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Quadratics, SMB-015

The diagram shows the curve with equation  . The curve intersects the -axis at points . The point on the curve has the same -coordinate as the -intercept of the curve.
 

 

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

  2. Write down the coordinates of   (2 marks)

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i.   
 

 

 

ii.   


 

 

 

Quadratics, SMB-010

  1. Factorise    (2 marks)

  2. Find the vertex of the parabola with equation    (2 marks)

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i.     
   
   
   

 

ii.   

 

 
 

Quadratics, SMB-006

  1. Complete the table of values for the equation  .  (1 mark)

  1. Sketch the graph    (2 marks)  
      

      
  2. For what range of -values is the parabola concave up?  (1 mark)

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i.   

ii. 

 

iii.   

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i.   

ii. 

 

iii.   

Quadratics, SMB-005

  1. Complete the table of values for the equation  .  (1 mark)

  1. Sketch the graph    (2 marks) 
      
  2. For what range of -values is the parabola concave down?  (1 mark)

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i.   

ii. 

 

iii.   

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i.   

ii. 

 

iii.   

Quadratics, SMB-004

  1. Complete the table of values for the equation  .  (1 mark)

  1. Sketch the graph    (2 marks)  
      
  2. What are the coordinates of the vertex of the parabola?  (1 mark)

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i.   

ii. 

 

iii.   

Algebra, STD1 A3 2019 HSC 9 MC

The container shown is initially full of water.
 

Water leaks out of the bottom of the container at a constant rate.

Which graph best shows the depth of water in the container as time varies?
 

A. B.
C. D.
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Algebra, STD2 A4 2020 HSC 19

A fence is to be built around the outside of a rectangular paddock. An internal fence is also to be built.

The side lengths of the paddock are metres and metres, as shown in the diagram.
 

 
A total of 900 metres of fencing is to be used. Therefore  .
 
The area, , in square metres, of the rectangular paddock is given by  .

The graph of this equation is shown.
  

  1. If the area of the paddock is , what is the largest possible value of ?   (1 mark)

  2. Find the values of and so that the area of the paddock is as large as possible.   (2 marks)

  3. Using your value from part (b), find the largest possible area of the paddock.   (1 mark)

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a.     

♦ Mean mark part (a) 39%.

 


 

b.   

♦♦ Mean mark part (b) 34%.

 

♦ Mean mark part (c) 40%.
c.   
   
   

Algebra, STD2 A4 2012 HSC 30b

A golf ball is hit from point to point , which is on the ground as shown. Point is 30 metres above the ground and the horizontal distance from point to point is  300 m.
 

The path of the golf ball is modelled using the equation 

 

where 

is the height of the golf ball above the ground in metres, and 

is the horizontal distance of the golf ball from point in metres.

The graph of this equation is drawn below.

  

  1. What is the maximum height the ball reaches above the ground?    (1 mark)

  2. There are two occasions when the golf ball is at a height of 35 metres.

     

    What horizontal distance does the ball travel in the period between these two occasions?   (1 mark)

  3. What is the height of the ball above the ground when it still has to travel a horizontal distance of 50 metres to hit the ground at point ?   (1 mark)

  4. Only part of the graph applies to this model.

     

    Find all values of that are not suitable to use with this model, and explain why these values are not suitable.   (2 marks)

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i.   

COMMENT: With a mean mark of 92% in (i), a classic example of low hanging fruit in later questions.

 

ii.  

 

 

iii.   

MARKER’S COMMENT: Responses for (iii) in the range    were deemed acceptable estimates read off the graph.

 

iv.   

♦♦♦ Mean mark (iv) 12%
MARKER’S COMMENT: Many students did not refer to the domain as unsuitable to the model.