| Exam Board | Edexcel |
|---|---|
| Module | FD1 (Further Decision 1) |
| Year | 2022 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Find missing early/late times |
| Difficulty | Moderate -0.5 This is a standard Critical Path Analysis question covering routine techniques (precedence tables, late times, critical activities, float, resource histograms, Gantt charts). While multi-part with several marks, each component requires straightforward application of well-defined algorithms taught in FD1 with no novel problem-solving or insight needed. The constraint on x adds minor complexity but remains procedural. |
| 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 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Four correct rows (F, G, H, J, K with correct IPAs): F→C, G→A,B,E, H→A,B,E, J→D,G, K→D,F,G,H | B1 | Four correct rows not including A, B, C |
| All rows correct (A, B, C have no IPA / dash) | B1 | Any letters in A, B, C rows scores B0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(m = 9\) | B1 | cao; allow \(4 < x\), 9 or \(x\), 9 but not \(x=9\) or \(m\), 9 unless stating correct value |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Any four of the bottom boxes completed correctly | M1 | |
| All bottom boxes correct; \(15-x\) must be seen | A1 | cao; condone correct expression replaced by value of \(15-x\) ONLY if \(x\) explicitly stated |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| C, E, H and K must be critical | B1 | cao (C, E, H and K only) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Total float for activity G is \(15 - 11 - 3 = 1\) | B1 | cao; correct answer with no working (or no incorrect working) can imply this mark |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Any six values correct from the workers table | B1 | |
| All values correct | B1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(x = 6\) | B1 | cao; seen or implied by durations of D and F both correct |
| Cascade chart with at least 8 activities labelled, at least four with non-zero float | M1 | A scheduling diagram (no floats evident) scores M0 |
| Critical activities (C, E, H, K) correct | A1 | |
| Activities B, G and J correct | A1 | |
| Activities A, D and F correct | A1 |
# Question 5:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Four correct rows (F, G, H, J, K with correct IPAs): F→C, G→A,B,E, H→A,B,E, J→D,G, K→D,F,G,H | B1 | Four correct rows not including A, B, C |
| All rows correct (A, B, C have no IPA / dash) | B1 | Any letters in A, B, C rows scores B0 |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $m = 9$ | B1 | cao; allow $4 < x$, 9 or $x$, 9 but not $x=9$ or $m$, 9 unless stating correct value |
## Part (c)(i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Any four of the bottom boxes completed correctly | M1 | |
| All bottom boxes correct; $15-x$ must be seen | A1 | cao; condone correct expression replaced by value of $15-x$ ONLY if $x$ explicitly stated |
## Part (c)(ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| C, E, H and K must be critical | B1 | cao (C, E, H and K only) |
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Total float for activity G is $15 - 11 - 3 = 1$ | B1 | cao; correct answer with no working (or no incorrect working) can imply this mark |
## Part (e)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Any six values correct from the workers table | B1 | |
| All values correct | B1 | cao |
## Part (f)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x = 6$ | B1 | cao; seen or implied by durations of D and F both correct |
| Cascade chart with at least 8 activities labelled, at least four with non-zero float | M1 | A scheduling diagram (no floats evident) scores M0 |
| Critical activities (C, E, H, K) correct | A1 | |
| Activities B, G and J correct | A1 | |
| Activities A, D and F correct | A1 | |
---5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{27586973-89f4-45e1-9cc4-04c4044cd3db-08_1099_1700_194_139}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
The network in Figure 2 shows the activities that need to be completed for a project. Each activity is represented by an arc and the duration of the activity, in days, is shown in brackets. The early event times are shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Complete Table 1 in the answer book to show the immediately preceding activities for each activity.
It is given that $4 < x \leqslant m$
\item State the largest possible integer value of $m$.
\item \begin{enumerate}[label=(\roman*)]
\item Complete Diagram 1 in the answer book to show the late event times.
\item State the activities that must be critical.
\end{enumerate}\item Calculate the total float for activity G.
The resource histogram in Figure 3 shows the number of workers required when each activity starts at its earliest possible time. The histogram also shows which activities happen at each time.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{27586973-89f4-45e1-9cc4-04c4044cd3db-09_682_1612_356_230}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
\item Complete Table 2 in the answer book to show the number of workers required for each activity of the project.
\item Draw a Gantt chart on Grid 1 in the answer book to represent the activity network.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FD1 2022 Q5 [14]}}