.

• How large a sample will you use?

• How will you select your sample?

• What questions will you ask?

• What are the possible categories or types of travel that students at your school might use? List them.

• What will you do if there is a category you haven't thought of?

• What will you do if someone uses more than one method of transport? 2 Collect the information.

3 Answer the following questions.

• What is the most common method of travel used? • What is the least common method used?

• What effect does the location of your school have on the method of travel used by students?

4 Present your results in a report -this may be written or a Power Point presentation.

Figure

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References

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