Official June 2024 AQA A-level FURTHER MATHEMATICS 7367/1 Paper 1 Merged Question Paper + Mark Scheme Ace your Mocks!!! G/LM/Jun24/G4006/V8 7367/1 (JUN247367101) A-level FURTHER MATHEMATICS Paper 1 Wednesday 22 May 2024 Afternoon Time allowed: 2 hours Materials l You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics. l You should have a graphical or scientific calculator that meets the requirements of the specification. Instructions l Use black ink or black ball‑point pen. Pencil should only be used for drawing. l Fill in the boxes at the top of this page. l Answer all questions. l 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). l Do not write outside the box around each page or on blank pages. l Show all necessary working; otherwise marks for method may be lost. l Do all rough work in this book. Cross through any work that you do not want to be marked. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 100. Advice l Unless stated otherwise, you may quote formulae, without proof, from the booklet. l 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 17 18 TOTAL Please write clearly in block capitals. Centre number Candidate number Surname _________________________________________________________________________ Forename(s) _________________________________________________________________________ Candidate signature _________________________________________________________________________ I declare this is my own work. 2 Do not write outside the box (02) G/Jun24/7367/1 Answer all questions in the spaces provided. 1 The roots of the equation 20x3 – 16x2 – 4x + 7 = 0 are α, β and γ Find the value of αβ + βγ + γα Circle your answer. [1 mark] – 4 5 – 1 5 1 5 4 5 2 The complex number z = e iπ 3 Which one of the following is a real number? Circle your answer. [1 mark] z4 z5 z6 z7 3 Do not write outside the box (03) G/Jun24/7367/1 Turn over U 3 The function f is defined by f(x) = x2 (x ∈ ℝ) Find the mean value of f(x) between x = 0 and x = 2 Circle your answer. [1 mark] 2 3 4 3 8 3 16 3 4 Which one of the following statements is correct? Tick () one box. [1 mark] limx 0 (x2 ln x) = 0 limx 0 (x2 ln x) = 1 limx 0 (x2 ln x) = 2 limx 0 (x2 ln x) is not defined. Turn over for the next question 4 Do not write outside the box (04) G/Jun24/7367/1 5 The points A, B and C have coordinates A(5, 3, 4), B(8, –1, 9) and C(12, 5, 10) The points A, B and C lie in the plane ∏ 5 (a) Find a vector that is normal to the plane ∏ [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 5 Do not write outside the box (05) G/Jun24/7367/1 Turn over U 5 (b) Find a Cartesian equation of the plane ∏ [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 6 Do not write outside the box (06) G/Jun24/7367/1 6 The sequence u1, u2, u3, ... is defined by u1 = 1 un+1 = un + 3n Prove by induction that for all integers n ≥ 1 un = 3 2 n2 – 3 2 n + 1 [4 marks]