Mathematics > QUESTION PAPER (QP) > OCR Wednesday 20 October 2021 – Afternoon AS Level Further Mathematics A Y534/01 Discrete Mathemat (All)

Answer all the questions. 1 A set consists of five distinct non-integer values, A, B, C, D and E. The set is partitioned into non-empty subsets and there are at least two subsets in each partition. ... (a) Show that there are 15 different partitions into two subsets. [2] (b) Show that there are 25 different partitions into three subsets. [4] (c) Calculate the total number of different partitions. [2] The numbers 12, 24, 36, 48, 60, 72, 84 and 96 are marked on a number line. The number line is then cut into pieces by making cuts at A, B, C, D and E, where 0 1 A 1 B 1 C 1 D 1 E 1 100. (d) Explain why there must be at least one piece with two or more of the numbers 12, 24, 36, 48, 60, 72, 84 and 96. [2] 2 Seven items need to be packed into bins. Each bin has capacity 30kg. The sizes of the items, in kg, in the order that they are received, are as follows. 12 23 15 18 8 7 5 (a) Find the packing that results using each of these algorithms. (i) The next-fit method [2] (ii) The first-fit method [2] (iii) The first-fit decreasing method [2] (b) A student claims that all three methods from part (a) can be used for both ‘online’ and ‘offline’ lists. Explain why the student is wrong. [2] The bins of capacity 30kg are replaced with bins of capacity Mkg, where M is an integer. The item of size 23kg can be split into two items, of sizes xkg and (23 - x) kg, where x may be any integer value you choose from 1 to 11. No other item can be split. (c) Determine the smallest value of M for which four bins are needed to pack these eight items. Explain your reasoning carefully. [3]3 © OCR 2021 Y534/01 Oct21 Turn over 3 The diagram shows a simplified map of the main streets in a small town. B A C X Y D F E 2.1 1.2 0.9 0.8 0.6 0.4 0.7 1.0 2.0 1.1 0.8 0.6 Some of the junctions have traffic lights, these junctions are labelled A to F. There are no traffic lights at junctions X and Y. The numbers show distances, in km, between junctions. Alex needs to check that the traffic lights at junctions A to F are working correctly. (a) Find a route from A to E that has length 2.8km. [1] Alex has started to construct a table of shortest distances between junctions A to [Show More]

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