Topics
7. Graphs
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AustraliaAU
Year 11

7.015 Step graphs

Lesson
Worksheet
Practice
Worksheet
Step graphs
1

The graph shows the cost of sending parcels of various weights overseas:

a

Find the cost of sending a letter weighing:

i

100 \text{ g}

ii

300 \text{ g}

iii

125 \text{ g}

b

Find the heaviest letter that can be sent for \$2.

c

Find the heaviest letter that can be sent for \$4.

d

Write an inequality for the range of letter weights that can be sent for \$4.

50
100
150
200
250
300
350
\text{Weight (g)}
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
\text{Cost } (\$)
2

The graph shows the parking costs over different lengths of time:

a

Find the cost of 5 hours of parking.

b

Find the cost of 6 hours of parking.

c

Calculate the total cost of 6 hours of parking each day for 5 days.

d

The carpark offers a weekly pass for \$44. If Aaron parks his car for 6 hours each day, five days a week, how much does he save each week with the weekly pass?

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\text{time (hours)}
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13
\text{Cost } (\$)
3

The graph shows the amount (in dollars) an internet cafe charges its customers:

a

How much does a customer have to pay if they use the internet service for 2 hours and 40 minutes?

b

How much does a customer have to pay if they use the internet service for 4 hours?

c

Find the maximum number of hours that a customer can purchase for \$15.

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9
\text{Hours}
3
6
9
12
15
\text{Cost}
4

The graph shows the starting times of a shot put event for participants of different age groups:

a

Determine the time a participant who is aged 7 will start their event.

b

Determine the time a participant who is aged 13 will start their event.

c

Determine the time a participant who is aged 16 will start their event.

d

Do any of the events start at half past the hour?

7
9
11
13
15
17
\text{Age (years)}
4
5
6
7
8
\text{Time (pm) }
5

The graph shows the total cost of parking (in dollars) as a function of the number of hours parked:

a

Find the maximum number of hours you can park for free.

b

Janet goes to a movie and parks for 2.5 hours. How much will it cost her?

c

Connor works at the cinemas and parks for his entire 4.5 hour shift. How much will it cost him in parking?

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6
\text{Hours}
1
2
3
4
5
6
\text{Cost }(\$)
6

The graph shows the amount (in dollars) a lawyer charges for consultations:

a

How much does the lawyer charge for a 3 hour consultation?

b

How much does the lawyer charge for a 5.5 hour consultation?

c

How much does the lawyer charge for a 4 hour consultation?

d

Determine the shortest possible consultation time for which the lawyer will charge \$800.

1
2
3
4
5
6
7
\text{Hours}
400
800
1200
1600
2000
2400
\text{Cost}
7

The graph shows the cost per t-shirt (in dollars) when purchasing in bulk:

a

Find the cost per t-shirt when 45 t-shirts are bought in bulk.

b

Find the cost per t-shirt when 55 t-shirts are bought in bulk.

c

Find the maximum number of t-shirts that can be purchased at \$7.00 each.

5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
\text{T-shirts}
1
2
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10
\text{Cost}
8

The graph shows the cost (in dollars) of a mobile phone call as a function of the length of the call:

a

Find the cost of a 4 minute and 5 second call.

b

Find the cost of a 3 minute call.

c

Find the longest possible call that could be made for \$1.50.

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7
\text{Minutes}
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
\text{Cost}
9

The step graph shows the cost (in dollars) for postage of packages based on their weight:

a

Find how much it will cost to post a package that weighs:

i

1.7\text{ kg}

ii

2.5\text{ kg}

iii

0.5\text{ kg}

iv

3.2\text{ kg}

b

If Neil has \$11, what range of package weights that he can afford to send?

c

What range of package weights can be sent for:

i
\$6
ii
\$7
iii
\$5.50
iv
\$14
0.5\text{kg}
1\text{kg}
1.5\text{kg}
2\text{kg}
2.5\text{kg}
3\text{kg}
3.5\text{kg}
4\text{kg}
\text{Weight}
1
2
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5
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14
\text{Cost }
10

The cost of a train ticket, based on distance travelled, is indicated by the step graph:

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48
\text{distance (km)}
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
\text{Cost } (\$)
a

If Valentina needs to travel a distance of 11\text{ km}, how much does her train ticket cost?

b

Luke has a doctor's appointment 19\text{ km} away. Calculate the cost of a one way ticket.

c

Hence, calculate the cost of Luke's round-trip ticket.

d

Sally needs to travel 4\text{ km} to get to the grocery store. Calculate the cost of a one way ticket.

11

Maria commutes approximately 40\text{ km} each direction every weekday to work. The cost of a train ticket, based on distance travelled, is indicated by the step graph:

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48
\text{distance (km)}
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
\text{Cost } (\$)
a

How much does her one way ticket cost?

b

How much does her daily round-trip ticket cost?

c

Hence, how much is the ticket cost for the five days of travel?

12

The step graph shows the charges for a home phone plan:

a

How much will a 3 minute phone call cost?

b

How much will a phone call longer than 1 minute but less than 2 minutes cost?

c

Calculate the cost of 4 phone calls, each longer than 1 minute but less than 2 minutes.

1
2
3
4
5
6
\text{Time (min)}
0.5
1
1.5
2
2.5
3
\text{Cost } (\$)
13

The step graph shows the charges for a home phone plan. Hamish made 12 calls that were just under 2 minutes each, 13 calls just under 4 minutes each, and 5 calls of less than 1 minute each.

a

How much will each of the following phone calls cost?

i

A call just under 2 minutes long.

ii

A call just under 4 minutes long.

iii

A call just under 1 minute long.

b

How much will each of the following cost?

i

12 calls just under 2 minutes each.

ii

13 calls just under 4 minutes each.

iii

5 calls less than 1 minute each.

c

Hence, calculate the total cost for the calls Hamish made.

1
2
3
4
5
6
\text{Time (min)}
0.5
1
1.5
2
2.5
3
\text{Cost } (\$)
14

A telephone call is charged at \$0.70 for a call length of less than 1 minute, and \$0.20 extra per minute after that. Create a step graph that shows the cost of calls up to 5 minutes in length.

15

The cost of a train fare is calculated at \$1.30 for the first zone and then 20 cents per additional zone after that. Create a step graph that shows the fares for trips up to five zones.

16

Hiring helium tanks for balloons at a party costs \$20 up to and including the first hour, and \$5 per extra hour or any part thereof.

Create a step graph displaying the total cost of hiring helium tanks for up to five hours.

17

A plumber charges a call-out fee of \$20 to come out to the site and on top of that, charges \$10 per 15 minute block on site or part thereof. Create a step graph that matches this scenario.

18

Consider the following table and create a step graph for the charge for sending parcels:

\text{Express Post satchels (mm)}\text{Maximum weight (g)}\text{Charge per item}
\text{Small } (220\times 355)500\$2.50
\text{Medium } (310\times 405)3000\$4.25
\text{Large } (435\times 510)5000\$7.75
19

A hotel charges the following rates for hiring out their function room:

  • \$160 per hour for up to 2 hours inclusive.

  • \$120 per hour for more than 2 hours and up to 5 hours inclusive.

  • \$80 per hour for more than 5 hours and up to 10 hours inclusive.

Create a step graph that shows the amount charged per hour for the length of time the function room is booked.

20

At an indoor ski facility, the temperature is set to - 5 \degree \text{C} at 2 pm. At 3 pm, the temperature is immediately brought down to - 12 \degree \text{C} and left for 3 hours before immediately taking it down again to - 18 \degree \text{C}, where it stays for the rest of the day’s operation. The facility operates until 10 pm.

a

Complete the stepwise function that models the indoor temperature, y, at a certain time of the day, x hours after midday:

y = \begin{cases} -5\degree \text{C}, & ⬚ \leq x \lt 3 \\ ⬚\degree \text{C}, & 3 \leq x \lt 6 \\ ⬚\degree \text{C}, & 6 \leq x \leq ⬚ \end{cases}
b

Create a graph of the step function.

c

Lakota entered the ski facility at 3:30 pm. What was the temperature inside the facility at this time?

d

Xavier wants to wait till the indoor temperature is - 7 \degree \text{C} or lower. When is the earliest he can enter the facility?

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Outcomes

ACMEM037

interpret information presented in graphs, such as conversion graphs, line graphs, step graphs, column graphs and picture graphs

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