| Exam Board | Edexcel |
|---|---|
| Module | FD1 (Further Decision 1) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw resource histogram |
| Difficulty | Standard +0.3 This is a standard Further Maths Decision 1 question requiring routine application of critical path analysis algorithms (forward/backward pass) followed by drawing a resource histogram using earliest start times. While it involves multiple steps and careful bookkeeping, it requires no novel insight—just systematic application of well-practiced techniques from the syllabus. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
| Activity | Number of workers |
| A | 2 |
| B | 1 |
| C | 2 |
| D | 2 |
| E | 3 |
| F | 2 |
| G | 1 |
| H | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| All top boxes and bottom boxes completed with values generally increasing left to right (top) and decreasing right to left (bottom) | M1 | Condone missing 0s at source node and/or 11 in bottom box at sink for M only. Condone one rogue value in top boxes and one in bottom boxes |
| CAO - Top boxes and Bottom boxes all completed | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| 11 (hours) | A1ft | Follow through from their final early event time; units not required |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Plausible histogram correct up to time 4, no holes or overhangs, must reach at least time 10 | M1 | Do not consider placement of activities - consider only placement of each vertical bar |
| Histogram correct to time 8 | A1 | |
| Histogram correct from time 8 to time 11, no activities after time 11 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Six workers required in time intervals \(0-3\) and \(8-10\) | A1 | Allow any indication of interval from 0 to 3 and 8 to 10; accept \(<\), \(\leq\) or dash, but not e.g. 0 to 2.999... |
# Question 2:
## Part (a)(i)
| Answer | Mark | Guidance |
|--------|------|----------|
| All top boxes and bottom boxes completed with values generally increasing left to right (top) and decreasing right to left (bottom) | M1 | Condone missing 0s at source node and/or 11 in bottom box at sink for M only. Condone one rogue value in top boxes and one in bottom boxes |
| CAO - Top boxes and Bottom boxes all completed | A1 | |
## Part (a)(ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| 11 (hours) | A1ft | Follow through from their final early event time; units not required |
## Part (b)(i)
| Answer | Mark | Guidance |
|--------|------|----------|
| Plausible histogram correct up to time 4, no holes or overhangs, must reach at least time 10 | M1 | Do not consider placement of activities - consider only placement of each vertical bar |
| Histogram correct to time 8 | A1 | |
| Histogram correct from time 8 to time 11, no activities after time 11 | A1 | |
## Part (b)(ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Six workers required in time intervals $0-3$ and $8-10$ | A1 | Allow any indication of interval from 0 to 3 **and** 8 to 10; accept $<$, $\leq$ or dash, but not e.g. 0 to 2.999... |
---
2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{6ccce35f-4e62-4b6b-acf6-f9b3e18d4b52-04_474_958_210_555}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
The network in Figure 3 shows the activities that need to be undertaken to complete a project. Each activity is represented by an arc and the duration, in hours, of the corresponding activity is shown in brackets.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Complete Diagram 1 in the answer book to show the early event times and the late event times.
\item State the minimum completion time of the project.
The table below lists the number of workers required for each activity in the project.
\begin{center}
\begin{tabular}{ | c | c | }
\hline
Activity & Number of workers \\
\hline
A & 2 \\
\hline
B & 1 \\
\hline
C & 2 \\
\hline
D & 2 \\
\hline
E & 3 \\
\hline
F & 2 \\
\hline
G & 1 \\
\hline
H & 3 \\
\hline
\end{tabular}
\end{center}
Each worker is able to do any of the activities. Once an activity is started it must be completed without interruption. It is given that each activity begins at its earliest possible start time.
\end{enumerate}\item \begin{enumerate}[label=(\roman*)]
\item On Grid 1 in the answer book, draw a resource histogram to show the number of workers required at each time.
\item Hence state the time interval(s) when six workers are required.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel FD1 2023 Q2 [7]}}