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Graphs, MET2 2022 VCAA 9 MC

Let .

The shortest distance, , from the origin to the point on the graph of is given by

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Straight line distance is the shortest.

Therefore, using pythagoras and given  

 
   
   
   
 
   

  


♦ Mean mark 50%.

Calculus, MET2 2017 VCAA 1

Let  . Part of the graph of is shown below.
 

  1. Find the coordinates of the turning points.   (2 marks)

  2.   and   are two points on the graph of .

     

    1. Find the equation of the straight line through and .   (2 marks)

    2. Find the distance .   (1 mark)

Let  .

  1. Let  and be two points on the graph of .

     

    1. Find the distance in terms of .   (2 marks)

    2. Find the values of such that the distance is equal to  .   (1 mark)

  2. The diagram below shows part of the graphs of and  . These graphs intersect at the points with the coordinates and .
  3.  
       
  4.  
    1. Find the value of in terms of .   (1 mark)

    2. Find the area of the shaded region in terms of .   (2 marks)

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    2. ²
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a.   

 


 

b.i.  

 

MARKER’S COMMENT: Students skilled in the use of technology will be much more efficient and minimise errors here.
b.ii.   
   
   

 

c.i.   
   
   

 

c.ii.   


 

d.i.   


 

d.ii.   
    ²

Calculus, MET2 2016 VCAA 2

Consider the function  

  1.  i. Given that  ,
  2.      show that  .   (1 mark)

  3. ii. Find the values of for which the graph of    has a stationary point.   (1 mark)

The diagram below shows part of the graph of  , the tangent to the graph at    and a straight line drawn perpendicular to the tangent to the graph at  . The equation of the tangent at the point with coordinates    is  .

The tangent cuts the -axis at . The line perpendicular to the tangent cuts the -axis at .
 


 

  1.   i. Find the coordinates of .   (1 mark)

  2.  ii. Find the equation of the line that passes through and and, hence, find the coordinates of .   (2 marks)

  3. iii. Find the area of triangle .   (2 marks)

  4. The tangent at is parallel to the tangent at . It intersects the line passing through and at .

     


     
     i. Find the coordinates of .   (2 marks)

  5. ii. Find the length of .   (3 marks)

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  1.  i.
  2. ii.
  3.   i.
  4. ii.
  5.      
  6. iii. ²
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a.i.   
   
   
 

 

  

 

a.ii.   


 

b.i.   


 

b.ii.   

   

   


 

b.iii.  
   
    ²

 

♦ Mean mark part (c)(i) 43%.
MARKER’S COMMENT: Many students gave an incorrect -value here. Be careful!
c.i.   
 
 
   

  

 

c.ii.  

 

♦♦ Mean mark 32%.