| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2007 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Identify critical path and activities |
| Difficulty | Easy -1.2 This is a standard textbook critical path analysis question requiring routine application of the forward pass and backward pass algorithms. While it involves multiple steps (drawing network, calculating earliest/latest times, identifying critical path), these are mechanical procedures with no problem-solving insight required. The precedence table is straightforward with no ambiguities or traps. |
| 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 |
| Activity | Immediate Predecessors | Duration (weeks) |
| A | - | 2 |
| B | - | 1 |
| C | A | 3 |
| D | A, B | 2 |
| E | B | 4 |
| F | C | 1 |
| G | \(C , D , E\) | 3 |
| H | E | 5 |
| I | \(F , G\) | 2 |
| J | \(H , I\) | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Network attempted | M1 | SCA |
| Up to 2 slips (boxes or arrows) | A1 | |
| Correct network | A1 | Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Forward pass attempted | M1 | |
| Correct | A1 | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Backward pass attempted | M1 | |
| Correct | A1 | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Minimum completion time: 13 weeks | B1 | |
| Critical path: \(ACGIJ\) | B1 | |
| Critical path: \(BEGIJ\) | B1 | |
| Critical path: \(BEHJ\) | B1 | Total: 4 |
# Question 1:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Network attempted | M1 | SCA |
| Up to 2 slips (boxes or arrows) | A1 | |
| Correct network | A1 | **Total: 3** |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Forward pass attempted | M1 | |
| Correct | A1 | **Total: 2** |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Backward pass attempted | M1 | |
| Correct | A1 | **Total: 2** |
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Minimum completion time: 13 weeks | B1 | |
| Critical path: $ACGIJ$ | B1 | |
| Critical path: $BEGIJ$ | B1 | |
| Critical path: $BEHJ$ | B1 | **Total: 4** |
---1 [Figure 1, printed on the insert, is provided for use in this question.]\\
A building project is to be undertaken. The table shows the activities involved.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Immediate Predecessors & Duration (weeks) \\
\hline
A & - & 2 \\
\hline
B & - & 1 \\
\hline
C & A & 3 \\
\hline
D & A, B & 2 \\
\hline
E & B & 4 \\
\hline
F & C & 1 \\
\hline
G & $C , D , E$ & 3 \\
\hline
H & E & 5 \\
\hline
I & $F , G$ & 2 \\
\hline
J & $H , I$ & 3 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Complete an activity network for the project on Figure 1.
\item Find the earliest start time for each activity.
\item Find the latest finish time for each activity.
\item State the minimum completion time for the building project and identify the critical paths.
\end{enumerate}
\hfill \mbox{\textit{AQA D2 2007 Q1 [11]}}