Activity networks and precedence tablesEdexcel International A Level Maths: Subtopic test

1. 1
   A project has five activities, A to E. Activities A and B have no predecessors. C has immediate predecessor A only. D has immediate predecessors A and B. E has immediate predecessors C and D. The project is modelled by an activity network with activities on arcs.

   (a)

   Which activity can start as soon as A has finished, even if B has not yet finished?

   [1 mark]

   • AC and D
   • BD only
   • CC only
   • DE only

   (b)

   A student draws D starting at the event where B finishes, with no dummy, and C starting at the event where A finishes. What is wrong with this network?

   [1 mark]

   • AD would not depend on A
   • BC would depend on B as well as A
   • CE would not depend on C
   • DB would depend on A

   (c)

   Explain why the correct network needs a dummy activity, and state where the dummy is drawn.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A project has six activities, P to U. P and Q have no predecessors. R has immediate predecessor P only. S has immediate predecessors P and Q. T has immediate predecessor Q only. U has immediate predecessors R, S and T. The project is modelled by an activity-on-arc network.

   (a)

   Which activities have more than one immediate predecessor?

   [1 mark]

   • AS only
   • BR and T
   • CS, T and U
   • DS and U

   (b)

   What is the minimum number of dummy activities needed in an activity-on-arc network for this project?

   [1 mark]

   • A1
   • B2
   • C3
   • D4

   (c)

   Explain why S needs dummy activities but R and T do not.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An activity network has start event 1 and finish event 6. Its arcs are: A from event 1 to event 2; B from 1 to 3; C from 2 to 4; a dummy from 2 to 3; D from 3 to 4; E from 3 to 5; F from 4 to 6; G from 5 to 6.

   (a)

   Write down the immediate predecessors of each of the activities A, B, C, D, E, F and G.

   [3 marks]

   (b)

   A new activity H is added, with immediate predecessors C and E only. F and G keep their predecessors. Explain why H cannot simply start at event 4, and describe how the network must be redrawn.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A project has activities A to G. A, B and C have no predecessors. D has immediate predecessor A only. E has immediate predecessors A and B. F has immediate predecessors B and C. G has immediate predecessors D, E and F, and is the last activity. The project is modelled by an activity-on-arc network with a single start event, event 1.

   (a)

   Describe a valid network for this project using exactly 3 dummy activities, by stating the start event and finish event of every activity and dummy.

   [6 marks]

   (b)

   A further activity H is added, with immediate predecessors D and F only. H is also a last activity, and G must still follow D, E and F. Describe the changes needed to your network from (a) and state how many dummy activities it now has.

   [6 marks]

   Total for question 4: 12 marks

End of questions