Four students, Peggy, Quincy, Radley and Sarah, are grouped together to complete a project. The project is in four parts, labelled \(W, X, Y\) and \(Z\). Each student must complete one part of the project.

The table below shows each student's estimate of the score they will receive if they complete each section.

\begin{array}{|c|c|c|c|c|}
\hline \rule{0pt}{2.5ex}\quad \quad \rule[-1ex]{0pt}{0pt}& \text{Peggy}& \text{Quincy}&\text{Radley}&\text{Sarah} \\
\hline \rule{0pt}{2.5ex}W \rule[-1ex]{0pt}{0pt}& 12 & 19 & 18 & 16 \\
\hline \rule{0pt}{2.5ex}X \rule[-1ex]{0pt}{0pt}& 16 & 15 & 15 & 16 \\
\hline \rule{0pt}{2.5ex}Y \rule[-1ex]{0pt}{0pt}& 10 & 16 & 17 & 15 \\
\hline \rule{0pt}{2.5ex}Z \rule[-1ex]{0pt}{0pt}& 19 & 20 & 18 & 18 \\
\hline
\end{array}

Based on the estimates, which allocation of project parts will maximise the students' group score on the project?

An athletics club needs to select one team of four athletes.

The team is required to have one long jump, one high jump, one shot put and one javelin competitor.

The following table shows the best distances, in metres, for each athlete for each event.

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \ \ \textbf{Athlete}\ \ & \textbf{Long jump} & \textbf{High jump} & \ \  \textbf{Shot put}  \ \ & \quad \textbf{Javelin} \quad \\
\rule[-1ex]{0pt}{0pt}& \textbf{(m)}& \textbf{(m)}& \textbf{(m)}& \textbf{(m)}\\
\hline
\rule{0pt}{2.5ex} \text{Eve} \rule[-1ex]{0pt}{0pt} & \text{4.8} & \text{1.7} & \text{13.1} & \text{40.9} \\
\hline
\rule{0pt}{2.5ex} \text{Harsha} \rule[-1ex]{0pt}{0pt} & \text{4.8} & \text{1.6} & \text{13.9} & \text{39.5} \\
\hline
\rule{0pt}{2.5ex} \text{Shona} \rule[-1ex]{0pt}{0pt} & \text{5.1} & \text{1.8} & \text{14.4} & \text{41.2} \\
\hline
\rule{0pt}{2.5ex} \text{Taylor} \rule[-1ex]{0pt}{0pt} & \text{4.8} & \text{1.7} & \text{12.8} & \text{39.8} \\
\hline
\end{array}

The athletics club will allocate each athlete to one event in order to maximise the total distance that the team jumps and throws.

Which allocation of athlete to event must occur in order to maximise the total distance?
 

Five friends ate fruit for morning tea.

The bipartite graph below shows which types of fruit each friend ate.
 

Which one of the following statements is not true?

1. Only Lee ate pear.
2. Eric and Kai each ate apple.
3. Van ate only strawberry.
4. Quinn and Kai each ate banana.
5. Orange was the most eaten type of fruit.

A cricket team has 11 players who are each assigned to a batting position.

Three of the new players, Alex, Bo and Cameron, can bat in position 1, 2 or 3.

The table below shows the average scores, in runs, for each player for the batting positions 1, 2 and 3.

Each player will be assigned to one batting position.

To which position should each player be assigned to maximise the team’s score? Write your answer in the table below.   (1 mark)

Lee, Mandy, Nola, Oscar and Pieter are each to be allocated one particular task at work.

The bipartite graph below shows which task(s), 1–5, each person is able to complete.
 

 
Each person completes a different task.

Task 4 must be completed by

1. `text(Lee.)`
2. `text(Mandy.)`
3. `text(Nola.)`
4. `text(Oscar.)`
5. `text(Pieter.)`

The bipartite graph below shows the tasks that each of four people is able to undertake.
 

All tasks must be allocated and each person can be allocated one task only.

A valid task allocation is

George, Harriet, Ian, Josie and Keith are a group of five musicians. 

They are forming a band where each musician will fill one position only. 

The following bipartite graph illustrates the positions that each is able to fill.

1. Which musician must play the guitar?   (1 mark)
   

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2. Complete the table showing the positions that the following musicians must fill in the band.   (2 marks)
   

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Four members of a train club, Andrew, Brianna, Charlie and Devi, have joined one or more interest groups for electric, steam, diesel or miniature trains.

The edges of the bipartite graph below show the interest groups that these four train club members have joined.

1. How many of these four members have joined the steam trains interest group?   (1 mark)
   

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2. Which interest group have both Brianna and Charlie joined?   (1 mark)
   

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