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  This document consists of 16  printed pages. DC (SM/SW) 41599/3 © UCLES 2012   [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSGeneral Certificate of Education Ordinary Level READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid.DO NOT  WRITE IN ANY BARCODES.Answer all  the questions.Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.The use of an electronic calculator is expected, where appropriate.You are reminded of the need for clear presentation in your answers.At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks for this paper is 80. *2 8 9 51 6 37 6 8* ADDITIONAL MATHEMATICS   4037/11 Paper 1 May/June 2012 2 hours Candidates answer on the Question Paper.No additional materials are required. For Examiner’s Use1234567891011Total   w  w  w  . X   t  r  e  m  e  P  a   p  e  r  s  . c  o  m    2 4037/11/M/J/12© UCLES 2012  Mathematical Formulae 1. ALGEBRA Quadratic    Equation  For the equation ax 2  + bx  + c  = 0,  x b b aca =  − − 2 42  Binomial Theorem ( a  + b ) n  = a n  + ( n 1 ) a n  –1   b  + ( n 2 ) a n  –2   b 2  + … + ( nr  ) a n  –  r    b r   + … + b n , where n  is a positive integer and ( nr  )  = n !( n  – r  )! r  ! 2. TRIGONOMETRY  Identities sin 2    A  + cos 2    A  = 1sec 2    A  = 1 + tan 2    A cosec 2    A  = 1 + cot 2    AFormulae for ∆  ABC a sin  A  = b sin  B  = c sin C a 2  = b 2  + c 2  – 2 bc  cos  A ∆  = 1 2   bc  sin  A  3 © UCLES 2012 [Turn over For  Examiner’sUse 4037/11/M/J/12 1 (i) Sketch the graph of  y  =  2  x  – 5  , showing the coordinates of the points where the graph meets the coordinate axes. [2]  y xO  (ii) Solve  2  x  – 5   = 3 . [2]  4 © UCLES 2012 For  Examiner’sUse 4037/11/M/J/12 2 The expression 2  x 3  + ax 2  + bx  – 30 is divisible by  x  + 2 and leaves a remainder of –35 when divided by 2  x  – 1. Find the values of the constants a  and b.   [5]
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