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Download 1. Actual 2024 AQA A-level MATHEMATICS 7357/2 Paper 2 Merged Question Paper + Mark Scheme and more Exams Mathematics in PDF only on Docsity!
Actual 2024 AQA A-level MATHEMATICS 7357/2 Paper 2 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 2 Tuesday 11 June 2024 Afternoon Time allowed: 2 hours Materials For Examiner’s Use e You must have the AQA Formulae for A-level Mathematics booklet Question Mark e You should have a graphical or scientific calculator that meets the 1 requirements of the specification. 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. 7 e If you need extra space for your answer(s), use the lined pages at the end of 8 this book. Write the question number against your answer(s). 9 e Do not write outside the box around each page or on blank pages. 10 e Show all necessary working; otherwise marks for method may be lost. 4 e Do all rough work in this book. Cross through any work that you do not want 42 to be marked. 13 Information if e The marks for questions are shown in brackets. 15 e The maximum mark for this paper is 100. & Advice 18 e Unless stated otherwise, you may quote formulae, without proof, from 19 the booklet. 20 e You do not necessarily need to use all the space provided. 21 TOTAL a ae Do not write outside the Section A Pox Answer all questions in the spaces provided. 1 One of the equations below is the equation of a circle. Identify this equation. [1 mark] Tick (Vv) one box. («+ 1)2—(v+ 2)? =-36 (x + 1)2—(v+ 2)2 = 36 (x + 1)2 + (y + 2)2 =-36 (x + 1)2 + (vp + 2)2 = 36 IML GiJun24/7357/2 2 IML Solve the inequality Tick (“) one box. {xix<1} U fxix>4} {xix<1} 9 fxix>4} {xix<1}U {fxix24} {xix< 1} fxix24} (1 —x)(x-4) <0 [1 mark] GiJun24/7357/2 Do not write outside the ‘box Do not write outside the 4 Use logarithms to solve the equation box 5x-2 = 71570 Give your answer to two decimal places. [3 marks] Turn over for the next question Turn over > GiJun24/7357/2 5 AM Do not write outside the It is given that box (2sin 6 + 3cos@)2 + (6sin@ — cos@)2 = 30 and that @ is obtuse. Find the exact value of sind. Fully justify your answer. [6 marks] Turn over > GiJun24/7357/2 7 7 (a) 7 (b) 7 (b) (i) AMM Do not write outside the On the first day of each month, Kate pays £50 into a savings account. box Interest is paid on the total amount in the account on the last day of each month. The interest rate is 0.2% At the end of the mth month, the total amount of money in Kate’s savings account is £7, Kate correctly calculates 7, and T, as shown below: T, = 50 x 1.002 = 50.10 Ty = (T; + 50) x 1.002 = ((50 x 1.002) + 50) x 1.002 =50 x 1.0022 + 50 x 1.002 = 100.30 Show that 73 is given by T3 = 50 x 1.0023 + 50 x 1.0022 + 50 x 1.002 [1 mark] Kate uses her method to correctly calculate how much money she can expect to have in her savings account at the end of 10 years. Find the amount of money Kate expects to have in her savings account at the end of 10 years. [3 marks] GiJun24/7357/2 8 10 Do not write outside the 8 A zookeeper models the median mass of infant monkeys born at their zoo, up to the box age of 2 years, by the formula y=ar blogigx where y is the median mass in kilograms, x is age in months and a and b are constants. The zookeeper uses the data shown below to determine the values of a and b. Age in months (x) 3 24 Median mass (y) 6.4 12 8 (a) The zookeeper uses the data for monkeys aged 3 months to write the correct equation 6.4=a+ blogyg3 8 (a) (i) Use the data for monkeys aged 24 months to write a second equation. [1 mark] 8 (a) (ii) Show that _ 56 be logio 8 [3 marks] GiJun24/7357/2 10 11 Do not write outside the box 8 (a) (iii) Find the value of a. Give your answer to two decimal places. [1 mark] Question 8 continues on the next question Turn over > 11 GiJun24/7357/2 11 13 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 > IM GiJun24/7357/2 13 14 Do not write outside the 9 (a) (i) Find the binomial expansion of (1 + 3x)-1 up to and including the term in x2 Pox [2 marks] 9 (a) (ii) Show that the first three terms in the binomial expansion of 1 2-—3x form a geometric sequence and state the common ratio. [5 marks] GiJun24/7357/2 14 16 Do not write outside the box 9 (c) (i) Using your answers to parts (a) and (b), find the binomial expansion of 12x (1 + 3x)(2 — 3x) up to and including the term in x2 [2 marks] 16 GiJun24/7357/2 16 17 Do not write outside the 9 (c) (ii) Find the range of values of x for which the binomial expansion of Pox 12x (1 + 3x)(2 — 3x) is valid. [1 mark] Turn over for the next question Turn over > GiJun24/7357/2 17 19 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 > IMI 9 GiJun24/7357/2 19 20 Do not write outside the 11 (a) A student states that 3 is the smallest value of & in the interval 3
