| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2008 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Effect of activity delay/change |
| Difficulty | Moderate -0.8 This is a routine Critical Path Analysis question testing standard algorithms (forward/backward pass, critical path identification, Gantt chart construction) with a straightforward 'what-if' scenario. Part (d) requires recalculating earliest start times after one activity duration changes—a mechanical process with no novel problem-solving. Typical D2 examination question but easier than average A-level maths overall. |
| 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 |
| Earliest start times: A=0, B=0, C=4, D=4, E=2, F=10, G=10, H=6, I=15, J=13, K=20 | B1 | For correct early times |
| Latest finish times working back from 22: K=22, I=20, J=20, G=15, F=19, H=13, D=10, C=19, E=13, A=4, B=10 | B1 | For correct late times |
| All values correct on diagram | B2 | Award B1 for at least half correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Critical path: \(B \to D \to G \to I \to K\) | B2 | B1 for each correct path identified |
| Minimum completion time = 22 days | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Gantt chart drawn with correct bars starting at earliest times | B3 | B1 for each correctly placed activity bar |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| C now takes 8 days, so earliest start of F becomes 12 | B1 | |
| No effect on minimum completion time (still 22 days) as F and C not on critical path | B1 |
# Question 1:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Earliest start times: A=0, B=0, C=4, D=4, E=2, F=10, G=10, H=6, I=15, J=13, K=20 | B1 | For correct early times |
| Latest finish times working back from 22: K=22, I=20, J=20, G=15, F=19, H=13, D=10, C=19, E=13, A=4, B=10 | B1 | For correct late times |
| All values correct on diagram | B2 | Award B1 for at least half correct |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Critical path: $B \to D \to G \to I \to K$ | B2 | B1 for each correct path identified |
| Minimum completion time = 22 days | B1 | |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Gantt chart drawn with correct bars starting at earliest times | B3 | B1 for each correctly placed activity bar |
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| C now takes 8 days, so earliest start of F becomes 12 | B1 | |
| No effect on minimum completion time (still 22 days) as F and C not on critical path | B1 | |
---1 [Figures 1 and 2, printed on the insert, are provided for use in this question.]\\
The following diagram shows an activity network for a project. The time needed for each activity is given in days.\\
\includegraphics[max width=\textwidth, alt={}, center]{f98d4434-458a-4118-92ed-309510d7975a-02_940_1698_721_164}
\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.
\item On Figure 2, draw a cascade diagram (Gantt chart) for the project, assuming each activity starts as early as possible.
\item Activity $C$ takes 5 days longer than first expected. Determine the effect on the earliest start time for other activities and the minimum completion time for the project.\\
(2 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA D2 2008 Q1 [12]}}