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Download AS level paper 2 2024 maths and more High school final essays Mathematics in PDF only on Docsity!
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 y y 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. 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). 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 s e The marks for questions are shown in brackets. 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. Jou 7356201 GILM/Jun24/G4004/E8 7356/2 | Do not write outside the Section A box 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 — sin2x cos2.x =—1 + sin2x cos?x=1—sin2x cos?x=1+sin2x IML GiJun24/7356/2 4 (a) 4 (b) 4 (c) IML Do not write outside the Curve C has equation y = 8sin x box 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] GiJun24/7356/2 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 GiJun24/7356/2 Do not write outside the 6 (b) (ii) Find the value of a mae [3 marks] Turn over for the next question Turn over > ov GiJun24/7356/2 Do not write outside the 7 Point A has coordinates (4, 1) and point B has coordinates (—8, 5) box T (a) Find the equation of the perpendicular bisector of AB [5 marks] IML GiJun24/7356/2 10 Do not write outside the 8 Prove that the graph of the curve with equation box 18 mig 8 y=x3+ 15x x has no stationary points. [5 marks] GiJun24/7356/2 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 GiJun24/7356/2 13 Do not write outside the 9 (b) On the diagram, the region enclosed between the curve and the line y = 2 is shaded. box 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 GiJun24/7356/2 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 | | | 3 at | I | 1 | | | I O 1 2 3 4 5 t GiJun24/7356/2 16 Do not write outside: the 10 (b) (i) Show that oF ap . [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 GiJun24/7356/2 17 | Do not write outside the Section B box 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 > GiJun24/7356/2 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 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 GiJun24/7356/2 
