| Exam Board | Edexcel |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2019 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Critical Path Analysis |
| Type | Draw activity network from table |
| Difficulty | Moderate -0.8 This is a standard D1 activity network drawing question requiring students to convert a precedence table into an activity-on-arc network diagram. It involves straightforward application of learned conventions (dummy activities, node numbering) with no problem-solving or novel insight required—purely procedural execution of a well-practiced technique. |
| Spec | 7.03j Sorting: bubble sort and shuttle sort7.04a Shortest path: Dijkstra's algorithm |
| \(\mathbf { A }\) | \(\mathbf { B }\) | \(\mathbf { C }\) | \(\mathbf { D }\) | \(\mathbf { E }\) | \(\mathbf { F }\) | |
| \(\mathbf { A }\) | - | 73 | 56 | 27 | 38 | 48 |
| \(\mathbf { B }\) | 73 | - | 58 | 59 | 43 | 34 |
| \(\mathbf { C }\) | 56 | 58 | - | 46 | 38 | 42 |
| \(\mathbf { D }\) | 27 | 59 | 46 | - | 25 | 32 |
| \(\mathbf { E }\) | 38 | 43 | 38 | 25 | - | 21 |
| \(\mathbf { F }\) | 48 | 34 | 42 | 32 | 21 | - |
| VIIIV SIHI NI III IM ION OC | VIIV SIHI NI JIHM ION OC | VEYV SIHI NI JIIIM ION OO |
| VIIIV SIHI NI JIHM 10 N OC | VIIV SIHI NI JIHM I ON OC | VI4V SIHI NI JIIYM ION OO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| [Network diagram with: Activities A, B, C, D (from start), E, F, G, H, I, J, K, L, M (all labelled on arcs). One start and at least two dummies placed. Precedences correctly shown.] | M1 A1 A1 A1 A1 | a1M1: At least eight activities (labelled on arc), one start and at least two dummies placed. a1A1: Activities A, B, C, first two dummies (\(+\) correct arrows on these two dummies) and D dealt with correctly – the first two dummies are those that meet at the end of activity B. a2A1: Activities E, F, G, H and I dealt with correctly. a3A1: Activities J, K, L and M and 3rd dummy (\(+\) correct arrow on this dummy) dealt with correctly – 3rd dummy is the one that begins at the end of activity G. a4A1: CSO – Final dummy \(+\) arrow, all arrows correctly placed for each activity with one finish and no additional dummies. Note that this is not a unique solution e.g. J and K could be interchanged, or the dummy could come immediately after E, etc. so please check these carefully. Please check all arcs carefully for arrows – if there are no arrows on dummies then M1 only. Note that additional (but unnecessary) 'correct' dummies that still maintain precedence for the network should only be penalised with the final A mark if earned. |
| Critical path: A – E – K | B1 | b1B1: CAO (A, E and K only) |
| First critical path: C – I – L – M; Second critical path: C – H – I – L | B1 B1 | c1B1: One correct path (with at most three paths stated). c2B1: Both correct with no others. |
| Total: 8 marks |
| Answer | Marks | Guidance |
|--------|-------|----------|
| [Network diagram with: Activities A, B, C, D (from start), E, F, G, H, I, J, K, L, M (all labelled on arcs). One start and at least two dummies placed. Precedences correctly shown.] | M1 A1 A1 A1 A1 | a1M1: At least eight activities (labelled on arc), one start and at least two dummies placed. a1A1: Activities A, B, C, first two dummies ($+$ correct arrows on these two dummies) and D dealt with correctly – the first two dummies are those that meet at the end of activity B. a2A1: Activities E, F, G, H and I dealt with correctly. a3A1: Activities J, K, L and M and 3rd dummy ($+$ correct arrow on this dummy) dealt with correctly – 3rd dummy is the one that begins at the end of activity G. a4A1: CSO – Final dummy $+$ arrow, all arrows correctly placed for each activity with one finish and no additional dummies. Note that this is not a unique solution e.g. J and K could be interchanged, or the dummy could come immediately after E, etc. so please check these carefully. **Please check all arcs carefully for arrows – if there are no arrows on dummies then M1 only.** **Note that additional (but unnecessary) 'correct' dummies that still maintain precedence for the network should only be penalised with the final A mark if earned.** |
| Critical path: A – E – K | B1 | b1B1: CAO (A, E and K only) |
| First critical path: C – I – L – M; Second critical path: C – H – I – L | B1 B1 | c1B1: One correct path (with at most three paths stated). c2B1: Both correct with no others. |
| **Total: 8 marks** | | |
**Notes for Question 6:**
Condone lack of, or incorrect, numbered events throughout. 'Dealt with correctly' means that the activity starts from the correct event but need not necessarily finish at the event. 'F dealt with correctly' requires the correct precedences for this activity, i.e. A, B and C labelled correctly and leading into the same node and F starting from that node but do not consider the end event for F. **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 second A mark and the final (CSO) A mark – they can still earn the third 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 correct place for where a dummy should be).
**Ignore incorrect or lack of arrows on the activities for the first four marks only.**6.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | }
\hline
& $\mathbf { A }$ & $\mathbf { B }$ & $\mathbf { C }$ & $\mathbf { D }$ & $\mathbf { E }$ & $\mathbf { F }$ \\
\hline
$\mathbf { A }$ & - & 73 & 56 & 27 & 38 & 48 \\
\hline
$\mathbf { B }$ & 73 & - & 58 & 59 & 43 & 34 \\
\hline
$\mathbf { C }$ & 56 & 58 & - & 46 & 38 & 42 \\
\hline
$\mathbf { D }$ & 27 & 59 & 46 & - & 25 & 32 \\
\hline
$\mathbf { E }$ & 38 & 43 & 38 & 25 & - & 21 \\
\hline
$\mathbf { F }$ & 48 & 34 & 42 & 32 & 21 & - \\
\hline
\end{tabular}
\end{center}
2.
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{aef6a6dd-76ec-47f7-b8c9-449006da29d3-12_1374_1529_267_210}
\end{center}
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Key:}
\includegraphics[alt={},max width=\textwidth]{aef6a6dd-76ec-47f7-b8c9-449006da29d3-12_266_579_1720_1146}
\end{center}
\end{figure}
Shortest route: $\_\_\_\_$
Length of shortest route: $\_\_\_\_$
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{aef6a6dd-76ec-47f7-b8c9-449006da29d3-13_899_881_319_534}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
3.
$\begin{array} { l l l l l l l l l l } 8 & 17 & 9 & 14 & 18 & 12 & 22 & 10 & 15 & 7 \end{array}$
$\begin{array} { l l l l l l l l l l } 8 & 17 & 9 & 14 & 18 & 12 & 22 & 10 & 15 & 7 \end{array}$\\
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{aef6a6dd-76ec-47f7-b8c9-449006da29d3-18_711_1143_299_404}
\captionsetup{labelformat=empty}
\caption{Figure 2\\[0pt]
[The total weight of the network is 227.2]}
\end{center}
\end{figure}
4.
\includegraphics[max width=\textwidth, alt={}, center]{aef6a6dd-76ec-47f7-b8c9-449006da29d3-20_572_1454_1021_248}
\section*{Key:}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{aef6a6dd-76ec-47f7-b8c9-449006da29d3-20_357_167_1610_1375}
\end{center}
\section*{Diagram 1}
5.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
VIIIV SIHI NI III IM ION OC & VIIV SIHI NI JIHM ION OC & VEYV SIHI NI JIIIM ION OO \\
\hline
\end{tabular}
\end{center}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{aef6a6dd-76ec-47f7-b8c9-449006da29d3-23_840_1590_309_181}
\end{center}
\section*{Diagram 1}
6.
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{aef6a6dd-76ec-47f7-b8c9-449006da29d3-28_2632_1830_121_121}
\end{center}
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
VIIIV SIHI NI JIHM 10 N OC & VIIV SIHI NI JIHM I ON OC & VI4V SIHI NI JIIYM ION OO \\
\hline
\end{tabular}
\end{center}
\hfill \mbox{\textit{Edexcel D1 2019 Q6 [8]}}