OCR D1 2006 June — Question 12

Exam BoardOCR
ModuleD1 (Decision Mathematics 1)
Year2006
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPermutations & Arrangements
TypeGraph theory problems
DifficultyModerate -0.5 This is a standard Dijkstra's algorithm application from D1, requiring systematic labeling of vertices to find shortest paths. While it requires careful execution and multiple steps, it's a routine algorithmic procedure that students practice extensively, making it easier than average for A-level but not trivial due to the computational work involved.
Spec7.04a Shortest path: Dijkstra's algorithm

12 JUNE 2006
Afternoon
1 hour 30 minutes
  • This insert should be used to answer Question 6.
  • Write your name, centre number and candidate number in the spaces provided at the top of this page.
  • Write your answers to Question 6 in the spaces provided in this insert, and attach it to your answer booklet.
6

  1. Key: \includegraphics[max width=\textwidth, alt={}, center]{f2b85dfb-49df-4ea5-b118-9b95f0b27bad-10_193_949_214_712} Do not cross out your working values (temporary labels) \includegraphics[max width=\textwidth, alt={}, center]{f2b85dfb-49df-4ea5-b118-9b95f0b27bad-10_1157_1600_648_303} Route of shortest path from \(A\) to \(J =\) \(\_\_\_\_\) Length of shortest path from \(A\) to \(J =\) \(\_\_\_\_\) metres
    1. \(\_\_\_\_\) Shortest distance \(=\) \(\_\_\_\_\) metres
    2. \includegraphics[max width=\textwidth, alt={}, center]{f2b85dfb-49df-4ea5-b118-9b95f0b27bad-11_979_1429_276_440}
      Shortest distance = \(\_\_\_\_\) metres

12 JUNE 2006\\
Afternoon\\
1 hour 30 minutes

\begin{itemize}
  \item This insert should be used to answer Question 6.
  \item Write your name, centre number and candidate number in the spaces provided at the top of this page.
  \item Write your answers to Question 6 in the spaces provided in this insert, and attach it to your answer booklet.
\end{itemize}

6
\begin{enumerate}[label=(\alph*)]
\item \\
Key:\\
\includegraphics[max width=\textwidth, alt={}, center]{f2b85dfb-49df-4ea5-b118-9b95f0b27bad-10_193_949_214_712}

Do not cross out your working values (temporary labels)\\
\includegraphics[max width=\textwidth, alt={}, center]{f2b85dfb-49df-4ea5-b118-9b95f0b27bad-10_1157_1600_648_303}

Route of shortest path from $A$ to $J =$ $\_\_\_\_$\\
Length of shortest path from $A$ to $J =$ $\_\_\_\_$ metres
\item \begin{enumerate}[label=(\roman*)]
\item $\_\_\_\_$\\

Shortest distance $=$ $\_\_\_\_$ metres
\item \\
\includegraphics[max width=\textwidth, alt={}, center]{f2b85dfb-49df-4ea5-b118-9b95f0b27bad-11_979_1429_276_440}\\

Shortest distance = $\_\_\_\_$ metres
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{OCR D1 2006 Q12}}