| Exam Board | Edexcel |
|---|---|
| Module | FD1 (Further Decision 1) |
| Year | 2021 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Identify guaranteed critical activities |
| Difficulty | Moderate -0.5 This is a standard Critical Path Analysis question from Further Maths Decision 1. Part (a) requires reading a network diagram, part (b) is routine network construction with dummies, and part (c) asks for conceptual understanding of critical activities. While it requires careful work and understanding of CPA conventions, it follows standard textbook patterns with no novel problem-solving required. Slightly easier than average A-level due to being methodical rather than requiring insight. |
| Spec | 7.05a Critical path analysis: activity on arc networks |
| Activity | Immediately preceding activities |
| I | D, E, G, H |
| J | D, E, G, H |
| K | E, G, H |
| L | I, J, K |
| M | J, K |
| N | J, K |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Either row G or H correct: G preceded by B, F; H preceded by B, C, F | B1 | 1.1b |
| All rows correct (condone blanks in A, B, C rows) | B1 | 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| At least five activities (labelled on arc), at least two dummies placed | M1 | 2.1 |
| Activities I, J, K and first dummy + arrow dealt with correctly | A1 | 1.1b |
| Activities L, M, N and a second dummy + arrows dealt with correctly | A1 | 1.1b |
| cso – all arrows present for every activity, exactly one finish, exactly three dummies | A1 | 1.1b; note M and N could be interchanged |
| Answer | Marks | Guidance |
|---|---|---|
| Activity | I | J |
| IPA | D, E, G, H | D, E, G, H |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| All critical paths must contain 5 activities (oe, e.g. forward/backward pass with equal durations) | B1 | 2.4 |
| D cannot be critical as all paths through D only contain 4 activities (oe, e.g. total float on D is non-zero) | B1 | 2.4; SCB1 for stating/implying D has float of 1 by forward pass consideration |
# Question 7(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Either row G or H correct: G preceded by B, F; H preceded by B, C, F | B1 | 1.1b |
| All rows correct (condone blanks in A, B, C rows) | B1 | 1.1b |
# Question 7(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| At least five activities (labelled on arc), at least two dummies placed | M1 | 2.1 |
| Activities I, J, K and first dummy + arrow dealt with correctly | A1 | 1.1b |
| Activities L, M, N and a second dummy + arrows dealt with correctly | A1 | 1.1b |
| cso – all arrows present for every activity, exactly one finish, exactly three dummies | A1 | 1.1b; note M and N could be interchanged |
**IPA reference table:**
| Activity | I | J | K | L | M | N |
|----------|---|---|---|---|---|---|
| IPA | D, E, G, H | D, E, G, H | E, G, H | I, J, K | J, K | J, K |
# Question 7(c):
| Answer | Mark | Guidance |
|--------|------|----------|
| All critical paths must contain 5 activities (oe, e.g. forward/backward pass with equal durations) | B1 | 2.4 |
| D cannot be critical as all paths through D only contain 4 activities (oe, e.g. total float on D is non-zero) | B1 | 2.4; SCB1 for stating/implying D has float of 1 by forward pass consideration |7.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{43bc1e60-d8b2-4ea5-9652-4603a26c2f78-08_583_670_260_699}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{center}
\end{figure}
Figure 5 shows a partially completed activity network for a project that consists of 14 activities.
\begin{enumerate}[label=(\alph*)]
\item Complete the precedence table in the answer book for the 8 activities in Figure 5.
The precedence table for the remaining 6 activities is given below.
\begin{center}
\begin{tabular}{ | c | c | }
\hline
Activity & Immediately preceding activities \\
\hline
I & D, E, G, H \\
\hline
J & D, E, G, H \\
\hline
K & E, G, H \\
\hline
L & I, J, K \\
\hline
M & J, K \\
\hline
N & J, K \\
\hline
\end{tabular}
\end{center}
\item Complete the activity network in the answer book for the project. Your completed activity network must contain only the minimum number of dummies.
Given that all 14 activities have the same duration,
\item explain why activity D cannot be critical.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FD1 2021 Q7 [8]}}