| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2009 |
| Session | January |
| 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 D1 question testing standard knowledge of dummy activities in activity networks. Part (a) requires drawing a network following given precedence rules (mechanical application), and part (b) asks for textbook explanations of why dummies are needed—typically to show correct precedence or avoid duplicate arcs. No problem-solving or novel insight required, just recall and application of standard techniques. |
| Spec | 7.05a Critical path analysis: activity on arc networks |
| Activity | Immediately preceding activities |
| A | - |
| B | - |
| C | - |
| D | B |
| E | B, C |
| F | B, C |
| G | F |
| H | F |
| I | G, H |
| J | I |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| One start node and activities A to C and one of D, E or F drawn correctly | M1 | One start and A to C and one of D, E or F drawn correctly |
| \(1^{\text{st}}\) dummy (+arrow) and D, E and F drawn correctly | A1 | |
| G, H, I and J drawn in correct place | A1 | |
| Second dummy (+arrow) drawn in correct place | A1 | |
| All arrows correct and one finish node | A1 | cso |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(1^{\text{st}}\) dummy: D depends on B only, but E and F depend on B and C | B1 | cao, but B, C, D, E and/or F referred to, generous |
| \(2^{\text{nd}}\) dummy: G and H both must be able to be described uniquely in terms of the events at each end | B1 | cao, but generous |
# Question 3:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| One start node and activities A to C and one of D, E or F drawn correctly | M1 | One start and A to C and one of D, E or F drawn correctly |
| $1^{\text{st}}$ dummy (+arrow) and D, E and F drawn correctly | A1 | |
| G, H, I and J drawn in correct place | A1 | |
| Second dummy (+arrow) drawn in correct place | A1 | |
| All arrows correct and one finish node | A1 | cso |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $1^{\text{st}}$ dummy: D depends on B only, but E and F depend on B and C | B1 | cao, but B, C, D, E and/or F referred to, generous |
| $2^{\text{nd}}$ dummy: G and H both must be able to be described uniquely in terms of the events at each end | B1 | cao, but generous |
---3. (a) Draw the activity network described in this precedence table, using activity on arc and exactly two dummies.\\
(5)
\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & - \\
\hline
D & B \\
\hline
E & B, C \\
\hline
F & B, C \\
\hline
G & F \\
\hline
H & F \\
\hline
I & G, H \\
\hline
J & I \\
\hline
\end{tabular}
\end{center}
(b) Explain why each of the two dummies is necessary.\\
\hfill \mbox{\textit{Edexcel D1 2009 Q3 [7]}}