Questions - Edexcel D1 - A-Level Maths

Use Dijkstra's algorithm to find the shortest time needed to travel from A to K . State the quickest route. On a particular day Oliver must travel from B to K via A .
Find a route of minimal time from B to K that includes A , and state its length. Oliver needs to travel along each road to check that it is in good repair. He wishes to minimise the total time required to traverse the network.
Use the route inspection algorithm to find the shortest time needed. You must state all combinations of edges that Oliver could repeat, making your method and working clear.

Edexcel D1 2018 Specimen Q5

5. A linear programming problem in $x$ and $y$ is described as follows. $$\begin{array} { l l } \text { Maximise } & \mathrm { P } = 5 x + 3 y
\text { subject to: } & x \geqslant 3
& x + y \leqslant 9
& 15 x + 22 y \leqslant 165
& 26 x - 50 y \leqslant 325 \end{array}$$

Add lines and shading to Diagram 2 in the answer book to represent these constraints. Hence determine the feasible region and label it R .
Use the objective line method to find the optimal vertex, V, of the feasible region. You must draw and label your objective line and label vertex V clearly.
Calculate the exact coordinates of vertex V and hence calculate the corresponding value of P at V . The objective is now to minimise $5 x + 3 y$, where $x$ and $y$ are integers.
Write down the minimum value of $5 x + 3 y$ and the corresponding value of $x$ and corresponding value of $y$.

Edexcel D1 2018 Specimen Q6

6. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{71a3bf06-0305-44fa-9038-d3c8b69522a6-7_659_1518_242_278} \captionsetup{labelformat=empty} \caption{Figure 2}

\end{figure} A project is modelled by the activity network shown in Figure 2. The activities are represented by the arcs. The number in brackets on each arc gives the time required, in hours, to complete the activity. The numbers in circles are the event numbers. Each activity requires one worker.

Explain the significance of the dummy activity
1. from event 5 to event 6
2. from event 7 to event 9 .
Complete Diagram 3 in the answer book to show the early event times and the late event times.
State the minimum project completion time.
Calculate a lower bound for the minimum number of workers required to complete the project in the minimum time. You must show your working.
On Grid 1 in your answer book, draw a cascade (Gantt) chart for this project.
On Grid 2 in your answer book, construct a scheduling diagram to show that this project can be completed with three workers in just one more hour than the minimum project completion time.

Edexcel D1 2001 January Q1

This question should be answered on the sheet provided in the answer booklet.

A school wishes to link 6 computers. One is in the school office and one in each of rooms $\mathrm { A } , B , C , D$ and $E$. Cables need to be laid to connect the computers. The school wishes to use a minimum total length of cable. The table shows the shortest distances, in metres, between the various sites.

	Office	Room $A$	Room $B$	Room $C$	Room $D$	Room $E$
Office	-	8	16	12	10	14
Room $A$	8	-	14	13	11	9
Room $B$	16	14	-	12	15	11
Room $C$	12	13	12	-	11	8
Room $D$	10	11	15	11	-	10
Room $E$	14	9	11	8	10	-

Starting at the school office, use Prim's algorithm to find a minimum spanning tree. Indicate the order in which you select the edges and draw your final tree.
(5 marks)
Using your answer to part (a), calculate the minimum total length of cable required.
(1 mark)

Edexcel D1 2001 January Q2

2. (a) Use the binary search algorithm to locate the name HUSSAIN in the following alphabetical list. Explain each step of the algorithm.

ALLEN
BALL
COOPER
EVANS
HUSSAIN
JONES
MICHAEL
PATEL
RICHARDS
TINDALL
WU
(b) State the maximum number of comparisons that need to be made to locate a name in an alphabetical list of 11 names.
(1 mark)

\begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{c1b75596-bbab-4278-8503-7cfbea0bc5f1-3_816_1298_343_391} \captionsetup{labelformat=empty} \caption{Fig. 1}

\end{figure} (a) Using an appropriate algorithm, obtain a suitable route starting and finishing at $A$.
(b) Calculate the total length of this route.

Edexcel D1 2001 January Q4

4. This question should be answered on the sheet provided in the answer booklet. A manager has five workers, Mr. Ahmed, Miss Brown, Ms. Clough, Mr. Dingle and Mrs. Evans. To finish an urgent order he needs each of them to work overtime, one on each evening, in the next week. The workers are only available on the following evenings: $$\begin{aligned} & \text { Mr. Ahmed } ( A ) \text { - Monday and Wednesday; }
& \text { Miss Brown } ( B ) \text { - Monday, Wednesday and Friday; }
& \text { Ms. Clough } ( C ) \text { - Monday; }
& \text { Mr. Dingle } ( D ) \text { - Tuesday, Wednesday and Thursday; }
& \text { Mrs. Evans } ( E ) \text { - Wednesday and Thursday. } \end{aligned}$$ The manager initially suggests that $A$ might work on Monday, $B$ on Wednesday and $D$ on Thursday.

Using the nodes printed on the answer sheet, draw a bipartite graph to model the availability of the five workers. Indicate, in a distinctive way, the manager's initial suggestion.
Obtain an alternating path, starting at $C$, and use this to improve the initial matching.
Find another alternating path and hence obtain a complete matching.
(3 marks)

Edexcel D1 2001 January Q5

5. This question should be answered on the sheet provided in the answer booklet. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{c1b75596-bbab-4278-8503-7cfbea0bc5f1-5_542_1389_483_352} \captionsetup{labelformat=empty} \caption{Fig. 2}

\end{figure} Figure 2 shows the activity network used to model a small building project. The activities are represented by the edges and the number in brackets on each edge represents the time, in hours, taken to complete that activity.

Calculate the early time and the late time for each event. Write your answers in the boxes on the answer sheet.
(6 marks)
Hence determine the critical activities and the length of the critical path.
(2 marks)
Each activity requires one worker. The project is to be completed in the minimum time.
Schedule the activities for the minimum number of workers using the time line on the answer sheet. Ensure that you make clear the order in which each worker undertakes his activities.
(5 marks)

Edexcel D1 2001 January Q6

6. This question should be answered on the sheet provided in the answer booklet. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{c1b75596-bbab-4278-8503-7cfbea0bc5f1-6_732_1308_433_388} \captionsetup{labelformat=empty} \caption{Fig. 3}

\end{figure} Figure 3 shows a capacitated, directed network. The number on each arc indicates the capacity of that arc.

State the maximum flow along
1. SAET,
2. SBDT,
3. SCFT.
  (3 marks)
Show these maximum flows on Diagram 1 on the answer sheet.
Taking your answer to part (b) as the initial flow pattern, use the labelling procedure to find a maximum flow from $S$ to $T$. Your working should be shown on Diagram 2. List each flow augmenting route you find, together with its flow.
Indicate a maximum flow on Diagram 3.
Prove that your flow is maximal.

Edexcel D1 2001 January Q7

7. A tailor makes two types of garment, $A$ and $B$. He has available $70 \mathrm {~m} ^ { 2 }$ of cotton fabric and $90 \mathrm {~m} ^ { 2 }$ of woollen fabric. Garment $A$ requires $1 \mathrm {~m} ^ { 2 }$ of cotton fabric and $3 \mathrm {~m} ^ { 2 }$ of woollen fabric. Garment $B$ requires $2 \mathrm {~m} ^ { 2 }$ of each fabric. The tailor makes $x$ garments of type $A$ and $y$ garments of type $B$.

Explain why this can be modelled by the inequalities $$\begin{aligned} & x + 2 y \leq 70
& 3 x + 2 y \leq 90
& x \geq 0 , y \geq 0 \end{aligned}$$ The tailor sells type $A$ for $\pounds 30$ and type $B$ for $\pounds 40$. All garments made are sold. The tailor wishes to maximise his total income.
Set up an initial Simplex tableau for this problem.
Solve the problem using the Simplex algorithm. Figure 4 shows a graphical representation of the feasible region for this problem. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c1b75596-bbab-4278-8503-7cfbea0bc5f1-7_686_1277_1319_453} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}
Obtain the coordinates of the points A, $C$ and $D$.
Relate each stage of the Simplex algorithm to the corresponding point in Fig. 4.

Edexcel D1 2002 January Q1

Ann, Bryn, Daljit, Gareth and Nickos have all joined a new committee. Each of them is to be allocated to one of five jobs $1,2,3,4$ or 5 . The table shows each member's preferences for the jobs.

Ann	1 or 2
Bryn	3 or 1
Daljit	2 or 4
Gareth	5 or 3
Nickos	1 or 2

Initially Ann, Bryn, Daljit and Gareth are allocated the first job in their lists shown in the table.

Draw a bipartite graph to model the preferences shown in the table and indicate, in a distinctive way, the initial allocation of jobs.
Use the matching improvement algorithm to find a complete matching, showing clearly your alternating path.
Find a second alternating path from the initial allocation.

Edexcel D1 2002 January Q2

2. (i) Use the binary search algorithm to try to locate the name SABINE in the following alphabetical list. Explain each step of the algorithm.

ABLE
BROWN
COOKE
DANIEL
DOUBLE
FEW
OSBORNE
PAUL
SWIFT
TURNER
(ii) Find the maximum number of iterations of the binary search algorithm needed to locate a name in a list of 1000 names.

	A	$B$	C	$D$	$E$	$F$
A	-	10	12	13	20	9
B	10	-	7	15	11	7
C	12	7	-	11	18	3
D	13	15	11	-	27	8
E	20	11	18	27	-	18
$F$	9	7	3	8	18	-

The table shows the distances, in metres, between six nodes $A , B , C , D , E$, and $F$ of a network.

Use Prim's algorithm, starting at $A$, to solve the minimum connector problem for this table of distances. Explain your method and indicate the order in which you selected the edges.
Draw your minimum spanning tree and find its total length.
State whether your minimum spanning tree is unique. Justify your answer.
(ii) A connected network $N$ has seven vertices.

Edexcel D1 2002 January Q5

5. Two fertilizers are available, a liquid $X$ and a powder $Y$. A bottle of $X$ contains 5 units of chemical $A$, 2 units of chemical $B$ and $\frac { 1 } { 2 }$ unit of chemical $C$. A packet of $Y$ contains 1 unit of $A , 2$ units of $B$ and 2 units of $C$. A professional gardener makes her own fertilizer. She requires at least 10 units of $A$, at least 12 units of $B$ and at least 6 units of $C$. She buys $x$ bottles of $X$ and $y$ packets of $Y$.

Write down the inequalities which model this situation.
On the grid provided construct and label the feasible region. A bottle of $X$ costs $\pounds 2$ and a packet of $Y$ costs $\pounds 3$.
Write down an expression, in terms of $x$ and $y$, for the total cost $\pounds T$.
Using your graph, obtain the values of $x$ and $y$ that give the minimum value of $T$. Make your method clear and calculate the minimum value of $T$.
Suggest how the situation might be changed so that it could no longer be represented graphically.
(2)

Edexcel D1 2002 January Q6

6. \begin{figure}[h]

\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{2f4d2383-823a-4a6f-ad4b-69cf01566052-6_615_1204_363_414}

\end{figure} A company has 3 warehouses $W _ { 1 } , W _ { 2 }$, and $W _ { 3 }$. It needs to transport the goods stored there to 2 retail outlets $R _ { 1 }$ and $R _ { 2 }$. The capacities of the possible routes, in van loads per day, are shown in Fig 2. Warehouses $W _ { 1 } , W _ { 2 }$ and $W _ { 3 }$ have 14, 12 and 14 van loads respectively available per day and retail outlets $R _ { 1 }$ and $R _ { 2 }$ can accept 6 and 25 van loads respectively per day.

On Diagram 1 on the answer sheet add a supersource $W$, a supersink $R$ and the appropriate directed arcs to obtain a single-source, single-sink capacitated network. State the minimum capacity of each arc you have added.
State the maximum flow along
1. $W \quad W _ { 1 } \quad A \quad R _ { 1 } \quad R$,
2. $W W _ { 3 } \quad C \quad R _ { 2 } \quad R$.
Taking your answers to part (b) as the initial flow pattern, use the labelling procedure to obtain a maximum flow through the network from $W$ to $R$. Show your working on Diagram 2. List each flow-augmenting route you use, together with its flow.
From your final flow pattern, determine the number of van loads passing through $B$ each day. The company has the opportunity to increase the number of vans loads from one of the warehouses $W _ { 1 } , W _ { 2 } , W _ { 3 }$, to $A , B$ or $C$.
Determine how the company should use this opportunity so that it achieves a maximal flow.

Edexcel D1 2002 January Q7

7. \begin{figure}[h]

\captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{2f4d2383-823a-4a6f-ad4b-69cf01566052-7_478_1515_408_335}

\end{figure} A project is modelled by the activity network shown in Fig 3. The activities are represented by the edges. The number in brackets on each edge gives the time, in days, taken to complete the activity.

Calculate the early time and the late time for each event. Write these in the boxes on the answer sheet.
Hence determine the critical activities and the length of the critical path.
Obtain the total float for each of the non-critical activities.
On the first grid on the answer sheet, draw a cascade (Gantt) chart showing the information obtained in parts (b) and (c). Each activity requires one worker. Only two workers are available.
On the second grid on the answer sheet, draw up a schedule and find the minimum time in which the 2 workers can complete the project.

Edexcel D1 2003 January Q1

1. \section*{Figure 1}

\includegraphics[max width=\textwidth, alt={}]{01b167aa-2a77-4487-882c-20b1b74ecc90-2_540_869_358_470}

Use the planarity algorithm to show that the graph in Fig. 1 is planar.
(4)

Edexcel D1 2003 January Q2

2. At Tesafe supermarket there are 5 trainee staff, Homan $( H )$, Jenna $( J )$, Mary $( M )$, Tim $( T )$ and Yoshie ( $Y$ ). They each must spend one week in each of 5 departments, Delicatessen ( $D$ ), Frozen foods $( F )$, Groceries $( G )$, Pet foods $( P )$, Soft drinks $( S )$. Next week every department requires exactly one trainee. The table below shows the departments in which the trainees have yet to spend time.

Trainee	Departments
$H$	$D , F , P$
$J$	$G , D , F$
$M$	$S , P , G$
$T$	$F , S , G$
$Y$	$D$

Initially $H , J , M$ and $T$ are allocated to the first department in their list.

Draw a bipartite graph to model this situation and indicate the initial matching in a distinctive way. Starting from this matching,
use the maximum matching algorithm to find a complete matching. You must make clear your alternating path and your complete matching.
(4)

Edexcel D1 2003 January Q3

3. A manager wishes to purchase seats for a new cinema. He wishes to buy three types of seat; standard, deluxe and majestic. Let the number of standard, deluxe and majestic seats to be bought be $x , y$ and $z$ respectively.
He decides that the total number of deluxe and majestic seats should be at most half of the number of standard seats.
The number of deluxe seats should be at least $10 \%$ and at most $20 \%$ of the total number of seats.
The number of majestic seats should be at least half of the number of deluxe seats.
The total number of seats should be at least 250 .
Standard, deluxe and majestic seats each cost $\pounds 20 , \pounds 26$ and $\pounds 36$, respectively. The manager wishes to minimize the total cost, $\pounds C$, of the seats. Formulate this situation as a linear programming problem, simplifying your inequalities so that all the coefficients are integers.
(9) \begin{figure}[h]

\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{01b167aa-2a77-4487-882c-20b1b74ecc90-4_579_1159_397_370}

\end{figure} The arcs in Fig. 2 represent roads in a town. The weight on each arc gives the time, in minutes, taken to drive along that road. The times taken to drive along $A B$ and $D E$ vary depending upon the time of day. A police officer wishes to drive along each road at least once, starting and finishing at $A$. The journey is to be completed in the least time.

Briefly explain how you know that a route between $B$ and $E$ will have to be repeated.
List the possible routes between $B$ and $E$. State how long each would take, in terms of $x$ where appropriate.
Find the range of values that $x$ must satisfy so that $D E$ would be one of the repeated arcs. Given that $x = 7$,
find the total time needed for the police officer to carry out this journey.

Edexcel D1 2003 January Q5

5. \begin{figure}[h]

\captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{01b167aa-2a77-4487-882c-20b1b74ecc90-5_796_1564_333_189}

\end{figure} A project is modelled by the activity network in Fig. 3. The activities are represented by the arcs. One worker is required for each activity. The number in brackets on each arc gives the time, in hours, to complete the activity. The earliest event time and the latest event time are given by the numbers in the left box and right box respectively.

State the value of $x$ and the value of $y$.
List the critical activities.
Explain why at least 3 workers will be needed to complete this project in 38 hours.
Schedule the activities so that the project is completed in 38 hours using just 3 workers. You must make clear the start time and finish time of each activity.
(4)

Edexcel D1 2003 January Q6

6. $\quad \begin{array} { l l l l l l l l } 25 & 22 & 30 & 18 & 29 & 21 & 27 & 21 \end{array}$ The list of numbers above is to be sorted into descending order.

1. Perform the first pass of a bubble sort, giving the state of the list after each exchange.
2. Perform further passes, giving the state of the list after each pass, until the algorithm terminates.
  (5) The numbers represent the lengths, in cm, of pieces to be cut from rods of length 50 cm .
1. Show the result of applying the first fit decreasing bin packing algorithm to this situation.
2. Determine whether your solution to (b) (i) has used the minimum number of 50 cm rods.
  (4) \begin{figure}[h]
  \captionsetup{labelformat=empty} \caption{Figure 4} \includegraphics[alt={},max width=\textwidth]{01b167aa-2a77-4487-882c-20b1b74ecc90-7_714_1807_353_138}
  \end{figure} Figure 4 shows a capacitated directed network. The number on each arc is its capacity. The numbers in circles show a feasible flow from sources $A$ and $B$ to sinks $I , J$ and $K$. \section*{Take this as the initial flow pattern.}
On Diagram 1 in the answer booklet, add a supersource $S$ and a supersink $W$ to obtain a capacitated network with a single source and single sink. State the minimum capacities of the arcs you have added.
(3)
1. Use the given initial flow and the labelling procedure on Diagram 2 to find the maximum flow through the network. You must list each flow-augmenting route you use together with its flow.
2. Verify that your flow is maximal.
Show your maximum flow pattern on Diagram 3.

Edexcel D1 2003 January Q8

8. The tableau below is the initial tableau for a maximising linear programming problem.

Basic Variable	$x$	$y$	$z$	$r$	$s$	Value
$r$	2	3	4	1	0	8
$s$	3	3	1	0	1	10
$P$	- 8	- 9	- 5	0	0	0

For this problem $x \geq 0 , y \geq 0 , z \geq 0$. Write down the other two inequalities and the objective function.
Solve this linear programming problem.
State the final value of $P$, the objective function, and of each of the variables. END

Edexcel D1 2004 January Q1

Define the terms
1. bipartite graph,
2. alternating path,
3. matching,
4. complete matching.
5. A three-variable linear programming problem in $x , y$ and $z$ is to be solved. The objective is to maximise the profit P . The following tableau was obtained.
Basic variable $x$ $y$ $z$ $r$ $s$ $t$ Value
$s$ 3 0 2 0 1 $- \frac { 2 } { 3 }$ $\frac { 2 } { 3 }$
$r$ 4 0 $\frac { 7 } { 2 }$ 1 0 8 $\frac { 9 } { 2 }$
$y$ 5 1 7 0 0 3 7
P 3 0 2 0 0 8 63

Edexcel D1 2004 January Q6

	$A$	B	C	D	$E$	$F$
A	-	7	3	-	8	11
B	7	-	4	2	-	7
C	3	4	-	5	9	-
D	-	2	5	-	6	3
E	8	-	9	6	-	-
$F$	11	7	-	3	-	-

The matrix represents a network of roads between six villages $A , B , C , D , E$ and $F$. The value in each cell represents the distance, in km, along these roads.

Show this information on the diagram in the answer book.
(2)
Use Kruskal's algorithm to determine the minimum spanning tree. State the order in which you include the arcs and the length of the minimum spanning tree. Draw the minimum spanning tree.
(5)
Starting at $D$, use Prim's algorithm on the matrix given in the answer book to find the minimum spanning tree. State the order in which you include the arcs.
(3)

Edexcel D1 2004 January Q7

7. Becky's bird food company makes two types of bird food. One type is for bird feeders and the other for bird tables. Let $x$ represent the quantity of food made for bird feeders and $y$ represent the quantity of food made for bird tables. Due to restrictions in the production process, and known demand, the following constraints apply. $$\begin{gathered} x + y \leq 12
y < 2 x
2 y \geq 7
y + 3 x \geq 15 \end{gathered}$$

On the axes provided, show these constraints and label the feasible region $R$. The objective is to minimise $C = 2 x + 5 y$.
Solve this problem, making your method clear. Give, as fractions, the value of $C$ and the amount of each type of food that should be produced.
(4) Another objective (for the same constraints given above) is to maximise $P = 3 x + 2 y$, where the variables must take integer values.
Solve this problem, making your method clear. State the value of $P$ and the amount of each type of food that should be produced.

Edexcel D1 2004 January Q8

8. \begin{figure}[h]

\captionsetup{labelformat=empty} \caption{Figure 4} \includegraphics[alt={},max width=\textwidth]{a21a4565-800c-45c0-a513-bb813ef1086f-8_864_1705_356_173}

\end{figure} A trainee at a building company is using critical path analysis to help plan a project. Figure 4 shows the trainee's activity network. Each activity is represented by an arc and the number in brackets on each arc is the duration of the activity, in hours.

Find the values of $x , y$ and $z$.
State the total length of the project and list the critical activities.
Calculate the total float time on
1. activity $N$,
2. activity $H$.
  (3) The trainee's activity network is checked by the supervisor who finds a number of errors and omissions in the diagram. The project should be represented by the following precedence table.
  Activity Must be preceded by: Duration
  A - 4
  B - 3
  C - 5
  D B 2
  E A, $D$ 8
  $F$ B 2
  G C 2
  $H$ C 3
  I $F , G$ 4
  J $F , G$ 2
  K $F , G$ 7
  L E, I 9
  M H, J 3
  N E, I, K, M 3
  $P$ E, $I$ 6
  $Q$ H, J 5
  $R$ $Q$ 7
By adding activities and dummies amend the diagram in the answer book so that it represents the precedence table. (The durations of activities $A , B , \ldots , N$ are all correctly given on the diagram in the answer book.)
Find the total time needed to complete this project.

Edexcel D1 2005 January Q1

1. \begin{figure}[h]

\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{e64b50bc-13a3-4051-b8c1-d4e7ea49e3a5-2_770_794_434_607}

\end{figure} The bipartite graph in Figure 1 shows a mapping between six people, Andy (A), David ( $D$ ), Joan $( J )$, Preety $( P )$, Sally $( S )$ and Trevor $( T )$, and six tasks $1,2,3,4,5$ and 6. The initial matching is $A$ to $2 , D$ to $1 , J$ to 3 and $P$ to 4.

Indicate this initial matching in a distinctive way on the bipartite graph drawn in the answer book.
Starting from this initial matching, use the maximum matching algorithm to find a complete matching. List clearly the alternating paths you use.
(5)

Trainee	Departments
\(H\)	\(D , F , P\)
\(J\)	\(G , D , F\)
\(M\)	\(S , P , G\)
\(T\)	\(F , S , G\)
\(Y\)	\(D\)

Basic Variable	\(x\)	\(y\)	\(z\)	\(r\)	\(s\)	Value
\(r\)	2	3	4	1	0	8
\(s\)	3	3	1	0	1	10
\(P\)	- 8	- 9	- 5	0	0	0

Basic variable	\(x\)	\(y\)	\(z\)	\(r\)	\(s\)	\(t\)	Value
\(s\)	3	0	2	0	1	\(- \frac { 2 } { 3 }\)	\(\frac { 2 } { 3 }\)
\(r\)	4	0	\(\frac { 7 } { 2 }\)	1	0	8	\(\frac { 9 } { 2 }\)
\(y\)	5	1	7	0	0	3	7
P	3	0	2	0	0	8	63

	\(A\)	B	C	D	\(E\)	\(F\)
A	-	7	3	-	8	11
B	7	-	4	2	-	7
C	3	4	-	5	9	-
D	-	2	5	-	6	3
E	8	-	9	6	-	-
\(F\)	11	7	-	3	-	-

Activity	Must be preceded by:	Duration
A	-	4
B	-	3
C	-	5
D	B	2
E	A, \(D\)	8
\(F\)	B	2
G	C	2
\(H\)	C	3
I	\(F , G\)	4
J	\(F , G\)	2
K	\(F , G\)	7
L	E, I	9
M	H, J	3
N	E, I, K, M	3
\(P\)	E, \(I\)	6
\(Q\)	H, J	5
\(R\)	\(Q\)	7

	Office	Room \(A\)	Room \(B\)	Room \(C\)	Room \(D\)	Room \(E\)
Office	-	8	16	12	10	14
Room \(A\)	8	-	14	13	11	9
Room \(B\)	16	14	-	12	15	11
Room \(C\)	12	13	12	-	11	8
Room \(D\)	10	11	15	11	-	10
Room \(E\)	14	9	11	8	10	-

	A	\(B\)	C	\(D\)	\(E\)	\(F\)
A	-	10	12	13	20	9
B	10	-	7	15	11	7
C	12	7	-	11	18	3
D	13	15	11	-	27	8
E	20	11	18	27	-	18
\(F\)	9	7	3	8	18	-

Questions — Edexcel D1 (480 questions)

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Edexcel D1 2018 Specimen Q4

Edexcel D1 2018 Specimen Q5

Edexcel D1 2018 Specimen Q6

Edexcel D1 2001 January Q1

Edexcel D1 2001 January Q2

Edexcel D1 2001 January Q4

Edexcel D1 2001 January Q5

Edexcel D1 2001 January Q6

Edexcel D1 2001 January Q7

Edexcel D1 2002 January Q1

Edexcel D1 2002 January Q2

Edexcel D1 2002 January Q5

Edexcel D1 2002 January Q6

Edexcel D1 2002 January Q7

Edexcel D1 2003 January Q1

Edexcel D1 2003 January Q2

Edexcel D1 2003 January Q3

Edexcel D1 2003 January Q5

Edexcel D1 2003 January Q6

Edexcel D1 2003 January Q8

Edexcel D1 2004 January Q1

Edexcel D1 2004 January Q6

Edexcel D1 2004 January Q7

Edexcel D1 2004 January Q8

Edexcel D1 2005 January Q1