2023 AQA A-level MATHEMATICS 7357/2 Paper 2 Question Paper & Mark scheme (Merged) June 2023 [VERIFIED]

2023 AQA A-level MATHEMATICS 7357/2 Paper 2 Question Paper & Mark scheme (Merged) June 2023 [VERIFIED] A-level MATHEMATICS Paper 2 Tuesday 13 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. 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 PB/KL/Jun23/E6 7357/2 2 Section A Answer all questions in the spaces provided. 1 The graph of y ¼ ax 2 þ bx þ c has roots x ¼ 2 and x ¼ 5 , as shown in the diagram below. y O 2 5 x State the set of values of x which satisfy ax 2 þ bx þ c > 0 Tick (3) one box. [1 mark] fx : x < 2g ¨ fx : x > 5g fx : 0 < x < 2g ˙ fx : x > 5g fx : 2 < x < 5g fx : 2 > x > 5g Do not write outside the box (02) Jun23/7357/2 3 2 It is given that ð6 ð6 f (x) d x ¼ 20 and f (x) d x ¼ 10 0 3 ð 3 Find the value of f (x) d x 0 Circle your answer. [1 mark] 3 A circle has equation (x 5) 2 þ (y 13)2 ¼ 16 Find the radius of the circle. Circle your answer. [1 mark] Turn over for the next question Turn over s (03) Jun23/7357/2 Do not write outside the box 4 4 A curve has equation x 2 4 p x y ¼ 8 þ ffiffiffi 4 (a) Find an expression for dy d x [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 4 (b) The point P with coordinates (4, 10) lies on the curve. Find an equation of the tangent to the curve at the poin