AQA D1 2005 June — Question 7 10 marks

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2005
SessionJune
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicShortest Path
TypeDijkstra with vertex or edge exclusion
DifficultyModerate -0.3 This is a straightforward application of Dijkstra's algorithm with a minor variation in part (b) requiring re-application with one edge removed. The algorithm is mechanical and well-practiced in D1, requiring no novel insight—just careful execution and comparison of two results.
Spec7.04a Shortest path: Dijkstra's algorithm

7 [Figure 1, printed on the insert, is provided for use in this question.]
The diagram shows some of the main roads connecting Royton to London. The numbers on the edges represent the travelling times, in minutes, between adjacent towns. David lives in Royton and is planning to travel along some of the roads to a meeting in London. \includegraphics[max width=\textwidth, alt={}, center]{a1290c22-f28d-42aa-89d5-10d60ca4741c-06_2196_1479_557_310}
    1. Use Dijkstra's algorithm on Figure 1 to find the minimum travelling time from Royton to London.
    2. Write down the route corresponding to this minimum travelling time.
  1. On a particular day, before David leaves Royton, he knows that the road connecting Walsall and Marston is closed. Find the minimum extra time required to travel from Royton to London on this day. Write down the corresponding route.

7 [Figure 1, printed on the insert, is provided for use in this question.]\\
The diagram shows some of the main roads connecting Royton to London. The numbers on the edges represent the travelling times, in minutes, between adjacent towns. David lives in Royton and is planning to travel along some of the roads to a meeting in London.\\
\includegraphics[max width=\textwidth, alt={}, center]{a1290c22-f28d-42aa-89d5-10d60ca4741c-06_2196_1479_557_310}
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Use Dijkstra's algorithm on Figure 1 to find the minimum travelling time from Royton to London.
\item Write down the route corresponding to this minimum travelling time.
\end{enumerate}\item On a particular day, before David leaves Royton, he knows that the road connecting Walsall and Marston is closed.

Find the minimum extra time required to travel from Royton to London on this day. Write down the corresponding route.
\end{enumerate}

\hfill \mbox{\textit{AQA D1 2005 Q7 [10]}}