Questions — Edexcel D1 (480 questions)

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Edexcel D1 2019 January Q7
7. A company makes two types of wooden bookcase, the Manhattan and the Brooklyn. The pieces of wood used for each bookcase go through three stages. They must be cut, assembled and packaged. The table below shows the time, in hours, needed to complete each of the three stages for a single bookcase, and the profit made, in pounds, when each type of bookcase is sold. The table also shows the amount of time, in hours, that is available each week for each of the three stages. Shortest route: \(\_\_\_\_\)
Length of shortest route: \(\_\_\_\_\)
3.
\includegraphics[max width=\textwidth, alt={}]{e7f89fa1-0afa-4aec-a430-14ec98f487c8-14_896_1514_293_200}
\section*{Diagram 1} \section*{Grid 1} 4. \(\begin{array} { l l l l l l l l l l l } 180 & 80 & 250 & 115 & 100 & 230 & 150 & 95 & 105 & 90 & 390 \end{array}\) \(\begin{array} { l l l l l l l l l l l } 180 & 80 & 250 & 115 & 100 & 230 & 150 & 95 & 105 & 90 & 390 \end{array}\) 5.
  1. (a)
    \includegraphics[max width=\textwidth, alt={}, center]{e7f89fa1-0afa-4aec-a430-14ec98f487c8-22_616_1477_735_230}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e7f89fa1-0afa-4aec-a430-14ec98f487c8-23_609_1468_310_239} \captionsetup{labelformat=empty} \caption{Figure 3
[0pt] [The weight of the network is \(20 \mathrm { x } + 17\) ]}
\end{figure}
VIIIV SIUI NI IIIUM IONOOVIAV SIHI NI JALYM LON OOVEYV SIHI NI JLIYM LON OO
7.
VIAN SIHI NI III M I ION OCVI4V SIHI NI ALIVM IONOOVJYV SIHI NI JLIYM LON OO
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e7f89fa1-0afa-4aec-a430-14ec98f487c8-27_1734_1538_299_210} \captionsetup{labelformat=empty} \caption{Diagram 1}
\end{figure}
(Total 13 marks)
Leave blank
Q7
Edexcel D1 2020 January Q1
  1. The table below shows the distances, in km , between six data collection points, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E }\) and F .
ABCDEF
A-3542554850
B35-40495231
C4240-475349
D554947-3944
E48525339-52
F5031494452-
Ferhana must visit each data collection point. She will start and finish at A and wishes to minimise the total distance she travels.
  1. Starting at A, use the nearest neighbour algorithm to obtain an upper bound for the distance Ferhana must travel. Make your method clear.
    (2)
  2. Starting by deleting B , and all of its arcs, find a lower bound for the distance Ferhana must travel. Make your calculation clear.
    (3)
Edexcel D1 2020 January Q2
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b6d09c46-abfd-4baa-80bd-7485d1bf8e0d-03_759_1401_196_331} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure}
  1. Define the terms
    1. tree,
    2. minimum spanning tree.
  2. Use Kruskal's algorithm to find the minimum spanning tree for the network shown in Figure 1. You must clearly show the order in which you consider the edges. For each edge, state whether or not you are including it in the minimum spanning tree.
  3. Draw the minimum spanning tree using the vertices given in Diagram 1 in the answer book and state the weight of the minimum spanning tree.
Edexcel D1 2020 January Q3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b6d09c46-abfd-4baa-80bd-7485d1bf8e0d-04_865_1636_246_219} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} The network in Figure 2 shows the activities that need to be undertaken by a company to complete a project. Each activity is represented by an arc and the duration, in days, is shown in brackets. Each activity requires one worker. The early event times and late event times are shown at each vertex. The total float on activity D is twice the total float on activity E .
  1. Find the values of \(x , y\) and \(z\).
  2. Draw a cascade chart for this project on Grid 1 in the answer book.
  3. Use your cascade chart to determine a lower bound for the minimum number of workers needed to complete the project in the shortest possible time. You must make specific reference to time and activities. (You do not need to provide a schedule of the activities.)
Edexcel D1 2020 January Q4
4. $$\begin{array} { l l l l l l l l l l } 35 & 17 & 10 & 7 & 28 & 23 & 41 & 15 & 20 & 29 \end{array}$$
  1. Use the first-fit bin packing algorithm to determine how the numbers listed above can be packed into bins of size 60
  2. The list of numbers is to be sorted into descending order. Use a quick sort to obtain the sorted list. You should show the result of each pass and identify your pivots clearly.
  3. Use the first-fit decreasing bin packing algorithm on your ordered list to pack the numbers into bins of size 60 The ten distinct numbers below are to be sorted into descending order. $$\begin{array} { l l l l l l l l l l } 20 & 24 & 17 & 26 & 8 & 15 & x & y & 19 & 12 \end{array}$$ A bubble sort, starting at the left-hand end of the list, is to be used to obtain the sorted list.
    After the second complete pass the list is $$\begin{array} { l l l l l l l l l l } 24 & 26 & 20 & 17 & 15 & y & 19 & 12 & x & 8 \end{array}$$
  4. Find the constraints on the values of \(x\) and \(y\).
Edexcel D1 2020 January Q5
5.
ActivityImmediately preceding activities
A-
B-
C-
DA
EC
FA, B, C
GA, B, C
HD, F, G
IA, B, C
JD, F, G
KH
LD, E, F, G, I
  1. Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain only the minimum number of dummies. Given that all critical paths for the network include activity H ,
  2. state which activities cannot be critical.
    (2)
Edexcel D1 2020 January Q6
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b6d09c46-abfd-4baa-80bd-7485d1bf8e0d-07_913_1555_182_248} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} [The total weight of the network is 269] Figure 3 models a network of roads. The number on each edge gives the time taken, in minutes, to travel along the corresponding road.
  1. Use Dijkstra's algorithm to find the shortest time needed to travel from A to J. State the quickest route. Alan needs to travel along all the roads to check that they are in good repair. He wishes to complete his route as quickly as possible and will start at his home, H, and finish at his workplace, D.
  2. By considering the pairings of all relevant nodes, find the arcs that will need to be traversed twice in Alan's inspection route from H to D. You must make your method and working clear. For Alan's inspection route from H to D
    1. state the number of times vertex C will appear,
    2. state the number of times vertex D will appear.
  4. Determine whether it would be quicker for Alan to start and finish his inspection route at H , instead of starting at H and finishing at D . You must explain your reasoning and show all your working.
Edexcel D1 2021 January Q1
  1. Use the binary search algorithm to try to locate the word "Parallelogram" in the following alphabetical list. Clearly indicate how you choose your pivots and which part of the list you are rejecting at each stage.
Arc Centre Chord Circle Circumference Diameter Radius Sector Segment Tangent
Edexcel D1 2021 January Q2
2. A restaurant sells two sizes of pizza, small and large. The restaurant owner knows that, each evening, she needs to make
  • at least 85 pizzas in total
  • at least twice as many large pizzas as small pizzas
In addition, at most \(80 \%\) of the pizzas must be large.
Each small pizza costs \(\pounds 2\) to make and each large pizza costs \(\pounds 3\) to make.
The restaurant owner wants to minimise her costs. Let \(x\) represent the number of small pizzas made each evening and let \(y\) represent the number of large pizzas made each evening. Formulate the information above as a linear programming problem. State the objective and list the constraints as simplified inequalities with integer coefficients. You should not attempt to solve the problem.
Edexcel D1 2021 January Q3
3. \(\quad \begin{array} { l l l l l l l l l l } 2.6 & 0.8 & 2.1 & 1.2 & 0.9 & 1.7 & 2.3 & 0.3 & 1.8 & 2.7 \end{array}\)
  1. Use the first-fit bin packing algorithm to determine how the numbers listed above can be packed into bins of size 5 The list is to be sorted into descending order.
    1. Starting at the left-hand end of the above list, perform two passes through the list using a bubble sort. Write down the lists that result at the end of the first pass and the second pass.
    2. Write down, in the table in the answer book, the number of comparisons and the number of swaps performed during each of these two passes. After a third pass using this bubble sort, the updated list is $$\begin{array} { l l l l l l l l l l } 2.6 & 2.1 & 1.7 & 2.3 & 1.2 & 1.8 & 2.7 & 0.9 & 0.8 & 0.3 \end{array}$$
  3. Use a quick sort on this updated list to obtain the fully sorted list. You must make your pivots clear.
  4. Apply the first-fit decreasing bin packing algorithm to the fully sorted list to pack the numbers into bins of size 5
Edexcel D1 2021 January Q4
4. (a) Explain the difference between the classical and the practical travelling salesperson problems. The table below shows the distances, in km, between seven museums, A, B, C, D, E, F and G.
ABCDEFG
A-253128353032
B25-3424273239
C3134-40352729
D282440-373536
E35273537-2831
F3032273528-33
G323929363133-
Fran must visit each museum. She will start and finish at A and wishes to minimise the total distance travelled.
(b) Starting at A, use the nearest neighbour algorithm to obtain an upper bound for the length of Fran's route. Make your method clear. Starting at D, a second upper bound of 203 km was found.
(c) State whether this is a better upper bound than the answer to (b), giving a reason for your answer. A reduced network is formed by deleting \(G\) and all the arcs that are directly joined to \(G\).
(d) (i) Use Prim's algorithm, starting at A, to construct a minimum spanning tree for the reduced network. You must clearly state the order in which you select the arcs of your tree.
(ii) Hence calculate a lower bound for the length of Fran's route. By deleting A, a second lower bound was found to be 188 km .
(e) State whether this is a better lower bound than the answer to (d)(ii), giving a reason for your answer.
(f) Using only the results from (c) and (e), write down the smallest interval that you can be confident contains the length of Fran's optimal route.
Edexcel D1 2021 January Q5
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{48e785c0-7de5-450f-862c-4dd4d169adf9-06_952_1511_230_278} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} [The total weight of the network is 253] Figure 1 represents a network of roads between 10 cities, A, B, C, D, E, F, G, H, J and K. The number on each edge represents the length, in miles, of the corresponding road. One day, Mabintou wishes to travel from A to H. She wishes to minimise the distance she travels.
  1. Use Dijkstra's algorithm to find the shortest path from A to H . State your path and its length. On another day, Mabintou wishes to travel from F to K via A.
  2. Find a route of minimum length from F to K via A and state its length. The roads between the cities need to be inspected. James must travel along each road at least once. He wishes to minimise the length of his inspection route. James will start his inspection route at A and finish at J.
  3. By considering the pairings of all relevant nodes, find the length of James' route. State the arcs that will need to be traversed twice. You must make your method and working clear.
    (6)
  4. State the number of times that James will pass through F. It is now decided to start the inspection route at D. James must minimise the length of his route. He must travel along each road at least once but may finish at any vertex.
  5. State the vertex where the new inspection route will finish.
  6. Calculate the difference between the lengths of the two inspection routes.
Edexcel D1 2021 January Q6
6.
ActivityDuration (days)Immediately preceding activities
A4-
B7-
C6-
D10A
E5A
F7C
G6B, C, E
H6B, C, E
I7B, C, E
J9D, H
K8B, C, E
L4F, G, K
M6F, G, K
N7F, G
P5M, N
The table above shows the activities required for the completion of a building project. For each activity the table shows the duration, in days, and the immediately preceding activities. Each activity requires one worker. The project is to be completed in the shortest possible time. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{48e785c0-7de5-450f-862c-4dd4d169adf9-08_668_1271_1658_397} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a partially completed activity network used to model the project. The activities are represented by the arcs and the numbers in brackets on the arcs are the times taken, in days, to complete each activity.
  1. Complete the network in Diagram 1 in the answer book by adding activities \(\mathrm { G } , \mathrm { H }\) and I and the minimum number of dummies.
  2. Add the early event times and the late event times to Diagram 1 in the answer book.
  3. State the critical activities.
  4. Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time. You must show your working.
  5. Schedule the activities on Grid 1 in the answer book, using the minimum number of workers, so that the project is completed in the minimum time.
Edexcel D1 2021 January Q7
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{48e785c0-7de5-450f-862c-4dd4d169adf9-10_993_1268_221_402} \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. The equations of two of the lines have been shown in Figure 3. Given that \(k\) is a positive constant,
  1. determine, in terms of \(k\) where necessary, the inequalities that define \(R\). The objective is to maximise \(P = 5 x + k y\)
    Given that the value of \(P\) is 38 at the optimal vertex of \(R\),
  2. determine the possible value(s) of \(k\). You must show algebraic working and make your method clear.
    (Total 11 marks)
Edexcel D1 2022 January Q1
1.
\(\begin{array} { l l l l l l l l l l } 17 & 9 & 15 & 8 & 20 & 13 & 28 & 4 & 12 & 5 \end{array}\)
Edexcel D1 2022 January Q2
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba13c470-e91c-4579-928a-42f800b10b3f-06_477_1052_239_504} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba13c470-e91c-4579-928a-42f800b10b3f-06_474_1052_1361_504} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} \section*{D} \begin{verbatim} B $$\mathrm { A }$$ \end{verbatim} \begin{verbatim} \(\stackrel { \bullet } { \text { E } }\) \end{verbatim} \section*{Diagram 1} Weight of the minimum spanning tree: \(\_\_\_\_\)
Edexcel D1 2022 January Q3
3.
ActivityImmediately preceding activities
A-
B-
C-
DA, B, C
EA, B, C
FC
GF
HD
ID, E, G
JD, E
Please redraw your activity network on this page if you need to do so.
Edexcel D1 2022 January Q4
4.
.
\section*{Grid 1}
Edexcel D1 2022 January Q5
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba13c470-e91c-4579-928a-42f800b10b3f-12_705_1237_239_411} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} [The total weight of the network is 82]
Edexcel D1 2022 January Q6
6.
\includegraphics[max width=\textwidth, alt={}]{ba13c470-e91c-4579-928a-42f800b10b3f-14_1468_1779_285_143}
ABCDEFGH
A-
B-1424111819
C14-1210152223
D212-291617
E4102-71415
F111597-78
G182216147-1
H1923171581-
(b) \(\_\_\_\_\)
(c)
BCDEFGH
B-1424111819
C14-1210152223
D212-291617
E4102-71415
F111597-78
G182216147-1
H1923171581-
Edexcel D1 2023 January Q1
1.
ABCDEFG
A-435247595355
B43-5945465247
C5259-51505551
D474551-524955
E59465052-5748
F5352554957-55
G554751554855-
ABCDEFG
A-435247595355
B43-5945465247
C5259-51505551
D474551-524955
E59465052-5748
F5352554957-55
G554751554855-
Edexcel D1 2023 January Q2
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{30e87893-41a3-4989-b43d-00994045492d-04_1369_1634_285_219} \captionsetup{labelformat=empty} \caption{Key:}
\end{figure} \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Key:} \includegraphics[alt={},max width=\textwidth]{30e87893-41a3-4989-b43d-00994045492d-04_266_579_1717_1343}
\end{figure} Shortest path from A to J: \(\_\_\_\_\)
Length of shortest path from A to J: \(\_\_\_\_\)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{30e87893-41a3-4989-b43d-00994045492d-05_876_1379_249_351} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} [The total weight of the network is 193]
Edexcel D1 2023 January Q3
3. \(\begin{array} { l l l l l l l l l l l } 1.8 & 1.4 & 2.6 & 1.6 & 2.8 & 0.9 & 3.1 & 0.8 & 1.2 & 2.4 & 0.6 \end{array}\)
Edexcel D1 2023 January Q4
4.
Activity
Immediately
preceded by
A-
B-
C-
DA
EC
FC
Activity
Immediately
preceded by
G
H
I
J
KD, G
LD, G
Activity
Immediately
preceded by
MD, G
N
P
Q
R
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{30e87893-41a3-4989-b43d-00994045492d-12_782_1776_902_141} \captionsetup{labelformat=empty} \caption{Diagram 1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{30e87893-41a3-4989-b43d-00994045492d-13_1098_1539_1356_264} \captionsetup{labelformat=empty} \caption{Diagram 2}
\end{figure}
Edexcel D1 2023 January Q5
5. \section*{D}
\includegraphics[max width=\textwidth, alt={}]{30e87893-41a3-4989-b43d-00994045492d-15_147_654_1254_806}
A
  • \({ } ^ { \text {B } }\)
  • F
    \(\stackrel { \bullet } { \mathrm { H } }\)
Diagram 1