| Exam Board | Edexcel |
|---|---|
| Module | FD1 AS (Further Decision 1 AS) |
| Year | 2019 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Identify guaranteed critical activities |
| Difficulty | Standard +0.3 This is a standard Further Maths Decision 1 activity network question requiring drawing a network with dummies and identifying critical activities. While it requires careful attention to precedence relationships and dummy placement, it follows routine algorithmic procedures taught in the module with no novel problem-solving required. The equal duration simplification makes parts (b) and (c) straightforward once the network is drawn. |
| Spec | 7.05a Critical path analysis: activity on arc networks |
| Activity | Immediately preceding activities |
| A | - |
| B | - |
| C | A |
| D | A |
| E | A |
| F | B, C |
| G | B, C |
| H | D |
| I | D, E, F, G |
| J | D, E, F, G |
| K | G |
| Answer | Marks |
|---|---|
| 3(a) | M1 |
| Answer | Marks |
|---|---|
| A1 | 1.1b |
| Answer | Marks |
|---|---|
| (b) | Activity F (and/or G) requires activity B and the two activities A and |
| Answer | Marks | Guidance |
|---|---|---|
| waiting for A and C to be completed and so B is therefore not critical. | B1 | 2.4 |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | Activities D, E and H | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Scheme | Marks |
Question 3:
--- 3(a) ---
3(a) | M1
A1
A1
A1
A1 | 1.1b
1.1b
1.1b
1.1b
1.1b
(5)
(b) | Activity F (and/or G) requires activity B and the two activities A and
C to be completed before F (and/or G) can begin. The time to
complete A and C is double that of B and so B can be delayed
waiting for A and C to be completed and so B is therefore not critical. | B1 | 2.4
(1)
(c) | Activities D, E and H | B1 | 2.2a
(1)
(7 marks)
Notes
In (a) condone lack of, or incorrect, numbered events throughout. ‘Dealt with correctly’ means that
the activity starts from the correct event but need not necessarily finishes at the correct event, e.g. ‘G
dealt with correctly’ requires the correct precedences for this activity, i.e. B and C labelled correctly
and leading into the same node and G starting from that node but do not consider the end node for G.
Activity on node is M0
If an arc is not labelled, for example, if the arc for activity G is not labelled (but the arc is present)
then this will lose the first A mark and the final (CSO) A mark – they can still earn the second A
mark on the bod. If two or more arcs are not labelled then mark according to the scheme. Assume
that a solid line is an activity which has not been labelled rather than a dummy (even if in the corrct
place for where a dummy should be)
(a)
M1: At least eight activities (labelled on arc), one start, and at least two dummies placed
A1: Activities A – G dealt with correctly (bod if no arrow on activity C)
A1: First two required dummies + arrows dealt with correctly
A1: Activities H – K dealt with correctly (A0 if no arrows on preceding dummies (oe))
A1: CSO – Final required dummy + all arrows present and correctly placed with one finish and no
additional dummies. Note that the arrow for the final dummy could be reversed. Note that there are
several correct viable positions for the final dummy
Note that additional (but unecessary) ‘correct’ dummies that still maintain precedence for the
network should only be penalised with the final A mark if earned
(b)
B1: CAO - some mention of the time required to complete A + C compared with B (for the next
activity to begin (either F and/or G)) oe e.g. paths through B have a maximum length of 3 (non-
dummy) activities and there is at least one path of length 4 which does not include B so B cannot be
critical OR the late time for B must be the same as the late time for A + C which is twice the
duration of B and therefore B is not critical. Give bod to responses that imply that B and C meet at
the same event, but C is also dependent on A (the key point for awarding this mark is that activities
A and C imply that B is not critical)
(c)
B1: All three correct with no extras (ignore any mention of activity B)
Question | Scheme | Marks | AOs\begin{center}
\begin{tabular}{|c|c|}
\hline
Activity & Immediately preceding activities \\
\hline
A & - \\
\hline
B & - \\
\hline
C & A \\
\hline
D & A \\
\hline
E & A \\
\hline
F & B, C \\
\hline
G & B, C \\
\hline
H & D \\
\hline
I & D, E, F, G \\
\hline
J & D, E, F, G \\
\hline
K & G \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain the minimum number of dummies. [5]
\end{enumerate}
Every activity shown in the precedence table has the same duration.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Explain why activity B cannot be critical. [1]
\item State which other activities are not critical. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FD1 AS 2019 Q3 [7]}}