Activity networks and precedence tablesEdexcel A-Level Further Maths: Subtopic test

1. 1
   A project has activities P, Q, R, S and T. The immediate predecessors are: P none; Q none; R is P; S is P and Q; T is R and S. The project is to be modelled by an activity network with the activities on the arcs.

   (a)

   What is the minimum number of dummy activities needed?

   [1 mark]

   • A1
   • B0
   • C2
   • D3

   (b)

   Where must the dummy activity be placed?

   [1 mark]

   • AFrom the end of Q to the start of R
   • BFrom the end of R to the start of T
   • CFrom the start of P to the start of Q
   • DFrom the end of P to the start of S

   (c)

   Explain why a dummy activity is needed in this network.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A project is modelled by an activity network with events numbered 1 to 6. The activities, with their start and end events, are: A (1 to 2), B (1 to 3), C (2 to 4), D (3 to 4), E (4 to 5), F (3 to 5) and G (5 to 6). There is also a dummy activity from event 2 to event 3.

   (a)

   What are the immediate predecessors of activity D?

   [1 mark]

   • AB only
   • BA and B
   • CA and C
   • DB and F

   (b)

   What are the immediate predecessors of activity G?

   [1 mark]

   • AD and F
   • BE only
   • CE and F
   • DC, D and F

   (c)

   State the immediate predecessors of activity E and of activity F.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A project has activities A, B, C, D and E. The immediate predecessors are: A none; B none; C is A and B; D is B; E is C and D. The project is to be modelled by an activity network with the activities on the arcs.

   (a)

   Explain why one dummy activity is needed, and state where it must be placed.

   [3 marks]

   (b)

   The project is changed so that E has immediate predecessor C only, and a new activity F has immediate predecessors D and E. Explain whether the dummy activity is still needed, and state where D ends in the new network.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A project is modelled by an activity network with events numbered 1 to 7. The activities, with their start and end events, are: A (1 to 2), B (1 to 3), C (2 to 4), D (3 to 5), E (3 to 4), F (4 to 6), G (5 to 6) and H (6 to 7). There is also a dummy activity from event 2 to event 3.

   (a)

   Complete a precedence table, showing the immediate predecessors, for activities C, D, E, F, G and H.

   [6 marks]

   (b)

   The dummy activity is removed from the network. State the immediate predecessors of D and E in the new network, and explain whether the dummy can be removed without changing the project.

   [6 marks]

   Total for question 4: 12 marks

End of questions