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A-Level MathematicsYear 2019Q4

P61640A 4 4. The table below gives the pay-off matrix for a zero-sum game between two players, Aljaz and Brendan. The values in the table show the pay-offs for Aljaz. Brendan Option X Option Y Option Z Aljaz Option P í í 2 Option Q 5 4 í Option R 5 6 3 (a) (i) Show that this game is stable. (ii) State the value of this game to Brendan. (3) Option R is removed from Aljaz’s choices and the reduced game, with option R removed, is no longer stable. (b) Find the best strategy for Aljaz in this reduced game, defining any variable you use. (7) (c) Explain why Brendan should never play option Y (1) Let Brendan play option X with probability q (d) (i) Explain why q satisfies the equation 6q í í q) = 1.6 (ii) Hence find the best strategy for Brendan in this reduced game. (4) (Total for Question 4 is 15 marks) TOTAL FOR DECISION MATHEMATICS 2 IS 40 MARKS END Please check the examination details below before entering your candidate information Candidate surname Other names Total Marks Centre Number Candidate Number Pearson Edexcel Level 3 GCE Answer Book Do not return the question paper with the answer book. Further Mathematics Advanced Subsidiary Further Mathematics options 28: Decision Mathematics 2 (Part of option K only) Paper Reference 8FM0-28 Afternoon Thursday 16 May 2019 P61640A ©2019 Pearson Education Ltd. 1/1/1/1/1/1/ Turn over 2 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 1. (a) ___________________________________________ _ _ _ _ _ P Q R S A 32 40 37 42 B 29 32 35 41 C 37 33 39 40 You may not need to use all of these tables You may not need to use all the rows and columns P Q R S A B C P Q R S A B C P Q R S A B C 3 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 1 continued (Total for Question 1 is 9 marks) P Q R S A B C P Q R S A B C P Q R S A B C P Q R S A B C P Q R S A B C 4 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 2 is 6 marks) 6 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 3. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 7 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 3 continued Question 3 continues on the next page. 14 A B C D E F G H J S T 18 4 6 7 24 2 7 2 3 0 11 5 3 0 5 19 14 7 26 0 2 6 5 6 12 0 12 2 6 0 4 5 17 21 4 0 7 8 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 3 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 9 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 3 continued A B C D E F G H J S T Diagram 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 3 is 10 marks) 10 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 4. Brendan Option X Option Y Option Z Aljaz Option P í í 2 Option Q 5 4 í Option R 5 6 3 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 11 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 4 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 12 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 4 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___________________________________________ (Total for Question 4 is 15 marks) TOTAL FOR DECISION MATHEMATICS 2 IS 40 MARKS

Paper Source:8FM0_28_que_20190517.pdf

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Exam Specification Info

This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.

Syllabus levelAdvanced Level (A-Level)

SubjectMathematics

Official MarksVariable (2–6 marks)