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Graphs, MET1 SM-Bank 20

The rule for   is    for  .  This function has an inverse,  .

  1. Sketch the graphs of    and    on the same set of axes. (Use the same scale on both axes.)   (2 marks)

  2. Find the rule for the inverse function  .    (2 marks)

  3. Evaluate  .    (1 mark)

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  1.  
    Inverse Functions, EXT1 2008 HSC 5a Answer
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a. 

Inverse Functions, EXT1 2008 HSC 5a Answer
b.  

 

 

 
 
 

 

 

c.   
   
   
   
   

Calculus, MET2 2011 VCAA 3

  1. Consider the function  .

     

    1. Find     (1 mark)

    2. Explain why   for all .   (1 mark)

  2. The cubic function is defined by  , where , , and are real numbers.

     

    1. If has stationary points, what possible values can have?   (1 mark)

    2. If has an inverse function, what possible values can have?   (1 mark)

  3. The cubic function is defined by  .

     

    1. Write down a expression for  .   (2 marks)

    2. Determine the coordinates of the point(s) of intersection of the graphs of    and  .   (2 marks)

  4. The cubic function is defined by  , where and are real numbers.

     

    1. If has exactly one stationary point, find the value of .   (3 marks)

    2. If this stationary point occurs at a point of intersection of    and  , find the value of .   (3 marks)

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a.i.  
  

a.ii.  

♦ Mean mark 47%.

 

b.i.  

♦♦♦ Mean mark part (b)(i) 9%, and part (b)(ii) 20%.
MARKER’S COMMENT: Good exam strategy should point students to investigate earlier parts for direction. Here, part (a) clearly sheds light on a solution!

 

b.ii.  

 

c.i.  


  

c.ii. 

   

 


  

♦ Mean mark part (d)(i) 44%.
d.i.   
 
 
 
 

 

d.ii.  

♦♦♦ Mean mark part (d)(ii) 14%.