RI_H2_Maths_P1_Qn

MATHEMATICS PAPER 1 9740/1 Higher 2 16 September 2014 Total Marks: 100 3 hours Additional materials: Answer Paper Graph 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. Answer all the questions. Give non-exact numerical answers correct to 3 signifi cant 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 ar e 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. 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.       This document consists of 6 printed pages. RAFFLES INSTITUTION Mathematics Department  RI2014 [Turn over RAFFLES INSTITUTION 2014 YEAR 6 PRELIMINARY EXAMINATION

2 H2 MA 9740/2014 RI Year 6 Preliminary Examination/01  1 A function f is given by 2 f( )   x ax bx x for ,0 xx R where a and b are positive real constants. Find f' ( )x and hence sketch the graph of f' ( )yx , stating the equations of any asymptotes and the coordinates of the points where the curve crosses the axes. [4] 2 A sequence 012, , , ...uuu is such that 0 20u  and 1 1 , for all 0.100 n nn uur u n   (i) Given that 2 3r , find the least value of n such that 1nu  . [2] (ii) Find the value of r such that 20nu  for all values of n . [2] (iii) It is given that 4 3r  and nul  as n . Showing your working, find the exact value of .l [2] 3 Let 22 1f( ) . (1 ) xx x   (i) Find the binomial expansion of f( )x in increasing powers of ,x up to and including the term in 4.x [3] (ii) Find the coefficient of 21rx  in the expansion for f( ) .x [3] 4 Prove by the method of mathematical induction that 1 sin(2 )sin sin( )sin( 1) n r rx x nx n x   for all positive integers n. [4] Hence find the exact value of 2 4 sin 3 sin 4 d. sin xx x x   [3]

3 H2 MA 9740/2014 RI Year 6 Preliminary Examination/01  5 The curve with equation 1y x undergoes a translation of 1 unit in the positive x-direction, followed by a stretch with factor 1 2