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Functions and Graphs, SMB-020

A circle has centre and radius 3.

  1.  Describe, with inequalities, the region that consists of the interior of the circle and more than 2 units above the -axis.  (2 marks)

  2.  Sketch the region.  (1 mark)

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i.   

ii.    
       

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i.   


 

COMMENT: The broken line on the graph represents an excluded boundary.

 

ii.   

Algebraic Techniques, SMB-074

Worker A picks a bucket of blueberries in hours. Worker B picks a bucket of blueberries in hours.

  1.  Write an algebraic expression for the fraction of a bucket of blueberries that could be picked in one hour if A and B worked together.  (2 marks)

  2.  What does the reciprocal of this fraction represent?  (1 mark)

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ii.   

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i.   

COMMENT: Note that the question asks for “a fraction”.


 


 

ii.   

Functions, EXT1 F2 2022 HSC 3 MC

Let be a polynomial of degree 5. When is divided by the polynomial , the remainder is .

Which of the following is true about the degree of ?

  1. The degree must be 1.
  2. The degree could be 1.
  3. The degree must be 2.
  4. The degree could be 2.
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♦ Mean mark 51%.

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%.


 

Networks, STD2 N2 SM-Bank 37

The map of Australia shows the six states, the Northern Territory and the Australian Capital Territory (ACT).
  

In the network diagram below, each of the vertices to represents one of the states or territories shown on the map of Australia. The edges represent a border shared between two states or between a state and a territory.
 

  1. In the network diagram, what is the order of the vertex that represents the Australian Capital Territory (ACT)?  (1 mark)

  2. In the network diagram, Queensland is represented by which letter? Explain why.  (2 marks)

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ii.   

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ii.   

Measurement, STD2 M1 2017 HSC 30e

A solid is made up of a sphere sitting partially inside a cone.

The sphere, centre , has a radius of 4 cm and sits 2 cm inside the cone. The solid has a total height of 15 cm. The solid and its cross-section are shown.
 


 

Using the formula    where  is the radius of the cone's circular base and is the perpendicular height of the cone, find the volume of the cone, correct to the nearest cm³?  (3 marks)

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Measurement, STD2 M1 2016 HSC 30c

A school playground consists of part of a circle, with centre , and a rectangle as shown in the diagram. The radius of the circle is 45 m, the width of the rectangle is 20 m and is 100°.
 

What is the area of the whole playground, correct to the nearest square metre?  (5 marks)

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²²

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²

 

  ²

 

²

 

²²

Measurement, STD2 M6 2010 HSC 26d

Find the area of triangle , correct to the nearest square metre.   (3 marks)

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²    ²

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♦♦ Mean mark 32%.
TIP: The allocation of 3 marks to this question should flag the need for more than 1 step.
 
 

 
 
  ²²