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EXAMCOPY Algebra, STD2 A4 2014 HSC 29a

The cost of hiring an open space for a music festival is  $120 000. The cost will be shared equally by the people attending the festival, so that    (in dollars) is the cost per person when    people attend the festival.

  1. Complete the table below by filling in the THREE missing values.   (1 mark)
  2. Using the values from the table, draw the graph showing the relationship between    and  .   (2 marks)
     
  3. What equation represents the relationship between and ?   (1 mark)

  4. Give ONE limitation of this equation in relation to this context.   (1 mark)

  5. Is it possible for the cost per person to be $94? Support your answer with appropriate calculations.   (1 mark)

Show Answers Only

i.   


 

ii. 

iii.   


 

iv.  

 

 
 

v.   

 

 

Show Worked Solution

i.   


 

ii. 

 

♦ Mean mark (iii) 48%

iii.   

 

♦♦♦ Mean mark (iv) 7%
COMMENT: When asked for limitations of an equation, look carefully at potential restrictions with respect to both the domain and range.

iv.  

 

 

 

v.   

 
♦ Mean mark (v) 38%

 

EXAMCOPY Algebra, STD2 A4 2022 HSC 24

A student believes that the time it takes for an ice cube to melt ( minutes) varies inversely with the room temperature . The student observes that at a room temperature of it takes 12 minutes for an ice cube to melt.

  1. Find the equation relating and .   (2 marks)

  2. By first completing this table of values, graph the relationship between temperature and time from to    (2 marks)

 
           

Show Answers Only
a.   
 
 
 
   

 

b.   

 

     

Show Worked Solution
a.   
 
 
 
   

 


♦♦ Mean mark part (a) 29%.

b.   

 

     


♦ Mean mark 44%.

Algebra, STD2 A4 2022 HSC 24

A student believes that the time it takes for an ice cube to melt ( minutes) varies inversely with the room temperature . The student observes that at a room temperature of it takes 12 minutes for an ice cube to melt.

  1. Find the equation relating and .   (2 marks)

  2. By first completing this table of values, graph the relationship between temperature and time from to    (2 marks)

 
           

Show Answers Only
a.   
 
 
 
   

 

b.   

 

     

Show Worked Solution
a.   
 
 
 
   

 


♦♦ Mean mark part (a) 29%.

b.   

 

     


♦ Mean mark 44%.

Algebra, STD2 A4 2014 HSC 29a

The cost of hiring an open space for a music festival is  $120 000. The cost will be shared equally by the people attending the festival, so that    (in dollars) is the cost per person when    people attend the festival.

  1. Complete the table below by filling in the THREE missing values.   (1 mark)
  2. Using the values from the table, draw the graph showing the relationship between    and  .   (2 marks)
     
  3. What equation represents the relationship between and ?   (1 mark)

  4. Give ONE limitation of this equation in relation to this context.   (1 mark)

  5. Is it possible for the cost per person to be $94? Support your answer with appropriate calculations.   (1 mark)

Show Answers Only

i.   


 

ii. 

iii.   


 

iv.  

 

 
 

v.   

 

 

Show Worked Solution

i.   


 

ii. 

 

♦ Mean mark (iii) 48%

iii.   

 

♦♦♦ Mean mark (iv) 7%
COMMENT: When asked for limitations of an equation, look carefully at potential restrictions with respect to both the domain and range.

iv.  

 

 

 

v.   

 
♦ Mean mark (v) 38%