| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2005 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate float times |
| Difficulty | Moderate -0.8 This is a straightforward critical path analysis question with only 5 activities and simple precedence relationships. Drawing the network, calculating early/late times, and finding float values are all standard algorithmic procedures taught in D1 with no problem-solving insight required. The small scale makes it computationally trivial compared to typical A-level questions. |
| 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 interpretation |
| Activity | Duration (hours) | Immediate predecessor(s) |
| A | 3 | - |
| B | 2 | - |
| C | 5 | - |
| D | 2 | A |
| E | 1 | A, B |
| Answer | Marks | Guidance |
|---|---|---|
| (i) [Network diagram with nodes A, B, C, D, E, F and values shown] | M1 A1 | |
| B1 B1 | ||
| (ii) Critical – A, D and C | B1 | |
| (iii) Total float for \(B = 2\) Independent float for \(B = 1\) Total float for \(E = 1\) Independent float for \(E = 0\) | B1 A1 A1 | both total floats B's independent E's independent |
| (i) [Network diagram with nodes A, B, C, D, E, F and values shown] | M1 A1 | |
| | B1 B1 | |
| (ii) Critical – A, D and C | B1 | |
| (iii) Total float for $B = 2$ Independent float for $B = 1$ Total float for $E = 1$ Independent float for $E = 0$ | B1 A1 A1 | both total floats B's independent E's independent |3 Table 3 gives the durations and immediate predecessors for the five activities of a project.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | c | c | c | }
\hline
Activity & Duration (hours) & Immediate predecessor(s) \\
\hline
A & 3 & - \\
\hline
B & 2 & - \\
\hline
C & 5 & - \\
\hline
D & 2 & A \\
\hline
E & 1 & A, B \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 3}
\end{center}
\end{table}
(i) Draw an activity-on-arc network to represent the precedences.\\
(ii) Find the early and late event times for the vertices of your network, and list the critical activities.\\
(iii) Give the total and independent float for each activity which is not critical.
\hfill \mbox{\textit{OCR MEI D1 2005 Q3 [8]}}