Official June 2024 AQA A-level MATHEMATICS 7357/3 Paper 3 Merged Question Paper + Mark Scheme Ace your Mocks!!! G/LM/Jun24/G4005/E6 7357/3 (JUN247357301) A-level MATHEMATICS Paper 3 Thursday 20 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 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/Jun24/7357/3 Section A Answer all questions in the spaces provided. 1 Each of the series below shows the first four terms of a geometric series. Identify the only one of these geometric series that is convergent. [1 mark] Tick () one box. 0.1 + 0.2 + 0.4 + 0.8 + … 1 – 1 + 1 – 1 + … 128 – 64 + 32 – 16 + … 1 + 2 + 4 + 8 + … 3 Do not write outside the box (03) G/Jun24/7357/3 Turn over U 2 The quadratic equation 4x2 + bx + 9 = 0 has one repeated real root. Find b Circle your answer. [1 mark] b = 0 b = ±12 b = ±13 b = ±36 Turn over for the next question 4 Do not write outside the box (04) G/Jun24/7357/3 3 One of the graphs shown below cannot have an equation of the form y = ax where a > 0 Identify this graph. Tick () one box. [1 mark] y O x y O x 5 Do not write outside the box (05) G/Jun24/7357/3 Turn over U 4 A curve has equation y = x4 + 2x Find an expression for dy dx [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over for the next question 6 Do not write outside the box (06) G/Jun24/7357/3 5 The diagram below shows a sector of a circle OAB. The chord AB divides the sector into a triangle and a shaded segment. Angle AOB is π 6 radians. The radius of the sector is 18 cm. Show that the area of the shaded segment is k (π – 3) cm2 where k is an integer to be found. [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over U 7 (07) G/Jun24/7357/3 Do not write outside the box Turn over for the next question DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED 8 Do not write outside the box (08) G/Jun24/7357/3 6 (a) Find ∫(6x2 – 5 √x) dx [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 9 Do not write outside the box (09) G/Jun24/7357/3 Turn over U 6 (b) The gradient of a curve is given by dy dx = 6x2 – 5 √x The curve passes through the point (4, 90). Find the equation of the curve. [2 marks]