AQA A-level MATHEMATICS 7357/3 Paper 3 Question Paper + Mark scheme (Merged) GRADE A+

AQA A-level MATHEMATICS 7357/3 Paper 3 Question Paper + Mark scheme (Merged) June 2021 Version: 1.0 Final 7357/3 PB/Jun21/E5 (JUN217357301) A-level MATHEMATICS Paper 3 Time allowed: 2 hours Materials l You m ...

AQA A-level MATHEMATICS 7357/3 Paper 3 Question Paper + Mark scheme (Merged) June 2021 Version: 1.0 Final 7357/3 PB/Jun21/E5 (JUN217357301) A-level MATHEMATICS Paper 3 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 TOTAL I declare this is my own work. 2 Section A Answer all questions inthespacesprovided. 1 The graphof y ¼ arccos x is shown. P x y State thecoordinatesoftheendpoint P. Circle youranswer. [1 mark] (p, 1)(1, p)  p 2 , 1   1, p 2   Jun21/7357/3 Do notwrite outside the box (02) 3 2 Simplify fully (x þ 3)(6  2x) (x  3)(3 þ x) for x 6¼ 3 Circle youranswer. [1 mark] 2 2 (6  2x) (x  3) (2x  6) (x  3) 3 f (x) ¼ 3x2 Obtain lim h!0 f (x þ h)  f (x) h Circle youranswer. [1 mark] 3h2 h x3 3(x þ h)2  3x2 h 6x Turn overforthenextquestion Do notwrite outside the box Jun21/7357/3 Turn over s (03) 4 4 (a) Show thatthefirstthreeterms,indescendingpowersof x, oftheexpansionof (2x  3)10 are givenby 1024x10 þ px9 þ qx8 where p and q are integerstobefound. [3 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 4 (b) Find theconstanttermintheexpansionof 2x  3 x  10 [2 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Do notwrite outside the box Jun21/7357/3 (04) 5 5 A gardeneriscreatingflowerbedsintheshapeofsectorsofcircles. The gardenerusesanedgingstriparoundtheperimeterofeachoftheflowerbeds. The costoftheedgingstripis£1.80permetreandcanbepurchasedforanylength. One oftheflowerbedshasaradiusof5metresandanangleatthecentreof 0.7 radiansasshowninthediagrambelow. 5 m 0.7 5 (a)(i) Find theareaofthisflowerbed. [2 marks]