A-Level Further Mathematics Paper 1

-level FURTHER MATHEMATICS Paper 1 Time allowed: 2 hours Materials l You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics. l You should have a scientific calculator that meets the requirements of the specification. (You may use a graphical calculator.) Instructions l Use black ink or black ball‑point pen. Pencil should only be used for drawing. l Fill in the boxes at the top of this page. l Answer all questions. l You must answer each question in the space provided for that question. If you require extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s). l Do not write outside the box around each page or on blank pages. l Show all necessary working; otherwise marks for method may be lost. l Do all rough work in this book. Cross through any work you do not want to be marked. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 100. Advice l Unless stated otherwise, you may quote formulae, without proof, from the booklet. l You do not necessarily need to use all the space provided. Please write clearly in block capitals. Centre number Candidate number Surname ________________________________________________________________________ Forename(s) ________________________________________________________________________ Candidate signature ________________________________________________________________________ For Examiner’s Use Question Mark 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 TOTAL I declare this is my own work. 2 Answer all questions in the spaces provided. 1 Find X 20 r¼1 (r 2 2r) Circle your answer. [1 mark] 2 Given that z ¼ 1 3i is one root of the equation z2 þ pz þ r ¼ 0 , where p and r are real, find the value of r. Circle your answer. [1 mark] 8 2 6 10 Jun21/7367/1 Do not write outside the box (02) 3 3 The curve C has polar equation r 2 sin 2y ¼ 4 Find a Cartesian equation for C. Circle your answer. [1 mark] y ¼ 2x y ¼ x 2 y ¼ 2 x y ¼ 4x Turn over for the next question Do not write outside the box Jun21/7367/1 Turn over s (03) 4 4 Show that the solutions to the equation 3 tanh2 x 2 sech x ¼ 2 can be expressed in the form x ¼ ln (a þ ffiffiffi b p ) where a and b are integers to be found. You may use without proof the result cosh1 y ¼ ln ( y þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi y2 1 p )