OCR D1 2005 January — Question 12

Exam BoardOCR
ModuleD1 (Decision Mathematics 1)
Year2005
SessionJanuary
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFixed Point Iteration
TypeApply iteration to find root (pure fixed point)
DifficultyModerate -1.0 This is a standard D1 (Decision Mathematics) question on network algorithms, not actually about fixed point iteration despite the topic label. The question involves applying Dijkstra's algorithm or similar shortest path methods to a weighted graph - a routine algorithmic procedure taught at AS-level. While it requires careful bookkeeping, it's a straightforward application of a learned algorithm with no novel problem-solving required, making it easier than average A-level questions.
Spec7.04a Shortest path: Dijkstra's algorithm7.04b Minimum spanning tree: Prim's and Kruskal's algorithms

12 JANUARY 2005
Afternoon
1 hour 30 minutes
  • This insert should be used to answer Questions 4 and 7.
  • Write your name, centre number and candidate number in the spaces provided at the top of this page.
  • Write your answers to Questions 4 and 7 in the spaces provided in this insert, and attach it to your answer booklet.
4
  1. \(A\)\(B\)CD\(E\)\(F\)G\(H\)
    A-423----
    \(B\)4-1-3---
    C21-2-65-
    \(D\)3-2---4-
    E-3---8-7
    \(F\)--6-8--8
    \(G\)--54---9
    \(H\)----789-
  2. B \(E\) \(C\) F
    • \(H\) \(A\) •
    • \({ } ^ { \text {F } }\)
    H D
    G
  3. \(\_\_\_\_\)
  4. \(\_\_\_\_\)
  5. \(\_\_\_\_\) 7
      1. \includegraphics[max width=\textwidth, alt={}, center]{197624b2-ca67-4bad-9c2c-dc68c10be0fd-11_191_1179_269_482} Do not cross out your working values (temporary labels) \includegraphics[max width=\textwidth, alt={}, center]{197624b2-ca67-4bad-9c2c-dc68c10be0fd-11_871_1557_612_335} Shortest route from \(A\) to \(E =\) \(\_\_\_\_\) Length = \(\_\_\_\_\) Shortest route from \(A\) to \(J =\) \(\_\_\_\_\) Length = \(\_\_\_\_\)
      2. Length of route \(=\) \(\_\_\_\_\) Vertices visited in order \(\_\_\_\_\)
      3. Explanation \(\_\_\_\_\)
    1. \(\_\_\_\_\) Length = \(\_\_\_\_\)

12 JANUARY 2005\\
Afternoon\\
1 hour 30 minutes

\begin{itemize}
  \item This insert should be used to answer Questions 4 and 7.
  \item Write your name, centre number and candidate number in the spaces provided at the top of this page.
  \item Write your answers to Questions 4 and 7 in the spaces provided in this insert, and attach it to your answer booklet.
\end{itemize}

4 (i)

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
 & $A$ & $B$ & C & D & $E$ & $F$ & G & $H$ \\
\hline
A & - & 4 & 2 & 3 & - & - & - & - \\
\hline
$B$ & 4 & - & 1 & - & 3 & - & - & - \\
\hline
C & 2 & 1 & - & 2 & - & 6 & 5 & - \\
\hline
$D$ & 3 & - & 2 & - & - & - & 4 & - \\
\hline
E & - & 3 & - & - & - & 8 & - & 7 \\
\hline
$F$ & - & - & 6 & - & 8 & - & - & 8 \\
\hline
$G$ & - & - & 5 & 4 & - & - & - & 9 \\
\hline
$H$ & - & - & - & - & 7 & 8 & 9 & - \\
\hline
\end{tabular}
\end{center}

(ii)

B\\
$E$\\
$C$\\
F

\begin{itemize}
  \item $H$\\
$A$\\
•
  \item ${ } ^ { \text {F } }$
\end{itemize}

H

D\\
G\\
(iii) $\_\_\_\_$\\

(iv) $\_\_\_\_$\\

(v) $\_\_\_\_$\\

7
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item \\
\includegraphics[max width=\textwidth, alt={}, center]{197624b2-ca67-4bad-9c2c-dc68c10be0fd-11_191_1179_269_482}

Do not cross out your working values (temporary labels)\\
\includegraphics[max width=\textwidth, alt={}, center]{197624b2-ca67-4bad-9c2c-dc68c10be0fd-11_871_1557_612_335}

Shortest route from $A$ to $E =$ $\_\_\_\_$ Length = $\_\_\_\_$\\
Shortest route from $A$ to $J =$ $\_\_\_\_$ Length = $\_\_\_\_$
\item Length of route $=$ $\_\_\_\_$\\
Vertices visited in order $\_\_\_\_$
\item Explanation $\_\_\_\_$
\end{enumerate}\item $\_\_\_\_$\\

Length = $\_\_\_\_$
\end{enumerate}

\hfill \mbox{\textit{OCR D1 2005 Q12}}