AQA A-level MATHEMATICS 7357/1 Paper 1 Version: 1.0 Final PB/KL/Jun23/E7 7357/1 A-level MATHEMATICS Paper 1 Time allowed: 2 hours MaterialsQUESTION PAPER & MARKING SCHEME/ [MERGED] Mark scheme June 2023

AQA A-level MATHEMATICS 7357/1 Paper 1 Version: 1.0 Final PB/KL/Jun23/E7 7357/1 A-level MATHEMATICS Paper 1 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. Please write clearly in block capitals. Centre number Candidate number Surname ________________________________________________________________________ Forename(s) ________________________________________________________________________ Candidate signature ________________________________________________________________________ For Examiner’s Use Question Mark 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 TOTAL I declare this is my own work. 2 Answer all questions in the spaces provided. 1 Find the coefficient of x7 in the expansion of (2x  3)7 Circle your answer. [1 mark] 2187 128 2 128 2 Given that y ¼ 2x3 find dy dx Circle your answer. [1 mark] dy dx ¼ 5x2 dy dx ¼ 6x2 dy dx ¼ x4 2 dy dx ¼ 6x3 Jun23/7357/1 Do not write outside the box (02) 3 3 The curve with equation y ¼ ln x is transformed by a stretch parallel to the x-axis with scale factor 2 Find the equation of the transformed curve. Circle your answer. [1 mark] y ¼ 1 2 ln x y ¼ 2 ln x y ¼ ln x 2 y ¼ ln 2x 4 Given that y is a small angle, find an approximation for cos 2y Circle your answer. [1 mark] 1  y2 2 2  2y2 1  2y2 1  y2 Turn over for the next question Do not write outside the box Jun23/7357/1 Turn over s (03) 4 5 The graph of y ¼ 5 ex  1 is shown in the diagram below. O 1 4 x y The trapezium rule with 6 ordinates (5 strips) is to be used to find an approximation for the shaded area. The values required to obtain this approximation are shown in the table below. x 1 1.6 2.2 2.8 3.4 4 y 2.90988 1.26485 0.62305 0.32374 0.17263 0.09329 5 (a) Use the trapezium rule with 6 ordinates (5 strips) to find an approximate value for the shaded area. Give your answer to four decimal places. [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box Jun23/7357/1 (04) 5 5 (b) Using your answer to part (a) deduce an estimate for ð 4 1 20 ex  1 d