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Download Actual 2024 AQA AS FURTHER MATHEMATICS 7366/1 Paper 1 Merged Question Paper + Mark Scheme and more Exams Mathematics in PDF only on Docsity!
Actual 2024 AQA AS FURTHER MATHEMATICS 7366/1 Paper 1 Merged Question Paper + Mark Scheme AQA va Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature | declare this is my own work. AS FURTHER MATHEMATICS Paper 1 Monday 13 May 2024 Afternoon Time allowed: 1 hour 30 minutes Materials For Examiner’s Use e You must have the AQA Formulae and statistical tables booklet for . A-level Mathematics and Aevel Further Mathematics. Question [INES e You should have a graphical or scientific calculator that meets the 1 requirements of the specification. 2 3 Instructions e Use black ink or black ball-point pen. Pencil should only be used for drawing. 4 e Fill in the boxes at the top of this page. 5 e Answer all questions. 6 e You must answer each question in the space provided for that question. 7 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). 8 e Do not write outside the box around each page or on blank pages. 9 e Show all necessary working; otherwise marks for method may be lost. 10 e Do all rough work in this book. Cross through any work that you do not want to be marked. M4 12 Information 13 e The marks for questions are shown in brackets. 14 e The maximum mark for this paper is 80. 16 Advice 16 e Unless stated otherwise, you may quote formulae, without proof, 17 from the booklet. e You do not necessarily need to use all the space provided. TOTAL TC 366) Do not write outside the box Answer all questions in the spaces provided. 1 Express cosh? x in terms of sinh x Circle your answer. [1 mark] 1+ sinh? x 4 — sinh? x sinh? x —1 —1— sinh? x 2 The function f is defined by f(x) =2x+3 O GiJun24/7366/1 5 Do not write outside the 7 The function fis defined by Pox f(x) = Find the mean value of f over the interval 4 AM GiJun24/7366/1 7 Do not write outside the 8 (a) The complex number z is given by = =x +iy where x,yeER box 8 (a) (i) Write down the complex conjugate =* in terms of x and y [1 mark] 8 (a) (ii) Hence prove that =s* is real for all = € C [2 marks] IML GiJun24/7366/1 8 10 Do not write outside the 9 (a) Show that, for all positive integers , Pox ie r+2 rt+1 (r+1)(r+2) [1 mark] 9 (b) Hence, using the method of differences, show that % 1 _ 1 Si r+1)(r+2) ant+b where a and b are integers to be determined. [3 marks] G/Jun24/7366/1 10 11 Do not write outside the box 9 (c) Hence find the exact value of 2000 1 roo Fer +2) [3 marks] Turn over > 11 G/Jun24/7366/1 11 13 10 (b) The line L has equation =-2 y= Bxt2 10 (b) (i) Draw the line L on Figure 1 [2 marks] 10 (b) (ii) Hence, or otherwise, solve the inequality 2x —10 2. 3x5 = 5t*? [2 marks] Turn over for the next question Turn over > wil _ Do not write outside the box 13 11 14 The matrices A and B are given by 3i -2 4 5 . and B= a -l where a is a real number. Calculate the product AB in terms of a Give your answer in its simplest form. [3 marks] GiJun24/7366/1 Do not write outside the box 14 13 13 (a) 13 (b) 16 16 The cubic equation x° —x-—7=0 has roots a, f andy The cubic equation p(x)=0 has roots a—1,f—1 and y—1 The coefficient of x9 in p(x) is 1 Describe fully the transformation that maps the graph of y= gee T onto the graph of y= p(x) Do not write outside the box [2 marks] Find p(x) [3 marks] G/Jun24/7366/1 16 17 Do not write outside the box Turn over for the next question Turn over > G/Jun24/7366/1 17 19 Do not write outside the 14 (c) The line L, has equation y=x+1 Pox The transformation T maps the line L, onto the line Lp Find the equation of Ly in the form y= mx +e [5 marks] Turn over > G/Jun24/7366/1 19 15 (a) 15 (b) IMU 20 Do not write outside the Use Maclaurin’s series expansion for In(1 + x) to show that the first three terms of the box Maclaurin’s series expansion of In(1+3x) are 3x - 3x? + 9x8 [1 mark] Julia attempts to use the series expansion found in part (a) to find an approximation for In4 Julia’s incorrect working is shown below. Let 1+3x=4 3x=3 x=1 So In4=3x1-2xq?+9x 1 =3-45+9 =T75 Explain the error in Julia’s working. [2 marks] G/Jun24/7366/1 20 
