| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Complete precedence table from network |
| Difficulty | Moderate -0.8 This is a standard D1 critical path analysis question requiring routine application of well-practiced algorithms (precedence tables, forward/backward pass, identifying critical path, drawing Gantt chart). All parts follow textbook procedures with no novel problem-solving or insight required, 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 interpretation7.05d Latest start and earliest finish: independent and interfering float7.05e Cascade charts: scheduling and effect of delays |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| The dotted line represents a dummy activity | B1 | |
| It is necessary because C and D depend only on A, but E depends on A and B | B1 | (2 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| A: \(-\); B: \(-\); C: A; D: A; E: A,B | B1 | To this point |
| F: C(A); G: C, D, E | B1 | For E & F, accepting correct "extra" |
| H: F, G | B1 | Last two rows, correct only (3 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Early times correctly calculated | M1A1 | |
| Late times correctly calculated | M1A1 | (4 marks total) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Critical activities: B, E, G, H | B1 | |
| Critical path: 16 days | B1ft | (2 marks total) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| At least 6 activities placed including at least 3 floats | M1 | |
| Critical activities correctly placed (B, E, G, H) | A1 | |
| A and C correctly scheduled | A1 | |
| D and F correctly scheduled | A1 | (4 marks total) |
# Question 6(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| The dotted line represents a dummy activity | B1 | |
| It is necessary because C and D depend only on A, but E depends on A and B | B1 | **(2 marks)** |
# Question 6(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| A: $-$; B: $-$; C: A; D: A; E: A,B | B1 | To this point |
| F: C(A); G: C, D, E | B1 | For E & F, accepting correct "extra" |
| H: F, G | B1 | Last two rows, correct only **(3 marks)** |
## Question 6:
**Part (c):**
| Answer | Mark | Guidance |
|--------|------|----------|
| Early times correctly calculated | M1A1 | |
| Late times correctly calculated | M1A1 | (4 marks total) |
**Part (d):**
| Answer | Mark | Guidance |
|--------|------|----------|
| Critical activities: B, E, G, H | B1 | |
| Critical path: 16 days | B1ft | (2 marks total) |
**Part (e):**
| Answer | Mark | Guidance |
|--------|------|----------|
| At least 6 activities placed including at least 3 floats | M1 | |
| Critical activities correctly placed (B, E, G, H) | A1 | |
| A and C correctly scheduled | A1 | |
| D and F correctly scheduled | A1 | (4 marks total) |
---6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{17bc9fb2-13bf-4ffa-93ac-bef170467570-7_614_1315_1027_374}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{center}
\end{figure}
Figure 5 is the activity network relating to a building project. The number in brackets on each arc gives the time taken, in days, to complete the activity.
\begin{enumerate}[label=(\alph*)]
\item Explain the significance of the dotted line from event (2) to event (3).
\item Complete the precedence table in the answer booklet.
\item Calculate the early time and the late time for each event, showing them on the diagram in the answer booklet.
\item Determine the critical activities and the length of the critical path.
\item On the grid in the answer booklet, draw a cascade (Gantt) chart for the project.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2010 Q6 [15]}}