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Algebra, MET1 SM-Bank 23

The function    with rule    is drawn below.

Inverse Functions, EXT1 2004 HSC 5b

  1. Copy or trace this diagram into your writing booklet.
  2. On the same set of axes, sketch    where   is the inverse function of  .   (1 mark)

  3. Find the domain of the inverse  .   (1 mark)

  4. Find an expression for    in terms of  .   (2 marks)

  5. The graphs of    and    meet at exactly one point  .Let  α  be the -coordinate of  . Explain why  α  is a root of the equation
  6.      .   (1 mark)

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a.  

Inverse Functions, EXT1 2004 HSC 5b Answer

b.  

 

c. 

 

 

 

d.   

 

α

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%.