| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Explain dummy activities |
| Difficulty | Moderate -0.8 Part (a) is a standard network drawing exercise requiring systematic application of precedence rules and dummy insertion. Part (b) asks for recall of two textbook reasons for dummies (logical dependencies and unique node pairs). This is routine D1 content 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 | B, C |
| E | A |
| F | C |
| G | D, E |
| H | D, E |
| I | \(F , G\) |
| J | C |
| K | \(G , H\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| 7 activities (labelled on arc) and one dummy placed | M1 | Ignore incorrect or lack of arrows for first four marks; activity on node is M0 |
| One start + activities A, B, C and E dealt with correctly | A1 | Condone lack of or incorrect numbered events; 'dealt with correctly' means activity starts from correct event |
| Activities D, F, G, H and J and the 1st dummy dealt with correctly | A1 | |
| Activities I, K and the 2nd and 3rd dummies dealt with correctly | A1 | |
| CSO – all arrows present and correctly placed with one finish | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Dummies needed to show dependency (where subsequent activities do not all depend on the same preceding activities) | B1 | Dependency + some explanation; generous – allow correct example based on correct network diagram |
| So that an activity can be uniquely represented in terms of its events | B1 | Must mention describing activities in terms of events at each end; 'so that activities can be defined uniquely' is not sufficient |
# Question 6:
## Part a
| Answer | Mark | Guidance |
|--------|------|----------|
| 7 activities (labelled on arc) and one dummy placed | M1 | Ignore incorrect or lack of arrows for first four marks; activity on node is M0 |
| One start + activities A, B, C and E dealt with correctly | A1 | Condone lack of or incorrect numbered events; 'dealt with correctly' means activity starts from correct event |
| Activities D, F, G, H and J and the 1st dummy dealt with correctly | A1 | |
| Activities I, K and the 2nd and 3rd dummies dealt with correctly | A1 | |
| CSO – **all** arrows present and correctly placed with one finish | A1 | |
## Part b
| Answer | Mark | Guidance |
|--------|------|----------|
| Dummies needed to show dependency (where subsequent activities **do not all** depend on the same preceding activities) | B1 | Dependency + some explanation; generous – allow correct example based on correct network diagram |
| So that an activity can be uniquely represented in terms of its events | B1 | Must mention describing activities in terms of events at each end; 'so that activities can be defined uniquely' is **not** sufficient |
---6. (a) Draw the activity network described in this precedence table, using activity on arc and dummies only where necessary.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & - \\
\hline
D & B, C \\
\hline
E & A \\
\hline
F & C \\
\hline
G & D, E \\
\hline
H & D, E \\
\hline
I & $F , G$ \\
\hline
J & C \\
\hline
K & $G , H$ \\
\hline
\end{tabular}
\end{center}
(b) Explain the possible reasons dummies may be needed in activity networks.\\
\hfill \mbox{\textit{Edexcel D1 2014 Q6 [7]}}