AQA 7356 AS MATHEMATICS PAPER 2 PURE AND STATS

AQA 7356 AS MATHEMATICS PAPER 2 PURE AND STATS AS MATHEMATICS Paper 2 Wednesday 22 May 2019 Morning Time allowed: 1 hour 30 minutes Materials  You must have the AQA Formulae for A‑level Mathematics booklet.  You should have a graphical or scientific calculator that meets the requirements of the specification. Instructions  Use black ink or black ball‑point pen. Pencil should only be used for drawing.  Fill in the boxes at the top of this page.  Answer all questions.  You must answer each question in the space provided for that question. If you require extra space, use an AQA supplementary answer book; do not use the space provided for a different question.  Show all necessary working; otherwise marks for method may be lost.  Do all rough work in this book. Cross through any work that you do not want to be marked. Information  The marks for questions are shown in brackets.  The maximum mark for this paper is 80. Advice  Unless stated otherwise, you may quote formulae, without proof, from the booklet.  You do not necessarily need to use all the space provided. (JUN) PB/Jun19/E3 7356/2 box 3 It is given that sin y ¼ —0:1 and 180° < y < 270° Find the exact value of cos y [2 marks] box 4 Show that, for x > 0 x4 3 log10 100 þ log10 9x — log10 x Ξ 2(—1 þ log10 3x) [4 marks] Turn over for the next question Turn over 5 A triangular prism has a cross section ABC as shown in the diagram below. box A C B Angle ABC ¼ 25° Angle ACB ¼ 30° BC ¼ 40 millimetres. The length of the prism is 300 millimetres. Calculate the volume of the prism, giving your answer to three significant figures. [4 marks] 6 A curve has equation box The region enclosed between the curve, the x-axis and the lines x 1 and x a has area 3 units. Given that a > 1 , find the value of a. Fully justify your answer. [5 marks] Turn over 7 The points A (a, 3) and B (10, 6) lie on a circle. AB is a diameter of the circle and passes through the point (2, 4) box The circle has equation (x — c)2 þ ( y — d)2 ¼ e where c, d and e are rational numbers. Find the values of a, c, d and e. [6 marks] box Turn over for the next question Turn over (07) 8 A curve has equation y ¼ x3 þ px2 þ qx — 45 box The curve passes through point R (2, 3) The gradient of the curve at R is 8 8 (a) Find the value of p and the value of q. [5 marks] (0 ) 8 (b) Calculate the area enclosed between the normal to the curve at R and the coordinate axes. box [5 marks] Turn over 9 A curve C has equation y ¼ f (x) where f (x) ¼ (x — 2)(x — 3)2 9 (a) Find the exact coordinates of the turning points of C. Determine the nature of each turning point. Fully justify your answer. [8 marks] box box 9 (b) State the coordinates of the turning points of the curve y ¼ f (x þ 1) — 4 [2 marks] Turn over for the next question Turn over 10 As part of an experiment, Zena puts a bucket of hot water outside on a day when the outside temperature is 0°C. She measures the temperature of the water after 10 minutes and after 20 minutes. Her results are shown below. box Time (minutes) 10 20 Temperature (degrees Celsius) 30 12 Zena models the relationship between y, the temperature of the water in °C, and t, the time in minutes, by where A and k are constants. y ¼ A × 10—kt 10 (a) Using t ¼ 0 , explain how the value of A relates to the experiment. [1 mark] 10 (b) Show that log10 y ¼ log10 A — kt [1 mark] 10 (c) Using Zena’s results, calculate the values of A and k. [4 marks] 10 (d) Zena states that the temperature of the water will be less than 1°C after 45 minutes. Determine whether the model supports this statement. [3 marks] 10 (e) Explain why Zena’s model is unlikely to accurately give the value of y after 45 minutes. [1 mark] Turn over Section B Answer all questions in the spaces provided. 11 A survey is undertaken to find out the most popular political party in London. The first 1100 available people from London are surveyed. Identify the name of this type of sampling. Circle your answer. [1 mark] simple random opportunity stratified quota 12 Manny is studying the price and number of pages of a random sample of books. He calculates the value of the product moment correlation coefficient between the price and number of pages in each book as 1.05 Which of the following best describes the value 1.05? Tick (3) one box. [1 mark] definitely correct probably correct probably incorrect definitely incorrect Turn over for the next question box DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Turn over 13 Denzel wants to buy a car with a propulsion type other than petrol or diesel. He takes a sample, from the Large Data Set, of the CO2 emissions, in g/km, of cars with one particular propulsion type. The sample is as follows 82 13 96 49 96 92 70 81 13 (a) Using your knowledge of the Large Data Set, state which propulsion type this sample is for, giving a reason for your answer. box [2 marks] 13 (b) Calculate the mean of the sample. [1 mark] 13 (c) Calculate the standard deviation of the sample. [1 mark] 13 (d) Denzel claims that the value 13 is an outlier. 13 (d) (i) Any value more than 2 standard deviations from the mean can be regarded as an outlier. box Verify that Denzel’s claim is correct. [1 mark] 13 (d) (ii) State what effect, if any, removing the value 13 from the sample would have on the standard deviation. [1 mark] Turn over for the next question Turn over (17) 14 A probability distribution is given by P(X ¼ x) ¼ c(4 — xÞ, for x ¼ 0, 1, 2, 3 where c is a constant. box 1 14 (a) Show that c ¼ 10 [2 marks] 14 (b) Calculate P(X ≥ 1) [2 marks] (1 ) 15 Two independent events, A and B, are such that P(A) ¼ 0:2 P(A ¨ B) ¼ 0:8 box 15 (a) (i) Find P(B) [4 marks] 15 (a) (ii) Find P(A ˙ B) [1 mark] 15 (b) State, with a reason, whether or not the events A and B are mutually exclusive. [1 mark] Turn over 16 Andrea is the manager of a company which makes mobile phone chargers. In the past, she had found that 12% of all chargers are faulty. 16 (a) Andrea decides to move the manufacture of chargers to a different factory. Andrea tests 60 of the new chargers and finds that 4 chargers are faulty. Investigate, at the 10% level of significance, whether the proportion of faulty chargers has reduced. box [7 marks] 16 (b) State, in context, two assumptions that are necessary for the distribution that you have used in part (a) to be valid. box [2 marks] END OF QUESTIONS There are no questions printed on this page box DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED There are no questions printed on this page box DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED There are no questions printed on this page box DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Copyright information For confidentiality purposes, from the November 2015 examination series, acknowledgements of third-party copyright material are published in a separate booklet rather than including them on the examination paper or support materials. This booklet is published after each examination series and is available for free download from after the live examination series. Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright-holders may have been unsuccessful and AQA will be happy to rectify any omissions of acknowledgements. If you have any queries please contact the Copyright Team, AQA, Stag Hill House, Guildford, GU2 7XJ. Copyright ª 2019 AQA and its licensors. All rights reserved. (24) Jun19/7356/2 (196A7356/2)