A-level MATHEMATICS Paper 1 JUNE 2022

A-level MATHEMATICS Paper 1 Time allowed: 2 hours 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 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).  Do not write outside the box around each page or on blank pages.  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 100. Advice  Unless stated otherwise, you may quote formulae, without proof, from the booklet.  You do not necessarily need to use all the space provided. Answer all questions in the spaces provided. 1 A curve is defined by the parametric equations x ¼ cos y and y ¼ sin y where 0 ≤ y ≤ 2p Which of the options shown below is a Cartesian equation for this curve? Circle your answer. y ¼ tan y x2 þ y2 ¼ 1 x2 — y2 ¼ 1 x2y2 ¼ 1 [1 mark] box 2 A periodic sequence is defined by State the period of the sequence. Un ¼ (—1)n Circle your answer. —1 0 1 2 [1 mark] 3 The curve y ¼ log4 x is transformed by a stretch, scale factor 2, parallel to the y-axis. State the equation of the curve after it has been transformed. Circle your answer. y ¼ 1 log x y ¼ 2 log x y ¼ log 2x y ¼ log x [1 mark] Turn over for the next question box DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Turn over 4 The graph of where is shown in Figure 1. y ¼ f (x) f (x) ¼ ax2 þ bx þ c box Figure 1 y x Which of the following shows the graph of y ¼ f 0(x)? Tick (3) one box. [1 mark] box y x y x y x y x Turn over 5 Find an equation of the tangent to the curve y ¼ (x — 2)4 box at the point where x ¼ 0 [3 marks] 6 (a) Find the first two terms, in ascending powers of x, of the binomial expansion of box 1 1 2 2 [2 marks] 6 (b) Hence, for small values of x, show that sin 4x þ pcos x ≈ A þ Bx þ Cx2 where A, B and C are constants to be found. [4 marks] Turn over (07) 7 Sketch the graph of for 0 ≤ x ≤ 2p y O y ¼ cot x — p л 2л [3 marks] x box Turn over for the next question box DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED