AQA Further AS Paper 2 Discrete (Further AS Paper 2 Discrete) 2021 June

1

1. A project consists of three activities \(A , B\) and \(C\)
   An activity network for the project is shown in the diagram below.
   \includegraphics[max width=\textwidth, alt={}, center]{18ce34aa-e4c3-4a84-a36d-6542d2319bf5-02_615_770_726_635} Find the value of \(x\) Circle your answer.
   5
   7
   8
   12 1
2. Find the value of \(y\)
   Circle your answer.
   5
   7
   8
   15

2 The set \(S\) is given by \(S = \{ 0,2,4,6 \}\) 2

1. Construct a Cayley table, using the grid below, for \(S\) under the binary operation addition modulo 8
   \includegraphics[max width=\textwidth, alt={}, center]{18ce34aa-e4c3-4a84-a36d-6542d2319bf5-03_561_563_607_831} 2
2. State the identity element for \(S\) under the binary operation addition modulo 8

3 The diagram shows a network of pipes. Each pipe is labelled with its upper capacity in \(\mathrm { m } ^ { 3 } \mathrm {~s} ^ { - 1 }\)
\includegraphics[max width=\textwidth, alt={}, center]{18ce34aa-e4c3-4a84-a36d-6542d2319bf5-04_513_832_440_605} 3

1. Find the value of Cut \(X\)
   3
2. Find the value of Cut \(Y\)
   3
3. Add a supersink \(T\) to the network.

5
7
8
12 1 (b) Find the value of \(y\)
Circle your answer.
5
7
8
15 2 The set \(S\) is given by \(S = \{ 0,2,4,6 \}\) 2 (a) Construct a Cayley table, using the grid below, for \(S\) under the binary operation addition modulo 8
\includegraphics[max width=\textwidth, alt={}, center]{18ce34aa-e4c3-4a84-a36d-6542d2319bf5-03_561_563_607_831} 2 (b) State the identity element for \(S\) under the binary operation addition modulo 8

8
12 1 (b) Find the value of \(y\)
Circle your answer.
5
7
8
15 2 The set \(S\) is given by \(S = \{ 0,2,4,6 \}\) 2 (a) Construct a Cayley table, using the grid below, for \(S\) under the binary operation addition modulo 8
\includegraphics[max width=\textwidth, alt={}, center]{18ce34aa-e4c3-4a84-a36d-6542d2319bf5-03_561_563_607_831} 2 (b) State the identity element for \(S\) under the binary operation addition modulo 8