| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2013 |
| Session | Specimen |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.8 This is a standard D1 critical path analysis question requiring routine application of well-practiced algorithms: forward/backward pass for event times, identifying critical path, and drawing a cascade chart. While multi-part with several marks, each step follows a mechanical procedure taught explicitly in the specification with no novel problem-solving or insight required. Easier than average A-level maths. |
| 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 interpretation7.05e Cascade charts: scheduling and effect of delays |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Top boxes completed generally increasing left to right | M1 | |
| Top box values correct | A1 | CAO |
| Bottom boxes completed generally decreasing right to left | M1 | |
| Bottom box values correct | A1 | CAO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Critical activities: C, E, H, J, L | B1 | CAO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| At least 10 activities placed with at least five floats shown | M1 | Scheduling diagram gets M0 |
| Critical activities correct | A1 | |
| Condone one error on non-critical activities | A1 | |
| All non-critical activities correct | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 4 workers needed; correct statement with either time (\(7 <\) time \(< 9\), \(8 <\) day \(< 10\)) or activities stated | B1 | e.g. at time \(8\frac{1}{2}\) activities E, D, F and G must be happening; bod gets B1; allow 1B (only) on ft from 12-activity 7-float diagram |
| Correct complete full statement with details of time AND activities | B1 |
# Question 8:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Top boxes completed generally increasing left to right | M1 | |
| Top box values correct | A1 | CAO |
| Bottom boxes completed generally decreasing right to left | M1 | |
| Bottom box values correct | A1 | CAO |
**Total: 4 marks**
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Critical activities: C, E, H, J, L | B1 | CAO |
**Total: 1 mark**
## Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| At least 10 activities placed with at least five floats shown | M1 | Scheduling diagram gets M0 |
| Critical activities correct | A1 | |
| Condone one error on non-critical activities | A1 | |
| All non-critical activities correct | A1 | |
**Total: 4 marks**
## Part (d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| 4 workers needed; correct statement with either time ($7 <$ time $< 9$, $8 <$ day $< 10$) or activities stated | B1 | e.g. at time $8\frac{1}{2}$ activities E, D, F and G must be happening; bod gets B1; allow 1B (only) on ft from 12-activity 7-float diagram |
| Correct complete full statement with details of time AND activities | B1 | |
**Total: 2 marks**8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{5fa867a2-0a3d-4f0b-9f9c-15584f2be5c0-10_705_1207_248_427}
\captionsetup{labelformat=empty}
\caption{Figure 7}
\end{center}
\end{figure}
A project is modelled by the activity network shown in Figure 7. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. Each activity requires one worker. The project is to be completed in the shortest possible time.
\begin{enumerate}[label=(\alph*)]
\item Complete Diagram 2 in the answer book to show the early and late event times.
\item State the critical activities.
\item On Grid 1 in the answer book, draw a cascade (Gantt) chart for this project.
\item Use your cascade chart to determine a lower bound for the number of workers needed. You must justify your answer.
\section*{END}
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2013 Q8 [11]}}