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Algebra, STD2 A4 2022 HSC 24

A student believes that the time it takes for an ice cube to melt ( minutes) varies inversely with the room temperature . The student observes that at a room temperature of it takes 12 minutes for an ice cube to melt.

  1. Find the equation relating and .   (2 marks)

  2. By first completing this table of values, graph the relationship between temperature and time from to    (2 marks)

 
           

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a.   
 
 
 
   

 

b.   

 

     

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a.   
 
 
 
   

 


♦♦ Mean mark part (a) 29%.

b.   

 

     


♦ Mean mark 44%.

Measurement, STD2 M6 2022 HSC 26

The diagram shows two right-angled triangles, and ,

where and .
 
     

Calculate the size of angle , to the nearest minute.  (4 marks)

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♦ Mean mark 50%.

Measurement, STD2 M6 2021 HSC 32

A right-angled triangle    is cut out from a semicircle with centre . The length of the diameter    is 16 cm and    = 30°, as shown on the diagram.
 


 

  1. Find the length of    in centimetres, correct to two decimal places.  (2 marks)

  2. Hence, find the area of the shaded region in square centimetres, correct to one decimal place.  (3 marks)

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a.   
 
   
   

 

b.   
   
   

♦ Mean mark part (b) 36%.
 
   
   

 

 
   
   

Functions, 2ADV F1 2020 HSC 24

The circle of    is reflected in the -axis.

Sketch the reflected circle, showing the coordinates of the centre and the radius.  (3 marks)

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♦ Mean mark 48%.


 

Plane Geometry, 2UA 2018 HSC 12c

The diagram shows the square . The point is chosen on and the point is chosen on so that  .
 

  1. Prove that is congruent to .   (2 marks)

  2. The side length of the square is 14 cm and has length 4 cm. Find the area of  .   (2 marks)

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i.   

 

ii.  
   

 

Measurement, STD2 M6 2018 HSC 30c

The diagram shows two triangles.

Triangle is right-angled, with    and  .

In triangle    and  . The area of triangle    is 30 cm².
 

 
What is the value of , correct to one decimal place?  (3 marks)

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♦ Mean mark 39%.

 

 

 
 

Algebra, STD2 A1 2015 HSC 28d

The formula    is used to convert temperatures between degrees Fahrenheit and degrees Celsius .

Convert 3°C to the equivalent temperature in Fahrenheit.  (2 marks)

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Measurement, STD2 M7 2015 HSC 27a

At a particular time during the day, a tower of height 19.2 metres casts a shadow. At the same time, a person who is 1.65 metres tall casts a shadow 5 metres long.

  

What is the length of the shadow cast by the tower at that time?  (2 marks)

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Measurement, STD2 M6 2006 HSC 24b

A 130 cm long garden rake leans against a fence. The end of the rake is 44 cm from the base of the fence.

  1. If the fence is vertical, find the value of to the nearest degree.  (2 marks)
      
          2UG-2006-24b-i

     

  2. The fence develops a lean and the rake is now at an angle of 53° to the ground. Calculate the new distance ( cm) from the base of the fence to the head of the rake. Give your answer to the nearest centimetre.  (2 marks)
     
          2UG-2006-24b-ii

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i.   

2UG-2006-24b1 Answer
 
 

 

ii.   

2UG-2006-24b2 Answer

 
 

Algebra, STD2 A1 2004 HSC 11 MC

If  , what is a possible value of    when  ?

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Measurement, STD2 M7 2008 HSC 20 MC

A point lies between a tree, 2 metres high, and a tower, 8 metres high. is 3 metres away from the base of the tree.

From , the angles of elevation to the top of the tree and to the top of the tower are equal.
 

What is the distance, , from to the top of the tower?

  1. 9 m
  2. 9.61 m
  3. 12.04 m
  4. 14.42 m
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