| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2009 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.3 This is a standard D1 critical path analysis question covering routine procedures: calculating early/late times, identifying critical path, computing float, and drawing a cascade chart. While multi-part with several marks, each component follows algorithmic procedures taught directly in the syllabus with no novel problem-solving required. Slightly easier than average A-level due to being a straightforward application of well-practiced techniques. |
| 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 |
| Upper half of activity network correct | M1 A1 | |
| Lower half of activity network correct | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Critical activities: A, I, K, M, N; Length 39 | B2, 1, 0; B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Float on F is \(34 - 15 - 15 = 4\) | M1 A1 | |
| Float on G is \(24 - 15 - 3 = 6\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Cascade (Gantt) chart drawn correctly — critical activities | M1 A1 | |
| Non-critical activities shown correctly with floats | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| e.g. At time \(14\tfrac{1}{2}\) there are 4 tasks: I, E, H and C must be happening | B2, 1, 0 |
# Question 8:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Upper half of activity network correct | M1 A1 | |
| Lower half of activity network correct | M1 A1 | |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Critical activities: A, I, K, M, N; Length 39 | B2, 1, 0; B1 | |
## Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Float on F is $34 - 15 - 15 = 4$ | M1 A1 | |
| Float on G is $24 - 15 - 3 = 6$ | B1 | |
## Part (d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Cascade (Gantt) chart drawn correctly — critical activities | M1 A1 | |
| Non-critical activities shown correctly with floats | M1 A1 | |
## Part (e):
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. At time $14\tfrac{1}{2}$ there are 4 tasks: I, E, H and C must be happening | B2, 1, 0 | |8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{ef029462-ffed-4cdf-87bc-56c8a13d671f-8_574_1362_242_349}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{center}
\end{figure}
The network in Figure 5 shows the activities involved in a process. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, taken to complete the activity.
\begin{enumerate}[label=(\alph*)]
\item Calculate the early time and the late time for each event, showing them on the diagram in the answer book.
\item Determine the critical activities and the length of the critical path.
\item Calculate the total float on activities F and G . You must make the numbers you used in your calculation clear.
\item On the grid in the answer book, draw a cascade (Gantt) chart for the process.
Given that each task requires just one worker,
\item use your cascade chart to determine the minimum number of workers required to complete the process in the minimum time. Explain your reasoning clearly.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2009 Q8 [16]}}