MathsFreePrintable

Linear Financial Modelling

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Linear Financial Modelling

Use Australian dollars. Show working for calculations and include units where appropriate.

Build and read linear cost models

1.A school radio station pays a $32 monthly platform fee and $1.80 for each hour of archived audio storage. Let h be the hours stored and C the monthly cost in dollars. Which rule models the cost?

C = 32h + 1.80
C = 32 + 1.80h
C = 33.80h
C = 1.80h − 32

2.For the model C = 18 + 4.50p, where p is the number of promotional posters printed, what does 18 represent?

The cost of printing each poster
A fixed charge that does not depend on the number of posters
The total number of posters
The maximum possible cost

3.Which statement describes how the rate of change behaves in a linear financial model?

It has a constant rate of change.
Its graph is a straight line.
It must have a non-zero fixed cost.
It must pass through the origin.

4.Harper's radio station orders soundproofing panels. The supplier charges a $120 delivery fee plus $28 per panel. If the invoice is $596, how many panels were ordered?

Construct and use financial models

5.Charlie is planning a run of radio-station merchandise. The monthly stall fee is $240, and each item costs $9 to produce. Each item sells for $24. Write a cost rule C and a revenue rule R for n items, then find the number of items needed to break even.

6.A radio-station streaming service charges a one-off activation fee of $54 and then $26 per month. Complete the cost row for the listed number of months.

Months (m)

Total cost ($)

7.In the streaming-service model C = 54 + 26m, what does the slope of 26 mean in this context?

Evaluate assumptions and apply models

8.A courier charges $6.20 for the first kilometre and $1.75 for each kilometre after that. The model is C = 6.20 + 1.75(k − 1), where k is the total distance in kilometres. Calculate the charge for a 9 km delivery.

9.Name two assumptions in the courier model that may not match actual pricing in every situation.

10.A student radio station is deciding whether to budget for a series of broadcasts. Explain one reason a linear cost model can help with planning, and one reason its predictions may differ from the final bill.

11.A radio station hires recording equipment for a fixed $85 booking fee plus $42 per recording session. Write a linear rule for the total cost T dollars for s sessions. Identify the fixed cost and the variable cost per session.