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Algebra, STD1 A3 2024 HSC 23

Carrie is organising a fundraiser.

The cost of hiring the venue and the band is $2500. The cost of providing meals is $50 per person.

  1. Complete the table of values to show the total cost of the fundraiser.   (1 mark)

  1. Carrie decides that tickets should be sold at $70 per person. The graph shows the expected revenue at this ticket price. Using the information in part (a), plot the line that shows the cost of the fundraiser.   (2 marks)

     

  1. How many tickets need to be sold for the fundraiser to break even?   (1 mark)

  2. Carrie sold 300 tickets. How much profit did the fundraiser make?   (3 marks)

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a.   

b.


c.    

d.   

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a.   

b.


c.   


 

Mean mark (c) 53%.

d.   

 
 
 
♦ Mean mark (d) 46%.

Algebra, STD1 A3 2022 HSC 25

Sam is making cupcakes to sell at a market. It costs Sam $60 to hire a stall, and each cupcake costs $1.50 to make. Sam intends to sell each cupcake for $4.00.

The equations representing Sam's cost and revenue , are

  and  , where is the number of cupcakes sold.

The graphs of and are shown below.
 


 

  1. How many cupcakes must Sam sell in order to break even?  (1 mark)

  2. If Sam sells 60 cupcakes, what profit is made?
  3. You may assume that  Profit = Revenue – Cost.  (2 marks)

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  1. 24
  2. $90
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a.   Break even occurs where the two graphs intersect.

→ 24 cupcakes
 

b.   If cupcakes sold () = 60:


  

Algebra, STD1 A3 2019 HSC 30

A small business makes and sells bird houses.

Technology was used to draw straight-line graphs to represent the cost of making the bird houses and the revenue from selling bird houses . The -axis displays the number of bird houses and the -axis displays the cost/revenue in dollars.
 


 

  1. How many bird houses need to sold to break even?  (1 mark)

  2. By first forming equations for cost and revenue , determine how many bird houses need to be sold to earn a profit of $1900.  (3 marks)

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a.   

 

b.   

♦ Mean mark part (b) 47%.


 


 

Algebra, STD2 A4 2018 HSC 27d

The graph displays the cost () charged by two companies for the hire of a minibus for hours.
 


  

Both companies charge $360 for the hire of a minibus for 3 hours.

  1. What is the hourly rate charged by Company A?  (1 mark)

  2. Company B charges an initial booking fee of $75.

     

    Write a formula, in the form of  , for the cost of hiring a minibus from Company B for hours.  (2 marks)

  3. A minibus is hired for 5 hours from Company B.

     

    Calculate how much cheaper this is than hiring from Company A.  (2 marks)

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Show Worked Solution
i.   
   

 

ii.   

 

 

iii.   
 

 

Algebra, STD2 A4 SM-Bank 4

Penny is a baker and makes meat pies every day.

The cost of making pies, ,  can be calculated using the equation

Penny sells the pies for $5.75 each, and her income is calculated using the equation

  1. On the graph, draw the graphs of    and  .  (2 marks)

  2. On the graph, label the breakeven point and the loss zone.  (2 marks)

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(i) and (ii)

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i.   

 

ii. 

Algebra, STD2 A4 2005 HSC 28b

Sue and Mikey are planning a fund-raising dance. They can hire a hall for $400 and a band for $300. Refreshments will cost them $12 per person.

  1. Write a formula for the cost ($C) of running the dance for people. (1 mark)

The graph shows planned income and costs when the ticket price is $20 

2005 28b

  1. Estimate the minimum number of people needed at the dance to cover the costs.  (1 mark)

  2. How much profit will be made if 150 people attend the dance? (1 mark)

Sue and Mikey plan to sell 200 tickets. They want to make a profit of $1500.

  1. What should be the price of a ticket, assuming all 200 tickets will be sold?  (3 marks)

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Show Worked Solution
i.   
   

 

ii. 

 

iii. 

 
 

 

 

 

iv.  

 

 


 

 

Algebra, STD2 A4 2011 HSC 20 MC

A function centre hosts events for up to 500 people. The cost , in dollars, for the centre
to host an event, where people attend, is given by:

The centre charges $100 per person. Its income , in dollars, is given by:


 

2UG 2011 20

How much greater is the income of the function centre when 500 people attend an event, than its income at the breakeven point?

  1.  
  3.  
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Show Worked Solution
♦ Mean mark 50%
COMMENT: Students can read the income levels directly off the graph to save time and then check with the equations given.

 

 

Algebra, STD2 A4 2010 HSC 24b

Ashley makes picture frames as part of her business. To calculate the cost,  , in dollars, of making    frames, she uses the equation  .

She sells the frames for $20 each and determines her income,  , in dollars, using the equation  .
 

Use the graph to solve the two equations simultaneously for    and explain the significance of this solution for Ashley's business.   (2 marks)

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Show Worked Solution

♦ Mean mark 36%.
MARKER’S COMMENT: The intersection on the graph is the same point at which the two simultaneous equations are solved for the given value of .