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NETWORKS, FUR2 2011 VCAA 1

Aden, Bredon, Carrie, Dunlop, Enwin and Farnham are six towns.

The network shows the road connections and distances between these towns in kilometres.

 

  1. In kilometres, what is the shortest distance between Farnham and Carrie?   (1 mark)

  2. How many different ways are there to travel from Farnham to Carrie without passing through any town more than once?   (1 mark)

An engineer plans to inspect all of the roads in this network.

He will start at Dunlop and inspect each road only once.

  1. At which town will the inspection finish?   (1 mark)

Another engineer decides to start and finish her road inspection at Dunlop.

If an assistant inspects two of the roads, this engineer can inspect the remaining six roads and visit each of the other five towns only once.

  1. How many kilometres of road will the assistant need to inspect?   (1 mark)

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a.  


  

b.  


  

c.   


  

d.  

NETWORKS, FUR2 2013 VCAA 1

The vertices in the network diagram below show the entrance to a wildlife park and six picnic areas in the park: , , , , and .

The numbers on the edges represent the lengths, in metres, of the roads joining these locations.

 

 

  1. In this graph, what is the degree of the vertex at the entrance to the wildlife park?   (1 mark)

  2. What is the shortest distance, in metres, from the entrance to picnic area ?   (1 mark)

  3. A park ranger starts at the entrance and drives along every road in the park once.
  4. i. At which picnic area will the park ranger finish?   (1 mark)

  5. ii. What mathematical term is used to describe the route the park ranger takes?   (1 mark)

  6. A park cleaner follows a route that starts at the entrance and passes through each picnic area once, ending at picnic area .

     

    Write down the order in which the park cleaner will visit the six picnic areas.   (1 mark)

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  3. i.
    ii.  
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a.  
  

b.  


  

c.i.   


  

c.ii.   
  

d.  

NETWORKS, FUR2 2015 VCAA 1

A factory requires seven computer servers to communicate with each other through a connected network of cables.

The servers, , , , , , and , are shown as vertices on the graph below.
 

Networks, FUR2 2015 VCAA 11

 
The edges on the graph represent the cables that could connect adjacent computer servers.

The numbers on the edges show the cost, in dollars, of installing each cable.

  1. What is the cost, in dollars, of installing the cable between server and server ?   (1 mark)

  2. What is the cheapest cost, in dollars, of installing cables between server and server ?   (1 mark)

  3. An inspector checks the cables by walking along the length of each cable in one continuous path.
    To avoid walking along any of the cables more than once, at which vertex should the inspector start and where would the inspector finish?   (1 mark)

     

  4. The computer servers will be able to communicate with all the other servers as long as each server is connected by cable to at least one other server.
    i.     The cheapest installation that will join the seven computer servers by cable in a connected network follows a minimum spanning tree.

    Draw the minimum spanning tree on the plan below?   (1 mark)


    Networks, FUR2 2015 VCAA 12
  5. ii. The factory’s manager has decided that only six connected computer servers will be needed, rather than seven. 

    How much would be saved in installation costs if the factory removed computer server from its minimum spanning tree network?
    A copy of the graph above is provided below to assist with your working.   (1 mark)

    Networks, FUR2 2015 VCAA 12

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  4. i. 

 Networks, FUR2 2015 VCAA 12 Answer
d.ii.

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a.   
  

b.  


  

c.   

MARKER’S COMMENT: Many students had difficulty finding the minimum spanning tree, often incorrectly excluding or .
d.i.    Networks, FUR2 2015 VCAA 12 Answer

 

d.ii.   

 

MATRICES, FUR2 2006 VCAA 1

A manufacturer sells three products, , and , through outlets at two shopping centres, Eastown () and Noxland (). 

The number of units of each product sold per month through each shop is given by the matrix , where

  1. Write down the order of matrix .   (1 mark)

The matrix , shown below, gives the selling price, in dollars, of products , , .

  1.   i. Evaluate the matrix , where .   (1 mark)

  2.  ii. What information does the elements of matrix provide?   (1 mark)

  3. Explain why the matrix is not defined.   (1 mark)

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a.  
 

b.i.   
   
   

 
b.ii.  

   
 

c.   

NETWORKS, FUR2 2010 VCAA 1

The members of one team are Kristy (), Lyn (), Mike () and Neil (). 

In one of the challenges, these four team members are only allowed to communicate directly with each other as indicated by the edges of the following network.
 

Network, FUR2 2011 VCAA 1
 

The adjacency matrix below also shows the allowed lines of communication.

 

  1. Explain the meaning of a zero in the adjacency matrix.   (1 mark)

  2. Write down the values of and in the adjacency matrix.   (1 mark)

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a.  
  

b.   

MATRICES, FUR2 2009 VCAA 1

Three types of cheese, Cheddar (), Gouda () and Blue (), will be bought for a school function.

The cost matrix lists the prices of these cheeses, in dollars, at two stores, Foodway and Safeworth.
 


 

  1. What is the order of matrix ?   (1 mark)

The number of packets of each type of cheese needed is listed in the quantity matrix .
 


 

    1. Evaluate the matrix  .   (1 mark)
    2. At which store will the total cost of the cheese be lower?   (1 mark)

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a.   

 

b.i.   
   
   

 

b.ii.   

MATRICES, FUR2 2010 VCAA 1

In a game of basketball, a successful shot for goal scores one point, two points, or three points, depending on the position from which the shot is thrown.

  is a column matrix that lists the number of points scored for each type of successful shot.

In one game, Oscar was successful with

    • 4 one-point shots for goal
    • 8 two-point shots for goal
    • 2 three-point shots for goal.
  1. Write a row matrix, , that shows the number of each type of successful shot for goal that Oscar had in that game.   (1 mark)

  2. Matrix is found by multiplying matrix with matrix so that  
  3. Evaluate matrix .   (1 mark)

  4. In this context, what does the information in matrix provide?   (1 mark)

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a.  
 

b.   
   
   

 
c.   

MATRICES, FUR2 2011 VCAA 1

The diagram below shows the feeding paths for insects (), birds () and lizards (). The matrix has been constructed to represent the information in this diagram. In matrix , a 1 is read as "eat" and a  0  is read as "do not eat".
 

MATRICES, FUR2 2011 VCAA 11

  1. Referring to insects, birds or lizards
  2.  i. what does the 1 in column , row , of matrix indicate?   (1 mark)

  3. ii. what does the row of zeros in matrix indicate?   (1 mark)

The diagram below shows the feeding paths for insects (), birds (), lizards () and frogs ().

The matrix has been set up to represent the information in this diagram.

Matrix has not been completed.
 

MATRICES, FUR2 2011 VCAA 12

  1. Complete the matrix above by writing in the seven missing elements.   (1 mark)

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a.i.   

a.ii.   

b.
     

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a.i.   
 

a.ii.   

   
 

b.   

MATRICES, FUR2 2013 VCAA 1

Five trout-breeding ponds, , , , and , are connected by pipes, as shown in the diagram below.
 

Matrices, FUR2 2013 VCAA 1 

The matrix is used to represent the information in this diagram.

In matrix

•  the 1 in column 1, row 2, for example, indicates that a pipe directly connects pond and pond

•  the 0 in column 1, row 5, for example, indicates that pond and pond are not directly connected by a pipe.

  1. Find the sum of the elements in row 3 of matrix .   (1 mark)

  2. In terms of the breeding ponds described, what does the sum of the elements in row 3 of matrix represent?   (1 mark)

The pipes connecting pond to pond and pond to pond are removed.

Matrix will be used to show this situation. However, it has missing elements.

  1. Complete matrix below by filling in the missing elements in row 1 and column 1.   (1 mark)

        
             Matrices, FUR2 2013 VCAA 1_c

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  3.  
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a.  
 

b.  


 

c.   

MATRICES, FUR1 2007 VCAA 2 MC

The number of tourists visiting three towns, Oldtown, Newtown and Twixtown, was recorded for three years. 

The data is summarised in the table below.

MATRICES, FUR1 2007 VCAA 2 MC

The matrix that could be used to show the number of tourists visiting the three towns in the year 2005 is

A.   B.  
   
C.   D.  
   
E.    

 

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MATRICES, FUR1 2011 VCAA 1 MC

The matrix below shows the airfares (in dollars) that are charged by Zeniff Airlines to fly between Adelaide (), Melbourne () and Sydney ().

 

The cost to fly from Melbourne to Sydney with Zeniff Airlines is

A.     

B.     

C.     

D.     

E.   

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GRAPHS, FUR2 2012 VCAA 1

The cost, , in dollars, of making phones, is shown by the line in the graph below.

GRAPHS, FUR2 2012 VCAA 1

    1. Calculate the gradient of the line, , drawn above.  (1 mark)
    2. Write an equation for the cost, , in dollars, of making phones.  (1 mark)

  2. The revenue, , in dollars, obtained from selling phones is given by  .

    1. Draw this line on the graph above.  (1 mark)
    2. How many phones would need to be sold to obtain $54 000 in revenue?  (1 mark)
  3. Determine the number of phones that would need to be made and sold to break even.  (1 mark) 
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a.i.  

 
 

 

a.ii.  

 

b.i.    GRAPHS, FUR2 2012 VCAA 1 Answer

 

b.ii.   
 
   

 

c.  

CORE*, FUR2 2013 VCAA 1

Hugo is a professional bike rider.

The value of his bike will be depreciated over time using the flat rate method of depreciation.

The graph below shows his bike’s initial purchase price and its value at the end of each year for a period of three years.
 

  1. What was the initial purchase price of the bike?   (1 mark)
    1. Show that the bike depreciates in value by $1500 each year.   (1 mark)
    2. Assume that the bike’s value continues to depreciate by $1500 each year.
    3. Determine its value five years after it was purchased.   (1 mark)

The unit cost method of depreciation can also be used to depreciate the value of the bike.

In a two-year period, the total depreciation calculated at $0.25 per kilometre travelled will equal the depreciation calculated using the flat rate method of depreciation as described above.

  1. Determine the number of kilometres the bike travels in the two-year period.   (1 mark)

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  2. i. 
    ii.

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a.  
  

b.i.   

 

  
b.ii.   

 

  
c.   

 

  

GRAPHS, FUR2 2013 VCAA 2

Students at the camp can participate in two different watersport activities: canoeing and surfing.

The cost of canoeing is $30 per hour and the cost of surfing is $20 per hour.

The budget allows each student to spend up to $200, in total, on watersport activities.

The way in which a student decides to spend the $200 is described by the following inequality.

30 × hours canoeing + 20 × hours surfing ≤ 200

  1. Hillary wants to spend exactly two hours canoeing during the camp.

     

    Calculate the maximum number of hours she could spend surfing.  (1 mark)

  2. Dennis would like to spend an equal amount of time canoeing and surfing.

     

    If he spent a total of $200 on these activities, determine the maximum number of hours he could spend on each activity.  (1 mark)

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a.  

 

b.  

GRAPHS, FUR2 2013 VCAA 1

The distance-time graph below shows the first two stages of a bus journey from a school to a camp.

GRAPHS, FUR2 2013 VCAA 1

  1. At what constant speed, in kilometres per hour, did the bus travel during stage 1 of the journey?  (1 mark)
  2. For how many minutes did the bus stop during stage 2 of the journey?  (1 mark)

The third stage of the journey is missing from the graph.

During stage 3, the bus continued its journey to the camp and travelled at a constant speed of 60 km/h for one hour.

  1. Draw a line segment on the graph above to represent stage 3 of the journey.  (1 mark)
  2. Find the average speed of the bus over the three hours.

    Write your answer in kilometres per hour.  (1 mark)

The distance, km, of the bus from the school, hours after departure is given by

  1. Determine the value of .  (1 mark)
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a.  

 

b.  

 

c.    GRAPHS, FUR2 2013 VCAA 1 Answer

 

d.  

♦ Mean mark of parts (c) and (d) consumed was 46%.

 

e.  

GRAPHS, FUR2 2015 VCAA 1

Ben is flying to Japan for a school cultural exchange program.

The graph below shows the cost of a particular flight to Japan, in dollars, on each day in February.

Graphs, FUR2 2015 VCAA 1

  1. What is the cost, in dollars, of this flight to Japan on 19 February?  (1 mark)
  2. On how many days in February is the cost of this flight to Japan more than $1000?  (1 mark) 
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a.   

b.  

Algebra, MET2 2014 VCAA 1

The population of wombats in a particular location varies according to the rule  , where is the number of wombats and is the number of months after 1 March 2013.

  1. Find the period and amplitude of the function .   (2 marks)

  2. Find the maximum and minimum populations of wombats in this location.   (2 marks)

  3. Find  .   (1 mark)

  4. Over the 12 months from 1 March 2013, find the fraction of time when the population of wombats in this location was less than  .   (2 marks)

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a.   

MARKER’S COMMENT: Expressing the amplitude as [800,1600] in part (a) is incorrect.


  

b.  


  

c.  
   

d.   

♦ Mean mark 48%.

 

GRAPHS, FUR2 2006 VCAA 1

Harry operates a mobile pet care service. The call-out fee charged depends on the distance he has to travel to tend to a pet. The call-out fees for distances up to 30 km are shown on the graph below.

GRAPHS, FUR2 2006 VCAA 1

  1. According to this graph

     

    1. what is the call-out fee to travel a distance of 20 km?  (1 mark)
    2. what is the maximum distance travelled for a call-out fee of $10?  (1 mark)

A call-out fee of $50 is charged to travel distances of more than 30 km but less than or equal to 40 km.

  1. Draw this information on the graph above.  (1 mark) 
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a.i.   

 

a.ii.   

 

b.   

Calculus, MET2 2015 VCAA 1

Let  . The point    is on the graph of  , as shown below.

The tangent at cuts the y-axis at and the x-axis at

VCAA 2015 1ai

  1. Write down the derivative   of .   (1 mark)

  2.  i. Find the equation of the tangent to the graph of   at the point  .   (1 mark)

    ii. Find the coordinates of points and .   (2 marks)

  3. Find the distance and express it in the form  , where and are positive integers.  (2 marks)

VCAA 2015 1di

  1. Find the area of the shaded region in the graph above.   (3 marks)

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  2.  i.
    ii.
  4. ²
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a.   
 
   

 

b.i.   


  

  
b.ii.   


  

 

  

c.  

 
 

 

d.  

MARKER’S COMMENT: Many students complicated their answer by splitting up the area.

  ²

GEOMETRY, FUR2 2007 VCAA 1-3

Question 1

Tessa is a student in a woodwork class.

The class will construct geometrical solids from a block of wood.

Tessa has a piece of wood in the shape of a rectangular prism.

This prism, , shown in Figure 1, has base length 24 cm, base width 28 cm and height 32 cm.

GEOMETRY, FUR2 2007 VCAA 11 

On the front face of Figure 1, , Tessa marks point halfway between and as shown in Figure 2 below. She then draws line segments and as shown.

GEOMETRY, FUR2 2007 VCAA 12

  1. Determine the length, in cm, of .  (1 mark)
  2. Calculate the angle . Write your answer in degrees, correct to one decimal place.  (1 mark)
  3. Calculate the angle correct to one decimal place.  (1 mark)
  4. What fraction of the area of the rectangle does the area of the triangle represent?  (1 mark)

 

Question 2

Tessa carves a triangular prism from her block of wood.

Using point , halfway between and on the back face, , of Figure 1, she constructs the triangular prism shown in Figure 3.

GEOMETRY, FUR2 2007 VCAA 2

  1. Show that, correct to the nearest centimetre, length is 34 cm.  (1 mark)
  2. Using length as 34 cm, find the total surface area, in cm², of the triangular prism in Figure 3.  (2 marks)

 

Question 3

Tessa's next task is to carve the right rectangular pyramid shown in Figure 4 below.

She marks a new point, , halfway between points and in Figure 3. She uses point to construct this pyramid.

GEOMETRY, FUR2 2007 VCAA 3

  1. Calculate the volume, in cm³, of the pyramid in Figure 4.  (1 mark)
  2. Show that, correct to the nearest cm, length is 37 cm.  (2 marks)
  3. Using as 37 cm, demonstrate the use of Heron's formula to calculate the area, in cm², of the triangular face .  (2 marks)
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Question 1

Question 2

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Question 3

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a.   
   
   

 

b.   VCAA GEO FUR2 2007 1bi
 
 

 

c.   
   
   

 

d.  
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a.   VCAA GEO FUR2 2007 2ai

 
 
 

 

b.  

²

 

a.   
   
    ³

 

b.   VCAA GEO FUR2 2007 3bi

 

 

VCAA GEO FUR2 2007 3bii

 
 
 

 

c.  

 

²

MATRICES, FUR2 2008 VCAA 1

Two subjects, Biology and Chemistry, are offered in the first year of a university science course. 

The matrix lists the number of students enrolled in each subject.

The matrix lists the proportion of these students expected to be awarded an , , , or grade in each subject.

  1. Write down the order of matrix .   (1 mark)

  2. Let the matrix  .
  3.  i. Evaluate the matrix .   (1 mark)

  4. ii. Explain what the matrix element  represents.   (1 mark)

  5. Students enrolled in Biology have to pay a laboratory fee of $110, while students enrolled in Chemistry pay a laboratory fee of $95.
  6.  i. Write down a clearly labelled row matrix, called , that lists these fees.   (1 mark)

  7. ii. Show a matrix calculation that will give the total laboratory fees, , paid in dollars by the students enrolled in Biology and Chemistry. Find this amount.   (1 mark)

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a.   
 

b.i.  
   
   

 
b.ii.

 
 

c.i.  

 
c.ii. 

 

MATRICES, FUR2 2012 VCAA 1

Matrix below shows the flight connections for an airline that serves four cities, Anvil (), Berga (), Cantor () and Dantel ().

In this matrix, the in column row , for example, indicates that, using this airline, you can fly directly from Cantor to Berga. The in column row , for example, indicates that you cannot fly directly from Cantor to Dantel.

  1. Complete the following sentence.
  2. On this airline, you can fly directly from Berga to ________ and ________.   (1 mark)

  3. List the route that you must follow to fly from Anvil to Cantor.   (1 mark)

  4. Evaluate the matrix product , where .   (1 mark)

     

  5. In the context of the problem, what information does matrix contain?   (1 mark)

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a.  
 

b.  
 

c.  
   
   

 
d.   

CORE, FUR2 2008 VCAA 1

In a small survey, twenty-five Year 8 girls were asked what they did (walked, sat, stood, ran) for most of the time during a typical school lunch time. 

Their responses are recorded below.
 

 

Use the data to

  1. complete the following frequency table  (1 mark)

     

     

         Core, FUR2 2008 VCAA 1

  2. determine the percentage of Year 8 girls who ran for most of the time during a typical school lunch time.  (1 mark) 
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  1.  
    Core, FUR2 2008 VCAA 1 Answer
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a.    Core, FUR2 2008 VCAA 1 Answer

 
b.  

MATRICES, FUR2 2015 VCAA 1

Students in a music school are classified according to three ability levels: beginner (), intermediate () or advanced ().

Matrix , shown below, lists the number of students at each level in the school for a particular week.

  1. How many students in total are in the music school that week?   (1 mark)

The music school has four teachers, David (), Edith (), Flavio () and Geoff ().

Each teacher will teach a proportion of the students from each level, as shown in matrix below.

The matrix product, , can be used to find the number of students from each level taught by each teacher.

  1.  i. Complete matrix , shown below, by writing the missing elements in the shaded boxes.   (1 mark) 

 Matrices, FUR2 2015 VCAA 1

  1. ii. How many intermediate students does Edith teach?  (1 mark)

The music school pays the teachers $15 per week for each beginner student, $25 per week for each intermediate student and $40 per week for each advanced student.

These amounts are shown in matrix below.

The amount paid to each teacher each week can be found using a matrix calculation.

  1.  i. Write down a matrix calculation in terms of and that results in a matrix that lists the amount paid to each teacher each week.   (1 mark)

  2. ii. How much is paid to Geoff each week?   (1 mark)

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a.   
 

b.i.  
   
   

 
b.ii.   

 
c.i.   

 
c.ii.   

CORE, FUR2 2009 VCAA 1

Table 1 shows the number of rainy days recorded in a high rainfall area for each month during 2008.
 

CORE, FUR2 2009 VCAA 11

The dot plot below displays the distribution of the number of rainy days for the 12 months of 2008.
 

CORE, FUR2 2009 VCAA 12

  1. Circle the dot on the dot plot that represents the number of rainy days in April 2008.   (1 mark)

  2. For the year 2008, determine

     

  3.  i. the median number of rainy days per month.   (1 mark)
  4. ii. the percentage of months that have more than 10 rainy days. Write your answer correct to the nearest per cent.   (1 mark) 
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  1.  
    CORE, FUR2 2009 VCAA 12 Answer
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a.    CORE, FUR2 2009 VCAA 12 Answer

 

b.i.   
   
   

 

b.ii.   

CORE, FUR2 2010 VCAA 1

Table 1 shows the percentage of women ministers in the parliaments of 22 countries in 2008.
 

CORE, FUR2 2010 VCAA 11
 

  1. What proportion of these 22 countries have a higher percentage of women ministers in their parliament than Australia?  (1 mark)

  2. Determine the median, range and interquartile range of this data.  (2 marks)

The ordered stemplot below displays the distribution of the percentage of women ministers in parliament for 21 of these countries. The value of Canada is missing.
 

    CORE, FUR2 2010 VCAA 12
 

  1. Complete the stemplot above by adding the value for Canada.  (1 mark)

  2. Both the median and the mean appropriate measures of centre for this distribution.
  3. Explain why.  (1 mark)

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  4.  

     

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a.  

b.  

 
 

 

 

 

 

 

c.   

♦♦ Part (d) was “poorly answered”.
MARKER’S COMMENT: The use of “symmetric” gained a mark while “evenly distributed” was deemed too vague.

 

d.   

CORE, FUR2 2013 VCAA 1

A development index is used as a measure of the standard of living in a country.

The bar chart below displays the development index for 153 countries in four categories: low, medium, high and very high.
 

CORE, FUR2 2013 VCAA 1

  1. How many of these countries have a very high development index?   (1 mark)

  2. What percentage of the 153 countries has either a low or medium development index?
  3. Write your answer, correct to the nearest percentage.   (1 mark)

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a.  

 

b.  

 
 

CORE, FUR2 2014 VCAA 1

The segmented bar chart below shows the age distribution of people in three countries, Australia, India and Japan, for the year 2010.
 

Core, FUR2 2015 VCAA 1

  1. Write down the percentage of people in Australia who were aged 0 – 14 years in 2010.
  2. Write your answer, correct to the nearest percentage.  (1 mark)

  3. In 2010, the population of Japan was 128 000 000.
  4. How many people in Japan were aged 65 years and over in 2010?  (1 mark)

  5. From the graph above, it appears that there is no association between the percentage of people in the 15 – 64 age group and the country in which they live.
  6. Explain why, quoting appropriate percentages to support your explanation.  (1 mark)

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  3.  
     
     

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a.   

 

b.  

 

c.   

♦ Mean mark 41%.

PATTERNS, FUR1 2015 VCAA 1 MC

The first four terms in a geometric sequence are:

The fifth term in this sequence is

A.     

B.     

C.     

D.     

E.   

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PATTERNS, FUR1 2006 VCAA 1 MC

Which one of the following sequences shows the first five terms of an arithmetic sequence?

A.    

B.   

C.    

D.   

E.   

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CORE, FUR1 2007 VCAA 11-13 MC

The following information relates to Parts 1, 2 and 3.

The time series plot below shows the revenue from sales (in dollars) each month made by a Queensland souvenir shop over a three-year period.

Part 1

This time series plot indicates that, over the three-year period, revenue from sales each month showed

A.   no overall trend.

B.   no correlation.

C.   positive skew.

D.   an increasing trend only.

E.   an increasing trend with seasonal variation.

 

Part 2

A three median trend line is fitted to this data.

Its slope (in dollars per month) is closest to

A.   

B.   

C.   

D.   

E.   

 

Part 3

The revenue from sales (in dollars) each month for the first year of the three-year period is shown below.

If this information is used to determine the seasonal index for each month, the seasonal index for September will be closest to

A.   

B.   

C.   

D.   

E.   

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♦ Mean mark 37%.
MARKERS’ COMMENT: A common error was to incorrectly use the 6 month and 30 month data points as the median.

 

 

 

CORE, FUR1 2007 VCAA 1-2 MC

The dot plot below shows the distribution of the number of bedrooms in each of 21 apartments advertised for sale in a new high-rise apartment block.
 

 

Part 1

The mode of this distribution is

A.   

B.   

C.   

D.   

E.   

 

Part 2

The median of this distribution is

A.   

B.   

C.   

D.   

E.   

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PATTERNS, FUR1 2008 VCAA 2 MC

For an examination, 8600 examination papers are to be printed at a rate of 25 papers per minute. After one hour, the number of examination papers that still need to be printed is

A.   

B.     

C.   

D.   

E.   

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CORE*, FUR2 2014 VCAA 1

The adult membership fee for a cricket club is $150.

Junior members are offered a discount of $30 off the adult membership fee.

  1. Write down the discount for junior members as a percentage of the adult membership fee.   (1 mark)

Adult members of the cricket club pay $15 per match in addition to the membership fee of $150.

  1. If an adult member played 12 matches, what is the total this member would pay to the cricket club?   (1 mark)

If a member does not pay the membership fee by the due date, the club will charge simple interest at the rate of 5% per month until the fee is paid.

Michael paid the $150 membership fee exactly two months after the due date.

  1. Calculate, in dollars, the interest that Michael will be charged.   (1 mark)

The cricket club received a statement of the transactions in its savings account for the month of January 2014.

The statement is shown below.

     BUSINESS, FUR2 2014 VCAA 1

    1. Calculate the amount of the withdrawal on 17 January 2014.   (1 mark)

    2. Interest for this account is calculated on the minimum balance for the month and added to the account on the last day of the month.
    3. What is the annual rate of interest for this account?  Write your answer, correct to one decimal place.   (1 mark)

  1.  

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a.  

  
b.  

 

 

c.   
   
   

 

d.i.  


    

d.ii.  

 

  

Harder Ext1 Topics, EXT2 2015 HSC 13c

A small spherical balloon is released and rises into the air. At time    seconds, it has radius   cm, surface area    and volume  .

As the balloon rises it expands, causing its surface area to increase at a rate of  . As the balloon expands it maintains a spherical shape.

  1. By considering the surface area, show that  
    1.   (2 marks)

  2. Show that  
    1.   (2 marks)

  3. When the balloon is released its volume is  ³. When the volume of the balloon reaches  ³  it will burst.
  4. How long after it is released will the balloon burst?  (2 marks)

 

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(i)   
 
 
   

 

(ii)  

­
­
­
­

 

(iii) 

 
 
 

Conics, EXT2 2015 HSC 13a

The hyperbolas    and    are shown in the diagram.

Let    lie on    as shown on the diagram.

Let    be the point  .

  1. Verify that the coordinates of    satisfy the equation for    (1 mark)

  2. Show that the equation of the line    is    (2 marks)

  3. Prove that the area of    is independent of    (3 marks)
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(i)  

 
 

 

(ii)   
   
   

 
♦ Mean mark 47%.

 

(iii)  

 

 

 
 
   
 

 

 
 
 

Conics, EXT2 2006 HSC 3b

The diagram shows the graph of the hyperbola

  1. Find the coordinates of the points where the hyperbola intersects the -axis.  (1 mark)
  2. Find the coordinates of the foci of the hyperbola.  (2 marks)
  3. Find the equations of the directrices and the asymptotes of the hyperbola.  (2 marks)
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(i)  

 

 

(ii) 

 

 

(iii)