Question 1 - A-Level Maths

OCR MEI D1 2011 January — Question 1 8 marks

Exam Board	OCR MEI
Module	D1 (Decision Mathematics 1)
Year	2011
Session	January
Marks	8
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Graph Theory Fundamentals
Type	Physical space modeling
Difficulty	Moderate -0.8 This is a straightforward graph theory question requiring basic translation between physical circuits and graphs, counting arcs, and finding a minimum cut. Parts (i)-(iii) involve direct application of definitions with minimal problem-solving, while part (iv) requires simple reasoning about the difference between arcs and wires. Easier than average A-level due to its routine nature and limited conceptual depth.
Spec	7.02a Graphs: vertices (nodes) and arcs (edges)7.02b Graph terminology: tree, simple, connected, simply connected

1 The diagram shows an electrical circuit with wires and switches and with five components, labelled A, B, C, D and E. \includegraphics[max width=\textwidth, alt={}, center]{11c2d98f-1f72-4f1b-b971-5521bee09358-2_328_730_609_319} \includegraphics[max width=\textwidth, alt={}, center]{11c2d98f-1f72-4f1b-b971-5521bee09358-2_261_519_621_1224}

Draw a graph showing which vertices are connected together, either directly or indirectly, when the two switches remain open.
How many arcs need to be added to your graph when both switches are closed? The graph below shows which components are connected to each other, either directly or indirectly, for a second electrical circuit. \includegraphics[max width=\textwidth, alt={}, center]{11c2d98f-1f72-4f1b-b971-5521bee09358-2_410_494_1356_788}
Find the minimum number of arcs which need to be deleted to create two disconnected sets of vertices, and write down your two separate sets.
Explain why, in the second electrical circuit, it might be possible to split the components into two disconnected sets by cutting fewer wires than the number of arcs which were deleted in part (iii).

Show LaTeX source

1 The diagram shows an electrical circuit with wires and switches and with five components, labelled A, B, C, D and E.\\
\includegraphics[max width=\textwidth, alt={}, center]{11c2d98f-1f72-4f1b-b971-5521bee09358-2_328_730_609_319}\\
\includegraphics[max width=\textwidth, alt={}, center]{11c2d98f-1f72-4f1b-b971-5521bee09358-2_261_519_621_1224}\\
(i) Draw a graph showing which vertices are connected together, either directly or indirectly, when the two switches remain open.\\
(ii) How many arcs need to be added to your graph when both switches are closed?

The graph below shows which components are connected to each other, either directly or indirectly, for a second electrical circuit.\\
\includegraphics[max width=\textwidth, alt={}, center]{11c2d98f-1f72-4f1b-b971-5521bee09358-2_410_494_1356_788}\\
(iii) Find the minimum number of arcs which need to be deleted to create two disconnected sets of vertices, and write down your two separate sets.\\
(iv) Explain why, in the second electrical circuit, it might be possible to split the components into two disconnected sets by cutting fewer wires than the number of arcs which were deleted in part (iii).

\hfill \mbox{\textit{OCR MEI D1 2011 Q1 [8]}}

This paper (6 questions)

View full paper

Q1 8 Q2 8 Q3 8 Q4 16 Q5 16 Q6 16