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Download ACTUAL AQA 2025 AQA AS LEVEL Mathematics Paper 1 JUNE 2025 WORKED EXAM SOLUTIONS and more Exams Mathematics in PDF only on Docsity!
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 15 May 2025 Afternoon Time allowed: 1 hour 30 minutes Materials For Examiner's Use e You must have the AQA Formulae for A-level Mathematics booklet. Question fae e You should have a graphical or scientific calculator that meets the 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. 6 e You must answer each question in the space provided for that question. 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 Pr to be marked. 12 Information 13 e The marks for questions are shown in brackets. 14 e The maximum mark for this paper is 80. 15 Advice he e Unless stated otherwise, you may quote formulae, without proof, from the booklet. 18 e You do not necessarily need to use all the space provided. 19 20 21 TOTAL IM LA N 2 GILM/Jun25/G4006/V6 "7356/1 1 1 Answer all questions in the spaces provided. Identify the expression that is equivalent to tan x Circle your answer. sin?x + cos2x Find the value of log, z Circle your answer. —2 02 Nis Section A sin2x — cos?x cos x sinx Nisa sinx cosx Do not write outside the box [1 mark] [1 mark] tyrionpapers.com G/Jun25/7356/1 2 5 Solve the equation 2tan 30-3=0 for 0° <0 < 180° Give your answers to the nearest degree. [3 marks] Jayven claims that for two real numbers a and b if a>b, then it must be true that ; > By using a counter example, show that Jayven is not correct. [2 marks] IMI tyrionpapers.com G/Jun25/7356/1 Do not write outside the box Do not write outside the box 6 It is given that p =log,x and g =log,y tog, Ly 6 (a) Express in terms of p and g [2 marks] 6 (b) Express log, (16x° yy) in terms of p and g Give your answer in a form not involving logarithms. [3 marks] Turn over > IMT a 05 G/Jun25/7356/1 5 Do not write outside the Sketch the graph of box y=(x—k)(x + 2k) where k is a positive constant. Label the coordinates of the points where the graph meets the axes. [4 marks] y O x Turn over for the next question Turn over > ll | ll ll tyrionpapers.com 07 G/Jun25/7356/1 7 Do not write outside the 9 (a) Find, in ascending powers of x, the first three terms in the expansion of Pox (1-5x)" [3 marks] IM a 0 8 G/Jun25/7356/1 8 10 Do not write outside the 10 A curve has the equation box y= and the point P lies on the curve, as shown in the diagram. ¥ O x The tangent to the curve at P is parallel to the line with equation x —9y = 23 Find the x-coordinate of P [5 marks] IM a 10 G/Jun25/7356/1 10 11 Do not write outside the box Turn over for the next question Turn over > Hi ll l ll tyrionpapers.com 11 G/Jun25/7356/1 11 13 Do not write outside the 11 (a) Expand x(x —2)(x + 4) box [1 mark] 11 (b) Show that 2 x(x — 2)(x +4) dx = 36 4 Fully justify your answer. [4 marks] Question 11 continues on the next page Turn over > Hi lll | ll tyrionpapers.com 13 G/Jun25/7356/1 13 14 Do not write outside the 11 (c) The curve C has equation box v= x(x—2)(x+ 4) A sketch of C is shown in the diagram. Ca 4 0 2 x 11 (c) (i) Explain why your answer to part (b) will not give the total area of the shaded region bounded by C and the x-axis. [1 mark] HI | ll ll tyrionpapers.com 14 G/Jun25/7356/1 14 12 (a) 12 (b) 16 It is given that 40, 40! Cee 18!p! Write down the value of p [1 mark] Use the result from part (a) to show that 6.5 _23 C47 q where q is an integer to be found. [2 marks] 16 tyrionpapers.com G/Jun25/7356/1 Do not write outside the box 16 17 Do not write outside the 13 A computer game awards points to a player based on the time taken to complete box a level. The points awarded decrease as the time taken to complete a level increases. Rebekah believes that the points awarded, P, can be modelled by the equation P= Ae where t is the time, in seconds, taken to complete the level and 4 and & are constants. 13 (a) Explain, in context, the meaning of the value of A [1 mark] 13 (b) Show that InP=InA+kt [2 marks] Question 13 continues on the next page Turn over > Hi | ll ll tyrionpapers.com 17 G/Jun25/7356/1 17 19 Do not write outside the 13 (d) Rebekah scores 20 points for completing a particular level. box Find, to the nearest second, the time taken to complete this level. [3 marks] END OF SECTION A Turn over for Section B Turn over > IM — "1 9 G/Jun25/7356/1 19 20 Do not write outside the Section B Pox Answer all questions in the spaces provided. 14 A particle of mass 2 kg is moving on a smooth horizontal surface under the action of a single horizontal force of 5 N Find the acceleration of the particle. Circle your answer. [1 mark] 04ms? 25ms? 10ms? 24.5ms? 20 tyrionpapers.com G/Jun25/7356/1 20 
