| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Effect of activity delay/change |
| Difficulty | Moderate -0.8 This is a standard critical path analysis question testing routine algorithmic procedures (forward pass, backward pass, identifying critical path, calculating float) with a straightforward extension about activity delays. The techniques are mechanical and well-practiced, requiring no problem-solving insight or novel reasoning—just careful application of the standard CPA algorithm. |
| 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 interpretation7.05d Latest start and earliest finish: independent and interfering float7.05e Cascade charts: scheduling and effect of delays |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Earliest start times: \(A=0, B=0, C=0, D=5, E=6, F=10, G=11, H=11, I=11, J=17, K=18, L=23\) | M1 | Forward pass method |
| Latest finish times correctly calculated | A1 | |
| All earliest start times correct | A1 | |
| All latest finish times correct | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Critical path: \(B \to D \to F \to I \to K \to L\) | B1 | Must be stated as a path |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Float of \(E\) = latest finish \(-\) duration \(-\) earliest start \(= 1\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(H\) overruns by 10, new duration \(= 16\) | M1 | Considering effect on paths through \(H\) and \(K\) |
| \(K\) overruns by 10, new duration \(= 17\) | M1 | |
| New minimum completion time \(= 39\) | A1 |
# Question 1:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Earliest start times: $A=0, B=0, C=0, D=5, E=6, F=10, G=11, H=11, I=11, J=17, K=18, L=23$ | M1 | Forward pass method |
| Latest finish times correctly calculated | A1 | |
| All earliest start times correct | A1 | |
| All latest finish times correct | A1 | |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| Critical path: $B \to D \to F \to I \to K \to L$ | B1 | Must be stated as a path |
## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| Float of $E$ = latest finish $-$ duration $-$ earliest start $= 1$ | B1 | |
## Part (d)
| Answer | Mark | Guidance |
|--------|------|----------|
| $H$ overruns by 10, new duration $= 16$ | M1 | Considering effect on paths through $H$ and $K$ |
| $K$ overruns by 10, new duration $= 17$ | M1 | |
| New minimum completion time $= 39$ | A1 | |
---1 Figure 1 opposite shows an activity diagram for a project. The duration required for each activity is given in hours. The project is to be completed in the minimum time.
\begin{enumerate}[label=(\alph*)]
\item Find the earliest start time and the latest finish time for each activity and insert their values on Figure 1.
\item Find the critical path.
\item Find the float time of activity $E$.
\item Given that activities $H$ and $K$ will both overrun by 10 hours, find the new minimum completion time for the project.
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{5123be51-168e-4487-8cd3-33aee9e3b23f-02_1515_1709_1192_153}
\end{center}
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{5123be51-168e-4487-8cd3-33aee9e3b23f-03_1656_869_627_611}
\end{center}
\end{figure}
\end{enumerate}
\hfill \mbox{\textit{AQA D2 2013 Q1 [9]}}