| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2005 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Explain dummy activities |
| Difficulty | Moderate -0.8 This is a routine Critical Path Analysis question testing standard network drawing skills. Part (a) requires systematic application of precedence rules with given dummy placements, while part (b) tests understanding of why dummies prevent ambiguity and maintain correct dependencies—both are textbook exercises with no problem-solving or novel insight required. |
| Spec | 7.05a Critical path analysis: activity on arc networks |
| Activity | Immediately preceding activities |
| \(A\) | -- |
| \(B\) | -- |
| \(C\) | -- |
| \(D\) | \(A\) |
| \(E\) | \(A\) |
| \(F\) | \(B\) |
| \(G\) | \(B\) |
| \(H\) | \(C, D\) |
| \(I\) | \(E\) |
| \(J\) | \(F, H\) |
| \(K\) | \(G, J\) |
| \(L\) | \(G\) |
| \(M\) | \(L\) |
| \(N\) | \(L\) |
| Answer | Marks |
|---|---|
| e.g. \(A \xrightarrow{2} E \xrightarrow{5} I \xrightarrow{k} II\) | M1, A1, A1, A1 |
| Answer | Marks |
|---|---|
| Reference to \(k\), \(J\), \(G\) and \(L\) – \(k\) depends on \(J\) and \(G\), but \(L\) depends on \(G\) only. Both \(m\) and \(N\) must be uniquely represented in named arc. | B2, 1, 0, B1 |
| Answer | Marks |
|---|---|
| 4(a) M1 | G activities + 1 dummy activity on arc. Candor lack of ends thereupon |
| A1 | A − F + ems + 1 start |
| A1 | G − h + dummy (7)−(8) (diagram label on dummy) + emes on dummy + emes (pends one end) |
| A1 | L − N + dummy (10)−(11). Note: dummy may be M or N (signs label on dummy as ems on dummy + emes (pends one end) |
| B2 | Complete + clear; h, J, G, L replaced; explanation clear + correct |
| B1 | Nearly there. 'Bad' set B1. All there but confused explanation/vague. KJ3GL rejected to unique representation (o.e.). start of first at same events |
## Part (a)
| e.g. $A \xrightarrow{2} E \xrightarrow{5} I \xrightarrow{k} II$ | M1, A1, A1, A1 | |
## Part (b)
| Reference to $k$, $J$, $G$ and $L$ – $k$ depends on $J$ and $G$, but $L$ depends on $G$ only. Both $m$ and $N$ must be uniquely represented in named arc. | B2, 1, 0, B1 | |
## Notes
| **4(a) M1** | G activities + 1 dummy activity on arc. Candor lack of ends thereupon | | |
| **A1** | A − F + ems + 1 start | | |
| **A1** | G − h + dummy (7)−(8) (diagram label on dummy) + emes on dummy + emes (pends one end) | | |
| **A1** | L − N + dummy (10)−(11). Note: dummy may be M or N (signs label on dummy as ems on dummy + emes (pends one end) | | |
| **B2** | Complete + clear; h, J, G, L replaced; explanation clear + correct | | |
| **B1** | Nearly there. 'Bad' set B1. All there but confused explanation/vague. KJ3GL rejected to unique representation (o.e.). start of first at same events | | |
---The precedence table shows the activities involved in a project.
\begin{center}
\begin{tabular}{|c|c|}
\hline
Activity & Immediately preceding activities \\
\hline
$A$ & -- \\
\hline
$B$ & -- \\
\hline
$C$ & -- \\
\hline
$D$ & $A$ \\
\hline
$E$ & $A$ \\
\hline
$F$ & $B$ \\
\hline
$G$ & $B$ \\
\hline
$H$ & $C, D$ \\
\hline
$I$ & $E$ \\
\hline
$J$ & $F, H$ \\
\hline
$K$ & $G, J$ \\
\hline
$L$ & $G$ \\
\hline
$M$ & $L$ \\
\hline
$N$ & $L$ \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw the activity network for this project, using activity on arc and using two dummies. [4]
\item Explain why each of the two dummies is necessary. [3]
\end{enumerate}
(Total 7 marks)
\hfill \mbox{\textit{Edexcel D1 2005 Q4 [7]}}