| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw network with specified dummies |
| Difficulty | Moderate -0.3 This is a standard D1 critical path analysis question requiring students to construct an activity network from a precedence table. Part (a) tests understanding of when dummies are needed (activities J and K both depend on G and I, creating parallel activities with identical precedence), while part (b) is a routine construction exercise. The question is slightly easier than average A-level maths as it's methodical application of a well-defined algorithm with no novel problem-solving required, though the dual dummy requirement adds minor complexity. |
| Spec | 7.05a Critical path analysis: activity on arc networks |
| Activity | Must be preceded by |
| \(A\) | \(-\) |
| \(B\) | \(A\) |
| \(C\) | \(B\) |
| \(D\) | \(A, C\) |
| \(E\) | \(A\) |
| \(F\) | \(E\) |
| \(G\) | \(E\) |
| \(H\) | \(G\) |
| \(I\) | \(D, F\) |
| \(J\) | \(G, I\) |
| \(K\) | \(G, I\) |
| \(L\) | \(H, K\) |
The precedence table for activities involved in producing a computer game is shown below.
\begin{center}
\begin{tabular}{|c|c|}
\hline
Activity & Must be preceded by \\
\hline
$A$ & $-$ \\
\hline
$B$ & $A$ \\
\hline
$C$ & $B$ \\
\hline
$D$ & $A, C$ \\
\hline
$E$ & $A$ \\
\hline
$F$ & $E$ \\
\hline
$G$ & $E$ \\
\hline
$H$ & $G$ \\
\hline
$I$ & $D, F$ \\
\hline
$J$ & $G, I$ \\
\hline
$K$ & $G, I$ \\
\hline
$L$ & $H, K$ \\
\hline
\end{tabular}
\end{center}
An activity on arc network is to be drawn to model this production process.
\begin{enumerate}[label=(\alph*)]
\item Explain why it is necessary to use at least two dummies when drawing the activity network. [2]
\item Draw the activity network using exactly two dummies. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2005 Q2 [7]}}