| Exam Board | OCR |
|---|---|
| Module | Further Discrete (Further Discrete) |
| Session | Specimen |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw cascade/Gantt chart |
| Difficulty | Standard +0.3 This is a standard cascade/Gantt chart construction question with routine float calculations. While it requires careful bookkeeping and understanding of critical path terminology (independent vs interfering float), it follows a mechanical procedure taught in all Decision Maths courses with no novel problem-solving or insight required. The resource constraint in part (iii) adds minimal difficulty as it's a straightforward scheduling adjustment. |
| 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 |
| Activity | |
| \(A\) | Structural survey |
| \(B\) | Replace damp course |
| \(C\) | Scaffolding |
| \(D\) | Repair brickwork |
| \(E\) | Repair roof |
| \(F\) | Check electrics |
| \(G\) | Replaster walls |
| Activity | |
| \(H\) | Planning |
| \(I\) | Build extension |
| \(J\) | Remodel internal layout |
| \(K\) | Kitchens and bathrooms |
| \(L\) | Decoration and furnishing |
| \(M\) | Landscape garden |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (i) | Critical activities: |
| Answer | Marks |
|---|---|
| (See page 15 for larger diagram) | M1 |
| Answer | Marks |
|---|---|
| [7] | i |
| Answer | Marks |
|---|---|
| 1.1 | m |
| Answer | Marks |
|---|---|
| All correct | A, H, I, L and no others |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (ii) | Latest start for J (cid:32)23(cid:16)6(cid:32)17 |
| Answer | Marks |
|---|---|
| 17(cid:16)15(cid:31)6, so float is all interfering | B1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 1.1 | No independent float | |
| 2 | (iii) | When each activity starts at its earliest start |
| Answer | Marks |
|---|---|
| then do the kitchens and bathrooms (K) | M1 |
| Answer | Marks |
|---|---|
| [3] | 2.2a |
| Answer | Marks |
|---|---|
| 3.4 | FT their cascade chart if possible |
| Answer | Marks |
|---|---|
| …in which precedence is not violated | If their cascade chart has no |
Question 2:
2 | (i) | Critical activities:
Survey, planning, extension, decoration
p
S
(See page 15 for larger diagram) | M1
A1
eB1
M1
A1
M1
A1
[7] | i
c2.2a
1.1
1.1
3.3
1.1
1.1
1.1 | m
At most one error
Activities labelled, one activity per row
Early start and finish times (solid boxes)
correct for A, B, C,F, G, H
All correct
Float (dashed boxes) any two correct
All correct | A, H, I, L and no others
May have critical activities on
a single row
2 | (ii) | Latest start for J (cid:32)23(cid:16)6(cid:32)17
Float for J (cid:32)(cid:11)23(cid:16)9(cid:12)(cid:16)6(cid:32)8
17(cid:16)15(cid:31)6, so float is all interfering | B1
M1
E1
[3] | 1.1
3.4
1.1 | No independent float
2 | (iii) | When each activity starts at its earliest start
time (as in the cascade chart) the only days
with more than three activities are days 28 to
31
e.g. Delay repairing the roof (E) until after
repairing the brickwork (D) has finished and
then do the kitchens and bathrooms (K) | M1
M1
A1
[3] | 2.2a
3.1b
3.4 | FT their cascade chart if possible
Identifying problem (at day 28)
(may be implied from resolution)
A schedule in the minimum completion
time witnh no more than three activities
each day…
…in which precedence is not violated | If their cascade chart has no
day with more than three
activities, and they say so (cid:159)
M1A02 Kirstie has bought a house that she is planning to renovate. She has broken the project into a list of activities and constructed an activity network, using activity on arc.
\begin{center}
\begin{tabular}{ | l | l | }
\hline
\multicolumn{2}{|c|}{Activity} \\
\hline
$A$ & Structural survey \\
\hline
$B$ & Replace damp course \\
\hline
$C$ & Scaffolding \\
\hline
$D$ & Repair brickwork \\
\hline
$E$ & Repair roof \\
\hline
$F$ & Check electrics \\
\hline
$G$ & Replaster walls \\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ | l | l | }
\hline
\multicolumn{2}{|c|}{Activity} \\
\hline
$H$ & Planning \\
\hline
$I$ & Build extension \\
\hline
$J$ & Remodel internal layout \\
\hline
$K$ & Kitchens and bathrooms \\
\hline
$L$ & Decoration and furnishing \\
\hline
$M$ & Landscape garden \\
\hline
\end{tabular}
\end{center}
\includegraphics[max width=\textwidth, alt={}, center]{0c9513fe-a471-427e-ba30-b18df11271e3-3_887_1751_1030_207}\\
(i) Construct a cascade chart for the project, showing the float for each non-critical activity.\\
(ii) Calculate the float for remodelling the internal layout stating how much of this is independent float and how much is interfering float.
Kirstie needs to supervise the project. This means that she cannot allow more than three activities to happen on any day.\\
(iii) Describe how Kirstie should organise the activities so that the project is completed in the minimum project completion time and no more than three activities happen on any day.
\hfill \mbox{\textit{OCR Further Discrete Q2 [13]}}