| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 12 |
| 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: reading a network to complete a precedence table, forward/backward pass for event times, calculating float, finding lower bound (sum of durations ÷ project duration), and resource scheduling. All techniques are textbook procedures with no novel problem-solving required, making it 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 interpretation7.05d Latest start and earliest finish: independent and interfering float7.05e Cascade charts: scheduling and effect of delays |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Completed precedence table (all 8 rows correct) | B2,1,0 | B2 all correct; B1 any four rows correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| All top boxes complete, values generally increasing left to right | M1 | Condone one rogue |
| Top boxes CAO | A1 | |
| All bottom boxes complete, values generally decreasing right to left | M1 | Condone one rogue |
| Bottom boxes CAO | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Float on \(D = 21-5-8 = 8\) | B1 | CAO – correct calculation seen |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Lower bound is \(\frac{142}{42} = 3.38\ldots = 4\) | B1 | CAO – correct calculation seen or awrt 3.4 then 4; answer of 4 with no working scores B0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Gantt chart (not cascade), 5 workers used at most, at least 8 new (14 total) activities placed | M1 | |
| 4 workers, all 11 new (17 total) activities present (just once), condone two errors either precedence or time interval or activity length | A1 | |
| 4 workers, all 11 new (17 total) activities present (just once), condone one error | A1 | |
| CAO | A1 |
# Question 6:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Completed precedence table (all 8 rows correct) | B2,1,0 | B2 all correct; B1 any four rows correct |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| All top boxes complete, values generally increasing left to right | M1 | Condone one rogue |
| Top boxes CAO | A1 | |
| All bottom boxes complete, values generally decreasing right to left | M1 | Condone one rogue |
| Bottom boxes CAO | A1 | |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Float on $D = 21-5-8 = 8$ | B1 | CAO – correct calculation seen |
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Lower bound is $\frac{142}{42} = 3.38\ldots = 4$ | B1 | CAO – correct calculation seen **or** awrt 3.4 then 4; answer of 4 with no working scores B0 |
## Part (e)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Gantt chart (not cascade), 5 workers used at most, at least 8 new (14 total) activities placed | M1 | |
| 4 workers, all 11 new (17 total) activities present (just once), condone two errors either precedence or time interval or activity length | A1 | |
| 4 workers, all 11 new (17 total) activities present (just once), condone one error | A1 | |
| CAO | A1 | |
---6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{6417303d-c42a-4da4-b0fa-fb7718959417-8_1180_1572_207_251}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{center}
\end{figure}
[The sum of the durations of all the activities is 142 days]\\
A project is modelled by the activity network shown in Figure 6. 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 the precedence table in the answer book.
\item Complete Diagram 1 in the answer book to show the early event times and late event times.
\item Calculate the total float for activity D. You must make the numbers you use in your calculation clear.
\item Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working.
Diagram 2 in the answer book shows a partly completed scheduling diagram for this project.
\item Complete the scheduling diagram, using the minimum number of workers, so that the project is completed in the minimum time.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2015 Q6 [12]}}