| Exam Board | OCR MEI |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2015 |
| Session | June |
| Marks | 20 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Shortest Path |
| Type | Floyd's algorithm with route extraction |
| Difficulty | Standard +0.3 This is a straightforward application of Floyd's algorithm route extraction from given matrices. Part (i) requires reading values from a distance matrix to draw a network (routine task), while part (ii) involves the standard procedure of tracing back through a route matrix—a technique directly taught in D2. No problem-solving insight or novel reasoning is required, just mechanical application of a learned algorithm. |
| Spec | 7.04a Shortest path: Dijkstra's algorithm |
| \cline { 2 - 5 } \multicolumn{1}{c|}{} | \(\mathbf { 1 }\) | \(\mathbf { 2 }\) | \(\mathbf { 3 }\) | \(\mathbf { 4 }\) |
| \(\mathbf { 1 }\) | 3 | 3 | 3 | 3 |
| \(\mathbf { 2 }\) | 3 | 3 | 3 | 4 |
| \(\mathbf { 3 }\) | 1 | 2 | 2 | 2 |
| \(\mathbf { 4 }\) | 2 | 2 | 2 | 2 |
I'd be happy to help clean up mark scheme content, but the text you've provided appears to be just numbers in a table format rather than actual mark scheme content with questions, solutions, and marking criteria.
Could you please provide the actual mark scheme content that needs to be cleaned up? I'm looking for text that includes:
- Question content or solutions
- Marking annotations (M1, A1, B1, DM1, etc.)
- Unicode symbols that need converting to LaTeX (θ, Σ, ≥, etc.)
- Guidance notes
Once you provide the full mark scheme text, I'll clean it up according to your specifications.$\mathbf { 4 }$ & 10 & 5 & 7 & 10 \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{table}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{final route matrix}
\begin{tabular}{ | l | l | l | l | l | }
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & $\mathbf { 1 }$ & $\mathbf { 2 }$ & $\mathbf { 3 }$ & $\mathbf { 4 }$ \\
\hline
$\mathbf { 1 }$ & 3 & 3 & 3 & 3 \\
\hline
$\mathbf { 2 }$ & 3 & 3 & 3 & 4 \\
\hline
$\mathbf { 3 }$ & 1 & 2 & 2 & 2 \\
\hline
$\mathbf { 4 }$ & 2 & 2 & 2 & 2 \\
\hline
\end{tabular}
\end{center}
\end{table}
(i) Draw the complete network of shortest times.\\
(ii) Explain how to use the final route matrix to find the quickest route from node $\mathbf { 4 }$ to node $\mathbf { 1 }$ in the original incomplete network. Give this quickest route.
A new node, node 5, is added to the original incomplete network. The new journey times are shown in the table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\cline { 2 - 5 }
\multicolumn{1}{c|}{} & $\mathbf { 1 }$ & $\mathbf { 2 }$ & $\mathbf { 3 }$ & $\mathbf { 4 }$ \\
\hline
\hfill \mbox{\textit{OCR MEI D2 2015 Q4 [20]}}