Actual 2024 AQA AS MATHEMATICS 7356/1 Paper 1 Merged Question Paper + Mark Scheme Actual, Exams of Mathematics

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Actual 2024 AQA AS MATHEMATICS 7356/1 Paper 1 Merged Question Paper + Mark Scheme AQA = 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 a 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 Mark requirements of the specification. 4 Instructions Z e Use black ink or black ball-point pen. Pencil should only be used for drawing. g Fill in the boxes at the top of this page. 4 Answer all questions. 5 6 7 8 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). 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 3 e The marks for questions are shown in brackets. 14 e The maximum mark for this paper is 80. 15 Advice 16 e Unless stated otherwise, you may quote formulae, without proof, from 17 the booklet. 48 e You do not necessarily need to use all the space provided. 19 TOTAL TT et Do not write outside the Section A Pox Answer all questions in the spaces provided. 1 It is given that tan 6° = k, where & is a constant. Find tan (0 + 180)° Circle your answer. [1 mark] 1 1 —k = = k k k . _ 2 Curve C has equation y= @1pP State the equations of the asymptotes to curve C Tick (Vv) one box. [1 mark] x=Oandy=0 x=Oandy=1 x=1andy=0 x=1andy=1 IML GiJun24/7356/1 2 Do not write outside the 4 (a) (i) By using a suitable trigonometric identity, show that the equation box sin 0 tan @=4 cos @ can be written as tan2 0=4 [1 mark] 4 (a) (ii) Hence solve the equation sin @ tan @=4 cos @ where 0° < @ < 360° Give your answers to the nearest degree. [3 marks] MMT GiJun24/7356/1 4 Do not write outside the 4 (b) Deduce all solutions of the equation box sin 3a tan 3a = 4 cos 3a where 0° IMI GiJun24/7356/1 5 Do not write outside the 6 Determine the set of values of x which satisfy the inequality Pox 3x2 + 3x >x+6 Give your answer in exact form using set notation. [4 marks] Turn over for the next question Turn over > AM GiJun24/7356/1 7 Do not write outside the £ 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] AMM GiJun24/7356/1 8 10 Do not write outside the 8 It is given that box Inx-Iny=3 8 (a) Express x in terms of y in a form not involving logarithms. [3 marks] 8 (b) Given also that xt+y=10 find the exact value of y and the exact value of x [3 marks] GiJun24/7356/1 10 11 Do not write outside the 9 A curve has equation y = f(x) where Pox 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] v 10 1) x Turn over > IMI GiJun24/7356/1 11 13 Do not write outside the box 11 It is given that for the continuous function g e g(1)=0 e g(4)=0 © g(x) =2-5 11 (a) Determine the nature of each of the turning points of g Fully justify your answer. [3 marks] 11 (b) Find the set of values of x for which g is an increasing function. [2 marks] Turn over > wu a 14 Do not write outside the 12 The monthly mean temperature of a city, T degrees Celsius, may be modelled by the Pox 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] GiJun24/7356/1 14 16 Do not write outside the Section B Pox Answer all questions in the spaces provided. 13 A particle is moving in a straight line with constant acceleration a m s~2 The particle’s velocity, v m s~1, varies with time, r seconds, so that v=3-4t Deduce the value of a Circle your answer. [1 mark] IMI GiJun24/7356/1 16 17 Do not write outside the 14 Two forces, F, = 3i + 2j newtons and F2 = i— 3j newtons, are added together to find a box resultant force, R newtons. This vector addition can be represented using a diagram. Identify the diagram below which correctly represents this vector addition. Tick (Vv) one box. [1 mark] F. F. tw oa / \r, } R 7 R rA_/ J J 1 1 F F Ww a \e [ FA / J J iT 1 Turn over for the next question Turn over > IMI 17 GiJun24/7356/1 17 19 Do not write outside the 15 (b) A student claims that box “The displacement of the particle is less than the distance travelled.” State the range of values of t for which this claim is true. [1 mark] Turn over for the next question Turn over > IMI 9 GiJun24/7356/1 19 20 Do not write outside the box 16 In this question use g = 9.8 ms-2 A ball is launched vertically upwards from the Earth’s surface with velocity um s~1 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] GiJun24/7356/1 20 IMU