> Wednesday 20 October 2021 – Afternoon A Level Further Mathematics B (MEI) Y433/01 Modelling with Algorithms. GRADED A+

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Answer all the questions. 1 The list below shows the sizes of 13 items. 5 16 12 15 21 10 17 5 3 6 13 24 5 (a) Show the result of applying the first fit algorithm to pack items with the sizes listed... above into bins that have a capacity of 45. [2] (b) Show the result of applying a full bin strategy to pack items with the sizes listed above into bins that have a capacity of 45. [2] 2 The table below shows the activities involved in a project, together with their immediate predecessors. The table also gives the duration (in hours) of each activity, apart from G and H. Activity Immediate predecessors Duration (hours) A – 6 B – 4 C – 8 D C 3 E A, B, D 6 F B, D 10 G C H C I E, F, G 10 J F, G 7 K F, G, H 9 (a) Draw an activity network, using activity on arc, to represent the project. [3] It is given that the only critical activities of the project are C, D, F, and I. (b) Carry out a forward pass and a backward pass through the activity network, showing the early event time and late event time at each vertex of your network. [3] (c) State the minimum completion time for the project. [1] (d) Calculate the interfering float at H, given that the independent float is not 0. [1] It is given that the total float of activity G is at most double the total float of activity E. Let x be the duration, in hours, of activity G. (e) Determine the range of possible values of x. [3]3 © OCR 2021 Y433/01 Oct21 Turn over 3 A vertex of a graph for which the order is an odd number is called an odd vertex. (a) (i) By considering the number of arc endings for a general graph, explain why, for every graph, the sum of the vertex orders must be an even number. [1] (ii) Hence explain why no graph can have an odd number of odd vertices [Show More]

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