AQA MATHEMATICS Paper 1 June 2023

A-level MATHEMATICS Paper 1 Tuesday 6 June 2023 Afternoon Time allowed: 2 hours Materials  You must have the AQA Formulae for A‑level Mathematics booklet.  You should have a graphical or scientific calculator that meets the requirements of the specification. Instructions  Use black ink or black ball‑point pen. Pencil should only be used for drawing.  Fill in the boxes at the top of this page.  Answer all questions.  You must answer each question in the space provided for that question.  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).  Do not write outside the box around each page or on blank pages.  Show all necessary working; otherwise marks for method may be lost.  Do all rough work in this book. Cross through any work that you do not want to be marked. Information  The marks for questions are shown in brackets.  The maximum mark for this paper is 100. Advice  Unless stated otherwise, you may quote formulae, without proof, from the booklet.  You do not necessarily need to use all the space provided. 7357/1 Answer all questions in the spaces provided. 1 Find the coefficient of x7 in the expansion of (2x — 3)7 Circle your answer. —2187 —128 2 128 [1 mark] box dy 2 Given that y = 2x find d x Circle your answer. [1 mark] dy d x = 5x 2 dy d x = 6x 2 dy x4 d x = 2 dy 3 d x = 6x 3 The curve with equation y ln x is transformed by a stretch parallel to the x-axis with scale factor 2 Find the equation of the transformed curve. box Circle your answer. y = 1 ln x y = 2 ln x y = ln x y = ln 2x [1 mark] 4 Given that y is a small angle, find an approximation for cos 2y Circle your answer. y2 2 [1 mark] 2 2 1 — 2 2 — 2y 1 — 2y 1 — y