| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Discrete (Further Paper 3 Discrete) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.8 This is a standard critical path analysis question requiring routine application of forward/backward pass algorithms, identifying the critical path, and drawing a Gantt chart. These are textbook procedures in Decision Maths with minimal problem-solving required. Part (c) requires basic understanding of how removing non-critical activities affects project duration. While multi-part, each component is algorithmic and well-practiced. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
| Answer | Marks | Guidance |
|---|---|---|
| Earliest start times correctly found | B1 | See activity network diagram |
| Latest finish times correctly found | B1 | See activity network diagram |
| Answer | Marks | Guidance |
|---|---|---|
| Critical path is \(BEFJK\) | B1 | Must be correct path stated |
| Answer | Marks | Guidance |
|---|---|---|
| Translates activity network into diagram showing and labelling all 11 activities | M1 | AO 3.1a |
| All 5 critical activities shown correctly, either on individual rows or all on single row | A1 | AO 1.1b |
| Fully correct diagram including all labelling and all floats. Condone float of 5 for activity \(A\) if latest finish time is 17 in (a)(i) | A1 | AO 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| Removing activity \(F\) makes \(G\) critical, and \(G\) has a duration 2 weeks less than activity \(F\). Explains that activity \(G\) now becomes critical OR earliest start time of \(H\), \(I\) and \(J\) each decreases by 2 weeks, PI by earliest start time of 34 for \(H\), \(I\) and \(J\) shown on activity network | B1 | AO 1.1b |
| Therefore the minimum completion time for the project reduces by 2 weeks. Deduces that minimum completion time reduces by 2 weeks or reduces to 47 weeks | B1 | AO 2.2a |
## Question 7(a)(i):
Earliest start times correctly found | B1 | See activity network diagram
Latest finish times correctly found | B1 | See activity network diagram
Activity network values:
- $A$: $0 \mid 12 \mid 18$
- $B$: $0 \mid 17 \mid 17$
- $C$: $0 \mid 16 \mid 17$
- $D$: $17 \mid 11 \mid 29$
- $E$: $17 \mid 12 \mid 29$
- $F$: $29 \mid 7 \mid 36$
- $G$: $29 \mid 5 \mid 36$
- $H$: $36 \mid 6 \mid 45$
- $I$: $36 \mid 8 \mid 45$
- $J$: $36 \mid 9 \mid 45$
- $K$: $45 \mid 4 \mid 49$
---
## Question 7(a)(ii):
Critical path is $BEFJK$ | B1 | Must be correct path stated
---
## Question 7(b):
Translates activity network into diagram showing and labelling all 11 activities | M1 | AO 3.1a
All 5 critical activities shown correctly, either on individual rows or all on single row | A1 | AO 1.1b
Fully correct diagram including all labelling and all floats. Condone float of 5 for activity $A$ if latest finish time is 17 in (a)(i) | A1 | AO 1.1b
---
## Question 7(c):
Removing activity $F$ makes $G$ critical, and $G$ has a duration 2 weeks less than activity $F$. Explains that activity $G$ now becomes critical OR earliest start time of $H$, $I$ and $J$ each decreases by 2 weeks, PI by earliest start time of 34 for $H$, $I$ and $J$ shown on activity network | B1 | AO 1.1b
Therefore the minimum completion time for the project reduces by 2 weeks. Deduces that minimum completion time reduces by 2 weeks or reduces to 47 weeks | B1 | AO 2.2a
---7
\begin{enumerate}[label=(\alph*)]
\item (i) Find the earliest start time and the latest finish time for each activity and write these values on the activity network in Figure 1
7 (a) (ii) Write down the critical path.
7
\item On Figure 2 below, draw a cascade diagram (Gantt chart) for the planned building project, assuming that each activity starts as early as possible.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{5ff6e3bb-6392-49cf-b64d-23bc595cd92e-11_1127_1641_539_201}
\end{center}
\end{figure}
7
\item During further planning of the building project, Nova Merit Construction find that activity $F$ is not necessary and they remove it from the project.
Explain the effect removing activity $F$ has on the minimum completion time of the project.
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 3 Discrete 2023 Q7 [6]}}