Questions - Edexcel - A-Level Maths

At least three-fifths of all the flowers must be roses.
For every 2 hydrangeas there must be at most 3 peonies.
The total number of flowers must be exactly 1000

The cost of each rose is $\pounds 1$, the cost of each hydrangea is $\pounds 5$ and the cost of each peony is $\pounds 4$ Ben wants to minimise the cost of the flowers. Let $x$ represent the number of roses, let $y$ represent the number of hydrangeas and let $z$ represent the number of peonies that he will order.

Formulate this as a linear programming problem in $x$ and $y$ only, stating the objective function and listing the constraints as simplified inequalities with integer coefficients. Ben decides to order the minimum number of roses that satisfy his constraints.
1. Calculate the number of each type of flower that he will order to minimise the cost of the flowers.
2. Calculate the corresponding total cost of this order. Please check the examination details below before entering your candidate information
  Candidate surname
  Other names Pearson Edexcel Level 3 GCE Centre Number
  \includegraphics[max width=\textwidth, alt={}, center]{103a0bcf-3adf-407c-aa98-a784b0b39bf5-09_122_433_356_991} Candidate Number
  □
  □
  □ \section*{Thursoay 16 May 2019} Afternoon
  Paper Reference 8FMO-27 \section*{Further Mathematics} \section*{Advanced Subsidiary
  Further Mathematics options
  27: Decision Mathematics 1
  (Part of options D, F, H and K)} \section*{Answer Book} Do not return the question paper with the answer book.
  1. 2. You may not need to use all the rows in this table. It may not be necessary to complete all boxes in each row.
  A B N H C D E F
  3.
  \includegraphics[max width=\textwidth, alt={}]{103a0bcf-3adf-407c-aa98-a784b0b39bf5-16_2530_1776_207_148}
  5.

Edexcel FD1 AS 2020 June Q1

1. $3.7 \quad 2.5$
$5.4 \quad 1.9$
2.7
3.2
3.1
2.7
4.2
2.0

Use the first-fit bin packing algorithm to determine how the numbers listed above can be packed into bins of size 8.5 The first-fit bin packing algorithm is to be used to pack $n$ numbers into bins. The number of comparisons is used to measure the order of the first-fit bin packing algorithm.
By considering the worst case, determine the order of the first-fit bin packing algorithm in terms of $n$. You must make your method and working clear.

Edexcel FD1 AS 2020 June Q2

2. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{a2a6e659-aab5-4eec-9af4-ca6ab895f1c8-03_693_1379_233_342} \captionsetup{labelformat=empty} \caption{Figure 1}

\end{figure} A project is modelled by the activity network shown in Figure 1. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, to complete the corresponding activity. Each activity requires one worker. The project is to be completed in the shortest possible time.

Complete the precedence table in the answer book.
Complete Diagram 1 in the answer book to show the early event times and the late event times.
1. State the minimum project completion time.
2. List the critical activities.
Calculate the maximum number of hours by which activity H could be delayed without affecting the shortest possible completion time of the project. You must make the numbers used in your calculation clear.
Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working.
Draw a cascade chart for this project on Grid 1 in the answer book.
Using the answer to (f), explain why it is not possible to complete the project in the shortest possible time using the number of workers found in (e).

Edexcel FD1 AS 2020 June Q3

3. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{a2a6e659-aab5-4eec-9af4-ca6ab895f1c8-04_720_1470_233_296} \captionsetup{labelformat=empty} \caption{Figure 2}

\end{figure} [The weight of the network is $5 x + 246$ ]

Explain why it is not possible to draw a graph with an odd number of vertices of odd valency. Figure 2 represents a network of 14 roads in a town. The expression on each arc gives the time, in minutes, to travel along the corresponding road. Prim's algorithm, starting at A, is applied to the network. The order in which the arcs are selected is $\mathrm { AD } , \mathrm { DH } , \mathrm { DG } , \mathrm { FG } , \mathrm { EF } , \mathrm { CG } , \mathrm { BD }$. It is given that the order in which the arcs are selected is unique.
Using this information, find the smallest possible range of values for $x$, showing your working clearly. A route that minimises the total time taken to traverse each road at least once is required. The route must start and finish at the same vertex. Given that the time taken to traverse this route is 318 minutes,
use an appropriate algorithm to determine the value of $x$, showing your working clearly.

Edexcel FD1 AS 2020 June Q4

4. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{a2a6e659-aab5-4eec-9af4-ca6ab895f1c8-05_1472_1320_233_376} \captionsetup{labelformat=empty} \caption{Figure 3}

\end{figure} Figure 3 shows the constraints of a linear programming problem in $x$ and $y$, where $R$ is the feasible region. Figure 3 also shows an objective line for the problem and the optimal vertex, which is labelled as $V$. The value of the objective at $V$ is 556
Express the linear programming problem in algebraic form. List the constraints as simplified inequalities with integer coefficients and determine the objective. Please check the examination details below before entering your candidate information
Candidate surname
Other names Pearson Edexcel
Centre Number
Candidate Number Level 3 GCE
\includegraphics[max width=\textwidth, alt={}, center]{a2a6e659-aab5-4eec-9af4-ca6ab895f1c8-09_122_433_356_991}
□
□
□
□ \section*{Thursday 14 May 2020} Afternoon
Paper Reference 8FMO/27 \section*{Further Mathematics} Advanced Subsidiary
Further Mathematics options
27: Decision Mathematics 1
(Part of options D, F, H and K) \section*{Answer Book} Do not return the question paper with the answer book.
1.
$\begin{array} { l l l l l l l l l l } 3.7 & 2.5 & 5.4 & 1.9 & 2.7 & 3.2 & 3.1 & 2.7 & 4.2 & 2.0 \end{array}$

\includegraphics[alt={},max width=\textwidth]{a2a6e659-aab5-4eec-9af4-ca6ab895f1c8-12_734_1646_925_196} \captionsetup{labelformat=empty} \caption{Diagram 1}

\end{figure} \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{a2a6e659-aab5-4eec-9af4-ca6ab895f1c8-13_1116_1475_979_296} \captionsetup{labelformat=empty} \caption{Grid 1}

\end{figure} 3. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{a2a6e659-aab5-4eec-9af4-ca6ab895f1c8-14_716_1467_255_299} \captionsetup{labelformat=empty} \caption{Figure 2}

\end{figure} [The weight of the network is $5 x + 246$ ] 4. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{a2a6e659-aab5-4eec-9af4-ca6ab895f1c8-18_1470_1319_255_388} \captionsetup{labelformat=empty} \caption{Figure 3}

\end{figure}

Edexcel FD2 2020 June Q1

Four workers, A, B, C and D, are to be assigned to four tasks, 1, 2, 3 and 4 . Each worker must be assigned to exactly one task and each task must be done by exactly one worker.

Worker A cannot do task 3 and worker B cannot do task 4 The table below shows the profit, in pounds, that each worker would earn if assigned to each of the tasks.

	1	2	3	4
A	29	20	-	23
B	32	30	28	-
C	35	32	34	25
D	29	31	27	30

Reducing rows first, use the Hungarian algorithm to obtain an allocation that maximises the total profit. You must make your method clear and show the table after each stage.
Determine the resulting total profit.

Edexcel FD2 2020 June Q2

2. Jenny can choose one of three options, A, B or C, when playing a game. The profit, in pounds, associated with each outcome and their corresponding probabilities are shown on the decision tree in Figure 1. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{e0fc09f9-06ea-4528-a2de-f409112d85cc-03_947_1319_349_374} \captionsetup{labelformat=empty} \caption{Figure 1}

\end{figure}

Calculate the optimal EMV to determine Jenny's best course of action. You must make your working clear. For a profit of $\pounds x$, Jenny's utility is given by $1 - \mathrm { e } ^ { - \frac { x } { 400 } }$
Using expected utility as the criterion for the best course of action, determine what Jenny should do now to maximise her profit. You must make your working clear.

Edexcel FD2 2020 June Q3

3. Table 1 shows the cost, in pounds, of transporting one unit of stock from each of four supply points, $\mathrm { A } , \mathrm { B } , \mathrm { C }$ and D , to three sales points, $\mathrm { P } , \mathrm { Q }$ and R . It also shows the number of units held at each supply point and the number of units required at each sales point. A minimum cost solution is required. \begin{table}[h]

	P	Q	R	Supply
A	25	24	17	42
B	7	12	14	68
C	13	11	20	25
D	16	15	13	40
Demand	59	72	44

\captionsetup{labelformat=empty} \caption{Table 1}

\end{table} Table 2 shows an initial solution given by the north-west corner method. \begin{table}[h]

	P	Q	R
A	42
B	17	51
C		21	4
D			40

\captionsetup{labelformat=empty} \caption{Table 2}

\end{table}

Taking AR as the entering cell, use the stepping-stone method to find an improved solution. Make your method clear.
Perform one further iteration of the stepping-stone method to obtain an improved solution. You must make your method clear by stating
- shadow costs
- improvement indices
- route
- entering cell and exiting cell.
- Determine whether the solution obtained from this second iteration is optimal, giving the reason for your answer.
- Formulate this situation as a linear programming problem. You must define your decision variables and make the objective function and constraints clear.
- Explain why the Simplex algorithm cannot be used to solve transportation linear programming problems such as that formulated in (d).

Edexcel FD2 2020 June Q4

The complementary function for the second order recurrence relation

$$u _ { n + 2 } + \alpha u _ { n + 1 } + \beta u _ { n } = 20 ( - 3 ) ^ { n } \quad n \geqslant 0$$ is given by $$u _ { n } = A ( 2 ) ^ { n } + B ( - 1 ) ^ { n }$$ where $A$ and $B$ are arbitrary non-zero constants.

Find the value of $\alpha$ and the value of $\beta$. Given that $2 u _ { 0 } = u _ { 1 }$ and $u _ { 4 } = 164$
find the solution of this second order recurrence relation to obtain an expression for $u _ { n }$ in terms of $n$.
(6)

Edexcel FD2 2020 June Q5

5. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{e0fc09f9-06ea-4528-a2de-f409112d85cc-06_830_1397_205_333} \captionsetup{labelformat=empty} \caption{Figure 2}

\end{figure} Figure 2 shows a capacitated, directed network. The network represents a system of pipes through which fluid can flow. The weights on the arcs show the lower capacities and upper capacities for the corresponding pipes, in litres per second.

State the source node.
Explain why the sink node must be G.
Calculate the capacity of the cut $C _ { 1 }$
Assuming that a feasible flow exists,
1. explain why arc JH must be at its upper capacity,
2. explain why arcs AD and CD must be at their lower capacities.
Use Diagram 1 in the answer book to show a flow of 18 litres per second through the system.
Prove that the answer to (e) is the maximum flow through the system.

Edexcel FD2 2020 June Q6

\multirow{6}{*}{Player A}	Player B
	\multirow[b]{2}{*}{Option Q}	Option X	Option Y	Option Z
		1	5	3
	Option R	4	-3	1
	Option S	2	-4	-2
	Option T	3	-2	0

A two person zero-sum game is represented by the pay-off matrix for player A, shown above.

Explain, with justification, why this matrix may be reduced to a $3 \times 3$ matrix by removing option S from player A's choices.
Verify that there is no stable solution to the reduced game. Player A intends to make a random choice between options $\mathrm { Q } , \mathrm { R }$ and T , choosing option Q with probability $p _ { 1 }$, option R with probability $p _ { 2 }$ and option T with probability $p _ { 3 }$ Player A wants to find the optimal values of $p _ { 1 } , p _ { 2 }$ and $p _ { 3 }$ using the Simplex algorithm. Player A formulates the following linear programme, writing the constraints as inequalities. Maximise $P = V$, where $V =$ the value of original game + 3 $$\begin{aligned} \text { subject to } & V \leqslant 4 p _ { 1 } + 7 p _ { 2 } + 6 p _ { 3 }
& V \leqslant 8 p _ { 1 } + p _ { 3 }
& V \leqslant 6 p _ { 1 } + 4 p _ { 2 } + 3 p _ { 3 }
& p _ { 1 } + p _ { 2 } + p _ { 3 } \leqslant 1
& p _ { 1 } \geqslant 0 , p _ { 2 } \geqslant 0 , p _ { 3 } \geqslant 0 , V \geqslant 0 \end{aligned}$$
Explain why $V$ cannot exceed any of the following expressions $$4 p _ { 1 } + 7 p _ { 2 } + 6 p _ { 3 } \quad 8 p _ { 1 } + p _ { 3 } \quad 6 p _ { 1 } + 4 p _ { 2 } + 3 p _ { 3 }$$
Explain why it is necessary to use the constraint $p _ { 1 } + p _ { 2 } + p _ { 3 } \leqslant 1$ The Simplex algorithm is used to solve the linear programming problem.
Given that the optimal value of $p _ { 1 } = \frac { 7 } { 11 }$ and the optimal value of $p _ { 3 } = 0$
calculate the value of the game to player A .
(3) Player B intends to make a random choice between options $\mathrm { X } , \mathrm { Y }$ and Z , choosing option X with probability $q _ { 1 }$, option Y with probability $q _ { 2 }$ and option Z with probability $q _ { 3 }$
Determine the optimal strategy for player B, making your working clear.

Edexcel FD2 2020 June Q7

7. A manufacturer can export five batches of footwear each year. Each exported batch contains just one type of footwear. The types of footwear are trainers, sandals or high heels. The table below shows the profit, in $\pounds 1000$ s, for the number of batches of each type of footwear.

	1	2	3	4
A
B
C
D

	1	2	3	4
A
B
C
D

	1	2	3	4
A
B
C
D

	1	2	3	4
A
B
C
D

	1	2	3	4
A
B
C
D

	1	2	3	4
A
B
C
D

	1	2	3	4
A
B
C
D

	1	2	3	4
A
B
C
D

2. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{e0fc09f9-06ea-4528-a2de-f409112d85cc-12_956_1333_258_283} \captionsetup{labelformat=empty} \caption{Figure 1}

\end{figure} \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{e0fc09f9-06ea-4528-a2de-f409112d85cc-13_954_1322_260_278} \captionsetup{labelformat=empty} \caption{Figure 1}

\end{figure} 3. \begin{table}[h]

	P	Q	R	Supply
A	25	24	17	42
B	7	12	14	68
C	13	11	20	25
D	16	15	13	40
Demand	59	72	44

\captionsetup{labelformat=empty} \caption{Table 1}

\end{table}

	P	Q	R
A
B
C
D

	P	Q	R
A
B
C
D

	P	Q	R
A
B
C
D

	P	Q	R
A
B
C
D

	P	Q	R
A
B
C
D

	P	Q	R
A
B
C
D

	P	Q	R
A
B
C
D

	P	Q	R
A
B
C
D

	P	Q	R
A
B
C
D

4. .
5. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{e0fc09f9-06ea-4528-a2de-f409112d85cc-21_666_1239_1155_413} \captionsetup{labelformat=empty} \caption{Diagram 1}

\end{figure} 6. Player A \begin{table}[h]

\captionsetup{labelformat=empty} \caption{Player B}

\cline { 2 - 4 } \multicolumn{1}{c\|}{}	Option X	Option Y	Option Z
Option Q	1	5	3
Option R	4	- 3	1
Option S	2	- 4	- 2
Option T	3	- 2	0

\end{table} 7.

Stage	State	Action	Destination	Value
Trainers	0	0	0	0

Stage	State	Action	Destination	Value

Edexcel FD2 2022 June Q1

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

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.
State the minimum total cost.

Edexcel FD2 2022 June Q2

2. The general solution of the second order recurrence relation $$u _ { n + 2 } + k _ { 1 } u _ { n + 1 } + k _ { 2 } u _ { n } = 0 \quad n \geqslant 0$$ is given by $$u _ { n } = ( A + B n ) ( - 3 ) ^ { n }$$ where $A$ and $B$ are arbitrary non-zero constants.

Find the value of $k _ { 1 }$ and the value of $k _ { 2 }$ Given that $u _ { 0 } = u _ { 1 } = 1$
find the value of $A$ and the value of $B$.

Edexcel FD2 2022 June Q3

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
\multirow{2}{*}{Car}	\multirow{2}{*}{52}	10	0.10
		25	0.02
\multirow{2}{*}{Train}	\multirow{2}{*}{45}	15	0.05
		25	0.03
\multirow{2}{*}{Coach}	\multirow{2}{*}{55}	5	0.05
		15	0.01

Draw a decision tree to model the transport options and the possible outcomes.
State the minimum expected travel time and the corresponding transport option indicated by the decision tree.

Edexcel FD2 2022 June Q4

4. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{cea07472-f93b-4a7b-b362-89fb8c0af4a9-04_931_1312_219_379} \captionsetup{labelformat=empty} \caption{Figure 1}

\end{figure} 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.

List the saturated arcs.
State the value of the initial flow.
Explain why arc FT cannot be full to capacity.
State the capacity of cut $C _ { 1 }$ and the capacity of cut $C _ { 2 }$
By inspection find one flow-augmenting route to increase the flow by three units. You must state your route.
Prove that, once the flow-augmenting route found in part (e) has been applied, the flow is maximal.

Edexcel FD2 2022 June Q5

5. A standard transportation problem is described in the linear programming formulation below. Let $X _ { i j }$ be the number of units transported from $i$ to $j$
where $i \in \{ \mathrm {~A} , \mathrm {~B} , \mathrm { C } , \mathrm { D } \}$ $$j \in \{ \mathrm { R } , \mathrm {~S} , \mathrm {~T} \} \text { and } x _ { i j } \geqslant 0$$ Minimise $P = 23 x _ { \mathrm { AR } } + 17 x _ { \mathrm { AS } } + 24 x _ { \mathrm { AT } } + 15 x _ { \mathrm { BR } } + 29 x _ { \mathrm { BS } } + 32 x _ { \mathrm { BT } }$ $$+ 25 x _ { \mathrm { CR } } + 25 x _ { \mathrm { CS } } + 27 x _ { \mathrm { CT } } + 19 x _ { \mathrm { DR } } + 20 x _ { \mathrm { DS } } + 25 x _ { \mathrm { DT } }$$ subject to $$\begin{aligned} & \sum x _ { \mathrm { A } j } \leqslant 34
& \sum x _ { \mathrm { B } j } \leqslant 27
& \sum x _ { \mathrm { C } j } \leqslant 41
& \sum x _ { \mathrm { D } j } \leqslant 18
& \sum x _ { i \mathrm { R } } \geqslant 44
& \sum x _ { i \mathrm {~S} } \geqslant 37
& \sum x _ { i \mathrm {~T} } \geqslant k \end{aligned}$$ Given that the problem is balanced,

state the value of $k$.
Explain precisely what the constraint $\sum x _ { i \mathrm { R } } \geqslant 44$ means in the transportation problem.
Use the north-west corner method to obtain the cost of an initial solution to this transportation problem.
Perform one iteration of the stepping-stone method to obtain an improved solution. You must make your method clear by showing the route and the
- shadow costs
- improvement indices
- entering cell and exiting cell.

Edexcel FD2 2022 June Q6

Bernie makes garden sheds. He can build up to four sheds each month.

If he builds more than two sheds in any one month, he must hire an additional worker at a cost of $\pounds 250$ for that month. In any month in which sheds are made, the overhead costs are $\pounds 35$ for each shed made that month. A maximum of three sheds can be held in storage at the end of any one month, at a cost of $\pounds 80$ per shed per month. Sheds must be delivered at the end of the month.
The order schedule for sheds is

Month	January	February	March	April	May
Number ordered	1	3	3	5	2

There are no sheds in storage at the beginning of January and Bernie plans to have no sheds left in storage after the May delivery. Use dynamic programming to determine the production schedule that minimises the costs given above. Complete the working in the table provided in the answer book and state the minimum cost.

Edexcel FD2 2022 June Q7

\multirow{2}{*}{}		Player B
		Option W	Option X	Option Y	Option Z
\multirow{3}{*}{Player A}	Option Q	4	3	-1	-2
	Option R	-3	5	-4	$k$
	Option S	-1	6	3	-3

A two person zero-sum game is represented by the pay-off matrix for player A shown above. It is given that $k$ is an integer.

Show that Q is the play-safe option for player A regardless of the value of $k$. Given that Z is the play-safe option for player B ,
determine the range of possible values of $k$. You must make your working clear.
Explain why player B should never play option X. You must make your reasoning clear. Player A intends to make a random choice between options $\mathrm { Q } , \mathrm { R }$ and S , choosing option Q with probability $p _ { 1 }$, option R with probability $p _ { 2 }$ and option S with probability $p _ { 3 }$ Player A wants to find the optimal values of $p _ { 1 } , p _ { 2 }$ and $p _ { 3 }$ using the Simplex algorithm.
Given that $k > - 4$, player A formulates the following objective function for the corresponding linear program. $$\text { Maximise } P = V \text {, where } V = \text { the value of the original game } + 4$$
1. Formulate the constraints of the linear programming problem for player A. You should write the constraints as equations.
2. Write down an initial Simplex tableau, making your variables clear. The Simplex algorithm is used to solve the linear programming problem. It is given that in the final Simplex tableau the optimal value of $p _ { 1 } = \frac { 7 } { 37 }$, the optimal value of $p _ { 2 } = \frac { 17 } { 37 }$ and all the slack variables are zero.
Determine the value of $k$, making your method clear.

Edexcel FD2 2022 June Q8

8. The owner of a new company models the number of customers that the company will have at the end of each month. The owner assumes that

a constant proportion, $p$ (where $0 < p < 1$ ), of the previous month's customers will be retained for the next month
a constant number of new customers, $k$, will be added each month.

Let $u _ { n }$ (where $n \geqslant 1$ ) represent the number of customers that the company will have at the end of $n$ months. The company has 5000 customers at the end of the first month.

By setting up a first order recurrence relation for $u _ { n + 1 }$ in terms of $u _ { n }$, determine an expression for $u _ { n }$ in terms of $n , p$ and $k$. The owner believes that $95 \%$ of the previous month’s customers will be retained each month and that there will be 10000 new customers each month. According to the model, the company will first have at least 135000 customers by the end of the $m$ th month.
Using logarithms, determine the value of $m$. Please check the examination details below before entering your candidate information \section*{Further Mathematics} Advanced
PAPER 4D: Decision Mathematics 2 \section*{Answer Book} Do not return the question paper with the answer book.
1.
1 2 3 4
A 32 45 34 48
B 37 39 50 46
C 46 44 40 42
D 43 45 48 52
You may not need to use all of these tables.
1 2 3 4
A
B
C
D

1 2 3 4
A
B
C
D

1 2 3 4
A
B
C
D

1 2 3 4
A
B
C
D
VALV SIHI NI IIIIIM ION OC
VIAV SIUL NI JAIIM ION OC
VIAV SIHI NI III IM ION OC
1 2 3 4
A
B
C
D

1 2 3 4
$A$
$B$
$C$
$D$

1 2 3 4
A
B
C
D

1 2 3 4
A
B
C
D

1 2 3 4
A
B
C
D
2.
VAMV SIHI NI IIIHM ION OO VIAV SIHI NI JIIIM I ON OC VJYV SIHI NI JIIIM ION OC
3. 4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{cea07472-f93b-4a7b-b362-89fb8c0af4a9-16_936_1317_255_376} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} 5.
$R$ $S$ $T$
$A$
$B$
$C$
$D$

$R$ $S$ $T$
$A$
$B$
$C$
$D$

$R$ $S$ $T$
$A$
$B$
$C$
$D$

$R$ $S$ $T$
$A$
$B$
$C$
$D$

$R$ $S$ $T$
$A$
$B$
$C$
$D$
6.
Stage State Action Destination Value
May 2 0 0 160
1 1 0 80 + 35
0 2 0 70

Stage State Action Destination Value

Month January February March April May
Number made
Minimum cost: $\_\_\_\_$
7. Player A \begin{table}[h]
\captionsetup{labelformat=empty} \caption{Player B}
Option W Option X Option Y Option Z
Option Q 4 3 -1 -2
Option R -3 5 -4 $k$
Option S -1 6 3 -3
\end{table} The tableau for (d)(ii) can be found at the bottom of page 16
b.v. □ □ □ □ Value
\includegraphics[max width=\textwidth, alt={}]{cea07472-f93b-4a7b-b362-89fb8c0af4a9-24_56_77_2348_182} □ □
P
8.

	1	2	3	4
\(A\)
\(B\)
\(C\)
\(D\)

	\(R\)	\(S\)	\(T\)
\(A\)
\(B\)
\(C\)
\(D\)

	\(R\)	\(S\)	\(T\)
\(A\)
\(B\)
\(C\)
\(D\)

	\(R\)	\(S\)	\(T\)
\(A\)
\(B\)
\(C\)
\(D\)

	\(R\)	\(S\)	\(T\)
\(A\)
\(B\)
\(C\)
\(D\)

b.v.			□	□	□	□	Value
\includegraphics[max width=\textwidth, alt={}]{cea07472-f93b-4a7b-b362-89fb8c0af4a9-24_56_77_2348_182}	□	□



P

Questions — Edexcel (9670 questions)

Browse by module

Browse by board

Edexcel FD1 AS 2019 June Q5

Edexcel FD1 AS 2020 June Q1

Edexcel FD1 AS 2020 June Q2

Edexcel FD1 AS 2020 June Q3

Edexcel FD1 AS 2020 June Q4

Edexcel FD2 2020 June Q1

Edexcel FD2 2020 June Q2

Edexcel FD2 2020 June Q3

Edexcel FD2 2020 June Q4

Edexcel FD2 2020 June Q5

Edexcel FD2 2020 June Q6

Edexcel FD2 2020 June Q7

Edexcel FD2 2022 June Q1

Edexcel FD2 2022 June Q2

Edexcel FD2 2022 June Q3

Edexcel FD2 2022 June Q4

Edexcel FD2 2022 June Q5

Edexcel FD2 2022 June Q6

Edexcel FD2 2022 June Q7

Edexcel FD2 2022 June Q8