AS FURTHER MATHEMATICS

AS FURTHER MATHEMATICS Paper 2 Discrete Friday 17 May 2024 Afternoon Time allowed: 1 hour 30 minutes Materials  You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics.  You should have a graphical or scientific calculator that meets the requirements of the specification.  You must ensure you have the other optional Question Paper/Answer Book for which you are entered (either Mechanics or Statistics). You will have 1 hour 30 minutes to complete both papers. Instructions  Use black ink or black ball‑point pen. Pencil should only be used for drawing.  Fill in the boxes at the top of this page.  Answer all questions.  You must answer each question in the space provided for that question. If you require extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s).  Do not write outside the box around each page or on blank pages.  Show all necessary working; otherwise marks for method may be lost.  Do all rough work in this book. Cross through any work that you do not want to be marked. Information  The marks for questions are shown in brackets.  The maximum mark for this paper is 40. Advice  Unless stated otherwise, you may quote formulae, without proof, from the booklet.  You do not necessarily need to use all the space provided. G/LM/Jun24/G4001/V4 7366/2D Answer all questions in the spaces provided. 1 A connected planar graph has v vertices, e edges and f faces. Which one of the formulae below is correct? Circle your answer. [1 mark] box v + e + f = 2 v – e + f = 2 v – e – f = 2 v + e – f = 2 2 Find an expression for the number of edges in the complete bipartite graph, Km, n Circle your answer. [1 mark] m m – n m + n mn 3 Which one of the graphs shown below is semi‑Eulerian? Tick () one box. [1 mark] box Turn over U 4 The set S is defined as S = {1, 2, 3, 4} 4 (a) Complete the Cayley Table shown below for S under the binary operation multiplication modulo 5 box [2 marks] ×5 1 2 3 4 1 2 3 4 4 (b) State the identity element for S under multiplication modulo 5 [1 mark] 4 (c) State the self‑inverse elements of S under multiplication modulo 5 [1 mark] 5 A network of roads connects the villages A, B, C, D, E, F and G The weight on each arc in the network represents the distance, in miles, between adjacent villages. The network is shown in the diagram below. box C 22 D 12 13 14 8 A 15 B 24 20 18 30 E 23 19 F G 5 (a) Draw, in the space below, the spanning tree of minimum total length for this road network. [3 marks] 5 (b) Find the total length of the spanning tree drawn in part (a). [1 mark] Turn over U 6 A Young Enterprise Company decides