| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Discrete (Further AS Paper 2 Discrete) |
| Year | 2020 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Calculate early and late times |
| Difficulty | Moderate -0.3 This is a standard critical path analysis question requiring construction of an activity network, forward and backward passes to find early/late times, and analysis of a duration change. While it involves multiple activities and dependencies, the techniques are routine algorithmic procedures taught in Decision Maths with no novel problem-solving required. The multi-part structure and computational work place it slightly below average difficulty for A-level. |
| 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 (weeks) |
| \(A\) | - | 10 |
| B | - | 5 |
| C | B | 12 |
| D | \(A\) | 8 |
| \(E\) | C, D | 4 |
| \(F\) | C, D | 3 |
| \(G\) | C, D | 7 |
| \(H\) | E, F | 8 |
| \(I\) | G | 6 |
| \(J\) | G | 15 |
| K | H, I | 5 |
| \(L\) | K | 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Activity network with activities \(A\) to \(G\) drawn with correct arcs | M1 | Constructs activity network |
| All activities with correct arcs (condone extra 'End' activity with duration 0) | A1 | Completes activity network |
| Earliest start times: \(A\): \(0\), \(B\): \(0\), \(C\): \(5\), \(D\): \(10\), \(E\): \(18\), \(F\): \(18\), \(G\): \(18\), \(H\): \(22\), \(I\): \(25\), \(J\): \(25\), \(K\): \(31\), \(L\): \(36\) | B1 | Finds correctly the earliest start time for each activity |
| Latest finish times: \(A\): \(10\), \(B\): \(6\), \(C\): \(18\), \(D\): \(18\), \(E\): \(23\), \(F\): \(23\), \(G\): \(25\), \(H\): \(31\), \(I\): \(31\), \(J\): \(40\), \(K\): \(36\), \(L\): \(40\) | B1F | Finds correctly the latest finish times (FT their earliest start times) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Activity \(C\) has a float of \(1\), so becomes critical as it is delayed by 3 weeks | M1 | Evaluates effect of increasing duration of \(C\) by 3 weeks (e.g. considers float of \(C\) or amends network) |
| The new minimum completion time is \(42\) weeks | A1F | Determines new minimum completion time as 42 weeks; condone '42' (FT their '40' from part (a)) |
## Question 5(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Activity network with activities $A$ to $G$ drawn with correct arcs | M1 | Constructs activity network |
| All activities with correct arcs (condone extra 'End' activity with duration 0) | A1 | Completes activity network |
| Earliest start times: $A$: $0$, $B$: $0$, $C$: $5$, $D$: $10$, $E$: $18$, $F$: $18$, $G$: $18$, $H$: $22$, $I$: $25$, $J$: $25$, $K$: $31$, $L$: $36$ | B1 | Finds correctly the earliest start time for each activity |
| Latest finish times: $A$: $10$, $B$: $6$, $C$: $18$, $D$: $18$, $E$: $23$, $F$: $23$, $G$: $25$, $H$: $31$, $I$: $31$, $J$: $40$, $K$: $36$, $L$: $40$ | B1F | Finds correctly the latest finish times (FT their earliest start times) |
## Question 5(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Activity $C$ has a float of $1$, so becomes critical as it is delayed by 3 weeks | M1 | Evaluates effect of increasing duration of $C$ by 3 weeks (e.g. considers float of $C$ or amends network) |
| The new minimum completion time is $42$ weeks | A1F | Determines new minimum completion time as 42 weeks; condone '42' (FT their '40' from part (a)) |
---5 A restoration project is divided into a number of activities.
The duration and predecessor(s) of each activity are shown in the table below.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Activity & Immediate predecessor(s) & Duration (weeks) \\
\hline
$A$ & - & 10 \\
\hline
B & - & 5 \\
\hline
C & B & 12 \\
\hline
D & $A$ & 8 \\
\hline
$E$ & C, D & 4 \\
\hline
$F$ & C, D & 3 \\
\hline
$G$ & C, D & 7 \\
\hline
$H$ & E, F & 8 \\
\hline
$I$ & G & 6 \\
\hline
$J$ & G & 15 \\
\hline
K & H, I & 5 \\
\hline
$L$ & K & 4 \\
\hline
\end{tabular}
\end{center}
5
\begin{enumerate}[label=(\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.\\[0pt]
[4 marks]
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{21ed3b4e-a089-4607-b5d6-69d8aac03f31-09_533_289_2124_1548}
\captionsetup{labelformat=empty}
\caption{Turn over -}
\end{center}
\end{figure}
5
\item Due to a change of materials during the project, the duration of activity $C$ is extended by 3 weeks.
Determine the new minimum completion time of the project.\\
\includegraphics[max width=\textwidth, alt={}, center]{21ed3b4e-a089-4607-b5d6-69d8aac03f31-11_2488_1716_219_153}
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2020 Q5 [6]}}