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Download Actual 2024 AQA A-level MATHEMATICS 7357/3 Paper 3 Merged Question Paper + Mark Scheme Ac and more Exams Mathematics in PDF only on Docsity!
Actual 2024 AQA A-level MATHEMATICS 7357/3 Paper 3 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. A-level MATHEMATICS Paper 3 Thursday 20 June 2024 Afternoon Time allowed: 2 hours Materials For Examiner’s Use e You must have the AQA Formulae for A-level Mathematics booklet. . e You should have a graphical or scientific calculator that meets the Question [INES requirements of the specification. ; 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. 7 e 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). 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 1 to be marked 12 Information ag e The marks for questions are shown in brackets. 14 e The maximum mark for this paper is 100. 15 16 Advice 17 e Unless stated otherwise, you may quote formulae, without proof, from 18 the booklet. 19 e You do not necessarily need to use all the space provided. TOTAL LL aerh IML Do not write outside the Section A Pox Answer all questions in the spaces provided. Each of the series below shows the first four terms of a geometric series. Identify the only one of these geometric series that is convergent. [1 mark] Tick (Vv) one box. 0.1+0.2+04+08+... 1-14+1-1+... 128 — 64+ 32-16+... 14+2+4+8+... Gidun24/7357/3, 2 Do not write outside the 3 One of the graphs shown below cannot have an equation of the form box y=ar where a> 0 Identify this graph. Tick (Vv) one box. [1 mark] y oO x y oO x y 2 x y IML Gidun24/7357/3, 4 Do not write outside the 4 A curve has equation y = x4 + 2* Pox Find an expression for 2 ¥ [2 marks] Turn over for the next question Turn over > Gidun24/7357/3, 5 Do not write outside the box Turn over for the next question DO NOT WRITE/ON THIS PAGE ANSWER IN THE/SPACES PROVIDED Turn over > IML Gidun24/7357/3, 7 Do not write outside the box 6 (a) Find Jlex “= [3 marks] IML Gidun24/7357/3, 8 10 Do not write outside the £ The graphs with equations box y=2+3x—2x2 and x+y=1 are shown in the diagram below. yH2+3x- 2x? x+y=1 The graphs intersect at the points A and B 7 (a) On the diagram above, shade and label the region, R, that is satisfied by the inequalities O1 [2 marks] G/dun24/7357/3 10 11 Do not write outside the box T (b) Find the exact coordinates of A [3 marks] Turn over for the next question Turn over > 11 G/dun24/7357/3 11 13 Do not write outside the box 8 (b) Find the value of 7 [2 marks] Question 8 continues on the next page Turn over > 13 G/dun24/7357/3 13 14 Do not write outside the 8 (c) The oven reaches a temperature of 86 °C one minute after it is switched on. box 8 (c) (i) Find the value of &. [2 marks] 8 (c) (ii) Find the time it takes for the temperature of the oven to be within 1°C of its maximum. [2 marks] G/dun24/7357/3 14 16 Do not write outside the 9 Figure 1 below shows a circle. box Figure 1 The centre of the circle is P and the circle intersects the y-axis at Q as shown in Figure 1. The equation of the circle is x2+ y2= 12y — 8x — 27 9 (a) Express the equation of the circle in the form (ea + (y—bP=k where a, b and k are constants to be found. [3 marks] IMI G/dun24/7357/3 16 17 Do not write outside the box 9 (b) State the coordinates of P [1 mark] 9 (c) Find the y-coordinate of Q [2 marks] Question 9 continues on the next page Turn over > G/dun24/7357/3 17 19 Do not write outside the 10 It is given that box f(x) =S5x3 +x Use differentiation from first principles to prove that f"(x)=15x2 +1 [5 marks] Turn over for the next question Turn over > G/dun24/7357/3 19 20 Do not write outside the 11 The curve C with equation box y= (x2—8x) Inx is defined for x > 0 and is shown in the diagram below. The shaded region, R, lies below the x-axis and is bounded by C and the x-axis. Show that the area of R can be written as ptqin2 where p and q are rational numbers to be found. [10 marks] IMU G/dun24/7357/3 20 
