OCR MEI D1 2008 January — Question 1 8 marks

Exam BoardOCR MEI
ModuleD1 (Decision Mathematics 1)
Year2008
SessionJanuary
Marks8
PaperDownload PDF ↗
TopicGraph Theory Fundamentals
TypeNetwork and route modeling
DifficultyModerate -0.8 This is a straightforward graph traversal question requiring only basic interpretation of a network diagram and systematic counting of paths. All parts involve direct observation and enumeration rather than algorithmic application or proof, making it easier than average A-level content.
Spec7.02a Graphs: vertices (nodes) and arcs (edges)7.02c Graph terminology: walk, trail, path, cycle, route
1 The graph shows routes that are available to an international lorry driver. The solid arcs represent motorways and the broken arcs represent ferry crossings. \includegraphics[max width=\textwidth, alt={}, center]{dfe6db33-33d0-4dff-95f7-fbf097e3963e-2_668_1131_587_466}
  1. Give a route from Milan to Chania involving exactly two ferry crossings. How many such routes are there?
  2. Give a route from Milan to Chania involving exactly three ferry crossings. How many such routes are there?
  3. Give a route from Milan to Chania using as many ferry crossings as possible, without repeating any arc.
    [0pt]
  4. Give a route leaving Piraeus and finishing elsewhere which uses every arc once and only once.[3]
1 The graph shows routes that are available to an international lorry driver. The solid arcs represent motorways and the broken arcs represent ferry crossings.\\
\includegraphics[max width=\textwidth, alt={}, center]{dfe6db33-33d0-4dff-95f7-fbf097e3963e-2_668_1131_587_466}\\
(i) Give a route from Milan to Chania involving exactly two ferry crossings. How many such routes are there?\\
(ii) Give a route from Milan to Chania involving exactly three ferry crossings. How many such routes are there?\\
(iii) Give a route from Milan to Chania using as many ferry crossings as possible, without repeating any arc.\\[0pt]
(iv) Give a route leaving Piraeus and finishing elsewhere which uses every arc once and only once.[3]

\hfill \mbox{\textit{OCR MEI D1 2008 Q1 [8]}}
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Q1 8 Q2 8 Q3 8 Q4 16 Q5 16 Q6 16