NYJC_H2_Maths_P2

This document consists of 6 printed pages. NANYANG JUNIOR COLLEGE Internal Examinations © NYJC 2014 [Turn Over NANYANG JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 MATHEMATICS 9740/02 Paper 2 17th September 2014 3 Hours Additional Materials: Cover Sheet Answer Paper Graph Paper List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your name and class 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 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. 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.

2 NYJC 2014 JC2 Preliminary Examination 9740/02 Section A: Pure Mathematics [40 marks] 1 The three vectors l, m and n are such that  nl m . Show that 0 ln . [1] With respect to an origin O, the position vectors of three non-collinear points A, B and C are a, b and c respectively. The scalars  and  are such that  ab is the projection of c onto the plane containing O, A and B. By considering CC'  , where C’ is the foot of perpendicular from C to the plane containing O, A and B, explain why there is a scalar t such that ()t    ab c a b , and deduce that ()() aa ab ac . [4] 2 The functions f, g and h are defined by     f : 2 , , where 2, g: e , , h: l n 2 , , 3 . x xx a x x a xx xx x x           (i) Show that the composite function gh exists and define gh in a similar form. State the range of gh. [4] (ii) Find, in terms of a, the exact range of x for which    fg h .x ax a  [3] (iii) The curve with equation f( )yx has a stationary point with coordinates  2 22 ,24 aa   . Sketch the graph of  1 fy x , stating clearly the equations of any asymptotes and the coordinates of the stationary point. [3] 3 Given that ln 1 1 xy x   , where 11 x  , show that d12(1 ) 2 d1 yxy x x   . [1] (i) By further differentiation, find the Maclaurin series for y up to and including the term in 3