A Level Mathematics Paper 1_2020 | AQA_2020_A Level Mathematics Paper 1

A-level MATHEMATICS Paper 1 Wednesday 3 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 t ...

A-level MATHEMATICS Paper 1 Wednesday 3 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 TOTAL I declare this is my own work.2 Answer all questions in the spaces provided. 1 The first three terms, in ascending powers of x, of the binomial expansion of (9 þ 2x) 12 are given by (9 þ 2x) 12 a þ x 3  x2 54 where a is a constant. 1 (a) State the range of values of x for which this expansion is valid. Circle your answer. [1 mark] jxj < 2 9 jxj < 2 3 jxj < 1 jxj < 9 2 1 (b) Find the value of a. Circle your answer. [1 mark] 1 2 3 9 Jun20/7357/1 Do not write outside the box (02)3 2 A student is searching for a solution to the equation f (x) ¼ 0 He correctly evaluates f (1) ¼ 1 and f (1) ¼ 1 and concludes that there must be a root between 1 and 1 due to the change of sign. Select the function f (x) for which the conclusion is incorrect. Circle your answer. [1 mark] f (x) ¼ 1 x f (x) ¼ x f (x) ¼ x3 f (x) ¼ 2x þ 1 x þ 2 3 The diagram shows a sector OAB of a circle with centre O and radius 2 B 2 A θ O The angle AOB is y radians and the perimeter of the sector is 6 Find the value of y Circle your answer. [1 mark] 1 ffiffiffi p3 2 3 Turn over for the next question Do not write outside the box Jun20/7357/1 Turn over s (03)4 4 (a) Sketch the graph of y ¼ 4  j2x  6j y O x [3 marks] 4 (b) Solve the inequality 4  j2x  6j > 2 [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box (04) Jun20/7357/15 5 Prove that, for integer values of n such that 0  n < 4 2nþ2 > 3n [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over for the next question Do not write outside the box Jun20/7357/1 Turn over s (05)6 6 Four students, Tom, Josh, Floella and Georgia are attempting to complete the indefinite integral ð 1x dx for x > 0 Each of the students’ solutions is shown below: Tom ð 1x dx ¼ ln x Josh ð 1x dx ¼ k ln x Floella ð 1x dx ¼ ln Ax Georgia ð 1x dx ¼ ln x þ c 6 (a) (i) Explain what is wrong with Tom’s answer. [1 mark] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 6 (a) (ii) Explain what is wrong with Josh’s answer. [1 mark] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 6 (b) Explain why Floella and Georgia’s answers are equivalent. [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do not write outside the box (06) Jun20/7357/17 7 Consecutive terms of a sequence are related by u nþ1 ¼ 3  (un)2 7 (a) In the case that u 1 ¼ 2 7 (a) (i) Find u 3 [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 7 (a) (ii) Find u 50 [1 mark] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 7 (b) State a different value for u 1 which gives the same value for u 50 as found in part (a)(ii). [1 mark] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over for the next question Do not write outside the box Jun20/7357/1