4 P62675A 3. Two teams, A and B, each have three team members. One member of Team A will compete against one member of Team B for 10 rounds of a competition. None of the rounds can end in a draw. Table 1 shows, for each pairing, the expected number of rounds that the member of Team A will win minus the expected number of rounds that the member of Team B will win. These numbers are the scores awarded to Team A. This competition between Teams A and B is a zero‑sum game. Each team must choose one member to play. Each team wants to choose the member who will maximise its score. Team B Paul Qaasim Rashid Team A Mischa 4 –6 2 Noel 0 –2 6 Olive –6 2 0 Table 1 (a) (i) Find the number of rounds that Team A expects to win if Team A chooses Mischa and Team B chooses Paul. (ii) Find the number of rounds that Team B expects to win if Team A chooses Noel and Team B chooses Qaasim. (2) Table 1 models this zero-sum game. (b) (i) Find the play‑safe strategies for the game. (ii) Explain how you know that the game is not stable. (4) (c) Determine which team member Team B should choose if Team B thinks that Team A will play safe. Give a reason for your answer. (1) At the last minute, Rashid is ill and is therefore unavailable for selection by Team B. (d) Find the best strategy for Team B, defining any variables you use. (7) (Total for Question 3 is 14 marks) 4. A sequence {un}, where n 1, satisfies the recurrence relation 2un = un – 1 – kn2 where 4u2 – u0 = 27k2 and k is a non‑zero constant. Show that, as n becomes large, un can be approximated by a quadratic function of the form an2 + bn + c where a, b and c are constants to be determined. (8) (Total for Question 4 is 8 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 D2 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) Afternoon Paper Reference 8FM0/28 Thursday 14 May 2020 P62675A ©2020 Pearson Education Ltd. 1/1/1/1/1/1/1/ Turn over 2 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 1. 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_____________________________________________________________________________________ _____________________________________________________________________________________ 3 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 1 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 1 is 9 marks) 4 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2. P Q R S A 72 98 59 84 B 67 87 68 86 C 70 – 62 79 D 78 93 64 81 _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ You may not need to use all of these tables. _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ _ ________________________________________________ P Q R S A B C D P Q R S A B C D P Q R S A B C D 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 9 marks) P Q R S A B C D P Q R S A B C D P Q R S A B C D P Q R S A B C D P Q R S A B C D 6 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 3. Team B Paul Qaasim Rashid Team A Mischa 4 –6 2 Noel 0 –2 6 Olive –6 2 0 Table 1 _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 3 is 14 marks) 10 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 4. _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 4 is 8 marks) TOTAL FOR DECISION MATHEMATICS 2 IS 40 MARKS