| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate lower bound for workers |
| Difficulty | Moderate -0.3 This is a standard Critical Path Analysis question covering routine D1 techniques: finding early/late times, identifying critical path, calculating float, and determining lower bound for workers. All parts follow textbook procedures with no novel problem-solving required, making it slightly easier than average A-level difficulty. |
| 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/Working | Marks | Guidance |
| [Network diagram with activities and floats] | M1, A1, M1, A1 | (4) |
| Critical activities: C, D, H, K, M and N | B1 | (1) |
| Float on E: \(20 - 13 - 4 = 3\) (days) | M1 A1 | (2) |
| \(\frac{88}{35} \approx 2.514 = 3\) (workers) | M1 A1 | (2) |
| [Gantt chart showing activities A through Q] | M1, A1, M1, A1 | (4) |
| 13 marks |
| Answer/Working | Marks | Guidance |
|---|---|---|
| [Network diagram with activities and floats] | M1, A1, M1, A1 | (4) |
| **Critical activities:** C, D, H, K, M and N | B1 | (1) |
| **Float on E:** $20 - 13 - 4 = 3$ (days) | M1 A1 | (2) |
| $\frac{88}{35} \approx 2.514 = 3$ (workers) | M1 A1 | (2) |
| [Gantt chart showing activities A through Q] | M1, A1, M1, A1 | (4) |
| | | **13 marks** |
**Notes for Question 6:**
- a1M1: All top boxes complete, values generally increasing in the direction of the arrows ('left to right'), condone one 'rogue' value – condone a missing 0 in the first box for the M mark only
- a1A1: CAO (top boxes)
- a2M1: All bottom boxes complete, values generally decreasing in the opposite direction of the arrows ('right to left'), condone one 'rogue' value – condone a missing 0 in the first box for the M mark only
- a2A1: CAO (bottom boxes)
- b1B1: CAO on the critical activities (C, D, H, K, M, N)
- c1M1: Correct calculation seen for activity E – all three numbers correct (following through the candidates completed diagram), float $\geq 0$
- c1A1: Float correct (no ft on this mark) – correct answer with no working scores M0A0
- d1M1: Attempt to find lower bound: (a value in the interval [79 – 97] / their finish time) or (sum of the activities / their finish time) or as a minimum an awrt 2.51
- d1A1: CSO – either a **correct calculation seen or awrt 2.51 then 3**. An answer of 3 with no working scores M0A0
- e1M1: At least 10 activities including 6 floats. Scheduling diagram scores M0
- e1A1: Critical activities dealt with correctly and five other non-critical activities dealt with correctly
- e2M1: Exactly 16 activities (just once) including all 10 floats (on the correct non-critical activities) – this mark is not dependent on the previous A mark
- e2A1: CAO (all activities correct and present just once)
---6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{049de386-42a9-4f16-8be3-9324382e4988-07_773_1353_226_372}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{center}
\end{figure}
A project is modelled by the activity network shown in Figure 5. 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 exactly one worker. The project is to be completed in the shortest possible time.
\begin{enumerate}[label=(\alph*)]
\item Complete Diagram 1 in the answer book to show the early event times and late event times.
\item State the critical activities.
\item Calculate the maximum number of days by which activity E could be delayed without lengthening the completion time of the project. You must make the numbers used 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.
\item Draw a cascade (Gantt) chart for this project on the grid provided in the answer book.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D1 2016 Q6 [13]}}