Activity networks and critical pathsAQA A-Level Further Maths: Subtopic test

1. 1
   A project has seven activities, $A$ to $G$, shown in an activity-on-node network. The durations in days and the immediate predecessors are: $A$ 3 (none), $B$ 5 (none), $C$ 4 ($A$), $D$ 6 ($A$ and $B$), $E$ 2 ($C$), $F$ 4 ($C$ and $D$) and $G$ 3 ($E$ and $F$).

   (a)

   What is the earliest start time of activity $F$?

   [1 mark]

   • ADay 11
   • BDay 7
   • CDay 15
   • DDay 4

   (b)

   What is the minimum completion time of the project?

   [1 mark]

   • A14 days
   • B15 days
   • C16 days
   • D18 days

   (c)

   Find the float on activity $C$ and explain what it means.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A different project has seven activities, $A$ to $G$. The durations in days and the immediate predecessors are: $A$ 4 (none), $B$ 6 (none), $C$ 5 ($A$), $D$ 3 ($A$), $E$ 4 ($B$ and $C$), $F$ 7 ($D$) and $G$ 2 ($E$ and $F$). The project has a minimum completion time of 16 days.

   (a)

   What is the latest finish time of activity $E$ for the project to finish in 16 days?

   [1 mark]

   • ADay 16
   • BDay 14
   • CDay 13
   • DDay 10

   (b)

   Which activities are not critical?

   [1 mark]

   • A$A$, $D$, $F$ and $G$
   • B$B$ and $C$ only
   • C$B$, $C$ and $E$
   • D$C$ and $E$ only

   (c)

   Activity $C$ is delayed by 2 days. State the effect on the completion time of the project, with working.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A project has seven activities, $A$ to $G$, in an activity-on-node network. The durations in days and the immediate predecessors are: $A$ 5 (none), $B$ 3 (none), $C$ 4 ($A$), $D$ 6 ($A$), $E$ 2 ($B$ and $C$), $F$ 5 ($B$ and $D$) and $G$ 4 ($E$ and $F$).

   (a)

   Find the earliest start times of activities $E$, $F$ and $G$.

   [3 marks]

   (b)

   Find the minimum completion time, the critical path and the float on activity $C$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A building project has eight activities. The durations in days and the immediate predecessors are: $A$ 6 (none), $B$ 4 (none), $C$ 5 ($A$), $D$ 7 ($A$), $E$ 3 ($B$), $F$ 6 ($C$ and $E$), $G$ 4 ($D$) and $H$ 5 ($F$ and $G$).

   (a)

   Carry out a forward pass and a backward pass. State the minimum completion time, the critical activities, and the float on $B$ and on $E$.

   [6 marks]

   (b)

   The client wants the project to finish sooner. Activity $D$ could be shortened by up to 3 days at extra cost. Evaluate this, and suggest a better way to save one day.

   [6 marks]

   Total for question 4: 12 marks

End of questions