| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.8 This is a standard Critical Path Analysis question requiring routine application of well-defined algorithms. Parts (a)-(b) involve straightforward network construction and critical path identification from a simple precedence table. Parts (c)-(d) add a timing constraint requiring a dummy activity, which is a textbook technique in D2. The question involves no novel problem-solving or complex reasoning—just methodical application of standard procedures. |
| 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 |
| Task | Duration (minutes) | Immediate predecessors |
| A | 18 | - |
| B | 23 | - |
| C | 13 | \(A , B\) |
| D | 9 | A |
| E | 28 | \(B , D\) |
| \(F\) | 23 | C |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| (a) Network with correct forward and backward scan values completed | M1 A2 | |
| (b) Lower figures give forward scan | M1 | |
| Upper figures give backward scan | M1 | |
| Critical path is \(BCF\) | A1 | |
| Minimum time is 59 minutes | A1 | |
| (c) New network with \(B\) split into \(B_1, B_2\); correct forward and backward scan values | M1 A1 | |
| (d) New minimum time is 65 minutes | M1 A1 | |
| New critical path is \(B_1ADE\) | A1 | (12) |
# Question 5:
| Answer/Working | Mark | Guidance |
|---|---|---|
| **(a)** Network with correct forward and backward scan values completed | M1 A2 | |
| **(b)** Lower figures give forward scan | M1 | |
| Upper figures give backward scan | M1 | |
| Critical path is $BCF$ | A1 | |
| Minimum time is 59 minutes | A1 | |
| **(c)** New network with $B$ split into $B_1, B_2$; correct forward and backward scan values | M1 A1 | |
| **(d)** New minimum time is 65 minutes | M1 A1 | |
| New critical path is $B_1ADE$ | A1 | **(12)** |
---\begin{enumerate}
\item A project involves six tasks, some of which cannot be started until others have been completed. This is shown in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Task & Duration (minutes) & Immediate predecessors \\
\hline
A & 18 & - \\
\hline
B & 23 & - \\
\hline
C & 13 & $A , B$ \\
\hline
D & 9 & A \\
\hline
E & 28 & $B , D$ \\
\hline
$F$ & 23 & C \\
\hline
\end{tabular}
\end{center}
(a) Draw an activity network for this project.\\
(b) By labelling your network, find the critical path and the minimum duration of the project.
An extra condition is now imposed. Task $A$ may not begin until task $B$ has been underway for at least 10 minutes.\\
(c) Draw a new network taking into account this restriction.\\
(d) Find a revised value for the minimum duration of the project and state the new critical path.\\
\hfill \mbox{\textit{OCR D2 Q5 [12]}}