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Aussie Maths & Science Teachers: Save your time with SmarterEd

Similarity, SMB-025

A triangular prism is pictured below.
 

By what factor will its volume change if

  1. Each dimension is doubled?   (1 mark)

  2. Each dimension is decreased by two-thirds?   (2 marks)
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i.   


 

ii.   

Similarity, SMB-014 MC

Spiro is making a scale drawing of his house.

  • The height of the garage in the scale model is 6 centimetres.
  • The height of Spiro's actual garage is 3 metres.

What does 1 centimetre in Spiro's scale drawing represent in his real house?

  1. 1800 cm
  2. 200 cm
  3. 100 cm
  4. 50 cm
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Similarity, SMB-013

Libby plays on a hockey field that is 120 metres long.

She makes a scale diagram of the field using a ratio of .
 

How long, in centimetres, should Libby make the scale diagram of the field?   (2 marks)

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Similarity, SMB-012

Poppy uses a photocopier to enlarge this picture.
 

   

The enlarged picture is 3 times as high and 3 times as wide as the original.

By what factor is the area of the picture increased?   (2 marks)

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Similarity, SMB-009

Juanita wanted to print a larger copy of her photo of a tree.

She increased the scale by a factor of 3.

She named the first picture Photo A and the second picture Photo B.
 

 If Photo B is 3.2 cm high, how high is Photo A in centimetres, correct to 1 decimal place?    (2 marks)

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Similarity, SMB-007

Two circles have the same centre, , as shown in the diagram below.
 

The radius of the small circle is    the radius of the large circle.

Arc is 21 cm and the angle between the lines and is 45°.

What is the length of the arc in centimetres?   (3 marks)

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Similarity, SMB-003

On a map, the distance between two towns is measured at 54 millimetres.

  1. The actual distance between the two towns is 16.2 kilometres. What is the scale of the map?  (1 mark)

  2. If two other towns on the same map are 9.2 centimetres apart, what is the actual distance between the two towns in kilometres?  (1 mark)

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i.   

 

 

 

ii.   
   
   
   

Similarity, SMB-002

A map is drawn to scale, on 1-cm paper, showing the position of a supermarket and a cinema. A reservoir is also shown.
 


 

It takes 10 minutes to walk in a straight line from the cinema to the supermarket at a constant speed of 3 km/h. Show that the scale of the map is 1 cm = 100 m.  (3 marks)

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♦ Mean mark part 49%.

Measurement, STD1 M5 2021 HSC 26

The diagrams show two similar shapes. The dimensions of the small shape are enlarged by a scale factor of 1.5 to produce the large shape.
 


 

Calculate the area of the large shape.  (3 marks)

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♦♦ Mean mark 32%.

 

Measurement, STD1 M5 2020 HSC 28

Two similar right-angled triangles are shown.
 


 

The length of side is 8 cm and the length of side is 4 cm.

The area of triangle is 20 cm2.

Calculate the length in centimetres of side in Triangle II, correct to two decimal places.   (4 marks)

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♦♦♦ Mean mark 11%.

 

 
 

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 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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Measurement, STD2 M7 2012 HSC 28c

Jacques and a flagpole both cast shadows on the ground. The difference between the lengths of their shadows is 3 metres.
 

What is the value of , the length of Jacques’ shadow?     (3 marks)

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♦♦ Mean mark 24%


 

 
 

Measurement, STD2 M7 2012 HSC 27c

A map has a scale of  1 : 500 000.

  1. Two mountain peaks are 2 cm apart on the map.

     

    What is the actual distance between the two mountain peaks, in kilometres?  (1 mark)

  2. Two cities are 75 km apart. How far apart are the two cities on the map, in centimetres?   (1 mark)

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♦ Mean mark 37%
MARKER’S COMMENT: Better responses realised that 1 unit on the map represented 1 unit x 500,000 in real life.
i. 
 
 
 

 

 

♦ Mean mark 44%

ii.