| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.8 This is a standard D1 critical path analysis question testing routine algorithmic procedures: forward/backward pass for event times, identifying critical path, drawing a Gantt chart, and finding minimum workers from the chart. All parts follow textbook methods with no problem-solving insight required, making it easier than average A-level maths questions. |
| 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 interpretation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Top boxes: 0, 0<br>A (4), B (2), C (3), D (5), E (6), F (9), G (10), H (2), I (4), J (5), K (3), L (6) | M1 A1 M1 A1 | M1: Top boxes completed generally increasing left to right.<br>1A1: CAO.<br>2M1: Bottom boxes completed generally decreasing right to left.<br>2A1: CAO. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Critical activities: C E H J L | B1 | 1B1: Critical activities cao. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Gantt chart with: C, E, H, J, L on critical path<br>A, B, D, F, G, I, K activities placed with at least 5 floats | M1 A1 A1 | M1: At least 10 activities placed, at least five floats. Scheduling diagram gets M0.<br>1A1: my critical activities correct.<br>2A1: condone one error on my non-critical activities.<br>3A1: my non-critical activities correct. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 4 workers needed e.g. at time 8 ½ (noon on day 9) activities E, D, F and G must be happening. | B2, 1, 0 | 1B1: A correct statement, details of either time (7<time<9, 8<day<10), or activities, bod gets B1. Allow 1 B mark (only) on ft from their 12 activity, 7 float diagram.<br>2B1: A correct, complete full statement details of time and activities. |
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Top boxes: 0, 0<br>A (4), B (2), C (3), D (5), E (6), F (9), G (10), H (2), I (4), J (5), K (3), L (6) | M1 A1 M1 A1 | M1: Top boxes completed generally increasing left to right.<br>1A1: CAO.<br>2M1: Bottom boxes completed generally decreasing right to left.<br>2A1: CAO. |
**Total: 4 marks**
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Critical activities: C E H J L | B1 | 1B1: Critical activities cao. |
**Total: 1 mark**
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Gantt chart with: C, E, H, J, L on critical path<br>A, B, D, F, G, I, K activities placed with at least 5 floats | M1 A1 A1 | M1: At least 10 activities placed, at least five floats. Scheduling diagram gets M0.<br>1A1: my critical activities correct.<br>2A1: condone one error on my non-critical activities.<br>3A1: my non-critical activities correct. |
**Total: 4 marks**
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| 4 workers needed e.g. at time 8 ½ (noon on day 9) activities E, D, F and G must be happening. | B2, 1, 0 | 1B1: A correct statement, details of either time (7<time<9, 8<day<10), or activities, bod gets B1. Allow 1 B mark (only) on ft from their 12 activity, 7 float diagram.<br>2B1: A correct, complete full statement details of time and activities. |
**Total: 2 marks**
**Grand Total for Q8: 11 marks**
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# Overall Mark Totals
- Q1: 8 marks
- Q2: 9 marks
- Q3: 9 marks
- Q4: 10 marks
- Q5: 8 marks
- Q6: 9 marks
- Q7: 11 marks
- Q8: 11 marks
**Total: 75 marks**\includegraphics{figure_7}
A project is modelled by the activity network shown in Figure 7. 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 Diagram 2 in the answer book to show the early and late event times.
[4]
\item State the critical activities.
[1]
\item On Grid 1 in the answer book, draw a cascade (Gantt) chart for this project.
[4]
\item Use your cascade chart to determine a lower bound for the number of workers needed.
You must justify your answer.
[2]
\end{enumerate}
(Total 11 marks)
TOTAL FOR PAPER: 75 MARKS
END
\hfill \mbox{\textit{Edexcel D1 2010 Q8 [11]}}