2020 paper 1.pdf - Please write clearly in block capitals....

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7357/1PB/Jun20/E7(JUN207357101)A-levelMATHEMATICSPaper 1Wednesday 3 June 2020AfternoonTime allowed: 2 hoursMaterialslYou must have the AQA Formulae for A‑level Mathematics booklet.lYou should have a graphical or scientific calculator that meets therequirements of the specification.InstructionslUse black ink or black ball‑point pen.Pencil should only be used for drawing.lFill in the boxes at the top of this page.lAnswerallquestions.lYou 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 endof this book.Write the question number against your answer(s).lShow all necessary working; otherwise marks for method may be lost.lDo all rough work in this book.Cross through any work that you do not wantto be marked.InformationlThe marks for questions are shown in brackets.lThe maximum mark for this paper is 100.AdvicelUnless stated otherwise, you may quote formulae, without proof, from thebooklet.lYou do not necessarily need to use all the space provided.Please write clearly in block capitals.Centre numberCandidate numberSurname________________________________________________________________________Forename(s)________________________________________________________________________Candidate signature________________________________________________________________________For Examiner’s UseQuestionMark123456789101112131415TOTALI declare this is my own work.
2Answerallquestions in the spaces provided.1The first three terms, in ascending powers ofx, of the binomial expansion of(9þ2x)12are given by(9þ2x)12±aþx3²x254whereais a constant.1 (a)State the range of values ofxfor which this expansion is valid.Circle your answer.[1 mark]jxj<29jxj<23jxj<1jxj<921 (b)Find the value ofa.Circle your answer.[1 mark]1239Jun20/7357/1Do not writeoutside thebox(02)
32A student is searching for a solution to the equationf(x)¼0He correctly evaluatesf(²1)¼ ²1 andf(1)¼1and concludes that there must be a root between²1 and 1 due to the change of sign.Select the functionf(x) for which the conclusion isincorrect.Circle your answer.Do not writeoutside thebox
3The diagram shows a sectorOABof a circle with centreOand radius 2B2AOθThe angleAOBisyradians and the perimeter of the sector is 6Find the value ofyCircle your answer.[1 mark]1ffiffiffi3p23Turn over for the next questionJun20/7357/1Turn overs(03)
44 (a)Sketch the graph ofy¼4² j2x²6jyxO[3 marks]4 (b)Solve the inequality4² j2x²6j>2[2 marks]____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Do not writeoutside theboxJun20/7357/1(04)
55Prove that, for integer values ofnsuch that 0³n<42nþ2>3n[2 marks]___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Turn over for the next questionDo not writeoutside theboxJun20/7357/1Turn overs(05)

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Natural logarithm

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