SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

MATRICES, FUR1 2021 VCAA 2 MC

Every Friday, the same number of workers from a large office building regularly purchase their lunch from one of two locations: the deli, , or the cafe, .

It has been found that:

    • of the workers who purchase lunch from the deli on one Friday, 65% will return to purchase from the deli on the next Friday
    • of the workers who purchase lunch  from the cafe on one Friday, 55% will return to purchase from the cafe on the next Friday.

A transition matrix that can be used to describe this situation is

A. 
       		 B. 
       		  
     
C. 
       		 D. 
       		  
     
E. 
       		    
Show Answers Only

Show Worked Solution


 

MATRICES, FUR1 2020 VCAA 7 MC

A small shopping centre has two coffee shops: Fatima’s (F) and Giorgio’s (G).

The percentage of coffee-buyers at each shop changes from day to day, as shown in the transition matrix .
 


 

On a particular Monday, 40% of coffee-buyers bought their coffees at Fatima’s.

The matrix recursion relation    is used to model this situation.

The percentage of coffee-buyers who are expected to buy their coffee at Giorgio’s on Friday of the same week is closest to

  1. 31%
  2. 32%
  3. 34%
  4. 45%
  5. 68%
Show Answers Only

Show Worked Solution
♦ Mean mark 38%.
 

MATRICES, FUR2-NHT 2019 VCAA 3

The basketball finals will be televised on from 12.00 noon until 4.00 pm.

It is expected that 600 Gillen residents will be watching at any time from 12.00 noon until 4.00 pm.

The remaining 1400 Gillen residents will not be watching from 12.00 noon until 4.00 pm (represented by NotC3).
 


 

Write down the values of and in the boxes provided below.   (2 marks)

 
 
 
Show Answers Only

Show Worked Solution


 


 

 

MATRICES, FUR1-NHT 2019 VCAA 5 MC

A population of birds feeds at two different locations, and , on an island.

The change in the percentage of the birds at each location from year to year can be determined from the transition matrix shown below.
 


 

In 2018, 55% of the birds fed at location .

In 2019, the percentage of the birds that are expected to feed at location is

  1. 32%
  2. 42%
  3. 48%
  4. 58%
  5. 62%
Show Answers Only

Show Worked Solution

MATRICES, FUR2 2010 VCAA 4

The Dinosaurs () and the Scorpions () are two basketball teams that play in different leagues in the same city.

The matrix is the attendance matrix for the first game. This matrix shows the number of people who attended the first Dinosaur game and the number of people who attended the first Scorpion game.
 


 

The number of people expected to attend the second game for each team can be determined using the matrix equation

where is the matrix     

    1. Determine , the attendance matrix for the second game.   (1 mark)

    2. Every person who attends either the second Dinosaur game or the second Scorpion game will be given a free cap. How many caps, in total, are expected to be given away?   (1 mark)

Assume that the attendance matrices for successive games can be determined as follows.

and so on such that

  1. Determine the attendance matrix (with the elements written correct to the nearest whole number) for game 10.   (1 mark)

  2. Describe the way in which the number of people attending the Dinosaurs’ games is expected to change over the next 80 or so games.   (1 mark)

The attendance at the first Dinosaur game was 2000 people and the attendance at the first Scorpion game was 1000 people.

Suppose, instead, that 2000 people attend the first Dinosaur game, and 1800 people attend the first Scorpion game.

  1. Describe the way in which the number of people attending the Dinosaurs’ games is expected to change over the next 80 or so games.   (1 mark)

Show Answers Only
    1.  
  2.  

  3.  

  4.  

Show Worked Solution
a.i.   
   
   

 

a.ii.   


 

b.   
   
   
   

 

c.   

 


 

d.  


 

MATRICES, FUR1 2009 VCAA 7-8 MC

In a country town, people only have the choice of doing their food shopping at a store called Marks () or at a newly opened store called Foodies ().

In the first week that Foodies opened, only 300 of the town’s 800 shoppers did their food shopping at Marks. The remainder did their food shopping at Foodies.
 

Part 1

A state matrix that can be used to represent this situation is
 

A.  

B.  

C.  

D.  

E.  

 

Part 2

A market researcher predicts that

    • of those who do their food shopping at Marks this week, 70% will shop at Marks next week and 30% will shop at Foodies
    • of those who do their food shopping at Foodies this week, 90% will shop at Foodies next week and 10% will shop at Marks.

A transition matrix that can be used to represent this situation is
 

MATRICES, FUR1 2009 VCAA 7-8 MC ab

MATRICES, FUR1 2009 VCAA 7-8 MC cd

MATRICES, FUR1 2009 VCAA 7-8 MC e

Show Answers Only

Show Worked Solution

 


 

MATRICES, FUR1 2010 VCAA 7 MC

A new colony of several hundred birds is established on a remote island. The birds can feed at two locations, A and B. The birds are expected to change feeding locations each day according to the transition matrix
 


 

In the beginning, approximately equal numbers of birds feed at each site each day.

Which of the following statements is not true

A.  70% of the birds that feed at B on a given day will feed at B the next day

B.  60% of the birds that feed at A on a given day will feed at B the next day.

C.  In the long term, more birds will feed at B than at A.

D.  The number of birds that change feeding locations each day will decrease over time to zero

E.  In the long term, some birds will always be found feeding at each location.

Show Answers Only

Show Worked Solution

 

MATRICES, FUR1 2011 VCAA 5-6 MC

Two politicians, Rob and Anna, are the only candidates for a forthcoming election. At the beginning of the election campaign, people were asked for whom they planned to vote. The numbers were as follows.
 

MATRICES, FUR1 2011 VCAA 5-6 MC 1
 

During the election campaign, it is expected that people may change the candidate that they plan to vote for each week according to the following transition diagram.
 

MATRICES, FUR1 2011 VCAA 5-6 MC 2

Part 1

The total number of people who are expected to change the candidate that they plan to vote for one week after the election campaign begins is

A.    

B.   

C.   

D.  

E.  

 

Part 2

The election campaign will run for ten weeks.

If people continue to follow this pattern of changing the candidate they plan to vote for, the expected winner after ten weeks will be

A.   Rob by about 50 votes.

B.   Rob by about 100 votes.

C.   Rob by fewer than 10 votes.

D.   Anna by about 100 votes.

E.   Anna by about 200 votes.

Show Answers Only

Show Worked Solution

 

♦ Mean mark 48%.

 

 

MATRICES, FUR1 2012 VCAA 5 MC

There are two fast-food shops in a country town: Big Burgers (B) and Fast Fries (F).

Every week, each family in the town will purchase takeaway food from one of these shops.

The transition diagram below shows the way families in the town change their preferences for fast food from one week to the next.
 

MATRICES, FUR1 2012 VCAA 5 MC 
 

A transition matrix that provides the same information as the transition diagram is

MATRICES, FUR1 2012 VCAA 5 MC ab

MATRICES, FUR1 2012 VCAA 5 MC cd

MATRICES, FUR1 2012 VCAA 5 MC e

Show Answers Only

Show Worked Solution

MATRICES, FUR1 2012 VCAA 5 MC Answer