2023 AQA A-level FURTHER MATHEMATICS 7367/2 Paper 2 Question Paper & Mark scheme (Merged) June 2023 [VERIFIED] A-level FURTHER MATHEMATICS Paper 2

2023 AQA A-level FURTHER MATHEMATICS 7367/2 Paper 2 Question Paper & Mark scheme (Merged) June 2023 [VERIFIED] A-level FURTHER MATHEMATICS Paper 2 onday 5 June 2023 fternoon Time allowed: 2 hours 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. 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 100. Advice Unless stated otherwise, you may quote formulae, without proof, from the booklet. You do not necessarily need to use all the space provided. For Examiner’s Use Question Mark 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 TOTAL PB/KL/Jun23/E4 7367/2 2 Answer all questions in the spaces provided. d 2 y 1Given that y ¼ sin x þ sinh x , find d x2 þ y Circle your answer. [1 mark] 2 sin x 2 sin x 2 sinh x 2 sinh x Do not write outside the box 2 Which one of the expressions below is not equal to zero? Circle your answer. 2 x 5 e x x ! 1(x e ) x ! 0 (x ln x) x ! 1 x5 lim lim lim [1 mark] lim (x 3 e x ) x ! 0 (02) Jun23/7367/2 3 ¼ 1 1 1 3 2 1 3 The determinant A 2 0 2 Which one of the determinants below has a value which is not equal to the value of A? Tick (3) one box. [1 mark] 2 0 2 3 1 3 3 2 1 1 0 2 1 2 3 1 2 1 1 0 1 2 2 2 3 2 1 3 2 1 1 1 1 2 0 2 4 It is given that f (x) ¼ cosh 1 (x 3) Which of the sets listed below is the greatest possible domain of the function f ? Circle your answer. [1 mark] fx : x 4g fx : x 3g fx : x 1g fx : x 0g Turn over s (03) Do not write outside the box Jun23/7367/2 4 5 Josh and Zoe are solving the following mathematics problem: The curve C1 has equation x 2 y 2 Do not write outside the box 16 9 " # 0 1 ¼ 1 The matrix M ¼ maps C1 onto C2 1 0 Find the equations of the asymptotes of C2 Josh says that to solve this problem you must first carry out the transformation on C1 to find C2, and then find the asymptotes of C2 Zoe says that you will get the same answer if you first find the asymptotes of C1, and then carry out the transformation on these asymptotes to obtain the asymptotes of C2 Show that Zoe is correct. [5 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (04) Jun23/7367/2 5 6 (a) Express 5 5i in the form re iy , where p < y p [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 6 (b) The point on an Argand diagram that represents 5 5i is one of the vertices of an equilateral triangle whose centre is at the origin. Find the complex numbers represented by the other two vertices of the triangle. Give your answers in the form re iy , where p < y p [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box Turn over (05) s Jun23/7367/2 6 7 Show that nXþ1 r 3 ¼ 1 4 (n2 þ an þ b)(n2 þ an þ c) r¼11 where a, b and c are integers to be found.