| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2002 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Schedule with limited workers - create schedule/chart |
| Difficulty | Standard +0.3 This is a standard D1 critical path analysis question requiring identification of critical activities, calculation of floats, drawing a Gantt chart, and determining minimum workers. All techniques are routine textbook exercises with no novel problem-solving required, making it slightly easier than average for A-level. |
| Spec | 7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation7.05d Latest start and earliest finish: independent and interfering float |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Critical activities \(B, F, J, K, N\) (not \(I\)); length 25 hours | B1; B1 | (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(A = 5-0-3=2\) | M1 A1 ft | |
| \(C = 9-0-6=3\) | ||
| \(D = 11-3-3=5\) | A1 | |
| \(E = 9-3-4=2\) | ||
| \(G = 9-4-3=2\) | ||
| \(H = 16-7-7=2\) | ||
| \(I = 16-9-5=2\) | ||
| \(L = 22-11-4=7\) | ||
| \(M = 22-16-2=4\) | ||
| \(P = 25-18-3=4\) | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct Gantt chart with critical activities \(B, F, J, K, N\) shown on top row | M1 A1 | |
| Non-critical activities with float shown correctly | A1 ft | |
| All activities correctly positioned | A1 ft | (implied) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct resource levelling diagram showing scheduling | M1 | |
| Activities correctly allocated to workers | A1 | |
| 3 workers needed | A1 | (3) |
| (12 marks) |
# Question 6:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Critical activities $B, F, J, K, N$ (not $I$); length 25 hours | B1; B1 | **(2)** |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $A = 5-0-3=2$ | M1 A1 ft | |
| $C = 9-0-6=3$ | | |
| $D = 11-3-3=5$ | A1 | |
| $E = 9-3-4=2$ | | |
| $G = 9-4-3=2$ | | |
| $H = 16-7-7=2$ | | |
| $I = 16-9-5=2$ | | |
| $L = 22-11-4=7$ | | |
| $M = 22-16-2=4$ | | |
| $P = 25-18-3=4$ | | **(3)** |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct Gantt chart with critical activities $B, F, J, K, N$ shown on top row | M1 A1 | |
| Non-critical activities with float shown correctly | A1 ft | |
| All activities correctly positioned | A1 ft | **(implied)** |
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct resource levelling diagram showing scheduling | M1 | |
| Activities correctly allocated to workers | A1 | |
| 3 workers needed | A1 | **(3)** |
| | **(12 marks)** | |
---6.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\includegraphics[alt={},max width=\textwidth]{652477eb-87dc-4a5a-8514-c9be39986142-6_1083_1608_421_259}
\end{center}
\end{figure}
A building project is modelled by the activity network shown in Fig. 4. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, taken to complete the activity. The left box entry at each vertex is the earliest event time and the right box entry is the latest event time.
\begin{enumerate}[label=(\alph*)]
\item Determine the critical activities and state the length of the critical path.
\item State the total float for each non-critical activity.
\item On the grid in the answer booklet, draw a cascade (Gantt) chart for the project.
Given that each activity requires one worker,
\item draw up a schedule to determine the minimum number of workers required to complete the project in the critical time. State the minimum number of workers.\\
(3)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2002 Q6 [12]}}