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RAFFLES JUNIOR COLLEGE JC2 Preliminary Examination 2007 MATHEMATICS  9740/01  Higher 2 Paper 1 12 September 2007 3 hours  Additional materials : Answer Paper List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your name and CT group on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid.  Answerall 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. You are expected to use a graphic calculator. Unsupported answers from a graphic calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphic calculator are not allowed in a question, you are required to present the mathematical steps using mathematical notations and not calculator commands. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question.  At the end of the examination, fasten all your work securely together. This document consists of6 printed pages. R AFFLESJUNIORCOLLEGE RJC IES 2007 Math Department [Turn over www.teachmejcmath-sg.webs.com teachmejcmath.sg@gmail.com

RJC 2007  9740/01/S/07  [Turn over  2   1  Find the set of values of x for which 2 e 8 01  x  x  x   . Hence solve 2 e 8 01  x  x  x   . [4] 2 Prove by induction that, for n  Z,  2 2 2 2 1 2(1)(2)(3)...(1)(1) (1) .2 n nn n n n n            [5] 3  A sequence of negative numbers is defined by 1 2 3 4 n n n  x x  x  , where 1 1 7  x   . (i) Write down the values of2 x and3 x, giving your answers correct to 3 significant figures. [2] (ii)Given that asn   ,n x  , find, without the use of a graphic calculator, the value of.  [3] 4  The graph of y= f( x) undergoes in succession, the following three transformations:  A: A translation of 1 unit in the negative x-direction.  B: A reflection about the y-axis. C : A stretch parallel to the x-axis (with y-axis invariant) with a scale factor of 2. The equation of the resulting curve is y = g( x) where g( x) = 2 2 3 2  x x  x    . (i)Express f( x) in the form g(ax+b), wherea andb are constants to be found. [2] (ii) Sketch the graph of y = g( x), showing clearly all the intersections with the axes, the asymptotes and the coordinates of turning points (if any). [4] 5 Given that 1f()r  r   , wherer  is a positive integer, find a single expression for f()f ( 1).r r    Hence, find the sum to 2n terms of the series 1 1 1 1 ...2 6 12 20    . [4] Deduce that the sum to 2n terms of the series2 2 2 2 1 1 1 1 ... 2 3 4 5      is less than 1. [2] www.teachmejcmath-sg.webs.com teachmejcmath.sg@gmail.com

RJC 2007  9740/01/S/07  [Turn over  3 6 Given that 3 2i2 z+- £ and 52i 3i z z++ ³ - , illustr