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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)

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i.   


 

ii. 

iii.   


 

iv.  

 

 
 

v.   

 

 

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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%

 

Plane Geometry, 2UA 2011 HSC 6a

The diagram shows a regular pentagon . Sides and are produced to meet at .
  

  1. Find the size of .    (1 mark)

  2. Hence, show that is isosceles.    (2 marks)

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i.  

 
MARKER’S COMMENT: Very few students solved part (i) efficiently. Remember the general formula for the sum of internal angles equals (# sides – 2) x 90°.

 
ii. 

Algebra, STD2 A1 2013 HSC 29a

Sarah tried to solve this equation and made a mistake in Line 2. 

 
Copy the equation in Line 1 and continue your solution to solve this equation for .

Show all lines of working.   (2 marks)

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♦♦ Mean mark 27%
STRATEGY: The RHS of the equation increases from 1 to 15 (from Line 1 to Line 2), indicating both sides must have been multiplied by 15.

Measurement, STD2 M7 2012 HSC 28c

Jacques and a flagpole both cast shadows on the ground. The difference between the lengths of their shadows is 3 metres.
 

What is the value of , the length of Jacques’ shadow?     (3 marks)

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♦♦ Mean mark 24%


 

 
 

Algebra, STD2 A2 2012 HSC 5 MC

The line    has intercepts    and  ,  where    and    are positive integers. 
  

What is the gradient of line   ? 

  1.  
  2.  
  3.  
  4.  
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♦ Mean mark 45%