| Exam Board | AQA |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2007 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Complete precedence table from network |
| Difficulty | Easy -1.2 This is a routine Critical Path Analysis question requiring standard algorithmic procedures: reading a network diagram to complete a precedence table, performing forward/backward passes for earliest/latest times, identifying the critical path, and calculating float times. All steps follow mechanical algorithms with no problem-solving or novel insight required—purely procedural application of taught methods. |
| 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 |
| Precedence table completed correctly showing: A,B precede C,D,E; C,D precede F,G; E precede H; F,G precede I; G,H precede J; I,J precede K | B1 B1 | B1 for each correct column of predecessors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Earliest start times: A=0, B=0, C=2, D=1, E=1, F=5, G=6, H=4, I=11, J=11, K=16 | M1 A1 | M1 for attempt at forward pass |
| Latest finish times: A=2, B=6, C=5, D=6, E=4, F=11, G=9, H=9, I=16, J=16, K=17 | M1 A1 | M1 for attempt at backward pass |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Critical path: \(B \to D \to G \to J \to K\) | B1 | Must be stated as a path |
| Minimum completion time = 17 days | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Activity \(E\) has greatest float | B1 | |
| Float = \(4 - 1 - 3 = 0\)... Activity \(A\): float \(= 6-0-2=4\) or Activity \(C\): float \(= 5-2-3=0\) | M1 A1 | M1 for correct float calculation method: LF - ES - duration |
# Question 1:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Precedence table completed correctly showing: A,B precede C,D,E; C,D precede F,G; E precede H; F,G precede I; G,H precede J; I,J precede K | B1 B1 | B1 for each correct column of predecessors |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Earliest start times: A=0, B=0, C=2, D=1, E=1, F=5, G=6, H=4, I=11, J=11, K=16 | M1 A1 | M1 for attempt at forward pass |
| Latest finish times: A=2, B=6, C=5, D=6, E=4, F=11, G=9, H=9, I=16, J=16, K=17 | M1 A1 | M1 for attempt at backward pass |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Critical path: $B \to D \to G \to J \to K$ | B1 | Must be stated as a path |
| Minimum completion time = 17 days | B1 | |
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Activity $E$ has greatest float | B1 | |
| Float = $4 - 1 - 3 = 0$... Activity $A$: float $= 6-0-2=4$ or Activity $C$: float $= 5-2-3=0$ | M1 A1 | M1 for correct float calculation method: LF - ES - duration |
---1 [Figures 1 and 2, printed on the insert, are provided for use in this question.]\\
The following diagram shows an activity diagram for a building project. The time needed for each activity is given in days.\\
\includegraphics[max width=\textwidth, alt={}, center]{0c40b693-72d3-459c-bbb7-b9584a108b8e-02_698_1321_767_354}
\begin{enumerate}[label=(\alph*)]
\item Complete the precedence table for the project on Figure 1.
\item Find the earliest start times and latest finish times for each activity and insert their values on Figure 2.
\item Find the critical path 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.
\end{enumerate}
\hfill \mbox{\textit{AQA D2 2007 Q1 [10]}}