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A-Level MathematicsYear 2019Q7

8 P61186A 7. Aisha is deciding whether or not to play a game. The game involves rolling three fair six-sided dice, which have faces numbered from 1 to 6 If the total score on the three dice is 16 or more then she wins a prize. If the total score is 15 or less then she loses and will have to pay the person running the game £3 (a) Given that the prize is £15 (i) draw a decision tree to model Aisha’s possible decisions and the possible outcomes (ii) determine Aisha’s optimal EMV and state the optimal strategy indicated by the decision tree. (6) The utility function of the game to Aisha is u(m) = 1 – e −m 500 where m is the amount of money that Aisha has available. Given that Aisha has exactly £3 and that the prize is now £x (b) find the expected utility to Aisha of playing the game in the form a b x c 1 500 − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ − + e ( ) where a, b and c are integers to be found. (2) Aisha decides to use the expected utilities to determine whether she should play the game or not. (c) Find the minimum prize for which Aisha would consider playing the game. (4) (Total for Question 7 is 12 marks) TOTAL FOR PAPER IS 75 MARKS 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 Paper 4D: Decision Mathematics 2 Paper Reference 9FM0/4D Tuesday 25 June 2019 Morning (Time: 1 hour 30 minutes) P61186A ©2019 Pearson Education Ltd. 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. P Q R S Supply A 15 14 17 11 23 B 10 9 16 12 42 C 11 13 8 10 18 D 15 13 16 17 19 Demand 25 45 12 20 Table 1 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 ________________________________ 3 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 1 continued 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 (Total for Question 1 is 10 marks) 4 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2. 1 2 3 4 T 103 97 74 80 H 201 155 145 155 J 111 80 77 92 M 203 188 137 184 1 2 3 4 T H J M 1 2 3 4 T H J M 1 2 3 4 T H J M 1 2 3 4 T H J M 5 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued 1 2 3 4 T H J M 1 2 3 4 T H J M 1 2 3 4 T H J M 1 2 3 4 T H J M (Total for Question 2 is 7 marks) 6 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 3. (a) _ _ _ Stage State Action Destination Value 7 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 3 continued Stage State Action Destination Value _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 3 is 13 marks) 8 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 4. Player B Option X Option Y Option Z Option P 3 –2 0 Player A Option Q –4 4 –2 Option R 1 2 –1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 9 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 4 continued b.v. Value P Only use the tableau below if you need to correct your initial tableau. b.v. Value P _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 10 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 4 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 11 Turn over 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 14 marks) 12 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 5. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 13 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 5 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 14 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 5 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 15 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 5 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (Total for Question 5 is 11 marks) 16 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 6. (a) (i) Capacity of cut C1 = (ii) Capacity of cut C2 = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 17 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 6 continued _ _ _ Minimum feasible flow B H D E F C G A S T Maximum feasible flow B H D E F C G A S T _ _ _ (Total for Question 6 is 8 marks) 18 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 7. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 19 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 7 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 20 DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 7 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___________________________________________ (Total for Question 7 is 12 marks) TOTAL FOR PAPER IS 75 MARKS

Paper Source:9FM0_4D_que_20190626.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)