| Exam Board | Edexcel |
|---|---|
| Module | FD1 AS (Further Decision 1 AS) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Identify guaranteed critical activities |
| Difficulty | Moderate -0.3 This is a standard Critical Path Analysis question requiring drawing an activity network with dummies, explaining dummy necessity, and identifying a non-critical activity. While it requires understanding of precedence relationships and dummy conventions, the equal-duration constraint makes part (c) straightforward (activity D has no successors affecting the critical path). This is typical Further Maths Decision content but involves routine application of learned techniques rather than problem-solving insight. |
| Spec | 7.05a Critical path analysis: activity on arc networks |
| Activity | Immediately preceding activities |
| A | - |
| B | - |
| C | - |
| D | - |
| E | A |
| F | A, B, C |
| G | C |
| H | C |
| I | E |
| J | E, F, G |
| K | D, H |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct network diagram with activities on arcs | M1, A1, A1, A1, A1 | Activity on node is M0; ignore incorrect/missing arrows on activities for first four marks only |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| e.g. Activity E preceded by activity A only, but activity F is preceded by activity B (and/or C) as well as activity A | B1 | Must mention activities A, E, F and at least one of B and C |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Activity D, as it is the only activity on a path from start to finish containing only two activities | M1 | cao — if more than one activity stated then M0 |
| All other activities appear on at least one longer path | A1 | Explain path through D is only one containing two activities, or all other routes have 3 activities, or mention C, H, K and that C and H together take longer than D |
# Question 2:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct network diagram with activities on arcs | M1, A1, A1, A1, A1 | Activity on node is M0; ignore incorrect/missing arrows on activities for first four marks only |
**Marking breakdown:**
- M1: At least eight activities (labelled on arc), one start, at least two dummies placed
- A1: Activities A, B, C, D, E, G and H dealt with correctly
- A1: Activity F dealt with correctly and first two dummies & correct arrows dealt with correctly
- A1: Activities I, J, K and final dummy dealt with correctly
- A1: cso — all arrows present and correctly placed, one finish, no additional dummies
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. Activity E preceded by activity A only, but activity F is preceded by activity B (and/or C) as well as activity A | B1 | Must mention activities A, E, F and at least one of B and C |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Activity D, as it is the only activity on a path from start to finish containing only two activities | M1 | cao — if more than one activity stated then M0 |
| All other activities appear on at least one longer path | A1 | Explain path through D is only one containing two activities, or all other routes have 3 activities, or mention C, H, K and that C and H together take longer than D |
---2.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & - \\
\hline
D & - \\
\hline
E & A \\
\hline
F & A, B, C \\
\hline
G & C \\
\hline
H & C \\
\hline
I & E \\
\hline
J & E, F, G \\
\hline
K & D, H \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain the minimum number of dummies only.
\item Explain why it is necessary to draw a dummy from the end of activity A .
Every activity shown in the precedence table has the same duration.
\item State which activity cannot be critical, justifying your answer.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FD1 AS 2022 Q2 [8]}}