| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2018 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Find missing early/late times |
| Difficulty | Moderate -0.5 This is a standard Critical Path Analysis question requiring systematic application of learned algorithms (forward/backward pass, float calculations) to find missing times and construct a Gantt chart. While it involves multiple steps and careful bookkeeping, it requires no novel insight or problem-solving—just methodical application of D1 techniques that students practice extensively. |
| 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 float |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(w = 20, x = 6, y = 12, z = 10\) | B4,3,2,1,0 | Award B1 for each correct value |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Scheduling diagram with at least 10 activities including at least 4 floats | M1 | At least ten activities including at least four floats; scheduling diagram scores M0 |
| Critical activities (A, C, E, H, I, J, M) dealt with correctly, appearing just once | A1 | Critical activities dealt with correctly and appearing just once |
| Any five non-critical activities correct | M1 | |
| Completely correct Gantt chart (exactly fourteen activities just once) | A1 | CSO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Minimum workers is 4 activities H, I, F and G | M1 | Either correct number of workers (4) and correct activities, with any time stated, OR correct number of workers and a correct time |
| together with \(14 < \text{time} < 16\) | A1 | Completely correct statement with details of both time and activities. Time must be within \(14 < \text{time} < 16\). Note strict inequalities. Time \(15-16\) is A0. |
# Question 2:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $w = 20, x = 6, y = 12, z = 10$ | B4,3,2,1,0 | Award B1 for each correct value |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Scheduling diagram with at least 10 activities including at least 4 floats | M1 | At least ten activities including at least four floats; scheduling diagram scores M0 |
| Critical activities (A, C, E, H, I, J, M) dealt with correctly, appearing just once | A1 | Critical activities dealt with correctly and appearing just once |
| Any five non-critical activities correct | M1 | |
| Completely correct Gantt chart (exactly fourteen activities just once) | A1 | CSO |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Minimum workers is 4 activities H, I, F and G | M1 | Either correct number of workers (4) and correct activities, with any time stated, OR correct number of workers and a correct time |
| together with $14 < \text{time} < 16$ | A1 | Completely correct statement with details of both time and activities. Time must be within $14 < \text{time} < 16$. Note strict inequalities. Time $15-16$ is A0. |
---2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e0c89aba-9d2e-469b-8635-d513df0b65a4-03_1031_1571_226_246}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
The network in Figure 3 shows the activities that need to be undertaken by a company to complete a project. Each activity is represented by an arc and the duration of the activity, in days, is shown in brackets. Each activity requires exactly one worker. The early event times and late event times are shown at each vertex.
Given that the total float on activity B is 2 days and the total float on activity F is also 2 days,
\begin{enumerate}[label=(\alph*)]
\item find the values of $w , x , y$ and $z$.
\item Draw a cascade (Gantt) chart for this project on Grid 1 in the answer book.
\item Use your cascade chart to determine the minimum number of workers needed to complete the project in the shortest possible time. You must make specific reference to time and activities. (You do not need to provide a schedule of the activities.)
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2018 Q2 [10]}}