AQA _ A Level Mathematics Paper 3_2020

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A-level MATHEMATICS Paper 3 Friday 12 June 2020 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 sci... entific 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. 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 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 123456789 10 11 12 13 14 15 16 17 18 TOTAL I declare this is my own work.2 Section A Answer all questions in the spaces provided. 1 Given that ð010 f (x) dx ¼ 7 deduce the value of ð010f (x) þ 1 dx Circle your answer. [1 mark] 3 7 8 17 2 Given that 6 cos y þ 8 sin y  R cos (y þ a) find the value of R. Circle your answer. [1 mark] 6 8 10 14 Jun20/7357/3 Do not write outside the box (02)3 3 Determine which one of these graphs does not represent y as a function of x. Tick (3) one box. [1 mark] x y x y x y x y Do not write outside the box Jun20/7357/3 Turn over s (03)4 4 p(x) ¼ 4x3 15x2 48x 36 4 (a) Use the factor theorem to prove that x 6 is a factor of p(x). [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 4 (b) (i) Prove that the graph of y ¼ p(x) intersects the x-axis at exactly one point. [4 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box (04) Jun20/7357/35 _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 4 (b) (ii) State the coordinates of this point of intersection. [1 mark] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over for the next question Do not write outside the box Jun20/7357/3 Turn over s (05)6 5 The number of radioactive atoms, N, in a sample of a sodium isotope after time t hours can be modelled by N ¼ N 0ekt where N 0 is the initial number of radioactive atoms in the sample and k is a positive constant. The model remains valid for large numbers of atoms. 5 (a) It takes 15.9 hours for half of the sodium atoms to decay. Determine the number of days required for at least 90% of the number of atoms in the original sample to decay. [5 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box (06) Jun20/7357/37 5 (b) Find the percentage of the atoms remaining after the first week. Give your answer to two significant figures [Show More]

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