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Financial Maths, 2ADV M1 2018 HSC 16c

Kara deposits an amount of $300 000 into an account which pays compound interest of 4% per annum, added to the account at the end of each year. Immediately after the interest is added, Kara makes a withdrawal for expenses for the coming year. The first withdrawal is . Each subsequent withdrawal is 5% greater than the previous one.

Let    be the amount in the account after the th withdrawal.

  1. Show that  .  (1 mark)

  2. Show that  .  (1 mark)

  3. Show that there will be money in the account when
     
      (3 marks)

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Show Worked Solution

♦ Mean mark 47%.

i.  
 
   
   

 

♦ Mean mark part (ii) 30%.

ii.  
   
   

 

iii.  
   
 
   

 

♦♦♦ Mean mark part (iii) 8%.

Probability, 2ADV S1 2018 HSC 16b

A game involves rolling two six-sided dice, followed by rolling a third six-sided die. To win the game, the number rolled on the third die must lie between the two numbers rolled previously. For example, if the first two dice show 1 and 4, the game can only be won by rolling a 2 or 3 with the third die.

  1. What is the probability that a player has no chance of winning before rolling the third die?   (2 marks)

  2. What is the probability that a player wins the game?   (2 marks)

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i.   

♦ Mean mark 40%.
COMMENT: Constructing the full sample space is a critical step here..


 

 
 

 

ii.   

♦♦♦ Mean mark 7%.

 
 
 

Calculus, 2ADV C3 2018 HSC 16a

A sector with radius 10 cm and angle    is used to form the curved surface of a cone with base radius cm, as shown in the diagram.
 


 

The volume of a cone of radius and height is given by  .

  1. Show that the volume, cm³, of the cone described above is given by
     
          .   (1 mark)

  2. Show that  .   (2 marks)

  3. Find the exact value of    for which is a maximum.   (3 marks)

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i.   


 

♦ Mean mark (ii) 45%.

ii.  
 
   
   
   

 

iii. 

♦♦ Mean mark (iii) 23%.

 


 

 

Trigonometry, 2ADV T3 2018 HSC 15a

The length of daylight, , is defined as the number of hours from sunrise to sunset, and can be modelled by the equation

,

where is the number of days after 21 December 2015, for  .

  1. Find the length of daylight on 21 December 2015.   (1 mark)

  2. What is the shortest length of daylight?  (1 mark)

  3. What are the two values of    for which the length of daylight is 11?  (2 marks)

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i.   

 

 

ii.   

♦ Mean mark 43%.


 

 

 

iii.   


 

   
 
     

 

Probability, 2ADV S1 2018 HSC 14e

Two machines, and , produce pens. It is known that 10% of the pens produced by machine are faulty and that 5% of the pens produced by machine are faulty.

  1. One pen is chosen at random from each machine.

     

    What is the probability that at least one of the pens is faulty?  (1 mark)

  2. A coin is tossed to select one of the two machines. Two pens are chosen at random from the selected machine.

     

    What is the probability that neither pen is faulty?  (2 marks)

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i.  
   
   
   

 

ii.   

♦ Mean mark 48%.

Financial Maths, 2ADV M1 2018 HSC 14d

An artist posted a song online. Each day there were    downloads, where  is the number of days after the song was posted.

  1. Find the number of downloads on each of the first 3 days after the song was posted.  (1 mark)

  2. What is the total number of times the song was downloaded in the first 20 days after it was posted?  (2 marks)

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i.   

 

ii. 

♦ Mean mark 38%.

Trigonometry, 2ADV T1 2018 HSC 14a

In    has length 3, has length 6 and is 60°. The point is chosen on side    so that    bisects . The length    is .
 


 

  1. Find the exact value of the area of  .  (1 mark)

  2. Hence, or otherwise, find the exact value of .  (2 marks)

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i.   

  ²

 

ii. 

♦ Mean mark 37%.

 

Probability, 2UG 2018 HSC 30d

A game consists of two tokens being drawn at random from a barrel containing 20 tokens. There are 17 tokens labelled 10 cents and 3 tokens labelled $2. The player wins the total value of the two tokens drawn.

  1. Complete the probability tree by writing the missing probabilities in the boxes.  (2 marks)
     

     
  2. Considering that the game costs $1 to play, calculate the financial expectation of the game.  (3 marks)
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  1.  
Show Worked Solution
i.   

 

ii.   

♦♦ Mean mark part (ii) 27%.
COMMENT: Financial expectation included here (one example only in database) as it is possible to argue that it is an application of expectation.

Measurement, STD2 M6 2018 HSC 30c

The diagram shows two triangles.

Triangle is right-angled, with    and  .

In triangle    and  . The area of triangle    is 30 cm².
 

 
What is the value of , correct to one decimal place?  (3 marks)

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Show Worked Solution

♦ Mean mark 39%.

 

 

 
 

Measurement, STD2 M1 2018 HSC 30a

A cylindrical water tank has a radius of 9 metres and a capacity of 1.26 megalitres.
 

What is the height of the water tank? Give your answer in metres, correct to two decimal places.  (3 marks)

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³³

♦ Mean mark 48%.

 
 

 

 
 

Algebra, STD2 A4 2018 HSC 29c

When people walk in snow, the depth ( cm) of each footprint depends on both the area ( cm²) of the shoe sole and the weight of the person. The graph shows the relationship between the area of the shoe sole and the depth of the footprint in snow, for a group of people of the same weight.
 


 

  1. The graph is a hyperbola because is inversely proportional to . The point lies on the hyperbola.

     

    Find the equation relating and .  (2 marks)

  2. A man from this group walks in snow and the depth of his footprint is 4 cm.

     

    Use your equation from part (i) to calculate the area of his shoe sole.  (1 mark)

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  2. ²
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i.     

♦♦ Mean mark part (i) 22%.

 

 

♦♦ Mean mark part (ii) 33%.

ii.   
 
    ²

Algebra, STD2 A1 2018 HSC 28e

Sophie is driving at 70 km/h. She notices a branch on the road ahead and decides to apply the brakes. Her reaction time is 1.5 seconds. Her braking distance ( metres) is given by  , where  is speed in km/h.

Stopping distance can be calculated using the following formula
 


 

What is Sophie’s stopping distance, to the nearest metre?  (3 marks)

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Show Worked Solution
 
 

 

♦ Mean mark 46%.

Financial Maths, STD2 F4 2018* HSC 28d

Yanika opens a new credit card account, with interest and fees as shown.
 

Interest

    • Compound interest calculated daily at the rate 12.41% p.a.
    • No interest-free period

Fees

    • $0 for online repayments
    • $3 for repayments in cash (fee added to balance immediately after repayment)
        

Yanika makes a single purchase of $849 with the credit card.

  1. Show that the balance owing on the credit card 24 days after making the purchase is $855.95 .  (2 marks)

  2. Yanika makes her first repayment 24 days after making the purchase. She makes a cash repayment of $450.

     

    What is the balance owing on the credit card immediately after her repayment is made and the repayment fee has been charged?  (1 mark)

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i.   

♦ Mean mark part (i) 48%, part (ii) 49%.

 
 
 

 

ii.   
   

Measurement, STD2 M7 2018 HSC 26g

A field diagram of a block of land has been drawn to scale. The shaded region is covered in grass.
 

 
The actual length of is 24 m.

  1. If the length of on the field diagram is 8 cm, what is the scale of the diagram?  (1 mark)

  2. How much fertiliser would be needed to fertilise the grassed area    at the rate of 26.5 g /m²?  (3 marks)

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Show Worked Solution

♦♦ Mean mark 32%.

i.   
 
 

 

ii.   

²
 

²
 

 

Probability, STD2 S2 2018 HSC 26f

A toy shop sells buckets and spades separately. Buckets are available in one of six colours. Spades are also available in one of the same six colours.

Abdul wants to buy a bucket-and-spade set where the bucket and spade are of different colours.

How many different bucket-and-spade sets are possible for Abdul to buy?  (1 mark)

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Show Worked Solution

♦ Mean mark 35%.

 
 

Statistics, STD2 S1 2018 HSC 26e

A cumulative frequency table for a data set is shown.

What is the interquartile range of this data set?   (2 marks)

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♦♦ Mean mark 27%.

 

 

Statistics, STD2 S1 2018 HSC 26d

The graph displays the mean monthly rainfall in Sydney and Perth.
 


 

  1. For how many months is the mean monthly rainfall higher in Perth than in Sydney?  (1 mark)

  2. For which of the two cities is the standard deviation of the mean monthly rainfall smaller? Justify your answer WITHOUT calculations.  (1 mark)

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i.   

♦ Mean mark part (ii) 38%.
COMMENT: Extremely volatile result between parts with part (i) producing a 91% mean mark.

 

ii.   

Probability, STD2 S2 2018 HSC 26a

Jeremy rolled a biased 6-sided die a number of times. He recorded the results in a table.
  

 

What is the relative frequency of rolling a 3?  (1 mark)

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♦ Mean mark 40%.

 
 

Measurement, STD2 M1 2018 HSC 24 MC

The coordinates of city A are (39°N, 75°W). City B lies on the same longitude and is 5700 km south of city A.

What is the latitude of city B, given the earth's radius is 6400 km?

  1. 51°N
  2. 51°S
  3. 12°N
  4. 12°S
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Show Worked Solution

♦ Mean mark 45%.
COMMENT: If the earth’s radius is stated, this past question is arguably within the scope of the new syllabus.

 

   

Financial Maths, STD2 F4 2018 HSC 19 MC

The table shows the compounded values of $1 at different interest rates over different periods.
 

 
Amy hopes to have $21 000 in 2 years to buy a car. She opens an account today which pays interest of 4% pa, compounded quarterly.

Using the table, which expression calculates the minimum single sum that Amy needs to invest today to ensure she reaches her savings goal?

  1. 21 000 × 1.0816
  2. 21 000 ÷ 1.0816
  3. 21 000 × 1.0829
  4. 21 000 ÷ 1.0829
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♦♦ Mean mark 33%.

Financial Maths, STD2 F1 2018 HSC 15 MC

Sam is the driver at fault in a car accident.

Which of the following is covered by Sam's compulsory third-party (CTP) insurance?

  1. Repairs to Sam's car
  2. Injury to the other driver
  3. Damage to the other driver's car
  4. Cost of repairing a building damaged in the accident
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♦♦ Mean mark 34%.

Financial Maths, STD2 F1 2018 HSC 14 MC

To determine the retail price of an item, a shop owner increases its cost price by 30%. In a sale, the retails price is reduced by 30% to give the sale price.

How does the sale price compare to the cost price?

  1. The sale price is less than the cost price.
  2. The sale price is the same as the cost price.
  3. The sale price is more than the cost price.
  4. It is impossible to compare without knowing the cost price.
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Show Worked Solution

♦ Mean mark 50%.

Plane Geometry, EXT1 2018 HSC 14c

In triangle is perpendicular to . Side has length , side has length and side has length . A quadrant of a circle of radius , centered at , is constructed. The arc meets side at . It touches the side at , and meets side at . The interval is perpendicular to .
 


 

  1. Show that and are similar.  (1 mark)
  2. Show that
     
    .  (1 mark)
     

  3. From , a line perpendicular to is drawn to meet at , forming the right-angled triangle . A new quadrant is constructed in triangle touching side at . The process is then repeated indefinitely.
     

                
     

  4. Show that the limiting sum of the areas of all the quadrants is
     
      (4 marks)
     

  5. Hence, or otherwise, show that
     
    .  (1 mark)

 

 

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(i)   


 


 

 

(ii)
   
   
   


(iii) 

♦♦♦ Mean mark part (iii) 19%.

 

 
 
   
 
   
   
 

 

 
 

 

 

(iv) 

♦♦ Mean mark part (iv) 21%.

Binomial, EXT1 2018 HSC 14b

  1. By considering the expansions of and show that
     

     
                                .  (3 marks)
     

  2. There are 23 people who have applied to be selected for a committee of 4 people.
     
    The selection process starts with Selector choosing a group of at least 4 people from the 23 people who applied.
     
    Selector then chooses the 4 people to be on the committee from the group Selector has chosen.
     
    In how many ways could this selection process be carried out?  (2 marks)

 

 

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(i)   


 


 

♦ Mean mark 46%.

 

  

 


 


 

 

(ii) 

♦♦ Mean mark 32%.


 

Plane Geometry, EXT1 2018 HSC 14a

The diagram shows quadrilateral    and the bisectors of the angles at  and . The bisectors at  and  intersect at the point . The bisectors at  and meet at . The bisectors at and meet at . The bisectors at  and meet at .
 

 
Copy or trace the diagram into your writing booklet.

Show that    is a cyclic quadrilateral.  (3 marks)

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Show Worked Solution

Mean mark 51%.

 

 

 
 
 

 

Functions, EXT1 F1 2018 HSC 13b

The diagram shows the graph  , for all real .
 


 

Consider the function  , for

The function    has an inverse. (Do NOT prove this.)

  1.  State the domain and range of    (2 marks)

  2.  Sketch the graph    (1 mark)

  3.  Find an expression for    (3 marks)

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i.   

♦♦ Mean mark part (i) 31%.


 

 

♦ Mean mark part (ii) 43%.

ii.  

 

iii. 

♦ Mean mark part (iii) 45%.

 

 

Mechanics, EXT2* M1 2018 HSC 13c

An object is projected from the origin with an initial velocity of  at an angle    to the horizontal. The equations of motion of the object are

  (Do NOT prove this.)

 

  1. Show that when the object is projected at an angle  , the horizontal range is

     

           (2 marks)

  2. Show that when the object is projected at an angle  , the horizontal range is also 

     

         .  (1 mark)

  3. The object is projected with initial velocity to reach a horizontal distance , which is less than the maximum possible horizontal range. There are two angles at which the object can be projected in order to travel that horizontal distance before landing.

     

    Let these angles be   and  , where 

     

    Let    be the maximum height reached by the object when projected at the angle to the horizontal.

     

    Let    be the maximum height reached by the object when projected at the angle to the horizontal.
     
         
     
    Show that the average of the two heights, , depends only on and .  (3 marks)

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i.   

 

 
 
 

 

ii. 

 
 

 

iii. 


  

 
 
 

 

♦ Mean mark 44%.
 

 
 
 
 

 

Quadratic, EXT1 2018 HSC 12e

The points    and    lie on the parabola  . The focus of the parabola is    and the tangents at    and    intersect at  . (Do NOT prove this.)

The tangents at    and    meet the -axis at    and    respectively, as shown.
 

 

  1. Show that  .  (2 marks)
  2. Explain why    are concyclic points.  (1 mark)
  3. Show that the diameter of the circle through    and    has length
     
    .  (2 marks)

 

 

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Show Worked Solution

(i)   

 
 

 


 

 
 

  

 

(ii)   

♦ Mean mark 37%.

 


 


 

   

 

(iii) 

♦ Mean mark 44%.

 
 
 
 
 
 

Calculus, EXT1 C2 2018 HSC 12c

Let  .

  1. Show that    (1 mark)

  2. Hence, or otherwise, prove
     
    .  (1 mark)

  3. Hence, sketch
     
    .  (1 mark)

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i.   

 

ii. 

♦ Mean mark (ii) 37%.

 
   

 

iii. 

♦ Mean mark (iii) 40%.

 

Networks, STD2 N3 EQ-Bank 19

An engineering project requires activities A to G to be completed, as shown in the table.
 


 

The minimum completion time for the project is 25 days and the critical path includes activities B, D, E and F. The float for activity G is two days and the float for activity C is four days.

Find the possible duration for each of the activities A, C, F and G. Include a network diagram in your answer.  (5 marks)

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Show Worked Solution


 

 

 
 

 

 
 

 


 

Networks, STD2 N3 EQ-Bank 18

An engineering project requires activities A to G to be completed, as shown in the table.
 


 

The minimum completion time for the project is 40 weeks and the critical path includes activities A, C, E and G. The float for activity F is six weeks and the float for activity D is 9 weeks.

Find the possible duration for each of the activities B, D, F and G. Include a network diagram in your answer.  (5 marks)

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Show Worked Solution

 

 
 

 

 
 

 

 

Mechanics, EXT2* M1 2018 HSC 10 MC

A particle is moving in simple harmonic motion. The displacement of the particle is    and its velocity, , is given by the equation  , where and are constants.

The particle is initially at  .

Which function, in terms of time , could represent the motion of the particle?

A.     

B.     

C.     

D.     

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♦♦ Mean mark 33%.

   

   
 

Networks, STD2 N3 2007 FUR2 4

A community centre is to be built on the new housing estate.

Nine activities have been identified for this building project.

The directed network below shows the activities and their completion times in weeks.

 

  1. Determine the minimum time, in weeks, to complete this project.  (1 mark)

  2. Determine the float time, in weeks, for activity .  (2 marks)

The builders of the community centre are able to speed up the project.

Some of the activities can be reduced in time at an additional cost.

The activities that can be reduced in time are , , , and .

  1. Which of these activities, if reduced in time individually, would not result in an earlier completion of the project?  (1 mark)

The owner of the estate is prepared to pay the additional cost to achieve early completion.

The cost of reducing the time of each activity is $5000 per week.

The maximum reduction in time for each one of the five activities, , , , , , is weeks.

  1. Determine the minimum time, in weeks, for the project to be completed now that certain activities can be reduced in time.  (1 mark)

  2. Determine the minimum additional cost of completing the project in this reduced time.  (1 mark)

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a.  
 

 

♦ Mean mark of all parts (combined) 40%.
 

 

b.   
 
 

 

c.  


 

d.  

 

e.   
   

Networks, STD2 N3 2006 FUR2 3

The five musicians are to record an album. This will involve nine activities.

The activities and their immediate predecessors are shown in the following table.

The duration of each activity is not yet known.
 

NETWORKS, FUR2 2006 VCAA 31
 

  1. Use the information in the table above to complete the network below by including activities ,  and .  (2 marks)
     

NETWORKS, FUR2 2006 VCAA 32
 

There is only one critical path for this project.

  1. How many non-critical activities are there?  (1 mark)

The following table gives the earliest start times (EST) and latest start times (LST) for three of the activities only. All times are in hours.


Networks, FUR2 2006 VCAA 3_3

  1. Write down the critical path for this project.  (1 mark)

The minimum time required for this project to be completed is 19 hours.

  1. What is the duration of activity ?  (1 mark)

The duration of activity is 3 hours.

  1. Determine the maximum combined duration of activities and .  (1 mark) 
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  1.  
    networks-fur2-2006-vcaa-3-answer
Show Worked Solution
a.    networks-fur2-2006-vcaa-3-answer

 

b.  


 

 

c.   

♦ Mean mark of parts (c)-(e) (combined) was 36%.

 

d.   
   

 

e.  

♦♦ MARKER’S COMMENT: Many students incorrectly answered 9 hours in part (e).

Networks, STD2 N3 2013 FUR2 2

A project will be undertaken in the wildlife park. This project involves the 13 activities shown in the table below. The duration, in hours, and predecessor(s) of each activity are also included in the table.


NETWORKS, FUR2 2013 VCAA 21
 

Activity is missing from the network diagram for this project, which is shown below.

 
NETWORKS, FUR2 2013 VCAA 22
 

  1. Complete the network diagram above by inserting activity .  (1 mark)
  2. Determine the earliest starting time of activity .  (1 mark)

  3. Given that activity  is not on the critical path

     

    1. write down the activities that are on the critical path in the order that they are completed  (1 mark)

    2. find the latest starting time for activity .  (1 mark)

  4. Consider the following statement.

     

    ‘If the time to complete just one of the activities in this project is reduced by one hour, then the minimum time to complete the entire project will be reduced by one hour.’

    Explain the circumstances under which this statement will be true for this project.  (1 mark)

  5. Assume activity  is reduced by two hours.
    What will be the minimum completion time for the project?  (1 mark)

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a.

networks-fur2-2013-vcaa-2-answer

b. 

c.i.  

c.ii. 

d. 
     

e. 

Show Worked Solution
a.    networks-fur2-2013-vcaa-2-answer

 

b.  


 

c.i.   

♦♦ Mean mark of parts (c)-(e) (combined) was 40%.
 

c.ii.  

 
 

d.  

MARKER’S COMMENT: Most students struggled with part (d).


 

e.  

Networks, STD2 N3 2012 FUR2 2

Thirteen activities must be completed before the produce grown on a farm can be harvested. 

The directed network below shows these activities and their completion times in days.
 


 

  1. Determine the earliest starting time, in days, for activity .  (1 mark)

  2. An activity with zero duration starts at the end of activity .

     

    Explain why this activity is used on the network diagram.  (1 mark)

  3. Determine the earliest starting time, in days, for activity .  (1 mark)

  4. In order, list the activities on the critical path.  (1 mark)

  5. Determine the latest starting time, in days, for activity .  (1 mark)

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Show Worked Solution
a.   
   
♦ Mean mark of all parts (combined) 47%.

 

b.  


 

♦♦ “Few students” were able to correctly deal with the zero duration activity in part (c).

c.  
 

  

 

d.  
 


 

e.  

MARKER’S COMMENT: A correct calculation based on an incorrect critical path in part (d) gained a consequential mark here. Show your working!.


 

 

Networks, STD2 N3 2009 FUR2 4

A walkway is to be built across the lake.

Eleven activities must be completed for this building project.

The directed network below shows the activities and their completion times in weeks.
 

NETWORKS, FUR2 2009 VCAA 4
 

  1. What is the earliest start time for activity E?  (1 mark)

  2. Write down the critical path for this project.  (1 mark)

  3. The project supervisor correctly writes down the float time for each activity that can be delayed and makes a list of these times.

     

    Determine the longest float time, in weeks, on the supervisor’s list.  (1 mark)

A twelfth activity, L, with duration three weeks, is to be added without altering the critical path.

Activity L has an earliest start time of four weeks and a latest start time of five weeks.
 

NETWORKS, FUR2 2009 VCAA 4
 

  1. Draw in activity L on the network diagram above.  (1 mark)
  2. Activity L starts, but then takes four weeks longer than originally planned.

     

    Determine the total overall time, in weeks, for the completion of this building project.  (1 mark)

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  4.  
    NETWORKS, FUR2 2009 VCAA 4 Answer
Show Worked Solution

a.  

♦ Mean mark of all parts (combined): 44%.

 

b. 
 

 

 

c.   


 

d.    NETWORKS, FUR2 2009 VCAA 4 Answer

 

e.  

Networks, STD2 N3 2011 FUR1 7 MC

Andy, Brian and Caleb must complete three activities in total (K, L and M)

The table shows the person selected to complete each activity, the time it will take to complete the activity in minutes and the immediate predecessor for each activity.
 

 
All three activities must be completed in a total of 40 minutes.

The instant that Andy starts his activity, Caleb gets a telephone call.

The maximum time, in minutes, that Caleb can speak on the telephone before he must start his allocated activity is

A.   

B.   

C.   

D.   

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Show Worked Solution

♦♦ Mean mark 33%.
MARKER’S COMMENT: Many students incorrectly answered the earliest starting time, C.

Networks, STD2 N3 2014 FUR1 8 MC

Which one of the following statements about critical paths is true?

  1. There can be only one critical path in a project.
  2. A critical path will always include the activity that takes the longest time to complete.
  3. Reducing the time of any activity on a critical path for a project will always reduce the minimum completion time for the project.
  4. If there are no other changes, increasing the time of any activity on a critical path will always increase the completion time of a project.
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♦ Mean mark 40%.

 

Networks, STD2 N3 SM-Bank 49

The directed graph below shows the sequence of activities required to complete a project.

The time to complete each activity, in hours, is also shown.
 


 

  1. Find the earliest starting time, in hours, for activity .   (2 marks)

To complete the project in minimum time, some activities cannot be delayed.

  1. Calculate the number of activities that cannot be delayed.  (1 mark)
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i.   
 


 

 
 

 

ii.   

Networks, STD2 N3 SM-Bank 47

The directed graph below shows the sequence of activities required to complete a project.

All times are in hours.
 


 

  1.  Find the number of activities that have exactly two immediate predecessors. (1 mark)

  2. Identify the critical path for this project. (3 marks)
  3. If Activity E is reduced by one hour, identify the two new critical paths. (1 mark)

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i.    

 

ii.   
 


 

 

iii.   

Networks, STD2 N3 SM-Bank 48

The network shows the activities that are needed to complete a particular project.
 

networks-fur1-2009-vcaa-5-6-mc
 

  1. Find the total number of activities that need to be completed before activity L can begin.   (1 mark)

The duration of every activity is initially 5 hours. 

  1. If the completion times of both activity F and activity K are reduced to 3 hours each, calculate the effect on the completion time for the project.   (2 marks)

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i.   

 

ii.   
 


 

Networks, STD2 N3 2008 FUR1 8-9 MC

The network below shows the activities that are needed to finish a particular project and their completion times (in days).
 

networks-fur1-2008-vcaa-8-mc

 
Part 1

The earliest start time for Activity K, in days, is

A.     

B.   

C.   

D.   

 

Part 2

This project currently has one critical path.

A second critical path, in addition to the first, would be created by

A.   increasing the completion time of D by 7 days.

B.   increasing the completion time of G by 1 day.

C.   increasing the completion time of I by 2 days.

D.   decreasing the completion time of C by 1 day.

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♦♦ Mean mark of Part 2 was 35%.


 

Networks, FUR2 2007 VCE 3

As an attraction for young children, a miniature railway runs throughout a new housing estate.

The trains travel through stations that are represented by nodes on the directed network diagram below.

The number of seats available for children, between each pair of stations, is indicated beside the corresponding edge.
 

NETWORKS, FUR2 2007 VCAA 3

 
Cut 1, through the network, is shown in the diagram above.

  1. Determine the capacity of Cut 1.  (1 mark)
  2. Determine the maximum number of seats available for children for a journey that begins at the West Terminal and ends at the East Terminal.  (1 mark)

On one particular train, 10 children set out from the West Terminal.

No new passengers board the train on the journey to the East Terminal.

  1. Determine the maximum number of children who can arrive at the East Terminal on this train.  (1 mark)
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a.  

♦♦ Mean mark for all parts (combined) was 33%.
MARKER’S COMMENT: A common error was counting the edge with “10” in the reverse direction (in part a).

 

b.    networks-fur2-2007-vcaa-3-answer
 
 

 

c.  


  

Networks, FUR2 2013 VCE 3

The rangers at the wildlife park restrict access to the walking tracks through areas where the animals breed.

The edges on the directed network diagram below represent one-way tracks through the breeding areas. The direction of travel on each track is shown by an arrow. The numbers on the edges indicate the maximum number of people who are permitted to walk along each track each day.
 

NETWORKS, FUR2 2013 VCAA 31
 

  1. Starting at , how many people, in total, are permitted to walk to each day?  (1 mark)

One day, all the available walking tracks will be used by students on a school excursion.

The students will start at and walk in four separate groups to .

Students must remain in the same groups throughout the walk.

    1. Group 1 will have 17 students. This is the maximum group size that can walk together from to .

      Write down the path that group 1 will take.  (1 mark)

    2. Groups 2, 3 and 4 will each take different paths from to .

      Complete the six missing entries shaded in the table below.  (2 marks)

       


      NETWORKS, FUR2 2013 VCAA 32

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    2.  
      Networks, FUR2 2013 VCAA 3_2 Answer1
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a.   
   
   
♦ Mean mark of all parts (combined) was 41%.

 

 

b.i.  

 

b.ii.   

 

 
  

Networks, FUR2 2013 VCAA 3_2 Answer1

Networks, FUR1 2017 VCE 8 MC

The flow of oil through a series of pipelines, in litres per minute, is shown in the network below.
 

 
The weightings of three of the edges are labelled .

Four cuts labelled A–D are shown on the network.

The maximum flow of oil from the source to the sink, in litres per minute, is given by the capacity of

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♦ Mean mark 44%.


 

Networks, STD2 N3 SM-Bank 36

In the network below, the values on the edges give the maximum flow possible between each pair of vertices. The arrows show the direction of flow. A cut that separates the source from the sink in the network is also shown.
 

vcaa-networks-fur1-2010-6-7

 

  1. Calculate the capacity of the cut shown in the diagram.  (1 mark)

  2. Calculate the maximum flow between source and sink.  (2 marks)

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i.   

♦ Mean mark part (a) 50%.
COMMENT: A quarter of students incorrectly included the “8” which is flowing in the opposite direction.

 

ii.

vcaa-networks-fur1-2010-6-7i

♦♦ Mean mark part (b) 24%.