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Download Actual 2024 AQA A-level FURTHER MATHEMATICS 7367/1 Paper 1 Merged Question Paper + Mark S and more Exams Mathematics in PDF only on Docsity!
Actual 2024 AQA A-level FURTHER MATHEMATICS 7367/1 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. A-level FURTHER MATHEMATICS Paper 1 Wednesday 22 May 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. 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 8 of this book. Write the question number against your answer(s). 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 11 to be marked. 12 Information 13 e The marks for questions are shown in brackets. 14 e The maximum mark for this paper is 100. 15 Advice 16 e Unless stated otherwise, you may quote formulae, without proof, 17 from the booklet. 18 e You do not necessarily need to use all the space provided. TOTAL a ert Do not write outside the Answer all questions in the spaces provided. box 1 The roots of the equation 20x3 — 16x2- 4x +7=0 are a,f and y Find the value of af + fy + ya Circle your answer. [1 mark] 4 1 1 4 5 5 5 5 in 2 The complex number == e% Which one of the following is a real number? Circle your answer. [1 mark] “4 36 -6 gf IML GiJun24/7367/1 2 Do not write outside the 5 The points A, B and C have coordinates A(5, 3, 4), B(8, -1, 9) and C(12, 5, 10) box The points A, B and Clie in the plane II 5 (a) Find a vector that is normal to the plane II [3 marks] MMT GiJun24/7367/1 4 Do not write outside the 5 (b) Find a Cartesian equation of the plane IT Pox [2 marks] Turn over > IMI GiJun24/7367/1 5 Do not write outside the box Turn over for the next question Turn over > AM GiJun24/7367/1 7 Do not write outside the 7 The complex numbers = and w satisfy the simultaneous equations Pox stwr=5 3c*§-w=6 + 41 Find zs and w [5 marks] IML GiJun24/7367/1 8 10 Do not write outside the 9 (a) It is given that box p= In(r + V2 + 1) Starting from the exponential definition of the sinh function, show that sinh p =r [4 marks] GiJun24/7367/1 10 11 Do not write outside the 9 (b) Solve the equation box cosh? x = 2sinh x + 16 Give your answers in logarithmic form. [4 marks] Turn over > 11 GiJun24/7367/1 11 13 Do not write outside the box 14 (a) ‘Find (e2tan-' x) . [1 mark] 11 (b) Hence find [axtan~ xdx [4 marks] Turn over > 13 GiJun24/7367/1 13 12 12 (a) 14 alse the The line L, has equation 4 1 Pox r=|2]/+/) 3 1 -1 The transformation T is represented by the matrix 2 10 3.4 6 -5 2 -3 The transformation T transforms the line L, to the line Ly Show that the angle between L, and Ly» is 0.701 radians, correct to three decimal places. [4 marks] GiJun24/7367/1 14 16 Do not write outside the 13 (a) Use de Moivre's theorem to show that box cos3@ = 4cos3 6 — 3cos@ [3 marks] 13 (b) Use de Moivre’s theorem to express sin36@ in terms of sin@ [2 marks] 16 GiJun24/7367/1 16 17 Do not write outside the 13 (c) Hence show that box cot? 6 — 3cot cot3 6 = aeotr et [4 marks] Turn over > GiJun24/7367/1 17 19 Do not write outside the box Turn over for the next question Turn over > GiJun24/7367/1 19 15 IMM 20 A curve is defined parametrically by the equations x= 3+5 g yat? (t2 0) Show that the arc length of the curve from t=0 to t=2 is equal to 26 units. [5 marks] GiJun24/7367/1 Do not write outside the box 20 
