NYJC_H2_Maths_P1

This document consists of 5 printed pages. NANYANG JUNIOR COLLEGE Internal Examinations © NYJC 2014 [Turn Over NANYANG JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 MATHEMATICS 9740/01 Paper 1 16th September 2014 3 Hours Additional Materials: Cover Sheet Answer 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 9740/01 1 The function f is defined by 2f: 2 ( 1 ) , , x xx x k  . (i) Determine the largest value of k for which the function 1f exists. [1] With this value of k, (ii) find 1f in a similar form. [3] (iii) show algebraically that the x-coordinate of the point of intersection of the curves   1f and fyx y x  satisfies the equation 2 31 0xx  and find the value of this x-coordinate, correct to 3 decimal places. [2] 2 The region enclosed by the curve es i nxyx where 0 2x   , the x-axis and the line 2x  is denoted by A. Find the exact area of A. [4] Find the volume of revolution when the region bounded by the curves es i nxy x , 23 1 3y xx x  and the line 2x  is rotated completely about the x- a x i s . [2] 3 For a curve with equation 23 33xx y y  , find (i) the coordinates of the point at which the tangent is parallel to the x-axis, [4] (ii) the equation(s) of the normal(s) at 1x   . [4] 4 The complex number z satisfies the relation 13 i 2z  . Illustrate, on an Argand diagram, the locus of points representing the complex number z. [2] (i) Find the greatest possible value of  arg 3 3iz . [3] (ii) Find the range of values of , where 0 2   , such that there exists a complex number w which satisfies the relations  arg 3 3iw   and  arg * 2w   , where *w is the conjugate of w. [4]

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