| Exam Board | Edexcel |
|---|---|
| Module | FD1 (Further Decision 1) |
| Session | Specimen |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw resource histogram |
| Difficulty | Moderate -0.3 This is a standard Further Maths Decision 1 question testing routine critical path analysis procedures (early/late times, Gantt chart, resource histogram). While it requires multiple steps and careful bookkeeping, each component follows algorithmic procedures taught directly in the syllabus with no novel problem-solving or insight required. The final part (d) is straightforward visual inspection of the histogram. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05d Latest start and earliest finish: independent and interfering float |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Top and bottom boxes completed | M1 | All top boxes increasing in arrow direction; all bottom boxes decreasing opposite to arrow direction |
| Top boxes correct | A1 | cao |
| Bottom boxes correct | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| At least 8 activities + 4 floats with clear distinction between activity and float | M1 | Scheduling diagram; clear distinction between activity notation and float notation |
| Correct critical activities + 4 correct non-critical activities | A1 | |
| All 13 correct | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Plausible histogram with no holes or overhangs (must reach at least time 10) | M1 | |
| Histogram correct to time \(= 13\) | A1 | |
| Histogram correct from time 14 to 24 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Until time 4 only A and B can happen; considering appropriate process to adjust Grid 2 | B1 | Correct argument that until time 4 only A and B can happen |
| After time 4, there are 6 worker-days to cover but only 4 worker-days available; uses histogram | M1 | Uses histogram when workers greater/less than minimum found in (b) |
| Hence project cannot be completed by time 24 with three workers | A1 | Dependent on correct histogram in (d) |
# Question 6:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Top and bottom boxes completed | M1 | All top boxes increasing in arrow direction; all bottom boxes decreasing opposite to arrow direction |
| Top boxes correct | A1 | cao |
| Bottom boxes correct | A1 | cao |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| At least 8 activities + 4 floats with clear distinction between activity and float | M1 | Scheduling diagram; clear distinction between activity notation and float notation |
| Correct critical activities + 4 correct non-critical activities | A1 | |
| All 13 correct | A1 | cao |
## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| Plausible histogram with no holes or overhangs (must reach at least time 10) | M1 | |
| Histogram correct to time $= 13$ | A1 | |
| Histogram correct from time 14 to 24 | A1 | |
## Part (d)
| Answer | Mark | Guidance |
|--------|------|----------|
| Until time 4 only A and B can happen; considering appropriate process to adjust Grid 2 | B1 | Correct argument that until time 4 only A and B can happen |
| After time 4, there are 6 worker-days to cover but only 4 worker-days available; uses histogram | M1 | Uses histogram when workers greater/less than minimum found in (b) |
| Hence project cannot be completed by time 24 with three workers | A1 | Dependent on correct histogram in (d) |
---6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{37435cc9-1e38-4c55-bd72-e2a1ec415ba7-08_1113_1319_169_374}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}
A project is modelled by the activity network shown in Figure 4. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete that activity. Each activity requires one worker. The project is to be completed in the shortest possible time.
\begin{enumerate}[label=(\alph*)]
\item Calculate the early time and the late time for each event, using Diagram 1 in the answer book.
\item On Grid 1 in the answer book, complete the cascade (Gantt) chart for this project.
\item On Grid 2 in the answer book, draw a resource histogram to show the number of workers required each day when each activity begins at its earliest time.
The supervisor of the project states that only three workers are required to complete the project in the minimum time.
\item Use Grid 2 to determine if the project can be completed in the minimum time by only three workers. Give reasons for your answer.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FD1 Q6 [12]}}