| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2010 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw resource histogram |
| Difficulty | Moderate -0.8 This is a routine Critical Path Analysis question testing standard algorithms (earliest/latest times, float, critical path) followed by a straightforward resource histogram construction. All steps are algorithmic with no problem-solving insight required—students simply apply learned procedures to given data. |
| 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 float |
| Activity | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) | \(J\) |
| Number of workers required | 2 | 2 | 3 | 2 | 3 | 2 | 1 | 3 | 5 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | 2 | 4 |
Question 1:
1 | 2 | 4 | 3 | 0 | 0 | 0 | 01 [Figures 1 and 2, printed on the insert, are provided for use in this question.]\\
Figure 1 shows the activity network and the duration, in days, of each activity for a particular project.
\begin{enumerate}[label=(\alph*)]
\item On Figure 1:
\begin{enumerate}[label=(\roman*)]
\item find the earliest start time for each activity;
\item find the latest finish time for each activity.
\end{enumerate}\item Find the float for activity $G$.
\item Find the critical paths and state the minimum time for completion.
\item The number of workers required for each activity is shown in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | }
\hline
Activity & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ & $I$ & $J$ \\
\hline
Number of workers required & 2 & 2 & 3 & 2 & 3 & 2 & 1 & 3 & 5 & 2 \\
\hline
\end{tabular}
\end{center}
Given that each activity starts as late as possible and assuming that there is no limit to the number of workers available, draw a resource histogram for the project on Figure 2, indicating clearly which activities take place at any given time.
\end{enumerate}
\hfill \mbox{\textit{AQA D2 2010 Q1 [13]}}