| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2011 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Moderate -0.5 This is a standard Critical Path Analysis question testing routine algorithmic procedures (forward/backward pass, float calculation, Gantt chart construction). While multi-part with several marks, it requires only methodical application of well-practiced techniques with no problem-solving insight or novel reasoning, making it slightly easier than average. |
| 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 | Mark | Guidance |
| Earliest start times: A=0, B=0, C=0, D=3, E=1, F=2, G=8, H=4, I=6, J=10, K=10, L=15 | B2 | B1 for at least 4 correct earliest start times |
| Latest finish times: A=3, B=8, C=6, D=8, E=8, F=10, G=10, H=10, I=16, J=15, K=16, L=16 | B2 | B1 for at least 4 correct latest finish times |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Critical path: B-E-H-J-L | B1 | Must be a path from start to finish |
| Critical path: C-F-I-K-L | B1 | Both paths required for full marks |
| Minimum completion time = 16 days | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Activity A (or D) has greatest float | B1 | Correct activity identified |
| Float time = 5 | B1 | For A: LFT - duration - EST = 3+5-3=5; must be consistent with answer |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Gantt chart drawn with activities starting as late as possible | B4 | B1 each for correct placement of activities on chart; deduct marks for activities not starting at latest start time; all 12 activities must be shown |
# Question 1:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Earliest start times: A=0, B=0, C=0, D=3, E=1, F=2, G=8, H=4, I=6, J=10, K=10, L=15 | B2 | B1 for at least 4 correct earliest start times |
| Latest finish times: A=3, B=8, C=6, D=8, E=8, F=10, G=10, H=10, I=16, J=15, K=16, L=16 | B2 | B1 for at least 4 correct latest finish times |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| Critical path: B-E-H-J-L | B1 | Must be a path from start to finish |
| Critical path: C-F-I-K-L | B1 | Both paths required for full marks |
| Minimum completion time = 16 days | B1 | |
## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| Activity A (or D) has greatest float | B1 | Correct activity identified |
| Float time = 5 | B1 | For A: LFT - duration - EST = 3+5-3=5; must be consistent with answer |
## Part (d)
| Answer | Mark | Guidance |
|--------|------|----------|
| Gantt chart drawn with activities starting as late as possible | B4 | B1 each for correct placement of activities on chart; deduct marks for activities not starting at latest start time; all 12 activities must be shown |
---1 Figure 1 below shows an activity diagram for a cleaning project. The duration of each activity is given in days.
\begin{enumerate}[label=(\alph*)]
\item Find the earliest start time and the latest finish time for each activity and insert their values on Figure 1.
\item Find the critical paths and state the minimum time for completion of the project.
\item Find the activity with the greatest float time and state the value of its float time.
\item On Figure 2 opposite, draw a cascade diagram (Gantt chart) for the project, assuming that each activity starts as late as possible.
(a)
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{1aca4e91-d1b3-4a78-8880-e42a4fbf3ddb-02_846_1488_1391_292}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{1aca4e91-d1b3-4a78-8880-e42a4fbf3ddb-03_1295_1714_219_150}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{(d)}
\includegraphics[alt={},max width=\textwidth]{1aca4e91-d1b3-4a78-8880-e42a4fbf3ddb-03_1023_1584_1589_278}
\end{center}
\end{figure}
\end{enumerate}
\hfill \mbox{\textit{AQA D2 2011 Q1 [13]}}