13 NCM7 2nd ed SB TXTweb2.hunterspt-h.schools.nsw.edu.au/studentshared... · 2008-07-21 ·...

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DATA

Information is collected by government departments, market researchers, opinion pollsters and others on almost every aspect of our lives. They ask questions such as: ‘What is your favourite brand of soft drink?’ ‘What type of movies do you like?’ ‘Should we change our national flag?’ ‘How do you travel to school?’ This chapter looks at the different ways such information can be displayed on graphs and tables.

13 NCM7 2nd ed SB TXT.fm Page 444 Saturday, June 7, 2008 7:15 PM

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In this chapter you will: Wordbank

• draw and interpret picture graphs, column graphs, divided bar graphs and sector graphs

• draw and interpret line graphs, travel graphs, conversion graphs and step graphs

• understand, use and choose the scale on the vertical and horizontal axes of a graph

• read and interpret information presented in tables

•

conversion graph

A line graph used to convert one unit to another.

•

divided bar graph

A rectangular graph divided into slices.

•

horizontal axis

The bottom border of a graph that runs across, with labels listing the categories or numbers.

•

key

A note or label that explains the symbols or colour code of a graph.

•

scale

What one unit or interval on a graph’s axis represents.

•

step graph

A graph made up of broken horizontal intervals, or separate flat ‘steps’.

•

vertical axis

The border of the graph that runs upwards, usually on the left-hand side, with labels listing the numerical values.


446

NEW CENTURY MATHS 7

Start up

1

Find the value of

x

in the diagram on the right.

2

For each of these diagrams, write:

i

the fraction of the circle shaded pink

ii

the size of the angle,

x

°

3

Copy and complete each of the following scales and state the size of one interval.

4

Refer to the number plane on the right and write the letters of the points with these coordinates.

a

(5, 6)

b

(5, 1)

c

(2, 1)

d

(4, 3)

e

(2, 6)

f

(6, 2)

g

(4, 2)

h

(1, 2)

i

(3, 4)

j

(1, 5)

Worksheet13-01

Brainstarters 13

210° x°

x°

x°

x°

x°

x°

x°

a b c

d e f

a60 80 100 120 140 160

b33 36 39 42 45 48 51

c70 80 90 100 110 120

d12 15 18 21 24 27

e0 12 24 36 48 60

y

2

1

3

4

5

6

1 2 3 4 5 6 x

D G

C

H

A

F

E

I

B

0

J

Skillsheet5-04

The number plane


447

CHAPTER 13

INTERPRETING GRAPHS AND TABLES

5

The picture graph shows the number of cars passing a school at different times of day.

a

How many cars does each represent?

b

What does represent? Can you see a disadvantage with this symbol?

c

What is the busiest time of day for traffic?

d

What is the quietest time?

e

List each time period and the number of cars at that time.

f

Suggest possible reasons for the flow of traffic at:

i

8:00–10:00am

ii

6:00–8:00am

iii

2:00–4:00pm

6

This column graph shows the populations of the eight Australian capital cities.

a

Which city has the biggest population?

b

Which city has the smallest population?

c

What does one interval on the vertical axis (the ‘Population’ axis) represent?

d

What is the population of Brisbane?

e

Which city has a population of 1.1 million?

f

How many times Hobart’s population is Melbourne’s population?

Key: Each represents 10 cars.

Number of cars passing the school gate

6:00–8:00am

8:00–10:00am

10:00am–12:00noon

12:00noon–2:00pm

2:00–4:00pm

4:00–6:00pm

Capital cities

Pop

ulat

ion

(mill

ions

)

3.0

4.0

2.0

1.0

0Adelaide Brisbane Canberra Darwin Hobart Melbourne Sydney Perth

Population of Australian cities

13 NCM7 2nd ed SB TXT.fm 47 Saturday, June 7, 2008 7:15 PM

448

NEW CENTURY MATHS 7

7

Use this train timetable to answer the following questions.

a

At what time does the 10:48am train from Kiama arrive at Sutherland?

b

Where will the 10:48am train from Kiama be at 12:59pm?

c

Suzi is standing at Wollongong station at 12:30pm. How long does she need to wait for the next train?

d

A train leaves Thirroul at 2:58pm. When will it arrive in Sydney?

e

The times for the 11:32am train from Wollongong are marked as a dash (-) at Sydenham. What does this mean?

f

A train leaves Dapto at 10:39am. How long, in hours and minutes, is its journey to Sydney?

am am pm pm

KIAMA

10:09 10:48 12:01 1:55

DAPTO

10:39 11:15 12:39 2:20

PORT KEMBLA

- 11:20 - 2:25

WOLLONGONG

10:54 11:32 12:54 2:47

THIRROUL

11:05 - 1:05 2:58

WATERFALL

- 12:39 - 3:33

SUTHERLAND

11:50 12:50 1:50 3:43

HURSTVILLE

11:59 12:59 1:59 3:53

SYDENHAM

- - 2:10 4:04

REDFERN

- 1:13 - 4:09

SYDNEY

12:16 1:16 2:16 4:12

Working mathematically

Collecting graphs and tablesDuring the next week, collect graphs and tables from newspapers and magazines. If it is not possible to cut them out, photocopy them.

Communicating


449

CHAPTER 13


13-01 Picture graphs

A

picture graph

(also called a

pictogram

) uses pictures or symbols to illustrate numbers or quantities. The key on a picture graph describes the amount that one picture represents.

1 Australian exports and imports

a

What does represent?

b

Why are the years written as 2001–02, etc. rather than 2001, 2002 and so on?

c

In which year was the value of exports the greatest?

d

What is the value of exports in 2003–04?

e

In which year was the value of exports $12.1 billion?

Australian imports

f

Use the graph and the table to answer the following questions.

i

In which year was the value of imports the lowest?

ii

Draw a picture graph for Australia imports.

iii

In which year was the value of exports almost equal to the value of imports?

iv

What was the difference between the values of exports and imports in 2006–07?

Exercise 13-01

Year $ billion

2001–02 12.0

2002–03 13.3

2003–04 13.1

2004–05 14.9

2005–06 16.8

2006–07 18.1

Australian exports

2001–02

2002–03

2003–04

2004–05

2005–06

2006–07

= $2 000 000 000 (2 billion)


450

NEW CENTURY MATHS 7

2

Draw a picture graph of the information shown in the table on the right.

Use to represent 2 hours.

3

Show the information from the table on the right using a picture graph.

4 a

State two advantages of using a picture graph to illustrate data.

b

State two disadvantages.

13-02 Column graphs and divided bar graphs

A

column graph

(also called a

bar chart

) uses columns to show quantities. Like a number plane it has two axes, usually with categories shown on the horizontal axis (across) and values on the vertical axis (up). If the data is divided into two or more types for comparing (for example male versus female, city versus country), then a

clustered

column graph is used, in which the columns are colour-coded, like the one below.

Name Hours

Mary 7

Jacob 5

Varum 10

Zachary 6

Stephanie 8

Ismail 7

12---

12---

14---

12---

Number of hours spent studying in 1 week

7maths

City or town Population

Bathurst 27 000

Dubbo 31 000

Goulburn 21 000

Griffith 15 000

Nowra–Bomaderry 25 000

Orange 32 000

Port Macquarie 38 000

Singleton 13 000

Population of some NSW cities (to the nearest thousand)

Year1994–95 1998–99 2003–04

60

50

40

10

20

30

0

Per

cent

age

recy

cled

70

Recycling rates for Sydney councils

Ku-ring-gai CouncilBankstown CouncilAll Sydney councils combined


451

CHAPTER 13


The clustered column graph on the previous page shows the recycling rate for some councils for different years. For example, in 1994–95, Ku-ring-gai Council recycled 25% of its waste, Bankstown council 10% and across Sydney, 18% was recycled.A

divided bar graph

is a rectangle sliced into pieces to illustrate the parts of a whole. Sometimes, the pieces are colour-coded and a key explains the meaning of each colour.

The divided bar graph above illustrates the relative proportions of motor vehicle accidents that happen each day of the week. Specifically, it shows that more accidents happen on Friday than on any other day, while Sunday has the fewest accidents. (Can you suggest reasons why this may be so?)

1

With our rubbish tips rapidly filling, councils are running out of space in which to put rubbish. The cost of burying garbage is increasing each year, as shown by the column graph below.

a

How much did it cost (per tonne) to bury garbage:

i

in 2000?

ii

in 2003?

b

In which year was the charge:

i

$18 per tonne?

ii

$70 per tonne?

c

Between which two years was there the greatest increase in charges?

d

Binnsville Council buried 1500 tonnes of garbage in 2003. How much more did it cost to bury the same amount in the year 2005?

e

Use the graph to predict the charge in the year 2008.

Exercise 13-02

Proportion of motor vehicle accidentsSu

nday

Mon

day

Tue

sday

Wed

nesd

ay

Thu

rsda

y

Frid

ay

Satu

rday

Dol

lars

per

tonn

e ($

/t)

2000 2001 2002 2003

70

60

50

40

20

10

0

Landfill charges to bury our garbage

2004 2005 2006

30

Year


452

NEW CENTURY MATHS 7

2

This graph shows the amount and type of waste collected by a council over four financial years.

a

On what date does a new financial year begin?

b

How many tonnes of each type of waste were collected in 2004–05?

c

How many tonnes of recycling waste were collected in 2003–04?

d

Why are there only two columns shown for 2003–04? Suggest a reason.

e

In which year were 30 000 tonnes of garden waste collected?

f

Why has the amount of garbage collected reduced over the years?

3

Sometimes a column graph is presented sideways. The following graph shows the percentage of the population that owned various consumer items in 2008.

a

What percentage of the population owned:

i a television set? ii a mobile phone? iii a DVD player?

b What item was owned by 42% of the population?c Did more people own mobile phones or computers?d What was the percentage difference between people owning a car and people owning

a computer?e How might this column graph be different if it described the ownership of consumer

items this year?

2006–07

Tonn

es c

olle

cted

2003–04 2004–05 2005–06

10 000

0

Amount and type of waste

20 000

30 000

40 000

50 000

60 000

Garbage Recycling Garden waste

L 3156

Leisure survey: popular sports

TLF

Mobile phone

Car

TV

Dishwasher

Computer

DVD player

Percentage of population

Ownership of consumer goods

0 10 20 30 40 50 60 70 80 90 100

Con

sum

er it

ems


453CHAPTER 13 INTERPRETING GRAPHS AND TABLES

4 This graph shows the number of DVDs rented from a video store on a Friday night.

a During which hour were the most DVDs rented and how many were rented at this time?

b How many DVDs were rented between 4:00pm and 5:00pm?c During which hour were 22 DVDs rented?d How many DVDs were rented between 6:00pm and 9:00pm?e When were the least number of DVDs rented? Give a reason why you think this

may be so.

5 The column graph compares the number of people living in Australian householdsin 1986, 1996 and 2006.

a What scale is used on the vertical axis?b What percentage of households were made up of more than two persons in 1996?c In which year were 30% of households made up of two people?d Which category was:

i most common? ii least common?

e Which category had the greatest difference between 1996 and 2006?f ‘There was a higher percentage of one-person households in 1996 than in 1986.’

True or false?

0

Num

ber

Time

DVDs rented

4:00–5:00pm

10

20

30

40

50

5:00–6:00pm 6:00–7:00pm 7:00–8:00pm 8:00–9:00pm

0

Per

cent

age

of h

ouse

hold

s

10

20

30

40

Persons per householdOne Two Three and four Five and over

Number of people in Australian households

198619962006


454 NEW CENTURY MATHS 7

6 This graph shows the net interstate migration for each state of Australia. This is the population change due to people moving between states.

a What was the net interstate migration for Queensland in 2006?b Which state’s population increased by about 3000 in 2005?c What do the negative values on the vertical axis mean?d Which state’s population was reduced by the greatest number of people in both

years?e Approximately how many fewer people left Victoria in 2006 than in 2005?f By how much did South Australia’s population decrease in 2006?g Which state attracts more interstate migrants than any other? Suggest a reason why

this may be so?h Which state showed the smallest change in population? Suggest a reason why this

may be so.

7 In what ways is a column graph better than a picture graph for displaying data?

8 This divided bar graph shows the relative proportions of motor vehicle accidents that happen at various distances from home.

a Where are accidents most likely to occur?b What fraction of accidents happen within 5 km of home?c Altogether, what fraction of accidents happen 15 km or less from home?d What happens as you get farther from home? Suggest a reason why this may be so.e What fraction of accidents happen more than 100 km from home?

f ‘More than of all accidents occur within 25 km of home.’ True or false?

−25 000

Per

sons

Source: Australian Bureau of Statistics

Interstate migration

20052006

−15 000

−10 000

−5000

0

5000

10 000

15 000

25 000

NSW Vic.

Qld

SA

WA Tas.

20 000

−20 000

5 km or less 5–10 km

15–2

5 km

55–1

00 k

m10

0–20

0 km

200

km o

r m

ore

Proportions of accidents at various distances from home

10–1

5 km

25–5

5 km

34---



9 This divided bar graph shows the relative proportions of reasons various councils gave for involving themselves in recycling.

a What is the total length of this bar graph, in millimetres?b What is the most common reason given? What fraction of the graph is this?c What fraction of the graph represents ‘Save natural resources’?d List the reasons in order of popularity (according to the graph).e What are the disadvantages of using a divided bar graph to illustrate this data?

10 There are eight different blood groups. This divided bar graph shows how these are represented within the Australian population.

a Which is the most common blood group in Australia?b Which is the rarest blood group?c What percentage of the population has the A− blood group?d What scale was used in this graph?e ‘O+ and A+ people together make up more than of the Australian population.’

True or false?

11 This table shows the favourite spectator sports of the members of a sporting club.a This information is to be graphed as a divided

bar graph of length 12 cm (120 mm). Copy and complete the following to find the length of each section of the graph.

Australian football = × 12 = cm

Horse racing = × 12 = 2.8 cm = mm

Rugby League = × 12 = cm = mm

Soccer = × 12 = cm = mm

Cricket = × 12 = cm = mm

Other = × 12 = cm = mm

b Illustrate this data on a divided bar graph of length 12 cm.

12 a State one disadvantage of using:i a column graph ii a divided bar graph.

b In what way is a divided bar graph better than a column graph for displaying data?

Meetcommunity

needsDecrease Save Reduce

Othercost naturalresources pollution

Council’s reasons for recycling

B− AB−AB+

Blood groups of Australian population

O+ O− (9%)

A+ A− (7%)

B+(8%)(40%) (31%)

(1%)(2%)(2%)

34---

Favourite sport Number

Australian football 20

Horse racing 14

Rugby League 12

Soccer 8

Cricket 5

Other 1

Favourite spectator sports

2060------

1460------

60------

60------

60------

60------



13-03 Sector graphsA sector graph (also called a pie chart) is a circle divided into ‘pizza slices’ or ‘pie slices’ called sectors to illustrate the parts of a whole. In this way, it is similar to a divided bar graph.

Using technology

Creating graphsUsing a column graph to show the pets students own

1 Survey members of your class. In your own workbook, tally the number of pets under the headings shown on the right.

2 Enter your results into a spreadsheet, as shown on the right

3 Use Chart Wizard to create a column graph. Give the graph an appropriate title and label the axes.

Using a bar chart to show how students get to school1 Survey members of your class. In your own

workbook, tally the mode of transport to school of each student.

2 Enter your results into an Excel spreadsheet, as shown on the right.

3 Use Chart Wizard to create a bar chart (horizontalcolumn graph). Give the graph an appropriate title and label the axes.

L 3161

Healthy life survey: lunchtime activities

TLF

Worksheet13-02

Sector graphs

Example 1

This graph shows the favourite holiday destinations of 70 shoppers surveyed at a Sydney shopping centre.a What is the most popular destination?b What fraction of shoppers prefer Uluru?c If 350 shoppers were surveyed, how many

would you expect to prefer the Gold Coast?

Solutiona Snowy Mountains (largest sector of the graph)

b =

c Number preferring Gold Coast = × 350 = 100

You would expect 100 people to prefer the Gold Coast.

Favourite holiday destinations

Gold Coast(20)

Uluru(15)

SnowyMountains

(23)

KangarooIsland (8)

PhillipIsland (4)

1570------ 3

14------

2070------



1 The sector graph at right shows the types of pizzaspreferred by customers of Poli’s Pizza Parlour.a Which is the most popular pizza?b Which two pizzas are equally popular?c Write the angle size for each sector of the graph.d If Poli made 288 pizzas one night, how many

of them would have been Hawaiian?

2 What is the meaning of ‘sector’? Look it up in the dictionary.

3 This sector graph shows the occupations of workers who are injured at work.

a What is this graph about?b Which group has the most injuries?c Which group has the least injuries?d What percentage of injuries are related to work on the land?e ‘Sheep shearers are more likely to be injured than farmers and farm managers.’

True or false?

4 This graph shows the results of a survey of30 students regarding their favourite pets.a What is the most popular pet in this survey?b What is the least popular pet?c What fraction of students:

i prefer goldfish? ii prefer birds?

d Do cats and guinea pigs together make up more than half of the preferred pets?e Assume the figures from the survey are the same for all students. List the number

of each type of pet you would expect to result if 90 students were surveyed.

Exercise 13-03

Ex 1

Capricciosa

Hawaiian

Marinara

Mexicana

Pizza preferences

Farm hands and assistants

44.6%Sheep shearers

18.7%

Farmers and farmmanagers 13.1%

Trades assistants andfactory hands 7.9%

Other tradespersons 3.3%

Other labourers andrelated workers 2.6%

Truck drivers 1.8%

Other occupations 5.9%

Other plant and machine operators 2.0%

Injured workers

cat (8)

dog (9)

bird (4)guinea pig (6)

Favourite pets

goldfish(3)



5 a In what ways is a sector graph better than a divided bar graph?b List one advantage and one disadvantage of using a sector graph to illustrate data.

6 These graphs show who buys and sells Australian shopping centres.

a Which seller is shown by ?b Which group is the largest buyer? Approximately what fraction of all buyers does this

group represent?c Which group is the second largest seller?d How many groups are there on the sellers’ graph?e Approximately what fraction of buyers are foreign?f Which groups appear on only one of these graphs?

Sellers Buyers

Key

Property company

Foreign

Property trustInstitution/super fund

Other

Mortgagee

Private Australianinvestor

Mental skills 13

Reading linear scalesUnderstanding and reading the scale on a measuring instrument, on a number line oron the axis of a graph is an important mathematical skill.

1 Examine these examples.a Complete the missing values on this scale.

• First, choose two values on the scale, say 100 and 120.• Count the number of intervals (‘spaces’) between the two values. There are four

intervals between 100 and 120.• To find the size of each interval, divide the difference between the two values by

the number of intervals:Difference = 120 − 100 = 20 km

Number of intervals = 4Size of an interval = 20 ÷ 4 = 5 km

• Use the calculated size of an interval to complete the missing values.

b Complete the values on this scale.

• Choose 50 and 60 on the scale.

100 160120 140 km

100 160120 140 km105 110 115 125 130 135 145 150 155

50 8060 70 Years

Maths without calculators



13-04 Line graphsA line graph uses lines instead of columns to show quantities. It has a horizontal axis and a vertical axis. This type of graph is especially useful for showing the differences or changes in a quantity over a period of time. If the data can be divided into two or more types for comparing, then the lines are colour-coded and a key explains the meaning of each colour.

• Number of intervals (between 50 and 60) = 5• Difference (between 50 and 60) = 60 − 50 = 10 years• Size of an interval = 10 ÷ 5 = 2 years.

2 Now copy and complete the following scales.50 8060 70 Years52 54 56 58 62 64 66 68 72 74 76 78 82 84

a

b

c

d

36 56 °C40 44 48 52 60 64

200 mL240 280 320 360

500 g520 540 560 580

160 280200 240 min

200 kg300 400 500 600 700

120 seconds180 240 300 360 420

100 mL300 400 500 600 700200

30 L45 75 90 10560e

f

g

h

Just for the record

The lady with the lampFlorence Nightingale (1820–1910) is famous for her work in nursing and in helping to change the way hospitals are run. She was also a very good statistician. Nightingale was taught at home by her father and showed great interest in mathematics and botany. She worked as a nurse during the Crimean War (1854–1856) and was shocked by the conditions in military hospitals. They were dirty and many soldiers died while in hospitals, because of poor hygiene.Nightingale gathered lots of information in order to convince people that conditions in hospitals must change. She invented pictorial charts and pie charts to conveniently and clearly display the data she had collected. Using statistics, she was able to force governments and doctors to change the practices in hospitals.Nightingale thought that statistics was the most important science in the world.

Find out why Florence Nightingale was called ‘the lady with the lamp’.

Worksheet13-03

Graphs 1

Worksheet13-04

Graphs 2



1 This line graph shows Kate’s height over her first 15 years. At birth she is 48 cm tall, and at age 10 she is about 140 cm tall. Use the graph to answer the following questions.

a What was Kate’s height:i on her first birthday? ii at age 7?

b At what age did Kate reach:i 1 metre? ii 150 cm?

c Between which two birthdays did Kate grow the most? Give a possible reason.d Between which two birthdays did Kate grow the least? Give a possible reason.e How long did it take Kate to double her height from birth?f How long did it take her to triple her height from birth? Compare this to your

answer to the previous question. Why is there a difference?g What do you think the graph will look like:

i after 15 years? ii after 20 years?h How might a graph of a boy’s height differ from this one?

2 These graphs show the percentage of deaths from cancer and heart disease at different ages.

a For males aged 70, what percentage of deaths are due to cancer?b Between what ages do 3% of women die of cancer?c For males aged 50, what percentage of deaths are caused by heart disease?d Generally, according to both graphs, what happens as people get older?e ‘More men die of heart disease than women.’ True or false? Give one reason why.

Exercise 13-04

010

Age (years)1 2 3 4 5 6 7 8 9 11 12 13 14 15

20

40

60

80

100

120

140

160

180

Hei

ght (

cent

imet

res)

Kate’s height

Age (years)

010 20 30 40 50 60 70 80

10

2

4

6

8

Cancer Heart disease

MalesFemales

Per

cent

age

of d

eath

s

MalesFemales

Age (years)10 20 30 40 50 60 70 80

0

15

3

6

9

12

Per

cent

age

of d

eath

s



f At what age does the rate of cancer-related death in men increase?g Between what ages do more women die of cancer than men? Discuss why.

3 The eight graphs below illustrate the mean (average) maximum (orange) and minimum (green) monthly temperatures of the Australian capital cities (Adelaide, Brisbane, Canberra, Darwin, Hobart, Melbourne, Perth and Sydney) over a 12-month period, but they are presented in jumbled order.

a From your knowledge of geography and climate, decide which graph belongs to which city.

b For graph G, list the maximum temperature of each month.c Graph D has two months with exactly the same minimum temperature. Which

months are they?d Find which graphs have one month with a minimum of 10°C. For each graph, state

which month it is.e Which graph has all the maximum temperatures approximately the same?f Which graph has the greatest difference between the highest maximum temperature

and the lowest minimum temperature for one month? What is this difference?

05

10152025

J F M A M J J A S O N D

30°C

05

10152025


30°C

05

10152025


30°C

05

10152025


30°C

05

10152025


30°C

05

10152025


30°C

05

10152025


30°C

05

10152025


30

A B

°C

C D

E F

G H



g Find the highest maximum temperature and state which graph shows it and in which month it occurs.

h Find the lowest minimum temperature and state which graph shows it and in which month it occurs.

4 The table below shows the average monthly UV index (amount of sunlight) for two cities. Display this information on a line graph.

Average monthly UV index

5 Write one advantage and one disadvantage of using a line graph to display data.

6 This line graph shows the temperature for the last 20 days of April.

a On what date was the highest temperature, and what was that temperature?b What was the lowest temperature?c What was the range (the difference between the highest temperature and the lowest

temperature)?d What is the scale shown on the vertical axis?e What was the temperature on 17 April?f On what days was the temperature 22°C?g Which day experienced the biggest drop in temperature?h On how many days was it colder than the day before?

7 a State one way in which a line graph is better than a column graph.b Give an example of when it is more appropriate to use a line graph (than a column

graph).c Give an example of when it is more appropriate to use a column graph.

8 a Survey your class on the number of hours each person slept last night.b In this chapter, you have considered the advantages and disadvantages of different

types of graphs. Decide whether it would be best to show the data from part a as a picture graph, sector graph, column graph or divided bar graph. Justify your answer.

c Draw the graph you have chosen.

Town Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Goulburn 12 11 9 5 3 2 2 4 6 8 10 12

Cairns 15 15 13 10 8 7 7 9 11 13 13 14

Tem

pera

ture

(°C

)

Date in April12

20

15

10

14 16 18 20 22 24 26 28 3010

Temperature in April

25



13-05 Travel graphs and conversion graphsTravel graphs and conversion graphs are special types of line graphs.A travel graph shows the distance travelled during a journey. The time is marked on the horizontal axis, while the distance from home (starting point) is shown on the vertical axis.


Temperature graphsMonitor the maximum temperatures and minimum temperatures in your town or city for 14 days. You can get data from newspapers, TV or the Internet (Bureau of Meteorology: www.bom.gov.au). The task of collecting data can be shared in a group. If your school has a maximum/minimum thermometer, you can collect your own data.1 Plot your temperature graphs in as similar way to the graphs shown in Question 3 of

Exercise 13-04. (You could use an Excel spreadsheet and Chart Wizard, graphing the data that you have collected as an XY scatter graph.)

2 Give your graph a title, label the axes clearly with names and units, and space the numbers evenly. Make the graph large enough to be easily read when hanging on the wall.

3 Write a short paragraph explaining how the temperatures have varied in 14 days.

4 As an extra challenge you could also plot the times of sunrise, sunset, moonrise and moonset (but on separate graphs).

Communicating and reasoning

Worksheet13-05

Currency conversion graph

Example 2

Simon and Joshua travel from Goulburn to Sydney to see a concert, and then return to Goulburn. This is a travel graph of their journey.

5pm11pm

180

140

20

60

100

0

Dis

tanc

e fr

om G

oulb

urn

(km

)

Simon and Joshua’s trip

200

160

120

40

80

6pm 7pm 8pm 9pm10pm

Midnight1am 2am 3am

Time of day



A conversion graph is used to convert from one unit to another, for example miles to kilometres, or Australian dollars to US dollars. It usually contains one straight line that begins at the origin (0, 0).

1 Ilhea and Jo decided to walk from their campsite to the beach. This travel graph shows their distance from camp at different times. They stopped three times during the day, once for lunch and twice for a rest.

Exercise 13-05

a What is the scale on the vertical axis?b What is the scale on the horizontal axis?c How far is Sydney from Goulburn?d How far did Simon and Joshua travel altogether?e How long were they at the concert?f What happened at 12:30am?g How long did the trip take altogether, excluding stops?

Solutiona 1 unit = 10 kmb 1 unit = h or 30 minc 200 kmd Goulburn to Sydney = 200 km Sydney to Goulburn = 200 km Total = 400 km

e From 8pm to 11:30pm = 3 h

f They stopped for 1 h. (The horizontal interval shows this.) g 5pm to 6pm = 1 h 6:30pm to 8pm = 1 h 11:30pm to 12:30am = 1h

1:30am to 2:30am = 1 h Total time = 4 h

12---

12---

12---

12---

Ex 2

Ilhea and Jo’s walk

Dis

tanc

e fr

om c

amp

(km

)

Time of day

2

4

6

8

10

12

14

16

9:00am 10:00am 12:00 noon1:00pm 2:00pm 3:00pm 4:00pm11:00am0



a What is the scale on the vertical axis?b What is the scale on the horizontal axis?c How far from camp is the beach?d At what time did they first stop?e How long did they stay at the beach?f At what time did they start heading back to camp?g How long did the journey back to camp take?h What happened at 2:30pm?i How far did Ilhea and Jo walk that day?

2 Tara rode her bicycle to a friend’s place. Here is a travel graph which describes her trip. Answer the questions after studying the graph.a At what time did Tara

leave home?b How far did she travel

altogether?c When did she take rests?d How long did she rest

altogether?e At what time is Tara

travelling the fastest?How can you tell?

3 This conversion graph is used to convert acres to hectares. The acre is an Imperial measure of land area while the hectare (ha) is the metric measure.

a What is the scale on the horizontal axis?b Use the graph to convert 12 acres to hectares.

Time of day

Dis

tanc

e fr

om h

ome

(km

)

10

11am Noon

20

30

40

1pm 2pm

Converting acres to hectares

Acres

Hec

tare

s

1

20

4 6 8 10 12 14

2

3

4

5

6



c A garden has an area of 5 acres. What is this area in hectares?d Use the graph to convert 4.4 hectares to acres.e Mr Ferguson has a property with an area of 5 hectares. How big is this in acres?f A rectangular playing field measures 250 m by 128 m.

i What is the area of the field in square metres?ii What is the area of the field in hectares? (1 ha = 10 000 m2)

iii What is the area of the field in acres?

4 This graph is used to convert Australian dollars (AUD) to euros (€).

a Change $15 into euros.b Change $50 into euros.c Change $100 into euros.d ‘The scales on the horizontal axis and vertical axis are identical.’ True or false?e Change €50 to AUD.f How many Australian dollars would you receive for €20?g Calculate the number of euros you should get for $120.

5 Copy and complete this travel graph. Make up a story to match the graph.

Conversion of Australian dollars to euros

$Australian (AUD)

Eur

o (€

)

10

100

20 30 40 50 60 70

20

30

40

50

80 90



13-06 Step graphsA step graph is a line graph of ‘broken’ horizontal intervals that look like steps. The step graph below shows the parking charges at a car park. The number of hours parked is shown on the horizontal axis while the cost, in dollars, is shown on the vertical axis.

In a step graph, the ends of each step are indicated with circles, but the part of the step that is to be read is shown by a shaded circle.So the cost of parking for 3 hours is $12 (shaded circle), not $16 (blank circle).

1 Use the parking charges step graph above to answer the following questions.a What is the cost of parking for:

i 2 hours? ii 4 hours? iii 3 hours 5 minutes?

b Explain in your own words the system of parking charges used by this car park.c On the graph, what is the difference between a shaded circle and a blank circle?d What would be the problem if all circles were shaded?e Hans was charged $16 for parking. How long could his car have been parked?f What does the arrow on the step graph after 8 hours mean?

Exercise 13-06

Cos

t ($)

Time (hours)

02468

101214161820

Parking charges

1 2 3 4 5 6 7 8

3

Not this

$12

2

$16

4

value

Thisvalue

Example 3

Use the parking charges step graph shown above to answer the following questions.

a What is the cost of parking for an hour?

b Simon is charged $8 for parking. For how long could his car have been parked?

Solutiona $4b More than 1 hour and up to 2 hours.

12---

Ex 3

12---



2 Vanessa uses this step graph to illustrate how much she charges for baby-sitting.

a How much does Vanessa charge for baby-sitting for:i 1 hours? ii 3 hours? iii 4 hours 15 minutes?

iv 6 hours? v 3 hours 1 minute? vi 2 hours 59 minutes?

b Last Sunday, Vanessa earned $19 from one baby-sitting job. How long could she have worked for?

3 This step graph shows the cost of sending parcels, according to the mass of the parcel.

a What is the scale on the horizontal axis?b What is the cost of sending:

i a 4.5 kg parcel? ii a 2.8 kg parcel? iii a 1 kg parcel?

c Find the cost of sending:i a 200 g parcel ii a 500 g parcel iii an 800 g parcel

d Robert needs to send a 3200 g parcel to his uncle. How much will it cost him?

Baby-sitting charges

Cos

t ($)

Time (hours)

0

4

8

12

16

20

1 2 3 4 5 6 7 8

2

6

10

14

18

22

12---

Cos

t ($)

Mass (kg)

0

2

3

4

5

6

1 2 3 4

7

1

5



e i Toula has to post the following packages: a 1.2 kg box, a 3 kg carton and a 400 g box. Find the total cost of posting these three packages separately.

ii Will Toula save any money if she posts the three packages together? How much will she save or lose if she does?

f Renata posted a parcel for $3.75. What could be the mass of the parcel?

4 This step graph shows the cost per box of blank CDs when they are bought in bulk.

a How much is each box of CDs if you buy five boxes?b How much is each box if you buy:

i 20 boxes? ii 40 boxes? iii 60 boxes?

c What happens to the price of each box of CDs as you purchase more boxes? Why do you think this is so?

d What is the cost per box if you buy 100 boxes?e What is the maximum number of boxes that can be bought for $4 each?f Jeff bought CDs for $5.50 per box. How many boxes of them could he have bought?

Cos

t per

box

($)

Number of boxes

010 30 40

3.50

5020 60

4.00

4.50

5.00

5.50

6.00

Boxes of CDs

70


Investigating graphsAs a group activity, use the graphs you collected at the beginning of this chapter.

1 Paste each graph on an A4 sheet of cardboard.

2 Make up at least five questions for each graph and write them on the cardboard. (Make sure you know the answers!)

3 Swap your work with another group and answer their questions. Ask the student who wrote the questions to mark your answers. Check with your teacher if there are any disagreements.

Questioning and communicating



13-07 Reading tablesA table shows numerical information presented in rows and columns (in a grid). It displays values (numbers) instead of diagrams and pictures.

1 The table below shows the total admissions charged by an aquatic centre for different combinations of adult and child visitors.

a What is the admission charge for:i 2 adults? ii 1 adult and 2 children?

iii 4 children? iv 2 adults and 4 children?b How many adults and children could visit the centre for $12.20?c Work out the cost for:

i 4 adults ii 8 childreniii 3 adults and 5 children iv 6 adults and 9 children.

2 The distance table below can be used to find the road distance, in kilometres, between any two mainland Australian capital cities. This is done by looking at the value where the column for one city crosses the row for the other city. For example, the distance between Canberra and Perth is 3812 km.

Exercise 13-07

Children

0 1 2 3 4

0 $2.70 $5.40 $8.10 $10.80

1 $4.10 $6.80 $9.50 $12.20 $14.90

2 $8.20 $10.90 $13.60 $16.30 $19.00

Worksheet13-06

Distance table

Worksheet13-07

Olympic medals

Ad

ult

s

Adelaide

2131 Brisbane

1210 1295 Canberra

3212 3493 4229 Darwin

745 1736 655 3957 Melbourne

2749 4390 3812 4342 3494 Perth

1431 1027 304 4060 893 3988 Sydney

Darwin

Brisbane

Sydney

Canberra

Hobart

Melbourne

AdelaidePerth



a Use the table to find the distance between:i Adelaide and Melbourne ii Canberra and Sydney

iii Melbourne and Brisbane iv Darwin and Perth.

b Copy and complete: The distance between and is 4390 km.c Which two of the cities are the farthest apart?d Which two of the cities are the closest?e Plan a return trip from Sydney, stopping at two or more other capital cities.

Calculate the total number of kilometres travelled.f Below is a table of air distances, in kilometres. Use it to find the air distance between:

i Adelaide and Melbourne ii Canberra and Sydneyiii Melbourne and Canberra iv Sydney and Adelaide.

g What is the difference between road distance and air distance? Which one is longer?h Between which two of the cities is there the greatest difference between air distance

and road distance?

3 When patients require blood transfusions, it is preferred that they receive a transfusion of the same blood group as their own. However, in an emergency, if the required blood type is not available, the patient may receive blood from another group but only according to this table.

a How many different blood groups are there?b People of which recipient type can receive the B+ blood type?c If Jill’s blood type is B+, what donor type of blood can she receive?d Which donor type can be given to anyone?e People with which recipient type can receive all donor types?f People with which recipient type can only receive their donor type (and not others)? g Find out which blood type you are and which blood group(s) you can receive.

Adelaide

987 Canberra

655 489 Melbourne

1202 238 716 Sydney

Donor type

0− 0+ B− B+ A− A+ AB− AB+

Rec

ipie

nt

typ

e

AB+ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

AB− ✓ ✓ ✓ ✓

A+ ✓ ✓ ✓ ✓

A− ✓ ✓

B+ ✓ ✓ ✓ ✓

B− ✓ ✓

0+ ✓ ✓

0− ✓



4 The table below shows a timetable for Thomson Airways’ flights to and from London airport. Note that not all flights operate every day. The days of operation are listed in the ‘Days’ columns: 1 = Monday, 2 = Tuesday, 3 = Wednesday, etc.a What is the flight number of the

plane that leaves London at 1500 hours bound for Amsterdam?

b When will the plane in part a arrive in Amsterdam?

c On which days of the week does flight TH5603 from Aberdeen to London operate?

d How long is the flight at 1740 hours from Aberdeen to London?

e What is the flight number of the plane that leaves London for Amsterdam at 7:00pm?

f On what day of the week does this flight not operate?g On which days can you fly from London to Adelaide?h On which days can you fly from Adelaide to London?

i Emilia wishes to fly from Amsterdam to London on a Saturday. What is the flight number of the latest flight she can take?

j The TH411 flight departs Amsterdam at 1500 hours and arrives in London at 1500 hours. How is this possible?

From London to: To London from:

Dep. Arriv. Days Flight No. Dep. Arriv. Days Flight No.

ABERDEEN 0720 0840 12345 TH5604 ABERDEEN 0700 0830 12345 TH5601

0915 1040 Daily TH5608 0800 0925 67 TH5603

1130 1255 12345 TH5610 0935 1100 12345 TH5605

1305 1430 Daily TH5612 1126 1250 Daily TH5609

1525 1650 Daily TH5614 1400 1525 12345 TH5611

1746 1905 12345 7 TH5618 1515 1640 Daily TH5613

2000 2120 Daily TH5620 1740 1905 Daily TH5615

2000 2125 12345 7 TH5619

ADELAIDE 2030 0925 6 TH011 ADELAIDE 1300 0555 1 TH012

2130 0610 1 TH011 1300 0640 5 TH010

2130 1030 3 TH009 1645 0555 3 TH012

AMSTERDAM 0800 1000 123456 TH406 AMSTERDAM 0900 0900 123456 TH401

1000 1200 12345 7 TH408 1100 1100 Daily TH407

1200 1400 123456 TH410 1300 1300 12345 7 TH409

1500 1700 Daily TH414 1500 1500 123456 TH411

1630 1830 Daily TH416 1800 1800 Daily TH415

1900 2100 12345 7 TH418 1930 1930 12345 7 TH417

L 764

Journey planner: quickest route 1

TLF



5 Use this pizza menu to answer the following questions.

a What is the cost of:i a family-sized Vegetarian pizza? ii a medium Marinara pizza?

b Which are the two most expensive pizza toppings?c What is the delivery fee?d Luke phones and orders a large Capricciosa, a small Hawaiian and one serve of garlic

bread to be delivered. What is the total cost?e If Cindy has only $9 to spend, how many different pizzas are available for her to

choose from?

PIZZA

Small Medium Large Family1. Supreme $8.50 $9.50 $11.50 $15.502. Margherita $7.90 $8.90 $10.90 $14.903. Capricciosa $7.90 $8.90 $10.90 $14.904. Vegetarian $7.90 $8.90 $10.90 $14.905. American $7.90 $8.90 $10.90 $14.906. Marinara $8.50 $9.50 $11.50 $15.507. Hawaiian $7.90 $8.90 $10.90 $14.908. Mexicana $7.90 $8.90 $10.90 $14.90Extras $0.40 $0.60 $0.80 $1.00

Garlic Bread $2.20 Herb Bread $2.20

Delivery fee $2.50

Power plus

1

a Which country received the most Australian exports overall?b How much were Australia’s exports to Mexico in 2004–05?c During which financial year did exports to Vietnam start to rise?d By how much did exports to Iraq decrease between 2001–02 and 2005–06?e During which financial year did exports to Vietnam show the biggest decrease?f When did exports to Mexico first rise above exports to Iraq?g What happened to the level of exports to Mexico between 2003–04 and 2004–05?h Exports to which country were similar between 2004–05 and 2005–06?

Australia’s exports of goods, by country

Dol

lars

($ m

illio

n)

0

200

400

600

1000

Year2001–02 2002–03 2003–04 2004–05 2005–06

IraqMexicoSpainVietnam

800



2

a Overall, which of the three categories showed the most construction activity?b How much was spent on:

i residential construction in 2003–04?ii engineering projects during 2005–06?

iii non-residential construction from 2002–03 to 2005–06?c Find the total amount spent on construction in 2005–06.d Over time, has the amount of construction generally increased or decreased?

3 Here is an incomplete distance grid for the distances along the Hume Highway, from Sydney to Melbourne.

a How many kilometres is it from Liverpool to Sydney?

b How far is it from Sydney to Albury?c Find the distance from Albury to Yass.d Copy the distance grid into your book,

and use the table shown on the right to help you complete the whole grid from Sydney to Melbourne.

SydneyLiverpool 39

Goulburn 150 189Yass 83 233 272

Gundagai 100 175 325 364Holbrook 114 214 289 439 478

Albury 65 179 279 354 504 543Wangaratta

BenallaEuroa

SeymourMelbourne

Construction activity

Types of constructionResidential

50

2002–032003–042004–052005–06

45

40

35

30

25

20

15

10

5

0Non-residential Engineering

Dol

lars

($ b

illio

n)

Places Distance (km)

Albury to Wangaratta 72

Wangaratta to Benalla 41

Benalla to Euroa 48

Euroa to Seymour 53

Seymour to Melbourne 100



Chapter 13 review

Language of mathsaxis/axes column graph conversion graph datadivided bar graph graph horizontal axis keyline graph picture graph pie chart scalesector sector graph step graph symboltable timetable travel graph vertical axis

1 What is the more formal name for a pie chart?

2 What is the name given to what one unit or interval represents on an axis of a graph?

3 What is usually shown on a travel graph’s:a horizontal axis? b vertical axis?

4 In what way are sector graphs and divided bar graphs similar to one another?

5 What does ‘conversion’ mean? Find two non-mathematical meanings.

Topic overview• Write in your own words what you have learnt in this chapter.• Was this work new to you? If not, in what subject have you studied it?• Did you have any difficulties? Discuss them with a friend or your teacher.• Give some further examples of where graphs and tables are used.Copy this summary into your workbook and complete it. Check your overview with your teacher.

Worksheet13-08

Graphs crossword

InterpretingGRAPHS

AND TABLES

Tables

C_________ L _________

S _____

T _________

C _________

S_______

D________b_____

P_________



Chapter revisionThe information in Questions 1 to 4 comes from the 2006 census.

1

a What age group has the smallest percentage of the population?b What percentage are in the 15–24 years age group?c Why might the 25–54 years group be the largest?

2

a What percentage of the population is Catholic?b Which religions are followed by 19% of the population?c How might this graph have been different in 1950?

3

a What does UK stand for?b What fraction of the population was born in Australia?c In a town of 25 000 people, how many would you

expect to have been born in the UK?

4 The sector graph shows data about connectionto the Internet.a Which is the largest category?b What fraction of the population is not

connected to the internet?c In a city of 3.5 million people, how many

would you expect to use dial-up connection?

Exercise 13-01 Age of Australia’s population0–4 years

5–14 years

15–24 years

25–54 years

55–64 years

65+ years = 3% of population

Source: Australian Bureau of Statistics

Exercise 13-02 Religion of Australia’s population

Per

cent

age

0

5

1015

30

Religion

Catholic Anglican Other No religion Buddhist

20

Christian

25

Muslim Other

Exercise 13-02 Country of birth of Australia’s population

Australia UK Other

Exercise 13-03

Internet connectionfor Australia’s population

Broadband

Dial-upNot

(41%)

(22%)connected

(37%)

Topic test 13



5 The graph below shows temperature data for Dubbo.a Which month(s) has the

highest mean minimum temperature? What is that temperature?

b Name two months withthe same mean minimum temperature.

c What month has a mean minimum temperature of 10°C?

d Between which two months is the smallest drop in mean minimum temperature?

6 Keith cycled from Wollongong to Sydney. This is a graph of his trip.a How far is it from Wollongong

to Sydney?b What is the scale on the

vertical axis?c Keith’s bike had a puncture. At

what time did this occur?d How long did the trip take,

excluding the stop?e How far did Keith have left to

ride after his puncture?

7 The step graph on the right shows the charges made by an auto mechanic for his services.a What is the scale on the vertical axis?b What is the cost of:

i 2 hours work? ii 6 hours work?

iii 3 hours work?

c What is the cost per hour for 6 hours work?d Megan pays the mechanic $180. How long

might the mechanic have worked on her car?

8 The following table shows the cost per day of car hire.

a What is the cost per day of hiring a medium car for 12 days?b What is the total cost of hiring a medium car for 12 days?c What is the cost per day of hiring a small car for 30 days?d What is the total cost of hiring a small car for 30 days?e How much is saved by hiring a medium car for 20 days instead of a large car?

Type of car 1–3 days hire 4–14 days hire 15–28 days hire 29+ days hire

Small car $45 $43 $41 $39

Medium car $50 $47 $44 $41

Large car $55 $51 $47 $43

Exercise 13-04

Mean monthly minimum temperatures for Dubbo

Tem

pera

ture

(°C

)

0

5

10

15

MonthJan Feb Mar Apr May

20

Jun Jul Aug Sep Oct Nov Dec

Exercise 13-05

Dis

tanc

e fr

om W

ollo

ngon

g (k

m)

0

10

20

30

40

50

60

70

80

9am 10am 11am Noon 1pm 2pm 3pmTime of day

Dol

lars

($)

0

60

120

180

240

300

1 2 3 4 5 6 7Hours

Exercise 13-06

12---

Exercise 13-07



Mixed revision 41 Change these to improper fractions.

a 1 b 3 c 2 d 7

2 Change these to mixed numerals.

a b c d

3 a Find the HCF of 18 and 30.b Find the LCM of 4 and 5

4 Write three equivalent fractions for each of these.

a b c

5 Simplify these fractions.

a b c d

6 Use < or > to make each of these statements true.

a b c

7 Find:

a + b + c − d 2 +

e 3 − 1 f + g 1 − h +

8 Find:

a of $18 b of 2 m c of 12

9 Find:

a × b × c 3 × 2 d 1 ×

10 Find:

a ÷ b ÷ 5 c 2 ÷ d 4 ÷ 1

11 Convert these fractions to percentages.

a b c d 2

12 Convert these decimals to percentages.

a 0.4 b 0.05 c 1.2 d 2.03

13 a Find the value of:i 5% of $200 ii 60% of 1200

iii 10% of 1 hour iv 4% of 2 tonnes

b Chloe owns 20 pairs of shoes. Of these, 5% are black. How many black pairs of shoes does Chloe own?

Exercise 10-0112--- 3

4--- 1

8--- 3

10------

Exercise 10-01

125

------ 72--- 5

3--- 11

6------

Exercise 10-02

Exercise 10-03

12--- 1

5--- 3

8---

Exercise 10-04

810------ 12

18------ 15

24------ 70

100---------

Exercise 10-05

13--- 1

4--- 2

5--- 5

10------ 5

7--- 3

5---

Exercise 10-06

Exercise 10-0712--- 1

3--- 1

3--- 2

5--- 1

2--- 3

8--- 1

2--- 3

5---

45--- 2

3--- 3

5--- 1

2--- 2

7--- 7

12------ 3

4--- 1

2---

Exercise 10-08

23--- 1

4--- 2

5---

Exercise 10-09

35--- 1

2--- 2

3--- 7

12------ 1

3--- 1

2--- 1

4--- 4

5---

Exercise 10-10

34--- 1

2--- 2

10------ 1

2--- 3

5--- 1

2--- 1

5---

Exercise 10-11

14--- 3

5--- 1

9--- 1

6---

Exercise 10-12

Exercise 10-14


479MIXED REVISION 4

14 Copy and complete the following.

a 2000 mg = g b 2 t = kg

c 56 days = weeks d 6.5 L = mL

e 3 days = hours f 4 kg = g

g 1500 g = kg h 3000 mL = L

i 480 s = min j 2500 kg = t

k 9.5 g = mg l 12 000 000 mg = kg

15 Find the volume of each of these prisms.

16 Round 3 h 41 min 12 s to the nearest hour.

17 Convert 445 minutes to hours and minutes.

18 How long (in hours and minutes) is it from:a 4:30am to 9:55am? b 7:15pm to 8:25pm?c 9:24pm to 9:05am? d 1505 hours to 2210 hours?

19 At 2:00pm in Greenwich (England), what time is it in:a Sydney? (GMT + 10 h) b Moscow? (GMT + 3 h)c Honolulu? (GMT − 8 h)

20 Complete each table of values for the given rule.a y = x − 2 b p = 2y + 1

21 Write algebraic expressions for:a the sum of w and 8 b k minus 9c the product of 5 and g d half of me the difference between p and 7 f the number after t

22 Select the like terms from:

2a, 4b, a2, 6ab, a, 10a

x −1 0 1 5 y 0 2 4 6

y p

Exercise 11-01

Exercise 11-03

Exercise 11-04

Exercise 11-02

44 mm18 mm

15 mm

11 cm

6 cm

5 cm

5 m

3 m

3 m

a b c

Exercise 11-06

Exercise 11-06

Exercise 11-07

Exercise 11-08

Exercise 12-01

Exercise 12-02

Exercise 12-04



23 Simplify each of the following.a 3p + 7p b 6q − qc 2a + 3b + 4a + 7b d 12x + 5y − 2x − 2ye 9k + 7 + 3k + 12 f 7a × 9cg 3p × 3p h 12m × 3i 9a × 3a j 20 × 4m

24 Expand each of the following.a 2(x + 4) b 7(k − 2) c m(m + 4)

25 Expand and simplify each of the following.a 4(g − 2) + 12 b 6(y + 4) + 3(y − 2) c 5(p + 1) − 2(2p − 8)

26 If k = 4, find the value of:a 3k + 2 b 48 ÷ k c (k + 1) × (k − 1) d 24 − 2k

27 If x = 3 and y = −4, find the value of:a x + y b xy c 6x + 3y d y2

28 Copy and complete the table.

29 Find out how many children there are in the family of each student in your class. Present this information as:a a column graph b a divided bar graph

30 a Draw a conversion graph for converting Australian dollars (AUD) to US dollars(USD), given that 100 Australian dollars equals 93 US dollars.

b Use your graph to convert:i $35 Australian to USD ii 10 US dollars to AUD

y y + 4 3y 8 − y

0

1

3

7

Exercise 12-05

Exercise 12-06

Exercise 12-07

Exercise 12-08

Exercise 12-09

Exercise 12-09

Exercise 12-09

Exercise 13-02

Exercise 13-05


13 NCM7 2nd ed SB TXTweb2.hunterspt-h.schools.nsw.edu.au/studentshared... · 2008-07-21 ·...

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