AQA D1 2016 June — Question 1 5 marks

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2016
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMatchings and Allocation
TypeMaximum matching algorithm application
DifficultyEasy -1.2 This is a standard bipartite matching problem requiring application of the maximum matching algorithm (likely Hungarian algorithm or inspection method). It's a routine D1 question with clear setup and algorithmic procedure, requiring less mathematical sophistication than typical pure maths questions. The mechanical nature and structured approach make it easier than average A-level content.
Spec7.01g Arrangements in a line: with repetition and restriction

1 Alfred has bought six different chocolate bars. He wants to give a chocolate bar to each of his six friends. The table gives the names of the friends and indicates which of Alfred's six chocolate bars they like.

AnswerMarks Guidance
(a) Bipartite graph; 2 sets of 6 labelled (condone errors) vertices; at least 10 edgesM1
All correct, including labellingA1 2 marks total
(b) \(I - M + G\) or \(C - F + N\) (Allow different notations e.g. those below on the left)M1
Correct path e.g. \(I - M + G - L + H - O + K - P + J - N + F - C\) or \(I - M + G - L + H - O + K - P + J - N + F - C\) or \(IMGLHOKPJNFC\)A1
Match FC, GL, HO, IM, JN, KPB1 3 marks total
**(a)** Bipartite graph; 2 sets of 6 labelled (condone errors) vertices; at least 10 edges | M1 | 
All correct, including labelling | A1 | 2 marks total

**(b)** $I - M + G$ or $C - F + N$ (Allow different notations e.g. those below on the left) | M1 |
Correct path e.g. $I - M + G - L + H - O + K - P + J - N + F - C$ or $I - M + G - L + H - O + K - P + J - N + F - C$ or $IMGLHOKPJNFC$ | A1 |
Match FC, GL, HO, IM, JN, KP | B1 | 3 marks total | oe; Must be a list

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1 Alfred has bought six different chocolate bars. He wants to give a chocolate bar to each of his six friends. The table gives the names of the friends and indicates which of Alfred's six chocolate bars they like.

\hfill \mbox{\textit{AQA D1 2016 Q1 [5]}}