AQA A-level MATHEMATICS 7357/3 Paper 3 Version: 1.0 Final PB/KL/Jun23/E7 7357/3QUESTION PAPER & MARKING SCHEME/ [MERGED] Mark scheme June 2023

AQA A-level MATHEMATICS 7357/3 Paper 3 Version: 1.0 Final PB/KL/Jun23/E7 7357/3 A-level MATHEMATICS Paper 3 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). 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 17 TOTAL I declare this is my own work. l 2 Section A Answer all questions in the spaces provided. 1 The graph of y ¼ f (x) is shown below. O y x One of the four equations listed below is the equation of the graph y ¼ f (x) Identify which one is the correct equation of the graph. Tick (3) one box. [1 mark] y ¼ jx þ 2j þ 3 y ¼ jx þ 2j  3 y ¼ jx  2j þ 3 y ¼ jx  2j  3 Jun23/7357/3 Do not write outside the box (02) 3 2 The trapezium rule is used to estimate the area of the shaded region in each of the graphs below. Identify the graph for which the trapezium rule produces an overestimate. Tick (3) one box. [1 mark] O x y O x y O x y O x y Do not write outside the box Jun23/7357/3 Turn over s (03) 4 3 A curve with equation y ¼ f (x) passes through the point (3, 7) Given that f ’(3) ¼ 0 find the equation of the normal to the curve at (3, 7) Circle your answer. [1 mark] y ¼ 7 3 x y ¼ 0 x ¼ 3 x ¼ 7 4 Express 5  ffiffiffi x p3 x2 in the form 5x p  xq where p and q are constants. [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box Jun23/7357/3 (04) 5 5 A curve has equation y ¼ 3e2x Find the gradient of the curve at the point where y ¼ 1