| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Discrete (Further AS Paper 2 Discrete) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate early and late times |
| Difficulty | Standard +0.3 This is a standard critical path analysis question requiring construction of an activity network and identification of the critical path. While it involves multiple activities and careful tracking of precedences, it follows a routine algorithmic procedure taught in Further Maths discrete modules with no novel problem-solving required. The calculations are straightforward once the network is drawn correctly. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities |
| Activity | Immediate Predecessor(s) | Duration (Days) |
| \(A\) | None | 1 |
| \(B\) | None | 1 |
| \(C\) | \(A\) | 10 |
| \(D\) | \(A\) | 2 |
| \(E\) | \(B, D\) | 5 |
| \(F\) | \(E\) | 6 |
| \(G\) | \(E\) | 1 |
| \(H\) | \(F\) | 1 |
| \(I\) | \(F\) | 2 |
| \(J\) | \(C, G, H, I\) | 4 |
| Answer | Marks |
|---|---|
| 9(a) | Constructs an activity network |
| Answer | Marks | Guidance |
|---|---|---|
| least 4 correct connections | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Condone omission of arrows | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| correct network | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| for each activity on the network | 1.1b | A1 |
| Subtotal | 4 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 9(b) | Identifies the minimum completion |
| Answer | Marks | Guidance |
|---|---|---|
| comment about Robert’s claim | 3.2a | E1F |
| Answer | Marks | Guidance |
|---|---|---|
| activities | 2.2b | E1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
Question 9:
--- 9(a) ---
9(a) | Constructs an activity network
with at least 9 activities and at
least 4 correct connections | 3.1b | M1 | See below
Activity network fully correct with
all activities and correct
connections
Condone omission of arrows | 1.1b | A1
Finds the correct earliest start
time for each activity on the
correct network | 1.1b | A1
Finds the correct latest finish time
for each activity on the network | 1.1b | A1
Subtotal | 4
Q | Marking instructions | AO | Marks | Typical solution
--- 9(b) ---
9(b) | Identifies the minimum completion
time for their activity network and
compares it to 20 days to make a
comment about Robert’s claim | 3.2a | E1F | As the minimum completion time of
the project is 20 days, Robert’s
claim appears to be valid.
However, it may take longer than
20 days if Robert’s team is not
large enough to begin all activities
at the earliest start times.
Identifies a possible reason for
Robert’s claim not being valid, for
example:
• Depends if activities can be
worked on simultaneously
• Depends if there are enough
builders to allow each activity to
begin at its earliest start time
• Depends on if there are any
delays to the earliest start time
for any of the critical activities
A, D, E, F, I or J
OR
Identifies a possible condition that
needs to be met for Robert’s
claim to be valid, for example:
• Activities will need to be
worked on simultaneously
• There must be enough builders
to allow each activity to begin
at its earliest start time
• There must be no delay to
beginning any of the critical
activities | 2.2b | E1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
Robert, a project manager, and his team of builders are working on a small building project.
Robert has divided the project into ten activities labelled $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, $I$ and $J$ as shown in the precedence table below:
\begin{tabular}{|c|c|c|}
\hline
Activity & Immediate Predecessor(s) & Duration (Days) \\
\hline
$A$ & None & 1 \\
\hline
$B$ & None & 1 \\
\hline
$C$ & $A$ & 10 \\
\hline
$D$ & $A$ & 2 \\
\hline
$E$ & $B, D$ & 5 \\
\hline
$F$ & $E$ & 6 \\
\hline
$G$ & $E$ & 1 \\
\hline
$H$ & $F$ & 1 \\
\hline
$I$ & $F$ & 2 \\
\hline
$J$ & $C, G, H, I$ & 4 \\
\hline
\end{tabular}
\begin{enumerate}[label=9 (\alph*)]
\item On the opposite page, construct an activity network for the project and fill in the earliest start time and latest finish time for each activity.
[4 marks]
\item Robert claims that the project can be completed in 20 days.
Comment on the validity of Robert's claim.
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2024 Q9 [6]}}