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v1 Algebra, STD2 A4 2020 HSC 24

There are two tanks at an industrial plant, Tank A and Tank B. Initially, Tank A holds 2520 litres of liquid fertiliser and Tank B is empty.

  1. Tank A begins to empty liquid fertiliser into a transport vehicle at a constant rate of 40 litres per minute.

     

    The volume of liquid fertiliser in Tank A is modelled by    where is the volume in litres and  is the time in minutes from when the tank begins to drain the fertiliser.

     

    On the grid below, draw the graph of this model and label it as Tank A.   (1 mark)
     

     

  2. Tank B remains empty until    when liquid fertiliser is added to it at a constant rate of 60 litres per minute.
     By drawing a line on the grid (above), or otherwise, find the value of    when the two tanks contain the same volume of liquid fertiliser.  (2 marks)

  3. Using the graphs drawn, or otherwise, find the value of    (where  ) when the total volume of liquid fertiliser in the two tanks is 1400 litres.  (1 mark)

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c.  


  

♦♦ Mean mark part (c) 22%.

v1 Algebra, STD2 A4 EQ-Bank 8

Two farmers, River and Jacqueline, sold organic honey at the the local market.

River sold his 500 gram jars of honey for $8 each and Jacqueline sold her 200 gram jars of honey for $4 each. In the first hour, their total combined sales were $40.

If River sold jars of honey and Jacqueline sold jars of honey, then the following equation can be formed:

In the first hour, the friends sold a total of 6 jars of honey between them.

Find the number of jars of honey each of the friends sold during this time by forming a second equation and solving the simultaneous equations graphically.  (5 marks)

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v1 Algebra, STD2 A4 2023 HSC 21

Electricity provider charges 30 cents per kilowatt hour (kWh) for electricity, plus a fixed monthly charge of $90.

  1. Complete the table showing Provider 's monthly charges for different levels of electricity usage.   (1 mark)


Provider charges 52.5 cents per kWh, with no fixed monthly charge. The graph shows how Provider 's charges vary with the amount of electricity used in a month.
 

 
  1. On the grid above, graph Provider 's charges from the table in part (a).   (1 mark)
  2. Use the two graphs to determine the number of kilowatt hours per month for which Provider and Provider charge the same amount.   (1 mark)

  3. A customer uses an average of 600 kWh per month.
  4. Which provider, or , would be the cheaper option and by how much?   (2 marks)

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b.    
         

c.   

d.   

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a.   

b. 
          
 

c.   


 

d.