Official June 2024 AQA A-level MATHEMATICS 7357/1 Paper 1 Merged Question Paper + Mark Scheme Ace your Mocks!!! G/LM/Jun24/G4005/E6 7357/1 (JUN247357101) A-level MATHEMATICS Paper 1 Tuesday 4 June 2024 Afternoon Time allowed: 2 hours Materials l You must have the AQA Formulae for A‑level Mathematics booklet. 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. l If you need 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 19 20 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/Jun24/7357/1 Answer all questions in the spaces provided. 1 Find the coefficient of x in the expansion of (4x3 – 5x2 + 3x – 2)(x5 + 4x + 1) Circle your answer. [1 mark] –5 –2 7 11 3 Do not write outside the box (03) G/Jun24/7357/1 Turn over U 2 The function f is defined by f(x) = ex + 1 for x ℝ Find an expression for f –1(x) Tick () one box. [1 mark] f –1(x) = ln (x – 1) f –1(x) = ln (x) – 1 f –1(x) = 1 ex + 1 f –1(x) = x – 1 e Turn over for the next question 4 Do not write outside the box (04) G/Jun24/7357/1 3 The expression 12x2 + 3x + 7 3x – 5 can be written as Ax + B + C 3x – 5 State the value of A Circle your answer. [1 mark] 3 4 7 9 5 Do not write outside the box (05) G/Jun24/7357/1 Turn over U 4 One of the diagrams below shows the graph of y = arccos x Identify the graph of y = arccos x Tick () one box. [1 mark] y O x π 2 –1 y O 1 x π 2 Turn over for the next question 6 Do not write outside the box (06) G/Jun24/7357/1 5 Solve the equation sin2 x = 1 for 0° < x>