AQA _ A Level Mathematics Paper 2_2020

A-level MATHEMATICS Paper 2 Wednesday 10 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 scientific calculator ...

A-level MATHEMATICS Paper 2 Wednesday 10 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 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. 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 19 TOTAL I declare this is my own work.2 Section A Answer all questions in the spaces provided. 1 Which one of these functions is decreasing for all real values of x? Circle your answer. [1 mark] f (x) ¼ ex f (x) ¼ e1x f (x) ¼ ex1 f (x) ¼ ex 2 Which one of the following equations has no real solutions? Tick (3) one box. [1 mark] cot x ¼ 0 ln x ¼ 0 jx þ 1j ¼ 0 sec x ¼ 0 Jun20/7357/2 Do not write outside the box (02)3 3 Find the coefficient of x2 in the binomial expansion of 2x 3  x 8 [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over for the next question Do not write outside the box Jun20/7357/2 Turn over s (03)4 4 Using small angle approximations, show that for small, non-zero, values of x x tan 5x cos 4x 1  A where A is a constant to be determined. [4 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box (04) Jun20/7357/2DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED 5 Turn over for the next question Do not write outside the box Jun20/7357/2 Turn over s (05)6 5 Use integration by substitution to show that ð6 1 4 x ffiffiffiffiffiffiffiffiffiffiffiffiffiffi p4x þ 1 dx ¼ 875 12 Fully justify your answer