Questions - OCR MEI D1 - A-Level Maths

	A	B	C	D	E	F
A	-	22	-	12	10	-
B	22	-	-	-	-	13
C	-	-	-	6	5	11
D	12	-	6	-	-	-
E	10	-	5	-	-	26
F	-	13	11	-	26	-

Draw the network.
Use Dijkstra's algorithm to find the shortest route from A to F . Give the route and its length.
Use Kruskal's algorithm to find a minimum connector for the network, showing your working. Draw your connector and give its total length.
How much shorter would AD have to be if it were to be included in
(A) a shortest route from A to F ,
(B) a minimum connector?

OCR MEI D1 2010 January Q6

6 An apple tree has 6 apples left on it. Each day each remaining apple has a probability of $\frac { 1 } { 3 }$ of falling off the tree during the day.

Give a rule for using one-digit random numbers to simulate whether or not a particular apple falls off the tree during a given day.
Use the random digits given in your answer book to simulate how many apples fall off the tree during day 1 . Give the total number of apples that fall during day 1 .
Continue your simulation from the end of day 1 , which you simulated in part (ii), for successive days until there are no apples left on the tree. Use the same list of random digits, continuing from where you left off in part (ii). During which day does the last apple fall from the tree? Now suppose that at the start of each day the gardener picks one apple from the tree and eats it.
Repeat your simulation with the gardener picking the lowest numbered apple remaining on the tree at the start of each day. Give the day during which the last apple falls or is picked. Use the same string of random digits, a copy of which is provided for your use in this part of the question.
How could your results be made more reliable?

OCR MEI D1 2011 January Q1

1 The diagram shows an electrical circuit with wires and switches and with five components, labelled A, B, C, D and E.
\includegraphics[max width=\textwidth, alt={}, center]{11c2d98f-1f72-4f1b-b971-5521bee09358-2_328_730_609_319}
\includegraphics[max width=\textwidth, alt={}, center]{11c2d98f-1f72-4f1b-b971-5521bee09358-2_261_519_621_1224}

Draw a graph showing which vertices are connected together, either directly or indirectly, when the two switches remain open.
How many arcs need to be added to your graph when both switches are closed? The graph below shows which components are connected to each other, either directly or indirectly, for a second electrical circuit.
\includegraphics[max width=\textwidth, alt={}, center]{11c2d98f-1f72-4f1b-b971-5521bee09358-2_410_494_1356_788}
Find the minimum number of arcs which need to be deleted to create two disconnected sets of vertices, and write down your two separate sets.
Explain why, in the second electrical circuit, it might be possible to split the components into two disconnected sets by cutting fewer wires than the number of arcs which were deleted in part (iii).

OCR MEI D1 2011 January Q2

2 King Elyias has been presented with eight flagons of fine wine. Intelligence reports indicate that at least one of the eight flagons has been poisoned. King Elyias will have the wine tasted by the royal wine tasters to establish which flagons are poisoned. Samples for testing are made by using wine from one or more flagons. If a royal wine taster tastes a sample of wine which includes wine from a poisoned flagon, the taster will die. The king has to make a very generous payment for each sample tasted. To minimise payments, the royal mathematicians have devised the following scheme:
Test a sample made by mixing wine from flagons $1,2,3$ and 4.
If the taster dies, then test a sample made by mixing wine from flagons $5,6,7$ and 8 .
If the taster lives, then there is no poison in flagons $1,2,3$ or 4 . So there is poison in at least one of flagons 5, 6, 7 and 8, and there is no need to test a sample made by mixing wine from all four of them. If the sample from flagons $1,2,3$ and 4 contains poison, then test a fresh sample made by mixing wine from flagons 1 and 2, and proceed similarly, testing a sample from flagons 3 and 4 only if the taster of the sample from flagons 1 and 2 dies. Continue, testing new samples made from wine drawn from half of the flagons corresponding to a poisoned sample, and testing only when necessary.

Record what happens using the mathematicians' scheme when flagon number 7 is poisoned, and no others.
Record what happens using the mathematicians' scheme when two flagons, numbers 3 and 7, are poisoned.

OCR MEI D1 2011 January Q3

1 marks

3 The network shows distances between vertices where direct connections exist.
\includegraphics[max width=\textwidth, alt={}, center]{11c2d98f-1f72-4f1b-b971-5521bee09358-3_518_691_1742_687}

Use Dijkstra's algorithm to find the shortest distance and route from A to F .
Explain why your solution to part (i) also provides the shortest distances and routes from A to each of the other vertices.
[0pt]
Explain why your solution to part (i) also provides the shortest distance and route from B to F. [1]

OCR MEI D1 2011 January Q4

4 The table shows the tasks involved in preparing breakfast, and their durations.

Task	Description	Duration (mins)
A	Fill kettle and switch on	0.5
B	Boil kettle	1.5
C	Cut bread and put in toaster	0.5
D	Toast bread	2
E	Put eggs in pan of water and light gas	1
F	Boil eggs	5
G	Put tablecloth, cutlery and crockery on table	2.5
H	Make tea and put on table	0.5
I	Collect toast and put on table	0.5
J	Put eggs in cups and put on table	1

Show the immediate predecessors for each of these tasks.
Draw an activity on arc network modelling your precedences.
Perform a forward pass and a backward pass to find the early time and the late time for each event.
Give the critical activities, the project duration, and the total float for each activity.
Given that only one person is available to do these tasks, and noting that tasks B, D and F do not require that person's attention, produce a cascade chart showing how breakfast can be prepared in the least possible time.

OCR MEI D1 2011 January Q5

5 Viola and Orsino are arguing about which striker to include in their fantasy football team. Viola prefers Rocinate, who creates lots of goal chances, but is less good at converting them into goals. Orsino prefers Quince, who is not so good at creating goal chances, but who is better at converting them into goals. The information for Rocinate and Quince is shown in the tables.

\multirow{2}{*}{}	Number of chances created per match
	Rocinate				Quince
Number	6	7	8	9	5	6	7	8
Probability	$\frac { 1 } { 20 }$	$\frac { 1 } { 4 }$	$\frac { 1 } { 2 }$	$\frac { 1 } { 5 }$	$\frac { 1 } { 3 }$	$\frac { 1 } { 3 }$	$\frac { 1 } { 6 }$	$\frac { 1 } { 6 }$

Probability of converting a chance into a goal
Rocinate	Quince
0.1	0.12

Give an efficient rule for using 2-digit random numbers to simulate the number of chances created by Rocinate in a match.
Give a rule for using 2-digit random numbers to simulate the conversion of chances into goals by Rocinate.
Your Printed Answer Book shows the result of simulating the number of goals scored by Rocinate in nine matches. Use the random numbers given to complete the tenth simulation, showing which of your simulated chances are converted into goals.
Give an efficient rule for using 2-digit random numbers to simulate the number of chances created by Quince in a match.
Your Printed Answer Book shows the result of simulating the number of goals scored by Quince in nine matches. Use the random numbers given to complete the tenth simulation, showing which of your simulated chances are converted into goals.
Which striker, if any, is favoured by the simulation? Justify your answer.
How could the reliability of the simulation be improved?

OCR MEI D1 2011 January Q6

6 A manufacturing company holds stocks of two liquid chemicals. The company needs to update its stock levels. The company has 2000 litres of chemical A and 4000 litres of chemical B currently in stock. Its storage facility allows for no more than a combined total of 12000 litres of the two chemicals. Chemical A is valued at $\pounds 5$ per litre and chemical B is valued at $\pounds 6$ per litre. The company intends to hold stocks of these two chemicals with a total value of at least $\pounds 61000$. Let $a$ be the increase in the stock level of A, in thousands of litres ( $a$ can be negative).
Let $b$ be the increase in the stock level of B , in thousands of litres ( $b$ can be negative).

Explain why $a \geqslant - 2$, and produce a similar inequality for $b$.
Explain why the value constraint can be written as $5 a + 6 b \geqslant 27$, and produce, in similar form, the storage constraint.
Illustrate all four inequalities graphically.
Find the policy which will give a stock value of exactly $\pounds 61000$, and will use all 12000 litres of available storage space.
Interpret your solution in terms of stock levels, and verify that the new stock levels do satisfy both the value constraint and the storage constraint.

OCR MEI D1 2012 January Q1

1 A graph is obtained from a solid by producing a vertex for each exterior face. Vertices in the graph are connected if their corresponding faces in the original solid share an edge. The diagram shows a solid followed by its graph. The solid is made up of two cubes stacked one on top of the other. This solid has 10 exterior faces, which correspond to the 10 vertices in the graph. (Note that in this question it is the exterior faces of the cubes that are being counted.)
\includegraphics[max width=\textwidth, alt={}, center]{3239d012-5699-4789-ba64-f1295f4b4642-2_455_309_571_653}
\includegraphics[max width=\textwidth, alt={}, center]{3239d012-5699-4789-ba64-f1295f4b4642-2_444_286_573_1135}

Draw the graph for a cube.
Obtain the number of vertices and the number of edges for the graph of three cubes stacked on top of each other.
\includegraphics[max width=\textwidth, alt={}, center]{3239d012-5699-4789-ba64-f1295f4b4642-2_643_305_1302_881}

OCR MEI D1 2012 January Q2

2 The following is called the '1089' algorithm. In steps 1 to 4 numbers are to be written with exactly three digits; for example 42 is written as 042. Step 1 Choose a 3-digit number, with no digit being repeated.
Step 2 Form a new number by reversing the order of the three digits.
Step 3 Subtract the smaller number from the larger and call the difference D. If the two numbers are the same then $\mathrm { D } = 000$. Step 4 Form a new number by reversing the order of the three digits of D , and call it R .
Step 5 Find the sum of D and R .

Apply the algorithm, choosing 427 for your 3-digit number, and showing all of the steps.
Apply the algorithm to a 3-digit number of your choice, showing all of the steps.
Investigate what happens if digits may be repeated in the 3 -digit number in step 1 .

OCR MEI D1 2012 January Q3

3 Solve the following LP problem graphically.
Maximise $2 x + 3 y$
subject to $\quad x + y \leqslant 11$ $$\begin{aligned} 3 x + 5 y & \leqslant 39
x + 6 y & \leqslant 39 . \end{aligned}$$

OCR MEI D1 2012 January Q4

4 The table defines a network in which the numbers represent lengths.

	A	B	C	D	E	F	G
A	-	5	2	3	-	-	-
B	5	-	-	-	1	1	-
C	2	-	-	-	4	1	-
D	3	-	-	-	4	2	-
E	-	1	4	4	-	-	1
F	-	1	1	2	-	-	5
G	-	-	-	-	1	5	-

Draw the network.
Use Dijkstra's algorithm to find the shortest paths from A to each of the other vertices. Give the paths and their lengths.
Draw a new network containing all of the edges in your shortest paths, and find the total length of the edges in this network.
Find a minimum connector for the original network, draw it, and give the total length of its edges.
Explain why the method defined by parts (i), (ii) and (iii) does not always give a minimum connector.

OCR MEI D1 2012 January Q5

5 Five gifts are to be distributed among five people, A, B, C, D and E. The gifts are labelled from 1 to 5. Each gift is allocated randomly to one of the five people. A person can receive more than one gift.

Use one-digit random numbers to simulate this process. One-digit random numbers are provided in your answer book. Explain how your simulation works. Produce a table, showing how many gifts each person receives.
Carry out four more simulations showing, in each case, how many gifts each person receives.
Use your simulation to estimate the probabilities of a person receiving $0,1,2,3,4$ and 5 gifts.
Describe what you would have to do differently if there were six people and six gifts.

OCR MEI D1 2012 January Q6

6 The table shows the tasks involved in making a salad, their durations and their precedences.

Task		Duration (seconds)	Immediate predecessors
B	get out bowl and implements	10	-
I	get out ingredients	10	-
L	chop lettuce	15	B, I
W	wash tomatoes and celery	25	B, I
T	chop tomatoes	15	W
C	chop celery	10	W
P	peel apple	20	B, I
A	chop apple	10	P
D	dress salad	10	L, T, C, A

Draw an activity on arc network for these activities.
Mark on your diagram the early and late times for each event. Give the minimum completion time and the critical activities.
Given that each task can only be done by one person, how many people are needed to prepare the salad in the minimum time? What is the minimum time required to prepare the salad if only one person is available?
Show how two people can prepare the salad as quickly as possible.

OCR MEI D1 2013 January Q1

1 The weights on the arcs in the network represent times in minutes to travel between vertices.
\includegraphics[max width=\textwidth, alt={}, center]{d1e0f047-6484-435b-a685-2cbbf81a6b02-2_606_782_402_628}

Use Dijkstra's algorithm to find the fastest route from A to F . Give the route and the time.
Use an algorithm to find the minimum connector for the network, showing your working. Find the minimum time to travel from A to F using only arcs in the minimum connector.

OCR MEI D1 2013 January Q2

2 A small party is held in a country house. There are 10 men and 10 women, and there are 10 dances. For each dance a number of pairings, each of one man and one woman, are formed. The same pairing can appear in more than one dance. A graph is to be drawn showing who danced with whom during the evening, ignoring repetitions.

Name the type of graph which is appropriate.
What is the maximum possible number of arcs in the graph? Dashing Mr Darcy dances with every woman except Elizabeth, who will have nothing to do with him. She dances with eight different men. Prince Charming only dances with Cinderella. Cinderella only dances with Prince Charming and with Mr Darcy. The three ugly sisters only have one dance each.
Add arcs to the graph in your answer book to show this information.
What is the maximum possible number of arcs in the graph?

OCR MEI D1 2013 January Q3

3 The following algorithm computes an estimate of the square root of a number which is between 0 and 2.
Step 1 Subtract 1 from the number and call the result $x$
Step 2 Set oldr = 1
Step 3 Set $i = 1$
Step 4 Set $j = 0.5$
Step 5 Set $k = 0.5$
Step 6 Set change $= x ^ { i } \times k$
Step 7 Set newr $=$ oldr + change
Step 8 If $- 0.005 <$ change < 0.005 then go to Step 17
Step 9 Set oldr = newr
Step 10 Set $i = i + 1$
Step 11 Set $j = j - 1$
Step 12 Set $k = k \times j \div i$
Step 13 Set change $= x ^ { i } \times k$
Step 14 Set newr $=$ oldr + change
Step 15 If $- 0.005 <$ change < 0.005 then go to Step 17
Step 16 Go to Step 9
Step 17 Print out newr

Use the algorithm to find an estimate of the square root of 1.44 , showing all of the steps.
Consider what happens if the algorithm is applied to 0.56 , and then use your four values of change from part (i) to calculate an estimate of the square root of 0.56 .

OCR MEI D1 2013 January Q4

4 A room has two windows which have the same height but different widths. Each window is to have one curtain. The table lists the tasks involved in making the two curtains, their durations, and their immediate predecessors. The durations assume that only one person is working on the activity.

Task		Duration (minutes)	Immediate predecessor(s)
A	measure windows	5	-
B	calculate material required	5	A
C	choose material	15	-
D	buy material	15	B, C
E	cut material	5	D
F	stitch sides of wide curtain	30	E
G	stitch top of wide curtain	30	F
H	stitch sides of narrow curtain	30	E
I	stitch top of narrow curtain	15	H
J	hang curtains and pin hems	20	G, I
K	hem wide curtain	30	J
L	hem narrow curtain	15	J
M	fit curtains	10	K, L

Draw an activity on arc network for these activities.
Mark on your diagram the early time and the late time for each event. Give the minimum completion time and the critical activities. Kate and Pete have two rooms to curtain, each identical to that above. Tasks A, B, C and D only need to be completed once each. All other tasks will have two versions, one for room 1 and one for room 2, eg E1 and E2. Kate and Pete share the tasks between them so that each task is completed by only one person.
Complete the diagram to show how the tasks can be shared between them, and scheduled, so that the project can be completed in the least possible time. Give that least possible time.
How much extra help would be needed to curtain both rooms in the minimum completion time from part (ii)? Explain your answer.

OCR MEI D1 2013 January Q5

5 A chairlift for a ski slope has 160 4-person chairs. At any one time half of the chairs are going up and half are coming down empty. An observer watches the loading of the chairs during a moderately busy period, and concludes that the number of occupants per 'up' chair has the following probability distribution.

number of occupants	0	1	2	3	4
probability	0.1	0.2	0.3	0.2	0.2

Give a rule for using 1-digit random numbers to simulate the number of occupants of an up chair in a moderately busy period.
Use the 10 random digits provided to simulate the number of occupants in 10 up chairs. The observer estimates that, at all times, on average $20 \%$ of chairlift users are children.
Give an efficient rule for using 1-digit random numbers to simulate whether an occupant of an up chair is a child or an adult.
Use the random digits provided to simulate how many of the occupants of the 10 up chairs are children, and how many are adults. There are more random digits than you will need.
Use your results from part (iv) to estimate how many children and how many adults are on the chairlift (ie on the 80 up chairs) at any instant during a moderately busy period. In a very busy period the number of occupants of an up chair has the following probability distribution.
number of occupants 0 1 2 3 4
probability $\frac { 1 } { 13 }$ $\frac { 1 } { 13 }$ $\frac { 3 } { 13 }$ $\frac { 3 } { 13 }$ $\frac { 5 } { 13 }$
Give an efficient rule for using 2-digit random numbers to simulate the number of occupants of an up chair in a very busy period.
Use the 2-digit random numbers provided to simulate the number of occupants in 5 up chairs. There are more random numbers provided than you will need.
Simulate how many of the occupants of the 5 up chairs are children and how many are adults, and thus estimate how many children and how many adults are on the chairlift at any instant during a very busy period.
Discuss the relative merits of simulating using a sample of 10 chairs as against simulating using a sample of 5 chairs.

OCR MEI D1 2013 January Q6

6 Jean knits items for charity. Each month the charity provides her with 75 balls of wool.
She knits hats and scarves. Hats require 1.5 balls of wool each and scarves require 3 balls each. Jean has 100 hours available each month for knitting. Hats require 4 hours each to make, and scarves require 2.5 hours each. The charity sells the hats for $\pounds 7$ each and the scarves for $\pounds 10$ each, and wants to gain as much income as possible. Jean prefers to knit hats but the charity wants no more than 20 per month. She refuses to knit more than 20 scarves each month.

Define appropriate variables, construct inequality constraints, and draw a graph representing the feasible region for this decision problem.
Give the objective function and find the integer solution which will give Jean's maximum monthly income.
If the charity drops the price of hats in a sale to $\pounds 4$ each, what would be an optimal number of hats and scarves for Jean to knit? Assuming that all hats and scarves are sold, by how much would the monthly income drop?

OCR MEI D1 2005 June Q3

8 marks

3 Table 3 gives the durations and immediate predecessors for the five activities of a project. \begin{table}[h]

Activity	Duration (hours)	Immediate predecessor(s)
A	3	-
B	2	-
C	5	-
D	2	A
E	1	A, B

\captionsetup{labelformat=empty} \caption{Table 3}

\end{table}

Draw an activity-on-arc network to represent the precedences.
Find the early and late event times for the vertices of your network, and list the critical activities.
Give the total and independent float for each activity which is not critical.

OCR MEI D1 2005 June Q5

3 marks

5 A computer store has a stock of 10 laptops to lend to customers while their machines are being repaired. On any particular day the number of laptop loans requested follows the distribution given in Table 5.1. \begin{table}[h]

Number requested	0	1	2	3	4
Probability	0.20	0.30	0.20	0.15	0.15

\captionsetup{labelformat=empty} \caption{Table 5.1}

\end{table}

Give an efficient rule for using two-digit random numbers to simulate the daily number of requests for laptop loans.
Use two-digit random numbers from the list below to simulate the number of loans requested on each of ten successive days. Random numbers: $23,02,57,80,31,72,92,78,04,07$ The number of laptops returned from loan each day is modelled by the distribution given in Table 5.2, independently of the number on loan (which is always at least 5 ). \begin{table}[h]
Number returned 0 1 2 3
Probability $\frac { 1 } { 6 }$ $\frac { 1 } { 4 }$ $\frac { 1 } { 4 }$ $\frac { 1 } { 3 }$
\captionsetup{labelformat=empty} \caption{Table 5.2}
\end{table}
Give an efficient rule for using two-digit random numbers to simulate the daily number of laptop returns.
Use two-digit random numbers from the list below to simulate the number of returns on each of ten successive days. Random numbers: $32,98,01,32,14,21,32,71,82,54,47$ At the end of day 0 there are 7 laptops out on loan and 3 in stock. Each day returns are made in the morning and loans go out in the afternoon. If there is no laptop available the customer is disappointed and never gets a loaned laptop.
Use your simulated numbers of requests and returns to simulate what happens over the next 10 days. For each day record the day number, the number of laptops in stock at the end of the day, and the number of customers that have to be disappointed.
[0pt] [3] To try to avoid disappointing customers, if the number of laptops in stock at the end of a day is 2 or fewer, the store sends out e-mails to customers with loaned laptops asking for early return if possible. This changes the return distribution for the next day to that given in Table 5.3. \begin{table}[h]
Number returned 0 1 2 3 4
Probability 0.1 0.1 0.4 0.2 0.2
\captionsetup{labelformat=empty} \caption{Table 5.3}
\end{table}
Simulate the 10 days again, but using this new policy. Use the requests you produced in part (ii). Use the random numbers given in part (iv) to simulate returns, but use either the distribution given in Table 5.2 or that given in Table 5.3, depending on the number of laptops in stock at the end of the previous day. Is the new policy better?

OCR MEI D1 2005 June Q6

1 marks

6 A company manufactures two types of potting compost, Flowerbase and Growmuch. The weekly amounts produced of each are constrained by the supplies of fibre and of nutrient mix. Each litre of Flowerbase requires 0.75 litres of fibre and 1 kg of nutrient mix. Each litre of Growmuch requires 0.5 litres of fibre and 2 kg of nutrient mix. There are 12000 litres of fibre supplied each week, and 25000 kg of nutrient mix. The profit on Flowerbase is 9 p per litre. The profit on Growmuch is 20 p per litre.

Formulate an LP to maximise the weekly profit subject to the constraints on fibre and nutrient mix.
Solve your LP using a graphical approach.
Consider each of the following separate circumstances.
(A) There is a reduction in the weekly supply of fibre from 12000 litres to 10000 litres. What effect does this have on profit?
(B) The price of fibre is increased. Will this affect the optimal production plan? Justify your answer.
[0pt] (C) The supply of nutrient mix is increased to 30000 kg per week. What is the new profit? [1]

OCR MEI D1 2006 June Q2

2 Fig. 2.1 represents the two floors of a house. There are 5 rooms shown, plus a hall and a landing, which are to be regarded as separate rooms. Each " × " represents an internal doorway connecting two rooms. The " ⊗ " represents the staircase, connecting the hall and the landing. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{c429bfed-9241-409a-9cd5-9553bf16c9df-3_401_1287_447_388} \captionsetup{labelformat=empty} \caption{Fig. 2.1}

\end{figure}

Draw a graph representing this information, with vertices representing rooms, and arcs representing internal connections (doorways and the stairs). What is the name of the type of graph of which this is an example?
A larger house has 12 rooms on two floors, plus a hall and a landing. Each ground floor room has a single door, which leads to the hall. Each first floor room has a single door, which leads to the landing. There is a single staircase connecting the hall and the landing. How many arcs are there in the graph of this house?
Another house has 12 rooms on three floors, plus a hall, a first floor landing and a second floor landing. Again, each room has a single door on to the hall or a landing. There is one staircase from the hall to the first floor landing, and another staircase joining the two landings. How many arcs are there in the graph of this house?
Fig. 2.2 shows the graph of another two-floor house. It has 8 rooms plus a hall and a landing. There is a single staircase. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c429bfed-9241-409a-9cd5-9553bf16c9df-3_208_666_1896_694} \captionsetup{labelformat=empty} \caption{Fig. 2.2}
\end{figure} Draw a possible floor plan, showing internal connections.

OCR MEI D1 2006 June Q3

3 An incomplete algorithm is specified in Fig. 3.
$\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 2$
Initial values: $\mathrm { L } = 0 , \mathrm { R } = 2$.
Step 1 Compute $\mathrm { M } = \frac { \mathrm { L } + \mathrm { R } } { 2 }$.
Step 2 Compute $\mathrm { f } ( \mathrm { M } )$.
Step 3 If $\mathrm { f } ( \mathrm { M } ) < 0$ change the value of L to that of M .
Otherwise change the value of $R$ to that of $M$.
Step 4 Go to Step 1. \section*{Fig. 3}

Apply two iterations of the algorithm.
After 10 iterations $\mathrm { L } = 1.414063 , \mathrm { R } = 1.416016 , \mathrm { M } = 1.416016$ and $\mathrm { f } ( \mathrm { M } ) = 0.005100$. Say what the algorithm achieves.
Say what is needed to complete the algorithm.

\multirow{2}{*}{}	Number of chances created per match
	Rocinate				Quince
Number	6	7	8	9	5	6	7	8
Probability	\(\frac { 1 } { 20 }\)	\(\frac { 1 } { 4 }\)	\(\frac { 1 } { 2 }\)	\(\frac { 1 } { 5 }\)	\(\frac { 1 } { 3 }\)	\(\frac { 1 } { 3 }\)	\(\frac { 1 } { 6 }\)	\(\frac { 1 } { 6 }\)

number of occupants	0	1	2	3	4
probability	\(\frac { 1 } { 13 }\)	\(\frac { 1 } { 13 }\)	\(\frac { 3 } { 13 }\)	\(\frac { 3 } { 13 }\)	\(\frac { 5 } { 13 }\)

Number returned	0	1	2	3
Probability	\(\frac { 1 } { 6 }\)	\(\frac { 1 } { 4 }\)	\(\frac { 1 } { 4 }\)	\(\frac { 1 } { 3 }\)

	A	B	C	D	E	F
A	-	22	-	12	10	-
B	22	-	-	-	-	13
C	-	-	-	6	5	11
D	12	-	6	-	-	-
E	10	-	5	-	-	26
F	-	13	11	-	26	-

	A	B	C	D	E	F	G
A	-	5	2	3	-	-	-
B	5	-	-	-	1	1	-
C	2	-	-	-	4	1	-
D	3	-	-	-	4	2	-
E	-	1	4	4	-	-	1
F	-	1	1	2	-	-	5
G	-	-	-	-	1	5	-

	A	B	C	D	E	F
A	-	22	-	12	10	-
B	22	-	-	-	-	13
C	-	-	-	6	5	11
D	12	-	6	-	-	-
E	10	-	5	-	-	26
F	-	13	11	-	26	-

	A	B	C	D	E	F	G
A	-	5	2	3	-	-	-
B	5	-	-	-	1	1	-
C	2	-	-	-	4	1	-
D	3	-	-	-	4	2	-
E	-	1	4	4	-	-	1
F	-	1	1	2	-	-	5
G	-	-	-	-	1	5	-

Questions — OCR MEI D1 (128 questions)

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OCR MEI D1 2010 January Q5

OCR MEI D1 2010 January Q6

OCR MEI D1 2011 January Q1

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OCR MEI D1 2011 January Q3

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OCR MEI D1 2011 January Q5

OCR MEI D1 2011 January Q6

OCR MEI D1 2012 January Q1

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OCR MEI D1 2013 January Q1

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OCR MEI D1 2013 January Q3

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OCR MEI D1 2013 January Q5

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OCR MEI D1 2005 June Q3

OCR MEI D1 2005 June Q5

OCR MEI D1 2005 June Q6

OCR MEI D1 2006 June Q2

OCR MEI D1 2006 June Q3

	A	B	C	D	E	F
A	-	22	-	12	10	-
B	22	-	-	-	-	13
C	-	-	-	6	5	11
D	12	-	6	-	-	-
E	10	-	5	-	-	26
F	-	13	11	-	26	-

	A	B	C	D	E	F	G
A	-	5	2	3	-	-	-
B	5	-	-	-	1	1	-
C	2	-	-	-	4	1	-
D	3	-	-	-	4	2	-
E	-	1	4	4	-	-	1
F	-	1	1	2	-	-	5
G	-	-	-	-	1	5	-