| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2021 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Identify guaranteed critical activities |
| Difficulty | Moderate -0.8 This is a straightforward D1 critical path question requiring standard network drawing, identification of activity I as guaranteed critical (it's the only activity that all paths must pass through), and simple calculation with uniform durations. The conceptual demand is low—recognizing a bottleneck activity and applying basic critical path algorithm—making it easier than average A-level maths 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 | Immediately preceding activities |
| A | - |
| B | - |
| C | - |
| D | A |
| E | A |
| F | A, B, C |
| G | C |
| H | G |
| I | D, E, F, H |
| J | I |
| K | I |
| L | I |
| M | L |
**(a)** M1
A1
A1
A1
A1 (5)
**Activity on node is M0. In (a) condone lack of, or incorrect, numbered events throughout. 'Dealt with correctly' means that the activity starts from the correct event but need not necessarily finish at the correct event. For example, 'I dealt with correctly' requires the correct precedences for this activity, i.e. D, E, F and H labelled correctly and that they lead directly into the same node (possibly with the aid of a dummy activity). Activity I then starts from that node but ignore the end event for I.**
**Eight activities (labelled on arc), one start and at least two dummies placed**
**Activities A, B, C, 1st two dummies, D, E and G dealt with correctly. The first two dummies are those at the end of activities A and C. Both dummies must have arrows pointing in the correct direction**
**Activities F, H and 3rd dummy dealt with correctly. The 3rd dummy is the one at the end of D. The dummy must have an arrow pointing in the correct direction**
**Activities I, J, K, L and M dealt with correctly**
**CSO – all arrows correctly placed for each activity with one finish and a 4th dummy (with a correct arrow) at the end of activity J. Please check all arcs carefully for arrows – if there are no arrows on any dummies then M1 only. Note that additional (but unnecessary) 'correct' dummies that still maintain precedence for the network should only be penalised with the final A mark, if earned, in (a)**
**Ignore incorrect or lack of arrows on the activities for the first four marks only**
**Note additional valid solutions:**
- Activities D and E interchanged or J and K interchanged (or both)
- The dummy at the end of D could appear before activity D, similarly for the dummy at the end of J
- A combination of6.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & - \\
\hline
D & A \\
\hline
E & A \\
\hline
F & A, B, C \\
\hline
G & C \\
\hline
H & G \\
\hline
I & D, E, F, H \\
\hline
J & I \\
\hline
K & I \\
\hline
L & I \\
\hline
M & L \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw the activity network for the project described in the precedence table above, using activity on arc and the minimum number of dummies.\\
(5)
\item State which activity is guaranteed to be critical, giving a reason for your answer.\\
(2)
It is given that each activity in the table takes two hours to complete.
\item State the minimum completion time and write down the critical path for the project.\\
(2)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2021 Q6 [9]}}