| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2014 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.8 This is a straightforward application of standard activity network construction from a precedence table. It requires only mechanical application of rules for drawing activity-on-arc networks with no problem-solving or novel insight—purely procedural recall of D2 techniques, making it easier than average. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct boxes for \(B\) and \(C\) (predecessors of \(A\), durations 3 and 4) | B1 | Both boxes correctly drawn with EST and duration |
| Correct boxes for \(D\), \(E\), \(F\), \(G\), \(H\) with correct predecessors | B1 | All arrows correctly showing dependencies |
| Correct boxes for \(I\), \(J\), \(K\), \(L\) with correct predecessors and single end node | B1 | \(L\) correctly shown with predecessors \(H\), \(I\), \(J\), \(K\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(A=0\), \(B=3\), \(C=3\), \(H=3\), \(F=7\), \(G=7\) | M1 | Forward pass attempted |
| \(D=7\), \(E=7\), \(I=12\), \(J=9\), \(K=8\), \(L=18\) | A1 | All correct ESTs |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Backward pass attempted from \(L=19\) | M1 | Working backwards correctly |
| \(L=19\), \(K=19\), \(J=19\), \(I=19\), \(H=18\), \(G=9\), \(F=13\), \(E=14\), \(D=13\), \(C=7\), \(B=7\), \(A=3\) | A1 | All correct LFTs |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Correct identification of critical path | B1 | \(A\), \(C\), \(D\), \(I\), \(L\) or equivalent stated |
| All critical activities listed correctly | B1 | Must follow from correct EST/LFT values |
# Question 1:
## Part (a) - Activity Network [3 marks]
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct boxes for $B$ and $C$ (predecessors of $A$, durations 3 and 4) | B1 | Both boxes correctly drawn with EST and duration |
| Correct boxes for $D$, $E$, $F$, $G$, $H$ with correct predecessors | B1 | All arrows correctly showing dependencies |
| Correct boxes for $I$, $J$, $K$, $L$ with correct predecessors and single end node | B1 | $L$ correctly shown with predecessors $H$, $I$, $J$, $K$ |
## Part (b) - Earliest Start Times [2 marks]
| Answer | Mark | Guidance |
|--------|------|----------|
| $A=0$, $B=3$, $C=3$, $H=3$, $F=7$, $G=7$ | M1 | Forward pass attempted |
| $D=7$, $E=7$, $I=12$, $J=9$, $K=8$, $L=18$ | A1 | All correct ESTs |
## Part (c) - Latest Finish Times [2 marks]
| Answer | Mark | Guidance |
|--------|------|----------|
| Backward pass attempted from $L=19$ | M1 | Working backwards correctly |
| $L=19$, $K=19$, $J=19$, $I=19$, $H=18$, $G=9$, $F=13$, $E=14$, $D=13$, $C=7$, $B=7$, $A=3$ | A1 | All correct LFTs |
## Part (d) - Critical Activities [2 marks]
| Answer | Mark | Guidance |
|--------|------|----------|
| Correct identification of critical path | B1 | $A$, $C$, $D$, $I$, $L$ or equivalent stated |
| All critical activities listed correctly | B1 | Must follow from correct EST/LFT values |
---1 A major project has been divided into a number of tasks, as shown in the table. The minimum time required to complete each task is also shown.
\section*{Answer space for question 1}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{c2b62fee-d320-4701-a5bb-b2e4b8cc0952-03_424_410_296_685}
\end{center}
\hfill \mbox{\textit{AQA D2 2014 Q1 [9]}}