Oxford Cambridge and RSA
A-LEVEL FURTHER MATHEMATICS A (Y544/01) DISCRETE MATHEMATICS WINTER EXAM PAPER
(AUTHENTIC MARKING SCHEME ATTACHED)
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provi...
A-LEVEL FURTHER MATHEMATICS A (Y544/01)
DISCRETE MATHEMATICS WINTER EXAM PAPER
(AUTHENTIC MARKING SCHEME ATTACHED)
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
* 9 4 5 9 5 9 1 5 3 5 *
Booklet. If you need extra space use the lined pages at the end of the Printed
Answer Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
–2
• The acceleration due to gravity is denoted by g m s . When a numerical value
is needed use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
1 Four children, A, B, C and D, discuss how many of the 23 birthday parties
held by their classmates they had gone to. Each party was attended by at
least one of the four children.
The results are shown in the Venn diagram below.
A C
0 0
1 0
1
B 9 3 2 4
0 3
0 D
Construct a complete
, with vertices representing the four children
(a) graph K4 and arcs
weighted to show the number of parties each pair of children went to. [3]
(b) State a piece of information about the number of parties the children went to
that is shown in
the Venn diagram but is not shown in the graph. [1]
A fifth child, E, also went to some of the 23 parties shown in the Venn
diagram.
Every party that E went to was also attended by at least one of A, B, C and D.
• A was at 8 of these parties, B at 7, C at 5 and D at 8.
• These include 5 parties attended by both A and B, 2 by both A and C, 3 by
both A and D, 3 by both B and D and 4 by both C and D.
• These include 1 party attended by A, B and D and 1 party attended by A, C
and D.
(c) Use the inclusion-exclusion principle to determine the number of parties
that E went to. [2]
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