| Exam Board | OCR |
|---|---|
| Module | Further Discrete AS (Further Discrete AS) |
| Year | 2023 |
| Session | June |
| Marks | 11 |
| 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 covering routine algorithmic procedures (forward pass, backward pass, float calculation) that are directly taught and practiced. Part (d) requires slightly more thought about network modification, but the overall question is more straightforward than average A-level maths due to its purely procedural nature with no proof or novel problem-solving required. |
| 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 (hours) | |
| A | Choose the topics | - | 0.5 |
| B | Find questions for round 1 | A | 2 |
| C | Check answers for round 1 | B | 2.5 |
| D | Find questions for round 2 | A | 2 |
| E | Check answers for round 2 | D | 2.5 |
| F | Choose pictures for picture round | A | 1 |
| G | Get permission to use pictures | F | 1.5 |
| H | Choose music for music round | A | 2 |
| I | Get permission to use music | H | 1.5 |
| J | Produce answer sheets | G | 0.5 |
| Answer | Marks |
|---|---|
| 5 | 11 |
| Answer | Marks |
|---|---|
| 5 | 11 |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (a) | 2.5 2.5 |
| Answer | Marks |
|---|---|
| 5 (hours) | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.4 |
| 1.1 | Forward pass seen (first value in bold at each vertex) |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (b) | See answer given in part (a) |
| A, B, C, D, E (in any order) | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.4 |
| 1.1 | Backward pass seen (second value in bold at each vertex) |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (c) | F = 3 – 0.5 – 1 = 1.5 (hours) |
| Answer | Marks |
|---|---|
| I = 5 – 2.5 – 1.5 = 1 (hour) | M1 ft |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | Any two correct, or from their forward and backward passes |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (d) | (i) |
| Answer | Marks |
|---|---|
| H | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 3.5c | C, E, G, I correct |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (d) | (ii) |
| Answer | Marks |
|---|---|
| Duration of L = 2 hours | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.4 |
| 2.2a | Appropriate working seen, with evidence of what the values |
Question 5:
5 | 11
15 12 11
5 | 11
15 11
5 | (a) | 2.5 2.5
B(2) C(2.5)
D(2) E(2.5)
2.5 2.5
A(0.5) F(1) G(1.5) J(0.5)
0 0.5 0.5 1.5 3 3 4.5 5
H(2) I(1.5)
2.5 3.5
5 (hours) | B1
B1
[2] | 3.4
1.1 | Forward pass seen (first value in bold at each vertex)
Allow 0 and/or 5 missing but otherwise correct
cao 5 stated (not implied from diagram)
5 | (b) | See answer given in part (a)
A, B, C, D, E (in any order) | B1
B1
[2] | 3.4
1.1 | Backward pass seen (second value in bold at each vertex)
Allow 0 and/or 5 missing but otherwise correct
cao
5 | (c) | F = 3 – 0.5 – 1 = 1.5 (hours)
G = 4.5 – 1.5 – 1.5 = 1.5 (hours)
J = 5 – 3 – 0.5 = 1.5 (hours)
H = 3.5 – 0.5 – 2 = 1 (hour)
I = 5 – 2.5 – 1.5 = 1 (hour) | M1 ft
A1
A1
[3] | 1.1
1.1
1.1 | Any two correct, or from their forward and backward passes
Working need not be seen
F, G, J = 1.5 (cao)
Working need not be seen
H, I = 1 (cao)
Working need not be seen
5 | (d) | (i) | B
C
D
E
A F G L J
I
H | B1
B1
[2] | 3.3
3.5c | C, E, G, I correct
Activity L is after C, E, G and I
(directions may be implied)
Activity L is before J
(directions may be implied)
5 | (d) | (ii) | Time to start of L = 5 hours
So L + J take 2.5 hours
Duration of L = 2 hours | B1
B1
[2] | 3.4
2.2a | Appropriate working seen, with evidence of what the values
represent e.g A + B + C + L + J = 7.5 or A + D + E + L + J = 7.5
o.e. use of critical path
No FT
2 (cao)5 Hiro has been asked to organise a quiz.\\
The table below shows the activities involved, together with the immediate predecessors and the duration of each activity in hours.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
& Activity & Immediate predecessors & Duration (hours) \\
\hline
A & Choose the topics & - & 0.5 \\
\hline
B & Find questions for round 1 & A & 2 \\
\hline
C & Check answers for round 1 & B & 2.5 \\
\hline
D & Find questions for round 2 & A & 2 \\
\hline
E & Check answers for round 2 & D & 2.5 \\
\hline
F & Choose pictures for picture round & A & 1 \\
\hline
G & Get permission to use pictures & F & 1.5 \\
\hline
H & Choose music for music round & A & 2 \\
\hline
I & Get permission to use music & H & 1.5 \\
\hline
J & Produce answer sheets & G & 0.5 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item A sketch of the activity network is provided in the Printed Answer Booklet.
Apply a forward pass to determine the minimum project completion time.
\item Use a backward pass to determine the critical activities.
You can show your working on the activity network from part (a).
\item Give the total float for each non-critical activity.
Hiro decides that there should be a final check of the answers which he will include as activity $L$.
Activity L needs to be done after checking the answers for rounds 1 and 2 and also after getting permission to use the pictures and music but before producing the answer sheets.
\item \begin{enumerate}[label=(\roman*)]
\item Complete the activity network provided in the Printed Answer Booklet to show the new precedences, with the final check of the answers included as activity $L$.
\item As a result of including L , the minimum project completion time found in part (a) increases by 2.5 hours.
Determine the duration of L .
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR Further Discrete AS 2023 Q5 [11]}}