OCR 2023 GCE FURTHER MATHEMATICS A Y544/01: DISCRETE MATHEMATICS A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

The table below shows the activities involved in a project together with the immediate predecessors and the duration of each activity. Activity Immediate predecessors Duration (hours) A – 2 B A 3 C – 4 D C 2 E B, C 2 F D, E 3 G E 2 H F, G 1 (a) Model the project using an activity network. [3] (b) Determine the minimum project completion time. [2] The start of activity C is delayed by 2 hours. (c) Determine the minimum project completion time with this delay. [2] 2 A graph is shown below. A D (a) Write down a cycle through all six vertices. [1] (b) Write down a continuous route that uses every arc exactly once. [2] (c) Use Kuratowski’s theorem to show that the graph is not planar. [2] (d) Show that the graph has thickness 2. [3] B C E F 3 © OCR 2023 Y544/01 Jun23 Turn over 3 An initial simplex tableau is given below. P x y z s t RHS 1 -2 3 -1 0 0 0 0 5 -4 1 1 0 20 0 2 -1