Questions D1 (932 questions)

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Edexcel D1 Q6
13 marks Standard +0.3
This question should be answered on the sheet provided. There are 5 computers in an office, each of which must be dedicated to a single application. The computers have different specifications and the following table shows which applications each computer is capable of running.
ComputerApplications
\(E\)Animation
\(F\)Office, Data
\(G\)Simulation
\(H\)Animation, Office
\(I\)Data, CAD, Simulation
  1. Draw a bipartite graph to model this situation. [1 mark]
Initially it is decided to run the Office application on computer \(F\), Animation on computer \(H\), and Data on computer \(I\).
  1. Starting from this matching, use the maximum matching algorithm to find a complete matching. Indicate clearly how the algorithm has been applied. [9 marks]
  2. Computer \(H\) is upgraded to allow it to run CAD. Find an alternative matching to that found in part (b). [3 marks]
Edexcel D1 Q7
18 marks Standard +0.3
An engineer makes three components \(X\), \(Y\) and \(Z\). Relevant details are as follows: Component \(X\) requires 6 minutes turning, 3 minutes machining and 1 minute finishing. Component \(Y\) requires 15 minutes turning, 3 minutes machining and 4 minutes finishing. Component \(Z\) requires 12 minutes turning, 1 minute machining and 4 minutes finishing. The engineer gets access to 185 minutes turning, 30 minutes machining and 60 minutes finishing each day. The profits from selling components \(X\), \(Y\) and \(Z\) are £40, £90 and £60 respectively and the engineer wishes to maximise the profit from her work each day. Let the number of components \(X\), \(Y\) and \(Z\) the engineer makes each day be \(x\), \(y\) and \(z\) respectively.
  1. Write down the 3 inequalities that apply in addition to \(x \geq 0\), \(y \geq 0\) and \(z \geq 0\). [3 marks]
  2. Explain why it is not appropriate to use a graphical method to solve the problem. [1 mark]
It is decided to use the simplex algorithm to solve the problem.
  1. Show that a possible initial tableau is:
    Basic Variable\(x\)\(y\)\(z\)\(r\)\(s\)\(t\)Value
    \(r\)61512100185
    \(s\)33101030
    \(t\)14400160
    \(P\)\(-4\)\(-9\)\(-6\)0000
    [2 marks]
It is decided to increase \(y\) first.
  1. Perform sufficient complete iterations to obtain a final tableau and explain how you know that your solution is optimal. You may assume that work in progress is allowed. [9 marks]
  2. State the number of each component that should be made per day and the total daily profit that this gives, assuming that all items can be sold. [1 mark]
  3. If work in progress is not practicable, explain how you would obtain an integer solution to this problem. You are not expected to find this solution. [2 marks]
Edexcel D1 2022 January Q17
Moderate -0.8
17 & 9 & 15 & 8 & 20 & 13 & 28 & 4 & 12 & 5 \end{array}$$ The numbers in the list shown above are the weights, in kilograms, of ten boxes. The boxes are to be transported in containers that will each hold a maximum weight of 40 kilograms.
  1. Calculate a lower bound for the number of containers that will be needed to transport the boxes. You must show your working.
  2. Use the first-fit bin packing algorithm to allocate the boxes to the containers.
  3. Using the list provided, carry out a quick sort to produce a list of the weights in ascending order. You must make your pivots clear.
  4. Use the binary search algorithm to try to locate the weight of 9 in the sorted list. Clearly indicate how you choose your pivots and which part of the list is being rejected at each stage.
Edexcel D1 2022 January Q0
Easy -1.8
0 \leqslant x & \leqslant 27
Edexcel D1 2023 January Q10
Moderate -0.8
10 x + 7 y & \leqslant 140
& x + y \leqslant 15
& 2 x + 3 y \geqslant 36
& x \geqslant 0 , \quad y \geqslant 0 \end{aligned} \end{array}$$ (c) Represent these constraints on Diagram 1 in the answer book. Hence determine, and label, the feasible region, \(R\).
(d) Use the objective line method to find the optimal number of each type of cake that Martin should make, and the amount of sugar used.
(e) Determine how much flour and how many eggs Martin will have left over after making the optimal number of cakes. BLANK PAGE \end{document}
Edexcel D1 2022 January Q7
Moderate -0.8
7. \section*{Question 7 continued} \section*{Question 7 continued} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{765ea64e-d4b8-4f0f-9a43-2619f9db0c18-19_2109_1335_299_372} \captionsetup{labelformat=empty} \caption{Diagram 1}
\end{figure} \section*{Question 7 continued} \section*{Pearson Edexcel International Advanced Level} Time 1 hour 30 minutes \section*{Paper reference WDM11/01} \section*{Mathematics} \section*{You must have:} Decision Mathematics Answer Book (enclosed), calculator Candidates may use any calculator permitted by Pearson regulations. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. \section*{Instructions}
  • Use black ink or ball-point pen.
  • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
  • Write your answers for this paper in the Decision Mathematics answer book provided.
  • Fill in the boxes at the top of the answer book with your name, centre number and candidate number.
  • Do not return the question paper with the answer book.
  • Answer all questions and ensure that your answers to parts of questions are clearly labelled.
  • Answer the questions in the spaces provided
  • there may be more space than you need.
  • You should show sufficient working to make your methods clear. Answers without working may not gain full credit.
  • Inexact answers should be given to three significant figures unless otherwise stated.
\section*{Information}
  • There are 7 questions in this question paper. The total mark for this paper is 75.
  • The marks for each question are shown in brackets
  • use this as a guide as to how much time to spend on each question.
\section*{Advice}
  • Read each question carefully before you start to answer it.
  • Try to answer every question.
  • Check your answers if you have time at the end.
  • If you change your mind about an answer, cross it out and put your new answer and any working underneath.
\section*{Write your answers in the D1 answer book for this paper.}
Edexcel D1 2023 January Q6
Easy -1.3
6. \section*{Question 6 continued}
\includegraphics[max width=\textwidth, alt={}]{ed8418c4-cdc9-480f-aa09-a16e16933acb-17_1845_1463_296_303}
\section*{Diagram 1} \section*{Question 6 continued} \section*{Question 6 continued} \section*{Question 6 continued} \section*{Pearson Edexcel International Advanced Level} Time 1 hour 30 minutes \section*{Paper reference} \section*{Mathematics} \section*{You must have:} Decision Mathematics Answer Book (enclosed), calculator Candidates may use any calculator allowed by Pearson regulations. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. \section*{Instructions}
  • Use black ink or ball-point pen.
  • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). Coloured pencils and highlighter pens must not be used.
  • Fill in the boxes on the top of the answer book with your name, centre number and candidate number.
  • Answer all questions and ensure that your answers to parts of questions are clearly labelled.
  • Answer the questions in the D1 answer book provided - there may be more space than you need.
  • You should show sufficient working to make your methods clear. Answers without working may not gain full credit.
  • When a calculator is used, the answer should be given to an appropriate degree of accuracy.
  • Do not return the question paper with the answer book.
\section*{Information}
  • The total mark for this paper is 75.
  • The marks for each question are shown in brackets
  • use this as a guide as to how much time to spend on each question.
\section*{Advice}
  • Read each question carefully before you start to answer it.
  • Try to answer every question.
  • Check your answers if you have time at the end.
\section*{Write your answers in the D1 answer book for this paper.}