OCR Thursday 21 October 2021 – Afternoon A Level Further Mathematics A Y544/01 Discrete Mathematics

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Answer all the questions. 1 Sam is packing for a holiday. The table shows the mass of each item to be packed. Item A B C D E F G H Mass (kg) 3 4 3.5 2.5 6 7.5 8 5 Sam’s bags can each carry 10kg,... but no more. (a) Use first-fit to show a possible packing that Sam could use. Indicate the items by using the letters A, B, … rather than their masses. [3] The total mass of the 8 items is 39.5 kg. Sam says that this means they can be packed using just 4 bags. (b) Explain why Sam cannot pack the items using just 4 bags. [2] Sam is only allowed to take 4 bags. Each item is given a value out of 20 representing how important it is to Sam. Item A B C D E F G H Mass (kg) 3 4 3.5 2.5 6 7.5 8 5 Value 6 10 12 10 16 12 20 14 (c) Sam wishes to pack items with a large total value. • State which item Sam should leave behind to maximise the total value. • Write down a possible packing with this item omitted. • Explain why no larger total is possible. [3]3 © OCR 2021 Y544/01 Oct21 Turn over 2 A simply connected semi-Eulerian graph G has 6 vertices and 8 arcs. Two of the vertex degrees are 3 and 4. (a) (i) Determine the minimum possible vertex degree. [1] (ii) Determine the maximum possible vertex degree. [1] (b) Write down the two possible degree sequences (ordered lists of vertex degrees [Show More]

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