RI_H2_Maths_P2_Qn

MATHEMATICS PAPER 2 9740/2 Higher 2 23 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/02  Section A : Pure Mathematics [40 marks] 1 (i) Differentiate 2 1 14 x with respect to x. [2] (ii) Find    1 32 sin 2 d 14 xx x x   . [3] 2 It is given that a is a constant, where 1a . Find, in terms of a , the solution to each of the following inequalities. (i) 2 2 21 6 3aa a x xx  , [4] (ii) 221 6 3aa a x x x  . [2] 3 The function f is defined by 2f : 4 3 for , 3.xx x x x   (i) Sketch the graph of f( )yx . [1] (ii) If the domain of f is further restricted to x k , state with a reason the greatest value of k for which the function 1f exists. [2] In the rest of this question, the domain of f is , 3 xx  , as originally defined. The function g is defined by g : ln(2 ) for , , . 2 axx a x x a     (iii) Find the smallest possible value of a for which the function gf exists. [2] (iv) With this value of a, find gf. [2] (v) Find the range of gf. [2]

3 H2 MA 9740/2014 RI Year 6 Preliminary Examination/02  4 Do not use a calculator in answering this question. The complex number z satisfies both the relations 23 i 4z  and 5 arg i6 z   . (i) On an Argand diagram, shade the region in which the point representing z can lie. [4] (ii) Find the least possible