| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2020 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Find missing early/late times |
| Difficulty | Moderate -0.3 This is a standard D1 critical path analysis question requiring calculation of missing times using the float relationship and drawing a cascade chart. While it involves multiple parts and understanding of float concepts, the techniques are routine and algorithmic once the float formula is applied. The constraint that float_D = 2×float_E provides a straightforward equation to solve for the unknowns. This is slightly easier than average as it's a textbook application of standard CPA algorithms without requiring novel problem-solving insight. |
| 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 |
|---|---|---|
| \(x = 8, y = 12, z = 17\) | B3, 2, 1, 0 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| At least ten activities labelled including at least five floats. A scheduling diagram scores M0 | M1 | |
| The critical activities dealt with correctly and appearing just once (C, H, I and J) and three non-critical activities dealt with correctly | A1 | |
| Any six non-critical activities correct (this mark is not dependent on the previous A mark) | A1 | (4) |
| Lower bound is 4 workers e.g. activities J, K, L and M together with 24 < time < 26 | M1 A1 | (2) |
| $x = 8, y = 12, z = 17$ | B3, 2, 1, 0 | (3) |
[Gantt chart diagram with activities A through M]
| At least ten activities labelled including at least five floats. A scheduling diagram scores M0 | M1 | |
| The critical activities dealt with correctly and appearing just once (C, H, I and J) and three non-critical activities dealt with correctly | A1 | |
| Any six non-critical activities correct (this mark is not dependent on the previous A mark) | A1 | (4) |
| Lower bound is 4 workers e.g. activities J, K, L and M together with 24 < time < 26 | M1 A1 | (2) |
**Notes for Question 3:**
- **a1B1:** $x$ value correct
- **a2B1:** $y$ value correct
- **a3B1:** $z$ value correct
- **b1M1:** At least ten activities labelled including at least five floats. A scheduling diagram scores M0
- **b1A1:** The critical activities dealt with correctly and appearing just once (C, H, I and J) and three non-critical activities dealt with correctly
- **b2A1:** Any six non-critical activities correct (this mark is not dependent on the previous A mark)
- **b3A1:** CSO – completely correct Gantt chart (exactly thirteen activities appearing just once)
- **c1M1:** Either a statement with the correct number of workers (4) and the correct activities (J, K, L and M) with any numerical time stated or the correct number of workers (4) and a time in the interval 24 ≤ x ≤ 26 – mark the numerical value only not their use of day/time
- **c1A1:** A completely correct statement with details of both time and activities. Candidates must give a time within the correct interval of 24 < x < 26. Please note the strict inequalities for the time interval (e.g. implying a time of 24 is incorrect). Answers given as an interval of time are acceptable provided the time interval stated is correct for all its possible values (e.g. time 25 – 26 is A0). Note that 'on day 25' or 'on day 26' are correct but 'on day 24' is not correct. A completely correct statement with an additional incorrect statement scores A0 (so no isw)
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{b6d09c46-abfd-4baa-80bd-7485d1bf8e0d-04_865_1636_246_219}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
The network in Figure 2 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, in days, is shown in brackets. Each activity requires one worker. The early event times and late event times are shown at each vertex.
The total float on activity D is twice the total float on activity E .
\begin{enumerate}[label=(\alph*)]
\item Find the values of $x , y$ and $z$.
\item Draw a cascade chart for this project on Grid 1 in the answer book.
\item Use your cascade chart to determine a lower bound for 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 2020 Q3 [9]}}