| Exam Board | OCR |
|---|---|
| Module | Further Discrete (Further Discrete) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Effect of activity delay/change |
| Difficulty | Moderate -0.5 This is a straightforward critical path analysis question requiring standard techniques: drawing an activity network, finding earliest/latest times, and analyzing the effect of a delay. While it involves multiple steps, all are routine algorithmic procedures covered in any Decision Maths textbook with no novel problem-solving required. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
| Activity | Immediate predecessors | Duration (hours) |
| A | - | 2 |
| B | A | 3 |
| C | - | 4 |
| D | C | 2 |
| E | B, C | 2 |
| F | D, E | 3 |
| G | E | 2 |
| H | F, G | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | A(2) B(3) E(2) G(2) |
| Answer | Marks |
|---|---|
| C(4) D(2) F(3) | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.3 |
| Answer | Marks |
|---|---|
| 3.3 | Activity on arc |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (b) | A(2) 2 B(3) 5 E(2) 7 G(2) |
| Answer | Marks |
|---|---|
| 11 (hours) | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.4 |
| 1.1 | Forward pass attempted for their network |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (c) | A(2) 2 B(3) 6 E(2) 8 G(2) |
| Answer | Marks |
|---|---|
| 12 (hours) | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.4 |
| 2.2a | Appropriate reasoning |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | 0 | 2 |
| 1 | 0 | 0.5 |
| 1 | 0 | 0 |
Question 1:
1 | (a) | A(2) B(3) E(2) G(2)
H(1)
C(4) D(2) F(3) | M1
A1
B1
[3] | 3.3
1.1
3.3 | Activity on arc
Durations not necessary, ignore any working
Single start, precedences correct for A, B, C, D
Single finish, precedences correct for E, F, G, H
Correct use of exactly 2 directed dummy activities
1 | (b) | A(2) 2 B(3) 5 E(2) 7 G(2)
0 10 11
H(1)
C(4) 4 D(2) 7 F(3)
11 (hours) | M1
A1
[2] | 3.4
1.1 | Forward pass attempted for their network
Ignore backward pass if shown
Or 2+3+2+3+1 seen
cao
SC B1 answer 11 without valid method seen
1 | (c) | A(2) 2 B(3) 6 E(2) 8 G(2)
0 11 12
H(1)
C(6) 6 D(2) 8 F(3)
12 (hours) | M1
A1
[2] | 3.4
2.2a | Appropriate reasoning
e.g. C becomes critical
delays E by 1 hour o.e.
E starts at 6 instead of 5, E finishes at 8, o.e.
Or 6 + 2 + 3 + 1 seen
cao
SC B1 answer 12 without valid method seen
1 | 0 | 2 | -1 | 0 | 1 | 6
1 | 0 | 0.5 | 0 | 1 | -1.5 | 11
1 | 0 | 0 | 60/k1 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 (hours) \\
\hline
A & - & 2 \\
\hline
B & A & 3 \\
\hline
C & - & 4 \\
\hline
D & C & 2 \\
\hline
E & B, C & 2 \\
\hline
F & D, E & 3 \\
\hline
G & E & 2 \\
\hline
H & F, G & 1 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Model the project using an activity network.
\item Determine the minimum project completion time.
The start of activity C is delayed by 2 hours.
\item Determine the minimum project completion time with this delay.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Discrete 2023 Q1 [7]}}