| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2024 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Identify guaranteed critical activities |
| Difficulty | Moderate -0.3 This is a standard D1 critical path question requiring network drawing and logical deduction about critical activities. Part (a) is routine application of precedence table conversion. Part (b) requires understanding that if E is critical and there's only one critical path, activities must lie on the path through E, but the logic is straightforward once the network is drawn—easier than average A-level maths questions overall. |
| Spec | 7.05a Critical path analysis: activity on arc networks |
| Activity | Immediately preceding activities |
| A | - |
| B | - |
| C | A, B |
| D | A, B |
| E | B |
| F | C, D, E |
| G | F |
| H | B |
| I | F |
| J | F |
| K | G |
| L | G, H, I, J |
| M | G, I |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Nine activities on arcs, one start, at least two dummies placed | a1M1 | |
| Activities A, B, 1st dummy (correct arrow), C, D, E, H dealt with correctly | a1A1 | |
| 2nd dummy (correct arrow), activities F, G, I, J dealt with correctly | a2A1 | |
| Activities K, L, M dealt with correctly (third and fourth dummies + arrows) | a3A1 | |
| All arrows correctly placed, one finish, at most four dummies | 4A1 | CSO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Activities A, C, D and H cannot be critical | b1B1 | CAO (A, C, D, H and no others) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Activities B and F must be critical | b2B1 | CAO (B and F and no others - accept if E mentioned) |
# Question 4 (Precedence Network):
## Part (a) - Activity Network:
| Answer | Mark | Guidance |
|--------|------|----------|
| Nine activities on arcs, one start, at least two dummies placed | a1M1 | |
| Activities A, B, 1st dummy (correct arrow), C, D, E, H dealt with correctly | a1A1 | |
| 2nd dummy (correct arrow), activities F, G, I, J dealt with correctly | a2A1 | |
| Activities K, L, M dealt with correctly (third and fourth dummies + arrows) | a3A1 | |
| All arrows correctly placed, one finish, at most four dummies | 4A1 | CSO |
## Part (b)(i) - Non-critical Activities:
| Answer | Mark | Guidance |
|--------|------|----------|
| Activities A, C, D and H cannot be critical | b1B1 | CAO (A, C, D, H and no others) |
## Part (b)(ii) - Must be Critical:
| Answer | Mark | Guidance |
|--------|------|----------|
| Activities B and F must be critical | b2B1 | CAO (B and F and no others - accept if E mentioned) |4.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & A, B \\
\hline
D & A, B \\
\hline
E & B \\
\hline
F & C, D, E \\
\hline
G & F \\
\hline
H & B \\
\hline
I & F \\
\hline
J & F \\
\hline
K & G \\
\hline
L & G, H, I, J \\
\hline
M & G, I \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw the activity network described in the precedence table, using activity on arc and the minimum number of dummies.
\item Given that
\begin{itemize}
\item the activity network contains only one critical path
\item activity E is on this critical path\\
state
\begin{enumerate}[label=(\roman*)]
\item which activities could never be critical,
\item which activities must be critical.
\end{itemize}
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2024 Q4 [7]}}