| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Graph Theory Fundamentals |
| Type | Game and interaction modeling |
| Difficulty | Moderate -0.8 This is a straightforward interpretation question requiring students to read two graph representations and convert between them. Parts (i)-(iii) involve basic counting and graph drawing with no complex reasoning. Part (iv) tests understanding of discrete vs continuous data representation, which is conceptually simple. The question requires careful reading but minimal problem-solving or mathematical sophistication. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread7.02a Graphs: vertices (nodes) and arcs (edges)7.02b Graph terminology: tree, simple, connected, simply connected7.02e Bipartite graphs: K_{m,n} notation |
**Note:** Question 1 content not provided in mark scheme pages shown.1 Two students draw graphs to represent the numbers of pairs of shoes owned by members of their class. Andrew produces a bipartite graph, but gets it wrong. Barbara produces a completely correct frequency graph. Their graphs are shown below.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{2e03f6fb-69db-438a-a79e-3e04fab0d08a-2_652_593_575_278}
\captionsetup{labelformat=empty}
\caption{Andrew's graph}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{2e03f6fb-69db-438a-a79e-3e04fab0d08a-2_663_652_667_1142}
\captionsetup{labelformat=empty}
\caption{Barbara's graph}
\end{center}
\end{figure}
(i) Draw a correct bipartite graph.\\
(ii) How many people are in the class?\\
(iii) How many pairs of shoes in total are owned by members of the class?\\
(iv) Which points on Barbara's graph may be deleted without losing any information?
Charles produces the same frequency graph as Barbara, but joins consecutive points with straight lines.\\
(v) Criticise Charles's graph.
\hfill \mbox{\textit{OCR MEI D1 2011 Q1 [8]}}