| Exam Board | OCR |
|---|---|
| Module | Further Discrete (Further Discrete) |
| Year | 2022 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate early and late times |
| Difficulty | Moderate -0.5 This is a standard critical path analysis question requiring routine application of well-defined algorithms (drawing network, forward/backward pass, calculating floats). While it involves multiple steps and careful bookkeeping, it requires no problem-solving insight or novel approaches—just methodical execution of textbook procedures. Slightly easier than average due to the small network size (8 activities) and straightforward precedence relationships. |
| 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 interpretation |
| Activity | Immediate predecessors | Duration (minutes) |
| A | - | 4 |
| B | - | 1 |
| C | A | 2 |
| D | A, B | 5 |
| E | D | 1 |
| F | B, C | 2 |
| G | D, F | 5 |
| H | E, F | 4 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (a) | C F |
| Answer | Marks |
|---|---|
| D E | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | Durations and working for parts (b) and (c) may be seen |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (b) | Minimum project completion time = 14 minutes |
| Answer | Marks |
|---|---|
| [3] | 3.4 |
| Answer | Marks |
|---|---|
| 1.1 | Forward pass for their network, provided it includes at least one |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (c) | See answer to part (b) |
| Answer | Marks |
|---|---|
| B = 3 | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.4 |
| Answer | Marks |
|---|---|
| 1.1 | Their backward pass used to find any one non-zero float |
Question 2:
2 | (a) | C F
A G
B H
D E | M1
A1
A1
[3] | 3.1a
1.1
1.1 | Durations and working for parts (b) and (c) may be seen
Single start with activities A, B and single end with activities G, H
(and no others at either end)
Precedences for activities C, D, E, F all correct
All dummies directed and correct with at most 1 extra
2 | (b) | Minimum project completion time = 14 minutes | M1
A1
B1
[3] | 3.4
3.4
1.1 | Forward pass for their network, provided it includes at least one
burst and at least one merge (other than at start and finish)
All forward pass labels correct for a correct network
For reference:
14 cao
2 | (c) | See answer to part (b)
C = 1, F = 1
B = 3 | M1
A1
A1
[3] | 3.4
3.4
1.1 | Their backward pass used to find any one non-zero float
Both cao
cao
If all three are correct but also any other activities are listed with
non-zero floats give M1 A1 A02 The table below shows the activities involved in a project together with the immediate predecessors and the duration of each activity.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Immediate predecessors & Duration (minutes) \\
\hline
A & - & 4 \\
\hline
B & - & 1 \\
\hline
C & A & 2 \\
\hline
D & A, B & 5 \\
\hline
E & D & 1 \\
\hline
F & B, C & 2 \\
\hline
G & D, F & 5 \\
\hline
H & E, F & 4 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Model the project using an activity network.
\item Determine the minimum project completion time.
\item Calculate the total float for each non-critical activity.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Discrete 2022 Q2 [9]}}