Download 2024 AQA A-level MATHEMATICS 7357/1 Paper 1 Merged Question Paper + Mark Scheme Actual 20 and more Exams Mathematics in PDF only on Docsity!
Actual 2024 AQA A-level MATHEMATICS 7357/1 Paper 1 Merged Question Paper + Mark Scheme AQA va Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature | declare this is my own work. A-level MATHEMATICS Paper 1 Tuesday 4 June 2024 Afternoon Time allowed: 2 hours Materials ae e You must have the AQA Formulae for A-level Mathematics booklet. For Examiner's Use e You should have a graphical or scientific calculator that meets the Question [Eas requirements of the specification. 1 2 Instructions 3 e Use black ink or black ball-point pen. Pencil should only be used for drawing. 4 e Fill in the boxes at the top of this page. 5 e Answer all questions. e You must answer each question in the space provided for that question. 6 e If you need extra space for your answer(s), use the lined pages at the end of 7 this book. Write the question number against your answer(s). 8 e Do not write outside the box around each page or on blank pages. 9 e Show all necessary working; otherwise marks for method may be lost. 10 e Do all rough work in this book. Cross through any work that you do not want to be marked. M 12 Information 13 e The marks for questions are shown in brackets. 14 e The maximum mark for this paper is 100. 15 Advice 16 e Unless stated otherwise, you may quote formulae, without proof, from the 7 booklet. 18 e You do not necessarily need to use all the space provided. 19 20 TOTAL a eh Do not write outside the Answer all questions in the spaces provided. box 1 Find the coefficient of x in the expansion of (4x8 —5x2 + 3x—2)(x5+4x +1) Circle your answer. [1 mark] -5 2 7 11 IML Gidun24/7357/1 2 IML The expression can be written as State the value of A Circle your answer. 12x2+ 3x +7 3x-5 Cc Ax+B+ 3x5 [1 mark] GiJun24/7357/1 Do not write outside the box Do not write outside the box 4 One of the diagrams below shows the graph of y = arccos x Identify the graph of vy = arccos x Tick (¥) one box. [1 mark] y y x 2 =| 0 1 x 4 O x y y un 2) u3 2 O 4 x O 1 x Turn over for the next question Turn over > 05 Gidun24/7357/1 5 Do not write outside the di . box 6 Use the chain rule to find SY when y= (x3 + 5x)? dx [2 marks] Turn over for the next question Turn over > AM Gidun24/7357/1 7 Do not write outside the £ Show that box 3+V8n 2n can be written as 4n—3+2n 2n-1 where z is a positive integer. [4 marks] Gidun24/7357/1 8 10 Do not write outside the 9 (a) Show that, for small values of @ measured in radians box cos 49+ 2sin30—tan 20~= 4+ BO+ Cé2 where A, B and C are constants to be found. [3 marks] GiJun24/7387/1 10 11 Do not write outside the 9 (b) Use your answer to part (a) to find an approximation for box cos 0.28 + 2 sin 0.21 — tan 0.14 Give your answer to three decimal places. [2 marks] Turn over for the next question Turn over > 11 Gidun24/7357/1 11 10 (b) IM 13 Do not write outside the A school holds a raffle at its summer fair. Pox There are nine prizes. The total value of the prizes is £1260 The values of the prizes form an arithmetic sequence. The top prize has the highest value, and the bottom prize has the least value. The value of the top prize is six times the value of the bottom prize. Find the value of the top prize. [4 marks] Turn over > Gidun24/7357/1 13 11 14 (a) IMI 14 Do not write outside the It is given that box f(x) =x(x —a)(x —6) where 0
IM Gidun24/7357/1 17 19 Do not write outside the 13 (c) Given that 7 is a positive integer, use your answer to part (b) to explain why Pox 4n3 + 8n2 + 11n + 4 is never prime. [2 marks] Turn over for the next question Turn over > Gidun24/7357/1 19 20 Do not write outside the 14 (a) The equation box gS gb has a single solution, x =a By considering a suitable change of sign, show that a lies between 0 and 4 [2 marks] 14 (b) Show that the equation x3 = e6-2* can be rearranged to give x=3- 3 Inx [3 marks] IMM Gidun24/7357/1 20 
