| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2004 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.8 This is a standard textbook-style critical path analysis question covering routine D1 algorithms (early/late times, critical path, float, Gantt chart). All parts follow mechanical procedures with no novel problem-solving required, making it easier than average A-level maths questions which typically involve more conceptual understanding or multi-step reasoning. |
| 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 |
\includegraphics{figure_5}
A project is modelled by the activity network shown in Fig. 5. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, to complete the activity. The numbers in circles give the event numbers. Each activity requires one worker.
\begin{enumerate}[label=(\alph*)]
\item Explain the purpose of the dotted line from event 4 to event 5. [1]
\item Calculate the early time and the late time for each event. Write these in the boxes in the answer book. [4]
\item Determine the critical activities. [1]
\item Obtain the total float for each of the non-critical activities. [3]
\item On the grid in the answer book, draw a cascade (Gantt) chart, showing the answers to parts (c) and (d). [4]
\item Determine the minimum number of workers needed to complete the project in the minimum time. Make your reasoning clear. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2004 Q7 [15]}}