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Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature | declare this is my own work. AS MATHEMATICS Paper 1 Thursday 16 May 2024 Afternoon Time allowed: 1 hour 30 minutes Materials ner « You must have the AQA Formulae for A-level Mathematics booklet. For Examiners Use e You should have a graphical or scientific calculator that meets the Question Mark requirements of the specification. 4 Instructions 5 e Use black ink or black ball-point pen. Pencil should only be used for drawing. Fill in the boxes at the top of this page. 4 e Answer all questions. 5 e You must answer each question in the space provided for that question. 6 « 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. e Show all necessary working; otherwise marks for method may be lost. 9 e Do all rough work in this book. Cross through any work that you do not want 10 to be marked. 11 12 Information 13 e The marks for questions are shown in brackets. 14 © The maximum mark for this paper is 80. 15 Advice 16 e Unless stated otherwise, you may quote formulae, without proof, fram 17 the booklet. 18 e You do not necessarily need to use all the space provided. 19 TOTAL Jou 7356101 GILMJun24/G4004/E9 7356/1 Section A Answer all questions in the spaces provided. 1 It is given that tan @° = k, where / is a constant. Find tan (@ + 180)° Circle your answer. 1 1 —k - k k , _-_1 2 Curve C has equation y ete State the equations of the asymptotes to curve C Tick (“) one box. x=QOandy=0 x=OQOandy=1 x-1andy-0 x=1andy=1 O2 [1 mark] [1 mark] GiJun24/7356/1 Do not write outside the box Do not write outside the 4 (a) (i) By using a suitable trigonometric identity, show that the equation box sin 6 tan @=4 cos @ can be written as tan? @=4 [1 mark] 4 (a) (ii) Hence solve the equation sin @ tan 0=4 cos @ where 0° <@< 360° Give your answers to the nearest degree. [3 marks] 04 GiJun24/7356/1 Do not write outside the 4 (b) Deduce all solutions of the equation box sin 3a tan 3a = 4 cos 3a where 0° < @ < 180° Give your answers to the nearest degree. [3 marks] Turn over for the next question Turn over > 05 GiJun24/7356/1 Do not write outside the 6 Determine the set of values of x which satisfy the inequality box 3x2 + 3x >x+6 Give your answer in exact form using set notation. [4 marks] Turn over for the next question Turn over > 07 GiJun24/7356/1 Do not write outside the 7 A triangular field of grass, ABC, has boundaries with lengths as follows: box AB = 234m BC =225m AC =310m The field is shown in the diagram below. B 225m Cc 234m 310m 7 (a) Find angle A [2 marks] 08 GiJun24/7356/1 10 Do not write outside the 8 It is given that box Inx—Iny=3 8 (a) Express x in terms of » in a form not involving logarithms. [3 marks] 8 (b) Given also that xty=10 find the exact value of » and the exact value of x. [3 marks] 10 GiJun24/7356/1 11 9 Accurve has equation y = f(x) where f(x) =x (6 — x) 9 (a) Find f’(x) [2 marks] 9 (b) The diagram below shows the graph of y = f(x) On the same diagram sketch the gradient function for this curve, stating the coordinates of any points where the gradient function cuts the axes. [3 marks] ya 10 > Oo x Turn over > 11 GiJun24/7356/1 Do not write outside the ‘box 1 11 (a) 11 (b) 13 13 It is given that for the continuous function g e g(x) =2x-5 Determine the nature of each of the turning points of g Fully justify your answer. [3 marks] Find the set of values of x for which g is an increasing function. [2 marks] Turn over > GiJun24/7356/1 Do not write outside the box 14 Do not write outside the box 12 The monthly mean temperature of a city, 7 degrees Celsius, may be modelled by the equation T= 15 + 8sin (30m — 120)° where m is the month number, counting January = 1, February = 2, through to December = 12 12 (a) Using this model, calculate the monthly mean temperature of the city for May, the fifth month. [2 marks] 12 (b) Using this model, find the month with the highest mean temperature. [2 marks] 12 (c) Climate change may affect the parameters, 8, 30, 120 and 15, used in this model. 12 (c) (i) State, with a reason, which parameter would be increased because of an overall rise in temperatures. [1 mark] 14 GiJun24/7356/1 16 Do not write outside the Section B box Answer all questions in the spaces provided. 13 A particle is moving in a straight line with constant acceleration ams 2 The particle’s velocity, v m s~1, varies with time, t seconds, so that v=3-4t Deduce the value of a Circle your answer. [1 mark] 16 GiJun24/7356/1 17 Do not write outside the ‘box 14 Two forces, F, = 3i + 2j newtons and F2 = i— 3j newtons, are added together to find a resultant force, R newtons. This vector addition can be represented using a diagram. Identify the diagram below which correctly represents this vector addition. Tick (“) one box. [1 mark] Fy Fy GiJun24/7356/1 17 15 (b) 19 A student claims that “The displacement of the particle is less than the distance travelled.” State the range of values of ¢ for which this claim is true. [1 mark] Turn over for the next question Turn over > GiJun24/7356/1 Do not write outside the ‘box 20 16 In this question use g-9.8ms 2 A ball is launched vertically upwards from the Earth’s surface with velocity um s~? The ball reaches a maximum height of 15 metres. You may assume that air resistance can be ignored. Find the value of w [3 marks] 20 GiJun24/7356/1 Do not write outside the ‘box 
