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Download ACTUAL AQA 2025 AQA AS LEVEL Mathematics Paper 2 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 2 Friday 23 May 2025 Afternoon Time allowed: 1 hour 30 minutes Materials a e You must have the AQA Formulae for A-level Mathematics booklet. Troy Sean Ue e You should have a graphical or scientific calculator that meets the Question Mark requirements of the specification. 4 Instructions 3 e Use black ink or black ball-point pen. Pencil should only be used for drawing. e 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 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. 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 e The maximum mark for this paper is 80. 16 Advice 16 e Unless stated otherwise, you may quote formulae, without proof, from 17 the booklet. 18 e You do not necessarily need to use all the space provided. 19 20 21 TOTAL I A GILM/Jun25/G4006/V8 N 2 "7356/2 1 Section A Answer all questions in the spaces provided. Accurve C has equation y=(xta)? where a is a positive constant. Identify which one of the graphs represents C Tick (Vv) one box. [1 mark] [I —a Seas ll ll l ll tyrionpapers.com 02 Do not write outside the ABC is the cross-section of a triangular prism. box The length of AB is 6 cm and the length of AC is 10 cm as shown in the diagram. A 6cm 10cm The prism has length 20 cm and volume 500 cm? Find the size of the obtuse angle CAB Give your answer to the nearest degree. [4 marks] ll | ll ll tyrionpapers.com 04 G/Jun25/7356/2 4 4 4 (a) 4 (b) 4 (b) (i) 4 (b) (ii) Find the coordinates of the point of intersection of AB and L The equation of the line L is 2x + 3y= 24 Find the gradient of L [1 mark] Point A has coordinates (2, —2) and point B has coordinates (10, p), where p is an integer. The line L is the perpendicular bisector of the line AB Find the value of p [3 marks] [1 mark] IMT a 05 Solve the simultaneous equations x=2y-11 y= 2x2 dx +1 Fully justify your answer. [4 marks] ll | ll ll tyrionpapers.com 07 £ It is given that f(x) =3x2+ 3x-8 7 (a) Express f(x) in the form a(x +b? +e where a, b and c are constants to be found. [3 marks] 7 (b) (i) State the minimum value of 3sin29 + 3sind—8 [1 mark] IM a 0 8 10 Find the coordinates of the minimum point of the curve with equation y=x3—5x?-8x+2 Fully justify your answer. [8 marks] 10 tyrionpapers.com 10 11 Do not write outside the 9 It is given that box 3 | f(x)dx=8 41 3 9 (a) Write down the value of | 2f(x)dx 1 [1 mark] 3 9 (b) Write down the value of | (f(x) + 2)dx 1 [1 mark] 4 9 (c) Write down the value of | f(x —1)dx 2 [1 mark] Turn over for the next question Turn over > Hi ll l ll tyrionpapers.com 11 G/Jun25/7356/2 11 13 Do not write outside the 11 The equation box x*+(2k-1)x+4-2k=0 has two distinct real roots. Find the range of possible values for & [4 marks] Turn over > Hi lll | ll tyrionpapers.com 13 G/Jun25/7356/2 13 14 12 In the triangle ABC, the length of AB = 12 cm and the angle ABC is a right angle. The point D lies on AC such that BD is perpendicular to AC as shown in the diagram. Cc D 0 A 12cm B 12 12 (a) Showthat AC= —— cos [1 mark] 12 (b) Write down an expression for AD in terms of cos@ [1 mark] 12 — 12cos?0 12 (c) Hence show that CD = a an Gos. [2 marks] HI | ll ll tyrionpapers.com 14 14 16 Section B Answer all questions in the spaces provided. 13 The table shows the favourite sport of a group of students from years 12 and 13. football rugby netball tennis Total Year 12 57 30 36 2 125 Year 13 33 11 19 12 75 Total 90 41 55 14 200 A student is chosen at random. Find the probability that the student chosen is a year 12 student whose favourite sport is netball. Circle your answer. [1 mark] 0.18 0.275 0.288 0.44 Hi ll | ll tyrionpapers.com 16 16 14 17 Do not write outside the The events 4 and B are independent. Pox Itis given that P(4)=0.25 and P(B) =0.6 Find the value of P(4 M B) Circle your answer. [1 mark] 0 0.15 0.35 0.85 Turn over for the next question Turn over > IM tyrionpapers.com G/Jun25/7356/2 17 16 1 The table shows the probability distribution for a discrete random variable XY 19 x 0 1 4 P(X=x) 0.2—p 0.05 + 3p 4p 2p 2p Find the value of the constant p [2 marks] 9 Turn over for the next question Turn over > tyrionpapers.com GiJun25/7356/2 Do not write outside the box 19 20 17 The owner of a shop recorded the average daily wind speed in mph and the total sales of raincoats in pounds over a period of 6 months. The data from a random selection of 15 days from the 6-month period is shown in the scatter diagram. 450 °B 400 }—w C ; 350 D 300 E a e Daily 250 E eS sales of raincoats eH | (£) 200 ° e J K 150 t L N 2 A100 eA eM 50 re) 0 0 5 10 15 20 25, 30 Wind speed (mph) One of the points on the scatter diagram is an outlier. 17 (a) State the letter from the diagram which corresponds to this outlier. [1 mark] 17 (b) State the effect on the numerical value of the correlation coefficient if the outlier was removed from the data. [1 mark] IMU a 20 20 
