Date | May Example question | Marks available | 2 | Reference code | EXM.2.AHL.TZ0.17 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Write down | Question number | 17 | Adapted from | N/A |
Question
A canal system divides a city into six land masses connected by fifteen bridges, as shown in the diagram below.
State with reasons whether or not this graph has
Draw a graph to represent this map.
Write down the adjacency matrix of the graph.
List the degrees of each of the vertices.
an Eulerian circuit.
an Eulerian trail.
Find the number of walks of length 4 from E to F.
Markscheme
A2
[2 marks]
M = ABCDEFABCDEF(012122100012200101101010210101221010)ABCDEFABCDEF⎛⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜⎝012122100012200101101010210101221010⎞⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎠ A2
Note: Award A1 for one error or omission, A0 for more than one error or omission. Two symmetrical errors count as one error.
[2 marks]
A B C D E F
(8, 4 4, 3 5, 6) A2
Note: Award no more than A1 for one error, A0 for more than one error.
[2 marks]
no, because there are odd vertices M1A1
[2 marks]
yes, because there are exactly two odd vertices M1A1
[2 marks]
M4 = ABCDEFABCDEF(30917414011817021417411710670122132140106117661341381187066538010217012213480157170214132138102170213)ABCDEFABCDEF⎛⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜⎝30917414011817021417411710670122132140106117661341381187066538010217012213480157170214132138102170213⎞⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎠ (M1)A1
number of walks of length 4 is 170
Note: The complete matrix need not be shown. Only one of the FE has to be shown.
[2 marks]