| Exam Board | Edexcel |
|---|---|
| Module | FD1 AS (Further Decision 1 AS) |
| Year | 2018 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.8 This is a standard textbook exercise in critical path analysis requiring routine application of well-defined algorithms: drawing an activity network from a precedence table, calculating early/late times using forward and backward passes, and identifying critical activities. While it requires careful attention to detail and understanding of dummies, it involves no problem-solving insight or novel reasoning—just methodical application of the standard CPA procedure taught in Decision Maths. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation |
| Activity | Time taken (days) | Immediately preceding activities |
| A | 5 | - |
| B | 8 | - |
| C | 4 | - |
| D | 14 | A |
| E | 10 | A |
| F | 3 | B, C, E |
| G | 7 | C |
| H | 5 | D, F, G |
| I | 7 | H |
| J | 9 | H |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Any three activities of D, E, G, J added with at least one dummy | M1 | |
| D, E, G and first dummy added correctly with arrows (first part of network correct) | A1 | |
| J and second dummy added correctly with arrows (second part of network correct) | A1 | SC: If M1A0A0 but only error is missing arrows, award M1A1A0; award M1A1A0 for correct diagram with more than two dummies |
| All top boxes complete, numbers increasing in direction of arrows (dependent on all four activities D,E,G,J added) | M1 | Condone lack of additional event node for J |
| All bottom boxes complete, numbers decreasing in opposite direction of arrows | M1 | Dependent on all four activities D,E,G,J added; condone lack of additional event node for J |
| Cso (including diagram) — must contain exactly 8 early and late event times and only two correct dummies with one finish | A1 | Note: some candidates may place dummy before activity I, giving both values as 24 at that node |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| The critical activities are A, D, H and J | B1 | Cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| No effect (as G is not one of the critical activities) | B1 | Explanation that there is no effect on completion time as G is not critical |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Activity C is the only affected activity | M1 | Use model to deduce C is the only activity affected |
| It can now start 4 days later at time 12 (rather than time 8) or finish as late as time 16 | A1 | Correct answer with a relevant time stated; e.g. finish at time 16 or start at time 12 |
## Question 3:
### Parts (a) and (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| Any three activities of D, E, G, J added with at least one dummy | M1 | |
| D, E, G and first dummy added correctly with arrows (first part of network correct) | A1 | |
| J and second dummy added correctly with arrows (second part of network correct) | A1 | SC: If M1A0A0 but only error is missing arrows, award M1A1A0; award M1A1A0 for correct diagram with more than two dummies |
| All top boxes complete, numbers increasing in direction of arrows (dependent on all four activities D,E,G,J added) | M1 | Condone lack of additional event node for J |
| All bottom boxes complete, numbers decreasing in opposite direction of arrows | M1 | Dependent on all four activities D,E,G,J added; condone lack of additional event node for J |
| Cso (including diagram) — must contain exactly 8 early and late event times and only two correct dummies with one finish | A1 | Note: some candidates may place dummy before activity I, giving both values as 24 at that node |
### Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| The critical activities are A, D, H and J | B1 | Cao |
### Part (d)(i)
| Answer | Mark | Guidance |
|--------|------|----------|
| No effect (as G is not one of the critical activities) | B1 | Explanation that there is no effect on completion time as G is not critical |
### Part (d)(ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Activity C is the only affected activity | M1 | Use model to deduce C is the only activity affected |
| It can now start 4 days later at time 12 (rather than time 8) or finish as late as time 16 | A1 | Correct answer with a relevant time stated; e.g. finish at time 16 or start at time 12 |
---3.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Time taken (days) & Immediately preceding activities \\
\hline
A & 5 & - \\
\hline
B & 8 & - \\
\hline
C & 4 & - \\
\hline
D & 14 & A \\
\hline
E & 10 & A \\
\hline
F & 3 & B, C, E \\
\hline
G & 7 & C \\
\hline
H & 5 & D, F, G \\
\hline
I & 7 & H \\
\hline
J & 9 & H \\
\hline
\end{tabular}
\end{center}
The table above shows the activities required for the completion of a building project. For each activity, the table shows the time it takes, in days, and the immediately preceding activities. Each activity requires one worker. The project is to be completed in the shortest possible time.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{3e853c6d-e90e-4a09-b990-1c2c146b54e1-4_486_1161_1194_551}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
Figure 2 shows a partially completed activity network used to model the project. The activities are represented by the arcs and the number in brackets on each arc is the time taken, in days, to complete the corresponding activity.
\begin{enumerate}[label=(\alph*)]
\item Add the missing activities and necessary dummies to Diagram 1 in the answer book.
\item Complete Diagram 1 in the answer book to show the early event times and the late event times.
\item State the critical activities.
At the beginning of the project it is decided that activity G is no longer required.
\item Explain what effect, if any, this will have on
\begin{enumerate}[label=(\roman*)]
\item the shortest completion time of the project if activity G is no longer required,
\item the timing of the remaining activities.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel FD1 AS 2018 Q3 [10]}}