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Download Actual 2024 AQA A-level FURTHER MATHEMATICS 7367/2 Paper 2 Merged Question Paper + Mark S and more Exams Mathematical Analysis in PDF only on Docsity!
Actual 2024 AQA A-level FURTHER MATHEMATICS 7367/2 Paper 2 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. A-level FURTHER MATHEMATICS Paper 2 Monday 3 June 2024 Afternoon Time allowed: 2 hours Materials _ For Examiner’s Use e You must have the AQA Formulae and statistical tables booklet for Question Mark A-level Mathematics and A-level Further Mathematics. e You should have a graphical or scientific calculator that meets the 1 requirements of the specification. 2 3 Instructions 4 e Use black ink or black ball-point pen. Pencil should only be used for drawing. 5 e Fill in the boxes at the top of this page. 6 e Answer all questions. 7 e 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 8 of this book. Write the question number against your answer(s). 9 e Do not write outside the box around each page or on blank pages. 10 e Show all necessary working; otherwise marks for method may be lost. 11 e Do all rough work in this book. Cross through any work that you do not want 12 to be marked. 13 Information 14 e The marks for questions are shown in brackets. 15 e The maximum mark for this paper is 100. 16 17 Advice 18 e Unless stated otherwise, you may quote formulae, without proof, 19 from the booklet. e You do not necessarily need to use all the space provided. 20 TOTAL IMM a 67/2 IML Do not write outside the Answer all questions in the spaces provided. box It is given that 2 5 1 Je} 2 |=0 3] |-6 where J is a constant. Find the value of A Circle your answer. [1 mark] -28 -8 8 28 The movement of a particle is described by the simple harmonic equation X¥ =-25x where x metres is the displacement of the particle at time t seconds, and ¥ ms-2 is the acceleration of the particle. The maximum displacement of the particle is 9 metres. Find the maximum speed of the particle. Circle your answer. [1 mark] 15ms1 45ms-1 75ms1 135 m s-1 Gldun24/7367/2 2 Do not write outside the 5 The first four terms of the series S can be written as box S=(1%2)+(2%3)+(x4)+(4X5)+... 5 (a) Write an expression, using > notation, for the sum of the first 7 terms of S [1 mark] 5 (b) Show that the sum of the first 7 terms of S is equal to Anta +1)(n + 2) [2 marks] MMT Gldun24/7367/2 4 Do not write outside the 6 The cubic equation box x3+5x2-4x+2=0 has roots a, f and y Find a cubic equation, with integer coefficients, whose roots are 3a, 36 and 3y [3 marks] Turn over for the next question Turn over > IMI Gldun24/7367/2 5 Do not write outside the box 2 0 8 The vectors a, b, and c are such that ax b=| 1 Jand ax c=| 0 0 3 Work out (a —4b + 3c) x (2a) [4 marks] Turn over > AM Gldun24/7367/2 7 IML Do not write outside the A curve passes through the point (—2, 4.73) and satisfies the differential equation Pox dy y2—x2 dx 2x+3y Use Euler’s step by step method once, and then the midpoint formula Vp =Vp_1 + 2hE (x, Vp), 4 =X, tA once, each with a step length of 0.02, to estimate the value of y when x =—1.96 Give your answer to five significant figures. [4 marks] Gldun24/7367/2 8 10 Do not write outside the 10 The matrix C is defined by box [i] Prove that the transformation represented by C has no invariant lines of the form y=kx [4 marks] GlJun24/7367/2 10 11 IMI 11 Do not write outside the box Latifa and Sam are studying polynomial equations of degree greater than 2, with real coefficients and no repeated roots. Latifa says that if such an equation has exactly one real root, it must be of degree 3 Sam says that this is not correct. State, giving reasons, whether Latifa or Sam is right. [3 marks] Turn over for the next question Turn over > GlJun24/7367/2 11 13 Do not write outside the box Turn over for the next question Turn over > GlJun24/7367/2 13 14 13 (a) Use the method of differences to show that n 1 11, 1 Upcaree 4 Dn " 2(n +1) [5 marks] GiJun24/7367/2 Do not write outside the box 14 16 Do not write outside the 14 The matrix M is defined as Pox 5 2 1 M=|6 3 2k+3 2 1 5 where k is a constant. 14 (a) Given that M is a non-singular matrix, find M-1 in terms of k [5 marks] iu ee 17 Do not write outside the 14 (b) State any restrictions on the value of k Pox [1 mark] 14 (c) Using your answer to part (a), show that the solution to the set of simultaneous equations below is independent of the value of k 6x + 2p + Zz = 1 6x + 3y + (2k+3)2 = 4k+3 ax + yt Oz = 9 [4 marks] Turn over > GlJun24/7367/2 17 19 Do not write outside the 15 (b) Find the solution of the inequality box |x2-4x|>5—x Give your answer in an exact form. [4 marks] Turn over > GlJun24/7367/2 19 20 Do not write outside the 16 The function f is defined by Pox ax+5 fe) +b where a and b are constants. The graph of y=f(x) has asymptotes x=-—2 and y=3 16 (a) Write down the value of a and the value of b [2 marks] 16 (b) The diagram shows the graph of y= f(x) and its asymptotes. The shaded region R is enclosed by the graph of y= f(x), the x-axis and the y-axis. yA RW mesnerdeesosescenthorssesccesse seas H == 16 (b)(i) The shaded region R is rotated through 360° about the x-axis to form a solid. Find the volume of this solid. Give your answer to three significant figures. [3 marks] IMU GlJun24/7367/2 20 
