Partial preview of the text
Download Actual 2024 AQA AS MATHEMATICS 7356/2 Paper 2 Merged Question Paper + Mark Scheme Actual and more Exams Mathematics in PDF only on Docsity!
Actual 2024 AQA AS MATHEMATICS 7356/2 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. AS MATHEMATICS Paper 2 Thursday 23 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 2 Instructions g e Use black ink or black ball-point pen. Pencil should only be used for drawing. A Fill in the boxes at the top of this page. 5 6 7 8 Answer all questions. 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. 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 11 to be marked. 12 Information 18 e The marks for questions are shown in brackets. ibs e The maximum mark for this paper is 80. 15 16 Advice 17 e Unless stated otherwise, you may quote formulae, without proof, from the booklet. TOTAL e You do not necessarily need to use all the space provided. TT 3862 | Do not write outside the Section A Pox Answer all questions in the spaces provided. 1 Line L has equation Sy=4x+6 Find the gradient of a line parallel to line L Circle your answer. [1 mark] 5 at 4 5 4 5 5 4 2 One of the equations below is true for all values of x Identify the correct equation. Tick (“) one box. [1 mark] cos? x =-1 — sin2 x cos? x =—1 + sin2x cos?x=1—sin2x cos?x=1+ sin2x IML Gidun24/7356/2, 2 4 (a) 4 (b) 4 (c) IML Do not write outside the Curve C has equation y = 8sin x Pox Curve C is transformed onto curve C1 by a translation of vector [4] Find the equation of C1 [1 mark] Curve C is transformed onto curve C2 by a stretch of scale factor 4 in the y direction. Find the equation of C2 [1 mark] Curve C is transformed onto curve C3 by a stretch of scale factor 2 in the x direction. Find the equation of C3 [1 mark] Gidun24/7356/2, 4 Do not write outside the box 5 A student suggests that for any positive integer n the value of the expression 4n2+3 is always a prime number. Prove that the student's statement is false by finding a counter example. Fully justify your answer. [3 marks] Turn over for the next question Turn over > AMM Gidun24/7356/2, 5 Do not write outside the 6 (b) (ii) Find the value of a ae [3 marks] Turn over for the next question Turn over > AM GiJun24/7356/2 7 Do not write outside the 7 Point A has coordinates (4, 1) and point B has coordinates (—8, 5) Pox T (a) Find the equation of the perpendicular bisector of AB [5 marks] IML Gidun24/7356/2, 8 10 Do not write outside the 8 Prove that the graph of the curve with equation box 18 magi 8 y=x3 + 15x x has no stationary points. [5 marks] G/Jun24/7356/2 10 11 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 Gidun24/7356/2, 11 13 Do not write outside the 9 (b) On the diagram, the region enclosed between the curve and the line y = 2 is shaded. Pox Show that the area of this shaded region is g Fully justify your answer. [6 marks] Turn over for the next question Turn over > 13 G/Jun24/7356/2 13 14 Do not write outside the 10 A singer has a social media account with a number of followers. The singer releases a box new song and the number of followers grows exponentially. The number of followers, F, may be modelled by the formula F=aekt where ¢ is the number of days since the song was released and a and & are constants. e Two days after the song is released the account has 2050 followers. e Five days after the song is released the account has 9200 followers. On the graph below In F has been plotted against ¢ for these two pieces of data. A line has been drawn passing through these two data points. InF T T 4 a2 FT t I 9 aa | 8tH t t vg 6 1 Scr | 4 T | | | 34 aH | I | 1 | | | I O 1 2 3 4 5 t GiJun24/7356/2 14 16 Do not write outside the 10 (b) (i) Show that oF ep . [2 marks] 10 (b) (ii) Using the model, estimate the rate at which the number of followers is increasing 5 days after the song is released. [2 marks] 10 (c) The singer claims that 30 days after the song is released, the account will have more than a billion followers. Comment on the singer’s claim. [1 mark] END OF SECTION A 16 G/Jun24/7356/2 16 17 | Do not write outside the Section B Pox Answer all questions in the spaces provided. 11 The table below shows the daily salt intake, x grams, and the daily Vitamin C intake, y milligrams, for a group of 10 adults. Adult A B c D E F G H | J x 5.3 6.2 3.6 | 10.4 | 24 9.4 6 5 7.1 11.2 y 90 145 88 48 114 44 80 95 55 41 A scatter diagram of the data is shown below. 160 140 x 120 100 y 80 60 40 x 20 0 0 2 4 6 8 10 12 14 One of the adults is an outlier. Identify the letter of the adult that is the outlier. Circle your answer below. [1 mark] A B E J 12 Which one of the following is not a measure of spread? Circle your answer. [1 mark] median range standard deviation variance Turn over > G/Jun24/7356/2 17 14 14 (a) 14 (b) 19 The discrete random variables _Y and Y can be modelled by the distributions X~ B(40 , p) Y~ B(25 , 0.6) It is given that the mean of X is equal to the variance of Y Find the value of p [3 marks] Find P(Y = 17) [1 mark] Turn over > GiJun24/7356/2 Do not write outside the box 19 20 Do not write outside the 15 The number of flowers which grow on a certain type of plant can be modelled by the box discrete random variable XY The probability distribution of X is given in the table below. x 0 1 2 3 4 5 or more P(X=x) | 0.03 | 0.15 | 0.22 | 0.31 | 0.09 Pp 15 (a) Find the value of p [2 marks] 15 (b) Two plants of this type are randomly selected from a large batch received from a local garden centre. Find the probability that the two plants will produce a total of three flowers. [3 marks] IMU G/Jun24/7356/2 20 
