100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
Previously searched by you
A-Level Pearson Edexcel GCE AL Further Mathematics (9FM0) Advanced Paper 4D Decision Mathematics 2 summer Exam Question Paper (AUTHENTIC MARKING SCHEME ATTACHED)£7.49
Add to cart
Pearson Edexcel Level 3 GCE
reference9FM0/4D
Paper
Time 1 hour 30 minutes
Further Mathematics
Advanced
PAPER 4D: Decision Mathematics 2
You must have:
Mathematical Formulae and Statistical Tables (Green),
calculator, Decision Mathematics Answer Book (enclosed)
A-Level Pearson Edexcel GCE
AL Further Mathematics (9FM0)
Advanced
Paper 4D Decision Mathematics 2
summer Exam Question Paper
(AUTHENTIC MARKING SCHEME
ATTACHED)
1/1/1/ *P72118A*
P72118A
,1. Four workers, A, B, C and D, are to be assigned to four tasks, 1, 2, 3
and 4. Each task must be assigned to just one worker and each
worker must do only one task.
The cost of assigning each worker to each task is shown in
the table below. The total cost is to be minimised.
1 2 3 4
A 32 45 34 48
B 37 39 50 46
C 46 44 40 42
D 43 45 48 52
(a) Reducing rows first, use the Hungarian algorithm to obtain an
allocation that minimises the total cost. You must make your
method clear and show the table after each stage.
(5)
(b) State the minimum total cost.
(1)
(Total for Question 1 is 6 marks)
2. The general solution of the second order recurrence relation
un + 2 + k1un + 1 + k2un = 0 n 0
is given by
un = (A + Bn)(–3)n
where A and B are arbitrary non-zero constants.
(a) Find the value of k1 and the value of k2
(2)
Given that u0 = u1 = 1
(b) find the value of A and the value of B.
(2)
(Total for Question 2 is 4 marks)
2 P72118A
,3. The table below shows the transport options, usual travel times, possible delay times
and corresponding probabilities of delay for a journey. All times are in minutes.
Transport option Usual travel time Possible delay time Probability of delay
10 0.10
Car 52
25 0.02
15 0.05
Train 45
25 0.03
5 0.05
Coach 55
15 0.01
(a) Draw a decision tree to model the transport options and the possible outcomes.
(5)
(b) State the minimum expected travel time and the corresponding transport option
indicated by the decision tree.
(2)
(Total for Question 3 is 7 marks)
P72118A 3
Turn over
, 4.
C1
A 20 20 E
C2
33 9 22 42
29 1
4 22 53
41 41 30 30
B
S G
10
30 25 12 14
6 14 F 72
C 6 75
5 8 24
C1 17 15 19
C2 T
D 4 4
Figure 1
Figure 1 shows a capacitated, directed network of pipes. The
uncircled number on each arc represents the capacity of the
corresponding pipe. The numbers in circles represent an initial flow.
(a) List the saturated arcs.
(1)
(b) State the value of the initial flow.
(1)
(c) Explain why arc FT cannot be full to capacity.
(1)
(d) State the capacity of cut C1 and the capacity of cut C2
(2)
(e) By inspection find one flow-augmenting route to increase the
flow by three units. You must state your route.
(1)
(f) Prove that, once the flow-augmenting route found in part (e) has
been applied, the flow is maximal.
(3)
(Total for Question 4 is 9 marks)
4 P72118A
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller StudyTimeOT. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £7.49. You're not tied to anything after your purchase.
