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Algebra, STD2 A4 2024 HSC 26

A sheet of metal is folded to make a gutter, as shown. The cross-section of the gutter is a rectangle of width cm and height cm.
 

 

The area, cm, of the cross-section can be modelled by the quadratic formula

A graph of this model is shown.
 

Find the width and height of the rectangle which will give the greatest possible area of the cross-section.   (3 marks)

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♦ Mean mark 43%.

Algebra, STD2 A4 2019 HSC 31

A rectangle has width centimetres. The area of the rectangle, , in square centimetres, is  .

The graph    is shown.
 


 

  1. Explain why, in this context, the model    only makes sense for the bold section of the graph.  (1 mark)

  2. The area of the rectangle is 18 cm². Calculate the perimeter of the rectangle.  (2 marks)

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a.   

♦ Mean mark 44%.

 

b.   

♦ Mean mark 42%.

 

 

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.